url stringlengths 6 1.61k | fetch_time int64 1,368,856,904B 1,726,893,854B | content_mime_type stringclasses 3 values | warc_filename stringlengths 108 138 | warc_record_offset int32 9.6k 1.74B | warc_record_length int32 664 793k | text stringlengths 45 1.04M | token_count int32 22 711k | char_count int32 45 1.04M | metadata stringlengths 439 443 | score float64 2.52 5.09 | int_score int64 3 5 | crawl stringclasses 93 values | snapshot_type stringclasses 2 values | language stringclasses 1 value | language_score float64 0.06 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
https://www.gktoday.in/question/two-pipes-a-and-b-can-separately-fill-a-cistern-in | 1,553,343,601,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912202804.80/warc/CC-MAIN-20190323121241-20190323143241-00283.warc.gz | 766,535,856 | 2,675 | Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time the third pipe alone can empty the cistern?
[A] 100 minutes
[B] 120 minutes
[C] 90 minutes
[D] 110 minutes | 99 | 368 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2019-13 | latest | en | 0.903632 |
http://wpressutexas.net/oldcoursewiki/index.php?title=Dan%27s_Segment_7 | 1,660,458,795,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571996.63/warc/CC-MAIN-20220814052950-20220814082950-00770.warc.gz | 53,126,138 | 5,747 | # Dan's Segment 7
## To Calculate
1. We have our function $F(x) = x^2 - 2ax + a^2$ and we want to take its derivative w.r.t. a, so we get $f(x) = -2x + 2a = 0$ and the solution is clearly a=x.
3. Good: the first big positive about the median over the mean is that the median always exists whereas the mean does not for some distributions. The other big advantage is that the median is more resistant to outliers in many situations. For example, if you have a data set that looks like this: (0,1,0,2,3,0,1,1000) your mean is going to be way bigger than the likely center of the distribution, while the median will still reside close to the center.
Bad: The median assumes that the data is uniformly distributed and that you have sufficient data. Without a lot of data, the median can easily come far away from the actual population center. For instance, a data set (1,2,1,300,150) would have a mean of 2, which might not accurately reflect the real population.
1. One option is to fit a function to the data and then use that function to calculate the moments. I won't claim to have thought of this myself, but wikipedia tells me that the formula $\frac{1}{n}\sum_{i = 1}^{n} X^k_i\,\!$ will calculate moments with decent accuracy for large samples. I'm kind of surprised this works, but unfortunately wikipedia lists no source or derivation. | 343 | 1,346 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2022-33 | latest | en | 0.92129 |
https://www.homeworkminutes.com/question/view/14961/Drexel-University-Econ-202-Winter-2014-Mid-term-Exam | 1,527,197,729,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794866870.92/warc/CC-MAIN-20180524205512-20180524225512-00283.warc.gz | 746,633,548 | 10,536 | Question
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# Drexel University Econ 202 Winter 2014 Mid-term Exam
Question # 00014961
Subject: Economics
Due on: 05/10/2014
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Drexel University
Econ 202: Principle of Macroeconomics
Winter 2014 - Midterm
MULTIPLE CHOICE SECTION (30 Points Total, 3 Points each)
1. Suppose that domestic prices increase. Which of the followings is most likely to happen?
(a) Net exports would increase
(b) Net exports would decrease
(c) No impact on net exports
(d) Exports will be equal to imports
2. Which of the followings will be most likely to shift the consumption function downward
(a) a stock market boom
(b) a price level decrease
(c) lower disposable income
(d) higher interest rates
3. Suppose that between 2008 and 2009 nominal GDP in the US grew by 3% and that between the same
years in.ation was 3%. The growh rate of real GDP between 2008-9 was:
(a) 6%
(b) 9%
(c) zero
(d) we can not tell
4. Suppose that, in the US, in 2012, disposable income increased by \$1 billion and that MPC was 0.9.
This means that (to a good approximation) total consumption increased by
(a) \$950 million
(b) \$1 billion
(c) \$900 million
(d) \$100 million
5. The AD curve describes the relationship between
(a) consumption and disposable income
(b) consumption and the price level
(c) the (demand-side) equilibrium level of output and the price level
(d) the (demand-side) equilibrium level of output and the interest rate
6. Economic growth is driven by:
(a) growth in the labor force
(b) growth in the capital stock
(c) growth in productivity of labor
(d) all of the above
7. A recession is a period of time (few months) where:
(a) in.ation is negative
(b) interest rate are equal to zero
(c) total real GDP falls
(d) .rms close due to holidays
8. The unemployment rate is the
(a) share of the population which is not working
(b) share of the labor force seeking jobs that is not working
(c) number of people that can not .nd a job
(d) share of the population that is retired
9. One USD is equal to roughly 90 Japanese Yen. Suppose that the exchange rate goes up to 100 Yen
per Dollar. Which of the followings is more likely to happen:
(a) Government spending (G) will increase
(b) US imports from Japan will decrease
(c) US imports from Japan will increase
(d) Consumption (C) will increase
10. In the US, monetary policy is decided by the Federal Reserve, which, in case of recession tries to
stimulate the economy by
(a) cutting taxes to households and .rms
(b) building new infrastuctures to help production
(c) cutting interest rates and/or printing more dollars
(d) exporting more American products to Europe
SHORT ANSWER SECTION (70 points total)
Please provide very short answers to the following questions
11.15 Points. Suppose that in an imaginary country called "Coconut Grove", people consume always
the same basket of goods: 100 coconuts and 25 bananas. The unit prices for these two goods are as
follows
Bananas Coconut
2011 \$1 20c
2012 \$2 15c
(a) Compute the dollar value of the basket in both years
(b) Using 2011 as your base year, compute the Consumer Price Index (CPI) in 2011 and 2012
(c) What is the CPI in.ation rate between 2011 and 2012?
12.10 Points.Consider the following table (numbers are in millions)
real GDP Population
2011 10000 10
2012 11000 12
Compute the growth rate of real GDP per capita between 2011 and 2012.
13.15 Points.Consumption is the largest component of aggregate demand in the US economy. Brie.y
explain how the following events might a¤ect its value. HINT:you have to say whether consumption
would increase or decrease, and give a brief economic explanation
(a) An increase in interest rates on checking accounts from 0% (current value) to 1.5%
(b) A higher in.ation rate
(c) A forecast of a sustained boom in real GDP starting in the Fall 2013.
14.15 Points. Between 2003 and 2009, US exports to Europe increased. As a result, US net exports
with Europe went from -\$110 billion to \$-72 billion. Highlight two factors that might have caused this
change and brie.y explain how:
15.15 Points.Consider the graph on pg. 12 of Slides Set #4.
Answer to the followings
(a) Brie.y explain why any point to the right of E cannot be an equilibrium.
(b) Suppose the price level goes up. On the same graph given above, draw the new expenditure
schedule and .nd the new equilibrium point.
Compute the level of national income Y for which total spending in the economy is equal to national
income.
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#### Drexel University Econ 202 Winter 2014 Mid-term Exam with all Correct Answers
Tutorial # 00014494
Posted On: 05/10/2014 09:00 AM
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Tutorial Preview …44:4% xx 10 xxxxxx Consider the xxxxxxxxx table (numbers xxx in xxxxxxxxx xxxx GDP xxxxxxxxxx 2011 10000 xx 2012 11000 xx Compute xxx xxxxxx rate xx real GDP xxx capita between xxxx and xxxx xxxxxx First xxxxx compute real xxx per capita xx the xxx xxxxx Recall xxxx real GDP xxx capita is xxxxx to xxxx xxx divided xx population GDP xxx capita 2011= xxxxx 10 x xxxx GDP xxx capita 2011= xxxxx 12 = xxxxx Second xxxxx xxxxxxx the xxxxxx rate of xxxx GDP per xxxxxx Growth xxxx xx real xxx per capita= xxxxxxxxxxxxx 1000100 =????8:34% xx population xxxxx xxxxxx than xxxxx real GDP, xxxx GDP per xxxxxx declines xx x 34% xx 15 Points xxxxxxxxxxx is the xxxxxxx component xx xxxxxxxxx demand xx the US xxxxxxx Brie y xxxxxxx how xxx xxxxxxxxx events xxxxx a¤ect its xxxxx HINT:you have xx say xxxxxxx xxxxxxxxxxx would xxxxxxxx or decrease, xxx give a xxxxx economic xxxxxxxxxxx xxx An xxxxxxxx in interest xxxxx on checking xxxxxxxx from xx xxxxxxxx value) xx 1 5% xxxxxx A positive xxxxxxxx rate xx xxxxxxxx accounts xxxxx people more xxxxxxx to save, xxxx as x xxxxxxx less xxxxxxx to consume xxx we should xxxxxx a xxxxxxxx xx consumption xxx NOTE:since the xxxxxxxx was on xxx interest xxxx xx checking xxxxxxxx (and not xx mortgages or xxxxx types xx xxxxxx an xxxxxx like "consumption xxxxx decrease because xx has xxxxxx xxxx expensive xx borrow from xxxxxx is not xxxxxxx Checking xxxxxxxx xxx a xxxxxx not a xxxxxxxxx instrument 3 xxx A xxxxxx xx ation xxxx ANSWER Higher xx ation erodes xxx purchase xxxxx xx both xxxxxx and disposable xxxxxx As a xxxxxxx if xxx xxxxxxx value xx wealth and xxxxxxxxxx income remains xxxxxxxxxx people xxxx xxxxxxxx in xxxx terms, and xxxxxxx less (c) x forecast…
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Loading... | 1,766 | 6,832 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2018-22 | longest | en | 0.882811 |
https://proofwiki.org/wiki/Axiom:Axiom_of_Unions/Set_Theoretical_and_Class_Theoretical | 1,716,104,891,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971057774.18/warc/CC-MAIN-20240519070539-20240519100539-00075.warc.gz | 431,704,325 | 11,127 | # Axiom:Axiom of Unions/Set Theoretical and Class Theoretical
## Axiom of Unions: Difference between Formulations
Recall the two formulations of the axiom of unions:
### Formulation 1
For every set of sets $A$, there exists a set $x$ (the union set) that contains all and only those elements that belong to at least one of the sets in the $A$:
$\forall A: \exists x: \forall y: \paren {y \in x \iff \exists z: \paren {z \in A \land y \in z} }$
### Formulation 2
Let $x$ be a set (of sets).
Then its union $\bigcup x$ is also a set.
Equivalence of Formulations of Axiom of Unions notwithstanding, the two formulations have a subtle difference.
The purely set theoretical (formulation 1) version starts with a given set (of sets), and from it allows the creation of its union by providing a rule by which this may be done.
The class theoretical (formulation 2) version accepts that such a construct is already constructible in the context of the union of a class, and is itself a class.
What formulation 2 then goes on to state is that if $x$ is actually a set (of sets), then $\bigcup x$ is itself a set.
This is consistent with how:
the philosophy of axiomatic set theory defines the constructibility of sets from nothing
differs from
the class theoretical approach, in which classes may be considered to be already in existence, and it remains a matter of determining which of these classes are actually sets. | 352 | 1,426 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.34375 | 3 | CC-MAIN-2024-22 | latest | en | 0.925709 |
https://www.physicsforums.com/threads/conical-pendulum.217234/ | 1,519,300,004,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891814101.27/warc/CC-MAIN-20180222101209-20180222121209-00470.warc.gz | 939,474,568 | 14,048 | # Conical Pendulum
1. Feb 22, 2008
### sailsinthesun
1. The problem statement, all variables and given/known data
Consider a conical pendulum with a 81.0 kg bob on a 10.0 m wire making an angle of theta= 2.00° with the vertical.
(a) Determine the horizontal and vertical components of the force exerted by the wire on the pendulum.
(b) What is the radial acceleration of the bob?
2. Relevant equations
F=ma
a=v^2/r
3. The attempt at a solution
(a)After drawing the FBD for the wire and resolving the vectors, I get the horizontal force to be Fsin(theta) and the vertical to be Fcos(theta). Fcos(th)=mg so F=mg/cos(th). Then Fsin(th)=27.7484N and Fcos(th)=794.61N.
I'm pretty sure I did these correctly, but I'm not sure how to get the second part.
(b)I calculated the radius using r=10sin(2deg). Here is where I'm lost. I know a=v^2/r, and I have r, but need to find v. Any help or hints?
2. Feb 22, 2008
### Dick
If you have the horizontal force, then you know the horizontal acceleration from F=ma. That 'a' is the same 'a' as in a=v^2/r. | 313 | 1,050 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2018-09 | latest | en | 0.871715 |
http://stackoverflow.com/questions/1526898/how-do-i-reproduce-this-heart-shaped-mesh-in-matlab | 1,417,117,234,000,000,000 | text/html | crawl-data/CC-MAIN-2014-49/segments/1416931009084.22/warc/CC-MAIN-20141125155649-00209-ip-10-235-23-156.ec2.internal.warc.gz | 288,899,632 | 22,462 | # How do I reproduce this heart-shaped mesh in MATLAB?
I want to plot a heart shape in framework as shown in the following image (found on the website zedomax.com/blog/2008/09/03/i-love-meth-t-shirt/):
I have tried to make it by using this MATLAB program:
n=100;
x=linspace(-3,3,n);
y=linspace(-3,3,n);
z=linspace(-3,3,n);
[X,Y,Z]=ndgrid(x,y,z);
F=((-(X.^2) .* (Z.^3) -(9/80).*(Y.^2).*(Z.^3)) + ((X.^2) + (9/4).* (Y.^2) + (Z.^2)-1).^3);
isosurface(F,0)
lighting phong
caxis
axis equal
colormap('flag');
view([55 34]);
But I didn't get the desired shape of framework as shown in the figure.
I have identified the problem: to create a wireframe we usually use the command mesh(). But this plotting facility only allow us to plot a function of two variables such as z=f(x,y). But my program makes use of three variables: F(x,y,z).
How can I solve the problem?
-
That link is not accessible without a login. Could you post the image somewhere else, like photobucket.com, etc.? – gnovice Oct 6 '09 at 17:14
Plese also reformat the code to make it more legible. – whatnick Oct 6 '09 at 17:17
When I run your program, I didn't see any heart built from wires. Only blue heart with white dots. I think we can only built a heart with wireframe (something like the figure on the course web site) using the matlab function mesh(). Anyway it is a good try. Keep searching in the internet wink. – izzat Oct 7 '09 at 7:32
It does draw a heart-shaped wireframe, you just have to rotate and zoom in a bit to get the view I showed!! – Amro Oct 7 '09 at 10:32
@izzat - don't vandalize questions; even your own. – Marc Gravell Oct 19 '09 at 18:35
Here's my best attempt at reproducing the entire figure:
## Generating the contoured heart mesh:
I used the CONTOURC function to generate a series of contours in the x-y, x-z, and y-z planes. Notice that in the image you want to reproduce, the mesh lines on the back-facing side of the heart are not rendered. The quickest and easiest way I could think of to reproduce that aspect of the plot was to use ISOSURFACE to render a white surface just beneath the inside surface of the mesh, blocking the view of the back side.
Here's the code for the function heart:
function heart
% Initialize the volume data, figure, and axes:
[X,Y,Z] = meshgrid(linspace(-3,3,101));
F = -X.^2.*Z.^3-(9/80).*Y.^2.*Z.^3+(X.^2+(9/4).*Y.^2+Z.^2-1).^3;
hFigure = figure('Position',[200 200 400 400],'Color','w');
hAxes = axes('Parent',hFigure,'Units','pixels',...
'DataAspectRatio',[1 1 1],'Visible','off',...
'CameraViewAngle',10,...
'XLim',[32 70],'YLim',[39 63],'ZLim',[34 73]);
view([-39 30]);
% Create and plot contours in the y-z plane:
for iX = [35 38 41 45 48 51 54 57 61 64 67]
plane = reshape(F(:,iX,:),101,101);
cData = contourc(plane,[0 0]);
xData = iX.*ones(1,cData(2,1));
plot3(hAxes,xData,cData(2,2:end),cData(1,2:end),'k');
end
% Create and plot contours in the x-z plane:
for iY = [41 44 47 51 55 58 61]
plane = reshape(F(iY,:,:),101,101);
cData = contourc(plane,[0 0]);
yData = iY.*ones(1,cData(2,1));
plot3(hAxes,cData(2,2:end),yData,cData(1,2:end),'k');
end
% Create and plot contours in the x-y plane:
for iZ = [36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 69 71]
plane = F(:,:,iZ);
cData = contourc(plane,[0 0]);
startIndex = 1;
if size(cData,2) > (cData(2,1)+1)
startIndex = cData(2,1)+2;
zData = iZ.*ones(1,cData(2,1));
plot3(hAxes,cData(1,2:(startIndex-1)),...
cData(2,2:(startIndex-1)),zData,'k');
end
zData = iZ.*ones(1,cData(2,startIndex));
plot3(hAxes,cData(1,(startIndex+1):end),...
cData(2,(startIndex+1):end),zData,'k');
end
% Fill the inside of the mesh with an isosurface to
% block rendering of the back side of the heart:
p = patch(isosurface(F,-0.001));
set(p,'FaceColor','w','EdgeColor','none');
end
## Putting the figure together:
To reproduce the entire figure I first generated the heart mesh using the heart function above, then added the other elements around it. I also used a few submissions from The MathWorks File Exchange:
Here's the code for the function I_Heart_Math (which generates the above figure):
function I_Heart_Math
% Initialize heart plot and adjust figure and axes settings:
heart;
set(gcf,'Position',[200 200 700 300],'Name','Original image');
offset = get(gca,'CameraPosition')-get(gca,'CameraTarget');
offset = 35.*offset./norm(offset);
set(gca,'Position',[65 -9 300 300],'CameraViewAngle',6,...
'XLim',[21+offset(1) 70],'YLim',[16+offset(2) 63],...
'ZLim',[32 81+offset(3)]);
% Create the axes and labels, offsetting them in front of the
% heart to give the appearance they are passing through it:
arrowStarts = [81 51 51; 51 86 51; 51 51 32]+repmat(offset,3,1);
arrowEnds = [21 51 51; 51 16 51; 51 51 81]+repmat(offset,3,1);
arrow(arrowStarts,arrowEnds,5,40,40);
text('Position',[22 52 48]+offset,'String','x','FontSize',12);
text('Position',[50 17 49]+offset,'String','y','FontSize',12);
text('Position',[46.5 51 81.5]+offset,'String','z','FontSize',12);
% Create the equation text:
text('Position',[51 47 28],'FontName','Bookman','FontSize',8,...
'HorizontalAlignment','center',...
'String',{'(x^2+^9/_4y^2+z^2-1)^3-x^2z^3-^9/_{80}y^2z^3=0'; ...
'-3 \leq x,y,z \leq 3'});
% Create the large-type text:
hI = text('Position',[4 52 69.5],'String','I',...
'FontAngle','italic','FontName','Trebuchet MS',...
'FontSize',116,'FontWeight','bold');
hM = text('Position',[80.5 50 42.5],'String','Math',...
'FontAngle','italic','FontName','Trebuchet MS',...
'FontSize',116,'FontWeight','bold');
% Create an anti-aliased version of the figure too (the larger
% fonts need some adjustment to do this... not sure why):
set(hI,'Position',[4 52 68],'FontSize',86);
set(hM,'Position',[80.5 50 41],'FontSize',86);
myaa;
set(hI,'Position',[4 52 69.5],'FontSize',116);
set(hM,'Position',[80.5 50 42.5],'FontSize',116);
set(gcf,'Name','Anti-aliased image');
end
-
thanx gnovice!!!!!!!!!!!!!!!!! – izzat Oct 19 '09 at 17:02
very nice. I was thinking of something of the sort (intersecting the volume with various perpendicular planes (slices), but this is far more better!). I also liked the way you handled hiding the back-face. – Amro Oct 19 '09 at 20:13
@Amro: Thanks. My first idea to hide the back side of the mesh was to plot each closed contour as a filled patch. This looks fine with parallel planes, but with perpendicular planes that cross one another MATLAB seems to get confused about how to layer the patches and everything looks screwed up. – gnovice Oct 19 '09 at 20:22
@gnovice: I recalculated your rep, as requested. – Bill the Lizard Oct 22 '09 at 17:48
@Bill: Thanks... it dropped by pretty much the amount I was expecting. – gnovice Oct 22 '09 at 17:50
EDIT: Updated to draw wireframe!
step = 0.05;
[X Y Z] = meshgrid(-3:step:3, -3:step:3, -3:step:3);
F=((-(X.^2).*(Z.^3)-(9/80).*(Y.^2).*(Z.^3))+((X.^2)+(9/4).*(Y.^2)+(Z.^2)-1).^3);
p = patch(isosurface(X,Y,Z,F,0));
set(p,'facecolor','w','EdgeColor','b');
daspect([1 1 1]), view(3), axis tight, axis equal
-
AMRO U DIDNT UNDERSTAND ME. i wanna plot the heart shape exactly in the picture. your plot contains many undesired lines which is SO DIFFERENT from the picture i showed. NICE TRY!!! – izzat Oct 19 '09 at 9:49
A very elegant solution is given by gnovice.
I though I extend it by adding the other elements to replicate the figure pointed by the OP. I also added some animation (I just couldn't help myself!)
% Initialize the volume data, figure, and axes:
[X,Y,Z] = meshgrid(linspace(-3,3,101));
F = -X.^2.*Z.^3-(9/80).*Y.^2.*Z.^3+(X.^2+(9/4).*Y.^2+Z.^2-1).^3;
hFigure = figure;
sz = get(hFigure, 'Position');
set(hFigure, 'Position', [sz(1)-0.15*sz(3) sz(2) 1.3*sz(3) sz(4)]);
'DataAspectRatio',[1 1 1],...
'XLim',[30 120],'YLim',[35 65],'ZLim',[30 75]);
view([-39 30]);
axis off
% hidden surface removal
hidden on
% Fill the inside of the mesh with an isosurface to
% block rendering of the back side of the heart
p = patch(isosurface(F,-0.001));
set(p,'FaceColor','w','EdgeColor','none');
% Create and plot contours in the y-z plane:
for iX = [35 38 41 45 48 51 54 57 61 64 67]
plane = reshape(F(:,iX,:),101,101);
cData = contourc(plane,[0 0]);
xData = iX.*ones(1,cData(2,1));
plot3(hAxes,xData,cData(2,2:end),cData(1,2:end),'k');
pause(.1), drawnow
end
% Create and plot contours in the x-z plane:
for iY = [41 44 47 51 55 58 61]
plane = reshape(F(iY,:,:),101,101);
cData = contourc(plane,[0 0]);
yData = iY.*ones(1,cData(2,1));
plot3(hAxes,cData(2,2:end),yData,cData(1,2:end),'k');
pause(.1), drawnow
end
% Create and plot contours in the x-y plane:
for iZ = [36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 69 71]
plane = F(:,:,iZ);
cData = contourc(plane,[0 0]);
startIndex = 1;
if size(cData,2) > (cData(2,1)+1)
startIndex = cData(2,1)+2;
zData = iZ.*ones(1,cData(2,1));
plot3(hAxes,cData(1,2:(startIndex-1)),...
cData(2,2:(startIndex-1)),zData,'k');
end
zData = iZ.*ones(1,cData(2,startIndex));
plot3(hAxes,cData(1,(startIndex+1):end),...
cData(2,(startIndex+1):end),zData,'k');
pause(.1), drawnow
end
pause(.2)
text(7,50,70,'I', 'fontWeight','bold','FontAngle','italic','fontsize',100)
pause(.5)
text(80,50,43,'Math', 'fontWeight','bold','FontAngle','italic','fontsize',100)
pause(.2)
line([20 80],[50 50],[52.5 52.5], 'color','k')
line([50 50],[20 80],[52.5 52.5], 'color','k')
line([50 50],[50 50],[30 80], 'color','k')
text(20,50,50,'x')
text(48,20,50,'y')
text(45,50,80,'z')
text(30,60,30,'(x^2+9/4y^2+z^2-1)^3 - x^2z^3-9/80y^2z^3=0', 'fontsize',8)
text(35,45,30,'-3<x,y,z<3', 'fontsize',8)
- | 3,219 | 9,505 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2014-49 | longest | en | 0.865904 |
https://stats.stackexchange.com/questions/444080/a-measure-theoretic-formulation-of-bayes-theorem | 1,720,997,050,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514654.12/warc/CC-MAIN-20240714220017-20240715010017-00048.warc.gz | 484,298,744 | 44,060 | # A Measure Theoretic Formulation of Bayes' Theorem
I am trying to find a measure theoretic formulation of Bayes' theorem, when used in statistical inference, Bayes' theorem is usually defined as:
$$p\left(\theta|x\right) = \frac{p\left(x|\theta\right) \cdot p\left(\theta\right)}{p\left(x\right)}$$
where:
• $$p\left(\theta|x\right)$$: the posterior density of the parameter.
• $$p\left(x|\theta\right)$$: the statistical model (or likelihood).
• $$p\left(\theta\right)$$: the prior density of the parameter.
• $$p\left(x\right)$$: the evidence.
Now how would we define Bayes' theorem in a measure theoretic way?
So, I started by defining a probability space:
$$\left(\Theta, \mathcal{F}_\Theta, \mathbb{P}_\Theta\right)$$
such that $$\theta \in \Theta$$.
I then defined another probability space:
$$\left(X, \mathcal{F}_X, \mathbb{P}_X\right)$$
such that $$x \in X$$.
From here now on I don't know what to do, the joint probability space would be:
$$\left(\Theta \times X, \mathcal{F}_\Theta \otimes \mathcal{F}_X, ?\right)$$
but I don't know what the measure should be.
Bayes' theorem should be written as follow:
$$? = \frac{? \cdot \mathbb{P}_\Theta}{\mathbb{P}_X}$$
where:
$$\mathbb{P}_X = \int_{\theta \in \Theta} ? \space \mathrm{d}\mathbb{P}_\Theta$$
but as you can see I don't know the other measures and in which probability space they reside.
I stumbled upon this thread but it was of little help and I don't know how was the following measure-theoretic generalization of Bayes' rule reached:
$${P_{\Theta |y}}(A) = \int\limits_{x \in A} {\frac{{\mathrm d{P_{\Omega |x}}}}{{\mathrm d{P_\Omega }}}(y)\mathrm d{P_\Theta }}$$
I'm self-studying measure theoretic probability and lack guidance so excuse my ignorance.
• Bayes' Theorem is not about "prior", "posterior", "likelihood", "evidence". Bayes Theorem is about marginal and conditional probabilities. Later research mapped this theorem to the concepts you mention. Commented Jan 10, 2020 at 11:09
One precise formulation of Bayes' Theorem is the following, taken verbatim from Schervish's Theory of Statistics (1995).
The conditional distribution of $$\Theta$$ given $$X=x$$ is called the posterior distribution of $$\Theta$$. The next theorem shows us how to calculate the posterior distribution of a parameter in the case in which there is a measure $$\nu$$ such that each $$P_\theta \ll \nu$$.
Theorem 1.31 (Bayes' theorem). Suppose that $$X$$ has a parametric family $$\mathcal{P}_0$$ of distributions with parameter space $$\Omega$$. Suppose that $$P_\theta \ll \nu$$ for all $$\theta \in \Omega$$, and let $$f_{X\mid\Theta}(x\mid\theta)$$ be the conditional density (with respect to $$\nu$$) of $$X$$ given $$\Theta = \theta$$. Let $$\mu_\Theta$$ be the prior distribution of $$\Theta$$. Let $$\mu_{\Theta\mid X}(\cdot \mid x)$$ denote the conditional distribution of $$\Theta$$ given $$X = x$$. Then $$\mu_{\Theta\mid X} \ll \mu_\Theta$$, a.s. with respect to the marginal of $$X$$, and the Radon-Nikodym derivative is $$\tag{1} \label{1} \frac{d\mu_{\Theta\mid X}}{d\mu_\Theta}(\theta \mid x) = \frac{f_{X\mid \Theta}(x\mid \theta)}{\int_\Omega f_{X\mid\Theta}(x\mid t) \, d\mu_\Theta(t)}$$ for those $$x$$ such that the denominator is neither $$0$$ nor infinite. The prior predictive probability of the set of $$x$$ values such that the denominator is $$0$$ or infinite is $$0$$, hence the posterior can be defined arbitrarily for such $$x$$ values.
Edit 1. The setup for this theorem is as follows:
1. There is some underlying probability space $$(S, \mathcal{S}, \Pr)$$ with respect to which all probabilities are computed.
2. There is a standard Borel space $$(\mathcal{X}, \mathcal{B})$$ (the sample space) and a measurable map $$X : S \to \mathcal{X}$$ (the sample or data).
3. There is a standard Borel space $$(\Omega, \tau)$$ (the parameter space) and a measurable map $$\Theta : S \to \Omega$$ (the parameter).
4. The distribution of $$\Theta$$ is $$\mu_\Theta$$ (the prior distribution); this is the probability measure on $$(\Omega, \tau)$$ given by $$\mu_\Theta(A) = \Pr(\Theta \in A)$$ for all $$A \in \tau$$.
5. The distribution of $$X$$ is $$\mu_X$$ (the marginal distribution mentioned in the theorem); this is the probability measure on $$(\mathcal{X}, \mathcal{B})$$ given by $$\mu_X(B) = \Pr(X \in B)$$ for all $$B \in \mathcal{B}$$.
6. There is a probability kernel $$P : \Omega \times \mathcal{B} \to [0, 1]$$, denoted $$(\theta, B) \mapsto P_\theta(B)$$ which represents the conditional distribution of $$X$$ given $$\Theta$$. This means that
• for each $$B \in \mathcal{B}$$, the map $$\theta \mapsto P_\theta(B)$$ from $$\Omega$$ into $$[0, 1]$$ is measurable,
• $$P_\theta$$ is a probability measure on $$(\mathcal{X}, \mathcal{B})$$ for each $$\theta \in \Omega$$, and
• for all $$A \in \tau$$ and $$B \in \mathcal{B}$$, $$\Pr(\Theta \in A, X \in B) = \int_A P_\theta(B) \, d\mu_\Theta(\theta).$$
This is the parametric family of distributions of $$X$$ given $$\Theta$$.
7. We assume that there exists a measure $$\nu$$ on $$(\mathcal{X}, \mathcal{B})$$ such that $$P_\theta \ll \nu$$ for all $$\theta \in \Omega$$, and we choose a version $$f_{X\mid\Theta}(\cdot\mid\theta)$$ of the Radon-Nikodym derivative $$d P_\theta / d \nu$$ (strictly speaking, the guaranteed existence of this Radon-Nikodym derivative might require $$\nu$$ to be $$\sigma$$-finite). This means that $$P_\theta(B) = \int_B f_{X\mid\Theta}(x \mid \theta) \, d\nu(x)$$ for all $$B \in \mathcal{B}$$. It follows that $$\Pr(\Theta \in A, X \in B) = \int_A \int_B f_{X \mid \Theta}(x \mid \theta) \, d\nu(x) \, d\mu_\Theta(\theta)$$ for all $$A \in \tau$$ and $$B \in \mathcal{B}$$. We may assume without loss of generality (e.g., see exercise 9 in Chapter 1 of Schervish's book) that the map $$(x, \theta) \mapsto f_{X\mid \Theta}(x\mid\theta)$$ of $$\mathcal{X}\times\Omega$$ into $$[0, \infty]$$ is measurable. Then by Tonelli's theorem we can change the order of integration: $$\Pr(\Theta \in A, X \in B) = \int_B \int_A f_{X \mid \Theta}(x \mid \theta) \, d\mu_\Theta(\theta) \, d\nu(x)$$ for all $$A \in \tau$$ and $$B \in \mathcal{B}$$. In particular, the marginal probability of a set $$B \in \mathcal{B}$$ is $$\mu_X(B) = \Pr(X \in B) = \int_B \int_\Omega f_{X \mid \Theta}(x \mid \theta) \, d\mu_\Theta(\theta) \, d\nu(x),$$ which shows that $$\mu_X \ll \nu$$, with Radon-Nikodym derivative $$\frac{d\mu_X}{d\nu} = \int_\Omega f_{X \mid \Theta}(x \mid \theta) \, d\mu_\Theta(\theta).$$
8. There exists a probability kernel $$\mu_{\Theta \mid X} : \mathcal{X} \times \tau \to [0, 1]$$, denoted $$(x, A) \mapsto \mu_{\Theta \mid X}(A \mid x)$$, which represents the conditional distribution of $$\Theta$$ given $$X$$ (i.e., the posterior distribution). This means that
• for each $$A \in \tau$$, the map $$x \mapsto \mu_{\Theta \mid X}(A \mid x)$$ from $$\mathcal{X}$$ into $$[0, 1]$$ is measurable,
• $$\mu_{\Theta \mid X}(\cdot \mid x)$$ is a probability measure on $$(\Omega, \tau)$$ for each $$x \in \mathcal{X}$$, and
• for all $$A \in \tau$$ and $$B \in \mathcal{B}$$, $$\Pr(\Theta \in A, X \in B) = \int_B \mu_{\Theta \mid X}(A \mid x) \, d\mu_X(x)$$
Edit 2. Given the setup above, the proof of Bayes' theorem is relatively straightforward.
Proof. Following Schervish, let $$C_0 = \left\{x \in \mathcal{X} : \int_\Omega f_{X \mid \Theta}(x \mid t) \, d\mu_\Theta(t) = 0\right\}$$ and $$C_\infty = \left\{x \in \mathcal{X} : \int_\Omega f_{X \mid \Theta}(x \mid t) \, d\mu_\Theta(t) = \infty\right\}$$ (these are the sets of potentially problematic $$x$$ values for the denominator of the right-hand-side of \eqref{1}). We have $$\mu_X(C_0) = \Pr(X \in C_0) = \int_{C_0} \int_\Omega f_{X \mid \Theta}(x \mid t) \, d\mu_\Theta(t) \, d\nu(x) = 0,$$ and $$\mu_X(C_\infty) = \int_{C_\infty} \int_\Omega f_{X \mid \Theta}(x \mid t) \, d\mu_\Theta(t) \, d\nu(x) = \begin{cases} \infty, & \text{if \nu(C_\infty) > 0,} \\ 0, & \text{if \nu(C_\infty) = 0.} \end{cases}$$ Since $$\mu_X(C_\infty) = \infty$$ is impossible ($$\mu_X$$ is a probability measure), it follows that $$\nu(C_\infty) = 0$$, whence $$\mu_X(C_\infty) = 0$$ as well. Thus, $$\mu_X(C_0 \cup C_\infty) = 0$$, so the set of all $$x \in \mathcal{X}$$ such that the denominator of the right-hand-side of \eqref{1} is zero or infinite has zero marginal probability.
Next, consider that, if $$A \in \tau$$ and $$B \in \mathcal{B}$$, then $$\Pr(\Theta \in A, X \in B) = \int_B \int_A f_{X \mid \Theta}(x \mid \theta) \, d\mu_\Theta(\theta) \, d\nu(x)$$ and simultaneously \begin{aligned} \Pr(\Theta \in A, X \in B) &= \int_B \mu_{\Theta \mid X}(A \mid x) \, d\mu_X(x) \\ &= \int_B \left( \mu_{\Theta \mid X}(A \mid x) \int_\Omega f_{X \mid \Theta}(x \mid t) \, d\mu_\Theta(t) \right) \, d\nu(x). \end{aligned} It follows that $$\mu_{\Theta \mid X}(A \mid x) \int_\Omega f_{X \mid \Theta}(x \mid t) \, d\mu_\Theta(t) = \int_A f_{X \mid \Theta}(x \mid \theta) \, d\mu_\Theta(\theta)$$ for all $$A \in \tau$$ and $$\nu$$-a.e. $$x \in \mathcal{X}$$, and hence $$\mu_{\Theta \mid X}(A \mid x) = \int_A \frac{f_{X \mid \Theta}(x \mid \theta)}{\int_\Omega f_{X \mid \Theta}(x \mid t) \, d\mu_\Theta(t)} \, d\mu_\Theta(\theta)$$ for all $$A \in \tau$$ and $$\mu_X$$-a.e. $$x \in \mathcal{X}$$. Thus, for $$\mu_X$$-a.e. $$x \in \mathcal{X}$$, $$\mu_{\Theta\mid X}(\cdot \mid x) \ll \mu_\Theta$$, and the Radon-Nikodym derivative is $$\frac{d\mu_{\Theta \mid X}}{d \mu_\Theta}(\theta \mid x) = \frac{f_{X \mid \Theta}(x \mid \theta)}{\int_\Omega f_{X \mid \Theta}(x \mid t) \, d\mu_\Theta(t)},$$ as claimed, completing the proof.
Lastly, how do we reconcile the colloquial version of Bayes' theorem found so commonly in statistics/machine learning literature, namely, $$\tag{2} \label{2} p(\theta \mid x) = \frac{p(\theta) p(x \mid \theta)}{p(x)},$$ with \eqref{1}?
On the one hand, the left-hand-side of \eqref{2} is supposed to represent a density of the conditional distribution of $$\Theta$$ given $$X$$ with respect to some unspecified dominating measure on the parameter space. In fact, none of the dominating measures for the four different densities in \eqref{2} (all named $$p$$) are explicitly mentioned.
On the other hand, the left-hand-side of \eqref{1} is the density of the conditional distribution of $$\Theta$$ given $$X$$ with respect to the prior distribution.
If, in addition, the prior distribution $$\mu_\Theta$$ has a density $$f_\Theta$$ with respect to some (let's say $$\sigma$$-finite) measure $$\lambda$$ on the parameter space $$\Omega$$, then $$\mu_{\Theta \mid X}(\cdot\mid x)$$ is also absolutely continuous with respect to $$\lambda$$ for $$\mu_X$$-a.e. $$x \in \mathcal{X}$$, and if $$f_{\Theta \mid X}$$ represents a version of the Radon-Nikodym derivative $$d\mu_{\Theta\mid X}/d\lambda$$, then \eqref{1} yields \begin{aligned} f_{\Theta \mid X}(\theta \mid x) &= \frac{d \mu_{\Theta \mid X}}{d\lambda}(\theta \mid x) \\ &= \frac{d \mu_{\Theta \mid X}}{d\mu_\Theta}(\theta \mid x) \frac{d \mu_{\Theta}}{d\lambda}(\theta) \\ &= \frac{d \mu_{\Theta \mid X}}{d\mu_\Theta}(\theta \mid x) f_\Theta(\theta) \\ &= \frac{f_\Theta(\theta) f_{X\mid \Theta}(x\mid \theta)}{\int_\Omega f_{X\mid\Theta}(x\mid t) \, d\mu_\Theta(t)} \\ &= \frac{f_\Theta(\theta) f_{X\mid \Theta}(x\mid \theta)}{\int_\Omega f_\Theta(t) f_{X\mid\Theta}(x\mid t) \, d\lambda(t)}. \end{aligned} The translation between this new form and \eqref{2} is \begin{aligned} p(\theta \mid x) &= f_{\Theta \mid X}(\theta \mid x) = \frac{d \mu_{\Theta \mid X}}{d\lambda}(\theta \mid x), &&\text{(posterior)}\\ p(\theta) &= f_\Theta(\theta) = \frac{d \mu_\Theta}{d\lambda}(\theta), &&\text{(prior)} \\ p(x \mid \theta) &= f_{X\mid\Theta}(x\mid\theta) = \frac{d P_\theta}{d\nu}(x), &&\text{(likelihood)} \\ p(x) &= \int_\Omega f_\Theta(t) f_{X\mid\Theta}(x\mid t) \, d\lambda(t). &&\text{(evidence)} \end{aligned}
• Why should $\Omega$ be a Borel space instead of some other measure space?
– Dave
Commented Jan 9, 2020 at 22:53
• @Dave Borel spaces are easier to work with for technical reasons, while also being fairly general. For example, conditional distributions of random variables taking values in a Borel space always exist, whereas they might not exist for random variables taking values in a non-Borel space. Fortunately, most spaces in practice are Borel spaces. For example, every Borel subset of a complete, separable metric space is a Borel space. Commented Jan 9, 2020 at 23:11
• I just checked the edit, your answer is extremely clear and detailed and helped me a lot, thank you very much for the time and effort @ArtemMavrin. Commented Jan 10, 2020 at 0:14
• @BlgKhalil yes, you could call it that if you want, and it would be more consistent with the rest of the notation Commented Jan 11, 2020 at 21:16
• @BlgKhalil glad to help :) Commented Jan 11, 2020 at 21:19 | 4,387 | 12,828 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 155, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2024-30 | latest | en | 0.865824 |
https://oeis.org/A268336 | 1,619,111,967,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039594341.91/warc/CC-MAIN-20210422160833-20210422190833-00410.warc.gz | 538,447,677 | 4,214 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
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A268336 a(n) = A174824(n)/n, where A174824(n) = lcm(A002322(n), n) and A002322(n) is the Carmichael lambda function (also known as the reduced totient function or the universal exponent of n). 7
1, 1, 2, 1, 4, 1, 6, 1, 2, 2, 10, 1, 12, 3, 4, 1, 16, 1, 18, 1, 2, 5, 22, 1, 4, 6, 2, 3, 28, 2, 30, 1, 10, 8, 12, 1, 36, 9, 4, 1, 40, 1, 42, 5, 4, 11, 46, 1, 6, 2, 16, 3, 52, 1, 4, 3, 6, 14, 58, 1, 60, 15, 2, 1, 12, 5, 66, 4, 22, 6, 70, 1, 72, 18, 4, 9, 30, 2, 78, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,3 LINKS FORMULA a(n) = A174824(n)/n. a(A124240(n)) = 1. - Michel Marcus, Feb 21 2016 MATHEMATICA Table[LCM[n, CarmichaelLambda@ n]/n, {n, 100}] (* Michael De Vlieger, Feb 03 2016, after T. D. Noe at A174824 *) PROG (MAGMA) [1] cat [Lcm(n, CarmichaelLambda(n))/n: n in [2..100]]: // Feb 03 2016 (PARI) a(n)=my(ps); ps=factor(n)[, 1]~; m = n; for(k=1, #ps, m=lcm(m, ps[k]-1)); m/n \\ Michel Marcus, Feb 21 2016 (PARI) apply( {A268336(n)=lcm(lcm([p-1|p<-factor(n)[, 1]]), n)/n}, [1..99]) \\ [...] = znstar(n)[2], but 3x faster. - M. F. Hasler, Nov 13 2019 CROSSREFS Cf. A002322, A068563, A124240, A174824. Sequence in context: A187730 A049559 A063994 * A295127 A076512 A128707 Adjacent sequences: A268333 A268334 A268335 * A268337 A268338 A268339 KEYWORD nonn,easy AUTHOR Juri-Stepan Gerasimov, Feb 01 2016 EXTENSIONS More terms from Vincenzo Librandi, Feb 03 2016 STATUS approved
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Last modified April 22 12:53 EDT 2021. Contains 343177 sequences. (Running on oeis4.) | 810 | 1,930 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2021-17 | latest | en | 0.605504 |
http://iitg.vlab.co.in/?sub=62&brch=271&sim=1388&cnt=2921 | 1,513,628,876,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948623785.97/warc/CC-MAIN-20171218200208-20171218222208-00537.warc.gz | 134,653,031 | 8,592 | . . . Inverse Kinematics - By Remotely Triggering Stationary Base Robot . . Click here to download the documentation Objective: To perform inverse kinematics on a 5-axis robotic arm. Just as in direct kinematics, we find the position and orientation of the tool of a robotic manipulator for a given vector of joint variables; the reverse procedure of determining the joint variables given a desired or known tool position and orientation is addressed in inverse kinematics. The inverse kinematics problem is more important from a practical point of view because any manipulation task is naturally stated in terms of the required position and orientation of the tool. Again when sensors for visual feedback such as cameras are used the information fedback is the position and orientation of the tool or the object to be manipulated and not the state of the joint variables. In direct kinematics, the “Arm Equation” served as a solution for the direct kinematics problem. It was a kind of one to one mapping tool since any particular vector of joint-variables would yield one and only one end-effector or tool configuration. In inverse kinematics, the solution would be a set or vector of joint-variables that will result in the given end-effector or tool configuration. But unlike the arm equation which behaves as a one to one mapping tool the solution to an inverse kinematics problem is not so straight forward. The obvious reason for this is, there can be more than one set of joint-variables that can ultimately result in the same end-effector configuration. In addition to the existence of multiple solutions especially for robots with more than 6 axes called “kinematically redundant” robots, a solution may not exist at all in many cases. Therefore what is usually done in inverse kinematics is that each robot or each class of robots is analysed separately in order to determine its inverse kinematic parameters. There are two approaches to the inverse kinematics problem: · To find a closed form solution using algebra or geometry. · To find a numerical solution by a successive approximation algorithm. Although it is highly desirable to go for the first approach, it is not always possible to find a closed form solution for arbitrary robot architecture. However, most of the industrial robots do have a fairly known tool configuration and this paves the way for using the first approach. The algebraic approach involves finding the joint angles through algebraic transformation and relations whereas the geometric approach involves finding the same through geometrical relations and heuristics by analyzing the structural geometry of the robot. Since the finding of a closed form solution in joint angles is a tool-configuration dependent task, the methods for finding the same for some specific robot architectures are discussed in theory. Cite this Simulator:iitg.vlab.co.in,. (2012). Inverse Kinematics - By Remotely Triggering Stationary Base Robot. Retrieved 19 December 2017, from iitg.vlab.co.in/?sub=62&brch=271&sim=1388&cnt=2921 ..... ..... ..... | 625 | 3,116 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2017-51 | longest | en | 0.91513 |
home.westman.wave.ca | 1,620,359,388,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988774.96/warc/CC-MAIN-20210507025943-20210507055943-00457.warc.gz | 23,076,971 | 5,111 | # Sorting Algorithms Demonstration in Java
### I wrote little of this code, and take no responsibility (nor credit) for any of it.
Demo Applet Algorithm Name Running Time (Efficiency) Stability Method Other notes
Best Average Worst
If you have any other sorting algorithms you would like to see included on this list please send them to mailinglistsandjunkmailandcrap@wcgwave.ca.
Bogosort O(n*n!) O(unbounded) Unstable Random Average time using Knuth shuffle.
Source: BogoSortAlgorithm.java
Bozo sort O(n*n!) O(n*n!) Unstable Random Average time is asymptotically half that of bogosort.
Source: BozoSortAlgorithm.java
Perm sort O(n) O(n*n!) Unstable Exchanging The algorithm works by trying every permutation until it finds one that's sorted.
Source: PermSortAlgorithm.java
Stooge sort O(n2.71) O(n2.71) O(n2.71) Unstable Exchanging The algorithm gets its name from slapstick routines of the Three Stooges, in which each stooge hits the other two.
Source: StoogeSortAlgorithm.java
Sift sort O(n2) Unstable Exchaning
Source: SiftSortAlgorithm.java
Bubble sort O(n) O(n2) Stable Exchanging Times are for best variant.
Source: BubbleSortAlgorithm.java
Several unique sort O(n) O(n2) Exchanging This new sort makes as many passes as there are unique records in the field.
Several Unique runs in time less than T(kn), proportional to the number of unique elements and the total number of elements — which is equivalent to T(n2) in the worst case.
This algorithm was invented by a computer program, Criticall.
Several unique sort vs. Bubble sort duel on list with several unique items.
Source: SeveralUniqueSortAlgorithm.java
Bidirectional Bubble sort O(n) O(n2) Stable Exchanging Aka. Cocktail sort.
Source: BidirectionalBubbleSortAlgorithm.java
Comb sort 11 O(nlog n) O(nlog n) O(nlog n) Unstable Exchanging
Source: CombSort11Algorithm.java
Gnome sort O(n) O(n2) Stable Exchanging
Source: GnomeSortAlgorithm.java
Selection sort O(n2) O(n2) O(n2) Unstable Selection
Source: SelectionSortAlgorithm.java
Bidirectional Selection sort O(n2) O(n2) O(n2) Unstable Selection Aka. Shaker sort.
Source: BidirectionalSelectionSortAlgorithm.java
Insertion sort O(n) O(n + d) O(n2) Stable Insertion d is the number of inversions, which is O(n2).
Source: InsertionSortAlgorithm.java
Flash sort O(n) O(n + d) O(n2) Insertion/? The flash sort algorithm consists of an initial "partial flash short" stage followed by a traditional insertion sort. The partial flash sort seems to decrease average insertion sort time noticably.
Source: FlashSortAlgorithm.java
Shell sort O(n1.5) Unstable Insertion
Source: ShellSortAlgorithm.java
Merge sort O(nlog n) O(nlog n) O(nlog n) Stable Merging Uses O(n) memory.
Source: ExtraStorageMergeSortAlgorithm.java
In-place merge sort O(nlog n) O(nlog n) O(nlog n) Stable Merging Uses O(1) memory.
Source: MergeSortAlgorithm.java
Bitonic Sorter O(n(log n)2)) Unstable Merging Requires list with a size that is a power of 2.
Designed for parallel processors.
Source: BitonicSortAlgorithm.java
See also: Extra storage merge sort, In-place merge sort, Bubble sort, Bidirectional bubble sort
Heap sort O(nlog n) O(nlog n) O(nlog n) Unstable Selection
Source: HeapSortAlgorithm.java
JSort Unstable Selection/Insertion JSort is an in-place sort algorithm that uses build heap twice to largely order the array then finishes with an insertion sort. JSort is attributed to Jason Morrison.
Source: JSortAlgorithm.java
Quick sort O(nlog n) O(nlog n) O(n2) Unstable Partitioning
Source: QSortAlgorithm.java
See also: 3-way quick sort, Qubble sort, Enhance quick sort, Fast quick sort
3-way quick sort O(nlog n) O(nlog n) O(n2) Unstable Partitioning
Source: QSortXAlgorithm.java
See also: Quick sort, Qubble sort, Enhance quick sort, Fast quick sort
Quick sort w/ Bubble sort O(nlog n) O(nlog n) O(n2) Unstable Partitioning/Exchanging Bubble sort if the number of elements in a partition is less than 6.
Source: QubbleSortAlgorithm.java
See also: 3-way quick sort, Quick sort, Enhance quick sort, Fast quick sort
Enhanced quick sort O(nlog n) O(nlog n) O(n2) Unstable Partitioning
Source: EQSortAlgorithm.java
See also: 3-way quick sort, Quick sort, Qubble sort, Fast quick sort
Quick sort w/ Insertion sort O(nlog n) O(nlog n) O(n2) Unstable Partitioning/Insertion Insertion sort if the number of elements in a partition is less than 4.
Source: FastQSortAlgorithm.java
See also: 3-way quick sort, Quick sort, Qubble sort, Enhance quick sort
Introsort O(nlog n) O(nlog n) O(nlog n) Unstable Hybrid Introsort, or introspective sort, begins with quicksort, switching to heapsort once the recursion depth exceeds a preset value.
Sublists smaller than a certain threshold are sorted with insertion sort.
Source: IntroSortAlgorithm.java
Patience sort O(n) O(nlog n) Unstable Insertion Finds all the longest increasing subsequences within O(n log log n).
Source: PatienceSortAlgorithm.java
Swap sort Swapping This isn't really a swap. This algorithm just demonstrates how long it takes java to perform n swaps.
Source: SwapSortAlgorithm.java
Radix sort O(n(k/b)) O(n(k/b)) O(n(k/b)) Stable Buckets/Counting Least significant variety of radix sort.
k is the maximum key value.
b is the base in which the key is evaluated.
Bucket sort O(n) O(n) O(n2) Stable Buckets Bucket sort is a generalization of pigeonhole sort.
Source: BucketSortAlgorithm.java
Binary bucket sort O(n) O(n) O(n2) Buckets
Source: BinaryBucketSortAlgorithm.java
Quick binary bucket sort O(n) O(n) O(n2) Buckets
Source: QuickBinaryBucketSortAlgorithm.java
Counting sort O(n + 2k) O(n + 2k) O(n + 2k) Buckets n and k are the lengths of the arrays A (the input array) and C (the counting array), respectively.
Source: CountingSortAlgorithm.java
Odd-even transposition sort O(n) Merging Batcher's odd-even (transposition) mergesort is a generic construction for sorting networks of size 2n.
Absolute Efficiency: O((log n)/n), when running on n processors.
Source: OETransSortAlgorithm.java | 1,544 | 5,948 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2021-21 | latest | en | 0.848653 |
www.ahsan.io | 1,713,368,111,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817158.8/warc/CC-MAIN-20240417142102-20240417172102-00230.warc.gz | 562,176,433 | 5,549 | I was watching a video on YouTube about the Internet’s networking infrastructure, and it got me thinking: “What is the modulation method used by modern electronic devices to communicate with networking hardware?”. The pursuit of an answer took me deep into the rabbit-hole that is communication theory.
TL;DR: WLAN 802.11 b/g standards use various PSK schemes; QPSK, BPSK being among them.
## FM and AM
For communication of analog signals, the two most popular modulation methods are FM (frequency modulation) and AM (amplitude modulation). This is the communication method still in use by the commercial analog radio today. The names of these methods are pretty self-explanatory. In each case, the amplitude of the input signal changes the corresponding attribute of the carrier wave. This can be easily observed in the following figure where blue wave is the input signal and the orange one is the output.
import numpy as np
import matplotlib.pyplot as plt
f_carrier = 10
w_carrier = 2 * np.pi * f_carrier
f_input = 1
w_input = 2 * np.pi * f_input
time_granularity = 1/300
time = np.arange(0, 1, time_granularity)
input_signal = np.sin(np.multiply(time, w_input))
am_output_signal = np.multiply(
np.sin(np.multiply(time, w_carrier)), input_signal)
fm_output_signal = np.zeros_like(time)
for i, t in enumerate(time):
fm_output_signal[i] = np.sin(
2. * np.pi * (f_carrier * t + input_signal[i]))
plt.subplot(1, 2, 1)
plt.plot(time, input_signal)
plt.plot(time, am_output_signal)
plt.title('Amplitude Modulation')
plt.xlabel('Time')
plt.ylabel('Amplitude')
plt.subplot(1, 2, 2)
plt.plot(time, input_signal)
plt.plot(time, fm_output_signal)
plt.title('Frequency Modulation')
plt.xlabel('Time')
plt.ylabel('Amplitude')
plt.show()
## QPSK
In case of digital signals, FM and AM just become Frequency-shift keying (FSK) and Amplitude-shift keying (ASK) because of the discrete jumps in the input signal.
Phase-shift keying (PSK) is another modulation method that, as its name suggests, modulates the phase of the carrier wave depending on the amplitude of the input signal. This is the method that is mostly used by digital electronics for wired and wireless communication. Various PSK schemes are used by the WLAN 802.11 b/g standards depending on the data rate requirements. Other applications include RFID, biometric passports, wireless credit cards, etc.
PSK trades off error probability for more bandwidth. Compared with Frequency-shift keying, PSK has more bandwidth whereas FSK has better noise rejection for the same signal power.
Quadrature phase-shift keying (QPSK) imposes 4 symbols on the carrier wave, and hence, can encode 2 bits of information per symbol. It’s known as “quadrature” PSK because, in addition to the “in-phase” component, it also has an orthogonal “in-quadrature” component in the carrier wave. What this means is that the carrier wave is a combination of a sine and a cosine component. This idea gets more understandable in the QPSK example encoding below:
import numpy as np
import matplotlib.pyplot as plt
freq = 1
w = 2 * np.pi * freq
symbol_phase_angles = [np.pi/4, 3*np.pi/4, 5*np.pi/4, 7*np.pi/4]
time_granularity = 1/100
time = np.arange(0, len(symbol_phase_angles), time_granularity)
signal = np.zeros(len(time))
for phase_ind, phase in enumerate(symbol_phase_angles):
start = int(phase_ind/time_granularity)+1
end = int((phase_ind + 1)/time_granularity)
time_slice = time[start:end]
signal[start:end] = np.sin(np.multiply(time_slice, w) + phase) + \
np.cos(np.multiply(time_slice, w) + phase)
plt.plot(time, signal)
plt.title('QPSK("11 01 00 10")')
plt.xlabel('Time ->')
plt.ylabel('Amplitude')
plt.yticks(np.array([]))
plt.xticks([i + freq/2 for i in range(len(symbol_phase_angles))],
['11', '01', '00', '10'])
plt.axhline(y=0, color='k')
plt.show()
As you can see, the start of each symbol has a jump in the phase of the modulated signal. The demodulator at the receiving end of this signal would have prior knowledge of the phase-to-symbol mapping, and in this way would be able to understand the message that was encoded. | 1,015 | 4,084 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2024-18 | longest | en | 0.771833 |
https://www.physicsforums.com/threads/how-does-the-perihelion-passage-affect-the-orbital-period-of-comet-neowise.991236/ | 1,713,243,633,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817043.36/warc/CC-MAIN-20240416031446-20240416061446-00558.warc.gz | 894,580,492 | 18,619 | # How does the perihelion passage affect the orbital period of comet Neowise?
• I
• Buzz Bloom
In summary: The following is a quote from the article."7 day motion", apparently referring to the separation between orbital points displayed. Another possible interpretation is that the diagram represents one complete Neowise orbit, and each loop of the sprial represents what happens to Neowise in different Earth years from Earth's perspective. That is, the loop in the sky gets smaller as Neowise moves further away, and vice versa. The point where the two spiral cones touch corresponds to the aphelion.If my guess is wrong, can someone please explain what is happening regarding these spirals in Neowise's orbit?.
Buzz Bloom
Gold Member
TL;DR Summary
The diagram of Neowise's orbit in the cited Wikipedia article seems very odd.
The orbit diagram
in the Wikipedia article
shows some very odd spirals.
My first guess is the picture shows what Neowise does in one Earth year (mostly 2020) as the Earth completes it's orbit. The caption says, "7 day motion", apparently referring to the separation between orbital points displayed. Another possible interpretation is that the diagram represents one complete Neowise orbit, and each loop of the sprial represents what happens to Neowise in different Earth years from Earth's perspective. That is, the loop in the sky gets smaller as Neowise moves further away, and vice versa. The point where the two spiral cones touch corresponds to the aphelion.
If my guess is wrong, can someone please explain what is happening regarding these spirals in Neowise's orbit?.
The following is a quote from the article.
This perihelion passage will increase the comet's orbital period from about 4500 years to about 6800 years.
Can someone explain how the perihelion passage causes this change in orbital period?
Buzz Bloom said:
The diagram of Neowise's orbit in the cited Wikipedia article seems very odd.
That's because it's not an orbit.
davenn
It looks like it's the comet's path across the sky, with its position marked weekly. I expect you'll find 52 positions marked per loop of the spiral, because we are observing from the Earth and you are seeing the parallax from our orbital motion superimposed on the comet's own orbital motion.
davenn and Buzz Bloom
Buzz Bloom said:
Summary:: The diagram of Neowise's orbit in the cited Wikipedia article seems very odd.
The orbit diagram
in the Wikipedia article
shows some very odd spirals.
My first guess is the picture shows what Neowise does in one Earth year (mostly 2020) as the Earth completes it's orbit. The caption says, "7 day motion", apparently referring to the separation between orbital points displayed. Another possible interpretation is that the diagram represents one complete Neowise orbit, and each loop of the sprial represents what happens to Neowise in different Earth years from Earth's perspective. That is, the loop in the sky gets smaller as Neowise moves further away, and vice versa. The point where the two spiral cones touch corresponds to the aphelion.
If my guess is wrong, can someone please explain what is happening regarding these spirals in Neowise's orbit?.
The following is a quote from the article.
This perihelion passage will increase the comet's orbital period from about 4500 years to about 6800 years.
Can someone explain how the perihelion passage causes this change in orbital period?
I think you've gotten the answer to your first question, which is that this is a plot of the position of the comet on the sky of the Earth, with the points being 7 days apart. You're right in that each loop of the spiral is one Earth year.
On your second question, comets don't follow simple Keplerian orbits. They are spewing out streams of gas and dust, and these streams act like rocket engines and change the comet's orbit. This effect is especially pronounced as the comet passes perihelion, where it gets the most solar heating and spews out the most evaporating gases. So the orbital elements after perihelion passage can be significantly different than before perihelion passage. In extreme cases, the comet simply boils away during perihelion passage and nothing is left but a cloud of dust.
Buzz Bloom
The confusing thing is that the tight spirals can be wrongly thought of as what happens when the comet is nearest. In fact, its the single large loop that shows the parallax around the time its orbital angular velocity is greatest and it distance from us is least. Then the gassing adds another factor.
I always take my hat off to astronomers who find that sort of thing second nature - after a lot of experience and hard work, no doubt.
Buzz Bloom
## 1. What is the orbit of comet Neowise?
The orbit of comet Neowise is an elliptical path around the sun, with a period of approximately 6,800 years.
## 2. How close does comet Neowise get to the sun?
At its closest point, comet Neowise gets within 43 million kilometers (26.7 million miles) of the sun.
## 3. How close does comet Neowise get to Earth?
In July 2020, comet Neowise made its closest approach to Earth at a distance of about 103 million kilometers (64 million miles).
## 4. What is the size of comet Neowise?
Comet Neowise has a diameter of about 5 kilometers (3.1 miles), making it a relatively small comet compared to others in our solar system.
## 5. How long will comet Neowise be visible from Earth?
Comet Neowise was visible from Earth for about a month in July 2020, and will not be visible again for another 6,800 years when it completes its orbit around the sun.
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3K | 1,418 | 6,134 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2024-18 | latest | en | 0.928844 |
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# Polar Equation of a Conic Watch
1. I am interested in how the following formula for conics is derived;
Which gives:
for an ellipse, and
for a hyperbola
I am able to derive the two individual formulas for the ellipse and hyperbola by geometric consideration but have trouble with the one containing the term in b. Any help is appreciated .
EDIT:
I forgot to mention that the focus is at (ae, 0) and the directrix is x = a/e
2. Bump
3. Do these substitutions into the Cartesian equations not work?
4. (Original post by Qwertish)
Do these substitutions into the Cartesian equations not work?
The thing is that they have different Cartesian equations. I know how to derive the two formulas for ellipse and hyperbola individually. It is the first formula I mentioned that I have trouble with.
5. (Original post by Ateo)
I am interested in how the following formula for conics is derived;
Which gives:
for an ellipse, and
for a hyperbola
I am able to derive the two individual formulas for the ellipse and hyperbola by geometric consideration but have trouble with the one containing the term in b. Any help is appreciated .
EDIT:
I forgot to mention that the focus is at (ae, 0) and the directrix is x = a/e
Right, let's do this in polar coordinates.
Put the pole at the focus and have the initial line be perpendicular to the directrix at .
The distance from the focus to a general point on the curve is , which depends on .
The distance from the directrix to the point will then be .
Since we are dealing with a conic section, by definition we have
Which then gives
Now and thus the result follows:
6. (Original post by Brister)
...
So you've basically considered the ellipse and derived the formula for this case. Then you used that formula to get the general equation. You can also consider the hyperbola in a similar way getting the other equation I mentioned which then you can use to get the general formula mentioned.
So essentially what we are doing is considering two cases from which the general formula follows. I already understand how to do this. What I was curious about is how the general formula is obtained without this individual consideration of each case. My book states this general formula and then gives the two separate cases. We have went in reverse. With that said though, I don't know if there is a direct proof of this, the book isn't great at introduction of theorems - it just seems to state them. Sorry for being a pain.
7. (Original post by Ateo)
So you've basically considered the ellipse and derived the formula for this case. Then you used that formula to get the general equation. You can also consider the hyperbola in a similar way getting the other equation I mentioned which then you can use to get the general formula mentioned.
So essentially what we are doing is considering two cases from which the general formula follows. I already understand how to do this. What I was curious about is how the general formula is obtained without this individual consideration of each case. My book states this general formula and then gives the two separate cases. We have went in reverse. With that said though, I don't know if there is a direct proof of this, the book isn't great at introduction of theorems - it just seems to state them. Sorry for being a pain.
Okay, I see what you are trying to say. I believe, though, that this general equation involving is just a convenient way of combining the two equations you get for the ellipse and hyperbola.
You will notice that is defined differently for the ellipse and hyperbola. This is because the value of is negative for a hyperbola so they decide that instead.
In other words, your general equation cannot define an ellipse and a hyperbola at the same time.
You cannot really derive the general equation without specifying the type of conic because the focus and directrix move depending on . For a hyperbola, you will find that the directrix moves to the left of the curve whereas for the ellipse it is on the right.
Circle
It is interesting to note that the equation works for a circle, which is basically a special case of the ellipse.
With , we first notice that such that .
The polar equation therefore reduces to with the pole at (ae,0) in Cartesian coordinates. This is clearly a circle centred on the focus.
Parabola
The choice of (ae,0) and x = a/e for the focus and directrix respectively means that the equation does not apply to a parabola. This is because for a parabola, and the focus would be on the directrix. However, if you just change the focus to (a,0) and the directrix to then you can use the same method.
but so
We rearrange to find
8. (Original post by Brister)
...
Fully agree to everything you say, that's a great response, thank you .
9. (Original post by Ateo)
Fully agree to everything you say, that's a great response, thank you .
No problem, it was pretty interesting to think about
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Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice. | 1,415 | 6,374 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2017-51 | latest | en | 0.956443 |
http://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-12th-edition/chapter-5-section-5-1-greatest-common-factors-and-factoring-by-grouping-5-1-exercises-page-329/16 | 1,524,249,863,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125944677.39/warc/CC-MAIN-20180420174802-20180420194802-00301.warc.gz | 417,985,550 | 12,743 | ## Intermediate Algebra (12th Edition)
Published by Pearson
# Chapter 5 - Section 5.1 - Greatest Common Factors and Factoring by Grouping - 5.1 Exercises: 16
#### Answer
$9z(z^{3}+9)$
#### Work Step by Step
The greatest common factor of $9z^{4}+81z$ is $9z$. We can use the distributive property to factor out the greatest common factor. 1. $9z^{4}+81z$ 2. $9z\times z^{3}+9z\times9$ 3. $9z(z^{3}+9)$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 177 | 567 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2018-17 | latest | en | 0.782553 |
http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut38_ratexp.htm | 1,553,517,558,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912203947.59/warc/CC-MAIN-20190325112917-20190325134917-00230.warc.gz | 406,775,318 | 9,367 | b b 2 c b g c c Title
Intermediate Algebra Tutorial 38: Rational Exponents
WTAMU > Virtual Math Lab > Intermediate Algebra
Learning Objectives
After completing this tutorial, you should be able to: Rewrite a rational exponent in radical notation. Simplify an expression that contains a rational exponent. Use rational exponents to simplify a radical expression.
Introduction
In this tutorial we are going to combine two ideas that have been discussed in earlier tutorials: exponents and radicals. We will look at how to rewrite, simplify and evaluate these expressions that contain rational exponents. What it boils down to is if you have a denominator in your exponent, it is your index or root number. So, if you need to, review radicals covered in Tutorial 37: Radicals. Also, since we are working with fractional exponents and they follow the exact same rules as integer exponents, you will need to be familiar with adding, subtracting, and multiplying them. If fractions get you down you may want to go to Beginning Algebra Tutorial 3: Fractions. To review exponents, you can go to Tutorial 23: Exponents and Scientific Notation Part I and Tutorial 24: Exponents and Scientific Notation Part II. Let's move onto rational exponents and roots.
Tutorial
Rational Exponents and Roots If x is positive, p and q are integers and q is positive,
In other words, when you have a rational exponent, the denominator of that exponent is your index or root number and the numerator of the exponent is the exponential part. I have found it easier to think of it in two parts. Find the root part first and then take it to the exponential part if possible. It makes the numbers a lot easier to work with. Radical exponents follow the exact same exponent rules as discussed in Tutorial 23: Exponents and Scientific Notation, Part I and Tutorial 24: Exponents and Scientific Notation, Part II. In those two tutorials we only dealt with integers, but you can extend those rules to rational exponents. Here is a quick review of those exponential rules:
Review of Exponential Rules
Example 1: Use radical notation to write the expression and simplify.
We are looking for the square root of 4 raised to the 1 power, which is the same as just saying the square root of 4. If your exponent's numerator is 1, you are basically just looking for the root (the denominator's exponent). Our answer is 2 since the square root of 4 is 2.
Example 2: Use radical notation to write the expression and simplify.
In this problem we are looking for the cube root of -27 squared. Again, I think it is easier to do the root part first if possible. The numbers will be easier to work with. The cube root of -27 is -3 and (-3) squared is 9.
Example 3: Use radical notation to write the expression and simplify.
In this problem we are looking for the square root of 36/49 cubed. Again, I think it is easier to do the root part first if possible. The numbers will be easier to work with. The square root of 36/49 is 6/7 and 6/7 cubed is 216/343.
Example 4: Write with a positive exponent and simplify.
In this problem we are looking for the cube root of 1/8 raised to the fifth power. Again, I think it is easier to do the root part first if possible. The numbers will be easier to work with. The cube root of 1/8 is 1/2 and 1/2 raised to the fifth power is 1/32.
Example 5: Simplify the expression. Write with positive exponents only.
Example 6: Simplify the expression. Write with positive exponents only.
Example 7: Multiply.
Since this is a binomial times a binomial, we can use the FOIL method as discussed in Tutorial 26: Multiplying Polynomials.
Example 8: Factor the common factor from the given expression.
Basically, we are factoring out a GCF as discussed in Tutorial 27: The GCF and Factoring by Grouping. Remember when you factor out the GCF, you our doing the reverse of the distributive property.
*Factor out x to the 1/4
Example 9: Use rational exponents to simplify the radical. Assume that the variable represents a positive number.
*Simplify exponent *Rewrite exponent 1/4 as a fourth root
Practice Problems
These are practice problems to help bring you to the next level. It will allow you to check and see if you have an understanding of these types of problems. Math works just like anything else, if you want to get good at it, then you need to practice it. Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument. In fact there is no such thing as too much practice. To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer.
Practice Problems 1a - 1c: Use radical notation to write the expression and simplify.
Practice Problem 2a: Write with a positive exponent and simplify.
Practice Problems 3a - 3b: Simplify the expression, write with positive exponents only.
Practice Problem 4a: Multiply.
Practice Problem 5a: Factor the common factor from the given expression.
Practice Problem 6a: Use rational exponents to simplify the radical. Assume that the variable represents a positive number.
Need Extra Help on these Topics?
Go to Get Help Outside the Classroom found in Tutorial 1: How to Succeed in a Math Class for some more suggestions.
Last revised on July 19, 2011 by Kim Seward. | 1,279 | 5,562 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.84375 | 5 | CC-MAIN-2019-13 | latest | en | 0.872513 |
https://groups.yahoo.com/neo/groups/Hyacinthos/conversations/topics/12577?xm=1&o=1&l=1 | 1,511,613,553,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934809778.95/warc/CC-MAIN-20171125105437-20171125125437-00470.warc.gz | 628,133,182 | 18,223 | ## New construction of the Tarry point
Expand Messages
• Hello all in geometry, I have always found the Tarry point mysterious. It is opposite the Steiner point in the circumcircle and the intersection of the
Message 1 of 1 , Apr 2, 2006
Hello all in geometry,
I have always found the Tarry point mysterious. It is opposite the
Steiner point in the circumcircle and the intersection of the
circumcircle with the Kiepert hyperbola. Both of these are nice, if
disconnected properties.
I have a new construction which both explains the above and shows
that the Tarry point is one example of a universal phenomenon.
We begin as I always begin, with a single point in the plane of the
triangle. We will choose this point to be K, the symmedian point.
There are now two natural lines, the dual of K and G—K. Natural in
this context means that the structure is affine invariant. The
endpoints of these lines map to antipodal points on the Steiner ellipse.
These lines meet at P. The isotomic of the two lines are
circumconics, one, the Kiepert hyperbola, has its perspector tS at
infinity, the second has perspector K. The isotomic of P is the
intersection between these conics. This is the Tarry point.
The constuction shows that this is construction is general. Slightly
more analysis shows that S and T are opposite on the K circumconic
and that this too is general.
Friendly,
Steve
Triangle web page:
http://paideiaschool.org/TeacherPages/Steve_Sigur/geometryIndex.htm
Other math:
http://paideiaschool.org/TeacherPages/Steve_Sigur/interesting2.htm
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# Alfred V. Aho - Data Structures and Algorithms
## Description: Alfred V. Aho - Data Structures and Algorithms
Data Structures and Algorithms: Table of Contents Data Structures and Algorithms Alfred V. Aho, Bell Laboratories, Murray Hill, New Jersey John E. Hopcroft, Cornell University, Ithaca, New York Jeffrey D. Ullman, Stanford University, Stanford, California PREFACE Chapter 1 Design and Analysis of Algorithms Chapter 2 Basic Data Types Chapter 3 Trees Chapter 4 Basic Operations on Sets Chapter 5 Advanced Set Representation Methods Chapter 6 Directed Graphs Chapter 7 Undirected Graphs Chapter 8 Sorting Chapter 9 Algorithm Analysis Techniques Chapter 10 Algorithm Design Techniques Chapter 11 Data Structures and Algorithms for External Storage Chapter 12 Memory Management Bibliography http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/toc.htm [1.7.2001 18:57:37]
Preface Preface This book presents the data structures and algorithms that underpin much of today's computer programming. The basis of this book is the material contained in the first six chapters of our earlier work, The Design and Analysis of Computer Algorithms. We have expanded that coverage and have added material on algorithms for external storage and memory management. As a consequence, this book should be suitable as a text for a first course on data structures and algorithms. The only prerequisite we assume is familiarity with some high-level programming language such as Pascal. We have attempted to cover data structures and algorithms in the broader context of solving problems using computers. We use abstract data types informally in the description and implementation of algorithms. Although abstract data types are only starting to appear in widely available programming languages, we feel they are a useful tool in designing programs, no matter what the language. We also introduce the ideas of step counting and time complexity as an integral part of the problem solving process. This decision reflects our longheld belief that programmers are going to continue to tackle problems of progressively larger size as machines get faster, and that consequently the time complexity of algorithms will become of even greater importance, rather than of less importance, as new generations of hardware become available. The Presentation of Algorithms We have used the conventions of Pascal to describe our algorithms and data structures primarily because Pascal is so widely known. Initially we present several of our algorithms both abstractly and as Pascal programs, because we feel it is important to run the gamut of the problem solving process from problem formulation to a running program. The algorithms we present, however, can be readily implemented in any high-level programming language. Use of the Book Chapter 1 contains introductory remarks, including an explanation of our view of the problem-to-program process and the role of abstract data types in that process. Also appearing is an introduction to step counting and \"big-oh\" and \"big-omega\" notation. Chapter 2 introduces the traditional list, stack and queue structures, and the mapping, which is an abstract data type based on the mathematical notion of a http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/preface.htm (1 of 3) [1.7.2001 18:57:42]
Preface function. The third chapter introduces trees and the basic data structures that can be used to support various operations on trees efficiently. Chapters 4 and 5 introduce a number of important abstract data types that are based on the mathematical model of a set. Dictionaries and priority queues are covered in depth. Standard implementations for these concepts, including hash tables, binary search trees, partially ordered trees, tries, and 2-3 trees are covered, with the more advanced material clustered in Chapter 5. Chapters 6 and 7 cover graphs, with directed graphs in Chapter 6 and undirected graphs in 7. These chapters begin a section of the book devoted more to issues of algorithms than data structures, although we do discuss the basics of data structures suitable for representing graphs. A number of important graph algorithms are presented, including depth-first search, finding minimal spanning trees, shortest paths, and maximal matchings. Chapter 8 is devoted to the principal internal sorting algorithms: quicksort, heapsort, binsort, and the simpler, less efficient methods such as insertion sort. In this chapter we also cover the linear-time algorithms for finding medians and other order statistics. Chapter 9 discusses the asymptotic analysis of recursive procedures, including, of course, recurrence relations and techniques for solving them. Chapter 10 outlines the important techniques for designing algorithms, including divide-and-conquer, dynamic programming, local search algorithms, and various forms of organized tree searching. The last two chapters are devoted to external storage organization and memory management. Chapter 11 covers external sorting and large-scale storage organization, including B-trees and index structures. Chapter 12 contains material on memory management, divided into four subareas, depending on whether allocations involve fixed or varying sized blocks, and whether the freeing of blocks takes place by explicit program action or implicitly when garbage collection occurs. Material from this book has been used by the authors in data structures and algorithms courses at Columbia, Cornell, and Stanford, at both undergraduate and graduate levels. For example, a preliminary version of this book was used at Stanford in a 10-week course on data structures, taught to a population consisting primarily of Juniors through first-year graduate students. The coverage was limited to Chapters 1- http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/preface.htm (2 of 3) [1.7.2001 18:57:42]
Preface 4, 9, 10, and 12, with parts of 5-7. Exercises A number of exercises of varying degrees of difficulty are found at the end of each chapter. Many of these are fairly straightforward tests of the mastery of the material of the chapter. Some exercises require more thought, and these have been singly starred. Doubly starred exercises are harder still, and are suitable for more advanced courses. The bibliographic notes at the end of each chapter provide references for additional reading. Acknowledgments We wish to acknowledge Bell Laboratories for the use of its excellent UNIX™- based text preparation and data communication facilities that significantly eased the preparation of a manuscript by geographically separated authors. Many of our colleagues have read various portions of the manuscript and have given us valuable comments and advice. In particular, we would like to thank Ed Beckham, Jon Bentley, Kenneth Chu, Janet Coursey, Hank Cox, Neil Immerman, Brian Kernighan, Steve Mahaney, Craig McMurray, Alberto Mendelzon, Alistair Moffat, Jeff Naughton, Kerry Nemovicher, Paul Niamkey, Yoshio Ohno, Rob Pike, Chris Rouen, Maurice Schlumberger, Stanley Selkow, Chengya Shih, Bob Tarjan, W. Van Snyder, Peter Weinberger, and Anthony Yeracaris for helpful suggestions. Finally, we would like to give our warmest thanks to Mrs. Claire Metzger for her expert assistance in helping prepare the manuscript for typesetting. A.V.A. J.E.H. J.D.U. Table of Contents Go to Chapter 1 http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/preface.htm (3 of 3) [1.7.2001 18:57:42]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms Design and Analysis of Algorithms There are many steps involved in writing a computer program to solve a given problem. The steps go from problem formulation and specification, to design of the solution, to implementation, testing and documentation, and finally to evaluation of the solution. This chapter outlines our approach to these steps. Subsequent chapters discuss the algorithms and data structures that are the building blocks of most computer programs. 1.1 From Problems to Programs Half the battle is knowing what problem to solve. When initially approached, most problems have no simple, precise specification. In fact, certain problems, such as creating a \"gourmet\" recipe or preserving world peace, may be impossible to formulate in terms that admit of a computer solution. Even if we suspect our problem can be solved on a computer, there is usually considerable latitude in several problem parameters. Often it is only by experimentation that reasonable values for these parameters can be found. If certain aspects of a problem can be expressed in terms of a formal model, it is usually beneficial to do so, for once a problem is formalized, we can look for solutions in terms of a precise model and determine whether a program already exists to solve that problem. Even if there is no existing program, at least we can discover what is known about this model and use the properties of the model to help construct a good solution. Almost any branch of mathematics or science can be called into service to help model some problem domain. Problems essentially numerical in nature can be modeled by such common mathematical concepts as simultaneous linear equations (e.g., finding currents in electrical circuits, or finding stresses in frames made of connected beams) or differential equations (e.g., predicting population growth or the rate at which chemicals will react). Symbol and text processing problems can be modeled by character strings and formal grammars. Problems of this nature include compilation (the translation of programs written in a programming language into machine language) and information retrieval tasks such as recognizing particular words in lists of titles owned by a library. Algorithms Once we have a suitable mathematical model for our problem, we can attempt to find a solution in terms of that model. Our initial goal is to find a solution in the form of an algorithm, which is a finite sequence of instructions, each of which has a clear meaning and can be performed with a finite amount of effort in a finite length of time. An integer assignment statement such as x := y + z is an example of an instruction that can be executed http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (1 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms in a finite amount of effort. In an algorithm instructions can be executed any number of times, provided the instructions themselves indicate the repetition. However, we require that, no matter what the input values may be, an algorithm terminate after executing a finite number of instructions. Thus, a program is an algorithm as long as it never enters an infinite loop on any input. There is one aspect of this definition of an algorithm that needs some clarification. We said each instruction of an algorithm must have a \"clear meaning\" and must be executable with a \"finite amount of effort.\" Now what is clear to one person may not be clear to another, and it is often difficult to prove rigorously that an instruction can be carried out in a finite amount of time. It is often difficult as well to prove that on any input, a sequence of instructions terminates, even if we understand clearly what each instruction means. By argument and counterargument, however, agreement can usually be reached as to whether a sequence of instructions constitutes an algorithm. The burden of proof lies with the person claiming to have an algorithm. In Section 1.5 we discuss how to estimate the running time of common programming language constructs that can be shown to require a finite amount of time for their execution. In addition to using Pascal programs as algorithms, we shall often present algorithms using a pseudo-language that is a combination of the constructs of a programming language together with informal English statements. We shall use Pascal as the programming language, but almost any common programming language could be used in place of Pascal for the algorithms we shall discuss. The following example illustrates many of the steps in our approach to writing a computer program. Example 1.1. A mathematical model can be used to help design a traffic light for a complicated intersection of roads. To construct the pattern of lights, we shall create a program that takes as input a set of permitted turns at an intersection (continuing straight on a road is a \"turn\") and partitions this set into as few groups as possible such that all turns in a group are simultaneously permissible without collisions. We shall then associate a phase of the traffic light with each group in the partition. By finding a partition with the smallest number of groups, we can construct a traffic light with the smallest number of phases. For example, the intersection shown in Fig. 1.1 occurs by a watering hole called JoJo's near Princeton University, and it has been known to cause some navigational difficulty, especially on the return trip. Roads C and E are oneway, the others two way. There are 13 turns one might make at this intersection. Some pairs of turns, like AB (from A to B) and EC, can be carried out simultaneously, while others, like AD and EB, cause lines of traffic to cross and therefore cannot be carried out simultaneously. The light at the intersection must permit turns in such an order that AD and EB are never permitted at the same time, while the light might permit AB and EC to be made simultaneously. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (2 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms Fig. 1.1. An intersection. We can model this problem with a mathematical structure known as a graph. A graph consists of a set of points called vertices, and lines connecting the points, called edges. For the traffic intersection problem we can draw a graph whose vertices represent turns and whose edges connect pairs of vertices whose turns cannot be performed simultaneously. For the intersection of Fig. 1.1, this graph is shown in Fig. 1.2, and in Fig. 1.3 we see another representation of this graph as a table with a 1 in row i and column j whenever there is an edge between vertices i and j. The graph can aid us in solving the traffic light design problem. A coloring of a graph is an assignment of a color to each vertex of the graph so that no two vertices connected by an edge have the same color. It is not hard to see that our problem is one of coloring the graph of incompatible turns using as few colors as possible. The problem of coloring graphs has been studied for many decades, and the theory of algorithms tells us a lot about this problem. Unfortunately, coloring an arbitrary graph with as few colors as possible is one of a large class of problems called \"NP-complete problems,\" for which all known solutions are essentially of the type \"try all possibilities.\" In the case of the coloring problem, \"try all possibilities\" means to try all assignments of colors to vertices using at first one color, then two colors, then three, and so on, until a legal coloring is found. With care, we can be a little speedier than this, but it is generally believed that no algorithm to solve this problem can be substantially more efficient than this most obvious approach. We are now confronted with the possibility that finding an optimal solution for the problem at hand is computationally very expensive. We can adopt Fig. 1.2. Graph showing incompatible turns. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (3 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms Fig. 1.3. Table of incompatible turns. one of three approaches. If the graph is small, we might attempt to find an optimal solution exhaustively, trying all possibilities. This approach, however, becomes prohibitively expensive for large graphs, no matter how efficient we try to make the program. A second approach would be to look for additional information about the problem at hand. It may turn out that the graph has some special properties, which make it unnecessary to try all possibilities in finding an optimal solution. The third approach is to change the problem a little and look for a good but not necessarily optimal solution. We might be happy with a solution that gets close to the minimum number of colors on small graphs, and works quickly, since most intersections are not even as complex as Fig. 1.1. An algorithm that quickly produces good but not necessarily optimal solutions is called a heuristic. One reasonable heuristic for graph coloring is the following \"greedy\" algorithm. Initially we try to color as many vertices as possible with the first color, then as many as possible of the uncolored vertices with the second color, and so on. To color vertices with a new color, we perform the following steps. 1. Select some uncolored vertex and color it with the new color. 2. Scan the list of uncolored vertices. For each uncolored vertex, determine whether it has an edge to any vertex already colored with the new color. If there is no such edge, color the present vertex with the new color. This approach is called \"greedy\" because it colors a vertex whenever it can, without considering the potential drawbacks inherent in making such a move. There are situations where we could color more vertices with one color if we were less \"greedy\" and skipped some vertex we could legally color. For example, consider the graph of Fig. 1.4, where having colored vertex 1 red, we can color vertices 3 and 4 red also, provided we do not color 2 first. The greedy algorithm would tell us to color 1 and 2 red, assuming we considered vertices in numerical order. Fig. 1.4. A graph. As an example of the greedy approach applied to Fig. 1.2, suppose we start by coloring AB blue. We can color AC, AD, and BA blue, because none of these four vertices has an edge in common. We cannot color BC blue because there is an edge between AB and BC. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (4 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms Similarly, we cannot color BD, DA, or DB blue because each of these vertices is connected by an edge to one or more vertices already colored blue. However, we can color DC blue. Then EA, EB, and EC cannot be colored blue, but ED can. Now we start a second color, say by coloring BC red. BD can be colored red, but DA cannot, because of the edge between BD and DA. Similarly, DB cannot be colored red, and DC is already blue, but EA can be colored red. Each other uncolored vertex has an edge to a red vertex, so no other vertex can be colored red. The remaining uncolored vertices are DA, DB, EB, and EC. If we color DA green, then DB can be colored green, but EB and EC cannot. These two may be colored with a fourth color, say yellow. The colors are summarized in Fig. 1.5. The \"extra\" turns are determined by the greedy approach to be compatible with the turns already given that color, as well as with each other. When the traffic light allows turns of one color, it can also allow the extra turns safely. Fig. 1.5. A coloring of the graph of Fig. 1.2. The greedy approach does not always use the minimum possible number of colors. We can use the theory of algorithms again to evaluate the goodness of the solution produced. In graph theory, a k-clique is a set of k vertices, every pair of which is connected by an edge. Obviously, k colors are needed to color a k-clique, since no two vertices in a clique may be given the same color. In the graph of Fig. 1.2 the set of four vertices AC, DA, BD, EB is a 4-clique. Therefore, no coloring with three or fewer colors exists, and the solution of Fig. 1.5 is optimal in the sense that it uses the fewest colors possible. In terms of our original problem, no traffic light for the intersection of Fig. 1.1 can have fewer than four phases. Therefore, consider a traffic light controller based on Fig. 1.5, where each phase of the controller corresponds to a color. At each phase the turns indicated by the row of the table corresponding to that color are permitted, and the other turns are forbidden. This pattern uses as few phases as possible. Pseudo-Language and Stepwise Refinement Once we have an appropriate mathematical model for a problem, we can formulate an algorithm in terms of that model. The initial versions of the algorithm are often couched in general statements that will have to be refined subsequently into smaller, more definite instructions. For example, we described the greedy graph coloring algorithm in terms such as \"select some uncolored vertex.\" These instructions are, we hope, sufficiently clear that http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (5 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms the reader grasps our intent. To convert such an informal algorithm to a program, however, we must go through several stages of formalization (called stepwise refinement) until we arrive at a program the meaning of whose steps are formally defined by a language manual. Example 1.2. Let us take the greedy algorithm for graph coloring part of the way towards a Pascal program. In what follows, we assume there is a graph G, some of whose vertices may be colored. The following program greedy determines a set of vertices called newclr, all of which can be colored with a new color. The program is called repeatedly, until all vertices are colored. At a coarse level, we might specify greedy in pseudo-language as in Fig. 1.6. procedure greedy ( var G: GRAPH; var newclr: SET ); { greedy assigns to newclr a set of vertices of G that may be given the same color } begin (1) newclr := Ø; † (2) for each uncolored vertex v of G do (3) if v is not adjacent to any vertex in newclr then begin (4) mark v colored; (5) add v to newclr end end; { greedy } Fig. 1.6. First refinement of greedy algorithm. We notice from Fig. 1.6 certain salient features of our pseudo-language. First, we use boldface lower case keywords corresponding to Pascal reserved words, with the same meaning as in standard Pascal. Upper case types such as GRAPH and SET‡ are the names of \"abstract data types.\" They will be defined by Pascal type definitions and the operations associated with these abstract data types will be defined by Pascal procedures when we create the final program. We shall discuss abstract data types in more detail in the next two sections. The flow-of-control constructs of Pascal, like if, for, and while, are available for pseudo- language statements, but conditionals, as in line (3), may be informal statements rather than Pascal conditional expressions. Note that the assignment at line (1) uses an informal expression on the right. Also, the for-loop at line (2) iterates over a set. To be executed, the pseudo-language program of Fig. 1.6 must be refined into a conventional Pascal program. We shall not proceed all the way to such a program in this example, but let us give one example of refinement, transforming the if-statement in line (3) of Fig. 1.6 into more conventional code. To test whether vertex v is adjacent to some vertex in newclr, we consider each member http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (6 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms w of newclr and examine the graph G to see whether there is an edge between v and w. An organized way to make this test is to use found, a boolean variable to indicate whether an edge has been found. We can replace lines (3)-(5) of Fig. 1.6 by the code in Fig. 1.7. procedure greedy ( var G: GRAPH; var newclr: SET ); begin (1) newclr : = Ø; (2) for each uncolored vertex v of G do begin (3.1) found := false; (3.2) for each vertex w in newclr do (3.3) if there is an edge between v and w in G then (3.4) found := true; (3.5) if found = false then begin { v is adjacent to no vertex in newclr } (4) mark v colored; (5) add v to newclr end end end; { greedy } Fig. 1.7. Refinement of part of Fig. 1.6. We have now reduced our algorithm to a collection of operations on two sets of vertices. The outer loop, lines (2)-(5), iterates over the set of uncolored vertices of G. The inner loop, lines (3.2)-(3.4), iterates over the vertices currently in the set newclr. Line (5) adds newly colored vertices to newclr. There are a variety of ways to represent sets in a programming language like Pascal. In Chapters 4 and 5 we shall study several such representations. In this example we can simply represent each set of vertices by another abstract data type LIST, which here can be implemented by a list of integers terminated by a special value null (for which we might use the value 0). These integers might, for example, be stored in an array, but there are many other ways to represent LIST's, as we shall see in Chapter 2. We can now replace the for-statement of line (3.2) in Fig. 1.7 by a loop, where w is initialized to be the first member of newclr and changed to be the next member, each time around the loop. We can also perform the same refinement for the for-loop of line (2) in Fig. 1.6. The revised procedure greedy is shown in Fig. 1.8. There is still more refinement to be done after Fig. 1.8, but we shall stop here to take stock of what we have done. procedure greedy ( var G: GRAPH; var newclr: LIST ); { greedy assigns to newclr those vertices that may be given the same color } http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (7 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms var found: boolean; v, w: integer; begin newclr := Ø; v := first uncolored vertex in G; while v < > null do begin found := false; w := first vertex in newclr; while w < > null do begin if there is an edge between v and w in G then found := true; w := next vertex in newclr end; if found = false do begin mark v colored; add v to newclr end; v := next uncolored vertex in G end end; { greedy } Fig. 1.8. Refined greedy procedure. Summary In Fig. 1.9 we see the programming process as it will be treated in this book. The first stage is modeling using an appropriate mathematical model such as a graph. At this stage, the solution to the problem is an algorithm expressed very informally. At the next stage, the algorithm is written in pseudo-language, that is, a mixture of Pascal constructs and less formal English statements. To reach that stage, the informal English is replaced by progressively more detailed sequences of statements, in the process known as stepwise refinement. At some point the pseudo-language program is sufficiently detailed that the Fig. 1.9. The problem solving process. operations to be performed on the various types of data become fixed. We then create abstract data types for each type of data (except for the elementary types such as integers, reals and character strings) by giving a procedure name for each operation and replacing http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (8 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms , and so on). The ADT encapsulates a data type in the sense that the definition of the type and all operations on that type can be localized to one section of the program. If we wish to change the implementation of an ADT, we know where to look, and by revising one small section we can be sure that there is no subtlety elsewhere in the program that will cause errors concerning this data type. Moreover, outside the section in which the ADT's operations are defined, we can treat the ADT as a primitive type; we have no concern with the underlying implementation. One pitfall is that certain operations may involve more than one ADT, and references to these operations must appear in the sections for both ADT's. To illustrate the basic ideas, consider the procedure greedy of the previous section which, in Fig. 1.8, was implemented using primitive operations on an abstract data type LIST (of integers). The operations performed on the LIST newclr were: 1. make a list empty, 2. get the first member of the list and return null if the list is empty, 3. get the next member of the list and return null if there is no next member, and 4. insert an integer into the list. There are many data structures that can be used to implement such lists efficiently, and we shall consider the subject in depth in Chapter 2. In Fig. 1.8, if we replace these operations by the statements 1. MAKENULL(newclr); 2. w := FIRST(newclr); 3. w := NEXT(newclr); 4. INSERT(v, newclr); then we see an important aspect of abstract data types. We can implement a type any way we like, and the programs, such as Fig. 1.8, that use objects of that type do not change; only the procedures implementing the operations on the type need to change. Turning to the abstract data type GRAPH we see need for the following operations: 1. get the first uncolored vertex, 2. test whether there is an edge between two vertices, 3. mark a vertex colored, and 4. get the next uncolored vertex. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (10 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms There are clearly other operations needed outside the procedure greedy, such as inserting vertices and edges into the graph and making all vertices uncolored. There are many data structures that can be used to support graphs with these operations, and we shall study the subject of graphs in Chapters 6 and 7. It should be emphasized that there is no limit to the number of operations that can be applied to instances of a given mathematical model. Each set of operations defines a distinct ADT. Some examples of operations that might be defined on an abstract data type SET are: 1. MAKENULL(A). This procedure makes the null set be the value for set A. 2. UNION(A, B, C). This procedure takes two set-valued arguments A and B, and assigns the union of A and B to be the value of set C. 3. SIZE(A). This function takes a set-valued argument A and returns an object of type integer whose value is the number of elements in the set A. An implementation of an ADT is a translation, into statements of a programming language, of the declaration that defines a variable to be of that abstract data type, plus a procedure in that language for each operation of the ADT. An implementation chooses a data structure to represent the ADT; each data structure is built up from the basic data types of the underlying programming language using the available data structuring facilities. Arrays and record structures are two important data structuring facilities that are available in Pascal. For example, one possible implementation for variable S of type SET would be an array that contained the members of S. One important reason for defining two ADT's to be different if they have the same underlying model but different operations is that the appropriateness of an implementation depends very much on the operations to be performed. Much of this book is devoted to examining some basic mathematical models such as sets and graphs, and developing the preferred implementations for various collections of operations. Ideally, we would like to write our programs in languages whose primitive data types and operations are much closer to the models and operations of our ADT's. In many ways Pascal is not well suited to the implementation of various common ADT's but none of the programming languages in which ADT's can be declared more directly is as well known. See the bibliographic notes for information about some of these languages. 1.3 Data Types, Data Structures and Abstract Data Types Although the terms \"data type\" (or just \"type\"), \"data structure\" and \"abstract data type\" http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (11 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms sound alike, they have different meanings. In a programming language, the data type of a variable is the set of values that the variable may assume. For example, a variable of type boolean can assume either the value true or the value false, but no other value. The basic data types vary from language to language; in Pascal they are integer, real, boolean, and character. The rules for constructing composite data types out of basic ones also vary from language to language; we shall mention how Pascal builds such types momentarily. An abstract data type is a mathematical model, together with various operations defined on the model. As we have indicated, we shall design algorithms in terms of ADT's, but to implement an algorithm in a given programming language we must find some way of representing the ADT's in terms of the data types and operators supported by the programming language itself. To represent the mathematical model underlying an ADT we use data structures, which are collections of variables, possibly of several different data types, connected in various ways. The cell is the basic building block of data structures. We can picture a cell as a box that is capable of holding a value drawn from some basic or composite data type. Data structures are created by giving names to aggregates of cells and (optionally) interpreting the values of some cells as representing connections (e.g., pointers) among cells. The simplest aggregating mechanism in Pascal and most other programming languages is the (one-dimensional) array, which is a sequence of cells of a given type, which we shall often refer to as the celltype. We can think of an array as a mapping from an index set (such as the integers 1, 2, . . . , n) into the celltype. A cell within an array can be referenced by giving the array name together with a value from the index set of the array. In Pascal the index set may be an enumerated type, such as (north, east, south, west), or a subrange type, such as 1..10. The values in the cells of an array can be of any one type. Thus, the declaration name: array[indextype] of celltype; declares name to be a sequence of cells, one for each value of type indextype; the contents of the cells can be any member of type celltype. Incidentally, Pascal is somewhat unusual in its richness of index types. Many languages allow only subrange types (finite sets of consecutive integers) as index types. For example, to index an array by letters in Fortran, one must simulate the effect by using integer indices, such as by using index 1 to stand for 'A', 2 to stand for 'B', and so on. Another common mechanism for grouping cells in programming languages is the record structure. A record is a cell that is made up of a collection of cells, called fields, of possibly dissimilar types. Records are often grouped into arrays; the type defined by the aggregation of the fields of a record becomes the \"celltype\" of the array. For example, the Pascal declaration http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (12 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms var reclist: array[l..4] of record data: real; next: integer end declares reclist to be a four-element array, whose cells are records with two fields, data and next. A third grouping method found in Pascal and some other languages is the file. The file, like the one-dimensional array, is a sequence of values of some particular type. However, a file has no index type; elements can be accessed only in the order of their appearance in the file. In contrast, both the array and the record are \"random-access\" structures, meaning that the time needed to access a component of an array or record is independent of the value of the array index or field selector. The compensating benefit of grouping by file, rather than by array, is that the number of elements in a file can be time-varying and unlimited. Pointers and Cursors In addition to the cell-grouping features of a programming language, we can represent relationships between cells using pointers and cursors. A pointer is a cell whose value indicates another cell. When we draw pictures of data structures, we indicate the fact that cell A is a pointer to cell B by drawing an arrow from A to B. In Pascal, we can create a pointer variable ptr that will point to cells of a given type, say celltype, by the declaration var ptr: ↑ celltype A postfix up-arrow is used in Pascal as the dereferencing operator, so the expression ptr↑ denotes the value (of type celltype) in the cell pointed to by ptr. A cursor is an integer-valued cell, used as a pointer to an array. As a method of connection, the cursor is essentially the same as a pointer, but a cursor can be used in languages like Fortran that do not have explicit pointer types as Pascal does. By treating a cell of type integer as an index value for some array, we effectively make that cell point to one cell of the array. This technique, unfortunately, works only when cells of arrays are pointed to; there is no reasonable way to interpret an integer as a \"pointer\" to a cell that is not part of an array. We shall draw an arrow from a cursor cell to the cell it \"points to.\" Sometimes, we shall also show the integer in the cursor cell, to remind us that it is not a true pointer. The reader should observe that the Pascal pointer mechanism is such that cells in arrays can only be http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (13 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms \"pointed to\" by cursors, never by true pointers. Other languages, like PL/I or C, allow components of arrays to be pointed to by either cursors or true pointers, while in Fortran or Algol, there being no pointer type, only cursors can be used. Example 1.3. In Fig. 1.10 we see a two-part data structure that consists of a chain of cells containing cursors to the array reclist defined above. The purpose of the field next in reclist is to point to another record in the array. For example, reclist[4].next is 1, so record 4 is followed by record 1. Assuming record 4 is first, the next field of reclist orders the records 4, 1, 3, 2. Note that the next field is 0 in record 2, indicating that there is no following record. It is a useful convention, one we shall adopt in this book, to use 0 as a \"NIL pointer,\" when cursors are being used. This idea is sound only if we also make the convention that arrays to which cursors \"point\" must be indexed starting at 1, never at 0. Fig. 1.10. Example of a data structure. The cells in the chain of records in Fig. 1.10 are of the type type recordtype = record cursor: integer; ptr: ↑ recordtype end The chain is pointed to by a variable named header, which is of type ↑ record-type; header points to an anonymous record of type recordtype.† That record has a value 4 in its cursor field; we regard this 4 as an index into the array reclist. The record has a true pointer in field ptr to another anonymous record. The record pointed to has an index in its cursor field indicating position 2 of reclist; it also has a nil pointer in its ptr field. 1.4 The Running Time of a Program When solving a problem we are faced frequently with a choice among algorithms. On what basis should we choose? There are two often contradictory goals. 1. We would like an algorithm that is easy to understand, code, and debug. 2. We would like an algorithm that makes efficient use of the computer's resources, especially, one that runs as fast as possible. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (14 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms When we are writing a program to be used once or a few times, goal (1) is most important. The cost of the programmer's time will most likely exceed by far the cost of running the program, so the cost to optimize is the cost of writing the program. When presented with a problem whose solution is to be used many times, the cost of running the program may far exceed the cost of writing it, especially, if many of the program runs are given large amounts of input. Then it is financially sound to implement a fairly complicated algorithm, provided that the resulting program will run significantly faster than a more obvious program. Even in these situations it may be wise first to implement a simple algorithm, to determine the actual benefit to be had by writing a more complicated program. In building a complex system it is often desirable to implement a simple prototype on which measurements and simulations can be performed, before committing oneself to the final design. It follows that programmers must not only be aware of ways of making programs run fast, but must know when to apply these techniques and when not to bother. Measuring the Running Time of a Program The running time of a program depends on factors such as: 1. the input to the program, 2. the quality of code generated by the compiler used to create the object program, 3. the nature and speed of the instructions on the machine used to execute the program, and 4. the time complexity of the algorithm underlying the program. The fact that running time depends on the input tells us that the running time of a program should be defined as a function of the input. Often, the running time depends not on the exact input but only on the \"size\" of the input. A good example is the process known as sorting, which we shall discuss in Chapter 8. In a sorting problem, we are given as input a list of items to be sorted, and we are to produce as output the same items, but smallest (or largest) first. For example, given 2, 1, 3, 1, 5, 8 as input we might wish to produce 1, 1, 2, 3, 5, 8 as output. The latter list is said to be sorted smallest first. The natural size measure for inputs to a sorting program is the number of items to be sorted, or in other words, the length of the input list. In general, the length of the input is an appropriate size measure, and we shall assume that measure of size unless we specifically state otherwise. It is customary, then, to talk of T(n), the running time of a program on inputs of size n. For example, some program may have a running time T(n) = cn2, where c is a constant. The units of T(n) will be left unspecified, but we can think of T(n) as being the number of instructions executed on an idealized computer. For many programs, the running time is really a function of the particular input, and not http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (15 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms just of the input size. In that case we define T(n) to be the worst case running time, that is, the maximum, over all inputs of size n, of the running time on that input. We also consider Tavg(n), the average, over all inputs of size n, of the running time on that input. While Tavg(n) appears a fairer measure, it is often fallacious to assume that all inputs are equally likely. In practice, the average running time is often much harder to determine than the worst-case running time, both because the analysis becomes mathematically intractable and because the notion of \"average\" input frequently has no obvious meaning. Thus, we shall use worst-case running time as the principal measure of time complexity, although we shall mention average-case complexity wherever we can do so meaningfully. Now let us consider remarks (2) and (3) above: that the running time of a program depends on the compiler used to compile the program and the machine used to execute it. These facts imply that we cannot express the running time T(n) in standard time units such as seconds. Rather, we can only make remarks like \"the running time of such-and-such an algorithm is proportional to n2.\" The constant of proportionality will remain unspecified since it depends so heavily on the compiler, the machine, and other factors. Big-Oh and Big-Omega Notation To talk about growth rates of functions we use what is known as \"big-oh\" notation. For example, when we say the running time T(n) of some program is O(n2), read \"big oh of n squared\" or just \"oh of n squared,\" we mean that there are positive constants c and n0 such that for n equal to or greater than n0, we have T(n) ≤ cn2. Example 1.4. Suppose T(0) = 1, T(1) = 4, and in general T(n) = (n+l)2. Then we see that T(n) is O(n2), as we may let n0 = 1 and c = 4. That is, for n ≥ 1, we have (n + 1)2 ≤ 4n2, as the reader may prove easily. Note that we cannot let n0 = 0, because T(0) = 1 is not less than c02 = 0 for any constant c. In what follows, we assume all running-time functions are defined on the nonnegative integers, and their values are always nonnegative, although not necessarily integers. We say that T(n) is O(f(n)) if there are constants c and n0 such that T(n) ≤ cf(n) whenever n ≥ n0. A program whose running time is O(f (n)) is said to have growth rate f(n). Example 1.5. The function T(n)= 3n3 + 2n2 is O(n3). To see this, let n0 = 0 and c = 5. Then, the reader may show that for n ≥ 0, 3n3 + 2n2 ≤ 5n3. We could also say that this T(n) is O(n4), but this would be a weaker statement than saying it is O(n3). As another example, let us prove that the function 3n is not O (2n). Suppose that there were constants n0 and c such that for all n ≥ n0, we had 3n ≤ c2n. Then c ≥ (3/2)n for any n ≥ n0. But (3/2)n gets arbitrarily large as n gets large, so no constant c can exceed (3/2)n for http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (16 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms all n. When we say T(n) is O(f(n)), we know that f(n) is an upper bound on the growth rate of T(n). To specify a lower bound on the growth rate of T(n) we can use the notation T(n) is Ω(g(n)), read \"big omega of g(n)\" or just \"omega of g(n),\" to mean that there exists a positive constant c such that T(n) ≥ cg(n) infinitely often (for an infinite number of values of n).† Example 1.6. To verify that the function T(n)= n3 + 2n2 is Ω(n3), let c = 1. Then T(n) ≥ cn3 for n = 0, 1, . . .. For another example, let T(n) = n for odd n ≥ 1 and T(n) = n2/100 for even n ≥ 0. To verify that T(n) is Ω (n2), let c = 1/100 and consider the infinite set of n's: n = 0, 2, 4, 6, . . .. The Tyranny of Growth Rate We shall assume that programs can be evaluated by comparing their running-time functions, with constants of proportionality neglected. Under this assumption a program with running time O(n2) is better than one with running time O(n3), for example. Besides constant factors due to the compiler and machine, however, there is a constant factor due to the nature of the program itself. It is possible, for example, that with a particular compiler- machine combination, the first program takes 100n2 milliseconds, while the second takes 5n3 milliseconds. Might not the 5n3 program be better than the 100n2 program? The answer to this question depends on the sizes of inputs the programs are expected to process. For inputs of size n < 20, the program with running time 5n3 will be faster than the one with running time 100n2. Therefore, if the program is to be run mainly on inputs of small size, we would indeed prefer the program whose running time was O(n3). However, as n gets large, the ratio of the running times, which is 5n3/100n2 = n/20, gets arbitrarily large. Thus, as the size of the input increases, the O(n3) program will take significantly more time than the O(n2) program. If there are even a few large inputs in the mix of problems these two programs are designed to solve, we can be much better off with the program whose running time has the lower growth rate. Another reason for at least considering programs whose growth rates are as low as possible is that the growth rate ultimately determines how big a problem we can solve on a computer. Put another way, as computers get faster, our desire to solve larger problems on them continues to increase. However, unless a program has a low growth rate such as O(n) or O(nlogn), a modest increase in computer speed makes very little difference in the size of the largest problem we can solve in a fixed amount of time. Example 1.7. In Fig. 1.11 we see the running times of four programs with different time complexities, measured in seconds, for a particular compiler-machine combination. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (17 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms Suppose we can afford 1000 seconds, or about 17 minutes, to solve a given problem. How large a problem can we solve? In 103 seconds, each of the four algorithms can solve roughly the same size problem, as shown in the second column of Fig. 1.12. Fig. 1.11. Running times of four programs. Suppose that we now buy a machine that runs ten times faster at no additional cost. Then for the same cost we can spend 104 seconds on a problem where we spent 103 seconds before. The maximum size problem we can now solve using each of the four programs is shown in the third column of Fig. 1.12, and the ratio of the third and second columns is shown in the fourth column. We observe that a 1000% improvement in computer speed yields only a 30% increase in the size of problem we can solve if we use the O(2n) program. Additional factors of ten speedup in the computer yield an even smaller percentage increase in problem size. In effect, the O(2n) program can solve only small problems no matter how fast the underlying computer. Fig. 1.12. Effect of a ten-fold speedup in computation time. In the third column of Fig. 1.12 we see the clear superiority of the O(n) program; it returns a 1000% increase in problem size for a 1000% increase in computer speed. We see that the O(n3) and O(n2) programs return, respectively, 230% and 320% increases in problem size for 1000% increases in speed. These ratios will be maintained for additional increases in speed. As long as the need for solving progressively larger problems exists, we are led to an almost paradoxical conclusion. As computation becomes cheaper and machines become faster, as will most surely continue to happen, our desire to solve larger and more complex problems will continue to increase. Thus, the discovery and use of efficient algorithms, those whose growth rates are low, becomes more rather than less important. A Few Grains of Salt We wish to re-emphasize that the growth rate of the worst case running time is not the sole, or necessarily even the most important, criterion for evaluating an algorithm or program. Let us review some conditions under which the running time of a program can be overlooked in favor of other issues. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (18 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms 1. If a program is to be used only a few times, then the cost of writing and debugging dominate the overall cost, so the actual running time rarely affects the total cost. In this case, choose the algorithm that is easiest to implement correctly. 2. If a program is to be run only on \"small\" inputs, the growth rate of the running time may be less important than the constant factor in the formula for running time. What is a \"small\" input depends on the exact running times of the competing algorithms. There are some algorithms, such as the integer multiplication algorithm due to Schonhage and Strassen [1971], that are asymptotically the most efficient known for their problem, but have never been used in practice even on the largest problems, because the constant of proportionality is so large in comparison to other simpler, less \"efficient\" algorithms. 3. A complicated but efficient algorithm may not be desirable because a person other than the writer may have to maintain the program later. It is hoped that by making the principal techniques of efficient algorithm design widely known, more complex algorithms may be used freely, but we must consider the possibility of an entire program becoming useless because no one can understand its subtle but efficient algorithms. 4. There are a few examples where efficient algorithms use too much space to be implemented without using slow secondary storage, which may more than negate the efficiency. 5. In numerical algorithms, accuracy and stability are just as important as efficiency. 1.5 Calculating the Running Time of a Program Determining, even to within a constant factor, the running time of an arbitrary program can be a complex mathematical problem. In practice, however, determining the running time of a program to within a constant factor is usually not that difficult; a few basic principles suffice. Before presenting these principles, it is important that we learn how to add and multiply in \"big oh\" notation. Suppose that T1(n) and T2(n) are the running times of two program fragments P1 and P2, and that T1(n) is O(f(n)) and T2(n) is O(g(n)). Then T1(n)+T2(n), the running time of P1 followed by P2, is O(max(f(n),g(n))). To see why, observe that for some constants c1, c2, n1, and n2, if n ≥ n1 then T1(n) ≤ c1f(n), and if n ≥ n2 then T2(n) ≤ c2g(n). Let n0 = max(n1, n2). If n ≥ n0, then T1(n) + T2(n) ≤ c1f(n) + c2g(n). From this we conclude that if n ≥ n0, then T1(n) + T2(n) ≤ (c1 + c2)max(f(n), g(n)). Therefore, the combined running time T1(n) + T2(n) is O (max(f (n), g (n))). http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (19 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms Example 1.8. The rule for sums given above can be used to calculate the running time of a sequence of program steps, where each step may be an arbitrary program fragment with loops and branches. Suppose that we have three steps whose running times are, respectively, O(n2), O(n3) and O(n log n). Then the running time of the first two steps executed sequentially is O(max(n2, n3)) which is O(n3). The running time of all three together is O(max(n3, n log n)) which is O(n3). In general, the running time of a fixed sequence of steps is, to within a constant factor, the running time of the step with the largest running time. In rare circumstances there will be two or more steps whose running times are incommensurate (neither is larger than the other, nor are they equal). For example, we could have steps of running times O(f (n)) and O(g (n)), where In such cases the sum rule must be applied directly; the running time is O(max(f(n), g(n))), that is, n4 if n is even and n3 if n is odd. Another useful observation about the sum rule is that if g(n) ≤ f(n) for all n above some constant n0, then O(f(n) + g(n)) is the same as O(f(n)). For example, O(n2+n) is the same as O(n2). The rule for products is the following. If T1(n) and T2(n) are O(f(n)) and O(g(n)), respectively, then T1(n)T2(n) is O(f(n)g(n)). The reader should prove this fact using the same ideas as in the proof of the sum rule. It follows from the product rule that O(cf(n)) means the same thing as O(f(n)) if c is any positive constant. For example, O(n2/2) is the same as O(n2). Before proceeding to the general rules for analyzing the running times of programs, let us take a simple example to get an overview of the process. Example 1.9. Consider the sorting program bubble of Fig. 1.13, which sorts an array of integers into increasing order. The net effect of each pass of the inner loop of statements (3)- (6) is to \"bubble\" the smallest element toward the front of the array. procedure bubble ( var A: array [1..n] of integer ); { bubble sorts array A into increasing order } var http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (20 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms i, j, temp: integer; begin (1) for i := 1 to n-1 do (2) for j := n downto i+1 do (3) if A[j-1] > A[j] then begin { swap A[j - 1] and A[j] } (4) temp := A[j-1]; (5) A[j-1] := A[j]; (6) AI> [j] := temp end end; { bubble } Fig. 1.13. Bubble sort. The number n of elements to be sorted is the appropriate measure of input size. The first observation we make is that each assignment statement takes some constant amount of time, independent of the input size. That is to say, statements (4), (5) and (6) each take O(1) time. Note that O(1) is \"big oh\" notation for \"some constant amount.\" By the sum rule, the combined running time of this group of statements is O(max(1, 1, 1)) = O(1). Now we must take into account the conditional and looping statements. The if- and for- statements are nested within one another, so we may work from the inside out to get the running time of the conditional group and each loop. For the if-statement, testing the condition requires O(1) time. We don't know whether the body of the if-statement (lines (4)- (6)) will be executed. Since we are looking for the worst-case running time, we assume the worst and suppose that it will. Thus, the if-group of statements (3)-(6) takes O(1) time. Proceeding outward, we come to the for-loop of lines (2)-(6). The general rule for a loop is that the running time is the sum, over each iteration of the loop, of the time spent executing the loop body for that iteration. We must, however, charge at least O(1) for each iteration to account for incrementing the index, for testing to see whether the limit has been reached, and for jumping back to the beginning of the loop. For lines (2)-(6) the loop body takes O(1) time for each iteration. The number of iterations of the loop is n-i, so by the product rule, the time spent in the loop of lines (2)-(6) is O((n-i) X 1) which is O(n-i). Now let us progress to the outer loop, which contains all the executable statements of the program. Statement (1) is executed n - 1 times, so the total running time of the program is bounded above by some constant times which is O(n2). The program of Fig. 1.13, therefore, takes time proportional to the square of the number of items to be sorted. In Chapter 8, we shall give sorting programs whose http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (21 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms running time is O(nlogn), which is considerably smaller, since for large n, logn† is very much smaller than n. Before proceeding to some general analysis rules, let us remember that determining a precise upper bound on the running time of programs is sometimes simple, but at other times it can be a deep intellectual challenge. There are no complete sets of rules for analyzing programs. We can only give the reader some hints and illustrate some of the subtler points by examples throughout this book. Now let us enumerate some general rules for the analysis of programs. In general, the running time of a statement or group of statements may be parameterized by the input size and/or by one or more variables. The only permissible parameter for the running time of the whole program is n, the input size. 1. The running time of each assignment, read, and write statement can usually be taken to be O(1). There are a few exceptions, such as in PL/I, where assignments can involve arbitrarily large arrays, and in any language that allows function calls in assignment statements. 2. The running time of a sequence of statements is determined by the sum rule. That is, the running time of the sequence is, to within a constant factor, the largest running time of any statement in the sequence. 3. The running time of an if-statement is the cost of the conditionally executed statements, plus the time for evaluating the condition. The time to evaluate the condition is normally O(1). The time for an if-then-else construct is the time to evaluate the condition plus the larger of the time needed for the statements executed when the condition is true and the time for the statements executed when the condition is false. 4. The time to execute a loop is the sum, over all times around the loop, of the time to execute the body and the time to evaluate the condition for termination (usually the latter is O(1)). Often this time is, neglecting constant factors, the product of the number of times around the loop and the largest possible time for one execution of the body, but we must consider each loop separately to make sure. The number of iterations around a loop is usually clear, but there are times when the number of iterations cannot be computed precisely. It could even be that the program is not an algorithm, and there is no limit to the number of times we go around certain loops. Procedure Calls If we have a program with procedures, none of which is recursive, then we can compute the running time of the various procedures one at a time, starting with those procedures that make no calls on other procedures. (Remember to count a function invocation as a \"call.\") There must be at least one such procedure, else at least one procedure is recursive. We can http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (22 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms then evaluate the running time of procedures that call only procedures that make no calls, using the already-evaluated running times of the called procedures. We continue this process, evaluating the running time of each procedure after the running times of all procedures it calls have been evaluated. If there are recursive procedures, then we cannot find an ordering of all the procedures so that each calls only previously evaluated procedures. What we must now do is associate with each recursive procedure an unknown time function T(n), where n measures the size of the arguments to the procedure. We can then get a recurrence for T(n), that is, an equation for T(n) in terms of T(k) for various values of k. Techniques for solving many different kinds of recurrences exist; we shall present some of these in Chapter 9. Here we shall show how to analyze a simple recursive program. Example 1.10. Figure 1.14 gives a recursive program to compute n!, the product of all the integers from 1 to n inclusive. An appropriate size measure for this function is the value of n. Let T(n) be the running time for fact(n). The running time for lines (1) and (2) is O(1), and for line (3) it is O(1) + T(n-1). Thus, for some constants c and d, function fact ( n: integer ): integer; { fact(n) computes n! } begin (1) if n <= 1 then (2) fact := 1 else (3) fact := n * fact(n-1) end; { fact } Fig. 1.14. Receursive program to compute factorials. Assuming n > 2, we can expand T(n-1) in (1.1) to obtain T(n) = 2c + T(n-2) if n > 2 That is, T(n-1) = c + T(n-2), as can be seen by substituting n-1 for n in (1.1). Thus, we may substitute c + T(n-2) for T(n-1) in the equation T(n) = c + T(n-1). We can then use (1.1) to expand T(n-2) to obtain http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (23 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms T(n) = 3c + T(n-3) if n > 3 and so on. In general, T(n) = ic + T(n-i) if n > i Finally, when i = n-1 we get T(n) = c(n-1) + T(1) = c(n-1) + d (1.2) From (1.2) we can conclude that T(n) is O(n). We should note that in this analysis we have assumed that the multiplication of two integers is an O(1) operation. In practice, however, we cannot use the program in Fig. 1.14 to compute n! for large values of n, because the size of the integers being computed will exceed the word length of the underlying machine. The general method for solving recurrence equations, as typified by Example 1.10, is repeatedly to replace terms T(k) on the right side of the equation by the entire right side with k substituted for n, until we obtain a formula in which T does not appear on the right as in (1.2). Often we must then sum a series or, if we cannot sum it exactly, get a close upper bound on the sum to obtain an upper bound on T(n). Programs with GOTO's In analyzing the running time of a program we have tacitly assumed that all flow of control within a procedure was determined by branching and 1ooping constructs. We relied on this fact as we determined the running time of progressively larger groups of statements by assuming that we needed only the sum rule to group sequences of statements together. Goto statments, however, make the logical grouping of statements more complex. For this reason, goto statements should be avoided, but Pascal lacks break- and continue-statements to jump out of loops. The goto-statement is often used as a substitute for statements of this nature in Pascal. We suggest the following approach to handling goto's that jump from a loop to code that is guaranteed to follow the loop, which is generally the only kind of goto that is justified. As the goto is presumably executed conditionally within the loop, we may pretend that it is never taken. Because the goto takes us to a statement that will be executed after the loop completes, this assumption is conservative; we can never underestimate the worst case running time of the program if we assume the loop runs to completion. However, it is a rare program in which ignoring the goto is so conservative that it causes us to overestimate the growth rate of the worst case running time for the program. Notice that if we were faced with a goto that jumped back to previously executed code we could not ignore it safely, since that goto may create a loop that accounts for the bulk of the running time. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (24 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms We should not leave the impression that the use of backwards goto's by themselves make running times unanalyzable. As long as the loops of a program have a reasonable structure, that is, each pair of loops are either disjoint or nested one within the other, then the approach to running time analysis described in this section will work. (However, it becomes the responsibility of the analyzer to ascertain what the loop structure is.) Thus, we should not hesitate to apply these methods of program analysis to a language like Fortran, where goto's are essential, but where programs written in the language tend to have a reasonable loop structure. Analyzing a Pseudo-Program If we know the growth rate of the time needed to execute informal English statements, we can analyze pseudo-programs just as we do real ones. Often, however, we do not know the time to be spent on not-fully-implemented parts of a pseudo-program. For example, if we have a pseudo-program in which the only unimplemented parts are operations on ADT's, one of several implementations for an ADT may be chosen, and the overall running time may depend heavily on the implementation. Indeed, one of the reasons for writing programs in terms of ADT's is so we can consider the trade-offs among the running times of the various operations that we obtain by different implementations. To analyze pseudo-programs consisting of programming language statements and calls to unimplemented procedures, such as operations on ADT's, we compute the running time as a function of unspecified running times for each procedure. The running time for a procedure will be parameterized by the \"size\" of the argument or arguments for that procedure. Just as for \"input size,\" the appropriate measure of size for an argument is a matter for the analyzer to decide. If the procedure is an operation on an ADT, then the underlying mathematical model for the ADT often indicates the logical notion of size. For example, if the ADT is based on sets, the number of elements in a set is often the right notion of size. In the remaining chapters we shall see many examples of analyzing the running time of pseudo-programs. 1.6 Good Programming Practice There are a substantial number of ideas we should bear in mind when designing an algorithm and implementing it as a program. These ideas often appear platitudinous, because by-and-large they can be appreciated only through their successful use in real problems, rather than by development of a theory. They are sufficiently important, however, that they are worth repeating here. The reader should watch for the application of these ideas in the programs designed in this book, as well as looking for opportunities to put them into practice in his own programs. 1. Plan the design of a program. We mentioned in Section 1.1 how a program can be designed by first sketching the algorithm informally, then as a pseudo-program, and gradually refining the pseudo-program until it becomes executable code. This http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (25 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms strategy of sketch-then-detail tends to produce a more organized final program that is easier to debug and maintain. 2. Encapsulate. Use procedures and ADT's to place the code for each principal operation and type of data in one place in the program listing. Then, if changes become necessary, the section of code requiring change will be localized. 3. Use or modify an existing program. One of the chief inefficiencies in the programming process is that usually a project is tackled as if it were the first program ever written. One should first look for an existing program that does all or a part of the task. Conversely, when writing a program, one should consider making it available to others for possibly unanticipated uses. 4. Be a toolsmith. In programming parlance, a tool is a program with a variety of uses. When writing a program, consider whether it could be written in a somewhat more general way with little extra effort. For example, suppose one is assigned the task of writing a program to schedule final examinations. Instead, write a tool that takes an arbitrary graph and colors the vertices with as few colors as possible, so that no two vertices connected by an edge have the same color. In the context of examination scheduling, the vertices are classes, the colors are examination periods, and an edge between two classes means that the classes have a student in common. The coloring program, together with routines that translate class lists into graphs and colors into specific times and days, is the examination scheduler. However, the coloring program can be used for problems totally unrelated to examination scheduling, such as the traffic light problem of Section 1.1. 5. Program at the command level. Often we cannot find in a library the one program needed to do a job, nor can we adapt one tool to do the job. A well-designed operating system will allow us to connect a network of available programs together without writing any programs at all, except for one list of operating system commands. To make commands composable, it is generally necessary that each behave as a filter, a program with one input file and one output file. Notice that any number of filters can be composed, and if the command language of the operating system is intelligently designed, merely listing the commands in the order in which they are to be performed will suffice as a program. Example 1.11. As an example, let us consider the program spell, as it was originally written by S.C. Johnson from UNIX† commands. This program takes as input a file f1consisting of English text and produces as output all those words in f1that are not found in a small dictionary.‡ spell tends to list proper names as misspellings and may also list real words not in its dictionary, but the typical output of spell is short enough that it can be scanned by eye, and human intelligence can be used to determine whether a word in the output of spell is a misspelling. (This book was checked using spell.) The first filter used by spell is a command called translate that, given appropriate parameters, replaces capital letters by lower case letters and blanks by newlines, leaving http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (26 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms other characters unchanged. The output of translate consists of a file f2 that has the words of f1, uncapitalized, one to a line. Next comes a command sort that sorts the lines of its input file into lexicographic (alphabetical) order. The output of sort is a file f3 that has all the words of f2 in alphabetical order, with repetitions. Then a command unique removes duplicate lines from its input file, producing an output file f4 that has the words of the original file, without capitalization or duplicates, in alphabetical order. Finally, a command diff, with a parameter indicating a second file f5 that holds the alphabetized list of words in the dictionary, one to a line, is applied to f4. The result is all words in f4 (and hence f1) but not in f5, i.e., all words in the original input that are not in the dictionary. The complete program spell is just the following sequence of commands. spell : translate [A-Z] → [a-z], blank → newline sort unique diff dictionary Command level programming requires discipline from a community of programmers; they must write programs as filters wherever possible, and they must write tools instead of special purpose programs wherever possible. Yet the reward, in terms of the overall ratio of work to results, is substantial. 1.7 Super Pascal Most of the programs written in this book are in Pascal. To make programs more readable, however, we occasionally use three constructs not found in standard Pascal, each of which can be mechanically translated into pure Pascal. One such construct is the nonnumeric label. The few times we need labels, we shall use nonnumeric labels since they make programs easier to understand. For example, \"goto output\" is invariably more meaningful than \"goto 561.\" To convert a program containing nonnumeric labels into pure Pascal, we must replace each nonnumeric label by a distinct numeric label and we must then declare those labels with a label declaration at the beginning of the program. This process can be clone mechanically. The second nonstandard construct is the return statement, which we use because it allows us to write more understandable programs without using goto statements to interrupt the flow of control. The return statement we use has the form return (expression) where the (expression) is optional. We can convert a procedure containing return statements into a standard Pascal program quite simply. First, we declare a new label, say 999, and let it label the last end statement of the procedure. If the statement return (x) appears in a function zap, say, we replace this statement with the block http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (27 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms begin zap := x; goto 999 end In a procedure, the statement return, which can have no argument, is simply replaced by goto 999. Example 1.12. Figure 1.15 shows the factorial program written using return statements. Figure 1.16 shows the resulting Pascal program if we apply this transformation systematically to Fig. 1.15. function fact ( n: integer ): integer; begin if n <= l then return (1) else return ( n * fact(n- 1)) end; { fact } Fig. 1.15. Factorial program with return statements. The third extension is that we use expressions as names of types function fact ( n: integer ) :integer; label 999; begin if n <= 1 then begin fact := 1; goto 999 end else begin fact := n * fact(n - 1); goto 999 end 999: end; { fact } http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (28 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms Fig. 1.16. Resulting Pascal program. uniformly throughout a program. For example, an expression like ↑ celltype, while permissible everywhere else, is not permitted as the type of a parameter of a procedure or the type of the value returned by a function. Technically, Pascal requires that we invent a name for the type expression, say ptrtocell. In this book, we shall allow such expressions, expecting that the reader could invent such a type name and mechanically replace type expressions by the type name. Thus, we shall write statements like function zap ( A: array[1..10] of integer ) : ↑ celltype to stand for function zap (A: arrayoftenints ) : ptrtocell Finally, a note on our typesetting conventions for programs. Pascal reserved words are in boldface, types are in roman, and procedure, function, and variable names are in italic. We distinguish between upper and lower case letters. Exercises There are six teams in the football league: the Vultures, the Lions, the Eagles, the Beavers, the Tigers, and the Skunks. The Vultures have already played the Lions and the Eagles; the Lions have also played the Beavers and Skunks. The Tigers have played the Eagles and Skunks. Each team plays one game per 1.1 week. Find a schedule so that all teams will have played each other in the fewest number of weeks. Hint. Create a graph whose vertices are the pairs of teams that have not yet played each other. What should the edges be so that in a legal coloring of the graph, each color can represent the games played in one week? Consider a robot arm that is fixed at one end. The arm contains two elbows at each of which it is possible to rotate the arm 90 degrees up and down in a *1.2 vertical plane. How would you mathematically model the possible movements of the end of the arm? Describe an algorithm to move the end of the robot arm from one permissible position to another. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (29 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms Suppose we wish to multiply four matrices of real numbers M1 × M2 × M3 × M4 where M1 is 10 by 20, M2 is 20 by 50, M3 is 50 by 1, and M4 is 1 by 100. Assume that the multiplication of a p × q matrix by a q × r matrix requires pqr *1.3 scalar operations, as it does in the usual matrix multiplication algorithm. Find the optimal order in which to multiply the matrices so as to minimize the total number of scalar operations. How would you find this optimal ordering if there are an arbitrary number of matrices? **1.4 Suppose we wish to partition the square roots of the integers from 1 to 100 into two piles of fifty numbers each, such that the sum of the numbers in the first pile is as close as possible to the sum of the numbers in the second pile. If we could use two minutes of computer time to help answer this question, what computations would you perform in those two minutes? 1.5 Describe a greedy algorithm for playing chess. Would you expect it to perform very well? In Section 1.2 we considered an ADT SET, with operations MAKE-NULL, UNION, and SIZE. Suppose for convenience that we assume all sets are subsets 1.6 of {0, 1, . . . , 31} and let the ADT SET be interpreted as the Pascal data type set of 0..31. Write Pascal procedures for these operations using this implementation of SET. The greatest common divisor of two integers p and q is the largest integer d that divides both p and q evenly. We wish to develop a program for computing the greatest common divisor of two integers p and q using the following algorithm. Let r be the remainder of p divided by q. If r is O, then q is the greatest common divisor. Otherwise, set p equal to q, then q equal to r, and repeat the process. 1.7 a. Show that this process does find the correct greatest common divisor. b. Refine this algorithm into a pseudo-language program. c. Convert your pseudo-language program into a Pascal program. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (30 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms We want to develop a program for a text formatter that will place words on lines that are both left and right justified. The program will have a word buffer and a line buffer. Initially both are empty. A word is read into the word buffer. If there is sufficient room in the line buffer, the word is transferred to the line buffer. Otherwise, additional spaces are inserted between words in the line buffer to fill out the line, and then the line buffer is emptied by printing the line. 1.8 a. Refine this algorithm into a pseudo-language program. b. Convert your pseudo-language program to a Pascal program. Consider a set of n cities and a table of distances between pairs of cities. Write a pseudo-language program for finding a short path that goes through each city 1.9 exactly once and returns to the city from which it started. There is no known method for obtaining the shortest such tour except by exhaustive searching. Thus try to find an efficient algorithm for this problem using some reasonable heuristic. Consider the following functions of n: 1.10 Indicate for each distinct pair i and j whether fi(n) is O(fj(n)) and whether fi(n) is Ω(fj(n)). http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (31 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms Consider the following functions of n: 1.11 Indicate for each distinct pair i and j whether gi(n) is O(gj(n)) and whether gi(n) is Ω(gj(n)). Give, using \"big oh\" notation, the worst case running times of the following procedures as a function of n. a. procedure matmpy ( n: integer); var i, j, k: integer; begin for i := 1 to n do for j := 1 to n do begin C[i, j] := O; for k := 1 to n do C[i, j] := C[i, j,] + A[i, k] * B[k, j] end end b. procedure mystery ( n: integer); var i, j, k: integer; begin for i:= 1 to n-1 do for j:= i + 1 to n do for k := 1 to j do { some statement requiring O(1) time } end 1.12 procedure veryodd ( n: integer ); c. var http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (32 of 37) [1.7.2001 18:58:22]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms i, j, x, y: integer; begin for i := 1 to n do if odd(i) then begin for j := i to n do x := x + 1; for j := 1 to i do y := y + l end end d. function recursive (n: integer ) : integer; begin if n <= 1 then return (l) else return (recursive(n-1) + recursive(n-1)) end Show that the following statements are true. a. 17 is O(1). b. n(n-1)/2 is O(n2). c. max(n3, 10n2) is O(n3). 1.13 e) If p(x) is any kth degree polynomial with a positive leading coefficient, then p(n) is O(nk) and Ω(nk). http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (33 of 37) [1.7.2001 18:58:23]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms Suppose T1(n) is Ω(f(n)) and T2(n) is Ω(g(n)). Which of the following statements are true? *1.14 a. T1(n) + T2(n) is Ω(max(f(n), g(n))). b. T1(n)T2(n) is Ω(f(n)g(n)). Some authors define big omega by saying f(n) is Ω(g(n)) if there is some n0 and c > 0 such that for all n ≥ n0 we have f(n) ≥ cg(n). *1.15 a. Is it true for this definition that f(n) is Ω(g(n)) if and only if g(n) is O(f(n))? b. Is (a) true for the definition of big omega in Section 1.4? c. Does Exercise 1.14(a) or (b) hold for this definition of big omega? 1.16 Order the following functions by growth rate: (a) n, (b) √¯n, (c) logn, (d) loglogn, (e) log2n, (f) n/logn, (g) √¯nlog2n, (h) (1/3)n, (i) (3/2)n, (j) 17. Assume the parameter n in the procedure below is a positive power of 2, i.e., n = 2, 4, 8, 16 , . . .. Give the formula that expresses the value of the variable count in terms of the value of n when the procedure terminates. procedure mystery ( n: integer ); var x, count: integer; begin 1.17 count := 0; x := 2; while x < n do begin x := 2 * x; count := count + 1 end; writeln(count) end http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (34 of 37) [1.7.2001 18:58:23]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms Here is a function max(i, n) that returns the largest element in positions i through i+n-1 of an integer array A. You may assume for convenience that n is a power of 2. function max ( i, n: integer ): integer; var m1, m2: integer; begin if n = 1 then return (A[i]) else begin m1 := max(i, n div 2); n div 2); m2 := max(i+n div 2, 1.18 if m1 < m2 then return (m2) else return (m1) end end a. Let T(n) be the worst-case time taken by max with second argument n. That is, n is the number of elements of which the largest is found. Write an equation expressing T(n) in terms of T(j) for one or more values of j less than n and a constant or constants that represent the times taken by individual statements of the max program. b. Give a tight big oh upper bound on T(n). Your answer should be equal to the big omega lower bound, and be as simple as possible. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (35 of 37) [1.7.2001 18:58:23]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms Bibliographic Notes The concept of an abstract data type can be traced to the class type in the language SIMULA 67 (Birtwistle et al. [1973]). Since that time, a variety of other languages that support abstract data types have been developed including Alphard (Shaw, Wulf, and London [1977]), C with classes (Stroustrup [1982]), CLU (Liskov, et al. [1977]), MESA (Geschke, Morris, and Satterthwaite [1977]), and Russell (Demers and Donahue [1979]). The ADT concept is further discussed in works such as Gotlieb and Gotlieb [1978] and Wulf et al. [1981]. Knuth [1968] was the first major work to advocate the systematic study of the running time of programs. Aho, Hopcroft, and Ullman [1974] relate the time and space complexity of algorithms to various models of computation, such as Turing machines and random- access machines. See also the bibliographic notes to Chapter 9 for more references to the subject of analysis of algorithms and programs. For additional material on structured programming see Hoare, Dahl, and Dijkstra [1972], Wirth [1973], Kernighan and Plauger [1974], and Yourdon and Constantine [1975]. Organizational and psychological problems arising in the development of large software projects are discussed in Brooks [1974] and Weinberg [1971]. Kernighan and Plauger [1981] show how to build useful software tools for a programming environment. † The symbol Ø stands for the empty set. ‡ We distinguish the abstract data type SET from the built-in set type of Pascal. † The record has no known name because it was created by a call new(header), which made header point to this newly-created record. Internal to the machine, however, there is a memory address that can be used to locate the cell. † Note the asymmetry between big-oh and big-omega notation. The reason such asymmetry is often useful is that there are many times when an algorithm is fast on many but not all inputs. For example, there are algorithms to test whether their input is of prime length that run very fast whenever that length is even, so we could not get a good lower bound on running time that held for all n ≥ n0. † Unless otherwise specified all logarithms are to the base 2. Note that O(logn) does not depend on the base of the logarithm since logan = clogbn, where c = logab. † UNIX is a Trademark of Bell Laboratories. ‡ We could use an unabridged dictionary, but many misspellings are real words one has never heard of. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (36 of 37) [1.7.2001 18:58:23]
Data Structures and Algorithms: CHAPTER 1: Design and Analysis of Algorithms Table of Contents Go to Chapter 2 http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1201.htm (37 of 37) [1.7.2001 18:58:23]
Data Structures and Algorithms: CHAPTER 2: Basic Abstract DataTypes Basic Abstract DataTypes In this chapter we shall study some of the most fundamental abstract data types. We consider lists, which are sequences of elements, and two special cases of lists: stacks, where elements are inserted and deleted at one end only, and queues, where elements are inserted at one end and deleted at the other. We then briefly study the mapping or associative store, an ADT that behaves as a function. For each of these ADT's we consider several implementations and compare their relative merits. 2.1 The Abstract Data Type \"List\" Lists are a particularly flexible structure because they can grow and shrink on demand, and elements can be accessed, inserted, or deleted at any position within a list. Lists can also be concatenated together or split into sublists. Lists arise routinely in applications such as information retrieval, programming language translation, and simulation. Storage management techniques of the kind we discuss in Chapter 12 use list-processing techniques extensively. In this section we shall introduce a number of basic list operations, and in the remainder of this chapter present data structures for lists that support various subsets of these operations efficiently. Mathematically, a list is a sequence of zero or more elements of a given type (which we generally call the elementtype). We often represent such a list by a comma-separated sequence of elements al, a2, . . . ,an where n ≥ 0, and each ai is of type elementtype. The number n of elements is said to be the length of the list. Assuming n ≥ 1, we say that a1 is the first element and an is the last element. If n = 0, we have an empty list, one which has no elements. An important property of a list is that its elements can be linearly ordered according to their position on the list. We say ai precedes ai+1 for i = 1, 2, . . . , n-1, and ai follows ai-1 for i = 2, 3, . . . ,n. We say that the element ai is at position i. It is also convenient to postulate the existence of a position following the last element on a list. The function END(L) will return the position following position n in an n- element list L. Note that position END(L) has a distance from the beginning of the http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1202.htm (1 of 40) [1.7.2001 18:58:59]
Data Structures and Algorithms: CHAPTER 2: Basic Abstract DataTypes list that varies as the list grows or shrinks, while all other positions have a fixed distance from the beginning of the list. To form an abstract data type from the mathematical notion of a list we must define a set of operations on objects of type LIST.† As with many other ADT's we discuss in this book, no one set of operations is suitable for all applications. Here, we shall give one representative set of operations. In the next section we shall offer several data structures to represent lists and we shall write procedures for the typical list operations in terms of these data structures. To illustrate some common operations on lists, let us consider a typical application in which we have a mailing list from which we wish to purge duplicate entries. Conceptually, this problem can be solved quite simply: for each item on the list, remove all equivalent following items. To present this algorithm, however, we need to define operations that find the first element on a list, step through all successive elements, and retrieve and delete elements. We shall now present a representative set of list operations. In what follows, L is a list of objects of type elementtype, x is an object of that type, and p is of type position. Note that \"position\" is another data type whose implementation will vary for different list implementations. Even though we informally think of positions as integers, in practice, they may have another representation. 1. INSERT(x, p, L). Insert x at position p in list L, moving elements at p and following positions to the next higher position. That is, if L is al, a2, . . . ,an, then L becomes a1, a2,. . . ,ap- 1, x, ap, . . . ,an. If p is END(L), then L becomes a1, a2, . . . , an, x. If list L has no position p, the result is undefined. 2. LOCATE(x, L). This function returns the position of x on list L. If x appears more than once, then the position of the first occurrence is returned. If x does not appear at all, then END(L) is returned. 3. RETRIEVE(p, L). This function returns the element at position p on list L. The result is undefined if p = END(L) or if L has no position p. Note that the elements must be of a type that can be returned by a function if RETRIEVE is used. In practice, however, we can always modify RETRIEVE to return a pointer to an object of type elementtype. 4. DELETE(p, L). Delete the element at position p of list L. If L is a1, a2, . . . ,an, then L becomes a1, a2, . . . ,ap- 1, ap+1, . . . ,an. The result is undefined if L has no position p or if p = END(L). 5. NEXT(p, L) and PREVIOUS(p, L) return the positions following and preceding position p on list L. If p is the last position on L, then NEXT(p, L) = END(L). NEXT is undefined if p is END(L). PREVIOUS is undefined if p is http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1202.htm (2 of 40) [1.7.2001 18:58:59]
Data Structures and Algorithms: CHAPTER 2: Basic Abstract DataTypes 1. Both functions are undefined if L has no position p. 6. MAKENULL(L). This function causes L to become an empty list and returns position END(L). 7. FIRST(L). This function returns the first position on list L. If L is empty, the position returned is END(L). 8. PRINTLIST(L). Print the elements of L in the order of occurrence. Example 2.1. Let us write, using these operators, a procedure PURGE that takes a list as argument and eliminates duplicates from the list. The elements of the list are of type elementtype, and a list of such elements has type LIST, a convention we shall follow throughout this chapter. There is a function same(x,y), where x and y are of elementtype, that is true if x and y are \"the same\" and false if not. The notion of sameness is purposely left vague. If elementtype is real, for example, we might want same(x,y) true if and only if x = y. However, if elementtype is a record containing the account number, name, and address of a subscriber as in type elementtype = record acctno: integer; name: packed array [1..20] of char; address: packed array [1..50] of char end then we might want same(x, y) to be true whenever x.acctno=y.acctno.† Figure 2.1 shows the code for PURGE. The variables p and q are used to represent two positions in the list. As the program proceeds, duplicate copies of any elements to the left of position p have been deleted from the list. In one iteration of the loop (2)-(8), q is used to scan the list following position p to delete any duplicates of the element at position p. Then p is moved to the next position and the process is repeated. In the next section we shall provide appropriate declarations for LIST and position, and implementations for the operations so that PURGE becomes a working program. As written, the program is independent of the manner in which lists are represented so we are free to experiment with various list implementations. procedure PURGE ( var L: LIST ); { PURGE removes duplicate elements from list L } var p, q: position; { p will be the \"current\" position in L, and q will move ahead to find equal elements } http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1202.htm (3 of 40) [1.7.2001 18:58:59]
Data Structures and Algorithms: CHAPTER 2: Basic Abstract DataTypes begin (1) p := FIRST(L); (2) while p <> END(L) do begin (3) q := NEXT(p, L); (4) while q <> END(L) do (5) if same(RETRIEVE(p, L), RETRIEVE(q, L)) then (6) DELETE(q, L) else (7) q := NEXT(q, L); (8) p := NEXT(p, L) end end; { PURGE } Fig. 2.1. Program to remove duplicates. A point worth observing concerns the body of the inner loop, lines (4)-(7) of Fig. 2.1. When we delete the element at position q at line (6), the elements that were at positions q+1, q+2, . . . , and so on, move up one position in the list. In particular, should q happen to be the last position on L, the value of q would become END(L). If we then executed line (7), NEXT(END(L), L) would produce an undefined result. Thus, it is essential that either (6) or (7), but never both, is executed between the tests for q = END(L) at line (4). 2.2 Implementation of Lists In this section we shall describe some data structures that can be used to represent lists. We shall consider array, pointer, and cursor implementations of lists. Each of these implementations permits certain list operations to be done more efficiently than others. Array Implementation of Lists In an array implementation of a list, the elements are stored in contiguous cells of an array. With this representation a list is easily traversed and new elements can be appended readily to the tail of the list. Inserting an element into the middle of the list, however, requires shifting all following elements one place over in the array to make room for the new element. Similarly, deleting any element except the last also requires shifting elements to close up the gap. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1202.htm (4 of 40) [1.7.2001 18:58:59]
Data Structures and Algorithms: CHAPTER 2: Basic Abstract DataTypes Fig. 2.2. Array implementation of a list. In the array implementation we define the type LIST to be a record having two fields. The first field is an array of elements whose length is sufficient to hold the maximum size list that will be encountered. The second field is an integer last indicating the position of the last list element in the array. The i th element of the list is in the ith cell of the array, for 1 ≤ i ≤ last, as shown in Fig. 2.2. Positions in the list are represented by integers, the ith position by the integer i. The function END(L) has only to return last + 1. The important declarations are: const maxlength = 100 { some suitable constant }; type LIST = record elements: array[1..maxlength] of elementtype; last: integer end; position = integer; function END ( var L: LIST ): position;† begin return (L.last + 1) end; { END } Figure 2.3 shows how we might implement the operations INSERT, DELETE, and LOCATE using this array-based implementation. INSERT moves the elements at locations p,p+1, . . . , last into locations p+1, p+2, . . . ,last+1 and then inserts the new element at location p. If there is no room in the array for an additional element, the routine error is invoked, causing its argument to be printed, followed by termination of execution of the program. DELETE removes the element at position p by moving the elements at positions p + 1, p + 2, . . . , last into positions p, p+ 1, . . . , last-1. LOCATE sequentially scans the array to look for a given element. If the element is not found, LOCATE returns last+ 1. It should be clear how to encode the other list operations using this implementation of lists. For example, FIRST always returns 1; NEXT returns one more than its argument and PREVIOUS returns one less, each first checking that the result is in range; MAKENULL(L) sets L.last to 0. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1202.htm (5 of 40) [1.7.2001 18:58:59]
Data Structures and Algorithms: CHAPTER 2: Basic Abstract DataTypes If procedure PURGE of Fig. 2.1 is preceded by 1. the definitions of elementtype and the function same, 2. the definitions of LIST, position and END(L) as above, 3. the definition of DELETE from Fig. 2.3, and 4. suitable definitions for the trivial procedures FIRST, NEXT, and RETRIEVE, then a working procedure PURGE results. At first, it may seem tedious writing procedures to govern all accesses to the underlying structures. However, if we discipline ourselves to writing programs in terms of the operations for manipulating abstract data types rather than making use of particular implementation details, then we can modify programs more readily by reimplementing the operations rather than searching all programs for places where we have made accesses to the underlying data structures. This flexibility can be particularly important in large software efforts, and the reader should not judge the concept by the necessarily tiny examples found in this book. Pointer Implementation of Lists Our second implementation of lists, singly-linked cells, uses pointers to link successive list elements. This implementation frees us from using contiguous memory for storing a list and hence from shifting elements to make room for new elements or to close up gaps created by deleted elements. However, one price we pay is extra space for pointers. In this representation, a list is made up of cells, each cell consisting of an element of the list and a pointer to the next cell on the list. If the list is a1, a2, . . . , an, the cell holding ai has a pointer to the cell holding ai+1, for procedure INSERT ( x: elementtype; p: position; var L: LIST ); { INSERT places x at position p in list L } var q: position; begin if L.last > = maxlength then error('list is full') else if (p > L.last + 1) or (p < 1) then error('position does not exist') else begin http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1202.htm (6 of 40) [1.7.2001 18:58:59]
Data Structures and Algorithms: CHAPTER 2: Basic Abstract DataTypes for q := L.last downto p do { shift elements at p, p + 1, . . . down one position } L.elements[q + 1 ]: = L.elements[q]; L.last := L.last + 1; L.elements[p] := x end end; { INSERT } procedure DELETE ( p: position; var L: LIST ); { DELETE removes the element at position p of list L } var q: position; begin if (p > L.last) or (p < 1) then error('position does not exist') else begin L.last := L.last - 1; for q := p to L.last do { shift elements at p + 1, p + 2,... up one position } L.elements[q] := L.elements[q + 1] end end; { DELETE } function LOCATE ( x: elementtype; L: LIST ): position; { LOCATE returns the position of x on list L } var q: position; begin for q := 1 to L.last do if L.elements[q] = x then return (q); return (L.last + 1) { if not found } end; { LOCATE } Fig. 2.3. Array-based implementation of some list operations. i = 1, 2 , . . . , n-1. The cell holding an has a nil pointer. There is also a header cell that points to the cell holding a1; the header holds no element.† In the case of an empty list, the header's pointer is nil, and there are no other cells. Figure 2.4 shows a linked list of this form. http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1202.htm (7 of 40) [1.7.2001 18:58:59]
Data Structures and Algorithms: CHAPTER 2: Basic Abstract DataTypes Fig. 2.4. A linked list. For singly-linked lists, it is convenient to use a definition of position that is somewhat different than the definition of position in an array implementation. Here, position i will be a pointer to the cell holding the pointer to ai for i = 2, 3 , . . . , n. Position 1 is a pointer to the header, and position END(L) is a pointer to the last cell of L. The type of a list happens to be the same as that of a position -- it is a pointer to a cell, the header in particular. We can formally define the essential parts of a linked list data structure as follows. type celltype = record element: elementtype; next: ↑ celltype end; LIST = ↑ celltype; position = ↑ celltype; The function END(L) is shown in Fig. 2.5. It works by moving pointer q down the list from the header, until it reaches the end, which is detected by the fact that q points to a cell with a nil pointer. Note that this implementation of END is inefficient, as it requires us to scan the entire list every time we need to compute END(L). If we need to do so frequently, as in the PURGE program of Fig. 2.1, we could either 1. Use a representation of lists that includes a pointer to the last cell, or 2. Replace uses of END(L) where possible. For example, the condition p <> END(L) in line (2) of Fig. 2.1 could be replaced by p ↑.next <> nil, at a cost of making that program dependent on one particular implementation of lists. function END ( L: LIST ): position; { END returns a pointer to the last cell of L } var q: position; begin (1) q := L; (2) while q↑.next <> nil do (3) q := q↑.next; http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1202.htm (8 of 40) [1.7.2001 18:58:59]
Data Structures and Algorithms: CHAPTER 2: Basic Abstract DataTypes (4) return (q) end; { END } Fig. 2.5. The function END. Figure 2.6 contains routines for the four operations INSERT, DELETE, LOCATE, and MAKENULL using this pointer implementation of lists. The other operations can be implemented as one-step routines, with the exception of PREVIOUS, which requires a scan of the list from the beginning. We leave these other routines as exercises. Note that many of the commands do not use parameter L, the list, and we omit it from those that do not. The mechanics of the pointer manipulations of the INSERT procedure in Fig. 2.6 are shown in Fig. 2.7. Figure 2.7(a) shows the situation before executing INSERT. We wish to insert a new element in front of the cell containing b, so p is a pointer to the list cell that contains the pointer to b. At line (1), temp is set to point to the cell containing b. At line (2) a new list cell is created and the next field of the cell containing a is made to point to this cell. At line (3) the element field of the newly- created cell is made to hold x, and at line (4) the next field is given the value of temp, thus making it point to the cell containing b. Figure 2.7(b) shows the result of executing INSERT. The new pointers are shown dashed, and marked with the step at which they were created. The DELETE procedure is simpler. Figure 2.8 shows the pointer manipulations of the DELETE procedure in Fig. 2.6. Old pointers are solid and the new pointers dashed. We should note that a position in a linked-list implementation of a list behaves differently from a position in an array implementation. Suppose we have a list with three elements a, b, c and a variable p, of type position, which currently has position 3 as its value; i.e., it points to the cell holding b, and thus represents the position of c. If we execute a command to insert x at position 2, the list becomes a, x, b, c, and element b now occupies position 3. If we use the array implementation of lists described earlier, b and c would be moved down the array, so b would indeed occupy the third position. procedure INSERT ( x: elementtype; p: position); var temp : position; begin (1) temp := p ↑.next; (2) new(p ↑.next ); http://www.ourstillwaters.org/stillwaters/csteaching/DataStructuresAndAlgorithms/mf1202.htm (9 of 40) [1.7.2001 18:58:59] | 25,495 | 108,662 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2024-30 | latest | en | 0.858788 |
https://www.ecologycenter.us/population-dynamics-2/annealing-acceptance-criterion.html | 1,566,652,807,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027321140.82/warc/CC-MAIN-20190824130424-20190824152424-00295.warc.gz | 800,947,989 | 8,121 | ## Annealing Acceptance Criterion
The annealing acceptance criterion noted above is sensitive to the temperature that is assumed at each iteration of the solution generation process. Early in the search, when the temperature is relatively high, the result of the acceptance criterion function is one of the larger numbers on the 0-1 scale. Thus the random number drawn between 0 and 1 will likely be lower than the result of the acceptance criterion, and subsequently more inferior adjustments to a solution will be allowed. As the temperature cools, however, the result of the acceptance criterion function will move to the lower end of the 0-1 scale, and fewer inferior adjustments will be allowed to a solution as it is being developed.
As one may gather, the choice of the initial temperature and the choice of the cooling rate will influence how many inferior adjustments to solutions will occur. If the initial temperature is too low, for example, very few inferior adjustments will be allowed, since the result of the acceptance criteria function will be on the lower end of the 0-1 scale. If the initial temperature is high, and the cooling rate is also high, resulting in a slow decline in temperature, a relatively large number of inferior adjustments will be allowed to the solution. Some calibration may be needed to assure that the choice of initial temperature produces probabilities near 1.0, and at lower temperatures, produces probabilities near 0.0. The high acceptance rate of the initial temperature makes the starting solution somewhat less important than with some other heuristics.
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Q: What's 20% of \$150?
A: 20% of \$150 is \$30. \$150 * 20/100 = \$30
Original conversation
User: What's 20% of \$150?
Weegy: 20% of \$150 is \$30.
\$150 * 20/100 = \$30
User: What is the percent of markup on an item that normally sells for \$18,but now sells for \$19? show work please.
Updated 7/19/2015 9:05:21 PM
Edited by jeifunk [7/19/2015 9:05:03 PM], Confirmed by jeifunk [7/19/2015 9:05:04 PM], Edited by jeifunk [7/19/2015 9:05:21 PM]
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3
6% is the percent of markup on an item that normally sells for \$18,but now sells for \$19.
(19 - 18)/18 = 1/18 = 0.05556 = 0.06 = 6%
(if decimal rounds to the neartest hundreds)
Confirmed by jeifunk [7/19/2015 9:05:34 PM]
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https://search.academickids.com/encyclopedia/index.php/Orthogonal | 1,638,396,118,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964360951.9/warc/CC-MAIN-20211201203843-20211201233843-00425.warc.gz | 565,701,855 | 8,366 | # Orthogonality
(Redirected from Orthogonal)
In mathematics, orthogonal is synonymous with perpendicular when used as a simple adjective that is not part of any longer phrase with a standard definition. It means at right angles. It comes from the Greek "ortho", meaning "right" and "gonia", meaning "angle". Two streets that cross each other at a right angle are orthogonal to each other. Two vectors in an inner product space are orthogonal if their inner product is zero. If the vectors are [itex]x[itex] and [itex]y[itex] this is written [itex]x \perp y[itex]. The word normal is sometimes also used for this concept by mathematicians, although that word is rather overburdened.
Contents
## In Euclidean vector spaces
For example, in a 2- or 3-dimensional Euclidean space, two vectors are orthogonal if their dot product is zero, i.e., they make an angle of 90° or π/2 radians. Hence orthogonality is a generalization of the concept of perpendicular.
Several vectors are called pairwise orthogonal if any two of them are orthogonal, and a set of such vectors is called an orthogonal set. They are said to be orthonormal if they are all unit vectors. Non-zero pairwise orthogonal vectors are always linearly independent.
## Orthogonal functions
We commonly use the following inner product to say that two functions f and g are orthogonal:
[itex] \langle f, g \rangle = \int_a^b f(x)g(x)w(x)\,dx = 0.[itex]
Here we introduce a nonnegative weight function [itex]w(x)[itex], and we write
[itex] \langle f, gw \rangle = \langle f, g\rangle_w[itex].
We write the norms with respect to this inner product and the weight function as
[itex]||f||_w[itex]
The members of a sequence { fi : i = 1, 2, 3, ... } are:
• orthogonal if
[itex]\langle f_i, f_j \rangle=\int_{-\infty}^\infty f_i(x) f_j(x) w(x)\,dx=||f_i||^2\delta_{i,j}=||f_j||^2\delta_{i,j}[itex]
• orthonormal
[itex]\langle f_i, f_j \rangle=\int_{-\infty}^\infty f_i(x) f_j(x) w(x)\,dx=\delta_{i,j}[itex]
where
[itex]\delta_{i,j}=\left\{\begin{matrix}1 & \mathrm{if}\ i=j \\ 0 & \mathrm{if}\ i\neq j\end{matrix}\right\}[itex]
is Kronecker's delta. In other words, any two of them are orthogonal and the norm of each is 1. See in particular orthogonal polynomials.
## Examples
• The vectors (1, 3, 2), (3, −1, 0), (1/3, 1, −5/3) are orthogonal to each other, since (1)(3) + (3)(−1) + (2)(0) = 0, (3)(1/3) + (−1)(1) + (0)(−5/3) = 0, (1)(1/3) + (3)(1) − (2)(5/3) = 0. Observe also that the dot product of the vectors with themselves are the norms of those vectors, so to check for orthogonality, we need only check the dot product with every other vector.
• The vectors (1, 0, 1, 0, ...)T and (0, 1, 0, 1, ...)T are orthogonal to each other. Clearly the dot product of these vectors is 0. We can then make the obvious generalization to consider the vectors in Z2n:
[itex]\mathbf{v}_k = \sum_{\begin{matrix}i=0\\ai+k < n\end{matrix}}^{n/a} \mathbf{e}_i[itex]
for some positive integer a, and for 1 ≤ ka − 1, these vectors are orthogonal, for example (1, 0, 0, 1, 0, 0, 1, 0)T, (0, 1, 0, 0, 1, 0, 0, 1)T, (0, 0, 1, 0, 0, 1, 0, 0)T are orthogonal.
• Take two quadratic functions 2t + 3 and 5t2 + t − 17/9. These functions are orthogonal with respect to a unit weight function on the interval from −1 to 1. The product of these two functions is 10t3 + 17t2 − 7/9 t − 17/3, and now,
[itex]\int_{-1}^{1} \left(10t^3+17t^2-{7\over 9}t-{17\over 3}\right)\,dt = \left[{5\over 2}t^4+{17\over 3}t^3-{7\over 18}t^2-{17\over 3}t\right]_{-1}^{1}[itex]
[itex]=\left({5\over 2}(1)^4+{17\over 3}(1)^3-{7\over 18}(1)^2-{17\over 3}(1)\right)-\left({5\over 2}(-1)^4+{17\over 3}(-1)^3-{7\over 18}(-1)^2-{17\over 3}(-1)\right)[itex]
[itex]={19\over 9}-{19\over 9}=0.[itex]
• The functions 1, sin(nx), cos(nx) : n = 1, 2, 3, ... are orthogonal with respect to Lebesgue measure on the interval from 0 to 2π. This fact is basic in the theory of Fourier series.
## Derived meanings
Other meanings of the word orthogonal evolved from its earlier use in mathematics.
In art the perspective lines at an imagined right angle to the picture plane, pointing to the vanishing point are referred to as 'orthogonal lines'.
In computer science, an instruction set is said to be orthogonal if any instruction can use any register in any addressing mode. This terminology results from considering an instruction as a vector whose components are the instruction fields. One field identifies the registers to be operated upon, and another specifies the addressing mode. As with a set of mathematical basis vectors, which must be orthogonal if they are to represent any vector uniquely, only an orthogonal instruction set can uniquely encode all combinations of registers and addressing modes.
Orthogonality is a system design property which enables the making of complex designs feasible and compact. The aim of an orthogonal design is to achieve that operations within one of its components do not create nor propagate side-effects to other components. For example a car has orthogonal components and controls, e.g. accelerating the vehicle does not influence anything else but the components involved in the acceleration. On the other hand, a car with non orthogonal design might have, for example, the acceleration influencing the radio tuning or the display of time. Consequently, this usage is seen to be derived from the use of orthogonal in mathematics; one may project a vector onto a subspace, by projecting it each member of a set of basis vectors separately and adding the projections if and only if the basis vectors are orthogonal to each other.
Orthogonality achieves that modifying the technical effect produced by a component of a system does not create or propagate side effects to other components of the system. The emergent behaviour of a system consisting of components should be controlled strictly by formal definitions of its logic and not by side effects resulting from poor integration, i.e. non-orthogonal design of modules and interfaces. Orthogonality reduces the test and development time, because it's easier to verify designs that neither cause side effects nor depend on them.
In radio communications, multiple access schemes are orthogonal when a receiver can (theoretically) completely reject an arbitrarily strong unwanted signal. The orthogonal schemes are TDMA and FDMA. A non-orthogonal scheme is Code Division Multiple Access, CDMA.
## References and external links
• Art and Cultures
• Musical Instruments (http://academickids.com/encyclopedia/index.php/List_of_musical_instruments)
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Ancient Civilizations (http://www.academickids.com/encyclopedia/index.php/Ancient_Civilizations)
• Industrial Revolution (http://www.academickids.com/encyclopedia/index.php/Industrial_Revolution)
• Middle Ages (http://www.academickids.com/encyclopedia/index.php/Middle_Ages)
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• Social Studies (http://www.academickids.com/encyclopedia/index.php/Social_Studies)
• Space and Astronomy
• Solar System (http://www.academickids.com/encyclopedia/index.php/Solar_System) | 2,086 | 7,453 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.40625 | 4 | CC-MAIN-2021-49 | latest | en | 0.872176 |
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Algebra Homework Help: How to Factor Polynomials
In our next piece of online algebra help, we’re going to discuss the world of polynomials. But before we get started, consider hiring an online algebra tutor from Studygate, you can’t go wrong. If there is a constant in the math universe, it is the letter X. In algebra, X is the source of many a mental math meltdown. “Finding ” is the instruction in every single problem. Learn here to factor polynomials.
But X can be fun! We can play with it, move it around, multiply it, divide it, and cancel it out. X really lets us see the relationship between numbers and how math theorems work.
Totally Awesome, I know!
But I know the only reason you’re here is to learn about polynomials and what to do with them.
Factoring polynomials is a crucial step to using the quadratic formula. Factoring polynomials is easier, though, and faster, too.
Let’s look at some X factors.
3x, x, -x2, 5x2, 5x, 7x, 20, -4
The first thing we do is put them in descending order of x.
-x2, 5x2, 3x, x, 5x, 7x, 20, -4
We can simplify them by adding like-factors together: all of the x2, then all the x, then the numbers without x
4x2 + 16x + 16
The next step is to look for common factors in all three groups. For example, these groups all have even numbered coefficients, so we know that 2 is a factor. Even more significant, we can see that all these integers are divisible by 4!
Take out the four from all of them.
4(x2 + 4x + 4)
We’re almost there!
Let’s look at (x2 + 4x + 4) . Can we break this down anymore?
The answer is yes! With the FOIL system!
FOIL stands for “first, outside, inside, last”. This is a cute way of saying that we got this expression by multiplying two parts separate factors together. Each of these factors is called a Binomial. (This is because each factor has two parts: an unknown and a number).
Here we are:
(a + b) X (c + d) = (x2 + 4x + 4) .
Basically, we end up with: ac+ ad + bc + bd. When we add them all together, we get (x2 + 4x + 4).
In this case, bd = 4, the last part of our expression, while ac = x2, the first part of our expression. The other two parts, ad+ bc, need to equal 4x.
We know that ac = x2, so A and C must be x. So that’s easy.
The hard part is figuring out ad and bc. But to solve that, we can look to bd. What are factors that, when multiplied together, give us 4? 4 breaks down to 1, 2, and 4. That means B or D must be 1, 2, or 4.
*****Let’s try 1 and 4. Plug them in and see what happens
(x + 1)(x + 4)
Use FOIL to multiply them together: First, Outside, Inside, Last.
We get x2 + 4x + x + 4
Add them together: x2 + 5x + 4 ≠ x2 + 4x + 4
Yikes! That didn’t work.****
Then it must be 2. This actually makes sense, since 2 + 2 = 4 or 2x + 2x = 4x!
Let’s double check
(x +2)(x + 2) → x2 + 2x + 2x + 4 → x2 + 4x + 4 Bravo!
We can even make this simpler. Since (x + 2) is the same, we can just square the binomial (x + 2)2
So the final answer is 4(x + 2)2
Here’s a rough one: 3x3 + 15x2 – 36x
First thing is to take out the greatest common factor: 3x Check it and see!
3x(x2 + 5x – 12)
Now, we can FOIL the larger expression.
****Here’s a trick: look at the coefficients in the middle (5) and end (12). You know that two factors multiplied together will bring you the end number, but they must be added/subtracted to form the middle number 5.
What are the multiplication factors of 12? 1 and 12, 2 and 6, and 3 and 4. None of these sets of factors, when added or subtracted, give you 5.
If you don’t believe me, try finding the binomials through trial and error. You’ll be at it forever!
Rats! We asked our online math tutors for additional info, and we can’t break this down further! We’ve been “foiled!”
3x(x2 + 5x – 12)
One more: -2x2 + 17x – 36
First of all, are there any common factors? Unfortunately, no. One number is odd, so 2 is not a factor in all three. The last number has no x, so that can’t be a factor, either.
We’ll just proceed to the FOIL, then.
This is a bit hard, since we have THREE GROUPS of numbers to deal with: 2, 13, 36. But we can still do this! Just take your time.
What are the factors of 36 that can add up to 36?
36 is broken down to: 1 and 36, 2 and 18, 3 and 12, 4, and 9, and 6 and 6.
None of these really add up to 17, but we have to consider the 2. There are two factors that make up 2: 1 and 2. Can we multiply any of the factors that make up 36 by 1 and 2, and then add them together to get 17?
YES!
Look at factors 4 and 9. They match up with 1 and 2. Multiply and add the sums:
1 x 9 = 9
2 x 4 = 8
9 + 8 = 17!!! Hooray!
Since the 2 and the 4 are multiplied together, they must be in separate factors: (2x, 9)(x, 4)
Now to determine which ones are positive and negative.
This might sound harder than it is.
We know that two positives multiplied together form a positive. (5 x 4) = 20
Two negatives multiplied together form a positive. (-7 x -9) = 63
A positive and negative multiplied together form a negative. (-8 x 2) = -16
Go back to the original equation and our factors:
-2x2 + 17x – 36
(2x, 9)(x, 4)
We know the first and last coefficients are negative. That means one integer in each binomial must be negative and one must be positive so that, when multiplied, we get negative numbers. But we also know that the middle coefficient is positive.
To get the middle coefficient we need to make sure they are positive. That’s the only way they can ADD up to a positive 17. We need a 9x and an 8x. We can multiply two positives together or two negatives together to get positives. | 1,658 | 5,583 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.71875 | 5 | CC-MAIN-2022-49 | latest | en | 0.922159 |
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What will be the output of following code segment? for (int i = 2; i<10; i++){ if ( i == 5) continue; cout i "," ; }
• 2,3,7,8,9
• 2,3,4,6,7,8,9
• 2,3,4
• 4,6,7,8,9
• 2,3,4,6,7,8,9
cause at 5, it will not print only.
why??? give reason plz
{ if ( i == 5) continue;
at 5, it will revert back to loop and will not print number "5"
but number "4" will be printed.
While loop becomes infinite in which scenario _______.
• When the condition is always False
• When the condition is always True
• Condition contains logical operators
• Condition contains arithmetic operators
true
• In loops the conditions are of ______ kind of expressions
• Boolean expressions
• Constant expressions
• Primary expressions
• Secondary expression
• Boolean expressions
What will be the output of the following while loop? int counter = 0 ; while(counter < 15) cout counter “ ”; counter++;
• 1 2 3 4
• 1 2 3 4 5
• Compile time error
• Infinite loop
error q??
correct ...error hi ata h
• When we call a function, its control
• transfers to its Prototype
• transfers to its definition
• returns to statement following function call
• The compiler stops execution of whole program
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# NPV() function to calculate Present Value
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This post is written by Paramdeep.
Today, let us learn how to use NPV() function in Excel & create a simple financial model.
### NPV – Introduction:
If you are dealing with cash and valuations, you are bound to have come across the NPV function. If you don’t know the assumptions behind the same, I bet it could cost you your job!
Let’s take a simple project – You buy a MSFT stock for USD 100. You receive a dividend of USD 10 in the first year, USD 20 in the second year, USD 40 in the third year and then you sell it out for USD 140. If you could have alternatively put this money in bank at 10% interest rate, have you gained anything?
How do you model this in excel? In this tutorial we understand how you can use NPV to do this analysis and what kind of pitfalls you can land into!!
### What is the NPV() function
Simply speaking, NPV function calculates present value of your cash flows. Let’s take a simple example first –
#### You invest \$100 in a bank, which pays 10% interest
• What is its value 1 year down the line?
• I am sure, you don’t need any coffee to get that value – 100 x 10% is the interest and 100 is the principal that you had. So the value 100 x (1+10%) = 110
• Simple 100 x (1 + 10%)^2 = 121
• So, if I were to ask you, the present value of a cash flow of 121, that you were to get 2 years down the line at 10% interest?
• Again simple, you told me initially, it was \$100
#### NPV does exactly that – gets you the present value of your cash flows
The function is simple, it does all the difficult calculations for you and gets you the solution!
### Beware – The function has its own assumptions!
Though the function is quite convenient, but it has its own pitfalls. And in my modelling experience I have seen a lot of people making that mistake! Lets model the situation described in the beginning (The MSFT Case). The cash flows are given to you as:
Let us see, internally what we get by modelling the NPV from the first principles and using the NPV function
You can clearly see that there are two ways of using NPV function (and each has its own assumption!)
### So what is happening internally?
Usually when we start a project, we assume that the investment is made upfront (On day 0). Then the revenues, costs and the cash would start flowing in. Since the investment is made on day 0, it should not be discounted.
But when you use the NPV function, excel internally makes an assumption that even the first cash flow is at the end of the year (Per se, this is not wrong, but in normal circumstances, you make the payment upfront!).
So the right usage of the function would be to add the first cash without discounting and then use the NPV function to discount the rest of the cash flows.
If you just use the NPV function on all the cash flows, then the inherent assumption is that even the first cash flow is at the end of the year.
### Few other ways of calculating NPV
When you are dealing with cash flows and valuations (typically that is when you come across the functions like NPV, etc) even small mistakes cost dear. You want to make sure that you are as accurate as you can ever be. At that point of time, if the cash is not flowing at the year ends, you can use a more powerful function in excel – XNPV. You can show it the cash and the exact dates and it would calculate the exact NPV for you. People don’t often use it as they don’t know the exact dates of cash flow!
### How do you calculate the discounted cash values in your models?
I know the easiest way would be to use the NPV function. It is easy to use but at the same time could be tricky. So how do you implement such functionality in your models?
I have created a template for you, where the subheadings are given and you have use the functions to get the right values for you! You can download the same from here. You can go through the case and fill in the yellow boxes. I also recommend that you try to create this structure on your own (so that you get a hang of what information is to be recorded).
Also you can download this filled template and check, if the information you recorded, matches mine or not!
For any queries regarding the cash impact or financial modeling, feel free to put the comments in the blog or write an email to paramdeep@edupristine.com
We are glad to inform that our new financial modeling & project finance modeling online class is ready for your consideration.
The article is written by Paramdeep from Pristine.
Chandoo.org has partnered with Pristine to launch a Financial Modeling Course. For details click here.
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### 7 Responses to “NPV() function to calculate Present Value”
1. Jason says:
How did you put "FY1 FY2 FY3..." for cells E1:I1?
2. Fred says:
@ Jason: custom cell format
Instead of using NPV I prefer to use XNPV. There is hardly any npv project that I have worked on that didn't change cash flow scenarios or any other parameters. So with dates showing to the viewers there is less ambiguity on the cash flow.
3. Hui... says:
@Jason
The cells have a custom number format aplied
The Cells contain the numbers 1, 2, 3 etc
But a custom number format of "FY" 0 has been aplied
and so they display as FY 1, FY 2, FY 3 etc
4. @Jason: As Fred and Hui have pointed out, it is based on custom formatting
@Fred: Thanks for your comments. I think in Excel 2003 XNPV was not available by default, so people didnt use it much.
@Hui: Thanks!
5. Hey there just wanted to give you a quick heads up. The text in your article seem to be running off the screen in Safari. I'm not sure if this is a formatting issue or something to do with browser compatibility but I thought I'd post to let you know. The style and design look great though! Hope you get the problem fixed soon. Thanks
6. Eric says:
1. The spreadsheet does not account for compounding periods per year. The IY must be divided by the PY/CY.
2. The bgn/end only adjusts the PV based upon CF0. How do you account for CF1:CFN being in advance or arrears?
Best,
Eric
7. Thanks for the introduction into NPV. For real estate, I've written something similar: http://www.invantive.com/about-invantive/news/entryid/802/introduction-of-the-net-present-value-for-real-estate-development
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One email per week with Excel and Power BI goodness. Join 100,000+ others and get it free. | 1,829 | 7,720 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2024-10 | longest | en | 0.940235 |
https://alex.state.al.us/cr2.php?std_id=54164 | 1,653,370,983,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662564830.55/warc/CC-MAIN-20220524045003-20220524075003-00359.warc.gz | 99,040,659 | 8,407 | # ALEX Classroom Resources
ALEX Classroom Resources
Subject: Mathematics (9 - 12)
Title: Central Tendency | Targeted Math Instruction
URL: https://aptv.pbslearningmedia.org/resource/ket-targetedmath4/central-tendency/
Description:
One way we analyze data is to look at measures of central tendency—mean, median, and mode. They are the tools to look at the information for the purpose of answering the question, “What is normal?” Understanding the measures of central tendency can help us make important life decisions. For example, averages can help us set goals or plan budgets. At the end of this lesson about central tendency, students will be able to recognize and apply the concepts of mean, median, and mode in real-life problems.
Subject: Mathematics (9 - 12)
Title: What Is Statistics? | Against All Odds: Unit 1
URL: https://aptv.pbslearningmedia.org/resource/b6826faf-b2a6-448e-ac82-2929f304ae6f/what-is-statistics-against-all-odds-unit-1/
Description:
Introduce high school students to the art and science of statistics in the 6-minute video, "What is Statistics?" from the Against All Odds series. This video resource will demonstrate how gathering, organizing, drawing, and analyzing data is applicable in everyday life and a variety of careers.
Subject: Mathematics (9 - 12)
Title: Measures of Center | Against All Odds: Unit 4
Description:
Discover how calculating median and mean reveal different ways to describe a center of distribution in this 9-minute video from the Against All Odds statistics series. This video resource will examine differences in comparable wages for men and women to see practical applications of statistics and data visualization.
Subject: Mathematics (9 - 12)
Title: Statistics: Using Sampling to Count Trees
URL: https://aptv.pbslearningmedia.org/resource/statistics-sampling-count-trees/statistics-using-sampling-to-count-trees/
Description:
This exercise was developed to complement the film The National Parks of Texas by Texas PBS & Villita Media. In this activity, students will learn about estimating the number of trees in a large area based on a smaller area.
This is one way statisticians measure forests and other wide expanses of land. It's also a great way to illustrate how polling works. Scientists will interview a smaller sample size of Americans, rather than every single American, and then make estimations based on their results. In the same way, we counted smaller samples of trees, rather than all of the trees individually to get an estimate of how many trees are in the park total.
Note: The corresponding lesson plan can be found under the "Support Materials for Teachers" link on the right side of the page.
Subject: Mathematics (9 - 12)
Title: Understanding a Crowd’s Predictive Ability | Prediction by the Numbers
URL: https://aptv.pbslearningmedia.org/resource/nvpn-sci-crowds/understanding-a-crowds-predictive-ability-prediction-by-the-numbers/
Description:
Examine a mathematical theory known as the “wisdom of crowds,” which holds that a crowd’s predictive ability is greater than that of an individual, in this video from NOVA: Prediction by the Numbers. Sir Francis Galton documented this phenomenon after witnessing a weight-guessing contest more than a hundred years ago at a fair. Statistician Talithia Williams tests Galton’s theory with modern-day fairgoers, asking them to guess the number of jelly beans in a jar. Use this resource to stimulate thinking and questions about the use of statistics in everyday life and to make evidence-based claims about predictive ability.
Subject: Mathematics (9 - 12)
Title: Histograms | Against All Odds: Unit 3
URL: https://aptv.pbslearningmedia.org/resource/5e9c3b66-9d17-400c-a605-a6c9c8a5e9e2/histograms-against-all-odds-unit-3/
Description:
Real-world examples demonstrate the benefits of histograms in this 10-minute video from the Against All Odds statistics series. Data visualization techniques help students understand the practical application of statistics in meteorology and in predicting traffic patterns. Hosted by Pardis Sabeti, this series walks students through understanding how statistics are used in everyday life.
Subject: Mathematics (9 - 12)
Title: Algebra I Module 2, Topic A: Shapes and Centers of Distributions
URL: https://www.engageny.org/resource/algebra-i-module-2-topic-overview
Description:
In Module 2, Topic A, students observe and describe data distributions. They reconnect with their earlier study of distributions in Grade 6 by calculating measures of center and describing overall patterns or shapes. Students deepen their understanding of data distributions recognizing that the value of the mean and median are different for skewed distributions and similar for symmetrical distributions. Students select a measure of center based on the distribution shape to appropriately describe a typical value for the data distribution. Topic A moves from the general descriptions used in Grade 6 to more specific descriptions of the shape and the center of data distribution.
Subject: Mathematics (9 - 12)
Title: Algebra I Module 2, Topic B: Describing Variability and Comparing Distributions
URL: https://www.engageny.org/resource/algebra-i-module-2-topic-b-overview
Description:
In Module 2, Topic B, students reconnect with methods for describing variability first seen in Grade 6. Topic B deepens students’ understanding of measures of variability by connecting a measure of the center of the data distribution to an appropriate measure of variability. The mean is used as a measure of center when the distribution is more symmetrical. Students calculate and interpret the mean absolute deviation and the standard deviation to describe variability for data distributions that are approximately symmetric. The median is used as a measure of center for distributions that are more skewed, and students interpret the interquartile range as a measure of variability for data distributions that are not symmetric. Students match histograms to box plots for various distributions based on an understanding of center and variability. Students describe data distributions in terms of shape, a measure of center, and a measure of variability from the center.
ALEX Classroom Resources: 8 | 1,306 | 6,253 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2022-21 | latest | en | 0.851 |
https://www.coursehero.com/file/7857040/D-We-have-I-X-X-H-X-H-X-X-/ | 1,493,472,943,000,000,000 | text/html | crawl-data/CC-MAIN-2017-17/segments/1492917123491.79/warc/CC-MAIN-20170423031203-00597-ip-10-145-167-34.ec2.internal.warc.gz | 859,030,647 | 22,865 | # D we have i x x h x h x x
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Unformatted text preview: ” X = 1 ˆ = Pr X = “?” . Hence, finding the rate distortion function consists of minimizing the mutual information under ˆ the constraint Pr X = “?” ≤ D . We have ˆ ˆ I (X ; X ) = H (X ) − H (X |X ) ˆ ˆ ˆ ˆ ˆ ˆ = 1 − Pr X = 0 H (X |X = 0) + Pr X = 1 H (X |X = 1) + Pr X = “?” H (X |X = “?”) =0 =0 ≤D ≤1 ≥ 1 − D · 1, where the last inequality is met with equality if PX |X (ˆ|x) = x ˆ 1 − D if x = x ˆ D if x = “?”. ˆ A simple coding scheme would be as follows. The encoder describes only the first (1 − D )n bits of X n . The decoder then pads the remaining D n p ositions with the erasure symbol. Rate Distortion Function with Infinite Distortion Problem 3 First, we note that for the computation of the rate distortion function we only need to consider ˆ D ∈ [0, 1/2], since for rate R = 0 we can achieve the distortion D = 1/2 by having X = 0 with probability 1. Note also that achieving finite distortion requires PX |X (ˆ = 0|x = 1) = 0. Hence, x ˆ ˆ th...
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## This note was uploaded on 05/18/2013 for the course EE Informatio taught by Professor Amoslapidoth during the Fall '11 term at Swiss Federal Institute of Technology Zurich.
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https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Inversion-of-matrix-of-dimension-greater-than-2-15-5/m-p/802338 | 1,685,505,532,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224646257.46/warc/CC-MAIN-20230531022541-20230531052541-00363.warc.gz | 204,273,138 | 47,982 | Intel® oneAPI Math Kernel Library
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## Inversion of matrix of dimension greater than 2^15.5
Beginner
361 Views
Hi, MKL matrix inversions are based on LAPACK and store matrices in vectors. Their dimension is thus limited by the integer size, namely sqrt(2^31). Is it possible to inverse a matrix greater than that?
PS. in animal breeding, large covariance matrix inversion is often used. Before, we are using the relationship expectation and its inversion has an O(n) algorithm. Now we are using realized relationship due to the advances of molecular genetics. Then we have to inverse such matrices with brute force.
At the moment, matirx dim=40k, dgetrf+dgetri take about 560min user time on Intel x5550. This is acceptable, so is their accuracy. If using dpotrf+dpotri, the time can be further reduced to 275 min.
13 Replies
Beginner
361 Views
Anyhow, using block matrix inversion can circumvent this. But a one step function is preferred.
Valued Contributor II
361 Views
I've checked IPP's Matrix Processing API:
- There are lots of functions to calculate a matrix inverse, like:
IppStatus ippmInvert_m_32f(
...
Ipp32u widthHeight,
... );
- A declaration for 'Ipp32u', is as follows:
typedef unsigned int Ipp32u;
- A max value for 'unsigned int' is as follows:
0xFFFFFFFF(base16) = 4294967295(Base10) = ((2^32) - 1)(Base10)
- And, there is another declaration:
#define IPP_MAX_32U ( 0xFFFFFFFF )
- A maximum size of a matrix could be 4294967295 x 4294967295
Moderator
361 Views
one note should be added specifically for IPP vector math function implementation - all of these functions are highly optimized for 2x2, 3x3... 6x6 matrixes. So, execution the ippmInvertr_m_32f function for the big inputs will take very long time...
Beginner
361 Views
Intel MKL uses instead of int variable MKL_INT. For MKL ILP64 integer type is MKL_INT64.
Beginner
361 Views
>PS. in animal breeding, large covariance matrix inversion is often used. Before, we are using the relationship expectation and its >inversion has an O(n) algorithm. Now we are using realized relationship due to the advances of molecular genetics. Then we have >to inverse such matrices with brute force.
Is the matrix sparse and symmetric?
Olaf
Black Belt
361 Views
> Is the matrix sparse and symmetric?
It is symmetric since multiplication is commutative. Often, elements that should be zero show up with small non-zero values because of noise in the data from which the covariance matrix is computed.
Beginner
361 Views
>It is symmetric since multiplication is commutative. Often, elements that should be zero show up with small non-zero values >because of noise in the data from which the covariance matrix is computed.
If it is symmtric and sparse you might use other options than the LAPACK routines. We are computing diagonal elements of the inverse in A in an animal breeding applications with millions of equations. Send me an email and we can discuss it offline.
olaf.schenk@unibas.ch
Beginner
361 Views
With the realized relationship, the matrix is not sparse, all values are in [0, 1]. But the matrix is symmetric. The matrix dimension is acturally the number of ID in a population, ie number of animals/plant individuals. So relationship between ID A & B is same to relationship of B&A.
I also realized that large matrix needs really `super' computers, e.g., even using half storage, 1M id need 3.7T memory.
Beginner
361 Views
You read my message? There it is written that you can work with matrixes of dimension greater than 2^15.5 on one computer, using Intel MKL.
Beginner
361 Views
I wrote a sample program as below
```[cpp]#include
#include
using namespace std;
int main(int argc, char *argv[])
{
MKL_INT c(4294967295), inc(1), i;
double a;
for(i=0; i=.5;
cout< Then I compiled with the following command:icpc -DMKL_ILP64 -mkl t.cppWhen running the binary, I got a segment fault error. My ulimit stack size is 6G. So I think the BLAS core is not ready for int64.```
Beginner
361 Views
MKL_INTc(4294967295) ???
Dynamic selection of storage is necessary.
Beginner
361 Views
Quoting qtl
With the realized relationship, the matrix is not sparse, all values are in [0, 1]. But the matrix is symmetric.
Intel MKL is able to process the symmetric matrixes in the packed form. It saves storage. But these algorithms in Intel MKL are ineffective: http://software.intel.com/en-us/forums/showthread.php?t=76595&o=d&s=lr
Moderator
361 Views | 1,132 | 4,553 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2023-23 | latest | en | 0.818569 |
https://worldwidescience.org/topicpages/r/ratio+star+project.html | 1,521,298,341,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257645177.12/warc/CC-MAIN-20180317135816-20180317155816-00748.warc.gz | 783,269,520 | 273,021 | #### Sample records for ratio star project
1. STAR Follow-Up Studies, 1996-1997: The Student/Teacher Achievement Ratio (STAR) Project.
Pate-Bain, Helen; Boyd-Zaharias, Jayne; Cain, Van A.; Word, Elizabeth; Binkley, M. Edward
The Student/Teacher Achievement Ratio (STAR) Project first investigated the effect of small class size on student achievement with over 6,000 Tennessee primary students in 1985 through 1989. The study found a consistent and significant benefit of small classes for all students, with the greatest advantages for minority, inner-city students from…
2. Interferometric star tracker Project
National Aeronautics and Space Administration — Optical Physics Company (OPC) proposes to develop a high accuracy version of its interferometric star tracker capable of meeting the milli-arcsecond-level pointing...
3. The Mass-Ratio Distribution of Visual Binary Stars
Hogeveen, S.J.
1990-01-01
The selection effects that govern the observations of Visual Binary Stars are in- vestigated, in order to obtain a realistic statistical distribution of the mass-ratio q = Msec=Mprim. To this end a numerical simulation programme has been developed, which generates' binary stars and looks' at
4. A method to deconvolve mass ratio distribution from binary stars
Cure, Michel; Christen, Alejandra; Cassetti, Julia; Boffin, Henri M J
2014-01-01
To better understand the evolution of stars in binary systems as well as to constrain the formation of binary stars, it is important to know the binary mass-ratio distribution. However, in most cases, i.e. for single-lined spectroscopic binaries, the mass ratio cannot be measured directly but only derived as the convolution of a function that depends on the mass ratio and the unknown inclination angle of the orbit on the plane of the sky. We extend our previous method to deconvolve this inverse problem (Cure et al. 2014), i.e., we obtain as an integral the cumulative distribution function (CDF) for the mass ratio distribution. After a suitable transformation of variables it turns out that this problem is the same as the one for rotational velocities $v \\sin i$, allowing a close analytic formulation for the CDF. We then apply our method to two real datasets: a sample of Am stars binary systems, and a sample of massive spectroscopic binaries in the Cyg OB2 Association.} {We are able to reproduce the previous re...
5. The lithium isotopic ratio in very metal-poor stars
Lind, Karin; Asplund, Martin; Collet, Remo; Magic, Zazralt
2013-01-01
Un-evolved, very metal-poor stars are the most important tracers of the cosmic abundance of lithium in the early universe. Combining the standard Big Bang nucleosynthesis model with Galactic production through cosmic ray spallation, these stars at [Fe/H]<-2 are expected to show an undetectably small 6Li/7Li isotopic signature. Evidence to the contrary may necessitate an additional pre-galactic production source or a revision of the standard model of Big Bang nucleosynthesis. We revisit the isotopic analysis of four halo stars, two with claimed 6Li-detections in the literature, to investigate the influence of improved model atmospheres and line formation treatment. For the first time, a combined 3D, NLTE (non-local thermodynamic equilibrium) modelling technique for Li, Na, and Ca lines is utilised to constrain the intrinsic line-broadening and to determine the Li isotopic ratio. We discuss the influence of 3D NLTE effects on line profile shapes and assess the realism of our modelling using the Ca excitation...
6. The carbon-to-oxygen ratio in stars with planets
Nissen, Poul Erik
2013-01-01
In some recent works, the C/O abundance ratio in high-metallicity stars with planets is found to vary from 0.4 to about 1.0. This has led to discussions about the existence of terrestrial planets with a carbon-dominated composition that is very different from the composition of the Earth. The C/O values were obtained by determining carbon abundances from high-excitation CI lines and oxygen abundances from the forbidden [OI] line at 6300 A. This weak line is, however, strongly affected by a nickel blend at high metallicities. Aiming for more precise C/O ratios, oxygen abundances in this paper are derived from the high-excitation OI triplet at 7774 A and carbon abundances from the CI lines at 5052 and 5380 A using MARCS model atmospheres and including non-LTE corrections. The results do not confirm the high C/O ratios previously found. C/O shows a tight, slightly increasing dependence on metallicity from C/O=0.58 at [Fe/H]=0.0 to C/O=0.70 at [Fe/H] =0.4 with an rms scatter of only 0.06. Assuming that the compos...
7. The Polaris Project / NorthStar implementation
Willson, L. A.; Bennett, D. H.; Engelhaupt, T.
2001-12-01
The advent of the World Wide Web opens new opportunities for education; it also changes the environment within which we teach. As Marshall McLuhan said many years ago: "The medium is the message". What kind of medium is the Web, and how is it best harnessed for use in astronomy education? We are developing a sequence of one-credit web-based courses covering basic astronomical topics as a means of exploring what the web can and cannot do. Our first course, NorthStar, deals with coordinates, sky motions, and navigation by the stars. It has been through "beta testing" and is being offered as an experimental course for spring. Our second course, EveningStar, is under development. The course materials are open and may be used as a supplement to any course, or for independent study; the homework, discussion group, and other human-intervention features require a student to register for the course. We invite people to make use of our open materials and, in exchange, to provide us with feedback about how well it works. We acknowledge support for this project from NASA (NAG 58465) and the Department of Physics and Astronomy, Iowa State University.
8. The MiMeS project: magnetism in massive stars
G.A. Wade; E. Alecian; D.A. Bohlender; J.C. Bouret; J.H. Grunhut; H. Henrichs; C. Neiner; V. Petit; N. St. Louis; M. Aurière; O. Kochukhov; J. Silvester; A. ud-Doula
2008-01-01
The Magnetism in Massive Stars (MiMeS) Project is a consensus collaboration among the foremost international researchers of the physics of hot, massive stars, with the basic aim of understanding the origin, evolution and impact of magnetic fields in these objects. The cornerstone of the project is t
9. The low Sr/Ba ratio on some extremely metal-poor stars
Spite, M; Bonifacio, P; Caffau, E; François, P; Sbordone, L
2014-01-01
It has been noted that, in classical extremely metal-poor (EMP) stars, the abundance ratio of Sr and Ba, is always higher than [Sr/Ba] = -0.5, the value of the solar r-only process; however, a handful of EMP stars have recently been found with a very low Sr/Ba ratio. We try to understand the origin of this anomaly by comparing the abundance pattern of the elements in these stars and in the classical EMP stars. Four stars with very low Sr/Ba ratios were observed and analyzed within LTE approximation through 1D (hydrostatic) model atmosphere, providing homogeneous abundances of nine neutron-capture elements. In CS 22950-173, the only turnoff star of the sample, the Sr/Ba ratio is, in fact, found to be higher than the r-only solar ratio, so the star is discarded. The remaining stars (CS 29493-090, CS 30322-023, HE 305-4520) are cool evolved giants. They do not present a clear carbon enrichment. The abundance patterns of the neutron-capture elements in the three stars are strikingly similar to a theoretical s-pro...
10. A Review of Research on Project STAR and Path Ahead
Sohn, Kitae
2016-01-01
Understanding the effects of class size reduction (CSR) has been an enduring issue in education. For the past 3 decades, Project STAR has stimulated research and policy discussions regarding the effects of CSR on a variety of outcomes. Schanzenbach (2007) reviewed STAR studies and concluded that small classes improved student academic outcomes.…
11. The puzzle of the CNO isotope ratios in asymptotic giant branch carbon stars
Abia, C.; Hedrosa, R. P.; Domínguez, I.; Straniero, O.
2017-02-01
Context. The abundance ratios of the main isotopes of carbon, nitrogen and oxygen are modified by the CNO-cycle in the stellar interiors. When the different dredge-up events mix the burning material with the envelope, valuable information on the nucleosynthesis and mixing processes can be extracted by measuring these isotope ratios. Aims: Previous determinations of the oxygen isotopic ratios in asymptotic giant branch (AGB) carbon stars were at odds with the existing theoretical predictions. We aim to redetermine the oxygen ratios in these stars using new spectral analysis tools and further develop discussions on the carbon and nitrogen isotopic ratios in order to elucidate this problem. Methods: Oxygen isotopic ratios were derived from spectra in the K-band in a sample of galactic AGB carbon stars of different spectral types and near solar metallicity. Synthetic spectra calculated in local thermodynamic equillibrium (LTE) with spherical carbon-rich atmosphere models and updated molecular line lists were used. The CNO isotope ratios derived in a homogeneous way, were compared with theoretical predictions for low-mass (1.5-3 M⊙) AGB stars computed with the FUNS code assuming extra mixing both during the RGB and AGB phases. Results: For most of the stars the 16O/17O/18O ratios derived are in good agreement with theoretical predictions confirming that, for AGB stars, are established using the values reached after the first dredge-up (FDU) according to the initial stellar mass. This fact, as far as the oxygen isotopic ratios are concerned, leaves little space for the operation of any extra mixing mechanism during the AGB phase. Nevertheless, for a few stars with large 16O/17O/18O, the operation of such a mechanism might be required, although their observed 12C/13C and 14N/15N ratios would be difficult to reconcile within this scenario. Furthermore, J-type stars tend to have lower 16O/17O ratios than the normal carbon stars, as already indicated in previous studies
12. The puzzle of the CNO isotope ratios in AGB carbon stars
Abia, Carlos; Domínguez, Inma; Straniero, Oscar
2016-01-01
Previous determinations of the oxygen isotopic ratios in AGB carbon stars were at odds with the existing theoretical predictions. We aim to redetermine the oxygen ratios in these stars using new spectral analysis tools and further develop discussions on the carbon and nitrogen isotopic ratios in order to elucidate this problem. Oxygen isotopic ratios were derived from spectra in the K-band in a sample of galactic AGB carbon stars of different spectral types and near solar metallicity. Synthetic spectra calculated in LTE with spherical carbon-rich atmosphere models and updated molecular line lists were used. The CNO isotope ratios derived in a homogeneous way, were compared with theoretical predictions for low-mass (1.5-3 M_o) AGB stars computed with the FUNS code assuming extra mixing both during the RGB and AGB phases. For most of the stars the 16O/17O/18O ratios derived are in good agreement with theoretical predictions confirming that, for AGB stars, are established using the values reached after the FDU a...
13. Square root two period ratios in Cepheid and RR Lyrae variable stars
Hippke, Michael; Zee, A
2014-01-01
We document the presence of nine Cepheid and RR Lyrae variable stars with previously unrecognized characteristics. These stars exhibit the statistically unlikely property of a period ratio of main pulsation divided by secondary pulsation (P1/P2) very close to sqrt(2). Other stars of these types have period ratios which show clustering not with a close association with a single remarkable and nonharmonic number. In the way of explanation, we suggest that this indicates a previously unknown resonance of pulsations. Close examination reveals a deviation of multiples of a few times 0.06% for these stars. This deviation seems to be present in discrete steps on the order of about 0.000388(5), indicating the possible presence of a sort of fine structure in this oscillation. Physical explanation of the source of these regularities remains for 3D simulations of variable stars, and we only claim to make note of the regularities which are suggestive of physical principles.
14. The GTC Variable Star One-Shot Project
García-Alvarez, D.; Cabrera-Lavers, A.; Alvarez-Iglesias, C. A.; Gómez-Velarde, G.; González-Pérez, J. M.; Reverte-Payá, D.; Scarpa, R.; Rutten, R.; Fernández-Acosta, S.; García-Rodríguez, A. M.; VSOP Team
2013-05-01
Stellar variability types are assigned on the basis of lightcurve appearance, which often remains unchallenged without further observational evidence. VSOP (Variable Star One-shot Project) is a large international collaboration, which has so far obtained spectra of more than 1200 stars during the past few years using ESO facilities. Operationally this program is perfectly suited for a modern and efficient observatory, providing GTC with a large pool of filler observations. Scientifically, our aims are: (1) obtain first spectroscopy of all unstudied variable stars suitable for GTC, (2) provide data products to the public in a fast and automatic way, and (3) generate an influx of serendipitous discoveries across all fields of astrophysics.
Johnson, Kimberly A.; Frank, Margaret M.
2012-01-01
This paper reports on findings and implications from a two-year evaluation of the Minnesota STudent Achievement in Reading (STAR) Project. This long-term, job-embedded, professional development activity is provided for Minnesota Adult Basic Education (ABE) practitioners serving intermediate-level adult students reading between 4.0 to 8.9 grade…
16. Mg isotope ratios in giant stars of the globular clusters M 13 and M 71
Yong, D; Lambert, D L; Yong, David; Aoki, Wako; Lambert, David L.
2006-01-01
We present Mg isotope ratios in 4 red giants of the globular cluster M 13 and 1 red giant of the globular cluster M 71 based on spectra obtained with HDS on the Subaru Telescope. We confirm earlier results by Shetrone that for M 13, the ratio varies from (25+26)Mg/24Mg = 1 in stars with the highest Al abundance to (25+26)Mg/24Mg = 0.2 in stars with the lowest Al abundance. However, we separate the contributions of all three isotopes and find a spread in the ratio 24Mg:25Mg:26Mg with values ranging from 48:13:39 to 78:11:11. As in NGC 6752, we find a positive correlation between 26Mg and Al, an anticorrelation between 24Mg and Al, and no correlation between 25Mg and Al. In M 71, our one star has a ratio 70:13:17. For both clusters, the lowest ratios of 25Mg/24Mg and 26Mg/24Mg exceed those observed in field stars at the same metallicity, a result also found in NGC 6752. The contribution of 25Mg to the total Mg abundance is constant within a given cluster and between clusters with 25Mg/(24+25+26)Mg = 0.13. For M...
17. C/O Ratios of Stars with Transiting Hot Jupiter Exoplanets
Teske, Johanna K; Smith, Verne V; Schuler, Simon C; Griffith, Caitlin A
2014-01-01
The relative abundances of carbon and oxygen have long been recognized as fundamental diagnostics of stellar chemical evolution. Now, the growing number of exoplanet observations enable estimation of these elements in exoplanetary atmospheres. In hot Jupiters, the C/O ratio affects the partitioning of carbon in the major observable molecules, making these elements diagnostic of temperature structure and composition. Here we present measurements of carbon and oxygen abundances in 16 stars that host transiting hot Jupiter exoplanets, and compare our C/O ratios to those measured in larger samples of host stars, as well as those estimated for the corresponding exoplanet atmospheres. With standard stellar abundance analysis we derive stellar parameters as well as [C/H] and [O/H] from multiple abundance indicators, including synthesis fitting of the [O I] 6300 {\\AA} line and NLTE corrections for the O I triplet. Our results, in agreement with recent suggestions, indicate that previously-measured exoplanet host star...
18. Galactic and Extragalactic Distance Scales: The Variable Star Project
Feast, Michael W
2008-01-01
This paper summaries the status of a large project to improve distance scales of various classes of variable stars. This is being carried out by a large group in Cape Town, Japan, England and the USA. The results are illustrated by giving the distances of the Large Magellanic Cloud and the Galactic Centre (Ro) as well as the value of the Hubble Constant, Ho, based on our current results. The classes of variables considered are; Classical Cepheids, Type II Cepheids, RR Lyrae stars, O- and C-Miras
19. AGB stars in the Magellanic Clouds. I. The C/M ratio
Habing, H J
2003-01-01
Regions of different metallicity have been identified in the Magellanic Clouds by using the ratio between Asymptotic Giant Branch stars of spectral type C and M. In the Large Magellanic Cloud the ratio appears to decrease radially while in the Small Magellanic Cloud (SMC) there is no clear trend, reflecting either the large extension of the SMC along the line of sight or a more complex star formation history. The distribution of the C/M ratio is clumpy and corresponds to a spread in [Fe/H] of 0.75 dex in both Clouds. There is an indication of increasing C/M ratio, thus decreasing metallicity, towards the Bridge region connecting the two Clouds.
20. Discovery of Seven Companions to Intermediate Mass Stars with Extreme Mass Ratios in the Scorpius-Centaurus Association
Hinkley, Sasha; Ireland, Michael J; Cheetham, Anthony; Carpenter, John M; Tuthill, Peter; Lacour, Sylvestre; Evans, Thomas M; Haubois, Xavier
2015-01-01
We report the detection of seven low mass companions to intermediate-mass stars (SpT B/A/F; $M$$\\approx1.5-4.5 solar masses) in the Scorpius-Centaurus Association using nonredundant aperture masking interferometry. Our newly detected objects have contrasts \\Delta L'$$\\approx$4-6, corresponding to masses as low as $\\sim$20 Jupiter masses and mass ratios of $q$$\\approx0.01-0.08, depending on the assumed age of the target stars. With projected separations \\rho$$\\approx$10-30 AU, our aperture masking detections sample an orbital region previously unprobed by conventional adaptive optics imaging of intermediate mass Scorpius-Centaurus stars covering much larger orbital radii ($\\approx$30-3000 AU). At such orbital separations, these objects resemble higher mass versions of the directly imaged planetary mass companions to the 10-30 Myr, intermediate-mass stars HR 8799, $\\beta$ Pictoris, and HD95086. These newly discovered companions span the brown dwarf desert, and their masses and orbital radii provide a new co...
1. THE HCN/HNC ABUNDANCE RATIO TOWARD DIFFERENT EVOLUTIONARY PHASES OF MASSIVE STAR FORMATION
Jin, Mihwa; Lee, Jeong-Eun [School of Space Research, Kyung Hee University, Yongin-Si, Gyeonggi-Do 446-701 (Korea, Republic of); Kim, Kee-Tae, E-mail: mihwajin.sf@gmail.com, E-mail: jeongeun.lee@khu.ac.kr, E-mail: ktkim@kasi.re.kr [Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 305-348 (Korea, Republic of)
2015-07-20
Using the H{sup 13}CN and HN{sup 13}C J = 1–0 line observations, the abundance ratio of HCN/HNC has been estimated for different evolutionary stages of massive star formation: infrared dark clouds (IRDCs), high-mass protostellar objects (HMPOs), and ultracompact H ii regions (UCH iis). IRDCs were divided into “quiescent IRDC cores (qIRDCc)” and “active IRDC cores (aIRDCc),” depending on star formation activity. The HCN/HNC ratio is known to be higher at active and high temperature regions related to ongoing star formation, compared to cold and quiescent regions. Our observations toward 8 qIRDCc, 16 aIRDCc, 23 HMPOs, and 31 UCH iis show consistent results; the ratio is 0.97 (±0.10), 2.65 (±0.88), 4.17 (±1.03), and 8.96 (±3.32) in these respective evolutionary stages, increasing from qIRDCc to UCH iis. The change of the HCN/HNC abundance ratio, therefore, seems directly associated with the evolutionary stages of star formation, which have different temperatures. One suggested explanation for this trend is the conversion of HNC to HCN, which occurs effectively at higher temperatures. To test the explanation, we performed a simple chemical model calculation. In order to fit the observed results, the energy barrier of the conversion must be much lower than the value provided by theoretical calculations.
2. The Close Companion Mass-Ratio Distribution of Intermediate-Mass Stars
Gullikson, Kevin; Dodson-Robinson, Sarah
2016-01-01
Binary stars and higher-order multiple systems are an ubiquitous outcome of star formation, especially as the system mass increases. The companion mass-ratio distribution is a unique probe into the conditions of the collapsing cloud core and circumstellar disk(s) of the binary fragments. Inside $a \\sim 1000$ AU the disks from the two forming stars can interact, and additionally companions can form directly through disk fragmentation. We should therefore expect the mass-ratio distribution of close companions ($a \\lesssim 100$ AU) to differ from that of wide companions. This prediction is difficult to test using traditional methods, especially with intermediate-mass primary stars, for a variety of observational reasons. We present the results of a survey searching for companions to A- and B-type stars using the direct spectral detection method, which is sensitive to late-type companions within $\\sim 1"$ of the primary and which has no inner working angle. We estimate the temperatures and surface gravity of most...
3. Harvard Observing Project monitoring of Boyajian's Star (KIC 8462852)
Schumer, Clea F.; Vanderburg, Andrew; Bieryla, Allyson; Carmichael, Theron; Garrison, Lehman H.; Huang, Jane; Lewis, John; Mayo, Andrew; Alam, Munazza; Gomez, Sebastian; Kamdar, Harshil; Yuan, Sihan; Cordova, Rodrigo
2017-01-01
Between 2009 and 2013, the Kepler spacecraft observed ~200,000 stars, repeatedly measuring their brightness to look for regular dimmings that could indicate the presence of a transiting planet (Borucki et al. 2010). This endeavor led to the discovery of thousands of planets. However, the data pertaining to one star, KIC 8462852, nicknamed “Tabby's Star” or “Boyajian's Star" indicated sporadic dimmings thought to be resulting from massive, evolving, and erratic shapes passing in front of the star (Boyajian et al. 2016, Wright and Sigurdsson 2016). Additional observations have indicated that KIC 8462852 has faded by approximately 20% over the past century (Wright and Sigurdsson 2016). Kepler is now observing other areas of space, and consequently, ground-based efforts have emerged in order to continue tracking the brightness of KIC 8462852. The Harvard Observing Project (HOP) is an observational astronomy initiative that engages undergraduate students and provides graduate students with the opportunity to lead sessions of data collection. During the fall 2016 semester, HOP will be observing KIC 8462852 in BVRI filters using Harvard's 16-inch DFM Clay telescope. We will present a light curve of the star spanning the course of three months.
4. The Araucaria Project : the Baade-Wesselink projection factor of pulsating stars
Nardetto, N; Gieren, W; Pietrzynski, G; Poretti, E
2013-01-01
The projection factor used in the Baade-Wesselink methods of determining the distance of Cepheids makes the link between the stellar physics and the cosmological distance scale. A coherent picture of this physical quantity is now provided based on several approaches. We present the lastest news on the expected projection factor for different kinds of pulsating stars in the Hertzsprung-Russell diagram.
5. The C-12/C-13 ratio in stellar atmospheres. VI - Five luminous cool stars
Hinkle, K. H.; Lambert, D. L.; Snell, R. L.
1976-01-01
A simple curve-of-growth technique is described for extracting the C-12/C-13 ratio for M stars from high-resolution spectra of CO infrared vibration-rotation lines. The technique is applied to the CO lines at 1.6 and 2.3 microns in spectra of two M supergiants (Alpha Ori and Alpha Sco), two M giants (Alpha Her and Beta Peg), and a Mira-type variable (Chi Cyg). As a check on the CO analysis, the C-12/C-13 ratio is derived from the red CN system at 8000 A for Alpha Sco, Alpha Ori, and Beta Peg. The CO analysis is also applied to the K giant Alpha Boo as a check. The CN and CO results are found to be in general agreement, and the C-12/C-13 ratio in all the examined stars is shown to be considerably lower than the solar-system value. It is suggested that these stars were formed from clouds with a C-12/C-13 ratio of 40 to 89 and that their atmospheres now exhibit an enhancement of C-13 abundance due to internal production and mixing to the surface.
6. 2008 HI STAR Projects: Comets, Asteroids and Extrasolar Planets
Kadooka, Mary Ann; Garland, C.; Nassir, M.; Moskovitz, N.; Johnson, J.; Pittichova, J.; Meech, K. J.
2008-09-01
The Hawaii Student/Teacher Astronomy Research (HI STAR) residential summer program strives to equip middle and high school students with the necessary research skills and background to conduct original research projects. Students are recruited through the mini-workshops conducted on the islands of Molokai, Maui, Kauai and Oahu. For one week in June, the students with a few teachers thrive on morning physics/astronomy lectures and afternoon image processing and photometry/light curve activities. They work in groups with astronomer mentors on comet, asteroid, galaxy, nebulae, variable star and extrasolar planet projects using image data sets. They also learn to do remote observing with 2 meter Faulkes Telescope on Haleakala Maui and 16 inch DeKalb Observatory Telescope in Auburn, Indiana. The asteroid, comet and extrasolar planet projects will be highlighted with slides taken from the students’ presentations on what they had accomplished. We will also discuss how these projects are being expanded upon for fall, 2008, to be ready for 2009 Science Fair entry. This network of roles and responsibilities of our astronomer mentors, teacher advisers and student participants has been developing to ensure exemplary astronomy research projects. Funding and support for this program has come from NASA IDEAS grant, NASA Astrobiology Institute, Las Cumbres Observatory Global Telescope, DeKalb Observatory, and a private donor.
7. Benchmarking the External Surrogate Ratio Method using the (alpha,alpha' f) reaction at STARS
Lesher, S R; Bernstein, L A; Ai, H; Beausang, C W; Bleuel, D; Burke, J T; Clark, R M; Fallon, P; Gibelin, J; Lee, I Y; Lyles, B F; Macchiavelli, A O; McMahan, M A; Moody, K J; Norman, E B; Phair, L; Rodriguez-Vieitez, E; Wiedeking, M
2008-01-09
We measured the ratio of the fission probabilities of {sup 234}U* relative to {sup 236}U* formed via an ({alpha},{alpha}{prime}) direct reactions using the STARS array at the 88-inch cyclotron at the Lawrence Berkeley National Laboratory. This ratio has a shape similar to the ratio of neutron capture probabilities from {sup 233}U(n; f) and {sup 235}U(n; f), indicating the alpha reactions likely formed a compound nucleus. This result indicates that the ratios of fission exit channel probabilities for two actinide nuclei populated via ({alpha}, {alpha}{prime}) can be used to determine an unknown fission cross section relative to a known one. The validity of the External Surrogate Ratio Method (ESRM) is tested and the results support the conclusions of Burke et al. [1].
8. The MACHO Project Sample of Galactic Bulge High-Amplitude Scuti Stars: Pulsation Behavior and Stellar Properties
Bennett, D.P.; Cook, K.H.; Freeman, K.C.; Geha, M.; Griest, K.; Lehner, M.J.; Marshall, S.L.; McNamara, B.J.; Minniti, D.; Nelson, C.; Peterson, B.A.; Popowski, P.; Pratt, M.R.; Quinn, P.J.; Rodgers, A.W.; Sutherland, W.; Templeton, M.R.; Vandehei, T.; Welch, D.L.
1999-11-16
We have detected 90 objects with periods and lightcurve structure similar to those of field {delta} Scuti stars, using the Massive Compact Halo Object (MACHO) Project database of Galactic bulge photometry. If we assume similar extinction values for all candidates and absolute magnitudes similar to those of other field high-amplitude {delta} Scuti stars (HADS), the majority of these objects lie in or near the Galactic bulge. At least two of these objects are likely foreground {delta} Scuti stars, one of which may be an evolved nonradial pulsator, similar to other evolved, disk-population {delta} Scuti stars. We have analyzed the light curves of these objects and find that they are similar to the light curves of field {delta} Scuti stars and the {delta} Scuti stars found by the Optical Gravitational Lens Experiment (OGLE). However, the amplitude distribution of these sources lies between those of low- and high-amplitude {delta} Scuti stars, which suggests that they may be an intermediate population. We have found nine double-mode HADS with frequency ratios ranging from 0.75 to 0.79, four probable double- and multiple-mode objects, and another four objects with marginal detections of secondary modes. The low frequencies (5-14 cycles d{sup -1}) and the observed period ratios of {approx}0.77 suggest that the majority of these objects are evolved stars pulsating in fundamental or first overtone radial modes.
9. Golden Ratio Sinusoidal Sequences and the Multimode Pulsation of the δ Sct Star V784 Cassiopeiae
Juan García Escudero
2004-01-01
Non periodic ordered sequences obtained by production rules in formal grammars are applied to the analysis of the multi-periodicity of the δ-Scuti type variable star V784 Cas.An artificial light curve for V784 Cas is generated by a non deterministic derivation in a context-sensitive grammar by concatenation of two sinusoidal fragments following certain word sequences.The two basic building blocks represent temporal segments in a golden ratio and the number of long and short segments in a word are also in a golden ratio.
10. PROJECT ICARUS: Son of Daedalus, Flying Closer to Another Star
Long, K F; Tziolas, A C; Mann, A; Osborne, R; Presby, A; Fogg, M
2010-01-01
During the 1970s members of the British Interplanetary Society embarked on a landmark theoretical engineering design study to send a probe to Barnard's star. Project Daedalus was a two-stage vehicle employing electron beam driven inertial confinement fusion engines to reach its target destination. This paper sets out the proposal for a successor interstellar design study called Project Icarus. This is an attempt to redesign the Daedalus vehicle with similar terms of reference. The aim of this study is to evolve an improved engineering design and move us closer to achieving interstellar exploration. Although this paper does not discuss prematurely what design modification are likely to occur some indications are given from the nature of the discussions. This paper is a submission of the Project Icarus Study Group.
11. THE ORIGIN OF LOW [α/Fe] RATIOS IN EXTREMELY METAL-POOR STARS
Kobayashi, Chiaki [School of Physics, Astronomy and Mathematics, Centre for Astrophysics Research, University of Hertfordshire, College Lane, Hatfield AL10 9AB (United Kingdom); Ishigaki, Miho N.; Tominaga, Nozomu; Nomoto, Ken' ichi, E-mail: c.kobayashi@herts.ac.uk [Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba 277-8583 (Japan)
2014-04-10
We show that the low ratios of α elements (Mg, Si, and Ca) to Fe recently found for a small fraction of extremely metal-poor stars can be naturally explained with the nucleosynthesis yields of core-collapse supernovae, i.e., 13-25 M {sub ☉} supernovae, or hypernovae. For the case without carbon enhancement, the ejected iron mass is normal, consistent with observed light curves and spectra of nearby supernovae. On the other hand, the carbon enhancement requires much smaller iron production, and the low [α/Fe] of carbon-enhanced metal-poor stars can also be reproduced with 13-25 M {sub ☉} faint supernovae or faint hypernovae. Iron-peak element abundances, in particular Zn abundances, are important to put further constraints on the enrichment sources from galactic archaeology surveys.
12. Nucleosynthesis in AGB stars traced by isotopic ratios. I - Determining the stellar initial mass by means of the $^{17}$O/$^{18}$O ratio
De Nutte, R; Olofsson, H; Lombaert, R; de Koter, A; Karakas, A; Milam, S; Ramstedt, S; Stancliffe, R J; Homan, W; Van de Sande, M
2016-01-01
The aim of this paper is to investigate the $^{17}$O/$^{18}$O ratio for a sample of AGB stars, containing M-, S- and C-type stars. These ratios are evaluated in relation to fundamental stellar evolution parameters: the stellar initial mass and pulsation period. This study is the first to explore these oxygen ratios for a sample covering the three spectral types. Circumstellar $^{13}$C$^{16}$O, $^{12}$C$^{17}$O and $^{12}$C$^{18}$O line observations were obtained for a sample of nine stars with various single-dish long-wavelength facilities. These data have been fully reduced and analyzed. The line intensity ratios obtained from these observations are then related directly to the surface $^{17}$O/$^{18}$O abundance ratio. Stellar evolution models predict the $^{17}$O/$^{18}$O ratio to be a sensitive function of initial mass and to remain constant throughout the entire TP-AGB phase for stars less massive than 5 M$_{\\odot}$. This allows the measured ratio to function as an effective method of determining the ini...
13. C/O and Mg/Si Ratios of Stars in the Solar Neighborhood
Brewer, John M
2016-01-01
The carbon to oxygen ratio in a protoplanetary disk can have a dramatic influence on the compositions of any terrestrial planets formed. In regions of high C/O, planets form primarily from carbonates and in regions of low C/O, the ratio of magnesium to silicon determines the types of silicates which dominate the compositions. We present C/O and Mg/Si ratios for 849 F, G, and K dwarfs in the solar neighborhood. We find that the frequency of carbon-rich dwarfs in the solar neighborhood is < 0.13% and that 156 known planet hosts in the sample follow a similar distribution as all of the stars as a whole. The cosmic distribution of Mg/Si for these same stars is broader than the C/O distribution and peaks near 1.0 with $\\sim 60$% of systems having $1 \\leq$ Mg/Si $< 2$, leading to rocky planet compositions similar to the Earth. This leaves 40% of systems that can have planets that are silicate rich and may have very different compositions than our own.
14. Gas-to-dust ratio in massive star-forming galaxies at z~1.4
Seko, Akifumi; Yabe, Kiyoto; Hatsukade, Bunyo; Aono, Yuya; Iono, Daisuke
2016-01-01
We present results of 12CO(J=2-1) observations toward four massive star-forming galaxies at z~1.4 with the Nobeyama 45~m radio telescope. The galaxies are detected with Spitzer/MIPS in 24 um, Herschel/SPIRE in 250 um, and 350 um and they mostly reside in the main sequence. Their gas-phase metallicities derived with N2 method by using the Ha and [NII]6584 emission lines are near the solar value. CO lines are detected toward three galaxies. The molecular gas masses obtained are (9.6-35) x 10^{10} Msun by adopting the Galactic CO-to-H2 conversion factor and the CO(2-1)/CO(1-0) flux ratio of 3. The dust masses derived with the modified blackbody model (assuming the dust temperature of 35 K and the emissivity index of 1.5) are (2.4-5.4) x 10^{8} Msun. The resulting gas-to-dust ratios (not accounting for HI mass) at z~1.4 are 220-1450, which are several times larger than those in local star-forming galaxies. A dependence of the gas-to-dust ratio on the far-infrared luminosity density is not clearly seen.
15. H{\\alpha} to FUV ratios in resolved star forming region populations of nearby spiral galaxies
Hermanowicz, Maciej T; Eldridge, John J
2013-01-01
We present a new study of H{\\alpha}/FUV flux ratios of star forming regions within a sample of nearby spiral galaxies. We search for evidence of the existence of a cluster mass dependent truncation in the underlying stellar initial mass function (IMF). We use an automated approach to identification of extended objects based on the SExtractor algorithm to catalogue resolved Hii regions within a set of nearby spiral galaxies. Corrections due to dust attenuation effects are applied to avoid artificially boosted H{\\alpha}/FUV values. We use the BPASS stellar population synthesis code of Eldridge & Stanway (2009) to create a benchmark population of star forming regions to act as a reference for our observations. Based on those models, we identify a zone of parameter space populated by regions that cannot be obtained with a cluster mass dependent truncation in the stellar IMF imposed. We find that the investigated galaxies display small subpopulations of star forming regions falling within our zone of interest,...
16. Interferometric Observations of High-Mass Star-Forming Clumps with Unusual N2H+/HCO+ Line Ratios
Stephens, Ian W; Sanhueza, Patricio; Whitaker, J Scott; Hoq, Sadia; Rathborne, Jill M; Foster, Jonathan B
2015-01-01
The Millimetre Astronomy Legacy Team 90 GHz (MALT90) survey has detected high-mass star-forming clumps with anomalous N$_2$H$^+$/HCO$^+$(1-0) integrated intensity ratios that are either unusually high ("N$_2$H$^+$ rich") or unusually low ("N$_2$H$^+$ poor"). With 3 mm observations from the Australia Telescope Compact Array (ATCA), we imaged two N$_2$H$^+$ rich clumps, G333.234-00.061 and G345.144-00.216, and two N$_2$H$^+$ poor clumps, G351.409+00.567 and G353.229+00.672. In these clumps, the N$_2$H$^+$ rich anomalies arise from extreme self-absorption of the HCO$^+$ line. G333.234-00.061 contains two of the most massive protostellar cores known with diameters of less than 0.1 pc, separated by a projected distance of only 0.12 pc. Unexpectedly, the higher mass core appears to be at an earlier evolutionary stage than the lower mass core, which may suggest that two different epochs of high-mass star formation can occur in close proximity. Through careful analysis of the ATCA observations and MALT90 clumps (incl...
17. Molecular gas, stars, and dust in sub-L* star-forming galaxies at z~2: evidence for universal star formation and nonuniversal dust-to-gas ratio
Dessauges-Zavadsky, Miroslava; Schaerer, Daniel; Combes, Francoise; Egami, Eiichi; Swinbank, A. Mark; Richard, Johan; Sklias, Panos; Rawle, Tim D.
2015-08-01
Only recently have CO measurements become possible in main sequence star-forming galaxies (SFGs) at z=1-3, but are still biased toward high star formation rates (SFR) and stellar masses (Ms), because of instrumental sensitivity limitations. It is essential to extend these studies toward the more numerous and typical SFGs, characterized by IR luminosities LIRstar, and dust properties in 8 such sub-L*, lensed SFGs at z=1.5-3.6, achieved thanks to the gravitational lensing and IRAM/PdBI, Herschel, Spitzer, and HST multi-wavelength data. Combined with our compilation of CO-detected galaxies from the literature, we revisit and propose new correlations between IR and CO luminosities, molecular gas, stellar and dust masses, specific SFR, molecular gas depletion timescales (tdepl), molecular gas fractions (fgas), dust-to-gas ratios, and redshift. These correlations betray the interplay between gas, dust, and star formation in galaxies.All the LIR, L'CO(1-0) data are best-fitted with a single relation, which spans 5 orders of magnitude in LIR, covers redshifts from z=0 to z=5.3, and samples spirals, main sequence SFGs, and starbursts. This favors a universal star formation. We find an increase of tdepl with Ms, as now revealed by low-Ms SFGs at z>1 and also observed at z=0, which contrasts with the acknowledged constant tdepl and refutes the linearity of the Kennicutt-Schmidt relation between molecular gas and SFR at galactic scales. A steady increase of fgas with redshift is predicted and is observed from z~0 to z~1.5, but is followed by a mild increase toward higher redshifts, which we further confirm with our highest redshift CO measurement in an L* galaxy at z=3.6. We provide the first fgas measure in z>1 SFGs at the low-Ms end 109.4ratio among high-redshift SFGs, high-redshift SMGs, local spirals, and local ULIRGs
18. Gravitational waves and mass ejecta from binary neutron star mergers: Effect of the mass ratio
Dietrich, Tim; Ujevic, Maximiliano; Tichy, Wolfgang; Bernuzzi, Sebastiano; Brügmann, Bernd
2017-01-01
We present new (3 +1 )D numerical relativity simulations of the binary neutron star (BNS) merger and postmerger phase. We focus on a previously inaccessible region of the binary parameter space spanning the binary's mass ratio q ˜1.00 - 1.75 for different total masses and equations of state, and up to q ˜2 for a stiff BNS system. We study the mass ratio effect on the gravitational waves (GWs) and on the possible electromagnetic (EM) emission associated with dynamical mass ejecta. We compute waveforms, spectra, and spectrograms of the GW strain including all the multipoles up to l =4 . The mass ratio has a specific imprint on the GW multipoles in the late-inspiral-merger signal, and it affects qualitatively the spectra of the merger remnant. The multipole effect is also studied by considering the dependency of the GW spectrograms on the source's sky location. Unequal mass BNSs produce more ejecta than equal mass systems with ejecta masses and kinetic energies depending almost linearly on q . We estimate luminosity peaks and light curves of macronova events associated with the mergers using a simple approach. For q ˜2 the luminosity peak is delayed for several days and can be up to 4 times larger than for the q =1 cases. The macronova emission associated with the q ˜2 BNS is more persistent in time and could be observed for weeks instead of a few days (q =1 ) in the near infrared. Finally, we estimate the flux of possible radio flares produced by the interaction of relativistic outflows with the surrounding medium. Also in this case a large q can significantly enhance the emission and delay the peak luminosity. Overall, our results indicate that the BNS merger with a large mass ratio has EM signatures distinct from the equal mass case and more similar to black hole-neutron star binaries.
19. Variations in H2O+/H2O ratios toward massive star-forming regions
Wyrowski, F; Herpin, F; Baudry, A; Bontemps, S; Chavarria, L; Frieswijk, W; Jacq, T; Marseille, M; Shipman, R; van Dishoeck, E F; Benz, A O; Caselli, P; Hogerheijde, M R; Johnstone, D; Liseau, R; Bachiller, R; Benedettini, M; Bergin, E; Bjerkeli, P; Blake, G; Braine, J; Bruderer, S; Cernicharo, J; Codella, C; Daniel, F; di Giorgio, A M; Dominik, C; Doty, S D; Encrenaz, P; Fich, M; Fuente, A; Giannini, T; Goicoechea, J R; de Graauw, Th; Helmich, F; Herczeg, G J; Jørgensen, J K; Kristensen, L E; Larsson, B; Lis, D; McCoey, C; Melnick, G; Nisini, B; Olberg, M; Parise, B; Pearson, J C; Plume, R; Risacher, C; Santiago, J; Saraceno, P; Tafalla, M; van Kempen, T A; Visser, R; Wampfler, S; Yıldız, U A; Black, J H; Falgarone, E; Gerin, M; Roelfsema, P; Dieleman, P; Beintema, D; De Jonge, A; Whyborn, N; Stutzki, J; Ossenkopf, V
2010-01-01
Early results from the Herschel Space Observatory revealed the water cation H2O+ to be an abundant ingredient of the interstellar medium. Here we present new observations of the H2O and H2O+ lines at 1113.3 and 1115.2 GHz using the Herschel Space Observatory toward a sample of high-mass star-forming regions to observationally study the relation between H2O and H2O+ . Nine out of ten sources show absorption from H2O+ in a range of environments: the molecular clumps surrounding the forming and newly formed massive stars, bright high-velocity outflows associated with the massive protostars, and unrelated low-density clouds along the line of sight. Column densities per velocity component of H2 O+ are found in the range of 10^12 to a few 10^13 cm-2 . The highest N(H2O+) column densities are found in the outflows of the sources. The ratios of H2O+/H2O are determined in a range from 0.01 to a few and are found to differ strongly between the observed environments with much lower ratios in the massive (proto)cluster e...
20. The MACHO Project LMC Variable Star Inventory; 4, Multimode RR Lyrae Stars, Distance to the LMC and Age of the Oldest Stars
Alcock, C B; Alves, D R; Axelrod, T S; Becker, A C; Bennett, D P; Cook, K H; Freeman, K C; Griest, K; Guern, J A; Lehner, M J; Marshall, S L; Minniti, D; Peterson, B A; Pratt, M R; Quinn, P J; Rodgers, A W; Sutherland, W; Welch, D L
1996-01-01
We report the discovery of 73 double-mode RR Lyrae (RRd) stars in fields near the bar of the LMC. The stars are detected among the MACHO database of short-period variables that currently contains about 7900 RR Lyrae stars. Fundamental periods (P_0) for these stars are found in the range 0.46-0.55 days and first overtone-to-fundamental period ratios are found to be in the range 0.742 < P_1/P_0 < 0.748. A significant fraction of our current sample have period ratios smaller than any previously discovered RRd variables. We present mean magnitudes, colors, and lightcurve properties for all LMC RRd stars detected to date. The range in period ratios is unexpectedly large. We present a determination of absolute magnitudes for these stars based primarily on pulsation theory and the assumption that all observed stars are at the fundamental blue edge (FBE) of the instability strip. Comparison of the calibrated MACHO V and R_KC photometry with these derived absolute magnitudes yields an absorption-corrected distan...
1. Gravitational waves and mass ejecta from binary neutron star mergers: Effect of the mass-ratio
Dietrich, Tim; Tichy, Wolfgang; Bernuzzi, Sebastiano; Bruegmann, Bernd
2016-01-01
We present new (3+1)D numerical relativity simulations of the binary neutron star (BNS) merger and postmerger phase. We focus on a previously inaccessible region of the binary parameter space spanning the binary's mass-ratio $q\\sim1.00-1.75$ for different total masses and equations of state, and up to $q\\sim2$ for a stiff BNS system. We study the mass-ratio effect on the gravitational waves (GWs) and on the possible electromagnetic emission associated to dynamical mass ejecta. We compute waveforms, spectra, and spectrograms of the GW strain including all the multipoles up to $l=4$. The mass-ratio has a specific imprint on the GW multipoles in the late-inspiral-merger signal, and it affects qualitatively the spectra of the merger remnant. The multipole effect is also studied by considering the dependency of the GW spectrograms on the source's sky location. Unequal mass BNSs produce more ejecta than equal mass systems with ejecta masses and kinetic energies depending almost linearly on $q$. We estimate luminosi...
2. N-Body Dynamics of Intermediate Mass-ratio Inspirals in Star Clusters
Haster, Carl-Johan; Antonini, Fabio; Kalogera, Vicky; Mandel, Ilya
2016-12-01
The intermediate mass-ratio inspiral of a stellar compact remnant into an intermediate-mass black hole (IMBH) can produce a gravitational wave (GW) signal that is potentially detectable by current ground-based GW detectors (e.g., Advanced LIGO) as well as by planned space-based interferometers (e.g., eLISA). Here, we present results from a direct integration of the post-Newtonian N-body equations of motion describing stellar clusters containing an IMBH and a population of stellar-mass black holes (BHs) and solar-mass stars. We take particular care to simulate the dynamics closest to the IMBH, including post-Newtonian effects up to an order of 2.5. Our simulations show that the IMBH readily forms a binary with a BH companion. This binary is gradually hardened by transient three-body or four-body encounters, leading to frequent substitutions of the BH companion, while the binary’s eccentricity experiences large-amplitude oscillations due to the Lidov-Kozai resonance. We also demonstrate suppression of these resonances by the relativistic precession of the binary orbit. We find an intermediate mass-ratio inspiral in 1 of the 12 cluster models we evolved for ˜100 Myr. This cluster hosts a 100{M}⊙ IMBH embedded in a population of 32 10{M}⊙ BH and 32,000 1{M}⊙ stars. At the end of the simulation, after ˜100 Myr of evolution, the IMBH merges with a BH companion. The IMBH-BH binary inspiral starts in the eLISA frequency window (≳ 1 {mHz}) when the binary reaches an eccentricity 1-e≃ {10}-3. After ≃ {10}5 yr the binary moves into the LIGO frequency band with a negligible eccentricity. We comment on the implications for GW searches, with a possible detection within the next decade.
3. Binary Neutron Stars with Generic Spin, Eccentricity, Mass ratio, and Compactness - Quasi-equilibrium Sequences and First Evolutions
Dietrich, Tim; Johnson-McDaniel, Nathan K; Bernuzzi, Sebastiano; Markakis, Charalampos M; Bruegmann, Bernd; Tichy, Wolfgang
2015-01-01
Information about the last stages of a binary neutron star inspiral and the final merger can be extracted from quasi-equilibrium configurations and dynamical evolutions. In this article, we construct quasi-equilibrium configurations for different spins, eccentricities, mass ratios, compactnesses, and equations of state. For this purpose we employ the SGRID code, which allows us to construct such data in previously inaccessible regions of the parameter space. In particular, we consider spinning neutron stars in isolation and in binary systems; we incorporate new methods to produce highly eccentric and eccentricity reduced data; we present the possibility of computing data for significantly unequal-mass binaries; and we create equal-mass binaries with individual compactness up to 0.23. As a proof of principle, we explore the dynamical evolution of three new configurations. First, we simulate a $q=2.06$ mass ratio which is the highest mass ratio for a binary neutron star evolved in numerical relativity to date. ...
4. Meteor Beliefs Project: Shakespeare revisited and the Elizabethan stage's blazing star'
Gheorghe, Andrei Dorian; McBeath, Alastair
2007-06-01
Some fresh Shakespearean citations of meteors, further to those given previously in the Project, are presented, along with a discussion of the Elizabethan stage's use of the blazing star', with especial reference to the great comet of 1577.
5. A cosmological view of extreme mass-ratio inspirals in nuclear star clusters
Mapelli, M; Vecchio, A; Graham, Alister W; Gualandris, A
2012-01-01
There is increasing evidence that many galaxies host both a nuclear star cluster (NC) and a super-massive black hole (SMBH). Their coexistence is particularly prevalent in spheroids with stellar mass 10^8-10^10 solar masses. We study the possibility that a stellar-mass black hole (BH) hosted by a NC inspirals and merges with the central SMBH. Due to the high stellar density in NCs, extreme mass-ratio inspirals (EMRIs) of BHs onto SMBHs in NCs may be important sources of gravitational waves (GWs). We consider sensitivity curves for three different space-based GW laser interferometric mission concepts: the Laser Interferometer Space Antenna (LISA), the New Gravitational wave Observatory (NGO) and the DECi-hertz Interferometer Gravitational wave Observatory (DECIGO). We predict that, under the most optimistic assumptions, LISA and DECIGO will detect up to thousands of EMRIs in NCs per year, while NGO will observe up to tens of EMRIs per year. We explore how a number of factors may affect the predicted rates. In ...
6. CNO abundances and carbon isotope ratios in evolved stars of the open clusters NGC 2324, NGC 2477, and NGC 3960
Tautvaišienė, Gražina; Drazdauskas, Arnas; Bragaglia, Angela; Randich, Sofia; Ženovienė, Renata
2016-10-01
Aims: Our main aim is to determine carbon-to-nitrogen and carbon isotope ratios for evolved giants in the open clusters NGC 2324, NGC 2477, and NGC 3960, which have turn-off masses of about 2 M⊙, and to compare them with predictions of theoretical models. Methods: High-resolution spectra were analysed using a differential synthetic spectrum method. Abundances of carbon were derived using the C2 Swan (0, 1) band heads at 5135 and 5635.5 Å. The wavelength interval 7940-8130 Å with strong CN features was analysed to determine nitrogen abundances and carbon isotope ratios. The oxygen abundances were determined from the [O i] line at 6300 Å. Results: The mean values of the CNO abundances are [C/Fe] = -0.35 ± 0.06 (s.d.), [N/Fe] = 0.28 ± 0.05, and [O/Fe] = -0.02 ± 0.10 in seven stars of NGC 2324; [C/Fe] = -0.26 ± 0.02, [N/Fe] = 0.39 ± 0.04, and [O/Fe] = -0.11 ± 0.06 in six stars of NGC 2477; and [C/Fe] = -0.39 ± 0.04, [N/Fe] = 0.32 ± 0.05, and [O/Fe] = -0.19 ± 0.06 in six stars of NGC 3960. The mean C/N ratio is equal to 0.92 ± 0.12, 0.91 ± 0.09, and 0.80 ± 0.13, respectively. The mean 12C /13C ratio is equal to 21 ± 1, 20 ± 1, and 16 ± 4, respectively. The 12C /13C and C/N ratios of stars in the investigated open clusters were compared with the ratios predicted by stellar evolution models. Conclusions: The mean values of the 12C /13C and C/N ratios in NGC 2324 and NGC 2477 agree well with the first dredge-up and thermohaline-induced extra-mixing models, which are similar for intermediate turn-off mass stars. The 12C /13C ratios in the investigated clump stars of NGC 3960 span from 10 to 20. The mean carbon isotope and C/N ratios in NGC 3960 are close to predictions of the model in which the thermohaline- and rotation-induced (if rotation velocity at the zero-age main sequence was 30% of the critical velocity) extra-mixing act together. Based on observations collected at ESO telescopes under programmes 072.D-0550 and 074.D-0571.
7. Black hole-neutron star mergers at realistic mass ratios: Equation of state and spin orientation effects
Foucart, Francois; Duez, Matthew D; Kidder, Lawrence E; MacDonald, Ilana; Ott, Christian D; Pfeiffer, Harald P; Scheel, Mark A; Szilagyi, Bela; Teukolsky, Saul A
2012-01-01
Black hole-neutron star mergers resulting in the disruption of the neutron star and the formation of an accretion disk and/or the ejection of unbound material are prime candidates for the joint detection of gravitational-wave and electromagnetic signals when the next generation of gravitational-wave detectors comes online. However, the disruption of the neutron star and the properties of the post-merger remnant are very sensitive to the parameters of the binary. In this paper, we study the impact of the radius of the neutron star and the alignment of the black hole spin for systems within the range of mass ratio currently deemed most likely for field binaries (M_BH ~ 7 M_NS) and for black hole spins large enough for the neutron star to disrupt (J/M^2=0.9). We find that: (i) In this regime, the merger is particularly sensitive to the radius of the neutron star, with remnant masses varying from 0.3M_NS to 0.1M_NS for changes of only 2 km in the NS radius; (ii) 0.01-0.05M_sun of unbound material can be ejected w...
8. The Galactic O-Star Spectral Survey (GOSSS) Project status and first results
Sota, Alfredo; Barbá, Rodolfo H; Walborn, Nolan R; Alfaro, Emilio J; Gamen, Roberto C; Morrell, Nidia I; Arias, Julia I; Ordaz, Miguel Penadés
2011-01-01
The Galactic O-Star Spectroscopic Survey (GOSSS) is a project that is observing all known Galactic O stars with B < 13 (~2000 objects) in the blue-violet part of the spectrum with R~2500. It also includes two companion surveys (a spectroscopic one at R~1500 and a high resolution imaging one). It is based on v2.0 of the Galactic O star catalog (v1, Ma\\'iz-Apell\\'aniz et al. 2004; v2, Sota et al. 2008). We have completed the first part of the main project. Here we present results on the first 400 objects of the sample.
9. Two-dimensional models of early-type fast rotating stars: the ESTER project
Rieutord, Michel
2015-01-01
In this talk I present the latest results of the ESTER project that has taken up the challenge of building two dimensional (axisymmetric) models of stars rotating at any rotation rate. In particular, I focus on main sequence massive and intermediate mass stars. I show what should be expected in such stars as far as the differential rotation and the associated meridional circulation are concerned, notably the emergence of a Stewartson layer along the tangent cylinder of the core. I also indicate what may be inferred about the evolution of an intermediate-mass star at constant angular momentum and how Be stars may form. I finally give some comparisons between models and observations of the gravity darkening on some nearby fast rotators as it has been derived from interferometric observations. In passing, I also discuss how 2D models can help to recover the fundamental parameters of a star.
10. Interferometric Star Tracker for High Precision Pointing Project
National Aeronautics and Space Administration — Optical Physics Company (OPC) proposes to adapt the precision star tracker it is currently developing under several DoD contracts for deep space lasercom beam...
11. Advanced Exoplanet Star Tracker for Orbit Self Determination Project
National Aeronautics and Space Administration — This proposal puts forth an innovative star tracker hardware sensor that allows for autonomous calculation of a spacecraft's orbit by employing Doppler Spectroscopy...
12. RV variable, hot post-AGB stars from the MUCHFUSS project - Classification, atmospheric parameters, formation scenarios
Reindl, N; Kupfer, T; Bloemen, S; Schaffenroth, V; Heber, U; Barlow, B N; Østensen, R H
2016-01-01
In the course of the MUCHFUSS project we have recently discovered four radial velocity (RV) variable, hot (Teff $\\approx$ 80,000 - 110,000 K) post-asymptotic giant branch (AGB) stars. Among them, we found the first known RV variable O(He) star, the only second known RV variable PG 1159 close binary candidate, as well as the first two naked (i.e., without planetary nebula (PN)) H-rich post-AGB stars of spectral type O(H) that show significant RV variations. We present a non-LTE spectral analysis of these stars along with one further O(H)-type star whose RV variations were found to be not significant. We also report the discovery of an far-infrared excess in the case of the PG 1159 star. None of the stars in our sample displays nebular emission lines, which can be explained well in terms of a very late thermal pulse evolution in the case of the PG 1159 star. The "missing" PNe around the O(H)-type stars seem strange, since we find that several central stars of PNe have much longer post-AGB times. Besides the non...
13. Project Runaway: Calibrating the Spectroscopic Distance Scale Using Runaway O and Wolf-Rayet Stars
Hartkopf, William I.; Mason, B. D.
2009-05-01
Well-determined O star masses are notoriously difficult to obtain, due to such factors as broad spectral lines, larger and less-reliable average distances, high multiplicity rates, crowded fields, and surrounding nebulosity. Some of these difficulties are reduced for the subset of O stars known as runaways, however. They have escaped some of the nebulosity and crowding, and the event leading to their ejection virtually guarantees that these objects are either single stars or extremely hard spectroscopic binaries. The goal of this project is to increase the sample of known runaway stars, using updated proper motions from the soon-to-be-released UCAC3 catalog, as well as published radial velocities and data from recent duplicity surveys of massive stars using AO and speckle interferometry. Input files include the Galactic O Star Catalog of Maiz-Apellaniz et al. (2004 ApJSS 151, 103) as well as the Seventh Catalogue of Galactic Wolf-Rayet Stars and its more recent Annex (van der Hucht 2001 NewAR 45, 135; 2006 A&A 458, 453). The new runaway star sample will form the basis for a list of SIM targets aimed at improving the distances of Galactic O and WR stars, calibrating the spectroscopic distance scale and leading to more accurate mass estimates for these massive stars.
14. An Upper Limit on the Ratio Between the Extreme Ultraviolet and the Bolometric Luminosities of Stars Hosting Habitable Planets
Sujan Sengupta
2016-06-01
A large number of terrestrial planets in the classical habitable zone of stars of different spectral types have already been discovered and many are expected to be discovered in the near future. However, owing to the lack of knowledge on the atmospheric properties, the ambient environment of such planets are unknown. It is known that sufficient amount of Extreme Ultraviolet (EUV) radiation from the star can drive hydrodynamic outflow of hydrogen that may drag heavier species from the atmosphere of the planet. If the rate of mass loss is sufficiently high, then substantial amount of volatiles would escape causing the planet to become uninhabitable. Considering energy-limited hydrodynamical mass loss with an escape rate that causes oxygen to escape alongwith hydrogen, an upper limit for the ratio between the EUV and the bolometric luminosities of stars which constrains the habitability of planets around them is presented here. Application of the limit to planet-hosting stars with known EUV luminosities implies that many M-type of stars should not have habitable planets around them.
15. Determinations of the 12C/13C Ratio for the Secondary Stars of AE Aquarii, SS Cygni, and RU Pegasi
Harrison, Thomas E.; Marra, Rachel E.
2017-07-01
We present new moderate-resolution near-infrared spectroscopy of three CVs obtained using GNIRS on Gemini-North. These spectra covered three 13CO bandheads found in the K-band, allowing us to derive the isotopic abundance ratios for carbon. We find small 12C/13C ratios for all three donor stars. In addition, these three objects show carbon deficits, with AE Aqr being the most extreme ([C/Fe] = -1.4). This result confirms the conjecture that the donor stars in some long-period CVs have undergone considerable nuclear evolution prior to becoming semi-contact binaries. In addition to the results for carbon, we find that the abundance of sodium is enhanced in these three objects, and the secondary stars in both RU Peg and SS Cyg suffer magnesium deficits. Explaining such anomalies appears to require higher mass progenitors than commonly assumed for the donor stars of CVs. Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), and Ministério da Ciência, Tecnologia e Inovação (Brazil).
16. PROJECTED ROTATIONAL VELOCITIES OF 136 EARLY B-TYPE STARS IN THE OUTER GALACTIC DISK
Garmany, C. D.; Glaspey, J. W. [National Optical Astronomy Observatory, 950 N. Cherry Ave., Tucson, AZ 85719 (United States); Bragança, G. A.; Daflon, S.; Fernandes, M. Borges; Cunha, K. [Observatório Nacional-MCTI, Rua José Cristino, 77. CEP: 20921-400, Rio de Janeiro, RJ (Brazil); Oey, M. S. [University of Michigan, Department of Astronomy, 311 West Hall, 1085 S. University Ave., Ann Arbor, MI: 48109-1107 (United States); Bensby, T., E-mail: garmany@noao.edu [Lund Observatory, Department of Astronomy and Theoretical Physics, Box 43, SE-22100, Lund (Sweden)
2015-08-15
We have determined projected rotational velocities, v sin i, from Magellan/MIKE echelle spectra for a sample of 136 early B-type stars having large Galactocentric distances. The target selection was done independently of their possible membership in clusters, associations or field stars. We subsequently examined the literature and assigned each star as Field, Association, or Cluster. Our v sin i results are consistent with a difference in aggregate v sin i with stellar density. We fit bimodal Maxwellian distributions to the Field, Association, and Cluster subsamples representing sharp-lined and broad-lined components. The first two distributions, in particular, for the Field and Association are consistent with strong bimodality in v sin i. Radial velocities are also presented, which are useful for further studies of binarity in B-type stars, and we also identify a sample of possible new double-lined spectroscopic binaries. In addition, we find 18 candidate Be stars showing emission at Hα.
17. Remote instrumentation and safeguards monitoring for the star project
Buettner, H M; Labiak, W; Spiridon, A
2000-06-15
A part of the Nuclear Energy Research Initiative (NERI) is the development of the Small Transportable Autonomous Reactor (STAR) for deployment in countries that do not have a nuclear industry. STARs would have an output of from 100 to 150 MW electric, would be fueled in the country of manufacture, and after 15 to 20 years of operation the reactor core would be returned to the country of manufacture for refueling. A candidate STAR design can be found in (Greenspan, 2000). This paper describes the design of the control and monitoring system that might be used. There are two unique features to this system. One is that the monitored information will be transmitted to a remote site for two purposes, safeguards, and allowing experts a great distance away direct access to view the reactor's operating parameters. The second feature is safeguards sensors will be designed into the system and there will monitoring of the safeguards aspects of the system for tampering. Any safeguards anomalies will be sent to the remote site as alarms. Encrypted satellite communications will be used to transmit the data. These features allow the STAR to be operated by a small staff and will reduce the costs of safeguards monitoring by reducing the number of plant visits by inspectors.
18. Remote instrumentation and safeguards monitoring for the star project
Buettner, H M; Labiak, W; Spiridon, A
2000-06-15
A part of the Nuclear Energy Research Initiative (NERI) is the development of the Small Transportable Autonomous Reactor (STAR) for deployment in countries that do not have a nuclear industry. STARs would have an output of from 100 to 150 MW electric, would be fueled in the country of manufacture, and after 15 to 20 years of operation the reactor core would be returned to the country of manufacture for refueling. A candidate STAR design can be found in (Greenspan, 2000). This paper describes the design of the control and monitoring system that might be used. There are two unique features to this system. One is that the monitored information will be transmitted to a remote site for two purposes, safeguards, and allowing experts a great distance away direct access to view the reactor's operating parameters. The second feature is safeguards sensors will be designed into the system and there will monitoring of the safeguards aspects of the system for tampering. Any safeguards anomalies will be sent to the remote site as alarms. Encrypted satellite communications will be used to transmit the data. These features allow the STAR to be operated by a small staff and will reduce the costs of safeguards monitoring by reducing the number of plant visits by inspectors.
19. CNO abundances and carbon isotope ratios in evolved stars of the open clusters NGC 2324, NGC 2477, and NGC 3960
Tautvaisiene, Grazina; Bragaglia, Angela; Randich, Sofia; Zenoviene, Renata
2016-01-01
Our main aim is to determine carbon-to-nitrogen and carbon isotope ratios for evolved giants in the open clusters NGC 2324, NGC 2477, and NGC 3960, which have turn-off masses of about 2 Msun, and to compare them with predictions of theoretical models. High-resolution spectra were analysed using a differential synthetic spectrum method. Abundances of carbon were derived using the C2 Swan (0,1) band heads at 5135 and 5635.5 A. The wavelength interval 7940-8130 A with strong CN features was analysed to determine nitrogen abundances and carbon isotope ratios. The oxygen abundances were determined from the [Oi] line at 6300 A. The mean values of the CNO abundances are [C/Fe]=-0.35+-0.06 (s.d.), [N/Fe]=0.28+-0.05, and [O/Fe]=-0.02+-0.10 in seven stars of NGC 2324; [C/Fe]=-0.26+-0.02, [N/Fe]=0.39+-0.04, and [O/Fe]=-0.11+-0.06 in six stars of NGC 2477; and [C/Fe]=-0.39+-0.04, [N/Fe]=0.32+-0.05, and [O/Fe]=-0.19+-0.06 in six stars of NGC 3960. The mean C/N ratio is equal to 0.92+-0.12, 0.91+-0.09, and 0.80+-0.13, resp...
20. Utilizing the AAVSO's Variable Star Index (VSX) In Undergraduate Research Projects
Larsen, Kristine
2016-01-01
Among the many important services that the American Association of Variable Star Observers (AAVSO) provides to the astronomical community is the Variable Star Index (VSX - https://www.aavso.org/vsx/). This online catalog of variable stars is the repository of data on over 334,000 variable stars, including information on spectral type, range of magnitude, period, and type of variable, among other properties. A number of these stars were identified as being variable through automated telescope surveys, such as ASAS (All Sky Automated Survey). The computer code of this survey classified newly discovered variables as best it could, but a significant number of false classifications have been noted. The reclassification of ASAS variables in the VSX data, as well as a closer look at variables identified as miscellaneous type in VSX, are two of many projects that can be undertaken by interested undergraduates. In doing so, students learn about the physical properties of various types of variable stars as well as statistical analysis and computer software, especially the VStar variable star data visualization and analysis tool that is available to the astronomical community free of charge on the AAVSO website (https://www.aavso.org/vstar-overview). Two such projects are described in this presentation, the first to identify BY Draconis variables erroneously classified as Cepheids in ASAS data, and the second to identify SRD semiregular variables misidentified as "miscellaneous" in VSX.
1. Utilizing the AAVSO's Variable Star Index (VSX) in Undergraduate Research Projects (Poster abstract)
Larsen, K.
2016-12-01
(Abstract only) Among the many important services that the American Association of Variable Star Observers (AAVSO) provides to the astronomical community is the Variable Star Index (VSX; https://www.aavso.org/vsx/). This online catalog of variable stars is the repository of data on over 334,000 variable stars, including information on spectral type, range of magnitude, period, and type of variable, among other properties. A number of these stars were identified as being variable through automated telescope surveys, such as ASAS (All Sky Automated Survey). The computer code of this survey classified newly discovered variables as best it could, but a significant number of false classifications have been noted. The reclassification of ASAS variables in the VSX data, as well as a closer look at variables identified as miscellaneous type in VSX, are two of many projects that can be undertaken by interested undergraduates. In doing so, students learn about the physical properties of various types of variable stars as well as statistical analysis and computer software, especially the vstar variable star data visualization and analysis tool that is available to the astronomical community free of charge on the AAVSO website (https://www.aavso.org/vstar-overview). Three such projects are described in this presentation, to identify BY Draconis variables misidentified as Cepheids or "miscellaneous", and SRD semiregular variables and ELL (rotating ellipsoidal) variables misidentified as "miscellaneous", in ASAS data and VSX.
2. Blue Straggler Stars a direct comparison of Star counts and population ratios in six Galactic Globular Clusters
Ferraro, F R; Rood, R T; Paltrinieri, B; Buonanno, R; Ferraro, Francesco R.; Sills, Alison; Rood, Robert T.; Paltrinieri, Barbara; Buonanno, Roberto
2003-01-01
The central regions of six Galactic Globular Clusters (GGCs) (M3, M80, M10, M13, M92 and NGC 288) have been imaged using HST-WFPC2 and the ultraviolet (UV) filters (F255W, F336W). The selected sample covers a large range in both central density and metallicity ([Fe/H]). In this paper, we present a direct cluster-to-cluster comparison of the Blue Stragglers Stars (BSS) population as selected from (m_{255},m_{255}-m_{336}) Color Magnitude Diagrams (CMDs). We have found:(a) BSS in three of the clusters (M3, M80, M92) are much more concentrated toward the center of the cluster than the red giants; because of the smaller BSS samples for the other clusters we can only note that the BSS radial distributions are consistent with central concentration; (b) the specific frequency of BSS varies greatly from cluster to cluster. The most interesting result is that the two clusters with largest BSS specific frequency are at the central density extremes of our sample: NGC 288 (lowest central density) and M80 (highest). This ...
3. DNC/HNC RATIO OF MASSIVE CLUMPS IN EARLY EVOLUTIONARY STAGES OF HIGH-MASS STAR FORMATION
Sakai, Takeshi [Institute of Astronomy, University of Tokyo, Osawa, Mitaka, Tokyo 181-0015 (Japan); Sakai, Nami; Yamamoto, Satoshi [Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033 (Japan); Furuya, Kenji; Aikawa, Yuri [Department of Earth and Planetary Sciences, Kobe University, Kobe 657-8501 (Japan); Hirota, Tomoya [National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588 (Japan)
2012-03-10
We have observed the HN{sup 13}C J = 1-0 and DNC J = 1-0 lines toward 18 massive clumps, including infrared dark clouds (IRDCs) and high-mass protostellar objects (HMPOs), by using the Nobeyama Radio Observatory 45 m telescope. We have found that the HN{sup 13}C emission is stronger than the DNC emission toward all of the observed sources. The averaged DNC/HNC ratio is indeed lower toward the observed high-mass sources (0.009 {+-} 0.005) than toward the low-mass starless and star-forming cores (0.06). The kinetic temperature derived from the NH{sub 3} (J, K) = (1, 1) and (2, 2) line intensities is higher toward the observed high-mass sources than toward the low-mass cores. However, the DNC/HNC ratio of some IRDCs involving the Spitzer 24 {mu}m sources is found to be lower than that of HMPOs, although the kinetic temperature of the IRDCs is lower than that of the HMPOs. This implies that the DNC/HNC ratio does not depend only on the current kinetic temperature. With the aid of chemical model simulations, we discuss how the DNC/HNC ratio decreases after the birth of protostars. We suggest that the DNC/HNC ratio in star-forming cores depends on the physical conditions and history in their starless-core phase, such as its duration time and the gas kinetic temperature.
4. DNC/HNC Ratio of Massive Clumps in Early Evolutionary Stages of High-mass Star Formation
Sakai, Takeshi; Sakai, Nami; Furuya, Kenji; Aikawa, Yuri; Hirota, Tomoya; Yamamoto, Satoshi
2012-03-01
We have observed the HN13C J = 1-0 and DNC J = 1-0 lines toward 18 massive clumps, including infrared dark clouds (IRDCs) and high-mass protostellar objects (HMPOs), by using the Nobeyama Radio Observatory 45 m telescope. We have found that the HN13C emission is stronger than the DNC emission toward all of the observed sources. The averaged DNC/HNC ratio is indeed lower toward the observed high-mass sources (0.009 ± 0.005) than toward the low-mass starless and star-forming cores (0.06). The kinetic temperature derived from the NH3 (J, K) = (1, 1) and (2, 2) line intensities is higher toward the observed high-mass sources than toward the low-mass cores. However, the DNC/HNC ratio of some IRDCs involving the Spitzer 24 μm sources is found to be lower than that of HMPOs, although the kinetic temperature of the IRDCs is lower than that of the HMPOs. This implies that the DNC/HNC ratio does not depend only on the current kinetic temperature. With the aid of chemical model simulations, we discuss how the DNC/HNC ratio decreases after the birth of protostars. We suggest that the DNC/HNC ratio in star-forming cores depends on the physical conditions and history in their starless-core phase, such as its duration time and the gas kinetic temperature.
5. SIM PlanetQuest Key Project Precursor Observations to Detect Gas Giant Planets Around Young Stars
Tanner, Angelle; Beichman, Charles; Akeson, Rachel; Ghez, Andrea; Grankin, Konstantin N.; Herbst, William; Hillenbrand, Lynne; Huerta, Marcos; Konopacky, Quinn; Metchev, Stanimir; Mohanty, Subhanjoy; Prato, L.; Simon, Michal
2008-01-01
We present a review of precursor observing programs for the SIM PlanetQuest Key project devoted to detecting Jupiter mass planets around young stars. In order to ensure that the stars in the sample are free of various sources of astrometric noise that might impede the detection of planets, we have initiated programs to collect photometry, high contrast images, interferometric data and radial velocities for stars in both the Northern and Southern hemispheres. We have completed a high contrast imaging survey of target stars in Taurus and the Pleiades and found no definitive common proper motion companions within one arcsecond (140 AU) of the SIM targets. Our radial velocity surveys have shown that many of the target stars in Sco-Cen are fast rotators and a few stars in Taurus and the Pleiades may have sub-stellar companions. Interferometric data of a few stars in Taurus show no signs of stellar or sub-stellar companions with separations of 0.1 mag) that would degrade the astrometric accuracy achievable for that star. While the precursor programs are still a work in progress, we provide a comprehensive list of all targets ranked according to their viability as a result of the observations taken to date. By far, the observable that removes the most targets from the SIM-YSO program is photometric variability.
6. Braneworld Stars:. Anisotropy Minimally Projected onto the Brane
Ovalle, J.
2010-04-01
In the context of the Randall-Sundrum braneworld, an exhaustive and detailed description of the approach based in the minimal anisotropic consequence onto the brane, which has been successfully used to generate exact interior solutions to Einstein's field equations for static and non-uniform braneworld stars with local and non-local bulk terms, is carefully presented. It is shown that this approach allows the generation of a braneworld version for any known general relativistic solution.
7. Braneworld Stars: Anisotropy Minimally Projected Onto the Brane
2009-01-01
In the context of the Randall-Sundrum braneworld, an exhaustive and detailed description of the approach based in the minimal anisotropic consequence onto the brane, which has been successfully used to generate exact interior solutions to Einstein's field equations for static and non-uniform braneworld stars with local and non-local bulk terms, is carefully presented. It is shown that this approach allows the generation of a braneworld version for any known general relativistic solution.
8. Comparison of International Normalized Ratio Measurement between CoaguChek XS Plus and STA-R Coagulation Analyzers
Mina Hur
2013-01-01
Full Text Available Background. Point-of-care testing (POCT coagulometers are increasingly being used in the hospital setting. We investigated whether the prothrombin time international normalized ratio (INR results by CoaguChek XS Plus (Roche Diagnostics GmbH, Mannheim, Germany can be used reliably without being confirmed with the INR results by STA-R system (Diagnostica Stago S.A.S, Asnières sur Seine, France. Methods. A total of 118 INR measurements by CoaguChek XS Plus and STA-R were compared using Passing/Bablok regression analysis and Bland-Altman plot. Agreement of the INR measurements was further assessed in relation to dosing decision. Results. The correlation of INR measurements between CoaguChek XS Plus and STA-R was excellent (correlation coefficient = 0.964. The mean difference tended to increase as INR results increased and was 0.25 INR in the therapeutic range (2.0-3.0 INR. The overall agreement was fair to good (kappa = 0.679, and 21/118 (17.8% INR measurements showed a difference in dosing decision. Conclusion. The positive bias of CoaguChek XS Plus may be obvious even in the therapeutic INR range, and dosing decision based on the CoaguChek XS Plus INR results would be different from that based on the STA-R results. The INR measurements by POCT coagulometers still need to be confirmed with the laboratory INR measurements.
9. StarPals International Young Astronomers' Network Collaborative Projects for IYA
Kingan, Jessi
2008-09-01
StarPals is a nascent non-profit organization with the goal of providing opportunities for international collaboration between students of all ages within space science research. We believe that by encouraging an interest in the cosmos, the one thing that is truly Universal, from a young age, students will not only further their knowledge of and interest in science but will learn valuable teamwork and life skills. The goal is to foster respect, understanding and appreciation of cultural diversity among all StarPals participants, whether students, teachers, or mentors. StarPals aims to inspire students by providing opportunities in which, more than simply visualizing themselves as research scientists, they can actually become one. The technologies of robotic telescopes, videoconferencing, and online classrooms are expanding the possibilities like never before. In honor of IYA2009, StarPals would like to encourage 400 schools to participate on a global scale in astronomy/cosmology research on various concurrent projects. We will offer in-person or online workshops and training sessions to teach the teachers. We will be seeking publication in scientific journals for some student research. For our current project, the Double Stars Challenge, students use the robotic telescopes to take a series of four images of one of 30 double stars from a list furnished by the US Naval Observatory and then use MPO Canopus software to take distance and position angle measurements. StarPals provides students with hands-on training, telescope time, and software to complete the imaging and measuring. A paper will be drafted from our research data and submitted to the Journal of Double Star Observations. The kids who participate in this project may potentially be the youngest contributors to an article in a vetted scientific journal. Kids rapidly adapt and improve their computer skills operating these telescopes and discover for themselves that science is COOL!
10. The mass-ratio and eccentricity distributions of barium and S stars, and red giants in open clusters
Van der Swaelmen, M.; Boffin, H. M. J.; Jorissen, A.; Van Eck, S.
2017-01-01
Context. A complete set of orbital parameters for barium stars, including the longest orbits, has recently been obtained thanks to a radial-velocity monitoring with the HERMES spectrograph installed on the Flemish Mercator telescope. Barium stars are supposed to belong to post-mass-transfer systems. Aims: In order to identify diagnostics distinguishing between pre- and post-mass-transfer systems, the properties of barium stars (more precisely their mass-function distribution and their period-eccentricity (P-e) diagram) are compared to those of binary red giants in open clusters. As a side product, we aim to identify possible post-mass-transfer systems among the cluster giants from the presence of s-process overabundances. We investigate the relation between the s-process enrichment, the location in the (P-e) diagram, and the cluster metallicity and turn-off mass. Methods: To invert the mass-function distribution and derive the mass-ratio distribution, we used the method pioneered by Boffin et al. (1992) that relies on a Richardson-Lucy deconvolution algorithm. The derivation of s-process abundances in the open-cluster giants was performed through spectral synthesis with MARCS model atmospheres. Results: A fraction of 22% of post-mass-transfer systems is found among the cluster binary giants (with companion masses between 0.58 and 0.87 M⊙, typical for white dwarfs), and these systems occupy a wider area than barium stars in the (P-e) diagram. Barium stars have on average lower eccentricities at a given orbital period. When the sample of binary giant stars in clusters is restricted to the subsample of systems occupying the same locus as the barium stars in the (P-e) diagram, and with a mass function compatible with a WD companion, 33% (=4/12) show a chemical signature of mass transfer in the form of s-process overabundances (from rather moderate - about 0.3 dex - to more extreme - about 1 dex). The only strong barium star in our sample is found in the cluster with
11. The mass-ratio and eccentricity distributions of red giants in open clusters, barium and S stars
Van der Swaelmen, Mathieu; Jorissen, Alain; Van Eck, Sophie
2016-01-01
In order to identify diagnostics distinguishing between pre- and post-mass-transfer systems, the mass-ratio distribution and period - eccentricity (P - e) diagram of barium and S stars are compared to those of the sample of binary red giants in open clusters from Mermilliod et al. (2007). From the analysis of the mass-ratio distribution for the cluster binary giants, we find an excess of systems with companion masses between 0.58 and 0.87 Msun, typical for white dwarfs. They represent 22% of the sample, which are thus candidate post-mass-transfer systems. Among these candidates which occupy the same locus as the barium and S stars in the (P-e) diagram, only 33% (= 4/12) show a chemical signature of mass transfer in the form of s-process overabundances (from rather moderate -- about 0.3 dex -- to more extreme -- about 1 dex). These s-process-enriched cluster stars show a clear tendency to be in the clusters with the lowest metallicity in the sample, confirming the classical prediction that the s-process nucleo...
12. Braneworld Stars: Anisotropy Minimally Projected Onto the Brane
Ovalle, J
2009-01-01
In the context of the Randall-Sundrum braneworld, an exhaustive and detailed description of the approach based in the minimal anisotropic consequence onto the brane, which has been successfully used to generate exact interior solutions to Einstein's field equations for static and non-uniform braneworld stars with local and non-local bulk terms, is carefully presented. It is shown that this approach allows the generation of a braneworld version for any known general relativistic solution. As a demonstration, the braneworld version of the Schwarzschild's interior solution is generated using this method.
13. The Intrinsic Eddington Ratio Distribution of Active Galactic Nuclei in Star-forming Galaxies from the Sloan Digital Sky Survey
Jones, M L; Black, C S; Hainline, K N; DiPompeo, M A; Goulding, A D
2016-01-01
An important question in extragalactic astronomy concerns the distribution of black hole accretion rates of active galactic nuclei (AGN). Based on observations at X-ray wavelengths, the observed Eddington ratio distribution appears as a power law, while optical studies have often yielded a lognormal distribution. There is increasing evidence that these observed discrepancies may be due to contamination by star formation and other selection effects. Using a sample of galaxies from the Sloan Digital Sky Survey Data Release 7, we test if an intrinsic Eddington ratio distribution that takes the form of a Schechter function is consistent with previous work that suggests that young galaxies in optical surveys have an observed lognormal Eddington ratio distribution. We simulate the optical emission line properties of a population of galaxies and AGN using a broad instantaneous luminosity distribution described by a Schechter function near the Eddington limit. This simulated AGN population is then compared to observe...
14. The StarLite Project Prototyping Real-Time Software
1991-10-01
An Annual Report ( -A D-A242 032 Grant No. N00014-91-J-1102 t 1III iII I 1IIIII 11111i II’ October 1, 1990 - September 30, 1991 THE STARLITE PROJECT...1990 - September 30, 1991 THE STARLITE PROJECT PROTOTYPING REAL-TIME SOFTWARE I Submitted to: Scientific Officer Code: 1211 Dr. James G. Smith Office...DATES COVERED 4 October 1991 Annual 10/1/90 - 9/30/91 4. TITLE AND SUBTITLE S. FUNDING NUMBERS The Starlite Project - Prototyping Real-Time Software
15. 77 FR 33210 - Shooting Star Wind Project, LLC; Supplemental Notice That Initial Market-Based Rate Filing...
2012-06-05
... From the Federal Register Online via the Government Publishing Office DEPARTMENT OF ENERGY Federal Energy Regulatory Commission Shooting Star Wind Project, LLC; Supplemental Notice That Initial Market... in the above-referenced proceeding of Shooting Star Wind Project, LLC's application for...
16. Gas-to-dust ratios in massive star-forming galaxies at z ˜ 1.4
Seko, Akifumi; Ohta, Kouji; Yabe, Kiyoto; Hatsukade, Bunyo; Aono, Yuya; Iono, Daisuke
2016-08-01
We present results of 12CO(J = 2-1) observations toward four massive star-forming galaxies at z ˜ 1.4 with the Nobeyama 45 m radio telescope. The galaxies are detected with Spitzer/MIPS in 24 μm and Herschel/SPIRE in 250 μm and 350 μm, and they mostly reside in the main sequence. Their gas-phase metallicities derived by the N2 method using the Hα and [N II]λ 6584 emission lines are near the solar value. CO lines are detected toward three galaxies. The molecular-gas masses obtained are (9.6-35) × 1010 M⊙ by adopting the Galactic CO-to-H2 conversion factor and a CO(2-1)/CO(1-0) flux ratio of 3. The dust masses derived from the modified blackbody model (assuming a dust temperature of 35 K and an emissivity index of 1.5) are (2.4-5.4) × 108 M⊙. Resulting gas-to-dust ratios (not accounting for H I mass) at z ˜ 1.4 are 220-1450, which are several times larger than those in local star-forming galaxies. A dependence of the gas-to-dust ratio on the far-infrared luminosity density is not clearly seen.
17. Nonrobustness of the Carryover Effects of Small Classes in Project STAR
Sohn, Kitae
2015-01-01
Background: Class size reduction (CSR) is an enduring school reform undertaken in an effort to improve academic achievement and has been widely encouraged in the United States. Supporters of CSR often cite the positive contemporaneous and carryover effects of Project STAR. Much has been discussed regarding the robustness of the contemporaneous…
18. Projected Axis Ratios of Galaxy Clusters in the Horizon-AGN Simulation: Impact of Baryon Physics and Comparison with Observations
Suto, Daichi; Dubois, Yohan; Kitayama, Tetsu; Nishimichi, Takahiro; Sasaki, Shin; Suto, Yasushi
2016-01-01
We characterize the non-sphericity of galaxy clusters by the projected axis ratio of spatial distribution of star, dark matter, and X-ray surface brightness (XSB). We select 40 simulated groups and clusters of galaxies with mass larger than 5E13 Msun from the Horizon simulation that fully incorporates the relevant baryon physics, in particular, the AGN feedback. We find that the baryonic physics around the central region of galaxy clusters significantly affects the non-sphericity of dark matter distribution even beyond the central region, approximately up to the half of the virial radius. Therefore it is very difficult to predict the the probability density function (PDF) of the projected axis ratio of XSB from dark-matter only N-body simulations as attempted in previous studies. Indeed we find that the PDF derived from our simulated clusters exhibits much better agreement with that from the observed X-ray clusters. This indicates that our present methodology to estimate the non-sphericity directly from the H...
19. Projected axis ratios of galaxy clusters in the Horizon-AGN simulation: Impact of baryon physics and comparison with observations
Suto, Daichi; Peirani, Sébastien; Dubois, Yohan; Kitayama, Tetsu; Nishimichi, Takahiro; Sasaki, Shin; Suto, Yasushi
2017-02-01
We characterize the non-sphericity of galaxy clusters by the projected axis ratio of spatial distribution of star, dark matter, and X-ray surface brightness (XSB). We select 40 simulated groups and clusters of galaxies with mass larger than 5 × 1013 M⊙ from the Horizon simulation that fully incorporates the relevant baryon physics, in particular, the active galactic nucleus feedback. We find that the baryonic physics around the central region of galaxy clusters significantly affects the non-sphericity of dark matter distribution even beyond the central region, approximately up to half of the virial radius. Therefore it is very difficult to predict the probability density function (PDF) of the projected axis ratio of XSB from dark-matter-only N-body simulations as attempted in previous studies. Indeed, we find that the PDF derived from our simulated clusters exhibits much better agreement with that from the observed X-ray clusters. This indicates that our present methodology to estimate the non-sphericity directly from the Horizon simulation is useful and promising. Further improvements in both numerical modeling and observational data will establish the non-sphericity of clusters as a cosmological test complementary to more conventional statistics based on spherically averaged quantities.
20. The first low-mass stars: critical metallicity or dust-to-gas ratio?
Schneider, Raffaella; Bianchi, Simone; Valiante, Rosa
2011-01-01
We explore the minimal conditions which enable the formation of metal-enriched solar and sub-solar mass stars. We find that in the absence of dust grains, gas fragmentation occurs at densities nH ~ [10^4-10^5]cm^{-3} when the metallicity exceeds Z ~ 10^{-4} Zsun. The resulting fragmentation masses are > 10 Msun. The inclusion of Fe and Si cooling does not affect the thermal evolution as this is dominated by molecular cooling even for metallicities as large as Z = 10^{-2} Zsun. The presence of dust is the key driver for the formation of low-mass stars. We focus on three representative core-collapse supernova (SN) progenitors, and consider the effects of reverse shocks of increasing strength: these reduce the depletion factors, fdep = Mdust/(Mdust+Mmet), alter the shape of the grain size distribution function and modify the relative abundances of grain species and of metal species in the gas phase. We find that the lowest metallicity at which fragmentation occurs is Z=10^{-6} Zsun for gas pre-enriched by the ex...
1. Constraint on the Gas-to-Dust Ratio in Massive Star-Forming Galaxies at z~1.4
Seko, Akifumi; Hatsukade, Bunyo; Yabe, Kiyoto; Takeuchi, Tomoe; Iono, Daisuke
2014-01-01
We carried out 12CO(J=2-1) observations toward three star-forming galaxies on the main sequence at z~1.4 with the Nobeyama 45m radio telescope. These galaxies are detected with Spitzer/MIPS in 24 um, Herschel/SPIRE in 250 um and 350 um, and their gas metallicity, derived from optical emission line ratios based on near infrared spectroscopic observations, is close to the solar metallicity. Although weak signal-like features of CO were seen, we could not detect significant CO emission. The dust mass and the upper limits on the molecular gas mass are (3.4-6.7) x 10^{8} Msun and (9.7-14) x 10^{10} Msun, respectively. The upper limits on the gas-to-dust ratios at z~1.4 are 150-410 which are comparable to the gas-to-dust ratios in local galaxies with similar gas metallicity. A line stacking analysis enables us to detect a significant CO emission and to derive an average molecular gas mass of 1.3 x 10^{11} Msun and gas-to-dust ratio of 250. This gas-to-dust ratio is also near that in local galaxies with solar metall...
2. Mind your Ps and Qs: the Interrelation between Period (P) and Mass-ratio (Q) Distributions of Binary Stars
Moe, Maxwell
2016-01-01
We compile observations of early-type binaries identified via spectroscopy, eclipses, long-baseline interferometry, sparse aperture masking, adaptive optics, lucky imaging, and common proper motion. We combine the samples from the various surveys and correct for their respective selection effects to determine a comprehensive nature of the intrinsic multiplicity statistics of O-type and B-type stars. We find the properties of companions to massive stars differ among three regimes. First, at short orbital periods P 0.95. Second, the companion frequency peaks at intermediate periods log P (days) = 3.5 (a = 10 AU), where the binaries have mass ratios weighted toward small values q = 0.2-0.3 and follow a Maxwellian "thermal" eccentricity distribution. Finally, companions with long orbital periods log P (days) = 5.5-7.5 (a = 200-5,000 AU) are outer tertiary components in hierarchical triples, and have a mass ratio distribution across q = 0.1-1.0 that is nearly consistent with random pairings drawn from the initial...
3. The Solaris project. A timing survey for circumbinary planets around eclipsing binary stars.
Konacki, M.
2014-03-01
The SOLARIS project aims to detect from the ground circumbinary planets with the timing of eclipses of eclipsing binary stars. For the SOLARIS project, we were granted 2.5 million Euro to establish a network of four robotic 0.5-m telescopes on three continents (Australia, Africa and South America) to carry out high cadence, high precision photometry of a sample of eclipsing binary stars. Three of the telescopes are already installed and the fourth one will become operational in early 2014. The project's web site is www.projectsolaris.eu/. This effort is accompanied by our radial velocity (RV) survey for circumbinary planets which employs our novel iodine cell based technique tailored to provide very high precision RVs of double-lined binaries. Altogether these two efforts, targeting about 300 eclipsing binary stars, constitute the biggest ground based survey for circumbinary planets. Moreover, we expect that both these efforts will have a significant impact on the observational stellar astronomy. In particular for at least half of our sample we expect to deliver masses of the stars with an accuracy 10-1000 times better than the current state of the art.
4. DNC/HNC Ratio of Massive Clumps in Early Evolutionary Stages of High-Mass Star Formation
Sakai, Takeshi; Furuya, Kenji; Aikawa, Yuri; Hirota, Tomoya; Yamamoto, Satoshi
2012-01-01
We have observed the HN13C J=1-0 and DNC J=1-0 lines toward 18 massive clumps, including infrared dark clouds (IRDCs) and high-mass protostellar objects (HMPOs), by using the Nobeyama Radio Observatory 45 m telescope. We have found that the HN13C emission is stronger than the DNC emission toward all the observed sources. The averaged DNC/HNC ratio is indeed lower toward the observed high-mass sources (0.009\\pm0.005) than toward the low-mass starless and star-forming cores (0.06). The kinetic temperature derived from the NH3 (J, K) = (1, 1) and (2, 2) line intensities is higher toward the observed high-mass sources than toward the low-mass cores. However the DNC/HNC ratio of some IRDCs involving the Spitzer 24 {\\mu}m sources is found to be lower than that of HMPOs, although the kinetic temperature of the IRDCs is lower than that of the HMPOs. This implies that the DNC/HNC ratio does not depend only on the current kinetic temperature. With the aid of chemical model simulations, we discuss how the DNC/HNC ratio ...
5. Projected Constraints on Scalarization with Gravitational Waves from Neutron Star Binaries
Sampson, Laura; Cornish, Neil; Ponce, Marcelo; Barausse, Enrico; Klein, Antoine; Palenzuela, Carlos; Lehner, Luis
2014-01-01
Certain scalar-tensor theories have the property of endowing stars with scalar hair, sourced either by the star's own compactness (spontaneous scalarization) or, for binary systems, by the companion's scalar hair (induced scalarization) or by the orbital binding energy (dynamical scalarization). Scalarized stars in binaries present different conservative dynamics than in General Relativity, and can also excite a scalar mode in the metric perturbation that carries away dipolar radiation. As a result, the binary orbit shrinks faster than predicted in General Relativity, modifying the rate of decay of the orbital period. In spite of this, scalar-tensor theories can pass existing binary pulsar tests, because observed pulsars may not be compact enough or sufficiently orbitally bound to activate scalarization. Gravitational waves emitted during the last stages of compact binary inspirals are thus ideal probes of scalarization effects. For the standard projected sensitivity of advanced LIGO, we here show that, if ne...
6. Eclipsing binary stars in the Large and Small Magellanic Clouds from the MACHO project: The Sample
Faccioli, L; Alcock, C; Cook, K; Prochter, G; Protopapas, P; Syphers, D
2007-03-29
We present a new sample of 4634 eclipsing binary stars in the Large Magellanic Cloud (LMC), expanding on a previous sample of 611 objects and a new sample of 1509 eclipsing binary stars in the Small Magellanic Cloud (SMC), that were identified in the light curve database of the MACHO project. We perform a cross correlation with the OGLE-II LMC sample, finding 1236 matches. A cross correlation with the OGLE-II SMC sample finds 698 matches. We then compare the LMC subsamples corresponding to center and the periphery of the LMC and find only minor differences between the two populations. These samples are sufficiently large and complete that statistical studies of the binary star populations are possible.
7. THE ABUNDANCE, ORTHO/PARA RATIO, AND DEUTERATION OF WATER IN THE HIGH-MASS STAR-FORMING REGION NGC 6334 I
Emprechtinger, M.; Lis, D. C.; Monje, R. R. [California Institute of Technology, Cahill Center for Astronomy and Astrophysics 301-17, Pasadena, CA 91125 (United States); Rolffs, R.; Schilke, P. [Physikalisches Institut, Universitaet zu Koeln, Zuelpicher Str. 77, D-50937 Koeln (Germany); Comito, C. [Max-Planck-Institut fuer Radioastronomie, Auf dem Huegel 69, D-53121 Bonn (Germany); Ceccarelli, C. [UJF-Grenoble 1/CNRS-INSU, Institut de Planetologie et d' Astrophysique de Grenoble (IPAG) UMR 5274, Grenoble F-38041 (France); Neufeld, D. A. [Department of Physics and Astronomy Johns Hopkins University, Baltimore, MD 21218 (United States); Van der Tak, F. F. S., E-mail: dcl@caltech.edu [SRON Netherlands Institute for Space Research and Kapteyn Astronomical Institute, University of Groningen, Groningen (Netherlands)
2013-03-01
We present Herschel/HIFI observations of 30 transitions of water isotopologues toward the high-mass star-forming region NGC 6334 I. The line profiles of H{sup 16} {sub 2}O, H{sup 17} {sub 2}O, H{sup 18} {sub 2}O, and HDO show a complex pattern of emission and absorption components associated with the embedded hot cores, a lower-density envelope, two outflow components, and several foreground clouds, some associated with the NGC 6334 complex, others seen in projection against the strong continuum background of the source. Our analysis reveals an H{sub 2}O ortho/para ratio of 3 {+-} 0.5 in the foreground clouds, as well as the outflow. The water abundance varies from {approx}10{sup -8} in the foreground clouds and the outer envelope to {approx}10{sup -6} in the hot core. The hot core abundance is two orders of magnitude below the chemical model predictions for dense, warm gas, but within the range of values found in other Herschel/HIFI studies of hot cores and hot corinos. This may be related to the relatively low gas and dust temperature ({approx}100 K), or time-dependent effects, resulting in a significant fraction of water molecules still locked up in dust grain mantles. The HDO/H{sub 2}O ratio in NGC 6334 I, {approx}2 Multiplication-Sign 10{sup -4}, is also relatively low, but within the range found in other high-mass star-forming regions.
8. Study on the faint star extraction technology with MEMS gyro aided APS star tracker
Xing, Fei; Zhao, Borui; Sun, Ting; Xu, Wei; You, Zheng
2013-08-01
Star tracker is the most accurate attitude sensor for satellite. Generally speaking, the higher the accuracy, the fainter the star can be sensed by the star tracker. How to extract the faint star from a star image is becoming a critical technology in dynamic condition for star tracker, especially using the APS (Active Pixels Sensor) detector. A novel APS star tracker with MEMS Gyroscope aided system was proposed in this paper that could extremely improve the detection effect and capability for the faint stars. During the exposure time of star tracker, the trajectory of star projection on the detector maybe occupy more than ten pixels due to the satellite rotation. In this situation, the signal-to-noise ratio will decline sharply, and the traditional star extraction method for faint star will take no effect. As a result, the accuracy of star tracker would decline sharply, even more, couldn't work. Using the MEMS Gyroscope, the track of star projection can be predicated and measured, on the basis of which the deconvolution algorithm could be taken to recover the faint star signal. The accuracy of the star projection centroid could be improved obviously, and the dynamic performance of the star tracker would be improved by a magnitude. Meanwhile, the MEMS gyroscope has not less volume, mass and power consumption, which make it more suitable for the application of APS star tracker.
9. The MACHO Project HST Follow-Up: The Large Magellanic Cloud Microlensing Source Stars
Nelson, C.A.; /LLNL, Livermore /UC, Berkeley; Drake, A.J.; /Caltech; Cook, K.H.; /LLNL, Livermore /UC, Berkeley; Bennett, D.P.; /Caltech /Notre Dame U.; Popowski, P.; /Garching, Max Planck Inst.; Dalal, N.; /Toronto U.; Nikolaev, S.; /LLNL, Livermore; Alcock, C.; /Caltech /Harvard-Smithsonian Ctr. Astrophys.; Axelrod, T.S.; /Arizona U.; Becker, A.C. /Washington U., Seattle; Freeman, K.C.; /Res. Sch. Astron. Astrophys., Weston Creek; Geha, M.; /Yale U.; Griest, K.; /UC, San Diego; Keller, S.C.; /LLNL, Livermore; Lehner, M.J.; /Harvard-Smithsonian Ctr. Astrophys. /Taipei, Inst. Astron. Astrophys.; Marshall, S.L.; /SLAC; Minniti, D.; /Rio de Janeiro, Pont. U. Catol. /Vatican Astron. Observ.; Pratt, M.R.; /Aradigm, Hayward; Quinn, P.J.; /Western Australia U.; Stubbs, C.W.; /UC, Berkeley /Harvard U.; Sutherland, W.; /Oxford U. /Oran, Sci. Tech. U. /Garching, Max Planck Inst. /McMaster U.
2009-06-25
We present Hubble Space Telescope (HST) WFPC2 photometry of 13 microlensed source stars from the 5.7 year Large Magellanic Cloud (LMC) survey conducted by the MACHO Project. The microlensing source stars are identified by deriving accurate centroids in the ground-based MACHO images using difference image analysis (DIA) and then transforming the DIA coordinates to the HST frame. None of these sources is coincident with a background galaxy, which rules out the possibility that the MACHO LMC microlensing sample is contaminated with misidentified supernovae or AGN in galaxies behind the LMC. This supports the conclusion that the MACHO LMC microlensing sample has only a small amount of contamination due to non-microlensing forms of variability. We compare the WFPC2 source star magnitudes with the lensed flux predictions derived from microlensing fits to the light curve data. In most cases the source star brightness is accurately predicted. Finally, we develop a statistic which constrains the location of the Large Magellanic Cloud (LMC) microlensing source stars with respect to the distributions of stars and dust in the LMC and compare this to the predictions of various models of LMC microlensing. This test excludes at {approx}> 90% confidence level models where more than 80% of the source stars lie behind the LMC. Exotic models that attempt to explain the excess LMC microlensing optical depth seen by MACHO with a population of background sources are disfavored or excluded by this test. Models in which most of the lenses reside in a halo or spheroid distribution associated with either the Milky Way or the LMC are consistent which these data, but LMC halo or spheroid models are favored by the combined MACHO and EROS microlensing results.
10. The catalogue of radial velocity variable hot subluminous stars from the MUCHFUSS project
Geier, S; Heber, U; Schaffenroth, V; Barlow, B N; stensen, R H O; O'Toole, S J; Ziegerer, E; Heuser, C; Maxted, P F L; Gänsicke, B T; Marsh, T R; Napiwotzki, R; Brünner, P; Schindewolf, M; Niederhofer, F
2015-01-01
The project Massive Unseen Companions to Hot Faint Underluminous Stars from SDSS (MUCHFUSS) aims to find sdBs with compact companions like massive white dwarfs, neutron stars or black holes. Here we provide classifications, atmospheric parameters and a complete radial velocity (RV) catalogue containing 1914 single measurements for an sample of 177 hot subluminous stars discovered based on SDSS DR7. 110 stars show significant RV variability, while 67 qualify as candidates. We constrain the fraction of close massive compact companions {of hydrogen-rich hot subdwarfs} in our sample to be smaller than $\\sim1.3\\%$, which is already close to the theoretical predictions. However, the sample might still contain such binaries with longer periods exceeding $\\sim8\\,{\\rm d}$. We detect a mismatch between the $\\Delta RV_{\\rm max}$-distribution of the sdB and the more evolved sdOB and sdO stars, which challenges our understanding of their evolutionary connection. Furthermore, irregular RV variations of unknown origin with ...
11. PROJECT VeSElkA: ANALYSIS OF BALMER LINE PROFILES OF SLOWLY ROTATING CHEMICALLY PECULIAR STARS
Khalack, V.; LeBlanc, F., E-mail: khalack.viktor@umoncton.ca [Département de Physique et d’Astronomie, Université de Moncton, Moncton, N.-B., E1A 3E9 (Canada)
2015-07-15
We present results for the estimation of gravity, effective temperature, and radial velocity of poorly studied chemically peculiar stars recently observed with the spectropolarimeter Echelle SpectroPolarimetric Device for Observations of Stars at the Canada–France–Hawaii Telescope in the frame of the Vertical Stratification of Element Abundances project. The effective temperature and surface gravity values are determined for the very first time for four of the stars from our sample (HD 23878, HD 83373, HD 95608, and HD 164584). Grids of stellar atmosphere models with the corresponding fluxes have been calculated using version 15 of the PHOENIX code for effective temperatures in the range of 5000–15,000 K, for the logarithm of surface gravities in the range of 3.0–4.5 and for the metallicities from −1.0 to +1.5. We used these fluxes to fit the Balmer line profiles employing the code FITSB2 that produces estimates of the effective temperature, gravity, and radial velocity for each star. When possible, our results are compared to those previously published. The physical characteristics of 16 program stars are discussed with the future aim to study the abundance anomalies of chemical species and the possible vertical abundance stratification in their stellar atmosphere.
12. The DEBRIS Project: Searching for Kuiper Belts around the Nearest Stars with Herschel
Matthews, Brenda
Building on the recent success of Spitzer in detecting debris disks around the nearest stars and the SCUBA instrument at the JCMT in imaging cold disks, DEBRIS (Disk Emission via a Bias-free Reconnaissance in the Infrared/Submillimetre) is an open time key project on Herschel which aims to conduct an unbiased statistical survey for debris disks around the nearest stars to unprecedented mass limits. The survey is driven by 100 and 160 micron observations and is flux-limited. The sample is drawn from a database of nearby stars (Phillips et al. in prep) of spectral types A0 through M7 and totals 446 primaries, 348 of which will be observed by the DEBRIS team and 98 of which are covered by another the DUNES (DUst disks around NEarby Stars) team. Each target will be observed to a 100 micron rms of 1.2 mJy, allowing the detection of disks with dust masses comparable that of our own Kuiper belt towar the nearest stars. The superior resolution of Herschel should provide resolved images of many of the closest disks, and even our most distant disks may be resolvable. I will discuss the current state of debris disk research and highlight the areas in which Herschel will make the biggest impacts: establishing the true incidence of debris disks; characterizing the debris disk population, resolving disks and modeling their structure for evidence of long period planets; and the placing of our own Solar System in context.
13. Limits on a Gravitational Field Dependence of the Proton--Electron Mass Ratio from H$_2$ in White Dwarf Stars
Bagdonaite, Julija; Preval, Simon P; Barstow, Martin A; Barrow, John D; Murphy, Michael T; Ubachs, Wim
2014-01-01
Spectra of molecular hydrogen (H$_2$) are employed to search for a possible proton-to-electron mass ratio ($\\mu$) dependence on gravity. The Lyman transitions of H$_2$, observed with the Hubble Space Telescope towards white dwarf stars that underwent a gravitational collapse, are compared to accurate laboratory spectra taking into account the high temperature conditions ($T \\sim 13\\,000$ K) of their photospheres. We derive sensitivity coefficients $K_i$ which define how the individual H$_2$ transitions shift due to $\\mu$-dependence. The spectrum of white dwarf star GD133 yields a $\\Delta\\mu/\\mu$ constraint of $(-2.7\\pm4.7_{\\rm stat}\\pm 0.2_{\\rm sys})\\times10^{-5}$ for a local environment of a gravitational potential $\\phi\\sim10^4\\ \\phi_\\textrm{Earth}$, while that of G29$-$38 yields $\\Delta\\mu/\\mu=(-5.8\\pm3.8_{\\rm stat}\\pm 0.3_{\\rm sys})\\times10^{-5}$ for a potential of $2 \\times 10^4$ $\\phi_\\textrm{Earth}$.
14. DNC/HNC and N2D+/N2H+ ratios in high-mass star-forming cores
Fontani, F.; Sakai, T.; Furuya, K.; Sakai, N.; Aikawa, Y.; Yamamoto, S.
2014-05-01
Chemical models predict that the deuterated fraction (the column density ratio between a molecule containing D and its counterpart containing H) of N2H+, Dfrac(N2H+), high in massive pre-protostellar cores, is expected to rapidly drop by an order of magnitude after the protostar birth, while that of HNC, Dfrac(HNC), remains constant for much longer. We tested these predictions by deriving Dfrac(HNC) in 22 high-mass star-forming cores divided in three different evolutionary stages, from high-mass starless core candidates (HMSCs, eight) to high-mass protostellar objects (HMPOs, seven) to ultracompact H II regions (UCHIIs, seven). For all of them, Dfrac(N2H+) was already determined through IRAM 30 m Telescope observations, which confirmed the theoretical rapid decrease of Dfrac(N2H+) after protostar birth. Therefore, our comparative study is not affected by biases introduced by the source selection. We have found average Dfrac(HNC) of 0.012, 0.009 and 0.008 in HMSCs, HMPOs and UCHIIs, respectively, with no statistically significant differences among the three evolutionary groups. These findings confirm the predictions of the chemical models, and indicate that large values of Dfrac(N2H+) are more suitable than large values of Dfrac(HNC) to identify cores on the verge of forming high-mass stars, likewise what was found in the low-mass regime.
15. Modelling Mechanical Heating in Star-Forming Galaxies: CO and 13CO Line Ratios as Sensitive Probes
Kazandjian, M V; Meijerink, R; Israel, F P; Spaans, M
2016-01-01
We apply photo-dissociation region (PDR) molecular line emission models, that have varying degrees of enhanced mechanical heating rates, to the gaseous component of simulations of star-forming galaxies taken from the literature. Snapshots of these simulations are used to produce line emission maps for the rotational transitions of the CO molecule and its 13CO isotope up to J = 4-3. We consider two galaxy models: a small disk galaxy of solar metallicity and a lighter dwarf galaxy with 0.2 \\zsun metallicity. Elevated excitation temperatures for CO(1 - 0) correlate positively with mechanical feedback, that is enhanced towards the central region of both model galaxies. The emission maps of these model galaxies are used to compute line ratios of CO and 13CO transitions. These line ratios are used as diagnostics where we attempt to match them These line ratios are used as diagnostics where we attempt to match them to mechanically heated single component (i.e. uniform density, Far-UV flux, visual extinction and velo...
16. The Frequency Ratio Method for the seismic modelling of gamma Doradus stars. II The role of rotation
Suárez, J C; Martin-Ruiz, S; Amado, P J; Garrido, A G R
2005-01-01
The effect of rotation on the Frequency Ratio Method (Moya et al. 2005) is examined. Its applicability to observed frequencies of rotating gamma Doradus stars is discussed taking into account the following aspects: the use of a perturbative approach to compute adiabatic oscillation frequencies; the effect of rotation on the observational Brunt-Vaisala integral determination and finally, the problem of disentangling multiplet-like structures from frequency patterns due to the period spacing expected for high-order gravity modes in asymptotic regime. This analysis reveals that the FRM produces reliable results for objects with rotational velocities up to 70 kms/s, for which the FRM intrinsic error increases one order of magnitude with respect to the typical FRM errors given in Moya et al. (2005). Our computations suggest that, given the spherical degree "l" identification, the FRM may be discriminating for m = 0 modes, in the sense that the method avoids any misinterpretation induced by the presence of rotation...
17. The Chemical Abundances of Stars in the Halo (CASH) Project. III. A New Classification Scheme for Carbon-enhanced Metal-poor Stars with s-process Element Enhancement
Hollek, Julie K.; Frebel, Anna; Placco, Vinicius M.; Karakas, Amanda I.; Shetrone, Matthew; Sneden, Christopher; Christlieb, Norbert
2015-12-01
We present a detailed abundance analysis of 23 elements for a newly discovered carbon-enhanced metal-poor (CEMP) star, HE 0414-0343, from the Chemical Abundances of Stars in the Halo Project. Its spectroscopic stellar parameters are Teff = 4863 K, {log}g=1.25,\\ξ = 2.20 km s-1, and [Fe/H] = -2.24. Radial velocity measurements covering seven years indicate HE 0414-0343 to be a binary. HE 0414-0343 has {{[C/Fe]}}=1.44 and is strongly enhanced in neutron-capture elements but its abundances cannot be reproduced by a solar-type s-process pattern alone. Traditionally, it could be classified as a “CEMP-r/s” star. Based on abundance comparisons with asymptotic giant branch (AGB) star nucleosynthesis models, we suggest a new physically motivated origin and classification scheme for CEMP-s stars and the still poorly understood CEMP-r/s. The new scheme describes a continuous transition between these two so-far distinctly treated subgroups: CEMP-sA, CEMP-sB, and CEMP-sC. Possible causes for a continuous transition include the number of thermal pulses the AGB companion underwent, the effect of different AGB star masses on their nucleosynthetic yields, and physics that is not well approximated in 1D stellar models such as proton ingestion episodes and rotation. Based on a set of detailed AGB models, we suggest the abundance signature of HE 0414-0343 to have arisen from a >1.3 M⊙ mass AGB star and a late-time mass transfer that transformed HE 0414-0343 into a CEMP-sC star. We also find that the [Y/Ba] ratio well parametrizes the classification and can thus be used to easily classify any future such stars. Based on observations obtained with the Hobby-Eberly Telescope, which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen.
18. Araucaria Project: Pulsating stars in binary systems and as distance indicators
Pilecki, Bogumił; Gieren, Wolfgang; Pietrzyński, Grzegorz; Smolec, Radosław
2017-09-01
Pulsating stars, like Cepheids or RR Lyrae stars, are ones of the most important distance indicators. They are also key objects for testing the predictions of stellar evolution and stellar pulsation theory. In the Araucaria Project we have studied these objects since 2002, measuring distances to the galaxies in the Local Group and beyond. In 2010 we have for the first time confirmed spectroscopically the existence of a classical Cepheid in an eclipsing binary system. This has opened an opportunity to study in great details and with high accuracy (better than 1%) the physical parameters of these very important objects. First dynamical mass determination (Mcep = 4.16 ± 0.03 M⊙) let us solve the long-standing mass discrepancy problem. Since then we have measured masses for 6 classical Cepheids in binary systems and determined projection factors for three of them. One of the analyzed systems was confirmed to consist of two first-overtone Cepheids. Type II Cepheids are recently becoming more important as distance indicators and astrophysics laboratory, although our knowledge of these stars is quite limited. Their evolutionary status is also not well understood and observational constraints are needed to confirm the current theories. We are presenting here our first results of the spectroscopic analysis of 4 of these systems. The masses of type II Cepheids seem consistent with the expected 0.5 - 0.6 M⊙. We also present first results of the fully modeled pulsator originally classified as peculiar W Vir star. The mass of this star is 1.51 ± 0.09 M⊙ and the p-factor 1.3 ± 0.03. It was eventually found not to belong to any typical Cepheid group.
19. Photometry of pulsating stars in the Magellanic Clouds as observed in the MOA project
Hearnshaw, J B; Rattenbury, N J; Noda, S; Takeuti, M; Abe, F; Carter, B S; Dodd, R J; Honda, M; Juga Ku Jun; Kabe, S; Kilmartin, P M; Matsubara, Y; Masuda, K; Muraki, Y; Nakamura, T; Reid, M; Rumsey, N J; Saitô, T; Sato, H; Sekiguchi, M; Sullivan, D J; Sumi, T; Watase, Y; Yanagisawa, T; Yock, P C M; Yoshizawa, M; Koribalski, B S; Saito, To.
1999-01-01
A review of the MOA (Microlensing Observations in Astrophysics) project is presented. MOA is a collaboration of approximately 30 astronomers from New Zealand and Japan established with the aim of finding and detecting microlensing events towards the Magellanic Clouds and the Galactic bulge, which may be indicative of either dark matter or of planetary companions. The observing program commenced in 1995, using very wide band blue and red filters and a nine-chip mosaic CCD camera. As a by-product of these observations a large database of CCD photometry for 1.4 million stars towards both LMC and SMC has been established. In one preliminary analysis 576 bright variable stars were confirmed, nearly half of them being Cepheids. Another analysis has identified large numbers of blue variables, and 205 eclipsing binaries are included in this sample. In addition 351 red variables (AGB stars) have been found. Light curves have been obtained for all these stars. The observations are carried out on a 61-cm f/6.25 telescop...
20. The EPOCH Project: I. Periodic Variable Stars in the EROS-2 LMC Database
Kim, Dae-Won; Bailer-Jones, Coryn A L; Byun, Yong-Ik; Chang, Seo-Won; Marquette, Jean-Baptiste; Shin, Min-Su
2014-01-01
The EPOCH (EROS-2 periodic variable star classification using machine learning) project aims to detect periodic variable stars in the EROS-2 light curve database. In this paper, we present the first result of the classification of periodic variable stars in the EROS-2 LMC database. In order to classify these variables, we first build a training set by compiling known variables in the Large Magellanic Could area from the OGLE and MACHO surveys. We crossmatch these variables with the EROS-2 sources and extract 22 variability features from 28,392 light curves of the corresponding EROS-2 sources. We then use Random Forests to classify the EROS-2 sources in the training set. We design the model to separate not only $\\delta$ Scuti stars, RR Lyraes, Cepheids, eclipsing binaries and long-period variables, the "superclasses", but also their subclasses, such as RRab, RRc, RRd and RRe for RR Lyraes, and similarly for the other variable types. The model trained using only the superclasses shows 99% recall and precision w...
1. Project VeSElkA: Analysis of Balmer line profiles in slowly rotating chemically peculiar stars
Khalack, Viktor
2015-01-01
We present results for the estimation of gravity, effective temperature, and radial velocity of poorly studied chemically peculiar stars recently observed with the spectropolarimeter Echelle SpectroPolarimetric Device for Observations of Stars at the Canada-France-Hawaii Telescope in the frame of the Vertical Stratification of Element Abundances project. The effective temperature and surface gravity values are determined for the very first time for four of the stars from our sample (HD23878, HD83373, HD95608, and HD164584). Grids of stellar atmosphere models with the corresponding fluxes have been calculated using version 15 of the PHOENIX code for effective temperatures in the range of 5000-15,000 K, for the logarithm of surface gravities in the range of 3.0-4.5 and for the metallicities from -1.0 to +1.5. We used these fluxes to fit the Balmer line profiles employing the code FITSB2 that produces estimates of the effective temperature, gravity, and radial velocity for each star. When possible, our results a...
2. The declared barriers of the large developing countries waste management projects: The STAR model.
Bufoni, André Luiz; Oliveira, Luciano Basto; Rosa, Luiz Pinguelli
2016-06-01
The aim of this study is to investigate and describe the barriers system that precludes the feasibility, or limits the performance of the waste management projects through the analysis of which are the declared barriers at the 432 large waste management projects registered as CDM during the period 2004-2014. The final product is a waste management barriers conceptual model proposal (STAR), supported by literature and corroborated by projects design documents. This paper uses the computer assisted qualitative content analysis (CAQCA) methodology with the qualitative data analysis (QDA) software NVivo®, by 890 fragments, to investigate the motives to support our conclusions. Results suggest the main barriers classification in five types: sociopolitical, technological, regulatory, financial, and human resources constraints. Results also suggest that beyond the waste management industry, projects have disadvantages added related to the same barriers inherent to others renewable energies initiatives. The STAR model sheds some light over the interactivity and dynamics related to the main constraints of the industry, describing the mutual influences and relationships among each one. Future researches are needed to better and comprehensively understand these relationships and ease the development of tools to alleviate or eliminate them.
3. The "Binarity and Magnetic Interactions in various classes of Stars" (BinaMIcS) project
Neiner, C; Alecian, E
2015-01-01
The "Binarity and Magnetic Interactions in various classes of stars" (BinaMIcS) project is based on two large programs of spectropolarimetric observations with ESPaDOnS at CFHT and Narval at TBL. Three samples of spectroscopic binaries with two spectra (SB2) are observed: known cool magnetic binaries, the few known hot magnetic binaries, and a survey sample of hot binaries to search for additional hot magnetic binaries. The goal of BinaMIcS is to understand the complex interplay between stellar magnetism and binarity. To this aim, we will characterise and model the magnetic fields, magnetospheric structure and coupling of both components of hot and cool close binary systems over a significant range of evolutionary stages, to confront current theories and trigger new ones. First results already provided interesting clues, e.g. about the origin of magnetism in hot stars.
4. The Abundance, Ortho/Para Ratio, and Deuteration of Water in the High-Mass Star Forming Region NGC 6334 I
Emprechtinger, M; Rolffs, R; Schilke, P; Monje, R R; Comito, C; Ceccarelli, C; Neufeld, D A; van der Tak, F F S
2012-01-01
We present Herschel/HIFI observations of 30 transitions of water isotopologues toward the high-mass star forming region NGC 6334 I. The line profiles of H_2^{16}O, H_2^{17}O, H_2^{18}O, and HDO show a complex pattern of emission and absorption components associated with the embedded hot cores, a lower-density envelope, two outflow components, and several foreground clouds, some associated with the NGC 6334 complex, others seen in projection against the strong continuum background of the source. Our analysis reveals an H2O ortho/para ratio of 3 +/- 0.5 in the foreground clouds, as well as the outflow. The water abundance varies from ~10^{-8} in the foreground clouds and the outer envelope to ~10^{-6} in the hot core. The hot core abundance is two orders of magnitude below the chemical model predictions for dense, warm gas, but within the range of values found in other Herschel/HIFI studies of hot cores and hot corinos. This may be related to the relatively low gas and dust temperature (~100 K), or time depende...
5. The Dependence of Signal-To-Noise Ratio (S/N) Between Star Brightness and Background on the Filter Used in Images Taken by the Vulcan Photometric Planet Search Camera
Mena-Werth, Jose
1998-01-01
The Vulcan Photometric Planet Search is the ground-based counterpart of Kepler Mission Proposal. The Kepler Proposal calls for the launch of telescope to look intently at a small patch of sky for four year. The mission is designed to look for extra-solar planets that transit sun-like stars. The Kepler Mission should be able to detect Earth-size planets. This goal requires an instrument and software capable of detecting photometric changes of several parts per hundred thousand in the flux of a star. The goal also requires the continuous monitoring of about a hundred thousand stars. The Kepler Mission is a NASA Discovery Class proposal similar in cost to the Lunar Prospector. The Vulcan Search is also a NASA project but based at Lick Observatory. A small wide-field telescope monitors various star fields successively during the year. Dozens of images, each containing tens of thousands of stars, are taken any night that weather permits. The images are then monitored for photometric changes of the order of one part in a thousand. These changes would reveal the transit of an inner-orbit Jupiter-size planet similar to those discovered recently in spectroscopic searches. In order to achieve a one part in one thousand photometric precision even the choice of a filter used in taking an exposure can be critical. The ultimate purpose of an filter is to increase the signal-to-noise ratio (S/N) of one's observation. Ideally, filters reduce the sky glow cause by street lights and, thereby, make the star images more distinct. The higher the S/N, the higher is the chance to observe a transit signal that indicates the presence of a new planet. It is, therefore, important to select the filter that maximizes the S/N.
6. Being WISE II: Reducing the Influence of Star Formation History on the Mass-to-Light Ratio of Quiescent Galaxies
Norris, Mark A; Schinnerer, Eva; Crain, Robert A; Meidt, Sharon; Groves, Brent; Bower, Richard G; Furlong, Michelle; Schaller, Matthieu; Schaye, Joop; Theuns, Tom
2016-01-01
Stellar population synthesis models can now reproduce the photometry of old stellar systems (age $>$ 2 Gyr) in the near-infrared (NIR) bands at 3.4 and 4.6$\\mu$m (WISE W1 $\\&$ W2 or IRAC 1 $\\&$ 2). In this paper we derive stellar mass-to-light ratios for these and optical bands, and confirm that the NIR M/L shows dramatically reduced sensitivity to both age and metallicity compared to optical bands, and further, that this behavior leads to significantly more robust stellar masses for quiescent galaxies with [Fe/H] > -0.5 regardless of star formation history (SFH). We then use realistic early-type galaxy SFHs and metallicity distributions from the EAGLE simulations of galaxy formation to investigate two methods to determine the appropriate M/L for a galaxy: 1) We show that the uncertainties introduced by an unknown SFH can be largely removed using a spectroscopically inferred luminosity-weighted age and metallicity for the population to select the appropriate single stellar population (SSP) equivalent ...
7. DNC/HNC and N2D+/N2H+ ratios in high-mass star forming cores
Fontani, F; Furuya, K; Sakai, N; Aikawa, Y; Yamamoto, S
2014-01-01
Chemical models predict that the deuterated fraction (the column density ratio between a molecule containing D and its counterpart containing H) of N2H+, Dfrac(N2H+), is high in massive pre-protostellar cores and rapidly drops of an order of magnitude after the protostar birth, while that of HNC, Dfrac(HNC), remains constant for much longer. We tested these predictions by deriving Dfrac(HNC) in 22 high-mass star forming cores divided in three different evolutionary stages, from high-mass starless core candidates (HMSCs, 8) to high-mass protostellar objects (HMPOs, 7) to Ultracompact HII regions (UCHIIs, 7). For all of them, Dfrac (N2H+) was already determined through IRAM-30m Telescope observations, which confirmed the theoretical rapid decrease of Dfrac(N2H+) after protostar birth (Fontani et al. 2011). Therefore our comparative study is not affected by biases introduced by the source selection. We have found average Dfrac(HNC) of 0.012, 0.009 and 0.008 in HMSCs, HMPOs and UCHIIs, respectively, with no stati...
8. Abundance Ratios in Stars vs. Hot Gas in Elliptical Galaxies: the Chemical Evolution Modeller Point of View
Pipino, A
2009-01-01
I will present predictions from chemical evolution model aimed at a self-consistent study of both optical (i.e. stellar) and X-ray (i.e.gas) properties of present-day elliptical galaxies. Detailed cooling and heating processes in the interstellar medium (ISM) are taken into and allow a reliable modelling of the SN-driven galactic wind. SNe Ia activity, in fact, may power a galactic wind lasting for a considerable amount of the galactic lifetime, even in the case for which the efficiency of energy transfer into the ISM per SN Ia event is less than unity. The model simultaneously reproduces the mass-metallicity, the colour-magnitude, the L_X - L_B and the L_X - T relations, as well as the observed trend of the [Mg/Fe] ratio as a function of sigma, by adopting the prescriptions of Pipino & Matteucci (2004) for the gas infall and star formation timescales. The "iron discrepancy", namely the too high predicted iron abundance in X-ray haloes of ellipticals compared to observations, can be solved by taking into ...
9. Projection of retirement adequacy using wealth-need ratio: A case study in Malaysia
Alaudin, Ros Idayuwati; Ismail, Noriszura; Isa, Zaidi
2015-02-01
Adequacy of retirement income is very important to maintain a comfortable living standard during retirement. Under a life cycle model, assets are mainly accumulated during an individual's work life to finance consumption after retirement. A generally accepted goal of retirement planning is to provide enough income during retirement to prevent the level of living from dropping much below the pre-retirement level. Retirement wealth can be defined as adequate if the total retirement income is equal or greater than the desired total retirement consumption (or needs). In this study, retirement adequacy is projected using the Malaysian Household Income Survey (HIS) 2009 data which is based on 5881 sample of households and contains information on income, demographic and socioeconomic status of each household. Besides the projection of retirement adequacy, a regression of the ratio of projected wealth to needs (or wealth-needs ratio) is performed to investigate the demographic and socioeconomic determinants of retirement adequacy in Malaysia. The results show that 69% of households in Malaysia are adequately prepared for retirement.
10. Hubble Tarantula Treasury Project V. The star cluster Hodge 301: the old face of 30 Doradus
Cignoni, M; van der Marel, R P; Lennon, D J; Tosi, M; Grebel, E K; Gallagher, J S; Aloisi, A; de Marchi, G; Gouliermis, D A; Larsen, S; Panagia, N; Smith, L J
2016-01-01
Based on color-magnitude diagrams (CMDs) from the Hubble Space Telescope Hubble Tarantula Treasury Project (HTTP) survey, we present the star formation history (SFH) of Hodge~301, the oldest star cluster in the Tarantula Nebula. The HTTP photometry extends faint enough to reach, for the first time, the cluster pre-main sequence (PMS) turn-on, where the PMS joins the main sequence. Using the location of this feature, along with synthetic CMDs generated with the latest PARSEC models, we find that Hodge~301 is older than previously thought, with an age between 26.5 and 31.5 Myr. From this age, we also estimate that between 38 and 61 supernovae Type-II exploded in the region. The same age is derived from the main sequence turn-off, whereas the age derived from the post-main sequence stars is younger and between 20 and 25 Myr. Other relevant parameters are a total stellar mass of $\\approx 8800\\,\\pm 800$M$_{\\odot}$ and average reddening E(B$-$V) $\\approx 0.22-0.24$ mag, with a differential reddening $\\delta$E(B$-$V...
11. Hubble Tarantula Treasury Project V. The Star Cluster Hodge 301: The Old Face of 30 Doradus
Cignoni, M.; Sabbi, E.; van der Marel, R. P.; Lennon, D. J.; Tosi, M.; Grebel, E. K.; Gallagher, J. S., III; Aloisi, A.; de Marchi, G.; Gouliermis, D. A.; Larsen, S.; Panagia, N.; Smith, L. J.
2016-12-01
Based on color-magnitude diagrams (CMDs) from the Hubble Space Telescope Hubble Tarantula Treasury Project (HTTP) survey, we present the star formation history of Hodge 301, the oldest star cluster in the Tarantula Nebula. The HTTP photometry extends faint enough to reach, for the first time, the cluster pre-main sequence (PMS) turn-on, where the PMS joins the main sequence. Using the location of this feature, along with synthetic CMDs generated with the latest PARSEC models, we find that Hodge 301 is older than previously thought, with an age between 26.5 and 31.5 Myr. From this age, we also estimate that between 38 and 61 Type II supernovae exploded in the region. The same age is derived from the main sequence turn-off, whereas the age derived from the post-main sequence stars is younger and between 20 and 25 Myr. Other relevant parameters are a total stellar mass of ≈8800 ± 800 M ⊙ and average reddening E(B - V) ≈ 0.22-0.24 mag, with a differential reddening δE(B - V) ≈ 0.04 mag. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA Inc., under NASA contract NAS 5-26555.
12. A possible formation channel for blue hook stars in globular cluster - II. Effects of metallicity, mass ratio, tidal enhancement efficiency and helium abundance
Lei, Zhenxin; Zeng, Aihua; Shen, Lihua; Lan, Zhongjian; Jiang, Dengkai; Han, Zhanwen
2016-01-01
Employing tidally enhanced stellar wind, we studied in binaries the effects of metallicity, mass ratio of primary to secondary, tidal enhancement efficiency and helium abundance on the formation of blue hook (BHk) stars in globular clusters (GCs). A total of 28 sets of binary models combined with different input parameters are studied. For each set of binary model, we presented a range of initial orbital periods that is needed to produce BHk stars in binaries. All the binary models could produce BHk stars within different range of initial orbital periods. We also compared our results with the observation in the Teff-logg diagram of GC NGC 2808 and {\\omega} Cen. Most of the BHk stars in these two GCs locate well in the region predicted by our theoretical models, especially when C/N-enhanced model atmospheres are considered. We found that mass ratio of primary to secondary and tidal enhancement efficiency have little effects on the formation of BHk stars in binaries, while metallicity and helium abundance would...
13. The Training Project of Star Researchers, Outstanding Teaching Staff and Leaders with Facilities Available
Ömer KARAHAN
2015-12-01
Full Text Available There is a general consensus on the requirement of a serious regulation at our universities. It is argued that it is necessary to change Constitution and Institution of Higher Education Law for the serious regulation. However, it is impossible to say that all the facilities of the present legislation are used. Our aim is to create a project based on benefiting from continuing education centers to meet the need of star researchers, outstanding teaching staff and leaders in Turkey via the legislation in force. In this study, accessible studies from publications related to university, higher education and continuing education centers are studied. Th e current situation and solution off ers, applications and continuing education centers'activities have been determined. In accordance with these data, solution off ers have been proposed and discussed in line with the literature. According to the data obtained, our students who come with deficiencies from high schools to universities are not given the adequate undergraduate, graduate and postgraduate education. Th ere are studies such as ‘Double Major Program', ‘Medical-Science Physicians Integrated (MD-PhD Doctorate Program which upgrade the qualities. However, these programs are not suff icient and common. Th erefore, it is imposssible to train outstanding teaching staff , star researchesr and leaders who will meet the needs of our country and contribute to the World. Our academic potential needs a quality training except for branch training. On the other hand, the contribution of the Continuing Education Centers existing in university embodiments is limited. It is possible to provide basic skills, integration and research education to the outstanding teaching staff , star researcher and leader candidates. Th ese trainings should be given in a continuous instutionalization and in the formal education system. For this purpose, an academician school can be established within the body continuing
14. The Variable Star One-shot Project, and its little child: Wikimbad
Foellmi, C; Pritchard, J; Curto, G Lo; Prieto, C Allende; Bruntt, H; Amado, P J; Arentoft, T; Baes, M; Depagne, E; Fernández, M; Ivanov, V D; Koesterke, L; Monaco, L; O'Brien, K; Sarro, L M; Saviane, I; Scharwächter, J; Schmidtobreick, L; Schuetz, O; Seifahrt, A; Selman, F; Stefanon, M; Sterzik, M
2007-01-01
The Variable Star One-shot Project (VSOP) aimed at providing to the world-wide stellar community the necessary one-shot spectrum of unstudied variable stars, too often classified as such by an analysis of photometric data only. The VSOP has established an new kind of observational model, where all steps from observations to spectral analysis, are automatized (or are underway to be fully automatized). The project is centralized on a collaborative wiki website. The VSOP operational model is very successful, data is continously flowing and being analyszed, and VSOP is now a worldwide open collaboration of people with very different and complementary skills and expertise. The idea of a central wiki website has been extended by one of us to propose a new service to the whole astronomical community, called Wikimbad. Wikimbad is an open wiki website aimed at collecting, organizing and making publicly available all kind of reduced and published astronomical data. Its strengths and a comparison with the Virtual Observ...
15. The Biases of Optical Line-Ratio Selection for Active Galactic Nuclei, and the Intrinsic Relationship between Black Hole Accretion and Galaxy Star Formation
Trump, Jonathan R; Zeimann, Gregory R; Luck, Cuyler; Bridge, Joanna S; Grier, Catherine J; Hagen, Alex; Juneau, Stephanie; Montero-Dorta, Antonio; Rosario, David J; Brandt, W Niel; Ciardullo, Robin; Schneider, Donald P
2015-01-01
We use 317,000 emission-line galaxies from the Sloan Digital Sky Survey to investigate line-ratio selection of active galactic nuclei (AGNs). In particular, we demonstrate that "star formation dilution" by HII regions causes a significant bias against AGN selection in low-mass, blue, star-forming, disk-dominated galaxies. This bias is responsible for the observed preference of AGNs among high-mass, green, moderately star-forming, bulge-dominated hosts. We account for the bias and simulate the intrinsic population of emission-line AGNs using a physically-motivated Eddington ratio distribution, intrinsic AGN narrow line region line ratios, a luminosity-dependent Lbol/L[OIII] bolometric correction, and the observed Mbh-sigma relation. These simulations indicate that, in massive (log(M*/Msun) > 10) galaxies, AGN accretion is correlated with specific star formation rate but is otherwise uniform with stellar mass. There is some hint of lower black hole occupation in low-mass (log(M*/Msun) < 10) hosts, although o...
16. Being WISE II: Reducing the Influence of Star formation History on the Mass-to-Light Ratio of Quiescent Galaxies
Norris, Mark A.; Van de Ven, Glenn; Schinnerer, Eva; Crain, Robert A.; Meidt, Sharon; Groves, Brent; Bower, Richard G.; Furlong, Michelle; Schaller, Matthieu; Schaye, Joop; Theuns, Tom
2016-12-01
Stellar population synthesis models can now reproduce the photometry of old stellar systems (age \\gt 2 Gyr) in the near-infrared (NIR) bands at 3.4 and 4.6 μm (WISE W1 and W2 or IRAC 1 and 2). In this paper, we derive stellar mass-to-light ratios for these and optical bands, and confirm that the NIR M/L shows dramatically reduced sensitivity to both age and metallicity compared to optical bands, and further, that this behavior leads to significantly more robust stellar masses for quiescent galaxies with [Fe/H] ≳ -0.5 regardless of star-formation history (SFH). We then use realistic early-type galaxy SFHs and metallicity distributions from the EAGLE simulations of galaxy formation to investigate two methods to determine the appropriate M/L for a galaxy. (1) We show that the uncertainties introduced by an unknown SFH can be largely removed using a spectroscopically inferred luminosity-weighted age and metallicity for the population to select the appropriate single stellar population (SSP) equivalent M/L. Using this method, the maximum systematic error due to SFH on the M/L of an early-type galaxy is \\lt 4 % at 3.4 μm and typical uncertainties due to errors in the age and metallicity create a scatter of ≲ 13 % . The equivalent values for optical bands are more than two to three times greater, even before considering uncertainties associated with internal dust extinction. (2) We demonstrate that if the EAGLE SFHs and metallicities accurately reproduce the true properties of early-type galaxies, the use of an iterative approach to select a mass dependent M/L can provide even more accurate stellar masses for early-type galaxies, with typical uncertainties of \\lt 9 % .
17. Lunar project ILOM: application of the analytical theory of Lunar physical libration for the simulation of star observations
PETROVA Nataliya; GUSEV Alexander; PING JinSong; IVANOVA Tamara; HANADA Hideo; KAWANO Nobuyuki; SU XiaoLi
2012-01-01
This study briefly describes the targets and problems of the future Japanese project In situ Lunar Orientation Measurement (ILOM),which is planned for the year 2017.One of the important parts of the project is to place a small optical telescope on the Lunar surface with the purpose to detect the Lunar physical libration with unprecedented accuracy 0.001 arcsec.At the present stage of research the computer simulation of future observations is going on,aiming to determine the moments of transition of a star through the first meridian and the polar distance of the star.Rotation of the Moon is being calculated under the analytical theory developed in the frame of a theme of the grant.A list of stars brighter than 12 m,whose coordinates are close to the Lunar precession pole motion,was constructed on the basis of several star catalogues.On average,for each moment of observation in the field of view of the telescope (1°) there are approximately 20-25 stars,Analyses of simulated stellar tracks observable from the Lunar surface (in a polar zone) reveal the significant difference from daily parallels of stars in comparison with the Earth.During one Lunar "day" equal 237 terrestrial days,a star moves on a spiral.However,depending on a longitude of a star,these spirals can be untwisted or twisted.In the latter case a star can describe a loop in the sky of the Moon during the period of supervision.Such an unusual astrometric phenomenon combined with the slow rotation of the Moon is compared with the Earth and the fast precession motion of the Lunar pole (in comparison with the precession motion of a terrestrial pole).
18. Optical/infrared ancillary photometry of young stars for the Herschell Key Project GASPS
Duchene, Gaspard; Dent, William; Montesinos, Benjamin
2009-08-01
This proposal aims at using the queue-mode 1.3m telescope at CTIO to gather near-contemporaneous photometric measurements of a sample of objects that will be observed with the Herschel Space Observatory in the upcoming months as part of the Open Time Key Program GASPS. This project is aimed at characterizing the gas content of circumstellar disks around young stars throughout the planet formation phase. In order to model the Herschel data in a coherent manner, it is necessary to determine each star's basic properties (effective temperature, mass, luminosity), which implies obtaining a complete broadband spectral energy distribution to combine with existing longer data (AKARI, Spitzer, Herschel and millimeter single-dish and interferometric fluxes). Here we propose to obtain new simultaneous optical and IR photometric measurements of 16 targets that cannot be observed from Northern observatories. In addition to provide a sound basis for our disk modeling effort, the observations proposed here will also offer new insight on the location, morphology and evolution of the disks' inner rim in conjunction with the currently ongoing AKARI observations.
19. The TAOS Project Stellar Variability II. Detection of 15 Variable Stars
Mondal, S; Lin, C C; Zhang, Z W; Alcock, C; Axelrod, T; Bianco, F B; Byun, Y I; Coehlo, N K; Cook, K H; Dave, R; Kim, D W; King, S K; Lee, T; Lehner, M J; Lin, H C; Marshall, S L; Protopapas, P; Rice, J A; Schwamb, M E; Wang, J H; Wang, S Y; Wen, C Y
2010-01-28
The Taiwanese-American Occultation Survey (TAOS) project has collected more than a billion photometric measurements since 2005 January. These sky survey data - covering timescales from a fraction of a second to a few hundred days - are a useful source to study stellar variability. A total of 167 star fields, mostly along the ecliptic plane, have been selected for photometric monitoring with the TAOS telescopes. This paper presents our initial analysis of a search for periodic variable stars from the time-series TAOS data on one particular TAOS field, No. 151 (RA = 17{sup h} 30{sup m} 6.67{sup s}, Dec = 27 degrees, 17 minutes, 30 seconds, J2000), which had been observed over 47 epochs in 2005. A total of 81 candidate variables are identified in the 3 square degree field, with magnitudes in the range 8 < R < 16. On the basis of the periodicity and shape of the lightcurves, 32 variables, 18 of which were previously unknown, are classified as RR Lyrae, Cepheid, {delta} Scuti, SX Phonencis, semi-regular and eclipsing binaries.
20. The PTF Orion Project: a Possible Planet Transiting a T-Tauri Star
van Eyken, Julian C; von Braun, Kaspar; Kane, Stephen R; Plavchan, Peter; Bender, Chad F; Brown, Timothy M; Crepp, Justin; Fulton, Benjamin J; Howard, Andrew W; Howell, Steve B; Mahadevan, Suvrath; Marcy, Geoffrey W; Shporer, Avi; Szkody, Paula; Akeson, Rachel L; Beichman, Charles A; Boden, Andrew F; Gelino, Dawn M; Hoard, D W; Ramírez, Solange V; Rebull, Luisa M; Stauffer, John R; Bloom, Joshua S; Cenko, S Bradley; Kasliwal, Mansi M; Kulkarni, Shrinivas R; Law, Nicholas M; Nugent, Peter E; Ofek, Eran O; Poznanski, Dovi; Quimby, Robert M; Walters, Richard; Grillmair, Carl J; Laher, Russ; Levitan, David B; Sesar, Branimir; Surace, Jason A
2012-01-01
We report observations of a possible young transiting planet orbiting a previously known weak-lined T-Tauri star in the 7-10Myr-old Orion-OB1a/25-Ori region. The candidate was found as part of the Palomar Transient Factory (PTF) Orion project. It has a photometric transit period of 0.448413 \\pm 0.000040 days, and appears in both 2009 and 2010 PTF data. Follow-up low-precision radial velocity observations and adaptive-optics imaging suggest that the star is not an eclipsing binary, and that it is unlikely that a background source is blended with the target and mimicking the observed transit. Radial-velocity observations with the Hobby-Eberly and Keck telescopes yield a radial velocity that has the same period as the photometric event, but is offset in phase from the transit center by \\approx -0.22 periods. The amplitude (half range) of the radial velocity variations is 2.4 km/s and is comparable with the expected radial velocity amplitude that stellar spots could induce. The radial velocity curve is likely dom...
1. The MACHO Project 9 Million Star Color-Magnitude Diagram of the Large Magellanic Cloud
Alcock, C B; Alves, D R; Axelrod, T S; Basu, A; Becker, A C; Bennett, D P; Cook, K H; Drake, A J; Freeman, K C; Geha, M; Griest, K; King, L; Lehner, M J; Marshall, S L; Minniti, D; Nelson, C; Peterson, B A; Popowski, P A; Pratt, M R; Quinn, P J; Stubbs, C W; Sutherland, W; Tomaney, A B; Vandehei, T; Welch, D L
2000-01-01
We present a 9 million star color-magnitude diagram (9M CMD) of the LMC bar. The 9M CMD reveals a complex superposition of different age and metallicity stellar populations, with important stellar evolutionary phases occurring over 3 orders of magnitude in number density. First, we count the non-variable supergiants, the associated Cepheids, and measure the effective temperatures defining the instability strip. Lifetime predictions of stellar evolution theory are tested, with implications for the origin of low-luminosity Cepheids. The highly-evolved AGB stars have a bimodal distribution in brightness, which we interpret as discrete old populations (>1 Gyr). The faint AGB may be metal-poor and very old. We identify the clusters NGC 411 and M3 as templates for the admixture of old stellar populations. However, there are indications that the old and metal-poor field population has a red HB morphology: the RR Lyraes lie on the red edge of the instability strip, the AGB-bump is very red, and the ratio of AGB-bump ...
2. The AMBRE Project: Parameterisation of FGK-type stars from the ESO:HARPS archived spectra
De Pascale, Marco; de Laverny, Patrick; Recio-Blanco, Alejandra; Hill, Vanessa; Bijaoui, Albert
2014-01-01
The AMBRE project is a collaboration between the European Southern Observatory (ESO) and the Observatoire de la Cote d'Azur (OCA). It has been established to determine the stellar atmospheric parameters (effective temperature, surface gravity, global metallicities and abundance of alpha-elements over iron) of the archived spectra of four ESO spectrographs. The analysis of the ESO:HARPS archived spectra is presented. The sample being analysed (AMBRE:HARPS) covers the period from 2003 to 2010 and is comprised of 126688 scientific spectra corresponding to 17218 different stars. For the analysis of the spectral sample, the automated pipeline developed for the analysis of the AMBRE:FEROS archived spectra has been adapted to the characteristics of the HARPS spectra. Within the pipeline, the stellar parameters are determined by the MATISSE algorithm, developed at OCA for the analysis of large samples of stellar spectra in the framework of galactic archaeology. In the present application, MATISSE uses the AMBRE grid ...
3. Popularizing a scientific project: star forming rate in different ages of the Universe
Zamorano, J.; Jáuregui, F.; Fernández-Castro, T.; Gallego, J.; Armentia, J.
In Spain we have to make a big effort in order to produce more activities dedicated to the popularization of Science. In this paper we show the activities we have developped, and others that will be done soon, in order to show to the general public, an example of how science is made. The project Star Forming Rate at Different z's is paid with public founds and included in its objectives, are some actions directed to the popularization of the science made in it. Exhibitions, public talks and planetarium shows are part of these activities presented to the general public in two of the main Science Centers of Spain, the Madrid and Pamplona planetaria.
4. Gamma Ray Burst and star formation rates: The physical origin for the redshift evolution of their ratio
Trenti, M; Tacchella, S
2013-01-01
Gamma Ray Bursts (GRBs) and galaxies at high redshift represent complementary probes of the star formation history of the Universe. In fact, both the GRB rate and the galaxy luminosity density are connected to the underlying star formation. Here, we combine a star formation model for the evolution of the galaxy luminosity function from z=0 to z=10 with a metallicity-dependent efficiency for GRB formation to simultaneously predict the comoving GRB rate. Our model sheds light on the physical origin of the empirical relation often assumed between GRB rate and luminosity density-derived star formation rate: Rgrb(z) = \\epsilon(z)*SFR_{obs}(z), with \\epsilon(z) (1+z)^{1.2}. At z0. Models with total suppression of GRB formation at log(Z/Zsun)>0 are disfavored. At z>4, most of the star formation happens in low-metallicity hosts with nearly saturated efficiency of GRB production per unit stellar mass. However at the same epoch, galaxy surveys miss an increasing fraction of the predicted luminosity density because of f...
5. A Coherent Study of Emission Lines from Broad-Band Photometry: Specific Star-Formation Rates and [OIII]/H{\\beta} Ratio at 3 < z < 6
Faisst, A L; Hsieh, B C; Laigle, C; Salvato, M; Tasca, L; Cassata, P; Davidzon, I; Ilbert, O; Fevre, O Le; Masters, D; McCracken, H J; Steinhardt, C; Silverman, J D; De Barros, S; Hasinger, G; Scoville, N Z
2016-01-01
We measure the H{\\alpha} and [OIII] emission line properties as well as specific star-formation rates (sSFR) of spectroscopically confirmed 33 cannot be fully explained in a picture of cold accretion driven growth. We find a progressively increasing [OIII]{\\lambda}5007/H{\\beta} ratio out to z~6, consistent with the ratios in local galaxies selected by increasing H{\\alpha} EW (i.e., sSFR). This demonstrates the potential of using "local high-z analogs" to investigate the spectroscopic properties and relations of galaxies in the re-ionization epoch.
6. The SERMON project: 48 new field Blazhko stars and an investigation of modulation-period distribution
Skarka, Marek; Auer, Reinhold F; Prudil, Zdeněk; Juráňová, Anna; Sódor, Ádam
2016-01-01
We investigated 1234 fundamental mode RR Lyrae stars observed by the All Sky Automated Survey (ASAS) to identify the Blazhko (BL) effect. A sample of 1547 BL stars from the literature was collected to compare the modulation-period distribution with stars newly identified in our sample. A classical frequency spectra analysis was performed using Period04 software. Data points from each star from the ASAS database were analysed individually to avoid confusion with artificial peaks and aliases. Statistical methods were used in the investigation of the modulation-period distribution. Altogether we identified 87 BL stars (48 new detections), 7 candidate stars, and 22 stars showing long-term period variations. The distribution of modulation periods of newly identified BL stars corresponds well to the distribution of modulation periods of stars located in the Galactic field, Galactic bulge, Large Magellanic Cloud, and globular cluster M5 collected from the literature. As a very important by-product of this comparison...
7. Rejecting the "At-Risk" Stereotype: Project U-STARS-PLUS Helps Kids "At-Potential." FPG Snapshot #61
FPG Child Development Institute, 2010
2010-01-01
Every day, schools and communities across the U.S. identify millions of young children as "at risk"--especially those with a minority background, who live in poor neighborhoods or are learning English as a second language. FPG's Project U-STARS-PLUS (Using Science, Talents, and Abilities to Recognize Students-Promoting Learning for…
8. The dust-to-stellar mass ratio as a valuable tool to probe the evolution of local and distant star forming galaxies
Calura, F; Cresci, G; Santini, P; Gruppioni, C; Pozzetti, L; Gilli, R; Matteucci, F; Maiolino, R
2016-01-01
The survival of dust grains in galaxies depends on various processes. Dust can be produced in stars, it can grow in the interstellar medium and be destroyed by astration and interstellar shocks. In this paper, we assemble a few data samples of local and distant star-forming galaxies to analyse various dust-related quantities in low and high redshift galaxies, to study how the relations linking the dust mass to the stellar mass and star formation rate evolve with redshift. We interpret the available data by means of chemical evolution models for discs and proto-spheroid (PSPH) starburst galaxies. In particular, we focus on the dust-to-stellar mass (DTS) ratio, as this quantity represents a true measure of how much dust per unit stellar mass survives the various destruction processes in galaxies and is observable. The theoretical models outline the strong dependence of this quantity on the underlying star formation history. Spiral galaxies are characterised by a nearly constant DTS as a function of the stellar ...
9. The C/O ratio at low metallicity: constraints on early chemical evolution from observations of Galactic halo stars
Fabbian, D; Asplund, M; Pettini, M; Akerman, C
2008-01-01
We present new measurements of the abundances of carbon and oxygen derived from high-excitation C I and O I absorption lines in metal-poor halo stars, with the aim of clarifying the main sources of these two elements in the early stages of the chemical enrichment of the Galaxy. We target 15 new stars compared to our previous study, with an emphasis on additional C/O determinations in the crucial metallicity range -3<[Fe/H]<-2. Departures from local thermodynamic equilibrium were accounted for in the line formation for both carbon and oxygen. The non-LTE effects are very strong at the lowest metallicities but, contrary to what has sometimes been assumed in the past due to a simplified assessment, of different degrees for the two elements. In addition, for the 28 stars with [Fe/H]<-1 previously analysed, stellar parameters were re-derived and non-LTE corrections applied in the same fashion as for the rest of our sample, giving consistent abundances for 43 halo stars in total. The new observations and n...
10. Solar hot water demonstration project at Red Star Industrial Laundry, Fresno, California
None
1980-07-01
The Final Report of the Solar Hot Water System located at the Red Star Industrial Laundry, 3333 Sabre Avenue, Fresno, California, is presented. The system was designed as an integrated wastewater heat recovery and solar preheating system to supply a part of the hot water requirements. It was estimated that the natural gas demand for hot water heating could be reduced by 56 percent (44 percent heat reclamation and 12 percent solar). The system consists of a 16,500 gallon tube-and-shell wastewater heat recovery subsystem combined with a pass-through 6,528 square foot flat plate Ying Manufacturing Company Model SP4120 solar collector subsystem, a 12,500 gallon fiber glass water storage tank subsystem, pumps, heat exchangers, controls, and associated plumbing. The design output of the solar subsystem is approximately 2.6 x 10/sup 9/ Btu/year. Auxiliary energy is provided by a gas fired low pressure boiler servicing a 4,000 gallon service tank. This project is part of the US Department of Energy's Solar Demonstration Program with DOE sharing $184,841 of the$260,693 construction cost. The system was turned on in July 1977, and acceptance tests completed in September 1977. The demonstration period for this project ends September 2, 1982.
11. On the Carbon-to-Oxygen Ratio Measurement in Nearby Sunlike Stars: Implications for Planet Formation and the Determination of Stellar Abundances
Fortney, Jonathan J
2012-01-01
Recent high resolution spectroscopic analysis of nearby FGK stars suggests that a high C/O ratio of greater than 0.8, or even 1.0, is relatively common. Two published catalogs of measurements find C/O>0.8 in 25-30% of systems, and C/O>1.0 in ~6-10% of systems. It has been suggested that in protoplanetary disks with C/O>0.8 that the condensation pathways to refractory planet-making material will differ from what occurred in our solar system, where C/O=0.55. The carbon-rich disks are calculated to make carbon-dominated rocky planets, rather than oxygen-dominated ones, which would be very unlike the Earth. Here we suggest that the derived stellar C/O ratios are overestimated, given the extreme paucity of carbon dwarfs stars (0.8 in 10-15% of stars, and C/O>1.0 in 1-5%, athough these are still likely overestimates. We suggest that infrared T-dwarf spectra could show how common high C/O is in the stellar neighborhood, as the chemistry and spectra of such objects would differ compared to those with solar-like abund...
12. The difficult early stages of embedded star clusters and the importance of the pre-gas expulsion virial ratio
Farias, J P; Fellhauer, M; Goodwin, S; Candlish, G N; Blaña, M; Dominguez, R
2015-01-01
We examine the effects of gas-expulsion on initially substructured distributions of stars. We perform N-body simulations of the evolution of these distributions in a static background potential to mimic the gas. We remove the static potential instantaneously to model gas-expulsion. We find that the exact dynamical state of the cluster plays a very strong role in affecting a cluster's survival, especially at early times: they may be entirely destroyed or only weakly affected. We show that knowing both detailed dynamics and relative star-gas distributions can provide a good estimate of the post-gas expulsion state of the cluster, but even knowing these is not an absolute way of determining the survival or otherwise of the cluster.
13. X-ray Spectroscopy of the Radiation-Driven Winds of Massive Stars: Line Profile and Line Ratio Diagnostics
Cohen, David H
2009-01-01
Massive stars drive powerful, supersonic winds via the radiative momentum associated with the thermal UV emission from their photospheres. Shock phenomena are ubiquitous in these winds, heating them to millions, and sometimes tens of millions, of degrees. The emission line spectra from the shock-heated plasma provide powerful diagnostics of the winds' physical conditions, which in turn provide constraints on models of wind shock heating. Here I show how x-ray line transfer is affected by photoelectric absorption in the partially ionized component of the wind and how it can be modeled to determine the astrophysically important mass-loss rates of these stellar winds. I also discuss how photoexcitation out of metastable excited levels of helium-like ions can provide critical information about the location of the hot plasma in magnetically channeled massive star winds.
14. The dust-to-stellar mass ratio as a valuable tool to probe the evolution of local and distant star-forming galaxies
Calura, F.; Pozzi, F.; Cresci, G.; Santini, P.; Gruppioni, C.; Pozzetti, L.; Gilli, R.; Matteucci, F.; Maiolino, R.
2017-02-01
The survival of dust grains in galaxies depends on various processes. Dust can be produced in stars, it can grow in the interstellar medium and be destroyed by astration and interstellar shocks. In this paper, we assemble a few data samples of local and distant star-forming galaxies to analyse various dust-related quantities in low- and high-redshift galaxies, and to study how the relations linking the dust mass to the stellar mass and star formation rate evolve with redshift. We interpret the available data by means of chemical evolution models for discs and proto-spheroid (PSPH) starburst galaxies. In particular, we focus on the dust-to-stellar mass (DTS) ratio, as this quantity represents a true measure of how much dust per unit stellar mass survives the various destruction processes in galaxies and is observable. The theoretical models outline the strong dependence of this quantity on the underlying star formation history. Spiral galaxies are characterized by a nearly constant DTS as a function of the stellar mass and cosmic time, whereas PSPHs present an early steep increase of the DTS, which stops at a maximal value and decreases in the latest stages. In their late starburst phase, these models show a decrease of the DTS with their mass, which allows us to explain the observed anti-correlation between the DTS and the stellar mass. The observed redshift evolution of the DTS ratio shows an increase from z ˜ 0 to z ˜ 1, followed by a roughly constant behaviour at 1 ≲ z ≲ 2.5. Our models indicate a steep decrease of the global DTS at early times, which implies an expected decrease of the DTS at larger redshift.
15. The difficult early stages of embedded star clusters and the importance of the pre-gas expulsion virial ratio
Farias, J. P.; Smith, R; Fellhauer, M.; Goodwin, S.; Candlish, G. N.; Blaña, M.; R. Dominguez
2015-01-01
We examine the effects of gas-expulsion on initially substructured distributions of stars. We perform N-body simulations of the evolution of these distributions in a static background potential to mimic the gas. We remove the static potential instantaneously to model gas-expulsion. We find that the exact dynamical state of the cluster plays a very strong role in affecting a cluster's survival, especially at early times: they may be entirely destroyed or only weakly affected. We show that know...
16. Mergers of neutron star black hole binaries with small mass ratios: nucleosynthesis, gamma-ray bursts and electromagnetic transients
Rosswog, S
2005-01-01
I discuss simulations of the coalescence of black hole neutron star binary systems with black hole masses between 14 and 20 \\msun. The calculations use a three-dimensional smoothed particle hydrodynamics code, a temperature-dependent, nuclear equation of state and a multi-flavor neutrino scheme. General relativistic effects are mimicked using the \\Pacz-Wiita pseudo-potential and gravitational radiation reaction forces. Opposite to previous, purely Newtonian calculations, in none of the explored cases episodic mass transfer occurs. The neutron star is always completely disrupted after most of its mass has been transferred directly into the hole. For black hole masses between 14 and 16 \\Msun an accretion disk forms, large parts of it, however, are inside the last stable orbit and therefore falling with large radial velocities into the hole. These disks are (opposite to the neutron star merger case) thin and -apart from a spiral shock- essentially cold. For higher mass black holes ($M_{\\rm BH} \\ge 18$ \\msun) alm...
17. The hidden AGN main sequence: Evidence for a universal SMBH accretion to star formation rate ratio since z~2 producing a M_BH-M* relation
Mullaney, J R; Béthermin, M; Elbaz, D; Juneau, S; Pannella, M; Sargent, M T; Alexander, D M; Hickox, R C
2012-01-01
Using X-ray stacking analyses we estimate the average amounts of supermassive black hole (SMBH) growth taking place in star-forming galaxies (SFGs) at z~1 and z~2 as a function of galaxy stellar mass (M*). We find the average rate of SMBH growth taking place in SFGs follows remarkably similar trends with both M* and redshift as the average star-formation rates (SFRs) of these galaxies (i.e., dM_BH/dt ~ M*^(0.86+/-0.39) for the z~1 sample and dM_BH/dt ~ M*^(1.05+/-0.36) for the z~2 sample). It follows that the ratio of SMBH growth rate to SFR is (a) flat with respect to galaxy stellar mass (b) not evolving with redshift and (c) close to the ratio required to maintain/establish a SMBH to stellar mass ratio of ~10^(-3) as also inferred from today's M_BH-M_Bulge relationship. We interpret this as evidence that SMBHs have, on average, grown in-step with their host galaxies since at least z~2, irrespective of host galaxy mass and AGN triggering mechanism and that the relative growth rates are more important in esta...
18. The SERMON project: 48 new field Blazhko stars and an investigation of modulation-period distribution
Skarka, M.; Liška, J.; Auer, R. F.; Prudil, Z.; Juráňová, A.; Sódor, Á.
2016-08-01
Aims: We investigated 1234 fundamental mode RR Lyrae stars observed by the All Sky Automated Survey (ASAS) to identify the Blazhko (BL) effect. A sample of 1547 BL stars from the literature was collected to compare the modulation-period distribution with stars newly identified in our sample. Methods: A classical frequency spectra analysis was performed using Period04 software. Data points from each star from the ASAS database were analysed individually to avoid confusion with artificial peaks and aliases. Statistical methods were used in the investigation of the modulation-period distribution. Results: Altogether we identified 87 BL stars (48 new detections), 7 candidate stars, and 22 stars showing long-term period variations. The distribution of modulation periods of newly identified BL stars corresponds well to the distribution of modulation periods of stars located in the Galactic field, Galactic bulge, Large Magellanic Cloud, and globular cluster M5 collected from the literature. As a very important by-product of this comparison, we found that pulsation periods of BL stars follow Gaussian distribution with the mean period of 0.54 ± 0.07 d, while the modulation periods show log-normal distribution with centre at log (Pm [d]) = 1.78 ± 0.30 dex. This means that 99.7% of all known modulated stars have BL periods between 7.6 and 478 days. We discuss the identification of long modulation periods and show, that a significant percentage of stars showing long-term period variations could be classified as BL stars.
19. The Karlsruhe Astrophysical Database of Nucleosynthesis in Stars Project - Status and Prospects
Dillmann, Iris; Fülöp, Zsolt; Plag, Ralf; Käppeler, Franz; Rauscher, Thomas
2014-01-01
The KADoNiS (Karlsruhe Astrophysical Database of Nucleosynthesis in Stars) project is an astrophysical online database for cross sections relevant for nucleosynthesis in the $s$ process and the $\\gamma$ process. The $s$-process database (www.kadonis.org) was started in 2005 and is presently facing its 4th update (KADoNiS v1.0). The $\\gamma$-process database (KADoNiS-p, www.kadonis.org/pprocess) was recently revised and re-launched in March 2013. Both databases are compilations for experimental cross sections with relevance to heavy ion nucleosynthesis. For the $s$ process recommended Maxwellian averaged cross sections for $kT$= 5-100~keV are given for more than 360 isotopes between $^{1}$H and $^{210}$Bi. For the $\\gamma$-process database all available experimental data from $(p,\\gamma), (p,n), (p,\\alpha), (\\alpha,\\gamma), (\\alpha,n)$, and $(\\alpha,p)$ reactions between $^{70}$Ge and $^{209}$Bi in or close to the respective Gamow window were collected and can be compared to theoretical predictions. The aim of...
20. Calibration of ionization energy loss at relativistic rise with STAR Time Projection Chamber
Xu, Yichun; Bichsel, Hans; Dong, Xin; Fachini, Patricia; Fisyak, Yuri; Kocolosky, Adam; Mohanty, Bedanga; Netrakanti, Pawan; Ruan, Lijuan; Suarez, Maria Cristina; Tang, Zebo; van Buren, Gene; Xu, Zhangbu
2008-01-01
We derive a method to improve particle identification (PID) at high transverse momentum ($p_T$) using the relativistic rise of the ionization energy loss ($rdE/dx$) when charged particles traverse the Time Projection Chamber (TPC) at STAR. Electrons triggered and identified by the Barrel Electro-Magnetic Calorimeter (BEMC), pure protons and pions from $\\Lambda\\to p+\\pi^{-}$ ($\\bar{\\Lambda}\\to \\bar{p}+\\pi^{+}$), and $K^{0}_{S}\\to\\pi^{+}+\\pi^{-}$ decays are used to obtain the $dE/dx$ value and its width at given $\\beta\\gamma=p/m$. We found that the deviation of the $dE/dx$ from the Bichsel function can be up to $0.4\\sigma$ ($\\sim3%$) in p+p collisions at $\\sqrt{s_{NN}}=200$ GeV taken and subsequently calibrated in year 2005. The deviation is approximately a function of $\\beta\\gamma$ independent of particle species and can be described with a function of $f(x) = A+\\frac{B}{C+x^{2}}$. The deviations obtained with this method are used to re-calibrate the data sample from p+p collision for physics analysis of ident...
1. Support Vector Machine-Based Human Behavior Classification in Crowd through Projection and Star Skeletonization
Yogameena, B.
2010-01-01
Full Text Available Problem statement: Detection of individuals abnormal human behaviors in the crowd has become a critical problem because in the event of terror strikes. This study presented a real-time video surveillance system which classifies normal and abnormal behaviors in crowds. The aim of this research was to provide a system which can aid in monitoring crowded urban environments. Approach: The proposed behaviour classification was through projection which separated individuals and using star skeletonization the features like body posture and the cyclic motion cues were obtained. Using these cues the Support Vector Machine (SVM classified the normal and abnormal behaviors of human. Results: Experimental results demonstrated the method proposed was robust and efficient in the classification of normal and abnormal human behaviors. A comparative study of classification accuracy between principal component analysis and Support Vector Machine (SVM classification was also presented. Conclusion: The proposed method classified the behavior such as running people in a crowded environment, bending down movement while most are walking or standing, a person carrying a long bar and a person waving hand in the crowd is classified.
2. Nonradial modes in RR Lyrae stars from the OGLE Collection of Variable Stars
Netzel, Henryka; Moskalik, Pawel
2016-01-01
The Optical Gravitational Lensing Experiment (OGLE) is a great source of top-quality photometry of classical pulsators. Collection of variable stars from the fourth part of the project contains more than 38 000 RR Lyrae stars. These stars pulsate mostly in the radial fundamental mode (RRab), in radial first overtone (RRc) or in both modes simultaneously (RRd). Analysis of the OGLE data allowed to detect additional non-radial modes in RRc and in RRd stars. We have found more than 260 double-mode stars with characteristic period ratio of the additional (shorter) period to first overtone period around 0.61, increasing the number of known stars of this type by factor of 10. Stars from the OGLE sample form three nearly parallel sequences in the Petersen diagram. Some stars show more than one non-radial mode simultaneously. These modes belong to different sequences.
3. The earliest phases of star formation - A Herschel key project. The thermal structure of low-mass molecular cloud cores
Launhardt, R; Schmiedeke, A; Henning, Th; Krause, O; Balog, Z; Beuther, H; Birkmann, S; Hennemann, M; Kainulainen, J; Khanzadyan, T; Linz, H; Lippok, N; Nielbock, M; Pitann, J; Ragan, S; Risacher, C; Schmalzl, M; Shirley, Y L; Stecklum, B; Steinacker, J; Tackenberg, J
2013-01-01
The temperature and density structure of molecular cloud cores are the most important physical quantities that determine the course of the protostellar collapse and the properties of the stars they form. Nevertheless, density profiles often rely either on the simplifying assumption of isothermality or on observationally poorly constrained model temperature profiles. With the aim of better constraining the initial physical conditions in molecular cloud cores at the onset of protostellar collapse, we initiated the Guaranteed Time Key Project (GTKP) "The Earliest Phases of Star Formation" (EPoS) with the Herschel satellite. This paper gives an overview of the low-mass sources in the EPoS project, including all observations, the analysis method, and the initial results of the survey. We study the thermal dust emission of 12 previously well-characterized, isolated, nearby globules using FIR and submm continuum maps at up to eight wavelengths between 100 micron and 1.2 mm. Our sample contains both globules with sta...
4. The Herschel Open Time Key Project; DUst Around NEarby Stars: Results from the Complete Survey
Danchi, William C.; Eiroa, C.; Consortium, DUNES
2013-01-01
The Herschel DUst Around Nearby Stars (DUNES) survey (Eiroa et al. 2010) was designed to address several fundamental questions regarding debris disks around nearby solar type stars, in order to put the Solar System into context. Our goals were to: (1) determine the fraction of stars with faint, Edgeworth-Kuiper Belt (EKB)-like disks, (2) explore collisional and dynamical evolution of EKB analogues, (3) observe dust properties and size distribution, and (4) determine the incidence of EKB-like disks vs. presence of planets. The final sample of stars directly observed by DUNES included 133 stars, including 27 F-type, 52 G-type and 54 K-type stars within 20 pc of the Sun. The integration time was set in order to make a 5-sigma detection of the expected photospheric emission at 100 and 160 microns, using the PACS instrument. In addition, 106 stars observed by DEBRIS survey (Mathews et al. 2010) satisfying the photospheric detection condition are shared targets, specifically 83 FGK stars - 51 F, 24 G and 8 K (the rest are A and M stars). We report the main conclusions from the survey including the frequency of detection of debris disks as a function of fractional luminosity of the dust, Ld/L*, and correlations of Ld/L* with metallicity, bolometric luminosity, effective temperature, and stellar age.
5. Precise observations of the 12C/13C ratios of HC3N in the low-mass star-forming region L1527
Araki, Mitsunori; Sakai, Nami; Yamamoto, Satoshi; Oyama, Takahiro; Kuze, Nobuhiko; Tsukiyama, Koichi
2016-01-01
Using the Green Bank 100 m telescope and the Nobeyama 45 m telescope, we have observed the rotational emission lines of the three 13C isotopic species of HC3N in the 3 and 7 mm bands toward the low-mass star-forming region L1527 in order to explore their anomalous 12C/13C ratios. The column densities of the 13C isotopic species are derived from the intensities of the J = 5-4 lines observed at high signal-to-noise ratios. The abundance ratios are determined to be 1.00:1.01 +- 0.02:1.35 +- 0.03:86.4 +- 1.6 for [H13CCCN]:[HC13CCN]:[HCC13CN]:[HCCCN], where the errors represent one standard deviation. The ratios are very similar to those reported for the starless cloud, Taurus Molecular Cloud-1 Cyanopolyyne Peak (TMC-1 CP). These ratios cannot be explained by thermal equilibrium, but likely reflect the production pathways of this molecule. We have shown the equality of the abundances of H13CCCN and HC13CCN at a high-confidence level, which supports the production pathways of HC3N via C2H2 and C2H2+. The average 12...
6. The Effect of Project Based Learning in "Ratio, Proportion and Percentage" Unit on Mathematics Success and Attitude
Özdemir, Ahmet Sükrü; Yildiz, Filiz; Yildiz, Sevda Göktepe
2015-01-01
In this paper, our aim is to examine the effect of project based learning on 7th grade students' mathematical success in "Ratio, Proportion and Percentage" unit and attitudes towards mathematics. This study was implemented with 70 7th grade students of Atatürk Primary School in Eminönü District in Istanbul. Before starting the…
7. Binary Neutron Star Mergers and Short Gamma-Ray Bursts: Effects of Magnetic Field Orientation, Equation of State, and Mass Ratio
Kawamura, Takumu; Kastaun, Wolfgang; Ciolfi, Riccardo; Endrizzi, Andrea; Baiotti, Luca; Perna, Rosalba
2016-01-01
We present fully GRMHD simulations of the merger of binary neutron star (BNS) systems. We consider BNSs producing a hypermassive neutron star (HMNS) that collapses to a spinning black hole (BH) surrounded by a magnetized accretion disk in a few tens of ms. We investigate whether such systems may launch relativistic jets and power short gamma-ray bursts. We study the effects of different equations of state (EOSs), different mass ratios, and different magnetic field orientations. For all cases, we present a detailed investigation of the matter dynamics and of the magnetic field evolution, with particular attention to its global structure and possible emission of relativistic jets. The main result of this work is that we found the formation of an organized magnetic field structure. This happens independently of EOS, mass ratio, and initial magnetic field orientation. We also show that those models that produce a longer-lived HMNS lead to a stronger magnetic field before collapse to BH. Such larger fields make it...
8. First stars IX -Mixing in extremely metal-poor giants. Variation of the 12C/13C, [Na/Mg] and [Al/Mg] ratios
Spite, M; Hill, V; Spite, F; François, P; Plez, B; Bonifacio, P; Molaro, P; Depagne, E; Andersen, J; Barbuy, B; Beers, T C; Nordström, B; Primas, F
2006-01-01
Extremely metal-poor (EMP) stars preserve a fossil record of the composition of the ISM when the Galaxy formed. It is crucial, however, to verify whether internal mixing has modified their surface. We aim to understand the CNO abundance variations found in some, but not all EMP field giants analysed earlier. Mixing beyond the first dredge-up of standard models is required, and its origin needs clarification.The 12C/13C ratio is the most robust diagnostic of deep mixing, because it is insensitive to the adopted stellar parameters and should be uniformly high in near-primordial gas. We have measured 12C and 13C abundances in 35 EMP giants from high-quality VLT/UVES spectra. Correlations with other abundance data are used to study the depth of mixing.The 12C/13C ratio is found to correlate with [C/Fe] (and Li/H), and clearly anti-correlate with [N/Fe]. Evidence for such deep mixing is observed in giants above log L/Lsolar = 2.6, brighter than in less metal-poor stars, but matching the bump in the luminosity func...
9. ANL/Star project: a new architecture for large scale theoretical physics computations
Rushton, A.M.
1985-01-01
The project reported consists of two phases, each of which has goals of substantial physics content on its own. In Phase 1, we have selected Star Technologies' ST-100 as the array processor for the prototype coupled system and have installed one on a Vax 11/750 host. Our goals with this system are to institute a substantial program in computational physics at Argonne based on the power provided by this system and thereby to gain experience with both the hardware and software architecture of the ST-100. In Phase II, we propose to build a prototype consisting of two coupled array processors with shared memory to prove that this design can achieve high speed and efficiency in a readily extensible and cost-effective manner. This will implement all of the hardware and software modifications necessary to extend this design to as many as 64 (or more) nodes. In our design, we seek to minimize the changes made in the standard system hardware and software; this drastically reduces the effort required by our group to implement such a design and enables us to more readily incorporate the companies' upgrades to the array processor. It should be emphasized that our design is intended as a special purpose system for theoretical calculations; however it can be efficiently applied to a surprisingly broad class of problems. I shall discuss first the architecture of the ST-100 and then the physics program being currently implemented on a single system. Finally the proposed design of the coupled system is presented.
10. Images of Gravitational and Magnetic Phenomena Derived from 2D Back-Projection Doppler Tomography of Interacting Binary Stars
Richards, Mercedes T; Fisher, John G; Conover, Marshall J
2014-01-01
We have used 2D back-projection Doppler tomography as a tool to examine the influence of gravitational and magnetic phenomena in interacting binaries which undergo mass transfer from a magnetically-active star onto a non-magnetic main sequence star. This multi-tiered study of over 1300 time-resolved spectra of 13 Algol binaries involved calculations of the predicted dynamical behavior of the gravitational flow and the dynamics at the impact site, analysis of the velocity images constructed from tomography, and the influence on the tomograms of orbital inclination, systemic velocity, orbital coverage, and shadowing. The H$\\alpha$ tomograms revealed eight sources: chromospheric emission, a gas stream along the gravitational trajectory, a star-stream impact region, a bulge of absorption or emission around the mass-gaining star, a Keplerian accretion disk, an absorption zone associated with hotter gas, a disk-stream impact region, and a hot spot where the stream strikes the edge of a disk. We described several me...
11. Discovery of a Low-mass Companion to a Metal-rich F Star with the MARVELS Pilot Project
Fleming, Scott W.; Ge, Jian; Mahadevan, Suvrath; Lee, Brian; Eastman, Jason D.; Siverd, Robert J.; Gaudi, B. Scott; Niedzielski, Andrzej; Sivarani, Thirupathi; Stassun, Keivan G.; Wolszczan, Alex; Barnes, Rory; Gary, Bruce; Nguyen, Duy Cuong; Morehead, Robert C.; Wan, Xiaoke; Zhao, Bo; Liu, Jian; Guo, Pengcheng; Kane, Stephen R.; van Eyken, Julian C.; De Lee, Nathan M.; Crepp, Justin R.; Shelden, Alaina C.; Laws, Chris; Wisniewski, John P.; Schneider, Donald P.; Pepper, Joshua; Snedden, Stephanie A.; Pan, Kaike; Bizyaev, Dmitry; Brewington, Howard; Malanushenko, Olena; Malanushenko, Viktor; Oravetz, Daniel; Simmons, Audrey; Watters, Shannon
2010-08-01
We report the discovery of a low-mass companion orbiting the metal-rich, main sequence F star TYC 2949-00557-1 during the Multi-object APO Radial Velocity Exoplanet Large-area Survey (MARVELS) pilot project. The host star has an effective temperature T eff = 6135 ± 40 K, logg = 4.4 ± 0.1, and [Fe/H] = 0.32 ± 0.01, indicating a mass of M = 1.25 ± 0.09 M sun and R = 1.15 ± 0.15 R sun. The companion has an orbital period of 5.69449 ± 0.00023 days and straddles the hydrogen burning limit with a minimum mass of 64 MJ , and thus may be an example of the rare class of brown dwarfs orbiting at distances comparable to those of "Hot Jupiters." We present relative photometry that demonstrates that the host star is photometrically stable at the few millimagnitude level on time scales of hours to years, and rules out transits for a companion of radius gsim0.8 RJ at the 95% confidence level. Tidal analysis of the system suggests that the star and companion are likely in a double synchronous state where both rotational and orbital synchronization have been achieved. This is the first low-mass companion detected with a multi-object, dispersed, fixed-delay interferometer.
12. Discovery of a Low-Mass Companion to a Metal-Rich F Star with the MARVELS Pilot Project
Fleming, Scott W; Mahadevan, Suvrath; Lee, Brian; Eastman, Jason D; Siverd, Robert J; Gaudi, B Scott; Niedzielski, Andrzej; Sivarani, Thirupathi; Stassun, Keivan; Wolszczan, Alex; Barnes, Rory; Gary, Bruce; Nguyen, Duy Cuong; Morehead, Robert C; Wan, Xiaoke; Zhao, Bo; Liu, Jian; Guo, Pengcheng; Kane, Stephen R; van Eyken, Julian C; De Lee, Nathan M; Crepp, Justin R; Shelden, Alaina C; Laws, Chris; Wisniewski, John P; Schneider, Donald P; Pepper, Joshua; Snedden, Stephanie A; Pan, Kaike; Bizyaev, Dmitry; Brewington, Howard; Malanushenko, Olena; Malanushenko, Viktor; Oravetz, Daniel; Simmons, Audrey; Watters, Shannon
2010-01-01
We report the discovery of a low-mass companion orbiting the metal-rich, main sequence F star TYC 2949-00557-1 during the MARVELS (Multi-object APO Radial Velocity Exoplanet Large-area Survey) Pilot Project. The host star has an effective temperature T_eff = 6135 +/- 40 K, log(g) = 4.4 +/- 0.1 and [Fe/H] = 0.32 +/- 0.01, indicating a mass of M = 1.25 +/- 0.09 M_\\odot and R = 1.15 +/- 0.15 R_\\odot. The companion has an orbital period of 5.69449 +/- 0.00023 days and straddles the hydrogen burning limit with a minimum mass of 64 M_J, and may thus be an example of the rare class of brown dwarfs orbiting at distances comparable to those of "Hot Jupiters." We present relative photometry that demonstrates the host star is photometrically stable at the few millimagnitude level on time scales of hours to years, and rules out transits for a companion of radius greater than 0.8 R_J at the 95% confidence level. Tidal analysis of the system suggests that the star and companion are likely in a double synchronous state wher...
13. Binary neutron star mergers and short gamma-ray bursts: Effects of magnetic field orientation, equation of state, and mass ratio
Kawamura, Takumu; Giacomazzo, Bruno; Kastaun, Wolfgang; Ciolfi, Riccardo; Endrizzi, Andrea; Baiotti, Luca; Perna, Rosalba
2016-09-01
We present fully general-relativistic magnetohydrodynamic simulations of the merger of binary neutron star (BNS) systems. We consider BNSs producing a hypermassive neutron star (HMNS) that collapses to a spinning black hole (BH) surrounded by a magnetized accretion disk in a few tens of ms. We investigate whether such systems may launch relativistic jets and hence power short gamma-ray bursts. We study the effects of different equations of state (EOSs), different mass ratios, and different magnetic field orientations. For all cases, we present a detailed investigation of the matter dynamics and of the magnetic field evolution, with particular attention to its global structure and possible emission of relativistic jets. The main result of this work is that we observe the formation of an organized magnetic field structure. This happens independently of EOS, mass ratio, and initial magnetic field orientation. We also show that those models that produce a longer-lived HMNS lead to a stronger magnetic field before collapse to a BH. Such larger fields make it possible, for at least one of our models, to resolve the magnetorotational instability and hence further amplify the magnetic field in the disk. However, by the end of our simulations, we do not (yet) observe a magnetically dominated funnel nor a relativistic outflow. With respect to the recent simulations of Ruiz et al. [Astrophys. J. 824, L6 (2016)], we evolve models with lower and more plausible initial magnetic field strengths and (for computational reasons) we do not evolve the accretion disk for the long time scales that seem to be required in order to see a relativistic outflow. Since all our models produce a similar ordered magnetic field structure aligned with the BH spin axis, we expect that the results found by Ruiz et al. (who only considered an equal-mass system with an ideal fluid EOS) should be general and—at least from a qualitative point of view—independent of the mass ratio, magnetic field
14. The circumstellar shell of the post-AGB star HD 56126 the $^{12}CN\\/^{13}CN$ isotope ratio and fractionation
Bakker, E J; Bakker, Eric J.; Lambert, David L.
1997-01-01
We have detected circumstellar absorption lines of the $^{12}$CN and $^{13}$CN Violet and Red System in the spectrum of the post-AGB star HD~56126. From a synthetic spectrum analysis, we derive a Doppler broadening parameter of $b=0.51\\pm0.04$ km~s$^{-1}$, $^{12}$CN/$^{13}$CN$=38\\pm2$, and a lower limit of $2000$ on $^{12}$CN/$^{14}$CN and $^{12}$C$^{14}$N/$^{12}$C$^{15}$N. A simple chemical model has been computed of the circumstellar shell surrounding HD~56126 that takes into account the gas-phase ion-molecule reaction between CN and C$^{+}$. From this we infer that this reaction leads to isotopic fractionation of CN. Taking into account the isotopic exchange reaction and the observed $^{12}$CN/$^{13}$CN we find $^{12}$C/$^{13}$C$\\sim 67$ (for $T_{\\rm kin}=25$ K). Our analysis suggests that $^{12}$CN has a somewhat higher rotational temperature than $^{13}$CN: $T_{\\rm rot}=11.5\\pm0.6$ and $8.0\\pm0.6$ K respectively. We identify possible causes for this difference in excitation temperature, among which the $... 15. Use of Leading Edge Waves to Increase Lift/Drag Ratio Project National Aeronautics and Space Administration — One of the goals of NASA's Fundamental Aeronautics "Subsonic Fixed Wing" project is to reduce fuel burn by 25% 5% by 2018. This corresponds approximately to an... 16. A Monte Carlo Study of Flux Ratios of Raman Scattered O vi Features at 6825 and 7082 Å in Symbiotic Stars Lee, Young-Min; Lee, Dae-Sub; Chang, Seok-Jun; Heo, Jeong-Eun; Lee, Hee-Won; Hwang, Narae; Park, Byeong-Gon; Lee, Ho-Gyu 2016-12-01 Symbiotic stars are regarded as wide binary systems consisting of a hot white dwarf and a mass losing giant. They exhibit unique spectral features at 6825 and 7082 Å, which are formed via Raman scattering of O vi λλ 1032 and 1038 with atomic hydrogen. We adopt a Monte Carlo technique to generate the same number of O vi λ1032 and λ1038 line photons and compute the flux ratio F(6825)/F(7082) of these Raman scattered O vi features formed in neutral regions with a simple geometric shape as a function of H i column density N H i . In cylindrical and spherical neutral regions with the O vi source embedded inside, the flux ratio F(6825)/F(7082) shows an overall decrease from 3 to 1 as N H i increases in the range {10}22{--24} {{cm}}-2. In cases of slab geometry and other geometries with the O vi source outside the H i region, Rayleigh escape operates to lower the flux ratio considerably. For moderate values of {N}{{H}{{I}}}˜ {10}23 {{cm}}-2 the flux ratio behaves in a complicated way to exhibit a broad bump with a peak value of 3.5 in the case of a sphere geometry. We find that the ratio of Raman conversion efficiencies of O vi λλ 1032, 1038 ranges from 0.8 to 3.5. Our high resolution spectra of “D” type HM Sge and “S” type AG Dra obtained with the Canada-France-Hawaii Telescope show that the flux ratio F(6825)/F(7082) of AG Dra is significantly smaller than that of HM Sge, implying that “S” type symbiotics are characterized by higher N H i than “D” type symbiotics. 17. High-Precision Instrumentation for CO2 Isotope Ratio Measurements Project National Aeronautics and Space Administration — Knowing atmospheric 13CO2/12CO2 ratios precisely is important to understanding biogenic and anthroprogenic sources and sinks for carbon. Currently available field... 18. Ultra-Miniaturized Star Tracker for Small Satellite Attitude Control Project National Aeronautics and Space Administration — Creare and Embry-Riddle Aeronautical University (ERAU) propose to complete the design, development, and testing of an ultra compact star tracker specifically... 19. Ultra-Miniaturized Star Tracker for Small Satellite Attitude Control Project National Aeronautics and Space Administration — Creare and Virginia Polytechnic Institute and State University propose to design, develop, test, and deliver an ultra compact star tracker specifically intended for... 20. Plug-and-Play Star Sensor for Rapid Spacecraft Integration Project National Aeronautics and Space Administration — Microcosm, with partners Space Micro and HRP Systems, will design, build, and test a plug-and play (PnP) star sensor for small satellites, achieving TRL 6 at the... 1. DUst around NEarby Stars (DUNES): description of the project and results Montesinos, B.; Eiroa, C.; Dunes Team 2013-05-01 DUNES is an Open Time Key Programme of the Herschel Space Observatory aimed at detecting and studying cold dusty --debris-- discs, i.e. Kuiper-belt analogues, around FGK stars of the solar neighbourhood, in a volume-limited sample of 133 stars. The sensitivity and wavelengths of the two instruments used, namely PACS (70, 100, and 160 μm) and SPIRE (250, 350, and 500 μm) are the appropriate ones for these tasks. Debris discs are the result of collisions of planetesimals formed at early stages of the star formation episode, when the star is younger than about 30 Myr, and the discs, so-called protoplanetary, are composed of gas and dust. The whole sample is already observed and the team is currently analysing the data. We outline here some of the main results we have found. 2. Integrated CubeSat ADACS with Reaction Wheels and Star Tracker Project National Aeronautics and Space Administration — A high performance ADACS (Attitude Determination and Control System) for CubeSats incorporating Miniature Star Trackers is proposed. The proposed program will focus... 3. Plug-and-Play Star Sensor for Rapid Spacecraft Integration Project National Aeronautics and Space Administration — Microcosm, with Space Micro., and HRP Systems will design a plug-and-play (PnP) star sensor for small satellites. All three companies are well experienced in... 4. On the use of the Fourier Transform to determine the projected rotational velocity of line-profile variable B stars Aerts, C; Groot, P J; Degroote, P 2014-01-01 The Fourier Transform method is a popular tool to derive the rotational velocities of stars from their spectral line profiles. However, its domain of validity does not include line-profile variables with time-dependent profiles. We investigate the performance of the method for such cases, by interpreting the line-profile variations of spotted B stars, and of pulsating B tars, as if their spectral lines were caused by uniform surface rotation along with macroturbulence. We perform time-series analysis and harmonic least-squares fitting of various line diagnostics and of the outcome of several implementations of the Fourier Transform method. We find that the projected rotational velocities derived from the Fourier Transform vary appreciably during the pulsation cycle whenever the pulsational and rotational velocity fields are of similar magnitude. The macroturbulent velocities derived while ignoring the pulsations can vary with tens of km/s during the pulsation cycle. The temporal behaviour of the deduced rotat... 5. Monash Chemical Yields Project (Monχey) Element production in low- and intermediate-mass stars Doherty, Carolyn; Lattanzio, John; Angelou, George; Campbell, Simon W.; Church, Ross; Constantino, Thomas; Cristallo, Sergio; Gil-Pons, Pilar; Karakas, Amanda; Lugaro, Maria; Stancliffe, Richard The Monχey project will provide a large and homogeneous set of stellar yields for the low- and intermediate- mass stars and has applications particularly to galactic chemical evolution modelling. We describe our detailed grid of stellar evolutionary models and corresponding nucleosynthetic yields for stars of initial mass 0.8 M⊙ up to the limit for core collapse supernova (CC-SN) ~ 10 M⊙. Our study covers a broad range of metallicities, ranging from the first, primordial stars (Z = 0) to those of super-solar metallicity (Z = 0.04). The models are evolved from the zero-age main-sequence until the end of the asymptotic giant branch (AGB) and the nucleosynthesis calculations include all elements from H to Bi. A major innovation of our work is the first complete grid of heavy element nucleosynthetic predictions for primordial AGB stars as well as the inclusion of extra-mixing processes (in this case thermohaline) during the red giant branch. We provide a broad overview of our results with implications for galactic chemical evolution as well as highlight interesting results such as heavy element production in dredge-out events of super-AGB stars. We briefly introduce our forthcoming web-based database which provides the evolutionary tracks, structural properties, internal/surface nucleosynthetic compositions and stellar yields. Our web interface includes user- driven plotting capabilities with output available in a range of formats. Our nucleosynthetic results will be available for further use in post processing calculations for dust production yields. 6. A Monte Carlo Study of Flux Ratios of Raman Scattered O~VI Features at 6825 \\AA\\ and 7082 \\AA\\ in Symbiotic Stars Lee, Young-Min; Chang, Seok-Jun; Heo, Jeong-Eun; Lee, Hee-Won 2016-01-01 Symbiotic stars are regarded as wide binary systems consisting of a hot white dwarf and a mass losing giant. They exhibit unique spectral features at 6825 \\AA\\ and 7082 \\AA, which are formed via Raman scattering of \\ion{O}{6}$\\lambda\\lambda$1032 and 1038 with atomic hydrogen. We adopt a Monte Carlo technique to generate the same number of \\ion{O}{6}$\\lambda$1032 and$\\lambda$1038 line photons and compute the flux ratio$F(6825)/F(7082)$of these Raman scattered \\ion{O}{6} features formed in neutral regions with a simple geometric shape as a function of \\ion{H}{1} column density$N_{HI}$. In cylindrical and spherical neutral regions with the \\ion{O}{6} source embedded inside, the flux ratio$F(6825)/F(7082)$shows an overall decrease from 3 to 1 as$N_{HI}$increases in the range$10^{22-24}{\\rm\\ cm^{-2}}$. In the cases of a slab geometry and other geometries with the \\ion{O}{6} source outside the \\ion{H}{1} region, Rayleigh escape operates to lower the flux ratio considerably. For moderate values of$N_{HI}\\...
7. The IACOB project . III. New observational clues to understand macroturbulent broadening in massive O- and B-type stars
Simón-Díaz, S.; Godart, M.; Castro, N.; Herrero, A.; Aerts, C.; Puls, J.; Telting, J.; Grassitelli, L.
2017-01-01
8. Superoutburst of CR Bootis: Estimation of Mass Ratio of a typical AM CVn star by Stage A Superhumps
Isogai, Keisuke; Ohshima, Tomohito; Kasai, Kiyoshi; Oksanen, Arto; Masumoto, Kazunari; Fukushima, Daiki; Maeda, Kazuki; Kawabata, Miho; Matsuda, Risa; Kojiguchi, Naoto; Sugiura, Yuki; Takeda, Nao; Matsumoto, Katsura; Itoh, Hiroshi; Pavlenko, Elena P; Antonyuk, Kirill; Antonyuk, Oksana; Pit, Nikolai; Sosnovskij, Aleksei; Baklanov, Alex; Babina, Julia; Sklyanov, Aleksandr; Kiyota, Seiichiro; Hambsch, Franz-josef; Littlefield, Colin; Maeda, Yutaka; Cook, Lewis M; Masi, Gianluca; Dubovsky, Pavol A; Novak, Rudolf; Dvorak, Shawn; Imada, Akira; Nogami, Daisaku
2016-01-01
We report on two superoutbursts of the AM CVn-type object CR Boo in 2014 April--March and 2015 May--June. A precursor outburst acompanied both of these superoutbursts. During the rising branch of the main superoutburst in 2014, we detected growing superhumps (stage A superhumps) whose period was $0.017669(24)$ d. Assuming that this period reflects the dynamical precession rate at the radius of the 3:1 resonance, we could estimate the mass ratio ($q=M_2/M_1$) of 0.101(4) by using the stage A superhump period and the orbital one of 0.0170290(6) d. This mass ratio is consistent with that expected by the theoretical evolutionary model of AM CVn-type objects. The detection of precursor outbursts and stage A superhumps is the second case in AM CVn-type objects. There are two interpretations of the outbursts of AM CVn-type objects. One is a dwarf nova (DN) outbursts analogy, which is caused by thermal and tidal instabilities. Another is the VY Scl-type variation, which is caused by the variation of the mass-transfer...
9. The SILCC project - III. Regulation of star formation and outflows by stellar winds and supernovae
Gatto, Andrea; Walch, Stefanie; Naab, Thorsten; Girichidis, Philipp; Wünsch, Richard; Glover, Simon C. O.; Klessen, Ralf S.; Clark, Paul C.; Peters, Thomas; Derigs, Dominik; Baczynski, Christian; Puls, Joachim
2017-04-01
We study the impact of stellar winds and supernovae on the multiphase interstellar medium using three-dimensional hydrodynamical simulations carried out with FLASH. The selected galactic disc region has a size of (500 pc)2 × ±5 kpc and a gas surface density of 10 M⊙ pc-2. The simulations include an external stellar potential and gas self-gravity, radiative cooling and diffuse heating, sink particles representing star clusters, stellar winds from these clusters that combine the winds from individual massive stars by following their evolution tracks, and subsequent supernova explosions. Dust and gas (self-) shielding is followed to compute the chemical state of the gas with a chemical network. We find that stellar winds can regulate star (cluster) formation. Since the winds suppress the accretion of fresh gas soon after the cluster has formed, they lead to clusters that have lower average masses (102-104.3 M⊙) and form on shorter time-scales (10-3-10 Myr). In particular, we find an anticorrelation of cluster mass and accretion time-scale. Without winds, the star clusters easily grow to larger masses for ∼5 Myr until the first supernova explodes. Overall, the most massive stars provide the most wind energy input, while objects beginning their evolution as B-type stars contribute most of the supernova energy input. A significant outflow from the disc (mass loading ≳1 at 1 kpc) can be launched by thermal gas pressure if more than 50 per cent of the volume near the disc mid-plane can be heated to T > 3 × 105 K. Stellar winds alone cannot create a hot volume-filling phase. The models that are in best agreement with observed star formation rates drive either no outflows or weak outflows.
10. Doubling the Performance-Cost Ratio of PV by Using Cheap Mirrors - a Secondary School Project
Breejen, H.; van Herwaarden, S.; Keijsers, B.; van Dijk, V.A.P.; van Sark, W.G.J.H.M.
2007-01-01
Reduction of cost is a major issue in the photovoltaics field. We have addressed this issue in a secondaryschool science project by considering the use of cheap mirrors in combination with solar panels, for application in developing countries. We have confirmed that it is possible to increase the pe
11. Doubling the Performance-Cost Ratio of PV by Using Cheap Mirrors - a Secondary School Project
Breejen, H.; van Herwaarden, S.; Keijsers, B.; van Dijk, V.A.P.; van Sark, W.G.J.H.M.|info:eu-repo/dai/nl/074628526
2007-01-01
Reduction of cost is a major issue in the photovoltaics field. We have addressed this issue in a secondaryschool science project by considering the use of cheap mirrors in combination with solar panels, for application in developing countries. We have confirmed that it is possible to increase the
12. Doubling the Performance-Cost Ratio of PV by Using Cheap Mirrors - a Secondary School Project
Breejen, H.; van Herwaarden, S.; Keijsers, B.; van Dijk, V.A.P.; van Sark, W.G.J.H.M.|info:eu-repo/dai/nl/074628526
2007-01-01
Reduction of cost is a major issue in the photovoltaics field. We have addressed this issue in a secondaryschool science project by considering the use of cheap mirrors in combination with solar panels, for application in developing countries. We have confirmed that it is possible to increase the pe
13. Project STARS (Studies on Trajectories of Adolescent Relationships and Sexuality) : A longitudinal, multi-domain study on sexual development of Dutch adolescents
Reitz, Ellen; van de Bongardt, Daphne; Baams, Laura; Doornwaard, Suzan; Dalenberg, Wieke; Dubas, Judith; van Aken, Marcel; Overbeek, Geertjan; ter Bogt, Tom; van der Eijnden, Regina; Vanwesenbeeck, Ine; Timmerman, Greetje; Kunnen, Elske; van Geert, Paul; Dekovic, Maja
2015-01-01
This study gives an overview of Project STARS (Studies on Trajectories of Adolescent Relationships and Sexuality), a four-wave longitudinal study of 1297 Dutch adolescents. First, the sample, measures and four sub-projects are described. Second, hierarchical regression analyses were conducted to
14. Project STARS (Studies on Trajectories of Adolescent Relationships and Sexuality): A longitudinal, multi-domain study on sexual development of Dutch adolescents
Reitz, E.; van de Bongardt, D.; Baams, L.; Doornwaard, S.; Dalenberg, W.; Dubas, J.; van Aken, M.; Overbeek, G.; ter Bogt, T.; van der Eijnden, R.; Vanwesenbeeck, I.; Kunnen, S.; Timmerman, G.; van Geert, P.; Deković, M.
2015-01-01
This study gives an overview of Project STARS (Studies on Trajectories of Adolescent Relationships and Sexuality), a four-wave longitudinal study of 1297 Dutch adolescents. First, the sample, measures and four sub-projects are described. Second, hierarchical regression analyses were conducted to
15. Hubble Tarantula Treasury Project. II. The Star-formation History of the Starburst Region NGC 2070 in 30 Doradus
Cignoni, M.; Sabbi, E.; van der Marel, R. P.; Tosi, M.; Zaritsky, D.; Anderson, J.; Lennon, D. J.; Aloisi, A.; de Marchi, G.; Gouliermis, D. A.; Grebel, E. K.; Smith, L. J.; Zeidler, P.
2015-10-01
We present a study of the recent star formation (SF) of 30 Doradus in the Large Magellanic Cloud (LMC) using the panchromatic imaging survey Hubble Tarantula Treasury Project. In this paper we focus on the stars within 20 pc of the center of 30 Doradus, the starburst region NGC 2070. We recovered the SF history by comparing deep optical and near-infrared color-magnitude diagrams (CMDs) with state-of-the-art synthetic CMDs generated with the latest PAdova and TRieste Stellar Evolution Code (PARSEC) models, which include all stellar phases from pre-main-sequence to post-main-sequence. For the first time in this region we are able to measure the SF using intermediate- and low-mass stars simultaneously. Our results suggest that NGC 2070 experienced prolonged activity. In particular, we find that the SF in the region (1) exceeded the average LMC rate ≈ 20 Myr ago, (2) accelerated dramatically ≈ 7 Myr ago, and (3) reached a peak value 1-3 Myr ago. We did not find significant deviations from a Kroupa initial mass function down to 0.5 {M}⊙ . The average internal reddening E(B-V) is found to be between 0.3 and 0.4 mag. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA Inc., under NASA contract NAS 5-26555.
16. The EBLM project. III. A Saturn-size low-mass star at the hydrogen-burning limit
von Boetticher, Alexander; Triaud, Amaury H. M. J.; Queloz, Didier; Gill, Sam; Lendl, Monika; Delrez, Laetitia; Anderson, David R.; Collier Cameron, Andrew; Faedi, Francesca; Gillon, Michaël; Gómez Maqueo Chew, Yilen; Hebb, Leslie; Hellier, Coel; Jehin, Emmanuël; Maxted, Pierre F. L.; Martin, David V.; Pepe, Francesco; Pollacco, Don; Ségransan, Damien; Smalley, Barry; Udry, Stéphane; West, Richard
2017-08-01
We report the discovery of an eclipsing binary system with mass-ratio q ˜ 0.07. After identifying a periodic photometric signal received by WASP, we obtained CORALIE spectroscopic radial velocities and follow-up light curves with the Euler and TRAPPIST telescopes. From a joint fit of these data we determine that EBLM J0555-57 consists of a sun-like primary star that is eclipsed by a low-mass companion, on a weakly eccentric 7.8-day orbit. Using a mass estimate for the primary star derived from stellar models, we determine a companion mass of 85 ± 4 MJup (0.081 M⊙) and a radius of 0.84+ 0.14-0.04RJup (0.084 R⊙) that is comparable to that of Saturn. EBLM J0555-57Ab has a surface gravity log g2 =5.50+ 0.03-0.13 and is one of the densest non-stellar-remnant objects currently known. These measurements are consistent with models of low-mass stars. The photometry tables and radial velocities are only available at the CDS and on demand via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/604/L6
17. Dissecting 30 Doradus: Optical and Near Infrared Star Formation History of the starburst cluster NGC2070 from the Hubble Tarantula Treasury Project
Cignoni, Michele
2015-08-01
I will present new results on the star formation history of 30 Doradus in the Large Magellanic Cloud based on the panchromatic imaging survey Hubble Tarantula Treasury Project (HTTP). Here the focus is on the starburst cluster NGC2070. The star formation history is derived by comparing the deepest ever optical and NIR color-magnitude diagrams (CMDs) with state-of-the-art synthetic CMDs generated with the latest PARSEC models, which include all stellar phases from pre-main sequence (PMS) to post-main sequence. For the first time in this region we are able to measure the star formation using intermediate and low mass stars simultaneously. Our results suggest that NGC2070 experienced a prolonged activity. I will discuss the detailed star formation history, initial mass function and reddening distribution and how these relate to previous studies of this starburst region.
18. The K2-ESPRINT Project V: a short-period giant planet orbiting a subgiant star
Van Eylen, Vincent; Gandolfi, Davide; Dai, Fei; Winn, Joshua N; Hirano, Teriyuki; Narita, Norio; Bruntt, Hans; Prieto-Arranz, Jorge; Bejar, Victor J S; Nowak, Grzegorz; Lund, Mikkel N; Palle, Enric; Ribas, Ignasi; Sanchis-Ojeda, Roberto; Yu, Liang; Arriagada, Pamela; Butler, R Paul; Crane, Jeffrey D; Handberg, Rasmus; Deeg, Hans; Jessen-Hansen, Jens; Johnson, John A; Nespral, David; Rogers, Leslie; Ryu, Tsuguru; Shectman, Stephen; Shrotriya, Tushar; Slumstrup, Ditte; Takeda, Yoichi; Teske, Johanna; Thompson, Ian; Vanderburg, Andrew; Wittenmyer, Robert
2016-01-01
We report on the discovery and characterization of the transiting planet K2-39b (EPIC 206247743b). With an orbital period of 4.6 days, it is the shortest-period planet orbiting a subgiant star known to date. Such planets are rare, with only a handful of known cases. The reason for this is poorly understood, but may reflect differences in planet occurrence around the relatively high-mass stars that have been surveyed, or may be the result of tidal destruction of such planets. K2-39 is an evolved star with a spectroscopically derived stellar radius and mass of $3.88^{+0.48}_{-0.42}~\\mathrm{R_\\odot}$ and $1.53^{+0.13}_{-0.12}~\\mathrm{M_\\odot}$, respectively, and a very close-in transiting planet, with $a/R_\\star = 3.4$. Radial velocity (RV) follow-up using the HARPS, FIES and PFS instruments leads to a planetary mass of $50.3^{+9.7}_{-9.4}~\\mathrm{M_\\oplus}$. In combination with a radius measurement of $8.3 \\pm 1.1~\\mathrm{R_\\oplus}$, this results in a mean planetary density of $0.50^{+0.29}_{-0.17}$ g~cm$^{-3}$...
19. The K2-ESPRINT Project V: a short-period giant planet orbiting a subgiant star
Van Eylen, Vincent; Albrecht, Simon; Gandolfi, Davide;
2016-01-01
{R_\\odot}$and$1.53^{+0.13}_{-0.12}~\\mathrm{M_\\odot}$, respectively, and a very close-in transiting planet, with$a/R_\\star = 3.4$. Radial velocity (RV) follow-up using the HARPS, FIES and PFS instruments leads to a planetary mass of$50.3^{+9.7}_{-9.4}~\\mathrm{M_\\oplus}$. In combination with a radius measurement......We report on the discovery and characterization of the transiting planet K2-39b (EPIC 206247743b). With an orbital period of 4.6 days, it is the shortest-period planet orbiting a subgiant star known to date. Such planets are rare, with only a handful of known cases. The reason for this is poorly...... understood, but may reflect differences in planet occurrence around the relatively high-mass stars that have been surveyed, or may be the result of tidal destruction of such planets. K2-39 is an evolved star with a spectroscopically derived stellar radius and mass of$3.88^{+0.48}_{-0.42}~\\mathrm...
20. SELECTION EFFECTS IN GAMMA-RAY BURST CORRELATIONS: CONSEQUENCES ON THE RATIO BETWEEN GAMMA-RAY BURST AND STAR FORMATION RATES
Dainotti, M. G.; Shigehiro, N. [Astrophysical Big Bang Laboratory, Riken, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Vecchio, R. Del [Obserwatorium Astronomiczne, Uniwersytet Jagielloński, ul. Orla 171, 31-501 Kraków (Poland); Capozziello, S., E-mail: maria.dainotti@riken.jp, E-mail: mdainott@stanford.edu, E-mail: delvecchioroberta@hotmail.it, E-mail: dainotti@oa.uj.edu.pl, E-mail: mariagiovannadainotti@yahoo.it, E-mail: capozziello@na.infn.it [Dipartimento di Fisica, Universitá di Napoli " Federico II," Compl. Univ. di Monte S. Angelo, Edicio G, Via Cinthia, I-80126 Napoli (Italy)
2015-02-10
Gamma-ray bursts (GRBs) visible up to very high redshift have become attractive targets as potential new distance indicators. It is still not clear whether the relations proposed so far originate from an unknown GRB physics or result from selection effects. We investigate this issue in the case of the L{sub X} -T{sub a}{sup ∗} (hereafter LT) correlation between the X-ray luminosity L{sub X} (T{sub a} ) at the end of the plateau phase, T{sub a} , and the rest-frame time T{sub a}{sup ∗}. We devise a general method to build mock data sets starting from a GRB world model and taking into account selection effects on both time and luminosity. This method shows how not knowing the efficiency function could influence the evaluation of the intrinsic slope of any correlation and the GRB density rate. We investigate biases (small offsets in slope or normalization) that would occur in the LT relation as a result of truncations, possibly present in the intrinsic distributions of L{sub X} and T{sub a}{sup ∗}. We compare these results with the ones in Dainotti et al. showing that in both cases the intrinsic slope of the LT correlation is ≈ – 1.0. This method is general and therefore relevant for investigating whether or not any other GRB correlation is generated by the biases themselves. Moreover, because the farthest GRBs and star-forming galaxies probe the reionization epoch, we evaluate the redshift-dependent ratio Ψ(z) = (1 + z){sup α} of the GRB rate to the star formation rate. We found a modest evolution –0.2 ≤ α ≤ 0.5 consistent with a Swift GRB afterglow plateau in the redshift range 0.99 < z < 9.4.
1. Payload Service System for the Small Satellites of Double Star Project
Sun, H. X.; Chen, X. M.
Double Star Project (DSP) is a cooperative program between ESA and China, which plan to be launched in 2003. The main objective of the program is to explore the magnetosphere of the earth. Using two small satellites, one is in near polar orbit, another is in near equatorial orbit; compensate CLUSTER II 4 satellites, to form 6 points measurements and to detect the 3-D small-scale structures and spatial-temporal variations of magnetosphere. ESA will provide several experiment payloads, which are identical to that of CLUSTER II, include Fluxgate Magnetometer (FGM), Active Spacecraft Potential Control experiment (ASPOC), Spatial- Temporal Analysis of Field Fluctuation experiment (STAFF), Plasma Electron And Current Experiment (PEACE), Hot Ion Analyzer (HIA) etc. China will provide the launcher, the satellite platform and several experiment payloads, include Heave Ion Detector (HID), High Energy Electron Detector (HEED), High Energy Proton Detector (HEPD), Low Frequency Electromagnetic Wave Detector etc. In order to reduce the cost, all the experiment payloads provided by ESA keep the same with that of CLUSTER II, include all interfaces even for data acquisition sequence. However the satellites and the interfaces of the payloads from China are different form CLUSTER II, so how to handle the data of the experiments became a challenge problem for the DSP. CSSAR designed a Payload Service System (PSS) to bridge the gap. PSS is a distributed system based on the 1553B data bus, it is consist of Bus Controller, Soiled State Recorder, High Rate Multiplexer, Remote Terminal, S-band Transmitter and Power Distributor. In Bus Controller the special interface designed to connect the ESA experiment payloads, which follow the same interface standard with CLUSTER II. All other payloads and instruments access the system via 1553B data bus. PSS acquire the science and housekeeping data of ESA experiments with the same sequence and period as they did in CLUSTER II, but the data will be
2. Projective rectification of infrared images from air-cooled condenser temperature measurement by using projection profile features and cross-ratio invariability.
Xu, Lijun; Chen, Lulu; Li, Xiaolu; He, Tao
2014-10-01
In this paper, we propose a projective rectification method for infrared images obtained from the measurement of temperature distribution on an air-cooled condenser (ACC) surface by using projection profile features and cross-ratio invariability. In the research, the infrared (IR) images acquired by the four IR cameras utilized are distorted to different degrees. To rectify the distorted IR images, the sizes of the acquired images are first enlarged by means of bicubic interpolation. Then, uniformly distributed control points are extracted in the enlarged images by constructing quadrangles with detected vertical lines and detected or constructed horizontal lines. The corresponding control points in the anticipated undistorted IR images are extracted by using projection profile features and cross-ratio invariability. Finally, a third-order polynomial rectification model is established and the coefficients of the model are computed with the mapping relationship between the control points in the distorted and anticipated undistorted images. Experimental results obtained from an industrial ACC unit show that the proposed method performs much better than any previous method we have adopted. Furthermore, all rectified images are stitched together to obtain a complete image of the whole ACC surface with a much higher spatial resolution than that obtained by using a single camera, which is not only useful but also necessary for more accurate and comprehensive analysis of ACC performance and more reliable optimization of ACC operations.
3. The K2-ESPRINT Project V: A Short-period Giant Planet Orbiting a Subgiant Star*
Van Eylen, Vincent; Albrecht, Simon; Gandolfi, Davide; Dai, Fei; Winn, Joshua N.; Hirano, Teriyuki; Narita, Norio; Bruntt, Hans; Prieto-Arranz, Jorge; Béjar, Víctor J. S.; Nowak, Grzegorz; Lund, Mikkel N.; Palle, Enric; Ribas, Ignasi; Sanchis-Ojeda, Roberto; Yu, Liang; Arriagada, Pamela; Butler, R. Paul; Crane, Jeffrey D.; Handberg, Rasmus; Deeg, Hans; Jessen-Hansen, Jens; Johnson, John A.; Nespral, David; Rogers, Leslie; Ryu, Tsuguru; Shectman, Stephen; Shrotriya, Tushar; Slumstrup, Ditte; Takeda, Yoichi; Teske, Johanna; Thompson, Ian; Vanderburg, Andrew; Wittenmyer, Robert
2016-11-01
We report on the discovery and characterization of the transiting planet K2-39b (EPIC 206247743b). With an orbital period of 4.6 days, it is the shortest-period planet orbiting a subgiant star known to date. Such planets are rare, with only a handful of known cases. The reason for this is poorly understood but may reflect differences in planet occurrence around the relatively high-mass stars that have been surveyed, or may be the result of tidal destruction of such planets. K2-39 (EPIC 206247743) is an evolved star with a spectroscopically derived stellar radius and mass of {3.88}-0.42+0.48 {R}ȯ and {1.53}-0.12+0.13 {M}ȯ , respectively, and a very close-in transiting planet, with a/{R}\\star =3.4. Radial velocity (RV) follow-up using the HARPS, FIES, and PFS instruments leads to a planetary mass of {50.3}-9.4+9.7 {M}\\oplus . In combination with a radius measurement of 8.3+/- 1.1 {R}\\oplus , this results in a mean planetary density of {0.50}-0.17+0.29 g cm‑3. We furthermore discover a long-term RV trend, which may be caused by a long-period planet or stellar companion. Because K2-39b has a short orbital period, its existence makes it seem unlikely that tidal destruction is wholly responsible for the differences in planet populations around subgiant and main-sequence stars. Future monitoring of the transits of this system may enable the detection of period decay and constrain the tidal dissipation rates of subgiant stars. Based on observations made with the NOT telescope under program ID. 50-022/51-503, 50-213(CAT), 52-201 (CAT), 52-108 (OPTICON), 51-211 (CAT), and ESOs 3.6 m telescope at the La Silla Paranal Observatory under program ID 095.C-0718(A).
4. Prenatal cocaine exposure decreases parvalbumin-immunoreactive neurons and GABA-to-projection neuron ratio in the medial prefrontal cortex.
McCarthy, Deirdre M; Bhide, Pradeep G
2012-01-01
Cocaine abuse during pregnancy produces harmful effects not only on the mother but also on the unborn child. The neurotransmitters dopamine and serotonin are known as the principal targets of the action of cocaine in the fetal and postnatal brain. However, recent evidence suggests that cocaine can impair cerebral cortical GABA neuron development and function. We sought to analyze the effects of prenatal cocaine exposure on the number and distribution of GABA and projection neurons (inhibitory interneurons and excitatory output neurons, respectively) in the mouse cerebral cortex. We found that the prenatal cocaine exposure decreased GABA neuron numbers and GABA-to-projection neuron ratio in the medial prefrontal cortex of 60-day-old mice. The neighboring prefrontal cortex did not show significant changes in either of these measures. However, there was a significant increase in projection neuron numbers in the prefrontal cortex but not in the medial prefrontal cortex. Thus, the effects of cocaine on GABA and projection neurons appear to be cortical region specific. The population of parvalbumin-immunoreactive GABA neurons was decreased in the medial prefrontal cortex following the prenatal cocaine exposure. The cocaine exposure also delayed the developmental decline in the volume of the medial prefrontal cortex. Thus, prenatal cocaine exposure produced persisting and region-specific effects on cortical cytoarchitecture and impaired the physiological balance between excitatory and inhibitory neurotransmission. These structural changes may underlie the electrophysiological and behavioral effects of prenatal cocaine exposure observed in animal models and human subjects.
5. The SILCC project: III. Regulation of star formation and outflows by stellar winds and supernovae
Gatto, A; Naab, T; Girichidis, P; Wünsch, R; Glover, S C O; Klessen, R S; Clark, P C; Peters, T; Derigs, D; Baczynski, C; Puls, J
2016-01-01
We study the impact of stellar winds and supernovae on the multi-phase interstellar medium using three-dimensional hydrodynamical simulations carried out with FLASH. The selected galactic disc region has a size of (500 pc)$^2$ x $\\pm$ 5 kpc and a gas surface density of 10 M$_{\\odot}$/pc$^2$. The simulations include an external stellar potential and gas self-gravity, radiative cooling and diffuse heating, sink particles representing star clusters, stellar winds from these clusters which combine the winds from indi- vidual massive stars by following their evolution tracks, and subsequent supernova explosions. Dust and gas (self-)shielding is followed to compute the chemical state of the gas with a chemical network. We find that stellar winds can regulate star (cluster) formation. Since the winds suppress the accretion of fresh gas soon after the cluster has formed, they lead to clusters which have lower average masses (10$^2$ - 10$^{4.3}$ M$_{\\odot}$) and form on shorter timescales (10$^{-3}$ - 10 Myr). In part...
6. Uncertainty analysis of projections of ozone-depleting substances: mixing ratios, EESC, ODPs, and GWPs
G. J. M. Velders
2013-10-01
7. Understanding the dynamical structure of pulsating stars: The center-of-mass velocity and the Baade-Wesselink projection factor of the beta-Cephei star alpha-Lupi
Nardetto, N; Fokin, A; Chapellier, E; Pietrzynski, G; Gieren, W; Graczyk, D; Mourard, D
2013-01-01
High-resolution spectroscopy of pulsating stars is a powerful tool to study the dynamical structure of their atmosphere. Lines asymmetry is used to derive the center-of-mass velocity of the star, while a direct measurement of the atmospheric velocity gradient helps determine the projection factor used in the Baade-Wesselink method of distance determination. We aim at deriving the center-of-mass velocity and the projection factor of the beta-Cephei star alpha-Lup. We present HARPS high spectral resolution observations of alpha-Lup. We calculate the first-moment radial velocities and fit the spectral line profiles by a bi-Gaussian to derive line asymmetries. Correlations between the gamma-velocity and the gamma-asymmetry (defined as the average values of the radial velocity and line asymmetry curves respectively) are used to derive the center-of-mass velocity of the star. By combining our spectroscopic determination of the atmospheric velocity gradient with a hydrodynamical modelof the photosphere of the star, ...
8. NLTE strontium abundance in a sample of extremely metal poor stars and the Sr/Ba ratio in the early Galaxy
Andrievsky, S M; Korotin, S A; Francois, P; Spite, M; Bonifacio, P; Cayrel, R; Hill, V
2011-01-01
Heavy element abundances in extremely metal-poor stars provide strong constraints on the processes of forming these elements in the first stars. We attempt to determine precise abundances of strontium in a homogeneous sample of extremely metal-poor stars. The abundances of strontium in 54 very or extremely metal-poor stars, was redetermined by abandoning the local thermodynamic equilibrium (LTE) hypothesis, and fitting non-LTE (NLTE) profiles to the observed spectral lines. The corrected Sr abundances and previously obtained NLTE Ba abundances are compared to the predictions of several hypothetical formation processes for the lighter neutron-capture elements. Our NLTE abundances confirm the previously determined huge scatter of the strontium abundance in low metallicity stars. This scatter is also found (and is even larger) at very low metallicities (i. e. early in the chemical evolution). The Sr abundance in the extremely metal-poor (EMP) stars is compatible with the main r-process involved in other processe...
9. Validating MODIS above-cloud aerosol optical depth retrieved from "color ratio" algorithm using direct measurements made by NASA's airborne AATS and 4STAR sensors
Jethva, Hiren; Torres, Omar; Remer, Lorraine; Redemann, Jens; Livingston, John; Dunagan, Stephen; Shinozuka, Yohei; Kacenelenbogen, Meloe; Segal Rosenheimer, Michal; Spurr, Rob
2016-10-01
We present the validation analysis of above-cloud aerosol optical depth (ACAOD) retrieved from the "color ratio" method applied to MODIS cloudy-sky reflectance measurements using the limited direct measurements made by NASA's airborne Ames Airborne Tracking Sunphotometer (AATS) and Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research (4STAR) sensors. A thorough search of the airborne database collection revealed a total of five significant events in which an airborne sun photometer, coincident with the MODIS overpass, observed partially absorbing aerosols emitted from agricultural biomass burning, dust, and wildfires over a low-level cloud deck during SAFARI-2000, ACE-ASIA 2001, and SEAC4RS 2013 campaigns, respectively. The co-located satellite-airborne matchups revealed a good agreement (root-mean-square difference < 0.1), with most matchups falling within the estimated uncertainties associated the MODIS retrievals (about -10 to +50 %). The co-retrieved cloud optical depth was comparable to that of the MODIS operational cloud product for ACE-ASIA and SEAC4RS, however, higher by 30-50 % for the SAFARI-2000 case study. The reason for this discrepancy could be attributed to the distinct aerosol optical properties encountered during respective campaigns. A brief discussion on the sources of uncertainty in the satellite-based ACAOD retrieval and co-location procedure is presented. Field experiments dedicated to making direct measurements of aerosols above cloud are needed for the extensive validation of satellite-based retrievals.
10. The impact of mass segregation and star-formation on the rates of gravitational-wave sources from extreme mass ratio inspirals
Aharon, Danor
2016-01-01
Compact stellar objects inspiralling into massive black holes (MBHs) in galactic nuclei are some of the most promising gravitational wave (GWs) sources for next generation GW-detectors. The rates of such extreme mass ratio inspirals (EMRIs) depend on the dynamics and distribution of compact objects around the MBH. Here we study the impact of mass-segregation processes on EMRI rates. In particular, we provide the expected mass function of EMRIs, given an initial mass function of stellar BHs (SBHs), and relate it to the mass-dependent detection rate of EMRIs. We then consider the role of star formation on the distribution of compact objects and its implication on EMRI rates. We find that the existence of a wide spectrum of SBH masses lead to the overall increase of EMRI rates, and to high rates of the EMRIs from the most-massive SBHs. However, it also leads to a relative quenching of EMRI rates from lower-mass SBHs, and together produces a steep dependence of the EMRI mass function on the highest-mass SBHs. Sta...
11. Carbon-rich presolar grains from massive stars. Subsolar 12C/13C and 14N/15N ratios and the mystery of 15N
Pignatari, M; Hoppe, P; Jordan, C J; Gibson, B K; Trappitsch, R; Herwig, F; Fryer, C; Hirschi, R; Timmes, F X
2015-01-01
Carbon-rich grains with isotopic anomalies compared to the Sun are found in primitive meteorites. They were made by stars, and carry the original stellar nucleosynthesis signature. Silicon carbide grains of Type X and C, and low-density graphites condensed in the ejecta of core-collapse supernovae. We present a new set of models for the explosive He shell and compare them with the grains showing 12C/13C and 14N/15N ratios lower than solar. In the stellar progenitor H was ingested into the He shell and not fully destroyed before the explosion. Different explosion energies and H concentrations are considered. If the SN shock hits the He-shell region with some H still present, the models can reproduce the C and N isotopic signatures in C-rich grains. Hot-CNO cycle isotopic signatures are obtained, including a large production of 13C and 15N. The short-lived radionuclides 22Na and 26Al are increased by orders of magnitude. The production of radiogenic 22Ne from the decay of 22Na in the He shell might solve the pu...
12. Validating MODIS Above-Cloud Aerosol Optical Depth Retrieved from Color Ratio Algorithm Using Direct Measurements Made by NASA's Airborne AATS and 4STAR Sensors
Jethva, Hiren; Torres, Omar; Remer, Lorraine; Redemann, Jens; Livingston, John; Dunagan, Stephen; Shinozuka, Yohei; Kacenelenbogen, Meloe; Segal Rozenhaimer, Michal; Spurr, Rob
2016-01-01
We present the validation analysis of above-cloud aerosol optical depth (ACAOD) retrieved from the color ratio method applied to MODIS cloudy-sky reflectance measurements using the limited direct measurements made by NASAs airborne Ames Airborne Tracking Sunphotometer (AATS) and Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research (4STAR) sensors. A thorough search of the airborne database collection revealed a total of five significant events in which an airborne sun photometer, coincident with the MODIS overpass, observed partially absorbing aerosols emitted from agricultural biomass burning, dust, and wildfires over a low-level cloud deck during SAFARI-2000, ACE-ASIA 2001, and SEAC4RS 2013 campaigns, respectively. The co-located satellite-airborne match ups revealed a good agreement (root-mean-square difference less than 0.1), with most match ups falling within the estimated uncertainties associated with the MODIS retrievals (about -10 to +50 ). The co-retrieved cloud optical depth was comparable to that of the MODIS operational cloud product for ACE-ASIA and SEAC4RS, however, higher by 30-50% for the SAFARI-2000 case study. The reason for this discrepancy could be attributed to the distinct aerosol optical properties encountered during respective campaigns. A brief discussion on the sources of uncertainty in the satellite-based ACAOD retrieval and co-location procedure is presented. Field experiments dedicated to making direct measurements of aerosols above cloud are needed for the extensive validation of satellite based retrievals.
13. The ISLAndS Project. II. The Lifetime Star Formation Histories of Six Andomeda dSphS
Skillman, Evan D.; Monelli, Matteo; Weisz, Daniel R.; Hidalgo, Sebastian L.; Aparicio, Antonio; Bernard, Edouard J.; Boylan-Kolchin, Michael; Cassisi, Santi; Cole, Andrew A.; Dolphin, Andrew E.; Ferguson, Henry C.; Gallart, Carme; Irwin, Mike J.; Martin, Nicolas F.; Martínez-Vázquez, Clara E.; Mayer, Lucio; McConnachie, Alan W.; McQuinn, Kristen B. W.; Navarro, Julio F.; Stetson, Peter B.
2017-03-01
The Initial Star formation and Lifetimes of Andromeda Satellites (ISLAndS) project employs Hubble Space Telescope imaging to study a representative sample of six Andromeda dSph satellite companion galaxies. Our main goal is to determine whether the star formation histories (SFHs) of the Andromeda dSph satellites demonstrate significant statistical differences from those of the Milky Way (MW). Our deep observations yield a time resolution at the oldest ages of ∼1 Gyr, allowing meaningful comparisons to the MW satellites. The six dSphs present a variety of SFHs (e.g., a significant range in quenching times, {τ }q, from 9 to 6 Gyr ago) that are not strictly correlated with luminosity or present distance from M31. In agreement with observations of MW companions of similar mass, there is no evidence of complete quenching of star formation by the cosmic UV background responsible for reionization, but the possibility of a degree of quenching at reionization cannot be ruled out. We do not find significant differences between the SFHs of the members and non-members of the vast, thin plane of satellites. The SFHs of the ISLAndS M31 dSphs appear to be more uniform than those of the MW dSphs. Specifically, the primary difference between the SFHs of the ISLAndS dSphs and MW dSph companions of similar luminosities and host distances is the absence of late-quenching ({τ }q≤slant 5 {Gyr}) dSphs in the ISLAndS sample. Thus, models that can produce satellite populations with and without late-quenching satellites are of extreme interest. Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with programs #13028, 13739.
14. The SOLA Team: A Star Formation Project To Study the Soul of Lupus with ALMA
De Gregorio-Monsalvo, Itziar; Saito, M.; Rodon, J.; Takahashi, S.
2017-06-01
The SOLA team is a multi-national and multi-wavelength collaboration composed by scientists with technical expertise in ALMA and in infrared and optical techniques. The aim of the team is to establish a low-mass star formation scenario based on the Lupus molecular clouds. In this talk I will present our unique catalog of pre-stellar and proto-stellar cores toward Lupus molecular clouds, the results on our latest studies in protoplanetary disks, as well as our ALMA Cycle 3 data aiming at testing the formation mechanism of sub-stellar objects in Lupus molecular clouds.
15. A revision of the fundamental parameters of the open cluster Hogg 15 and the projected star WR 47
Piatti, A. E.; Bica, E.; Santos, J. F. C., Jr.; Clariá, J. J.
2002-05-01
We revise the fundamental parameters of the faint open cluster Hogg 15, for which two recent colour-magnitude diagram (CMD) studies have obtained significantly different ages. In the present study, we combine a series of methods trying to constrain age, together with other fundamental parameters. We employ spatial extractions to construct the CMDs, and the cluster integrated spectrum to compare it with those of templates of known age. We derive fundamental parameters, in particular, distance, of the closely projected Wolf-Rayet star HDE 311884 (WR 47) - often proposed to be physically related to Hogg 15. Based on the WR 47 spectrum and available photometry, we conclude that the short distance implied by the Hipparcos parallax (216 pc) is affected by binary motion. From the WR 47 spectrum we estimate a reddening E(B-V) and a distance of 1.10 +/- 0.05 and 5.2 +/- 0.9 kpc, respectively. For Hogg 15 we derive an age of 20 +/- 10 Myr, a reddening of 1.10 +/- 0.05, and a distance of 3.1 +/- 0.5 kpc. We conclude that Hogg 15 is not related to WR 47 from the point of view of origin, since the cluster and the star do not belong to the same formation event.
16. The ISLAndS project II: The Lifetime Star Formation Histories of Six Andromeda dSphs
Skillman, Evan D; Weisz, Daniel R; Hidalgo, Sebastian L; Aparicio, Antonio; Bernard, Edouard J; Boylan-Kolchin, Michael; Cassisi, Santi; Cole, Andrew A; Dolphin, Andrew E; Ferguson, Henry C; Gallart, Carme; Irwin, Mike J; Martin, Nicolas F; Martinez-Vazquez, Clara E; Mayer, Lucio; McConnachie, Alan W; McQuinn, Kristen B W; Navarro, Julio F; Stetson, Peter B
2016-01-01
The Initial Star formation and Lifetimes of Andromeda Satellites (ISLAndS) project uses Hubble Space Telescope imaging to study a representative sample of six Andromeda dSph satellite companion galaxies. The main goal of the program is to determine whether the star formation histories (SFHs) of the Andromeda dSph satellites demonstrate significant statistical differences from those of the Milky Way, which may be attributable to the different properties of their local environments. Our observations reach the oldest main sequence turn-offs, allowing a time resolution at the oldest ages of ~ 1 Gyr, which is comparable to the best achievable resolution in the MW satellites. We find that the six dSphs present a variety of SFHs that are not strictly correlated with luminosity or present distance from M31. Specifically, we find a significant range in quenching times (lookback times from 9 to 6 Gyr), but with all quenching times more than ~ 6 Gyr ago. In agreement with observations of Milky Way companions of similar ...
17. The Chemical Abundances of Stars in the Halo (CASH) Project. III. A New Classification Scheme for Carbon-Enhanced Metal-poor Stars with S-process Element Enhancement
Hollek, Julie K; Placco, Vinicius M; Karakas, Amanda I; Shetrone, Matthew; Sneden, Christopher; Christlieb, Norbert
2015-01-01
We present a detailed abundance analysis of 23 elements for a newly discovered carbon-enhanced metal-poor (CEMP) star, HE 0414-0343, from the Chemical Abundances of Stars in the Halo (CASH) Project. Its spectroscopic stellar parameters are Teff = 4863 K, log g = 1.25, vmic = 2.20 km/s, and [Fe/H] = -2.24. Radial velocity measurements covering seven years indicate HE 0414-0343 to be a binary. HE 0414-0343 has [C/Fe] = 1.44 and is strongly enhanced in neutron-capture elements but its abundances cannot be reproduced by a solar-type s-process pattern alone. Traditionally, it could be classified as "CEMP-r/s" star. Based on abundance comparisons with AGB star nucleosynthesis models, we suggest a new physically-motivated origin and classification scheme for CEMP-s stars and the still poorly-understood CEMP-r/s. The new scheme describes a continuous transition between these two so-far distinctly treated subgroups: CEMP-sA, CEMP-sB, and CEMP-sC. Possible causes for a continuous transition include the number of therma...
18. Very Low-Mass Stellar and Substellar Companions to Solar-Like Stars from MARVELS I: A Low Mass Ratio Stellar Companion to TYC 4110-01037-1 in a 79-day Orbit
Wisniewski, John P; Crepp, Justin R; De Lee, Nathan; Eastman, Jason; Esposito, Massimiliano; Fleming, Scott W; Gaudi, B Scott; Ghezzi, Luan; Hernandez, Jonay I Gonzalez; Lee, Brian L; Stassun, Keivan G; Agol, Eric; Prieto, Carlos Allende; Barnes, Rory; Bizyaev, Dmitry; Cargile, Phillip; Chang, Liang; Da Costa, Luiz N; De Mello, G F Porto; Femenia, Bruno; Ferreira, Leticia D; Gary, Bruce; Hebb, Leslie; Holtzman, Jon; Liu, Jian; Ma, Bo; Mack, Claude E; Mahadevan, Suvrath; Maia, Marcio A G; Nguyen, Duy Cuong; Ogando, Ricardo L C; Oravetz, Daniel J; Paegert, Martin; Pan, Kaike; Pepper, Joshua; Rebolo, Rafael; Santiago, Basilio; Schneider, Donald P; Shelden, Alaina C; Simmons, Audrey; Tofflemire, Benjamin M; Wan, Xiaoke; Wang, Ji; Zhao, Bo
2012-01-01
TYC 4110-01037-1 has a low-mass stellar companion, whose small mass ratio and short orbital period are atypical amongst solar-like (Teff ~0.087 +/- 0.003, places it at the lowest end of observed values for short period stellar companions to solar-like (Teff ~< 6000 K) stars. One possible way to create such a system would be if a triple-component stellar multiple broke up into a short period, low q binary during the cluster dispersal phase of its lifetime. A candidate tertiary body has been identified in the system via single-epoch, high contrast imagery. If this object is confirmed to be co-moving, we estimate it would be a dM4 star. We present these results in the context of our larger-scale effort to constrain the statistics of low mass stellar and brown dwarf companions to FGK-type stars via the MARVELS survey.
19. Hubble Tarantula Treasury Project: Unraveling Tarantula's Web. II. Optical and Near Infrared Star Formation History of the Starburst Cluster NGC 2070 in 30 Doradus
Cignoni, M; van der Marel, R P; Tosi, M; Zaritsky, D; Anderson, J; Lennon, D J; Aloisi, A; de Marchi, G; Gouliermis, D A; Grebel, E K; Smith, L J; Zeidler, P
2015-01-01
We present a study of the recent star formation of 30 Doradus in the Large Magellanic Cloud (LMC) using the panchromatic imaging survey Hubble Tarantula Treasury Project (HTTP). In this paper we focus on the stars within 20 pc of the center of the massive ionizing cluster of 30 Doradus, NGC 2070. We recovered the star formation history by comparing deep optical and NIR color-magnitude diagrams (CMDs) with state-of-the-art synthetic CMDs generated with the latest PARSEC models, which include all stellar phases from pre-main sequence to post- main sequence. For the first time in this region we are able to measure the star formation using intermediate and low mass stars simultaneously. Our results suggest that NGC2070 experienced a prolonged activity. In particular, we find that the star formation in the region: i) exceeded the average LMC rate ~ 20 Myr ago; ii) accelerated dramatically ~ 7 Myr ago; and iii) reached a peak value 1-3 Myr ago. We did not find significant deviations from a Kroupa initial mass funct...
20. Herschel observations of extreme OH/IR stars - the isotopic ratios of oxygen as a sign-post for the stellar mass
Justtanont, K; Blommaert, J; Decin, L; Kerschbaum, F; Matsuura, M; Olofsson, H; Owen, P; Royer, P; Swinyard, B; Teyssier, D; Waters, L B F M; Yates, J
2015-01-01
Aim: The late stages of stellar evolution are mainly governed by the mass of the stars. Low- and intermediate-mass stars lose copious amounts of mass during the asymptotic giant branch (AGB) which obscure the central star making it difficult to study the stellar spectra and determine the stellar mass. In this study, we present observational data that can be used to determine lower limits to the stellar mass. Method: Spectra of nine heavily reddened AGB stars taken by the Herschel Space Observatory display numerous molecular emission lines. The strongest emission lines are due to H2O. We search for the presence of isotopologues of H2O in these objects. Result: We detected the 16O and 17O isotopologues of water in these stars, but lines due to H2^{18}O are absent. The lack of 18O is predicted by a scenario where the star has undergone hot-bottom burning which preferentially destroys 18O relative to 16O and 17O. From stellar evolution calculations, this process is thought to occur when the stellar mass is above ...
1. Chemical Cartography in the Milky Way with SDSS/APOGEE: Multi-element abundances and abundance ratio variations
Holtzman, Jon A.; Hasselquist, Sten; Johnson, Jennifer; Bird, Jonathan C.; Majewski, Steven R.; SDSS/APOGEE Team
2017-01-01
The SDSS/APOGEE project is measuring abundances of multiple elements for several hundred thousand stars across the Milky Way. These allow the mapping of abundances and abundance ratio variations. Results will be presented for multiple abundance ratios across of the Galactic disk. The interpretation of mean abundance maps is complicated by variations in star formation history across the disk and by changing abundance ratios that result from an overall metallicity gradient. Variations in chemical abundance sequences, however, show the potential for using abundance ratios to track the movement of stars through the disk, and provide key information for constraining Galaxy formation and chemical evolution models.
2. Spectroscopic twin to the hypervelocity sdO star US 708 and three fast sdB stars from the Hyper-MUCHFUSS project
Ziegerer, E.; Heber, U.; Geier, S.; Irrgang, A.; Kupfer, T.; Fürst, F.; Schaffenroth, J.
2017-05-01
Important tracers for the dark matter halo of the Galaxy are hypervelocity stars (HVSs), which are faster than the local escape velocity of the Galaxy and their slower counterparts, the high-velocity stars in the Galactic halo. Such HVSs are believed to be ejected from the Galactic centre (GC) through tidal disruption of a binary by the super-massive black hole (Hills mechanism). The Hyper-MUCHFUSS survey aims at finding high-velocity potentially unbound hot subdwarf stars. We present the spectroscopic and kinematical analyses of a He-sdO as well as three candidates among the sdB stars using optical Keck/ESI and VLT (X-shooter, FORS) spectroscopy. Proper motions are determined by combining positions from early-epoch photographic plates with those derived from modern digital sky surveys. The Galactic rest frame velocities range from 203 km s-1 to 660 km s-1, indicating that most likely all four stars are gravitationally bound to the Galaxy. With Teff = 47 000 K and a surface gravity of log g = 5.7, SDSS J205030.39-061957.8 (J2050) is a spectroscopic twin of the hypervelocity He-sdO US 708. As for the latter, the GC is excluded as a place of origin based on the kinematic analysis. Hence, the Hills mechanism can be excluded for J2050. The ejection velocity is much more moderate (385 ± 79 km s-1) than that of US 708 (998 ± 68 km s-1). The binary thermonuclear supernova scenario suggested for US 708 would explain the observed properties of J2050 very well without pushing the model parameters to their extreme limits, as required for US 708. Accordingly, the star would be the surviving donor of a type Ia supernova. Three sdB stars also showed extreme kinematics; one could be a HVS ejected from the GC, whereas the other two could be ejected from the Galactic disk through the binary supernova mechanism. Alternatively, they might be extreme halo stars.
3. Star operations and Pullbacks
Fontana, Marco; Park, Mi Hee
2003-01-01
In this paper we study the star operations on a pullback of integral domains. In particular, we characterize the star operations of a domain arising from a pullback of a general type'' by introducing new techniques for projecting'' and lifting'' star operations under surjective homomorphisms of integral domains. We study the transfer in a pullback (or with respect to a surjective homomorphism) of some relevant classes or distinguished properties of star operations such as $v-, t-, w-, b... 4. Very Low Mass Stellar and Substellar Companions to Solar-like Stars from MARVELS. I. A Low-mass Ratio Stellar Companion to TYC 4110-01037-1 in a 79 Day Orbit Wisniewski, John P.; Ge, Jian; Crepp, Justin R.; De Lee, Nathan; Eastman, Jason; Esposito, Massimiliano; Fleming, Scott W.; Gaudi, B. Scott; Ghezzi, Luan; Gonzalez Hernandez, Jonay I.; Lee, Brian L.; Stassun, Keivan G.; Agol, Eric; Allende Prieto, Carlos; Barnes, Rory; Bizyaev, Dmitry; Cargile, Phillip; Chang, Liang; Da Costa, Luiz N.; Porto De Mello, G. F.; Femenía, Bruno; Ferreira, Leticia D.; Gary, Bruce; Hebb, Leslie; Holtzman, Jon; Liu, Jian; Ma, Bo; Mack, Claude E.; Mahadevan, Suvrath; Maia, Marcio A. G.; Nguyen, Duy Cuong; Ogando, Ricardo L. C.; Oravetz, Daniel J.; Paegert, Martin; Pan, Kaike; Pepper, Joshua; Rebolo, Rafael; Santiago, Basilio; Schneider, Donald P.; Shelden, Alaina C.; Simmons, Audrey; Tofflemire, Benjamin M.; Wan, Xiaoke; Wang, Ji; Zhao, Bo 2012-05-01 TYC 4110-01037-1 has a low-mass stellar companion, whose small mass ratio and short orbital period are atypical among binary systems with solar-like (T eff TYC 4110-01037-1 reveals it to be a moderately aged (lsim5 Gyr) solar-like star having a mass of 1.07 ± 0.08 M ⊙ and radius of 0.99 ± 0.18 R ⊙. We analyze 32 radial velocity (RV) measurements from the SDSS-III MARVELS survey as well as 6 supporting RV measurements from the SARG spectrograph on the 3.6 m Telescopio Nazionale Galileo telescope obtained over a period of ~2 years. The best Keplerian orbital fit parameters were found to have a period of 78.994 ± 0.012 days, an eccentricity of 0.1095 ± 0.0023, and a semi-amplitude of 4199 ± 11 m s-1. We determine the minimum companion mass (if sin i = 1) to be 97.7 ± 5.8 M Jup. The system's companion to host star mass ratio, >=0.087 ± 0.003, places it at the lowest end of observed values for short period stellar companions to solar-like (T eff <~ 6000 K) stars. One possible way to create such a system would be if a triple-component stellar multiple broke up into a short period, low q binary during the cluster dispersal phase of its lifetime. A candidate tertiary body has been identified in the system via single-epoch, high contrast imagery. If this object is confirmed to be comoving, we estimate it would be a dM4 star. We present these results in the context of our larger-scale effort to constrain the statistics of low-mass stellar and brown dwarf companions to FGK-type stars via the MARVELS survey. 5. [$\\alpha$/Fe] Abundances of Four Outer M 31 Halo Stars Vargas, Luis C; Geha, Marla C; Tollerud, Erik J; Kirby, Evan N; Guhathakurta, Puragra 2014-01-01 We present alpha element to iron abundance ratios, [$\\alpha$/Fe], for four stars in the outer stellar halo of the Andromeda Galaxy (M 31). The stars were identified as high-likelihood field halo stars by Gilbert et al. (2012) and lie at projected distances between 70 and 140 kpc from M 31's center. These are the first alpha abundances measured for a halo star in a galaxy beyond the Milky Way. The stars range in metallicity between [Fe/H]= -2.2 and [Fe/H]= -1.4. The sample's average [$\\alpha$/Fe] ratio is +0.20+/-0.20. The best-fit average value is elevated above solar which is consistent with rapid chemical enrichment from Type II supernovae. The mean [$\\alpha$/Fe] ratio of our M31 outer halo sample agrees (within the uncertainties) with that of Milky Way inner/outer halo stars that have a comparable range of [Fe/H]. 6. RVM-Based Human Action Classification in Crowd through Projection and Star Skeletonization V. Abhaikumar 2009-01-01 Full Text Available Detection of abnormal human actions in the crowd has become a critical problem in video surveillance applications like terrorist attacks. This paper proposes a real-time video surveillance system which is capable of classifying normal and abnormal actions of individuals in a crowd. The abnormal actions of human such as running, jumping, waving hand, bending, walking and fighting with each other in a crowded environment are considered. In this paper, Relevance Vector Machine (RVM is used to classify the abnormal actions of an individual in the crowd based on the results obtained from projection and skeletonization methods. Experimental results on benchmark datasets demonstrate that the proposed system is robust and efficient. A comparative study of classification accuracy between Relevance Vector Machine and Support Vector Machine (SVM classification is also presented. 7. RVM-Based Human Action Classification in Crowd through Projection and Star Skeletonization Yogameena B 2009-01-01 Full Text Available Abstract Detection of abnormal human actions in the crowd has become a critical problem in video surveillance applications like terrorist attacks. This paper proposes a real-time video surveillance system which is capable of classifying normal and abnormal actions of individuals in a crowd. The abnormal actions of human such as running, jumping, waving hand, bending, walking and fighting with each other in a crowded environment are considered. In this paper, Relevance Vector Machine (RVM is used to classify the abnormal actions of an individual in the crowd based on the results obtained from projection and skeletonization methods. Experimental results on benchmark datasets demonstrate that the proposed system is robust and efficient. A comparative study of classification accuracy between Relevance Vector Machine and Support Vector Machine (SVM classification is also presented. 8. CARMA Large Area Star Formation Survey: project overview with analysis of dense gas structure and kinematics in Barnard 1 Storm, Shaye; Mundy, Lee G.; Lee, Katherine I.; Teuben, Peter; Pound, Marc W.; Salter, Demerese M.; Chen, Che-Yu; Gong, Hao [Department of Astronomy, University of Maryland, College Park, MD 20742 (United States); Fernández-López, Manuel; Looney, Leslie W.; Segura-Cox, Dominique M. [Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 West Green Street, Urbana, IL 61801 (United States); Rosolowsky, Erik [Departments of Physics and Statistics, University of British Columbia, Okanagan Campus, 3333 University Way, Kelowna BC V1V 1V7 (Canada); Arce, Héctor G.; Plunkett, Adele L. [Department of Astronomy, Yale University, P.O. Box 208101, New Haven, CT 06520-8101 (United States); Ostriker, Eve C. [Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (United States); Volgenau, Nikolaus H. [Owens Valley Radio Observatory, MC 105-24 OVRO, Pasadena, CA 91125 (United States); Shirley, Yancy L. [Steward Observatory, 933 North Cherry Avenue, Tucson, AZ 85721 (United States); Tobin, John J. [National Radio Astronomy Observatory, Charlottesville, VA 22903 (United States); Kwon, Woojin [SRON Netherlands Institute for Space Research, Landleven 12, 9747 AD Groningen (Netherlands); Isella, Andrea, E-mail: sstorm@astro.umd.edu [Astronomy Department, California Institute of Technology, 1200 East California Blvd., Pasadena, CA 91125 (United States); and others 2014-10-20 We present details of the CARMA Large Area Star Formation Survey (CLASSy), while focusing on observations of Barnard 1. CLASSy is a CARMA Key Project that spectrally imaged N{sub 2}H{sup +}, HCO{sup +}, and HCN (J = 1 → 0 transitions) across over 800 square arcminutes of the Perseus and Serpens Molecular Clouds. The observations have angular resolution near 7'' and spectral resolution near 0.16 km s{sup –1}. We imaged ∼150 square arcminutes of Barnard 1, focusing on the main core, and the B1 Ridge and clumps to its southwest. N{sub 2}H{sup +} shows the strongest emission, with morphology similar to cool dust in the region, while HCO{sup +} and HCN trace several molecular outflows from a collection of protostars in the main core. We identify a range of kinematic complexity, with N{sub 2}H{sup +} velocity dispersions ranging from ∼0.05 to 0.50 km s{sup –1} across the field. Simultaneous continuum mapping at 3 mm reveals six compact object detections, three of which are new detections. A new, non-binary dendrogram algorithm is used to analyze dense gas structures in the N{sub 2}H{sup +} position-position-velocity (PPV) cube. The projected sizes of dendrogram-identified structures range from about 0.01 to 0.34 pc. Size-linewidth relations using those structures show that non-thermal line-of-sight velocity dispersion varies weakly with projected size, while rms variation in the centroid velocity rises steeply with projected size. Comparing these relations, we propose that all dense gas structures in Barnard 1 have comparable depths into the sky, around 0.1-0.2 pc; this suggests that overdense, parsec-scale regions within molecular clouds are better described as flattened structures rather than spherical collections of gas. Science-ready PPV cubes for Barnard 1 molecular emission are available for download. 9. The ACS LCID project. IX. Imprints of the early Universe in the radial variation of the star formation history of dwarf galaxies Hidalgo, Sebastian L; Aparicio, Antonio; Gallart, Carme; Skillman, Evan D; Cassisi, Santi; Bernard, Edouard J; Mayer, Lucio; Stetson, Peter; Cole, Andrew; Dolphin, Andrew 2013-01-01 Based on Hubble Space Telescope observations from the Local Cosmology from Isolated Dwarfs project, we present the star formation histories, as a function of galactocentric radius, of four isolated Local Group dwarf galaxies: two dSph galaxies, Cetus and Tucana, and two transition galaxies (dTrs), LGS-3 and Phoenix. The oldest stellar populations of the dSphs and dTrs are, within the uncertainties, coeval ($\\sim 13 Gyr$) at all galactocentric radii. We find that there are no significative differences between the four galaxies in the fundamental properties (such as the normalized star formation rate or age-metallicity relation) of their outer regions (radii greater than four exponential scale lengths); at large radii, these galaxies consist exclusively of old ($\\geq 10.5 Gyr$) metal-poor stars. The duration of star formation in the inner regions vary from galaxy to galaxy, and the extended central star formation in the dTrs produces the dichotomy between dSph and dTr galaxy types. The dTr galaxies show promine... 10. CARMA Large Area Star Formation Survey: Project Overview with Analysis of Dense Gas Structure and Kinematics in Barnard 1 Storm, S; Fernández-López, M; Lee, K I; Looney, L W; Teuben, P J; Rosolowsky, E; Arce, H G; Ostriker, E C; Segura-Cox, D; Pound, M W; Salter, D M; Volgenau, N H; Shirley, Y L; Chen, C; Gong, H; Plunkett, A L; Tobin, J J; Kwon, W; Isella, A; Kauffmann, J; Tassis, K; Crutcher, R M; Gammie, C F; Testi, L 2014-01-01 We present details of the CARMA Large Area Star Formation Survey (CLASSy), while focusing on observations of Barnard 1. CLASSy is a CARMA Key Project that spectrally imaged N2H+, HCO+, and HCN (J=1-0 transitions) across over 800 square arcminutes of the Perseus and Serpens Molecular Clouds. The observations have angular resolution near 7" and spectral resolution near 0.16 km/s. We imaged ~150 square arcminutes of Barnard 1, focusing on the main core, and the B1 Ridge and clumps to its southwest. N2H+ shows the strongest emission, with morphology similar to cool dust in the region, while HCO+ and HCN trace several molecular outflows from a collection of protostars in the main core. We identify a range of kinematic complexity, with N2H+ velocity dispersions ranging from ~0.05-0.50 km/s across the field. Simultaneous continuum mapping at 3 mm reveals six compact object detections, three of which are new detections. A new non-binary dendrogram algorithm is used to analyze dense gas structures in the N2H+ position... 11. The Abundance, Ortho/Para Ratio, and Deuteration of Water in the High-mass Star-forming Region NGC 6334 I Emprechtinger, M.; Lis, D. C.; Rolffs, R.; Schilke, P.; Monje, R. R.; Comito, C.; Ceccarelli, C.; Neufeld, D. A.; van der Tak, F. F. S. 2013-01-01 We present Herschel/HIFI observations of 30 transitions of water isotopologues toward the high-mass star-forming region NGC 6334 I. The line profiles of (H2O)-O-16, (H2O)-O-17, (H2O)-O-18, and HDO show a complex pattern of emission and absorption components associated with the embedded hot cores, a 12. The Abundance, Ortho/Para Ratio, and Deuteration of Water in the High-mass Star-forming Region NGC 6334 I Emprechtinger, M.; Lis, D. C.; Rolffs, R.; Schilke, P.; Monje, R. R.; Comito, C.; Ceccarelli, C.; Neufeld, D. A.; van der Tak, F. F. S. 2013-01-01 We present Herschel/HIFI observations of 30 transitions of water isotopologues toward the high-mass star-forming region NGC 6334 I. The line profiles of H16 2O, H17 2O, H18 2O, and HDO show a complex pattern of emission and absorption components associated with the embedded hot cores, a lower-densit 13. The Abundance, Ortho/Para Ratio, and Deuteration of Water in the High-mass Star-forming Region NGC 6334 I Emprechtinger, M.; Lis, D. C.; Rolffs, R.; Schilke, P.; Monje, R. R.; Comito, C.; Ceccarelli, C.; Neufeld, D. A.; van der Tak, F. F. S. 2013-01-01 We present Herschel/HIFI observations of 30 transitions of water isotopologues toward the high-mass star-forming region NGC 6334 I. The line profiles of (H2O)-O-16, (H2O)-O-17, (H2O)-O-18, and HDO show a complex pattern of emission and absorption components associated with the embedded hot cores, a 14. Nebular Emission Line Ratios in z~2-3 Star-Forming Galaxies with KBSS-MOSFIRE: Exploring the Impact of Ionization, Excitation, and Nitrogen-to-Oxygen Ratio Strom, Allison L; Rudie, Gwen C; Trainor, Ryan F; Pettini, Max; Reddy, Naveen A 2016-01-01 We present a detailed study of the rest-optical (3600-7000 Angstrom) nebular spectra of ~380 star-forming galaxies at z~2-3 obtained with Keck/MOSFIRE as part of the Keck Baryonic Structure Survey (KBSS). The KBSS-MOSFIRE sample is representative of star-forming galaxies at these redshifts, with stellar masses M*=10^9-10^11.5 M_sun and star formation rates SFR=3-1000 M_sun/yr. We focus on robust measurements of many strong diagnostic emission lines for individual galaxies: [O II]3727,3729, [Ne III]3869, H-beta, [O III]4960,5008, [N II]6549,6585, H-alpha, and [S II]6718,6732. Comparisons with observations of typical local galaxies from the Sloan Digital Sky Survey (SDSS) and between subsamples of KBSS-MOSFIRE show that high-redshift galaxies exhibit a number of significant differences in addition to the well-known offset in log([O III]/H-beta) and log([N II]/H-alpha). We argue that the primary difference between H II regions in z~2.3 galaxies and those at z~0 is an enhancement in the degree of nebular excitati... 15. Strange nonchaotic stars Lindner, John F; Kia, Behnam; Hippke, Michael; Learned, John G; Ditto, William L 2015-01-01 The unprecedented light curves of the Kepler space telescope document how the brightness of some stars pulsates at primary and secondary frequencies whose ratios are near the golden mean, the most irrational number. A nonlinear dynamical system driven by an irrational ratio of frequencies generically exhibits a strange but nonchaotic attractor. For Kepler's "golden" stars, we present evidence of the first observation of strange nonchaotic dynamics in nature outside the laboratory. This discovery could aid the classification and detailed modeling of variable stars. 16. Nebular Emission Line Ratios in z ≃ 2–3 Star-forming Galaxies with KBSS-MOSFIRE: Exploring the Impact of Ionization, Excitation, and Nitrogen-to-Oxygen Ratio Strom, Allison L.; Steidel, Charles C.; Rudie, Gwen C.; Trainor, Ryan F.; Pettini, Max; Reddy, Naveen A. 2017-02-01 We present a detailed study of the rest-optical (3600–7000 Å) nebular spectra of ∼380 star-forming galaxies at z≃ 2{--}3, obtained with Keck/Multi-object Spectrometer for Infrared Exploration (MOSFIRE) as part of the Keck Baryonic Structure Survey (KBSS). The KBSS-MOSFIRE sample is representative of star-forming galaxies at these redshifts, with stellar masses {M}* ={10}9{--}{10}11.5 {M}ȯ and star formation rates SFR = 3–1000 {M}ȯ yr‑1. We focus on robust measurements of many strong diagnostic emission lines for individual galaxies: [O ii]λλ3727, 3729, [Ne iii]λ3869, Hβ, [O iii]λ λ 4960, 5008, [N ii]λλ 6549, 6585, Hα, and [S ii]λλ6718, 6732. Comparisons with observations of typical local galaxies from the Sloan Digital Sky Survey and between subsamples of KBSS-MOSFIRE show that high-redshift galaxies exhibit a number of significant differences in addition to the well-known offset in log([O iii]λ 5008/Hβ) and log([N ii]λ 6585/Hα). We argue that the primary difference between H ii regions in z∼ 2.3 galaxies and those at z∼ 0 is an enhancement in the degree of nebular excitation, as measured by [O iii]/Hβ and {{R}}23\\equiv {log}[([O iii]λ λ 4960,5008+[O ii]λ λ 3727,3729)/Hβ]. At the same time, KBSS-MOSFIRE galaxies are ∼10 times more massive than z∼ 0 galaxies with similar ionizing spectra and have higher N/O (likely accompanied by higher O/H) at fixed excitation. These results indicate the presence of harder ionizing radiation fields at fixed N/O and O/H relative to typical z∼ 0 galaxies, consistent with Fe-poor stellar population models that include massive binaries, and highlight a population of massive, high-specific star formation rate galaxies at high redshift with systematically different star formation histories than galaxies of similar stellar mass today. The data presented in this paper were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of 17. The Milky Way Project: Mapping star formation in our home Galaxy, one click at a time Jayasinghe, Tharindu K.; Povich, Matthew S.; Dixon, Don; Velasco, Jose; Milky Way Project Team 2017-01-01 In the recent years, citizen science has helped astronomers comb through large data sets to identify patterns and objects that are not easily found through automated processes. The Milky Way Project (MWP), a popular citizen science initiative, presents internet users with images from the GLIMPSE, MIPSGAL, SMOG and CYGNUS-X surveys of the Galactic plane using the Spitzer Space Telescope. These citizen scientists are directed to make "classification" drawings on the images to identify targeted classes of astronomical objects. We present an updated data reduction pipeline for the MWP. Written from the ground up in Python, this data reduction pipeline allows for the aggregation of classifications made by MWP users into catalogs of infrared (IR) bubbles, IR bow shocks and “yellowballs” (which may be the early precursors of IR bubbles). Coupled with the more accurate bubble classification tool used in the latest iterations of the MWP, this pipeline enables for better accuracy in the shapes and sizes of the bubbles when compared with those listed in the first MWP data release (DR1). We obtain an initial catalog of over 4000 bubbles using 2 million user classifications made between 2012 and 2015. Combined with the classifications from the latest MWP iteration (2016-2017), we will use a database of over 4 million classifications to produce a MWP DR2 bubble catalog. We will also create the first catalog of candidate IR bow shocks identified through citizen science and an updated “yellowball” catalog. This work is supported by the National Science Foundation under grants CAREER-1454334 and AST-1411851. 18. The UK Infrared Telescope M33 monitoring project. IV. Variable red giant stars across the galactic disc Javadi, Atefeh; van Loon, Jacco Th; Khosroshahi, Habib; Golabatooni, Najmeh; Mirtorabi, Mohammad Taghi 2014-01-01 We have conducted a near-infrared monitoring campaign at the UK InfraRed Telescope (UKIRT), of the Local Group spiral galaxy M33 (Triangulum). The main aim was to identify stars in the very final stage of their evolution, and for which the luminosity is more directly related to the birth mass than the more numerous less-evolved giant stars that continue to increase in luminosity. In this fourth paper of the series, we present a search for variable red giant stars in an almost square degree region comprising most of the galaxy's disc, carried out with the WFCAM instrument in the K band. These data, taken during the period 2005--2007, were complemented by J- and H-band images. Photometry was obtained for 403 734 stars in this region; of these, 4643 stars were found to be variable, most of which are Asymptotic Giant Branch (AGB) stars. The variable stars are concentrated towards the centre of M33, more so than low-mass, less-evolved red giants. Our data were matched to optical catalogues of variable stars and ca... 19. The SAURON project - XV. Modes of star formation in early-type galaxies and the evolution of the red sequence Shapiro, Kristen L.; Falcón-Barroso, Jesús; van de Ven, Glenn; de Zeeuw, P. Tim; Sarzi, Marc; Bacon, Roland; Bolatto, Alberto; Cappellari, Michele; Croton, Darren; Davies, Roger L.; Emsellem, Eric; Fakhouri, Onsi; Krajnović, Davor; Kuntschner, Harald; McDermid, Richard M.; Peletier, Reynier F.; van den Bosch, Remco C. E.; van der Wolk, Guido 2010-01-01 We combine SAURON integral field data of a representative sample of local early-type, red sequence galaxies with Spitzer/Infrared Array Camera imaging in order to investigate the presence of trace star formation in these systems. With the Spitzer data, we identify galaxies hosting low-level star for 20. The SAURON project : XV. Modes of star formation in early-type galaxies and the evolution of the red sequence Shapiro, Kristen L.; Falcon-Barroso, Jesus; van de Ven, Glenn; de Zeeuw, P. Tim; Sarzi, Marc; Bacon, Roland; Bolatto, Alberto; Cappellari, Michele; Croton, Darren; Davies, Roger L.; Emsellem, Eric; Fakhouri, Onsi; Krajnovic, Davor; Kuntschner, Harald; McDermid, Richard M.; Peletier, Reynier F.; van den Bosch, Remco C. E.; van der Wolk, Guido 2010-01-01 We combine SAURON integral field data of a representative sample of local early-type, red sequence galaxies with Spitzer/Infrared Array Camera imaging in order to investigate the presence of trace star formation in these systems. With the Spitzer data, we identify galaxies hosting low-level star for 1. The UK Infrared Telescope M33 monitoring project. II. The star formation history in the central square kiloparsec Javadi, Atefeh; Mirtorabi, Mohammad Taghi 2011-01-01 We have conducted a near-infrared monitoring campaign at the UK InfraRed Telescope (UKIRT), of the Local Group spiral galaxy M33 (Triangulum). The main aim was to identify stars in the very final stage of their evolution, and for which the luminosity is more directly related to the birth mass than the more numerous less-evolved giant stars that continue to increase in luminosity. In this second paper of the series, we construct the birth mass function and hence derive the star formation history. The star formation rate has varied between ~0.002 and 0.007 M Ì yr^-1 kpc^-2. We give evidence of two epochs of a star formation rate enhanced by a factor of a few -- one that happened \\geq 6 Gyr ago and produced \\geq 80% of the total mass in stars, and one around 250 Myr ago that lasted ~ 200 Myr and formed \\leq 6% of the mass in stars. We construct radial and azimuthal distributions in the image plane and in the galaxy plane for populations associated with old first-ascent red giant branch (RGB) stars, intermedia... 2. The UK Infrared Telescope M33 monitoring project. I. Variable red giant stars in the central square kiloparsec Javadi, Atefeh; Mirtorabi, Mohammad Taghi 2010-01-01 We have conducted a near-infrared monitoring campaign at the UK InfraRed Telescope (UKIRT), of the Local Group spiral galaxy M33 (Triangulum). The main aim was to identify stars in the very final stage of their evolution, and for which the luminosity is more directly related to the birth mass than the more numerous less-evolved giant stars that continue to increase in luminosity. The most extensive dataset was obtained in the K-band with the UIST instrument for the central 4'x 4' (1 square kpc) - this contains the nuclear star cluster and inner disc. These data, taken during the period 2003-2007, were complemented by J- and H-band images. Photometry was obtained for 18,398 stars in this region; of these, 812 stars were found to be variable, most of which are Asymptotic Giant Branch (AGB) stars. Our data were matched to optical catalogues of variable stars and carbon stars, and to mid-infrared photometry from the Spitzer Space Telescope. In this first of a series of papers, we present the methodology of the va... 3. Temperature profiles from expendable bathythermograph (XBT) casts from the USCGC POLAR STAR in the North Pacific Ocean in support of the Integrated Global Ocean Services System (IGOSS) project from 03 May 1976 to 30 May 1976 (NODC Accession 7601464) National Oceanic and Atmospheric Administration, Department of Commerce — XBT data were collected from the USCGC POLAR STAR in support of the Integrated Global Ocean Services System (IGOSS) project. Data were collected by the US Coast... 4. Dependence of the Sr-to-Ba and Sr-to-Eu Ratio on the Nuclear Equation of State in Metal Poor Halo Stars Famiano, M A; Aoki, W; Suda, T 2016-01-01 A model is proposed in which the light r-process element enrichment in metal-poor stars is explained via enrichment from a truncated r-process, or "tr-process." The truncation of the r-process from a generic core-collapse event followed by a collapse into an accretion-induced black hole is examined in the framework of a galactic chemical evolution model. The constraints on this model imposed by observations of extremely metal-poor stars are explained, and the upper limits in the [Sr/Ba] distributions are found to be related to the nuclear equation of state in a collapse scenario. The scatter in [Sr/Ba] and [Sr/Eu] as a function of metallicity has been found to be consistent with turbulent ejection in core collapse supernovae. Adaptations of this model are evaluated to account for the scatter in isotopic observables. This is done by assuming mixing in ejecta in a supernova event. 5. The ACS LCID project. IX. Imprints of the early universe in the radial variation of the star formation history of dwarf galaxies Hidalgo, Sebastian L.; Monelli, Matteo; Aparicio, Antonio; Gallart, Carme, E-mail: shidalgo@iac.es, E-mail: monelli@iac.es, E-mail: aparicio@iac.es, E-mail: carme@iac.es [Instituto de Astrofísica de Canarias, Vía Láctea s/n, E-38200 La Laguna, Tenerife, Canary Islands (Spain); and others 2013-12-01 Based on Hubble Space Telescope observations from the Local Cosmology from Isolated Dwarfs project, we present the star formation histories, as a function of galactocentric radius, of four isolated Local Group dwarf galaxies: two dSph galaxies, Cetus and Tucana, and two transition galaxies (dTrs), LGS-3 and Phoenix. The oldest stellar populations of the dSphs and dTrs are, within the uncertainties, coeval (∼13 Gyr) at all galactocentric radii. We find that there are no significative differences between the four galaxies in the fundamental properties (such as the normalized star formation rate or age-metallicity relation) of their outer regions (radii greater than four exponential scale lengths); at large radii, these galaxies consist exclusively of old (≳ 10.5 Gyr) metal-poor stars. The duration of star formation in the inner regions varies from galaxy to galaxy, and the extended central star formation in the dTrs produces the dichotomy between dSph and dTr galaxy types. The dTr galaxies show prominent radial stellar population gradients: The centers of these galaxies host young (≲ 1 Gyr) populations, while the age of the last formation event increases smoothly with increasing radius. This contrasts with the two dSph galaxies. Tucana shows a similar, but milder, gradient, but no gradient in age is detected Cetus. For the three galaxies with significant stellar population gradients, the exponential scale length decreases with time. These results are in agreement with outside-in scenarios of dwarf galaxy evolution, in which a quenching of the star formation toward the center occurs as the galaxy runs out of gas in the outskirts. 6. VERY LOW MASS STELLAR AND SUBSTELLAR COMPANIONS TO SOLAR-LIKE STARS FROM MARVELS. I. A LOW-MASS RATIO STELLAR COMPANION TO TYC 4110-01037-1 IN A 79 DAY ORBIT Wisniewski, John P.; Agol, Eric; Barnes, Rory [Astronomy Department, University of Washington, Box 351580, Seattle, WA 98195 (United States); Ge, Jian; De Lee, Nathan; Fleming, Scott W.; Lee, Brian L.; Chang, Liang [Department of Astronomy, University of Florida, 211 Bryant Space Science Center, Gainesville, FL 32611-2055 (United States); Crepp, Justin R. [Department of Astrophysics, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125 (United States); Eastman, Jason; Gaudi, B. Scott [Department of Astronomy, Ohio State University, 140 West 18th Avenue, Columbus, OH 43210 (United States); Esposito, Massimiliano; Gonzalez Hernandez, Jonay I.; Prieto, Carlos Allende [Instituto de Astrofisica de Canarias (IAC), E-38205 La Laguna, Tenerife (Spain); Ghezzi, Luan; Da Costa, Luiz N.; Porto De Mello, G. F. [Laboratorio Interinstitucional de e-Astronomia-LIneA, Rio de Janeiro, RJ 20921-400 (Brazil); Stassun, Keivan G.; Cargile, Phillip [Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235 (United States); Bizyaev, Dmitry, E-mail: jwisnie@u.washington.edu [Apache Point Observatory, P.O. Box 59, Sunspot, NM 88349-0059 (United States); and others 2012-05-15 TYC 4110-01037-1 has a low-mass stellar companion, whose small mass ratio and short orbital period are atypical among binary systems with solar-like (T{sub eff} {approx}< 6000 K) primary stars. Our analysis of TYC 4110-01037-1 reveals it to be a moderately aged ({approx}<5 Gyr) solar-like star having a mass of 1.07 {+-} 0.08 M{sub Sun} and radius of 0.99 {+-} 0.18 R{sub Sun }. We analyze 32 radial velocity (RV) measurements from the SDSS-III MARVELS survey as well as 6 supporting RV measurements from the SARG spectrograph on the 3.6 m Telescopio Nazionale Galileo telescope obtained over a period of {approx}2 years. The best Keplerian orbital fit parameters were found to have a period of 78.994 {+-} 0.012 days, an eccentricity of 0.1095 {+-} 0.0023, and a semi-amplitude of 4199 {+-} 11 m s{sup -1}. We determine the minimum companion mass (if sin i = 1) to be 97.7 {+-} 5.8 M{sub Jup}. The system's companion to host star mass ratio, {>=}0.087 {+-} 0.003, places it at the lowest end of observed values for short period stellar companions to solar-like (T{sub eff} {approx}< 6000 K) stars. One possible way to create such a system would be if a triple-component stellar multiple broke up into a short period, low q binary during the cluster dispersal phase of its lifetime. A candidate tertiary body has been identified in the system via single-epoch, high contrast imagery. If this object is confirmed to be comoving, we estimate it would be a dM4 star. We present these results in the context of our larger-scale effort to constrain the statistics of low-mass stellar and brown dwarf companions to FGK-type stars via the MARVELS survey. 7. Towards a greater understanding of the illicit tobacco trade in Europe: a review of the PMI funded 'Project Star' report. Gilmore, Anna B; Rowell, Andy; Gallus, Silvano; Lugo, Alessandra; Joossens, Luk; Sims, Michelle 2014-05-01 Following a legal agreement with the European Union (EU), Philip Morris International (PMI) commissions a yearly report ('Project Star', PS) on the European illicit cigarette trade from KPMG, the global accountancy firm. Review of PS 2010 report. Comparison with data from independent sources including a 2010 pan-European survey (N=18,056). Within PS, data covering all 27 EU countries are entered into a model. While the model itself seems appropriate, concerns are identified with the methodologies underlying the data inputs and thus their quality: there is little transparency over methodologies; interview data underestimate legal non-domestic product partly by failing to account for legal cross-border sales; illicit cigarette estimates rely on tobacco industry empty pack surveys which may overestimate illicit; and there is an over-reliance on data supplied by PMI with inadequate external validation. Thus, PMI sales data are validated using PMI smoking prevalence estimates, yet PMI is unable to provide sales (shipment) data for the Greek islands and its prevalence estimates differ grossly from independent data. Consequently, comparisons with independent data suggest PS will tend to overestimate illicit cigarette levels particularly where cross-border shopping is frequent (Austria, Finland, France) and in Western compared with Eastern European countries. The model also provides data on the nature of the illicit cigarette market independent of seizure data suggesting that almost a quarter of the illicit cigarette market in 2010 comprised PMI's own brands compared with just 5% counterfeited PMI brands; a finding hidden in PMI's public representation of the data. PS overestimates illicit cigarette levels in some European countries and suggests PMI's supply chain control is inadequate. Its publication serves the interests of PMI over those of the EU and its member states. PS requires greater transparency, external scrutiny and use of independent data. Published by the BMJ 8. The Triglyceride to HDL Ratio and Its Relationship to Insulin Resistance in Pre- and Postpubertal Children: Observation from the Wausau SCHOOL Project Karen Olson 2012-01-01 Full Text Available Insulin resistance (IR is a risk factor for ischemic heart disease and diabetes and raises the triglyceride/high-density lipoprotein (TG/HDL ratio in adults, but is not well defined in children. Purpose. To investigate the TG/HDL ratios in children as an IR marker. Methods. Wausau SCHOOL Project assessed 99 prepubertal and 118 postpubertal children. The TG/HDL ratio was correlated with numerous risk factors. Results. TG/HDL ratio was significantly correlated with QUICKI, HOMA-IR, zBMI, waist-to hip ratio, systolic and diastolic BP, LDL size and LDL number. A group of 32 IR children (HOMA-IR > 1 SD from the mean, i.e., >2.45 had significantly higher TG/HDL (3.11 ± 1.77 compared to non-IR children (1.86 ± 0.75. A TG/HDL ratio of ≥2.0 identified 32 of the 40 children deemed IR by HOMA-IR (>2.45 with a sensitivity of 0.80 and a specificity of 0.66. Children with TG/HDL ratio ≥3 were heavier and had higher BP, glucose, HOMA-IR, LDL number, and lower HDL level, QUICKI, and LDL size, regardless of pubertal status. Conclusion. The TG/HDL ratio is strongly associated with IR in children, and with higher BMI, waist hip ratio, BP, and more athrogenic lipid profile. 9. The SAURON project - XV. Modes of star formation in early-type galaxies and the evolution of the red sequence Shapiro, K L; van de Ven, G; de Zeeuw, P T; Sarzi, M; Bacon, R; Bolatto, A; Cappellari, M; Croton, D; Davies, R L; Emsellem, E; Fakhouri, O; Krajnovic, D; Kuntschner, H; McDermid, R M; Peletier, R F; Bosch, R C E van den; van der Wolk, G 2009-01-01 We combine SAURON integral field data of a representative sample of local early-type, red sequence galaxies with Spitzer/IRAC imaging in order to investigate the presence of trace star formation in these systems. With the Spitzer data, we identify galaxies hosting low-level star formation, as traced by PAH emission, with measured star formation rates that compare well to those estimated from other tracers. This star formation proceeds according to established scaling relations with molecular gas content, in surface density regimes characteristic of disk galaxies and circumnuclear starbursts. We find that star formation in early-type galaxies happens exclusively in fast-rotating systems and occurs in two distinct modes. In the first, star formation is a diffuse process, corresponding to widespread young stellar populations and high molecular gas content. The equal presence of co- and counter-rotating components in these systems strongly implies an external origin for the star-forming gas, and we argue that the... 10. The ACS LCID project. X. the star formation history of IC 1613: Revisiting the over-cooling problem Skillman, Evan D. [Minnesota Institute for Astrophysics, University of Minnesota, Minneapolis, MN 55455 (United States); Hidalgo, Sebastian L.; Monelli, Matteo; Gallart, Carme; Aparicio, Antonio, E-mail: skillman@astro.umn.edu, E-mail: shidalgo@iac.es, E-mail: monelli@iac.es, E-mail: carme@iac.es, E-mail: aparicio@iac.es [Instituto de Astrofísica de Canarias, Vía Láctea s/n, E-38200 La Laguna, Tenerife, Canary Islands (Spain); and others 2014-05-01 We present an analysis of the star formation history (SFH) of a field near the half-light radius in the Local Group dwarf irregular galaxy IC 1613 based on deep Hubble Space Telescope Advanced Camera for Surveys imaging. Our observations reach the oldest main sequence turn-off, allowing a time resolution at the oldest ages of ∼1 Gyr. Our analysis shows that the SFH of the observed field in IC 1613 is consistent with being constant over the entire lifetime of the galaxy. These observations rule out an early dominant episode of star formation in IC 1613. We compare the SFH of IC 1613 with expectations from cosmological models. Since most of the mass is in place at early times for low-mass halos, a naive expectation is that most of the star formation should have taken place at early times. Models in which star formation follows mass accretion result in too many stars formed early and gas mass fractions that are too low today (the 'over-cooling problem'). The depth of the present photometry of IC 1613 shows that, at a resolution of ∼1 Gyr, the star formation rate is consistent with being constant, at even the earliest times, which is difficult to achieve in models where star formation follows mass assembly. 11. The UK Infrared Telescope M 33 monitoring project - V. The star formation history across the galactic disc Javadi, Atefeh; van Loon, Jacco Th.; Khosroshahi, Habib G.; Tabatabaei, Fatemeh; Hamedani Golshan, Roya; Rashidi, Maryam 2017-01-01 We have conducted a near-infrared monitoring campaign at the UK Infrared Telescope of the Local Group spiral galaxy M 33 (Triangulum). On the basis of their variability, we have identified stars in the very final stage of their evolution, and for which the luminosity is more directly related to the birth mass than the more numerous less-evolved giant stars that continue to increase in luminosity. In this fifth paper of the series, we construct the birth mass function and hence derive the star formation history across the galactic disc of M 33. The star formation rate has varied between ˜0.010 ± 0.001 (˜0.012 ± 0.007) and 0.060±0.005 (0.052±0.009) M⊙ yr-1 kpc-2 statistically (systematically) in the central square kiloparsec of M 33, comparable with the values derived previously with another camera. The total star formation rate in M 33 within a galactocentric radius of 14 kpc has varied between ˜0.110 ± 0.005 (˜0.174 ± 0.060) and ˜0.560 ± 0.028 (˜0.503 ± 0.100) M⊙ yr-1 statistically (systematically). We find evidence of two epochs during which the star formation rate was enhanced by a factor of a few - one that started ˜6 Gyr ago and lasted ˜3 Gyr and produced ≥71 per cent of the total mass in stars, and one ˜250 Myr ago that lasted ˜200 Myr and formed ≤13 per cent of the mass in stars. Radial star formation history profiles suggest that the inner disc of M 33 was formed in an inside-out formation scenario. The outskirts of the disc are dominated by the old population, which may be the result of dynamical effects over many Gyr. We find correspondence to spiral structure for all stars, but enhanced only for stars younger than ˜100 Myr; this suggests that the spiral arms are transient features and not a part of a global density wave potential. 12. The ATLAS3D Project - XXX. Star formation histories and stellar population scaling relations of early-type galaxies McDermid, Richard M.; Alatalo, Katherine; Blitz, Leo; Bournaud, Frédéric; Bureau, Martin; Cappellari, Michele; Crocker, Alison F.; Davies, Roger L.; Davis, Timothy A.; de Zeeuw, P. T.; Duc, Pierre-Alain; Emsellem, Eric; Khochfar, Sadegh; Krajnović, Davor; Kuntschner, Harald; Morganti, Raffaella; Naab, Thorsten; Oosterloo, Tom; Sarzi, Marc; Scott, Nicholas; Serra, Paolo; Weijmans, Anne-Marie; Young, Lisa M. 2015-04-01 We present the stellar population content of early-type galaxies from the ATLAS3D survey. Using spectra integrated within apertures covering up to one effective radius, we apply two methods: one based on measuring line-strength indices and applying single stellar population (SSP) models to derive SSP-equivalent values of stellar age, metallicity, and alpha enhancement; and one based on spectral fitting to derive non-parametric star formation histories, mass-weighted average values of age, metallicity, and half-mass formation time-scales. Using homogeneously derived effective radii and dynamically determined galaxy masses, we present the distribution of stellar population parameters on the Mass Plane (MJAM, σe, R^maj_e), showing that at fixed mass, compact early-type galaxies are on average older, more metal-rich, and more alpha-enhanced than their larger counterparts. From non-parametric star formation histories, we find that the duration of star formation is systematically more extended in lower mass objects. Assuming that our sample represents most of the stellar content of today's local Universe, approximately 50 per cent of all stars formed within the first 2 Gyr following the big bang. Most of these stars reside today in the most massive galaxies (>1010.5 M⊙), which themselves formed 90 per cent of their stars by z ˜ 2. The lower mass objects, in contrast, have formed barely half their stars in this time interval. Stellar population properties are independent of environment over two orders of magnitude in local density, varying only with galaxy mass. In the highest density regions of our volume (dominated by the Virgo cluster), galaxies are older, alpha-enhanced, and have shorter star formation histories with respect to lower density regions. 13. The ATLAS3D project - XXII. Low-efficiency star formation in early-type galaxies: hydrodynamic models and observations Martig, Marie; Bournaud, Frederic; Emsellem, Eric; Gabor, Jared M; Alatalo, Katherine; Blitz, Leo; Bois, Maxime; Bureau, Martin; Cappellari, Michele; Davies, Roger L; Davis, Timothy A; Dekel, Avishai; de Zeeuw, P T; Duc, Pierre-Alain; Falcon-Barroso, Jesus; Khochfar, Sadegh; Krajnovic, Davor; Kuntschner, Harald; Morganti, Raffaella; McDermid, Richard M; Naab, Thorsten; Oosterloo, Tom; Sarzi, Marc; Scott, Nicholas; Serra, Paolo; Griffin, Kristen Shapiro; Teyssier, Romain; Weijmans, Anne-Marie; Young, Lisa M 2012-01-01 We study the global efficiency of star formation in high resolution hydrodynamical simulations of gas discs embedded in isolated early-type and spiral galaxies. Despite using a universal local law to form stars in the simulations, we find that the early-type galaxies are offset from the spirals on the large-scale Kennicutt relation, and form stars 2 to 5 times less efficiently. This offset is in agreement with previous results on morphological quenching: gas discs are more stable against star formation when embedded in early-type galaxies due to the lower disc self-gravity and increased shear. As a result, these gas discs do not fragment into dense clumps and do not reach as high densities as in the spiral galaxies. Even if some molecular gas is present, the fraction of very dense gas (above 10^4 cm-3) is significantly reduced, which explains the overall lower star formation efficiency. We also analyse a sample of local early-type and spiral galaxies, measuring their CO and HI surface densities and their star... 14. The IACOB project: III. New observational clues to understand macroturbulent broadening in massive O- and B-type stars Simón-Díaz, S; Castro, N; Herrero, A; Aerts, C; Puls, J; Telting, J; Grassitelli, L 2016-01-01 We aim to provide new empirical clues about macroturbulent spectral line broadening in O- and B-type stars to evaluate its physical origin. We use high-resolution spectra of ~430 stars with spectral types in the range O4-B9 (all luminosity classes). We characterize the line-broadening of adequate diagnostic metal lines using a combined FT and GOF technique. We perform a quantitative spectroscopic analysis of the whole sample using automatic tools coupled with a huge grid of FASTWIND models. We also incorporate quantitative information about line asymmetries to our observational description of the characteristics of the line-profiles, and present a comparison of the shape and type of line-profile variability found in a small sample of O stars and B supergiants with still undefined pulsational properties and B main sequence stars with variable line-profiles. We present a homogeneous and statistically significant overview of the (single snapshot) line-broadening properties of stars in the whole O and B star doma... 15. The ACS LCID project. X. The Star Formation History of IC 1613: Revisiting the Over-Cooling Problem Skillman, Evan D; Weisz, Daniel R; Monelli, Matteo; Gallart, Carme; Aparicio, Antonio; Bernard, Edouard J; Boylan-Kolchin, Michael; Cassisi, Santi; Cole, Andrew A; Dolphin, Andrew E; Ferguson, Henry C; Mayer, Lucio; Navarro, Julio F; Stetson, Peter B; Tolstoy, Eline 2014-01-01 We present an analysis of the star formation history (SFH) of a field near the half light radius in the Local Group dwarf irregular galaxy IC 1613 based on deep Hubble Space Telescope Advanced Camera for Surveys imaging. Our observations reach the oldest main sequence turn-off, allowing a time resolution at the oldest ages of ~1 Gyr. Our analysis shows that the SFH of the observed field in IC 1613 is consistent with being constant over the entire lifetime of the galaxy. These observations rule out an early dominant episode of star formation in IC 1613. We compare the SFH of IC 1613 with expectations from cosmological models. Since most of the mass is in place at early times for low mass halos, a naive expectation is that most of the star formation should have taken place at early times. Models in which star formation follows mass accretion result in too many stars formed early and gas mass fractions which are too low today (the "over-cooling problem"). The depth of the present photometry of IC 1613 shows that... 16. The UK Infrared Telescope M33 monitoring project. V. The star formation history across the galactic disc Javadi, Atefeh; Khosroshahi, Habib; Tabatabaei, Fatemeh; Golshan, Roya Hamedani; Rashidi, Maryam 2016-01-01 We have conducted a near-infrared monitoring campaign at the UK InfraRed Telescope (UKIRT), of the Local Group spiral galaxy M33 (Triangulum). On the basis of their variability, we have identified stars in the very final stage of their evolution, and for which the luminosity is more directly related to the birth mass than the more numerous less-evolved giant stars that continue to increase in luminosity. In this fifth paper of the series, we construct the birth mass function and hence derive the star formation history across the galactic disc of M33. The star formation rate has varied between$\\sim0.010\\pm0.001$($\\sim0.012\\pm0.007$) and 0.060$\\pm0.005$(0.052$\\pm0.009$)M$_\\odot$yr$^{-1}$kpc$^{-2}$statistically (systematically) in the central square kiloparsec of M33, comparable with the values derived previously with another camera. The total star formation rate in M33 within a galactocentric radius of 14 kpc has varied between$\\sim0.110\\pm0.005$($\\sim0.174\\pm0.060$) and$\\sim0.560\\pm0.028$($\\sim0.503\\...
17. Star Clusters within FIRE
Perez, Adrianna; Moreno, Jorge; Naiman, Jill; Ramirez-Ruiz, Enrico; Hopkins, Philip F.
2017-01-01
In this work, we analyze the environments surrounding star clusters of simulated merging galaxies. Our framework employs Feedback In Realistic Environments (FIRE) model (Hopkins et al., 2014). The FIRE project is a high resolution cosmological simulation that resolves star forming regions and incorporates stellar feedback in a physically realistic way. The project focuses on analyzing the properties of the star clusters formed in merging galaxies. The locations of these star clusters are identified with astrodendro.py, a publicly available dendrogram algorithm. Once star cluster properties are extracted, they will be used to create a sub-grid (smaller than the resolution scale of FIRE) of gas confinement in these clusters. Then, we can examine how the star clusters interact with these available gas reservoirs (either by accreting this mass or blowing it out via feedback), which will determine many properties of the cluster (star formation history, compact object accretion, etc). These simulations will further our understanding of star formation within stellar clusters during galaxy evolution. In the future, we aim to enhance sub-grid prescriptions for feedback specific to processes within star clusters; such as, interaction with stellar winds and gas accretion onto black holes and neutron stars.
18. The ACS LCID Project: RR Lyrae stars as tracers of old population gradients in the isolated dwarf spheroidal galaxy Tucana
Bernard, Edouard J; Monelli, Matteo; Aparicio, Antonio; Cassisi, Santi; Skillman, Evan D; Stetson, Peter B; Cole, Andrew A; Drozdovsky, Igor; Hidalgo, Sebastian L; Mateo, Mario; Tolstoy, Eline
2008-01-01
We present a study of the radial distribution of RR Lyrae variables, which present a range of photometric and pulsational properties, in the dwarf spheroidal galaxy Tucana. We find that the fainter RR Lyrae stars, having a shorter period, are more centrally concentrated than the more luminous, longer period RR Lyrae variables. Through comparison with the predictions of theoretical models of stellar evolution and stellar pulsation, we interpret the fainter RR Lyrae stars as a more metal-rich subsample. In addition, we show that they must be older than about 10 Gyr. Therefore, the metallicity gradient must have appeared very early on in the history of this galaxy.
19. The circumstellar shell of the post-AGB star HD 56126 the $^{12}C ^{12}C \\/ ^{12}C ^{13}C$isotope ratio and $^{12}C ^{16}O$ column density
Bakker, E J; Lambert, Eric J. Bakker & David L.
1998-01-01
We have made the first detection of circumstellar absorption lines of the 12C13C (Phillips) system 1-0 band and the 12C16O first-overtone 2-0 band in the spectrum of the post-AGB star HD56126 (IRAS07134+1005). The rotational temperatures are lower for molecules with a higher permanent dipole moment. Derived relative column densities ratios are 12C12C/12C13C=36+-13, 12C16O/(12C12C+12C13C)=606+-230, and 12C16O/(12C14N+13C14N)=475+-175. The isotopic exchange reaction for 12C12C is too slow to significantly alter the 12C12C/12C13C ratio and the 12C12C to 12C13C ratio a good measure of half the carbon isotope ratio: 12C/13C=2 X 12C12C/12C13C=72+-26. A fit of the 12C12C excitation model of van Dishoeck & Black (1982) to the relative population distribution of 12C12C yields n sigma / I = 3.3 +- 1.0 X 1e-14. At r=1e16cm this translates in n=1.7e7cm-3 and dM/dt=2.5e-4Msol/year.
20. The IACOB project. IV. New predictions for high-degree non-radial mode instability domains in massive stars and their connection with macroturbulent broadening
Godart, M.; Simón-Díaz, S.; Herrero, A.; Dupret, M. A.; Grötsch-Noels, A.; Salmon, S. J. A. J.; Ventura, P.
2017-01-01
Context. Asteroseismology is a powerful tool to access the internal structure of stars. Apart from the important impact of theoretical developments, progress in this field has been commonly associated with the analysis of time-resolved observations. Recently, the so-called macroturbulent broadening has been proposed as a complementary and less expensive way - in terms of observational time - to investigate pulsations in massive stars. Aims: We assess to what extent this ubiquitous non-rotational broadening component which shapes the line profiles of O stars and B supergiants is a spectroscopic signature of pulsation modes driven by a heat mechanism. Methods: We compute stellar main-sequence and post-main-sequence models from 3 to 70 M⊙ with the ATON stellar evolution code, and determine the instability domains for heat-driven modes for degrees ℓ = 1-20 using the adiabatic and non-adiabatic codes LOSC and MAD. We use the observational material compiled in the framework of the IACOB project to investigate possible correlations between the single snapshot line-broadening properties of a sample of ≈260 O and B-type stars and their location inside or outside the various predicted instability domains. Results: We present an homogeneous prediction for the non-radial instability domains of massive stars for degree ℓ up to 20. We provide a global picture of what to expect from an observational point of view in terms of the frequency range of excited modes, and we investigate the behavior of the instabilities with respect to stellar evolution and the degree of the mode. Furthermore, our pulsational stability analysis, once compared to the empirical results, indicates that stellar oscillations originated by a heat mechanism cannot explain alone the occurrence of the large non-rotational line-broadening component commonly detected in the O star and B supergiant domain. Based on observations made with the Nordic Optical Telescope, operated by NOTSA, and the Mercator
1. Gas and dust in the star-forming region rho Oph A: The dust opacity exponent beta and the gas-to-dust mass ratio g2d
Liseau, R; Lunttila, T; Olberg, M; Rydbeck, G; Bergman, P; Justtanont, K; Olofsson, G; de Vries, B L
2015-01-01
We aim at determining the spatial distribution of the gas and dust in star-forming regions and address their relative abundances in quantitative terms. We also examine the dust opacity exponent beta for spatial and/or temporal variations. Using mapping observations of the very dense rho Oph A core, we examined standard 1D and non-standard 3D methods to analyse data of far-infrared and submillimeter (submm) continuum radiation. The resulting dust surface density distribution can be compared to that of the gas. The latter was derived from the analysis of accompanying molecular line emission, observed with Herschel from space and with APEX from the ground. As a gas tracer we used N2H+, which is believed to be much less sensitive to freeze-out than CO and its isotopologues. Radiative transfer modelling of the N2H+(J=3-2) and (J=6-5) lines with their hyperfine structure explicitly taken into account provides solutions for the spatial distribution of the column density N(H2), hence the surface density distribution ...
2. The ACS LCID project : RR Lyrae stars as tracers of old population gradients in the isolated dwarf spheroidal galaxy tucana
Bernard, Edouard J.; Gallart, Carme; Monelli, Matteo; Aparicio, Antonio; Cassisi, Santi; Skillman, Evan D.; Stetson, Peter B.; Cole, Andrew A.; Drozdovsky, Igor; Hidalgo, Sebastian L.; Mateo, Mario; Tolstoy, Eline
2008-01-01
We present a study of the radial distribution of RR Lyrae variables, which present a range of photometric and pulsational properties, in the dwarf spheroidal galaxy Tucana. We find that the fainter RR Lyrae stars, having a shorter period, are more centrally concentrated than the more luminous, longe
3. The ATLAS3D Project - XXVIII. Dynamically-driven star formation suppression in early-type galaxies
Davis, Timothy A; Crocker, Alison F; Bureau, Martin; Blitz, Leo; Alatalo, Katherine; Emsellem, Eric; Naab, Thorsten; Bayet, Estelle; Bois, Maxime; Bournaud, Frederic; Cappellari, Michele; Davies, Roger L; de Zeeuw, P T; Duc, Pierre-Alain; Khochfar, Sadegh; Krajnovic, Davor; Kuntschner, Harald; McDermid, Richard M; Morganti, Raffaella; Oosterloo, Tom; Sarzi, Marc; Scott, Nicholas; Serra, Paolo; Weijmans, Anne-Marie
2014-01-01
We present measurements of the star formation rate (SFR) in the early-type galaxies (ETGs) of the ATLAS3D sample, based on Wide-field Infrared Survey Explorer (WISE) 22um and Galaxy Evolution Explorer (GALEX) far-ultraviolet emission. We combine these with gas masses estimated from 12CO and HI data in order to investigate the star formation efficiency (SFE) in a larger sample of ETGs than previously available. We first recalibrate (based on WISE data) the relation between old stellar populations (traced at Ks-band) and 22um luminosity, allowing us to remove the contribution of 22um emission from circumstellar dust. We then go on to investigate the position of ETGs on the Kennicutt-Schmidt (KS) relation. Molecular gas-rich ETGs have comparable star formation surface densities to normal spiral galaxy centres, but they lie systematically offset from the KS relation, having lower star formation efficiencies by a factor of ~2.5 (in agreement with other authors). This effect is driven by galaxies where a substantia...
4. The ACS LCID Project. X. The Star Formation History of IC 1613: Revisiting the Over-cooling Problem
Skillman, Evan D.; Hidalgo, Sebastian L.; Weisz, Daniel R.; Monelli, Matteo; Gallart, Carme; Aparicio, Antonio; Bernard, Edouard J.; Boylan-Kolchin, Michael; Cassisi, Santi; Cole, Andrew A.; Dolphin, Andrew E.; Ferguson, Henry C.; Mayer, Lucio; Navarro, Julio F.; Stetson, Peter B.; Tolstoy, Eline
We present an analysis of the star formation history (SFH) of a field near the half-light radius in the Local Group dwarf irregular galaxy IC 1613 based on deep Hubble Space Telescope Advanced Camera for Surveys imaging. Our observations reach the oldest main sequence turn-off, allowing a time
5. The ACS LCID Project. X. The Star Formation History of IC 1613: Revisiting the Over-cooling Problem
Skillman, Evan D.; Hidalgo, Sebastian L.; Weisz, Daniel R.; Monelli, Matteo; Gallart, Carme; Aparicio, Antonio; Bernard, Edouard J.; Boylan-Kolchin, Michael; Cassisi, Santi; Cole, Andrew A.; Dolphin, Andrew E.; Ferguson, Henry C.; Mayer, Lucio; Navarro, Julio F.; Stetson, Peter B.; Tolstoy, Eline
2014-01-01
We present an analysis of the star formation history (SFH) of a field near the half-light radius in the Local Group dwarf irregular galaxy IC 1613 based on deep Hubble Space Telescope Advanced Camera for Surveys imaging. Our observations reach the oldest main sequence turn-off, allowing a time resol
6. The ACS LCID project : RR Lyrae stars as tracers of old population gradients in the isolated dwarf spheroidal galaxy tucana
Bernard, Edouard J.; Gallart, Carme; Monelli, Matteo; Aparicio, Antonio; Cassisi, Santi; Skillman, Evan D.; Stetson, Peter B.; Cole, Andrew A.; Drozdovsky, Igor; Hidalgo, Sebastian L.; Mateo, Mario; Tolstoy, Eline
2008-01-01
We present a study of the radial distribution of RR Lyrae variables, which present a range of photometric and pulsational properties, in the dwarf spheroidal galaxy Tucana. We find that the fainter RR Lyrae stars, having a shorter period, are more centrally concentrated than the more luminous,
7. Hubble Tarantula Treasury Project. III. Photometric Catalog and Resulting Constraints on the Progression of Star Formation in the 30 Doradus Region
Sabbi, E.; Lennon, D. J.; Anderson, J.; Cignoni, M.; van der Marel, R. P.; Zaritsky, D.; De Marchi, G.; Panagia, N.; Gouliermis, D. A.; Grebel, E. K.; Gallagher, J. S., III; Smith, L. J.; Sana, H.; Aloisi, A.; Tosi, M.; Evans, C. J.; Arab, H.; Boyer, M.; de Mink, S. E.; Gordon, K.; Koekemoer, A. M.; Larsen, S. S.; Ryon, J. E.; Zeidler, P.
2016-01-01
We present and describe the astro-photometric catalog of more than 800,000 sources found in the Hubble Tarantula Treasury Project (HTTP). HTTP is a Hubble Space Telescope Treasury program designed to image the entire 30 Doradus region down to the sub-solar (˜0.5 M⊙) mass regime using the Wide Field Camera 3 and the Advanced Camera for Surveys. We observed 30 Doradus in the near-ultraviolet (F275W, F336W), optical (F555W, F658N, F775W), and near-infrared (F110W, F160W) wavelengths. The stellar photometry was measured using point-spread function fitting across all bands simultaneously. The relative astrometric accuracy of the catalog is 0.4 mas. The astro-photometric catalog, results from artificial star experiments, and the mosaics for all the filters are available for download. Color-magnitude diagrams are presented showing the spatial distributions and ages of stars within 30 Dor as well as in the surrounding fields. HTTP provides the first rich and statistically significant sample of intermediate- and low-mass pre-main sequence candidates and allows us to trace how star formation has been developing through the region. The depth and high spatial resolution of our analysis highlight the dual role of stellar feedback in quenching and triggering star formation on the giant H ii region scale. Our results are consistent with stellar sub-clustering in a partially filled gaseous nebula that is offset toward our side of the Large Magellanic Cloud. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA Inc., under NASA contract NAS 5-26555.
8. HUBBLE TARANTULA TREASURY PROJECT. III. PHOTOMETRIC CATALOG AND RESULTING CONSTRAINTS ON THE PROGRESSION OF STAR FORMATION IN THE 30 DORADUS REGION
Sabbi, E.; Anderson, J.; Cignoni, M.; Marel, R. P. van der; Panagia, N.; Sana, H.; Aloisi, A.; Arab, H.; Gordon, K. [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD, 21218 (United States); Lennon, D. J. [ESA—European Space Astronomy Center, Apdo. de Correo 78, E-28691 Associate Villanueva de la Cañada, Madrid (Spain); Zaritsky, D. [Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721 (United States); Marchi, G. De [Space Science Department, European Space Agency, Keplerlaan 1, 2200 AG Noordwijk (Netherlands); Gouliermis, D. A. [Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, D-69120 Heidelberg (Germany); Grebel, E. K. [Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchhofstr. 12-14, D-69120 Heidelberg (Germany); III, J. S. Gallagher [Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706 (United States); Smith, L. J. [ESA/STScI, 3700 San Martin Drive, Baltimore, MD, 21218 (United States); Tosi, M. [Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Bologna, Via Ranzani 1, I-40127 Bologna (Italy); Evans, C. J. [UK Astronomy Technology Center, Royal Observatory Edinburgh, Blackford Hill, Edinburgh, EH9 3HJ (United Kingdom); Boyer, M. [Observational Cosmology Lab, Code 665, NASA, Goddard Space Flight Center, Greenbelt, MD, 20771 (United States); Mink, S. E. de, E-mail: sabbi@stsci.edu [Astronomical Institute “Anton Pannekoek,”University of Amsterdam, P.O. Box 94249, NL-1090 GE Amsterdam (Netherlands); and others
2016-01-15
We present and describe the astro-photometric catalog of more than 800,000 sources found in the Hubble Tarantula Treasury Project (HTTP). HTTP is a Hubble Space Telescope Treasury program designed to image the entire 30 Doradus region down to the sub-solar (∼0.5 M{sub ⊙}) mass regime using the Wide Field Camera 3 and the Advanced Camera for Surveys. We observed 30 Doradus in the near-ultraviolet (F275W, F336W), optical (F555W, F658N, F775W), and near-infrared (F110W, F160W) wavelengths. The stellar photometry was measured using point-spread function fitting across all bands simultaneously. The relative astrometric accuracy of the catalog is 0.4 mas. The astro-photometric catalog, results from artificial star experiments, and the mosaics for all the filters are available for download. Color–magnitude diagrams are presented showing the spatial distributions and ages of stars within 30 Dor as well as in the surrounding fields. HTTP provides the first rich and statistically significant sample of intermediate- and low-mass pre-main sequence candidates and allows us to trace how star formation has been developing through the region. The depth and high spatial resolution of our analysis highlight the dual role of stellar feedback in quenching and triggering star formation on the giant H ii region scale. Our results are consistent with stellar sub-clustering in a partially filled gaseous nebula that is offset toward our side of the Large Magellanic Cloud.
9. First multi-color photometric study and preliminary elements for the low-mass ratio, possible progenitors of merging stars, W UMa systems TYC 3836-0854-1 and TYC 4157-0683-1
Acerbi, F.; Barani, C.; Martignoni, M.
2014-08-01
Here we present the first CCD multi-color B, V and Ic light curves of the eclipsing binary stars TYC 3836-0854-1 and TYC 4157-0683-1, the data were obtained in four nights in the year 2010 and three nights in the year 2012 for the first one and in four nights in the year 2010 for the second one. Based on our data the short orbital periods of the systems are confirmed and revised to P = 0.4155590 days for TYC 3836-0854-1 and P = 0.3960676 days for TYC 4157-0683-1. Our observations of TYC 3836-0854-1 show symmetric light curves in all passbands with brightness in both maxima at the same level, while the light curve of TYC 4157-0683-1 appear to exhibit the typical O’Connell effect, with Maximum I brighter than Maximum II. By analyzing simultaneously the complete light curves with the 2003 version of the Wilson-Devinney code (2005 revision), photometric solutions were determined. Both the systems shows a small difference between the components temperatures of ΔT = 14 K for TYC 3836-0854-1 and ΔT = 149 K for TYC 4157-0683-1. The orbital inclination is i = 78°.6 and i = 79°.7 respectively. The systems are found to be a high fill-out, extreme mass ratio overcontact binary with a mass ratio of q = 0.206 and a fill-out factor of f = 59.2% for TYC 3836-0854-1 and q = 0.150 and a fill-out factor of f = 76.3% for TYC 4157-0683-1, suggesting that both the systems are in the late stage of overcontact evolution. It is known that deep (f>50%), low-mass ratio (q<0.25) overcontact binary stars (DLMR) are a very important resource for understanding the phenomena of Blue Straggler/FK Com-type stars that is an unsolved problem in stellar astrophysics. One of the possible explanations for their formation is from the coalescence of W UMa-type overcontact binary systems. The absolute dimensions of both the systems are estimated from the logTeff - logL diagram and their dynamical evolution is inferred.
10. Strange Nonchaotic Stars
Lindner, John F.; Kohar, Vivek; Kia, Behnam; Hippke, Michael; Learned, John G.; Ditto, William L.
2015-08-01
Exploiting the unprecedented capabilities of the planet-hunting Kepler space telescope, which stared at 150 000 stars for four years, we discuss recent evidence that certain stars dim and brighten in complex patterns with fractal features. Such stars pulsate at primary and secondary frequencies whose ratios are near the famous golden mean, the most irrational number. A nonlinear system driven by an irrational ratio of frequencies is generically attracted toward a “strange” behavior that is geometrically fractal without displaying the “butterfly effect” of chaos. Strange nonchaotic attractors have been observed in laboratory experiments and have been hypothesized to describe the electrochemical activity of the brain, but a bluish white star 16 000 light years from Earth in the constellation Lyra may manifest, in the scale-free distribution of its minor frequency components, the first strange nonchaotic attractor observed in the wild. The recognition of stellar strange nonchaotic dynamics may improve the classification of these stars and refine the physical modeling of their interiors. We also discuss nonlinear analysis of other RR Lyrae stars in Kepler field of view and discuss some toy models for modeling these stars.References: 1) Hippke, Michael, et al. "Pulsation period variations in the RRc Lyrae star KIC 5520878." The Astrophysical Journal 798.1 (2015): 42.2) Lindner, John F., et al. "Strange nonchaotic stars." Phys. Rev. Lett. 114, 054101 (2015)
11. The Atlas3D project - XX. Mass-size and Mass-sigma projections of the Virial Plane of early-type galaxies: variation of morphology, kinematics, mass-to-light ratio and stellar initial mass function
Cappellari, Michele; Alatalo, Katherine; Blitz, Leo; Bois, Maxime; Bournaud, Frederic; Bureau, M; Crocker, Alison F; Davies, Roger L; Davis, Timothy A; de Zeeuw, P T; Duc, Pierre-Alain; Khochfar, Sadegh; Krajnovic, Davor; Kuntschner, Harald; Morganti, Raffaella; Naab, Thorsten; Oosterloo, Tom; Sarzi, Marc; Scott, Nicholas; Serra, Paolo; Weijmans, Anne-Marie; Young, Lisa M
2013-01-01
In the companion Paper XIX we derive accurate total (M/L)_JAM within a sphere of radius r=Re, as well as stellar (M/L)_stars for the volume-limited Atlas3D sample of 260 early-type galaxies. Here we study the two projections (M_JAM,sigma_e) and (M_JAM,R_e^max) of the thin Virial Plane (VP)(M_JAM,sigma_e,R_e^max) which describes the distribution of the galaxy population. The distribution of galaxy properties on both projections of the VP is characterized by (i) a boundary in the galaxy distribution, described by two power-laws, joined by a break at a characteristic mass M_JAM ~ 3*10^10 Msun, which corresponds to the minimum Re and maximum stellar density, and (ii) a characteristic mass M_JAM ~ 2*10^11 Msun which separates a population dominated by fast rotator with disks at lower masses, from one dominated by quite round slow rotators at larger masses. The distribution of ETGs properties on the two projections of the VP tends to be constant along lines of constant sigma_e, and forms a continuous and parallel s...
12. Visible and ultraviolet-B ocular-ambient exposure ratios for a general population. Salisbury Eye Evaluation Project Team.
Duncan, D D; Muñoz, B; Bandeen-Roche, K; West, S K
1997-04-01
To estimate the numerical value of the ocular-ambient exposure ratio (OAER) (ratio of the facial exposure to that on a horizontal plane) as a function of wavelength band, season, and job category and to establish the effect of various modifiers, such as geography and the use of hats, for use in general population studies. Two hundred sixty-four persons within several job categories representing the jobs in our Salisbury, Maryland, population were instrumented with ultraviolet-B (UVB) and visible band sensors for 1 complete day. Studies were done over all four seasons, both with and without hats. OAERs in the UVB wavelength band generally are higher than in the visible (13% versus 6%), display no significant variation with job category, show a seasonal effect (highest in the winter-spring [18%], lowest in the summer [10%], and intermediate in the fall [14%]), and are reduced 34% by the use of hats. In the visible wavelength band, OAERs are affected weakly by job function, although this variation is not significant, display a seasonal effect with three seasons as in the UVB, and are not affected significantly by the use of hats. In neither the UVB nor the visible portions of the spectrum did the authors find an effect on the OAER due to photophobia or eye color. With the authors' exposure model, the authors have at their disposal a valuable tool for exploring the relation between UVB, UVA, and visible radiation and a number of age-related eye diseases.
13. The Atlas3D Project - XXX. Star formation histories and stellar population scaling relations of early-type galaxies
McDermid, Richard M; Blitz, Leo; Bournaud, Frederic; Bureau, Martin; Cappellari, Michele; Crocker, Alison F; Davies, Roger L; Davis, Timothy A; de Zeeuw, P T; Duc, Pierre-Alain; Emsellem, Eric; Khochfar, Sadegh; Krajnovic, Davor; Kuntschner, Harald; Morganti, Raffaella; Naab, Thorsten; Oosterloo, Tom; Sarzi, Marc; Scott, Nicholas; Serra, Paolo; Weijmans, Anne-Marie; Young, Lisa M
2015-01-01
We present the stellar population content of early-type galaxies from the Atlas3D survey. Using spectra integrated within apertures covering up to one effective radius, we apply two methods: one based on measuring line-strength indices and applying single stellar population (SSP) models to derive SSP-equivalent values of stellar age, metallicity, and alpha enhancement; and one based on spectral fitting to derive non-parametric star-formation histories, mass-weighted average values of age, metallicity, and half-mass formation timescales. Using homogeneously derived effective radii and dynamically-determined galaxy masses, we present the distribution of stellar population parameters on the Mass Plane (M_JAM, Sigma_e, R_maj), showing that at fixed mass, compact early-type galaxies are on average older, more metal-rich, and more alpha-enhanced than their larger counterparts. From non-parametric star-formation histories, we find that the duration of star formation is systematically more extended in lower mass obje...
14. Pinellas County, Florida, Site Environmental Restoration Project Sitewide Environmental Monitoring Semiannual Progress Report for the Young - Rainey STAR Center June Through November 2016, January 2017
Surovchak, Scott [USDOE Office of Legacy Management, Washington, DC (United States); Daniel, Joe [Navarro Research and Engineering, Inc., Oak Ridge, TN (United States)
2017-01-01
The Young - Rainey STAR Center (Science, Technology, and Research Center) at the Pinellas County, Florida, Site is a former U.S. Department of Energy (DOE) facility constructed in the mid-1950s. The 96-acre STAR Center is located in Largo, Florida, and lies in the northeast quarter of Section 13, Township 30 South, Range 15 East (Figure 1). While it was owned by DOE, the purpose of the site was to develop and manufacture components for the nation’s nuclear weapons program. In 1987, the U.S. Environmental Protection Agency (EPA) performed a Resource Conservation and Recovery Act Facility Assessment (EPA 1988) at the site to gather information on potential releases of hazardous materials. In February of 1990, EPA issued a Hazardous and Solid Waste Amendments permit to DOE, requiring DOE to investigate and perform remediation activities in those areas designated as solid-waste management units (SWMUs) contaminated by hazardous materials resulting from DOE operations. A total of 17 SWMUs were identified and investigated at the STAR Center. By 1997, 13 of the 17 SWMUs had been remediated or approved for no further action. More recently, the Florida Department of Environmental Protection (FDEP) executed Conditional Site Rehabilitation Completion Orders for the Northeast Site and the Wastewater Neutralization Area on July 27, 2016, stating that no further action is required for those SWMUs. The Building 100 Area (a combination of the Old Drum Storage Site and the Building 100-Industrial Drain Leaks SWMUs) comprises the only two active SWMUs at the STAR Center (Figure 2). This document serves as the semiannual progress report for the SWMUs by providing the results of recent monitoring activities and a summary of ongoing and projected work. The STAR Center is owned by the Pinellas County Industrial Development Authority, but DOE is responsible for remediation activities at the site. Additional background information for the site is contained in the Long-Term Surveillance
15. The First Billion Years project: constraining the dust attenuation law of star-forming galaxies at z ≃ 5
Cullen, F.; McLure, R. J.; Khochfar, S.; Dunlop, J. S.; Dalla Vecchia, C.
2017-09-01
We present the results of a study investigating the dust attenuation law at z ≃ 5, based on synthetic spectral energy distributions (SEDs) calculated for a sample of N = 498 galaxies drawn from the First Billion Years (FiBY) simulation project. The simulated galaxies at z ≃ 5, which have M1500 ≤ -18.0 and 7.5 ≤ log(M/M}_{⊙}) ≤ 10.2, display a mass-dependent α-enhancement, with a median value of [α /{Fe}]_{z=5} ˜eq 4 × [α /{Fe}]_{Z_{⊙}}. The median Fe/H ratio of the simulated galaxies is 0.14 ± 0.05 which produces steep intrinsic ultraviolet (UV) continuum slopes; 〈βi〉 = -2.4 ± 0.05. Using a set of simple dust attenuation models, in which the wavelength-dependent attenuation is assumed to be of the form A(λ) ∝ λn, we explore the parameter values which best reproduce the observed z = 5 luminosity function (LF) and colour-magnitude relation (CMR). We find that a simple model in which the absolute UV attenuation is a linearly increasing function of log stellar mass (A1500 = 0.5 × log(M/M⊙) - 3.3), and the dust attenuation slope (n) is within the range -0.7 ≤ n ≤ -0.3, can successfully reproduce the LF and CMR over a wide range of stellar population synthesis model assumptions, including the effects of massive binaries. This range of attenuation curves is consistent with a power-law fit to the Calzetti attenuation law in the UV (n = -0.55). In contrast, curves as steep as the Small Magellanic Cloud extinction curve (n = -1.24) are formally ruled out. Finally, we show that our models are consistent with recent 1.3 mm Atacama Large Millimeter Array observations of the Hubble Ultra Deep Field, and predict the form of the z ≃ 5 infrared excess (IRX)-β relation.
16. Strong Nebular Line Ratios in the Spectra of z~2-3 Star-forming Galaxies: First Results from KBSS-MOSFIRE
Steidel, C C; Strom, A L; Pettini, M; Reddy, N A; Shapley, A E; Trainor, R F; Erb, D K; Turner, M L; Konidaris, N P; Kulas, K R; Mace, G; Matthews, K; McLean, I S
2014-01-01
We present initial results of a large near-IR spectroscopic survey covering the 15 fields of the Keck Baryonic Structure Survey (KBSS) using the recently-commissioned MOSFIRE instrument on the Keck 1 10m telescope. We focus on 179 galaxies with redshifts 2.0 < z < 2.6, most of which have high-quality MOSFIRE spectra in both H and K-band atmospheric windows, allowing sensitive measurements of [OIII]4960,5008, H-beta, [NII]6585, and H-alpha emission lines. We show unambiguously that the locus of z~2.3 galaxies in the "BPT" nebular diagnostic diagram exhibits an almost entirely disjoint, yet similarly tight, relationship between the line ratios [NII]/Halpha and [OIII]/Hbeta as compared to local galaxies. We argue that the offset of the z~2.3 BPT locus relative to that at z~0 is caused primarily by higher excitation (driven by both higher ionization parameter and harder stellar ionizing radiation field) than applies to most local galaxies. Also unlike nearby counterparts, a z~2.3 galaxy's position along the...
17. Hubble Tarantula Treasury Project. III. Photometric Catalog and Resulting Constraints on the Progression of Star Formation in the 30 Doradus Region
Sabbi, E; Anderson, J; Cignoni, M; van der Marel, R P; Zaritsky, D; de Marchi, G; Panagia, N; Gouliermis, D A; Grebel, E K; Gallager, J S; Smith, L J; Sana, H; Aloisi, A; Tosi, M; Evans, C J; Arab, H; Boyer, M; de Mink, S E; Gordon, K; Koekemoer, A M; Larsen, S S; Ryon, J E; Zeidler, P
2015-01-01
We present and describe the astro-photometric catalog of more than 800,000 sources found in the Hubble Tarantula Treasury Project (HTTP). HTTP is a Hubble Space Telescope (HST) Treasury program designed to image the entire 30 Doradus region down to the sub-solar (~0.5 solar masses) mass regime using the Wide Field Camera 3 (WFC3) and the Advanced Camera for Surveys (ACS). We observed 30 Doradus in the near ultraviolet (F275W, F336W), optical (F555W, F658N, F775W), and near infrared (F110W, F160W) wavelengths. The stellar photometry was measured using point-spread function (PSF) fitting across all the bands simultaneously. The relative astrometric accuracy of the catalog is 0.4 mas. The astro-photometric catalog, results from artificial star experiments and the mosaics for all the filters are available for download. Color-magnitude diagrams are presented showing the spatial distributions and ages of stars within 30 Dor as well as in the surrounding fields. HTTP provides the first rich and statistically signifi...
18. New galactic star clusters discovered in the VVV survey. Candidates projected on the inner disk and bulge
Borissova, J; Alegría, S Ramírez; Sharma, Saurabh; Clarke, J R A; Kurtev, R; Negueruela, I; Marco, A; Amigo, P; Minniti, D; Bica, E; Bonatto, C; Catelan, M; Fierro, C; Geisler, D; Gromadzki, M; Hempel, M; Hanson, M M; Ivanov, V D; Lucas, P; Majaess, D; Bidin, C Moni; Popescu, B; Saito, R K
2014-01-01
VISTA Variables in the V\\'ia L\\'actea (VVV) is one of six ESO Public Surveys using the 4 meter Visible and Infrared Survey Telescope for Astronomy (VISTA). The VVV survey covers the Milky Way bulge and an adjacent section of the disk, and one of the principal objectives is to search for new star clusters within previously unreachable obscured parts of the Galaxy. The primary motivation behind this work is to discover and analyze obscured star clusters in the direction of the inner Galactic disk and bulge. Regions of the inner disk and bulge covered by the VVV survey were visually inspected using composite JHKs color images to select new cluster candidates on the basis of apparent overdensities. DR1, DR2, CASU, and PSF photometry of 10x10 arcmin fields centered on each candidate cluster were used to construct color-magnitude and color-color diagrams. Follow-up spectroscopy of the brightest members of several cluster candidates was obtained in order to clarify their nature. We report the discovery of 58 new inf...
19. Early-type stars observed in the ESO UVES Paranal Observatory Project - V. Time-variable interstellar absorption
McEvoy, Catherine M; Dufton, Philip L; Smith, Keith T; Kennedy, Michael B; Keenan, Francis P; Lambert, David L; Welty, Daniel E; Lauroesch, James T
2015-01-01
The structure and properties of the diffuse interstellar medium (ISM) on small scales, sub-au to 1 pc, are poorly understood. We compare interstellar absorption-lines, observed towards a selection of O- and B-type stars at two or more epochs, to search for variations over time caused by the transverse motion of each star combined with changes in the structure in the foreground ISM. Two sets of data were used: 83 VLT- UVES spectra with approximately 6 yr between epochs and 21 McDonald observatory 2.7m telescope echelle spectra with 6 - 20 yr between epochs, over a range of scales from 0 - 360 au. The interstellar absorption-lines observed at the two epochs were subtracted and searched for any residuals due to changes in the foreground ISM. Of the 104 sightlines investigated with typically five or more components in Na I D, possible temporal variation was identified in five UVES spectra (six components), in Ca II, Ca I and/or Na I absorption-lines. The variations detected range from 7\\% to a factor of 3.6 in co...
20. Housing Star Schools Reforms.
Tushnet, Naida C.
The Star Schools Program has funded projects to explore innovative educational applications of technology in distance education. Funded projects have applied a variety of technologies, including videodisks, compressed data transmission, fiber optic technology, and computer networks. Program evaluation is a mandated aspect of the program. This…
1. STAR METRICS Project in U.S. and Its Enlightment to S＆T Evaluation in China%美国STAR METRICS项目及其对我国科技评价的启示
杨国梁; 肖小溪; 李晓轩
2011-01-01
联邦政府投资于科学，其产生的益处或者价值是什么？这是一个社会各界普遍关注的问题。2008年全球金融危机爆发之后，奥巴马政府出台了总额为7870亿美元的一揽子刺激经济复苏方案，其中76亿美元被直接用于科学研究。为了向公众展示科学研究资金如何对美国经济社会产生影响，美国政府提出了STARMETRICS项目，旨在通过联邦政府和研究机构之间的合作，创建跨部门共享的数据库以及数据展示工具，从而对联邦R＆D投入的影响进行评价。对STARMETRICS项目的情况进行了深入地调研和分析，并在此基础上提出对我国科技评价的若干思考。%What are the benefits of federal scientific funding has become the focus of public concern. The global fi- nancial crisis in 2008 put U.S. and a number of other countries into a recession. In order to stimulate U.S. econom- ic recovery, Obama issued a total of 787 billion U.S. dollars bailout, in which 7.6 billion were directly used in sci- entific research. In order to demonstrate for public how scientific research funding could influence U.S. economic and society, U.S. Government proposed STAR METRICS project, which was aimed to build an inter-agent shared data infrastructure and data demonstration tools through the cooperation between federal scientific funding agents and scientific institutions, so that the impact of federal＇s R＆D inputs could be evaluated directly. This paper aims to investigate the STAR METRICS projects and propose some thinking about the S＆T evaluation in China.
2. Does exposure to inhalation anesthesia gases change the ratio of X-bearing sperms and Y-bearing Sperms? A worth exploring project into an uncharted domain.
Gupta, Deepak; Mckelvey, George; Kaminski, Edward; Zestos, Maria Markakis
2016-09-01
According to recent surveys performed in United States and India, anesthesia care providers were observed to have sired female offspring in a higher proportion than male offspring as their firstborn progeny; however, the reasons for the skew are not clear. Our hypothesis is that the underlying biological evidence may be elucidated by unraveling differences (if any) between the concentrations of X-bearing sperms and Y-bearing sperms in the semen samples obtained from males exposed to varied levels of anesthetics in their lifetimes. Therefore, the objectives of the envisaged study would be to conduct a three-stage investigative study on in-vitro human semen samples to determine (a) X-bearing sperms and Y-bearing sperms concentrations' ratio in male pediatric anesthesia care providers' semen samples, (b) changes in X-bearing sperms and Y-bearing sperms concentrations' ratios between the pre-rotation and post-rotation semen samples of male medical student volunteers/observers, and (c) changes in X-bearing sperms and Y-bearing sperms concentrations' ratios between the pre-operative and post-operative day-3 semen samples of male patients presenting for outpatient procedures under inhalational anesthesia. The expected outcomes would be (a) linear and positive correlation of the anesthetic gas usage (exposure) with increased X-bearing sperms/Y-bearing sperms ratio in post-anesthesia day 3 sample as compared to the baseline preoperative sample, (b) linear and positive correlation of the anesthetic gas usage (exposure) with increased X-bearing sperms/Y-bearing sperms ratio in post-rotation sample as compared to the baseline sample, and (c) observation of high X-bearing sperms/Y-bearing sperms ratio in the pediatric anesthesia care providers. In summary, effects (if any) of occupational or personal exposure to inhalational anesthetic gases on the X-bearing sperms and Y-bearing sperms ratio is a worthy project wherein lots of questions that have arisen over decades could find
3. CARBON-RICH PRESOLAR GRAINS FROM MASSIVE STARS: SUBSOLAR {sup 12}C/{sup 13}C AND {sup 14}N/{sup 15}N RATIOS AND THE MYSTERY OF {sup 15}N
Pignatari, M. [Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, Hungarian Academy of Sciences, Konkoly Thege Miklos ut 15-17, H-1121 Budapest (Hungary); Zinner, E. [Laboratory for Space Sciences and Physics Department, Washington University, St. Louis, MO 63130 (United States); Hoppe, P. [Max Planck Institute for Chemistry, D-55128 Mainz (Germany); Jordan, C. J.; Gibson, B. K. [E.A. Milne Centre for Astrophysics, Dept of Physics and Mathematics, University of Hull, HU6 7RX (United Kingdom); Trappitsch, R. [Department of the Geophysical Sciences and Chicago Center for Cosmochemistry, Chicago, IL 60637 (United States); Herwig, F. [Department of Physics and Astronomy, University of Victoria, Victoria, BC V8P5C2 (Canada); Fryer, C. [Computational Physics and Methods (CCS-2), LANL, Los Alamos, NM, 87545 (United States); Hirschi, R. [Keele University, Keele, Staffordshire ST5 5BG (United Kingdom); Timmes, F. X. [The Joint Institute for Nuclear Astrophysics, Notre Dame, IN 46556 (United States)
2015-08-01
Carbon-rich grains with isotopic anomalies compared to the Sun are found in primitive meteorites. They were made by stars, and carry the original stellar nucleosynthesis signature. Silicon carbide grains of Type X and C and low-density (LD) graphites condensed in the ejecta of core-collapse supernovae. We present a new set of models for the explosive He shell and compare them with the grains showing {sup 12}C/{sup 13}C and {sup 14}N/{sup 15}N ratios lower than solar. In the stellar progenitor H was ingested into the He shell and not fully destroyed before the explosion. Different explosion energies and H concentrations are considered. If the supernova shock hits the He-shell region with some H still present, the models can reproduce the C and N isotopic signatures in C-rich grains. Hot-CNO cycle isotopic signatures are obtained, including a large production of {sup 13}C and {sup 15}N. The short-lived radionuclides {sup 22}Na and {sup 26}Al are increased by orders of magnitude. The production of radiogenic {sup 22}Ne from the decay of {sup 22}Na in the He shell might solve the puzzle of the Ne-E(L) component in LD graphite grains. This scenario is attractive for the SiC grains of type AB with {sup 14}N/{sup 15}N ratios lower than solar, and provides an alternative solution for SiC grains originally classified as nova grains. Finally, this process may contribute to the production of {sup 14}N and {sup 15}N in the Galaxy, helping to produce the {sup 14}N/{sup 15}N ratio in the solar system.
4. Gaia and Variable Stars
Udalski, A; Skowron, D M; Skowron, J; Pietrukowicz, P; Mróz, P; Poleski, R; Szymański, M K; Kozłowski, S; Wyrzykowski, Ł; Ulaczyk, K; Pawlak, M
2016-01-01
We present a comparison of the Gaia DR1 samples of pulsating variable stars - Cepheids and RR Lyrae type - with the OGLE Collection of Variable Stars aiming at the characterization of the Gaia mission performance in the stellar variability domain. Out of 575 Cepheids and 2322 RR Lyrae candidates from the Gaia DR1 samples located in the OGLE footprint in the sky, 559 Cepheids and 2302 RR Lyrae stars are genuine pulsators of these types. The number of misclassified stars is low indicating reliable performance of the Gaia data pipeline. The completeness of the Gaia DR1 samples of Cepheids and RR Lyrae stars is at the level of 60-75% as compared to the OGLE Collection dataset. This level of completeness is moderate and may limit the applicability of the Gaia data in many projects.
5. Mira Symbiotic Stars
Guo-Liang Lü; Chun-Hua Zhu; Zhan-Wen Han
2007-01-01
We have carried out a detailed study of Mira symbiotic stars by means of a population synthesis code. We estimate the number of Mira symbiotic stars in the Galaxy as 1700 - 3100 and the Galactic occurrence rate of Mira symbiotic novae as from ～ 0.9 to 6.0 yr-1,depending on the model assumptions. The distributions of the orbital periods, the masses of the components, mass-loss rates of cool components, mass-accretion rates of hot components and Mira pulsation periods in Mira symbiotic stars are simulated. By a comparison of the number ratio of Mira symbiotic stars to all symbiotic stars, we find the model with the stellar wind model of Winters et al. to be reasonable.
6. High-resolution spectroscopic studies of ultra metal-poor stars found in LAMOST survey
Li, Haining; Zhao, Gang; Honda, Satoshi; Christlieb, Norbert; Suda, Takuma
2015-01-01
We report on the observations of two ultra metal-poor (UMP) stars with [Fe/H]~-4.0 including one new discovery. The two stars are studied in the on-going and quite efficient project to search for extremely metal-poor (EMP) stars with LAMOST and Subaru. Detailed abundances or upper limits of abundances have been derived for 15 elements from Li to Eu based on high-resolution spectra obtained with Subaru/HDS. The abundance patterns of both UMP stars are consistent with the "normal-population" among the low-metallicity stars. Both of the two program stars show carbon-enhancement without any excess of heavy neutron-capture elements, indicating that they belong to the subclass of CEMP-no stars, as is the case of most UMP stars previously studied. The [Sr/Ba] ratios of both CEMP-no UMP stars are above [Sr/Ba]~-0.4, suggesting the origin of the carbon-excess is not compatible with the mass transfer from an AGB companion where the s-process has operated. Lithium abundance is measured in the newly discovered UMP star L...
7. The ATLAS(3D) project - XX. Mass-size and mass-Sigma distributions of early-type galaxies : bulge fraction drives kinematics, mass-to-light ratio, molecular gas fraction and stellar initial mass function
Cappellari, Michele; McDermid, Richard M.; Alatalo, Katherine; Blitz, Leo; Bois, Maxime; Bournaud, Frederic; Bureau, M.; Crocker, Alison F.; Davies, Roger L.; Davis, Timothy A.; de Zeeuw, P. T.; Duc, Pierre-Alain; Emsellem, Eric; Khochfar, Sadegh; Krajnovic, Davor; Kuntschner, Harald; Morganti, Raffaella; Naab, Thorsten; Oosterloo, Tom; Sarzi, Marc; Scott, Nicholas; Serra, Paolo; Weijmans, Anne-Marie; Young, Lisa M.
2013-01-01
In the companion Paper XV of this series, we derive accurate total mass-to-light ratios (M/L)(JAM) approximate to (M/L)(r = R-e) within a sphere of radius r = R-e centred on the galaxy, as well as stellar (M/L)(stars) (with the dark matter removed) for the volume-limited and nearly mass-selected (st
8. Star Clusters
Gieles, M.
1993-01-01
Star clusters are observed in almost every galaxy. In this thesis we address several fundamental problems concerning the formation, evolution and disruption of star clusters. From observations of (young) star clusters in the interacting galaxy M51, we found that clusters are formed in complexes of stars and star clusters. These complexes share similar properties with giant molecular clouds, from which they are formed. Many (70%) of the young clusters will not survive the fist 10 Myr, due to t...
9. Stars and Star Myths.
Eason, Oliver
Myths and tales from around the world about constellations and facts about stars in the constellations are presented. Most of the stories are from Greek and Roman mythology; however, a few Chinese, Japanese, Polynesian, Arabian, Jewish, and American Indian tales are also included. Following an introduction, myths are presented for the following 32…
10. Stars and Star Myths.
Eason, Oliver
Myths and tales from around the world about constellations and facts about stars in the constellations are presented. Most of the stories are from Greek and Roman mythology; however, a few Chinese, Japanese, Polynesian, Arabian, Jewish, and American Indian tales are also included. Following an introduction, myths are presented for the following 32…
11. TraMoS project III: Improved physical parameters, timing analysis, and star-spot modelling of the WASP-4b exoplanet system from 38 transit observations
Hoyer, S; Rojo, P; Nascimbeni, V; Hidalgo, S; Astudillo-Defru, N; Concha, F; Contreras, Y; Servajean, E; Hinse, T C
2013-01-01
We report twelve new transit observations of the exoplanet WASP-4b from the Transit Monitoring in the South Project (TraMoS) project. These transits are combined with all previously published transit data for this planet to provide an improved radius measurement of Rp = 1.395 +- 0.022 Rjup and improved transit ephemerides. In a new homogeneous analysis in search for Transit Timing Variations (TTVs) we find no evidence of those with RMS amplitudes larger than 20 seconds over a 4-year time span. This lack of TTVs rules out the presence of additional planets in the system with masses larger than about 2.5 M_earth, 2.0 M_earth, and 1.0 M_earth around the 1:2, 5:3 and 2:1 orbital resonances. Our search for the variation of other parameters, such as orbital inclination and transit depth also yields negative results over the total time span of the transit observations. Finally we perform a simple study of stellar spots configurations of the system and conclude that the star rotational period is about 34 days.
12. The ALFALFA Hα Survey. I. Project Description and The Local Star-formation Rate Density from the Fall Sample
Van Sistine, Angela; Salzer, John J.; Sugden, Arthur; Giovanelli, Riccardo; Haynes, Martha P.; Janowiecki, Steven; Jaskot, Anne E.; Wilcots, Eric M.
2016-06-01
The ALFALFA Hα survey utilizes a large sample of H i-selected galaxies from the ALFALFA survey to study star formation (SF) in the local universe. ALFALFA Hα contains 1555 galaxies with distances between ˜20 and ˜100 Mpc. We have obtained continuum-subtracted narrowband Hα images and broadband R images for each galaxy, creating one of the largest homogeneous sets of Hα images ever assembled. Our procedures were designed to minimize the uncertainties related to the calculation of the local SF rate density (SFRD). The galaxy sample we constructed is as close to volume-limited as possible, is a robust statistical sample, and spans a wide range of galaxy environments. In this paper, we discuss the properties of our Fall sample of 565 galaxies, our procedure for deriving individual galaxy SF rates, and our method for calculating the local SFRD. We present a preliminary value of log(SFRD[M ⊙ yr-1 Mpc-3]) = -1.747 ± 0.018 (random) ±0.05 (systematic) based on the 565 galaxies in our Fall sub-sample. Compared to the weighted average of SFRD values around z ≈ 2, our local value indicates a drop in the global SFRD of a factor of 10.2 over that lookback time.
13. The Chandra Delta Ori Large Project: Occultation Measurements of the Shocked Gas tn the Nearest Eclipsing O-Star Binary
Corcoran, Michael F.; Nichols, Joy; Naze, Yael; Rauw, Gregor; Pollock, Andrew; Moffat, Anthony; Richardson, Noel; Evans, Nancy; Hamaguchi, Kenji; Oskinova, Lida; Hamann, W. -R.; Gull, Ted; Ignace, Rico; Hole, Tabetha; Iping, Rosina; Walborn, Nolan; Hoffman, Jennifer; Lomax, Jamie; Waldron, Wayne; Owocki, Stan; Maiz-Apellaniz, Jesus; Leutenegger, Maurice; Hole, Tabetha; Gayley, Ken; Russell, Chris
2013-01-01
Delta Ori is the nearest massive, single-lined eclipsing binary (O9.5 II + B0.5III). As such it serves as a fundamental calibrator of the mass-radius-luminosity relation in the upper HR diagram. It is also the only eclipsing O-type binary system which is bright enough to be observable with the CHANDRA gratings in a reasonable exposure. Studies of resolved X-ray line complexes provide tracers of wind mass loss rate and clumpiness; occultation by the X-ray dark companion of the line emitting region can provide direct spatial information on the location of the X-ray emitting gas produced by shocks embedded in the wind of the primary star. We obtained phase-resolved spectra with Chandra in order to determine the level of phase-dependent vs. secular variability in the shocked wind. Along with the Chandra observations we obtained simultaneous photometry from space with the Canadian MOST satellite to help understand the relation between X-ray and photospheric variability.
14. A study of the effect of rotational mixing on massive stars evolution: surface abundances of Galactic O7-8 giant stars
Martins, F.; Simón-Díaz, S.; Barbá, R. H.; Gamen, R. C.; Ekström, S.
2017-02-01
Context. Massive star evolution remains only partly constrained. In particular, the exact role of rotation has been questioned by puzzling properties of OB stars in the Magellanic Clouds. Aims: Our goal is to study the relation between surface chemical composition and rotational velocity, and to test predictions of evolutionary models including rotation. Methods: We have performed a spectroscopic analysis of a sample of fifteen Galactic O7-8 giant stars. This sample is homogeneous in terms of mass, metallicity and evolutionary state. It is made of stars with a wide range of projected rotational velocities. Results: We show that the sample stars are located on the second half of the main sequence, in a relatively narrow mass range (25-40 M⊙). Almost all stars with projected rotational velocities above 100 km s-1 have N/C ratios about ten times the initial value. Below 100 km s-1 a wide range of N/C values is observed. The relation between N/C and surface gravity is well reproduced by various sets of models. Some evolutionary models including rotation are also able to consistently explain slowly rotating, highly enriched stars. This is due to differential rotation which efficiently transports nucleosynthesis products and allows the surface to rotate slower than the core. In addition, angular momentum removal by winds amplifies surface braking on the main sequence. Comparison of the surface composition of O7-8 giant stars with a sample of B stars with initial masses about four times smaller reveal that chemical enrichment scales with initial mass, as expected from theory. Conclusions: Although evolutionary models that include rotation face difficulties in explaining the chemical properties of O- and B-type stars at low metallicity, some of them can consistently account for the properties of main-sequence Galactic O stars in the mass range 25-40 M⊙.
15. Update of the National Surgical Adjuvant Breast and Bowel Project Study of Tamoxifen and Raloxifene (STAR) P-2 Trial: Preventing breast cancer.
Vogel, Victor G; Costantino, Joseph P; Wickerham, D Lawrence; Cronin, Walter M; Cecchini, Reena S; Atkins, James N; Bevers, Therese B; Fehrenbacher, Louis; Pajon, Eduardo R; Wade, James L; Robidoux, André; Margolese, Richard G; James, Joan; Runowicz, Carolyn D; Ganz, Patricia A; Reis, Steven E; McCaskill-Stevens, Worta; Ford, Leslie G; Jordan, V Craig; Wolmark, Norman
2010-06-01
The selective estrogen-receptor modulator (SERM) tamoxifen became the first U.S. Food and Drug Administration (FDA)-approved agent for reducing breast cancer risk but did not gain wide acceptance for prevention, largely because it increased endometrial cancer and thromboembolic events. The FDA approved the SERM raloxifene for breast cancer risk reduction following its demonstrated effectiveness in preventing invasive breast cancer in the Study of Tamoxifen and Raloxifene (STAR). Raloxifene caused less toxicity (versus tamoxifen), including reduced thromboembolic events and endometrial cancer. In this report, we present an updated analysis with an 81-month median follow-up. STAR women were randomly assigned to receive either tamoxifen (20 mg/d) or raloxifene (60 mg/d) for 5 years. The risk ratio (RR; raloxifene:tamoxifen) for invasive breast cancer was 1.24 (95% confidence interval [CI], 1.05-1.47) and for noninvasive disease, 1.22 (95% CI, 0.95-1.59). Compared with initial results, the RRs widened for invasive and narrowed for noninvasive breast cancer. Toxicity RRs (raloxifene:tamoxifen) were 0.55 (95% CI, 0.36-0.83; P = 0.003) for endometrial cancer (this difference was not significant in the initial results), 0.19 (95% CI, 0.12-0.29) for uterine hyperplasia, and 0.75 (95% CI, 0.60-0.93) for thromboembolic events. There were no significant mortality differences. Long-term raloxifene retained 76% of the effectiveness of tamoxifen in preventing invasive disease and grew closer over time to tamoxifen in preventing noninvasive disease, with far less toxicity (e.g., highly significantly less endometrial cancer). These results have important public health implications and clarify that both raloxifene and tamoxifen are good preventive choices for postmenopausal women with elevated risk for breast cancer.
16. The MACHO Project Large Magellanic Cloud Variable Star Inventory. XIII. Fourier Parameters for the First Overtone RR Lyrae Variables and the LMC Distance
Alcock, C; Alves, D; Axelrod, T; Becker, A; Bennett, D; Clement, C; Cook, K; Drake, A; Freeman, K; Geha, M; Griest, K; Lehner, M; Marshall, S; Minniti, D; Muzzin, A; Nelson, C; Peterson, B; Popowski, P; Pratt, M; Quinn, P; Rodgers, A; Rowe, J; Sutherland, W; Vandehei, T; Welch, D
2003-12-31
Shapes of RR Lyrae light curves can be described in terms of Fourier coefficients which past research has linked with physical characteristics such as luminosity, mass and temperature. Fourier coefficients have been derived for the V and R light curves of 785 overtone RR Lyrae variables in 16 MACHO fields near the bar of the LMC. In general, the Fourier phase differences {phi}{sub 21}, {phi}{sub 31} and {phi}{sub 41} increase and the amplitude ratio R{sub 21} decreases with increasing period. The coefficients for both the V and R magnitudes follow these patterns, but the phase differences for the R curves are on average slightly greater, and their amplitudes are about 20% smaller, than the ones for the V curves. The {phi}{sub 31} and R{sub 21} coefficients have been compared with those of the first overtone RR Lyrae variables in the Galactic globular clusters NGC 6441, M107, M5, M3, M2, {omega} Centauri and M68. The results indicate that many of the LMC variables have properties similar to the ones in M2, M3, M5 and the Oosterhoff type I variables in {omega} Cen, but they are different from the Oosterhoff type II variables in {omega} Cen. Equations derived from hydrodynamic pulsation models have been used to calculate the luminosity and temperature for the 330 bona fide first-overtone variables. The results indicate that they have Log L in the range 1.6 to 1.8 L{sub {center_dot}} and log T{sub eff} between 3.85 and 3.87. Based on these temperatures, a mean color excess E(V-R) = 0.08 mag, equivalent to E(B-V) = 0.14 mag, has been estimated for these 330 stars. The 80 M5-like variables (selected according to their location in the {phi}{sub 31} - log P plot) are used to determine an LMC distance. After correcting for the effects of extinction and crowding, a mean apparent magnitude < V{sub 0} > = 18.99 {+-} 0.02 (statistical) {+-} 0.16 (systematic) has been estimated for these 80 stars. Combining this with a mean absolute magnitude M{sub V} = 0.56 {+-} 0.06 for M5
17. The ATLAS3D project - XV. Benchmark for early-type galaxies scaling relations from 260 dynamical models: mass-to-light ratio, dark matter, Fundamental Plane and Mass Plane
Cappellari, Michele; Scott, Nicholas; Alatalo, Katherine; Blitz, Leo; Bois, Maxime; Bournaud, Frédéric; Bureau, M.; Crocker, Alison F.; Davies, Roger L.; Davis, Timothy A.; de Zeeuw, P. T.; Duc, Pierre-Alain; Emsellem, Eric; Khochfar, Sadegh; Krajnović, Davor; Kuntschner, Harald; McDermid, Richard M.; Morganti, Raffaella; Naab, Thorsten; Oosterloo, Tom; Sarzi, Marc; Serra, Paolo; Weijmans, Anne-Marie; Young, Lisa M.
2013-07-01
We study the volume-limited and nearly mass-selected (stellar mass Mstars ≳ 6 × 109 M⊙) ATLAS3D sample of 260 early-type galaxies (ETGs, ellipticals Es and lenticulars S0s). We construct detailed axisymmetric dynamical models (Jeans Anisotropic MGE), which allow for orbital anisotropy, include a dark matter halo and reproduce in detail both the galaxy images and the high-quality integral-field stellar kinematics out to about 1Re, the projected half-light radius. We derive accurate total mass-to-light ratios (M/L)e and dark matter fractions fDM, within a sphere of radius r={R_e} centred on the galaxies. We also measure the stellar (M/L)stars and derive a median dark matter fraction fDM = 13 per cent in our sample. We infer masses MJAM ≡ L × (M/L)e ≈ 2 × M1/2, where M1/2 is the total mass within a sphere enclosing half of the galaxy light. We find that the thin two-dimensional subset spanned by galaxies in the (M_JAM,σ _e,R_e^maj) coordinates system, which we call the Mass Plane (MP) has an observed rms scatter of 19 per cent, which implies an intrinsic one of 11 per cent. Here, R_e^maj is the major axis of an isophote enclosing half of the observed galaxy light, while σe is measured within that isophote. The MP satisfies the scalar virial relation M_JAM∝ σ _e^2 R_e^maj within our tight errors. This show that the larger scatter in the Fundamental Plane (FP) (L, σe, Re) is due to stellar population effects [including trends in the stellar initial mass function (IMF)]. It confirms that the FP deviation from the virial exponents is due to a genuine (M/L)e variation. However, the details of how both Re and σe are determined are critical in defining the precise deviation from the virial exponents. The main uncertainty in masses or M/L estimates using the scalar virial relation is in the measurement of Re. This problem is already relevant for nearby galaxies and may cause significant biases in virial mass and size determinations at high redshift
18. The SILCC project --- IV. Impact of dissociating and ionising radiation on the interstellar medium and Halpha emission as a tracer of the star formation rate
Peters, Thomas; Walch, Stefanie; Glover, Simon C O; Girichidis, Philipp; Pellegrini, Eric; Klessen, Ralf S; Wünsch, Richard; Gatto, Andrea; Baczynski, Christian
2016-01-01
We present three-dimensional radiation-hydrodynamical simulations of the impact of stellar winds, photoelectric heating, photodissociating and photoionising radiation, and supernovae on the chemical composition and star formation in a stratified disc model. This is followed with a sink-based model for star clusters with populations of individual massive stars. Stellar winds and ionising radiation regulate the star formation rate at a factor of ~10 below the simulation with only supernova feedback due to their immediate impact on the ambient interstellar medium after star formation. Ionising radiation (with winds and supernovae) significantly reduces the ambient densities for most supernova explosions to rho = 30 M_sun) with short lifetimes are responsible for significant fluctuations in the Halpha luminosities. The corresponding inferred star formation rates can underestimate the true instantaneous star formation rate by factors of ~10.
19. Wave Star
Kramer, Morten; Brorsen, Michael; Frigaard, Peter
Denne rapport beskriver numeriske beregninger af forskellige flydergeometrier for bølgeenergianlæget Wave Star.......Denne rapport beskriver numeriske beregninger af forskellige flydergeometrier for bølgeenergianlæget Wave Star....
20. Mid-Infrared Observations of Normal Star-Forming Galaxies The Infrared Space Observatory Key Project Sample
Dale, D A; Helou, G; Dale, Daniel A.; Silbermann, Nancy A.; Helou, George
2000-01-01
We present mid-infrared maps and preliminary analysis for 61 galaxies observed with the ISOCAM instrument aboard the Infrared Space Observatory. Many of the general features of galaxies observed at optical wavelengths---spiral arms, disks, rings, and bright knots of emission---are also seen in the mid-infrared, except the prominent optical bulges are absent at 6.75 and 15 microns. In addition, the maps are quite similar at 6.75 and 15 microns, except for a few cases where a central starburst leads to lower 6.75/15 ratios in the inner region. We also present infrared flux densities and mid-infrared sizes for these galaxies. The mid-infrared color 6.75/15 shows a distinct trend with the far-infrared color 60/100. The quiescent galaxies in our sample (60/100 < 0.6) show 6.75/15 near unity, whereas this ratio drops significantly for galaxies with higher global heating intensity levels. Azimuthally-averaged surface brightness profiles indicate the extent to which the mid-infrared flux is centrally concentrated,...
1. Massive Stars
Livio, Mario; Villaver, Eva
2009-11-01
Participants; Preface Mario Livio and Eva Villaver; 1. High-mass star formation by gravitational collapse of massive cores M. R. Krumholz; 2. Observations of massive star formation N. A. Patel; 3. Massive star formation in the Galactic center D. F. Figer; 4. An X-ray tour of massive star-forming regions with Chandra L. K. Townsley; 5. Massive stars: feedback effects in the local universe M. S. Oey and C. J. Clarke; 6. The initial mass function in clusters B. G. Elmegreen; 7. Massive stars and star clusters in the Antennae galaxies B. C. Whitmore; 8. On the binarity of Eta Carinae T. R. Gull; 9. Parameters and winds of hot massive stars R. P. Kudritzki and M. A. Urbaneja; 10. Unraveling the Galaxy to find the first stars J. Tumlinson; 11. Optically observable zero-age main-sequence O stars N. R. Walborn; 12. Metallicity-dependent Wolf-Raynet winds P. A. Crowther; 13. Eruptive mass loss in very massive stars and Population III stars N. Smith; 14. From progenitor to afterlife R. A. Chevalier; 15. Pair-production supernovae: theory and observation E. Scannapieco; 16. Cosmic infrared background and Population III: an overview A. Kashlinsky.
2. Star-forming galaxies versus low- and high-excitation radio AGN in the VLA-COSMOS 3GHz Large Project
Baran, N; Novak, M; Delhaize, J; Delvecchio, I; Capak, P; Civano, F; Herrera-Ruiz, N; Ilbert, O; Laigle, C; Marchesi, S; McCracken, H J; Middelberg, E; Salvato, M; Schinnerer, E
2016-01-01
We study the composition of the faint radio population selected from the VLA-COSMOS 3GHz Large Project, a radio continuum survey performed at 10 cm wavelength. The survey covers the full 2 square degree COSMOS field with mean $rms\\sim2.3$ $\\mu$Jy/beam, cataloging 10,899 source components above $5\\times rms$. By combining these radio data with UltraVISTA, optical, near-infrared, and Spitzer/IRAC mid-infrared data, as well as X-ray data from the Chandra Legacy, and Chandra COSMOS surveys, we gain insight into the emission mechanisms within our radio sources out to redshifts of $z\\sim5$. From these emission characteristics we classify our souces as star forming galaxies or AGN. Using their multi-wavelength properties we further separate the AGN into sub-samples dominated by radiatively efficient and inefficient AGN, often referred to as high- and low-excitation emission line AGN. We compare our method with other results based on fitting of the sources' spectral energy distributions using both galaxy and AGN spec...
3. The Atlas3D project - XII. Recovery of the mass-to-light ratio of simulated early-type barred galaxies with axisymmetric dynamical models
Lablanche, Pierre-Yves; Emsellem, Eric; Bournaud, Frederic; Michel-Dansac, Leo; Alatalo, Katherine; Blitz, Leo; Bois, Maxime; Bureau, Martin; Davies, Roger L; Davis, Timothy A; de Zeeuw, P T; Duc, Pierre-Alain; Khochfar, Sadegh; Krajnovic, Davor; Kuntschner, Harald; Morganti, Raffaella; McDermid, Richard M; Naab, Thorsten; Oosterloo, Tom; Sarzi, Marc; Scott, Nicholas; Serra, Paolo; Weijmans, Anne-Marie; Young, Lisa M
2012-01-01
We investigate the accuracy in the recovery of the stellar dynamics of barred galaxies when using axisymmetric dynamical models. We do this by trying to recover the mass-to-light ratio (M/L) and the anisotropy of realistic galaxy simulations using the Jeans Anisotropic Multi-Gaussian Expansion (JAM) method. However, given that the biases we find are mostly due to an application of an axisymmetric modeling algorithm to a non-axisymmetric system and in particular to inaccuracies in the de-projected mass model, our results are relevant for general axisymmetric modelling methods. We run N-body collisionless simulations to build a library with various luminosity distribution, constructed to mimic real individual galaxies, with realistic anisotropy. The final result of our evolved library of simulations contains both barred and unbarred galaxies. The JAM method assumes an axisymmetric mass distribution, and we adopt a spatially constant M/L and anisotropy beta_z=1-sigma_z^2/sigma_R^2 distributions. The models are f...
4. Catch a Star!
2006-11-01
ESO and the European Association for Astronomy Education are launching today the 2007 edition of 'Catch a Star!', their international astronomy competition for school students. Now in its fifth year, the competition offers students the chance to win a once-in-a-lifetime trip to ESO's flagship observatory in Chile, as well as many other prizes. Students are invited to 'become astronomers' and embark on a journey to explore the Universe. ESO PR Photo 42/06 The competition includes separate categories - 'Catch a Star Researchers' and 'Catch a Star Adventurers' - to ensure that every student, whatever their level, has the chance to enter and win exciting prizes. For the artistically minded, 'Catch a Star!' also includes an artwork competition, 'Catch a Star Artists'. "'Catch a Star!' offers a unique opportunity for students to learn more about astronomy and about the methods scientists use to discover new things about the Universe", said Douglas Pierce-Price, Education Officer at ESO. In teams, students choose an astronomical topic to study and produce an in-depth report. An important part of the project for 'Catch a Star Researchers' is to think about how ESO's telescopes or a telescope of the future can contribute to their investigations of the subject. As well as the top prize - a trip to one of ESO's observatory sites in Chile - visits to observatories in Germany, Austria and Spain, and many other prizes are also available to be won. 'Catch a Star Researchers' winners will be chosen by an international jury, and 'Catch a Star Adventurers' will be awarded further prizes by lottery. Entries for 'Catch a Star Artists' will be displayed on the web and winners chosen with the help of a public online vote. The first editions of 'Catch a Star!' have attracted several hundred entries from more than 25 countries worldwide. Previous winning entries have included "Star clusters and the structure of the Milky Way" (Budapest, Hungary), "Vega" (Acqui Terme, Italy) and "Venus
5. Binary stars can provide the missing photons' needed for reionization
Ma, Xiangcheng; Hopkins, Philip F.; Kasen, Daniel; Quataert, Eliot; Faucher-Giguère, Claude-André; Kereš, Dušan; Murray, Norman; Strom, Allison
2016-07-01
Empirical constraints on reionization require galactic ionizing photon escape fractions fesc ≳ 20 per cent, but recent high-resolution radiation-hydrodynamic calculations have consistently found much lower values ˜1-5 per cent. While these models include strong stellar feedback and additional processes such as runaway stars, they almost exclusively consider stellar evolution models based on single (isolated) stars, despite the fact that most massive stars are in binaries. We re-visit these calculations, combining radiative transfer and high-resolution cosmological simulations with detailed models for stellar feedback from the Feedback in Realistic Environments project. For the first time, we use a stellar evolution model that includes a physically and observationally motivated treatment of binaries (the Binary Population and Spectral Synthesis model). Binary mass transfer and mergers enhance the population of massive stars at late times (≳3 Myr) after star formation, which in turn strongly enhances the late-time ionizing photon production (especially at low metallicities). These photons are produced after feedback from massive stars has carved escape channels in the interstellar medium, and so efficiently leak out of galaxies. As a result, the time-averaged effective' escape fraction (ratio of escaped ionizing photons to observed 1500 Å photons) increases by factors ˜4-10, sufficient to explain reionization. While important uncertainties remain, we conclude that binary evolution may be critical for understanding the ionization of the Universe.
6. Hadron star models. [neutron stars
Cohen, J. M.; Boerner, G.
1974-01-01
The properties of fully relativistic rotating hadron star models are discussed using models based on recently developed equations of state. All of these stable neutron star models are bound with binding energies as high as about 25%. During hadron star formation, much of this energy will be released. The consequences, resulting from the release of this energy, are examined.
7. Catch a Star 2008!
2007-10-01
ESO and the European Association for Astronomy Education have just launched the 2008 edition of 'Catch a Star', their international astronomy competition for school students. Now in its sixth year, the competition offers students the chance to win a once-in-a-lifetime trip to ESO's flagship observatory in Chile, as well as many other prizes. CAS logo The competition includes separate categories - 'Catch a Star Researchers' and 'Catch a Star Adventurers' - to ensure that every student, whatever their level, has the chance to enter and win exciting prizes. In teams, students investigate an astronomical topic of their choice and write a report about it. An important part of the project for 'Catch a Star Researchers' is to think about how ESO's telescopes such as the Very Large Telescope (VLT) or future telescopes such as the Atacama Large Millimeter/submillimeter Array (ALMA) and the European Extremely Large Telescope (E-ELT) could contribute to investigations of the topic. Students may also include practical activities such as observations or experiments. For the artistically minded, 'Catch a Star' also offers an artwork competition, 'Catch a Star Artists'. Last year, hundreds of students from across Europe and beyond took part in 'Catch a Star', submitting astronomical projects and artwork. "'Catch a Star' gets students thinking about the wonders of the Universe and the science of astronomy, with a chance of winning great prizes. It's easy to take part, whether by writing about astronomy or creating astronomically inspired artwork," said Douglas Pierce-Price, Education Officer at ESO. As well as the top prize - a trip to ESO's Very Large Telescope in Chile - visits to observatories in Austria and Spain, and many other prizes, can also be won. 'Catch a Star Researchers' winners will be chosen by an international jury, and 'Catch a Star Adventurers' will be awarded further prizes by lottery. Entries for 'Catch a Star Artists' will be displayed on the web and winners
8. Neutron Star Science with the NuSTAR
Vogel, J. K. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-16
The Nuclear Spectroscopic Telescope Array (NuSTAR), launched in June 2012, helped scientists obtain for the first time a sensitive high-energy X-ray map of the sky with extraordinary resolution. This pioneering telescope has aided in the understanding of how stars explode and neutron stars are born. LLNL is a founding member of the NuSTAR project, with key personnel on its optics and science team. We used NuSTAR to observe and analyze the observations of different neutron star classes identified in the last decade that are still poorly understood. These studies not only help to comprehend newly discovered astrophysical phenomena and emission processes for members of the neutron star family, but also expand the utility of such observations for addressing broader questions in astrophysics and other physics disciplines. For example, neutron stars provide an excellent laboratory to study exotic and extreme phenomena, such as the equation of state of the densest matter known, the behavior of matter in extreme magnetic fields, and the effects of general relativity. At the same time, knowing their accurate populations has profound implications for understanding the life cycle of massive stars, star collapse, and overall galactic evolution.
9. The SILCC project - IV. Impact of dissociating and ionizing radiation on the interstellar medium and Hα emission as a tracer of the star formation rate
Peters, Thomas; Naab, Thorsten; Walch, Stefanie; Glover, Simon C. O.; Girichidis, Philipp; Pellegrini, Eric; Klessen, Ralf S.; Wünsch, Richard; Gatto, Andrea; Baczynski, Christian
2017-04-01
We present three-dimensional radiation-hydrodynamical simulations of the impact of stellar winds, photoelectric heating, photodissociating and photoionizing radiation, and supernovae on the chemical composition and star formation in a stratified disc model. This is followed by a sink-based model for star clusters with populations of individual massive stars. Stellar winds and ionizing radiation regulate the star formation rate at a factor of ∼10 below the simulation with only supernova feedback due to their immediate impact on the ambient interstellar medium after star formation. Ionizing radiation (with winds and supernovae) significantly reduces the ambient densities for most supernova explosions to ρ scale of 2 Gyr and shows the best agreement with observations. In the radiative models, the Hα emission is dominated by radiative recombination as opposed to collisional excitation (the dominant emission in non-radiative models), which only contributes ∼1-10 per cent to the total Hα emission. Individual massive stars (M ≥ 30 M⊙) with short lifetimes are responsible for significant fluctuations in the Hα luminosities. The corresponding inferred star formation rates can underestimate the true instantaneous star formation rate by a factor of ∼10.
10. Dynamics of Rotating, Magnetized Neutron Stars
Liebling, Steven L.
2010-01-01
Using a fully general relativistic implementation of ideal magnetohydrodynamics with no assumed symmetries in three spatial dimensions, the dynamics of magnetized, rigidly rotating neutron stars are studied. Beginning with fully consistent initial data constructed with Magstar, part of the Lorene project, we study the dynamics and stability of rotating, magnetized polytropic stars as models of neutron stars. Evolutions suggest that some of these rotating, magnetized stars may be minimally uns...
11. Rare variant associations with waist-to-hip ratio in European-American and African-American women from the NHLBI-Exome Sequencing Project.
Kan, Mengyuan; Auer, Paul L; Wang, Gao T; Bucasas, Kristine L; Hooker, Stanley; Rodriguez, Alejandra; Li, Biao; Ellis, Jaclyn; Adrienne Cupples, L; Ida Chen, Yii-Der; Dupuis, Josée; Fox, Caroline S; Gross, Myron D; Smith, Joshua D; Heard-Costa, Nancy; Meigs, James B; Pankow, James S; Rotter, Jerome I; Siscovick, David; Wilson, James G; Shendure, Jay; Jackson, Rebecca; Peters, Ulrike; Zhong, Hua; Lin, Danyu; Hsu, Li; Franceschini, Nora; Carlson, Chris; Abecasis, Goncalo; Gabriel, Stacey; Bamshad, Michael J; Altshuler, David; Nickerson, Deborah A; North, Kari E; Lange, Leslie A; Reiner, Alexander P; Leal, Suzanne M
2016-08-01
Waist-to-hip ratio (WHR), a relative comparison of waist and hip circumferences, is an easily accessible measurement of body fat distribution, in particular central abdominal fat. A high WHR indicates more intra-abdominal fat deposition and is an established risk factor for cardiovascular disease and type 2 diabetes. Recent genome-wide association studies have identified numerous common genetic loci influencing WHR, but the contributions of rare variants have not been previously reported. We investigated rare variant associations with WHR in 1510 European-American and 1186 African-American women from the National Heart, Lung, and Blood Institute-Exome Sequencing Project. Association analysis was performed on the gene level using several rare variant association methods. The strongest association was observed for rare variants in IKBKB (P=4.0 × 10(-8)) in European-Americans, where rare variants in this gene are predicted to decrease WHRs. The activation of the IKBKB gene is involved in inflammatory processes and insulin resistance, which may affect normal food intake and body weight and shape. Meanwhile, aggregation of rare variants in COBLL1, previously found to harbor common variants associated with WHR and fasting insulin, were nominally associated (P=2.23 × 10(-4)) with higher WHR in European-Americans. However, these significant results are not shared between African-Americans and European-Americans that may be due to differences in the allelic architecture of the two populations and the small sample sizes. Our study indicates that the combined effect of rare variants contribute to the inter-individual variation in fat distribution through the regulation of insulin response.
12. Runaway Stars in Supernova Remnants
Pannicke, Anna; Neuhaeuser, Ralph; Dinçel, Baha
2016-07-01
Half of all stars and in particular 70 % of the massive stars are a part of a multiple system. A possible development for the system after the core collapse supernova (SN) of the more massive component is as follows: The binary is disrupted by the SN. The formed neutron star is ejected by the SN kick whereas the companion star either remains within the system and is gravitationally bounded to the neutron star, or is ejected with a spatial velocity comparable to its former orbital velocity (up to 500 km/s). Such stars with a large peculiar space velocity are called runaway stars. We present our observational results of the supernova remnants (SNRs) G184.6-5.8, G74.0-8.5 and G119.5+10.2. The focus of this project lies on the detection of low mass runaway stars. We analyze the spectra of a number of candidates and discuss their possibility of being the former companions of the SN progenitor stars. The spectra were obtained with INT in Tenerife, Calar Alto Astronomical Observatory and the University Observatory Jena. Also we investigate the field stars in the neighborhood of the SNRs G74.0-8.5 and G119.5+10.2 and calculate more precise distances for these SNRs.
13. Star Wreck
Kusenko, Alexander; Shaposhnikov, Mikhail E.; Tinyakov, P. G.; Tkachev, Igor I.
1998-01-01
Electroweak models with low-energy supersymmetry breaking predict the existence of stable non-topological solitons, Q-balls, that can be produced in the early universe. The relic Q-balls can accumulate inside a neutron star and gradually absorb the baryons into the scalar condensate. This causes a slow reduction in the mass of the star. When the mass reaches a critical value, the neutron star becomes unstable and explodes. The cataclysmic destruction of the distant neutron stars may be the or...
14. Star polygons
Riosa, Blažka
2014-01-01
In mathematics we often encounter polygons, such us triangle, square, hexagon, etc., but we hardly encounter star polygons. Despite the fact that we do not meet them so often in mathematics, in nature they can be traced almost on every step. In this paper the emphasis is on the geometric meaning of regular star polygons. Star polygon is a generalization of the concept of regular polygons. In star polygons also non-adjacent sides intersect. Up to similarity they are determined by Schläfli symb...
15. The Century Survey Galactic Halo Project III: A Complete 4300 deg^2 Survey of Blue Horizontal Branch Stars in the Metal-Weak Thick Disk and Inner Halo
Brown, Warren R; Wilhelm, Ronald; Prieto, Carlos Allende; Geller, Margaret J; Kenyon, Scott J; Kurtz, Michael J
2007-01-01
We present a complete spectroscopic survey of 2414 2MASS-selected blue horizontal branch (BHB) candidates selected over 4300 deg^2 of the sky. We identify 655 BHB stars in this non-kinematically selected sample. We calculate the luminosity function of field BHB stars and find evidence for very few hot BHB stars in the field. The BHB stars located at a distance from the Galactic plane |Z|<4 kpc trace what is clearly a metal-weak thick disk population, with a mean metallicity of [Fe/H]= -1.7, a rotation velocity gradient of dv_{rot}/d|Z|= -28+-3.4 km/s in the region |Z|<6 kpc, and a density scale height of h_Z= 1.26+-0.1 kpc. The BHB stars located at 5<|Z|<9 kpc are a predominantly inner-halo population, with a mean metallicity of [Fe/H]= -2.0 and a mean Galactic rotation of -4+-31 km/s. We infer the density of halo and thick disk BHB stars is 104+-37 kpc^-3 near the Sun, and the relative normalization of halo to thick-disk BHB stars is 4+-1% near the Sun.
16. A study of the effect of rotational mixing on massive stars evolution: surface abundances of Galactic O7-8 giant stars
Martins, F; Barba, R H; Gamen, R C; Ekstroem, S
2016-01-01
Massive star evolution remains only partly constrained. In particular, the exact role of rotation has been questioned by puzzling properties of OB stars in the Magellanic Clouds. Our goal is to study the relation between surface chemical composition and rotational velocity, and to test predictions of evolutionary models including rotation. We have performed a spectroscopic analysis of a sample of fifteen Galactic O7-8 giant stars. This sample is homogeneous in terms of mass, metallicity and evolutionary state. It is made of stars with a wide range of projected rotational velocities. We show that the sample stars are located on the second half of the main sequence, in a relatively narrow mass range (25-40 Msun). Almost all stars with projected rotational velocities above 100 km/s have N/C ratios about ten times the initial value. Below 100 km/s a wide range of N/C values is observed. The relation between N/C and surface gravity is well reproduced by various sets of models. Some evolutionary models including ro...
17. Star centroiding error compensation for intensified star sensors.
Jiang, Jie; Xiong, Kun; Yu, Wenbo; Yan, Jinyun; Zhang, Guangjun
2016-12-26
A star sensor provides high-precision attitude information by capturing a stellar image; however, the traditional star sensor has poor dynamic performance, which is attributed to its low sensitivity. Regarding the intensified star sensor, the image intensifier is utilized to improve the sensitivity, thereby further improving the dynamic performance of the star sensor. However, the introduction of image intensifier results in star centroiding accuracy decrease, further influencing the attitude measurement precision of the star sensor. A star centroiding error compensation method for intensified star sensors is proposed in this paper to reduce the influences. First, the imaging model of the intensified detector, which includes the deformation parameter of the optical fiber panel, is established based on the orthographic projection through the analysis of errors introduced by the image intensifier. Thereafter, the position errors at the target points based on the model are obtained by using the Levenberg-Marquardt (LM) optimization method. Last, the nearest trigonometric interpolation method is presented to compensate for the arbitrary centroiding error of the image plane. Laboratory calibration result and night sky experiment result show that the compensation method effectively eliminates the error introduced by the image intensifier, thus remarkably improving the precision of the intensified star sensors.
18. STAR Calorimetry
Jacobs, W W, E-mail: jacobsw@indiana.ed [Indiana University Cyclotron Facility and Department of Physics, 2401 Milo B. Sampson Lane, Bloomington IN 47408 (United States)
2009-04-01
The main STAR calorimeters comprise a full Barrel EMC and single Endcap EMC plus a Forward Meson Spectrometer. Together they give a nearly complete coverage over the range -1 < pseudorapidity < 4 and provide EM readout and triggering that help drive STAR physics capabilities. Their description, status, performance and operations (and a few physics anecdotes) are briefly presented and discussed.
19. Wave Star
Kramer, Morten; Brorsen, Michael; Frigaard, Peter
Nærværende rapport beskriver numeriske beregninger af den hydrodynamiske interaktion mellem 5 flydere i bølgeenergianlægget Wave Star.......Nærværende rapport beskriver numeriske beregninger af den hydrodynamiske interaktion mellem 5 flydere i bølgeenergianlægget Wave Star....
20. Star Imager
Madsen, Peter Buch; Jørgensen, John Leif; Thuesen, Gøsta;
1997-01-01
The version of the star imager developed for Astrid II is described. All functions and features are described as well as the operations and the software protocol.......The version of the star imager developed for Astrid II is described. All functions and features are described as well as the operations and the software protocol....
1. Magnetic fields of Ap stars from the full Stokes spectropolarimetric observations
Rusomarov, N; Piskunov, N
2013-01-01
Current knowledge about stellar magnetic fields relies almost entirely on circular polarization observations. Few objects have been observed in all four Stokes parameters. The magnetic Ap star HD 24712 (DO Eri, HR 1217) was recently observed in the Stokes IQUV parameters with the HARPSpol instrument at the 3.6-m ESO telescope as part of our project at investigating Ap stars in all four Stokes parameters. The resulting spectra have dense phase coverage, resolving power > 10^5, and S/N ratio of 300-600. These are the highest quality full Stokes observations obtained for any star other than the Sun. We present preliminary results from magnetic Doppler imaging of HD 24712. This analysis is the first step towards obtaining detailed 3-D maps of magnetic fields and abundance structures for HD 24712 and other Ap stars that we currently observe with HARPSpol.
2. Carbon neutron star atmospheres
Suleimanov, V F; Pavlov, G G; Werner, K
2013-01-01
The accuracy of measuring the basic parameters of neutron stars is limited in particular by uncertainties in chemical composition of their atmospheres. For example, atmospheres of thermally - emitting neutron stars in supernova remnants might have exotic chemical compositions, and for one of them, the neutron star in CasA, a pure carbon atmosphere has recently been suggested by Ho & Heinke (2009). To test such a composition for other similar sources, a publicly available detailed grid of carbon model atmosphere spectra is needed. We have computed such a grid using the standard LTE approximation and assuming that the magnetic field does not exceed 10^8 G. The opacities and pressure ionization effects are calculated using the Opacity Project approach. We describe the properties of our models and investigate the impact of the adopted assumptions and approximations on the emergent spectra.
3. The StarLite Project
1988-09-01
34 IEEE Computer Special Issue on Rapid Prototyping, (submitted). (2) Cook, R. P., "An Empirical Analysis of the Lilith Instruction Set," IEEE...architecture is a 32-bit extension of Wirth’s Lilith architecture[l ], which in turn is a descendent of the Xerox Alto processor. It is also a contraction. For...instance, the Lilith uses an evaluation stack of registers with hardware stack pointer and no overfiow/underflow checking. This is a good idea in a
4. Stellar populations in star clusters
Li, Cheng-Yuan; de Grijs, Richard; Deng, Li-Cai
2016-12-01
Stellar populations contain the most important information about star cluster formation and evolution. Until several decades ago, star clusters were believed to be ideal laboratories for studies of simple stellar populations (SSPs). However, discoveries of multiple stellar populations in Galactic globular clusters have expanded our view on stellar populations in star clusters. They have simultaneously generated a number of controversies, particularly as to whether young star clusters may have the same origin as old globular clusters. In addition, extensive studies have revealed that the SSP scenario does not seem to hold for some intermediate-age and young star clusters either, thus making the origin of multiple stellar populations in star clusters even more complicated. Stellar population anomalies in numerous star clusters are well-documented, implying that the notion of star clusters as true SSPs faces serious challenges. In this review, we focus on stellar populations in massive clusters with different ages. We present the history and progress of research in this active field, as well as some of the most recent improvements, including observational results and scenarios that have been proposed to explain the observations. Although our current ability to determine the origin of multiple stellar populations in star clusters is unsatisfactory, we propose a number of promising projects that may contribute to a significantly improved understanding of this subject.
5. Surface abundances of ON stars
Martins, F; Palacios, A; Howarth, I; Georgy, C; Walborn, N R; Bouret, J -C; Barba, R
2015-01-01
Massive stars burn hydrogen through the CNO cycle during most of their evolution. When mixing is efficient, or when mass transfer in binary systems happens, chemically processed material is observed at the surface of O and B stars. ON stars show stronger lines of nitrogen than morphologically normal counterparts. Whether this corresponds to the presence of material processed through the CNO cycle or not is not known. Our goal is to answer this question. We perform a spectroscopic analysis of a sample of ON stars with atmosphere models. We determine the fundamental parameters as well as the He, C, N, and O surface abundances. We also measure the projected rotational velocities. We compare the properties of the ON stars to those of normal O stars. We show that ON stars are usually helium-rich. Their CNO surface abundances are fully consistent with predictions of nucleosynthesis. ON stars are more chemically evolved and rotate - on average - faster than normal O stars. Evolutionary models including rotation cann...
6. The Chromospheric Activity-Age Relation for M Dwarf Stars
Silvestri, N. M.; Oswalt, T. D.; Hawley, S. L.
2000-12-01
We present preliminary results from our study in which we use moderate resolution spectroscopy to determine the correlation between the chromospheric activity and age of M dwarf stars in wide binary systems. We have observed ~50 M dwarf stars from our sample with the Apache Point Observatory 3.5-m telescope. We measure the ratio of Hα luminosity to the bolometric luminosity (LHα /Lbol) of the M dwarf---a measure of activity that is proven to correlate well with age. This project is unique in that it will extend the chromospheric activity-age relation of low-mass main sequence stars beyond the ages provided by cluster methods. The ages so determined are also independent of the uncertainties in cluster age determinations. The technique has the potential to improve by at least a factor of two the precision and the range over which ages can currently be determined for main sequence stars. Work on this project is supported by the NASA Graduate Student Researchers Program grant NGT-50290 (N.M.S.).
7. Massive stars. A chemical signature of first-generation very massive stars.
Aoki, W; Tominaga, N; Beers, T C; Honda, S; Lee, Y S
2014-08-22
Numerical simulations of structure formation in the early universe predict the formation of some fraction of stars with several hundred solar masses. No clear evidence of supernovae from such very massive stars has, however, yet been found in the chemical compositions of Milky Way stars. We report on an analysis of a very metal-poor star SDSS J001820.5-093939.2, which possesses elemental-abundance ratios that differ significantly from any previously known star. This star exhibits low [α-element Fe] ratios and large contrasts between the abundances of odd and even element pairs, such as scandium/titanium and cobalt/nickel. Such features have been predicted by nucleosynthesis models for supernovae of stars more than 140 times as massive as the Sun, suggesting that the mass distribution of first-generation stars might extend to 100 solar masses or larger.
8. First stars evolution and nucleosynthesis
Bahena, D. [Institute of Astronomy of the Academy of Sciences, Bocni II 1401, 14131 Praha 4, (Czech Republic); Klapp, J. [ININ, 52750 La Marquesa, Estado de Mexico (Mexico); Dehnen, H. [Fachbereich Physik, Universitat Konstanz, 78457 Konstanz (Germany)]. e-mail: bahen@hotmail.com
2007-12-15
The first stars in the universe were massive and luminous with typical masses M {>=} 100M. Metal-free stars have unique physical characteristics and exhibit high effective temperatures and small radii. These so called Population III stars were responsible for the initial enrichment of the intergalactic medium with heavy elements. In this work, we study the structure, evolution and nucleosynthesis of 100, 200, 250 and 300M galactic and pregalactic Population III mass losing stars with metallicities Z 10{sup -6} and Z = 10{sup -9}, during the hydrogen and helium burning phases. Using a stellar evolution code, a system of 10 structure and evolution equations together with boundary conditions, and a set of 30 nuclear reactions, are solved simultaneously, obtaining the star's structure, evolution, isotopic abundances and their ratios. Motivated by recent stability analysis, almost all very massive star (VMS) calculations during the past few years have been performed with no mass loss. However, it has recently been claimed that VMS should have strong mass loss. We present in this work new VMS calculations that includes mass loss. The main difference between zero-metal and metal-enriched stars lies in the nuclear energy generation mechanism. For the first stars, nuclear burning proceeds in a non-standard way. Since Population III stars can reach high central temperatures, this leads to the first synthesis of primary carbon through the 3 {alpha} reaction activating the CNO-cycles. Zero-metal stars produce light elements, such as He, C, N and O. Thus, very massive pregalactic Population III stars experienced self-production of C, either at the zero-age main sequence or in later phases of central hydrogen burning. In advanced evolutionary phases, these stars contribute to the chemical enrichment of the intergalactic medium through supernova explosions. (Author)
9. Rising Star
Worley, Christiana
2012-01-01
Rising Star is a novel about appearances. Thailand Allen is a girl who thinks she understands what she sees. But when what she sees are cracks in her perfect world, maturation and new sight are not far off. Before growth can occur, Thailand must undergo a painful process of learning that carries with it embarrassment, sorrow, anger and confusion. Thailand lives with her mother in a small Texas town called Rising Star. Rising Star is like every other small town with its community gather...
10. The first stars: a classification of CEMP-no stars
Maeder, Andre
2015-01-01
We propose and apply a new classification for the CEMP-no stars, which are "carbon-enhanced metal-poor" stars with no overabundance of s-elements and with [Fe/H] generally inferior or equal to -2.5. This classification is based on the changes in abundances for the elements and isotopes involved in the CNO, Ne-Na, and Mg-Al nuclear cycles. These abundances change very much owing to successive back and forth mixing motions between the He- and H-burning regions in massive stars (the "source stars" responsible for the chemical enrichment of the CEMP-no stars). The wide variety of the ratios [C/Fe], 12C/13C, [N/Fe], [O/Fe], [Na/Fe], [Mg/Fe], [Al/Fe], [Sr/Fe], and [Ba/Fe], which are the main characteristics making the CEMP-no and low s stars so peculiar, is described well in terms of the proposed nucleosynthetic classification. We note that the [(C+N+O)/Fe] ratios significantly increase for lower values of [Fe/H]. The classification of CEMP-no stars and the behavior of [(C+N+O)/Fe] support the presence, in the firs...
11. Rock Stars
张国平
2000-01-01
Around the world young people are spending unbelievable sums of money to listen to rock music. Forbes Magazine reports that at least fifty rock stars have incomes between two million and six million dollars per year.
12. Carbon Stars
T. Lloyd Evans
2010-12-01
In this paper, the present state of knowledge of the carbon stars is discussed. Particular attention is given to issues of classification, evolution, variability, populations in our own and other galaxies, and circumstellar material.
13. Coronal thermal structure and abundances of supermetal-rich solar-type stars
Brickhouse, Nancy S. (Principal Investigator); Mushotzky, Richard F. (Technical Monitor)
2005-01-01
This observation is for grating spectroscopy of Tau Boo, a late-type star with very high metallicity (about twice solar). Despite the extreme condition of high metallicity in the photosphere, the abundance ratios of the corona appear consistent with the general picture of a coronal abundance/activity relation. The target was obtained by XMM-Newton on 24 June 2003 for 71900 sec. The European PI Antonio Maggio is responsible for data reduction. Members of our team presented at the Cool Stars Workshop 13 held in Hamburg, Germany in July 2004 and conferred at that time on the publication of results. This project is complete except for the final publication.
14. The circumstellar shell of the post-ABB star HD 56126: the 12C12C/12C13C isotope ratio and12C16O column density
Barker, E.J.; Lambert, D.L.
1998-01-01
We have made the first detection of circumstellar absorption lines of the 12C13C A 1Πu-X 1∑g+ (Phillips) system 1-0 band and the 12C16O X 1∑+ first-overtone 2-0 band in the spectrum of the post-AGB star HD 56126 (IRAS 07134+1005). All current detections of circumstellar molecular absorption lines to
15. Wave Star
Kramer, Morten; Frigaard, Peter
Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Byggeri og Anlæg med bølgeenergianlæget Wave Star.......Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Byggeri og Anlæg med bølgeenergianlæget Wave Star....
16. STAR POLYMERS
Ch. von Ferber; Yu.Holovatch
2002-01-01
It is our great pleasure to present a collection of papers devoted to theoretical, numerical, and experimental studies in the field of star polymers. Since its introduction in the early 80-ies, this field has attracted increasing interest and has become an important part of contemporary polymer physics. While research papers in this field appear regularly in different physical and chemical journals, the present collection is an attempt to join together the studies of star polymers showing the...
17. Wave Star
Kramer, Morten; Andersen, Thomas Lykke
Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star.......Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star....
18. The Star Formation History of Local Starbursts as Benchmark for High Redshifts
Schmitt, Henrique R.; Calzetti, Daniela; Armus, Lee
2001-08-01
We propose to use the WIYN telescope and MIMO to obtain broad band B and R, and narrow band H(alpha) and H(beta) images for a sample of 13 local starburst galaxies detected by ISO at 170-200(micron) and for which we are obtaining ultraviolet (1600Å) images with an approved HST/STIS program. With these observations we will complete the ground based portion of this project. This sample spans a wide range in the luminosity, star formation rate, metallicity and morphology parameters, and will be used as a low-redshift benchmark to explore the relationship between the Lyman-break and the SCUBA galaxies at z~3. The broad- band ground-based and HST images will be used to characterize the stellar populations and determine the ages of the star forming regions of these galaxies, while the H(alpha)/H(beta) ratio will be used to determine the reddening and gas morphology of these regions. We will study the conditions for the escape of UV light from a dusty galaxy, as a function of the sample parameters. The H(alpha) and UV HST images will be combined to derive a relative empirical calibration between these two star formation indicators. We will measure the fraction of nuclear and disk emission, the fraction of star formation in massive clusters and the properties of those star clusters, the structural properties of star forming bars, rings, and tidally-driven star formation in IR-bright galaxies.
19. The ACS LCID project. V. The Star Formation History of the Dwarf Galaxy \\objectname[]{LGS-3}: Clues for Cosmic Reionization and Feedback
Hidalgo, Sebastian L; Skillman, Evan; Monelli, Matteo; Gallart, Carme; Cole, Andrew; Dolphin, Andrew; Weisz, Daniel; Bernard, Edouard; Cassisi, Santi; Mayer, Lucio; Stetson, Peter; Tolstoy, Eline; Ferguson, Henry
2011-01-01
We present an analysis of the star formation history (SFH) of the transition-type (dIrr/dSph) Local Group galaxy \\objectname[]{LGS-3} (Pisces) based on deep photometry obtained with the {\\it Advanced Camera for Surveys} onboard the {\\it Hubble Space Telescope}. Our analysis shows that the SFH of \\objectname[]{LGS-3} is dominated by a main episode $\\sim 11.7$ Gyr ago with a duration of $\\sim$ 1.4 Gyr which formed $\\sim 90%$ of the stars. Subsequently, \\objectname[]{LGS-3} continued forming stars until the present, although at a much lower rate. The lack of early chemical enrichment is in contrast to that observed in the isolated dSph galaxies of comparable luminosity, implying that the dSphs were more massive and subjected to more tidal stripping. We compare the SFH of \\objectname[]{LGS-3} with expectations from cosmological models. Most or all the star formation was produced in \\objectname[]{LGS-3} after the reionization epoch, assumed to be completed at $z\\sim6$ or $\\sim 12.7$ Gyr ago. The total mass of the ...
20. The ACS LCID Project : V. The Star Formation History of the Dwarf Galaxy LGS-3: Clues to Cosmic Reionization and Feedback
Hidalgo, Sebastian L.; Aparicio, Antonio; Skillman, Evan; Monelli, Matteo; Gallart, Carme; Cole, Andrew; Dolphin, Andrew; Weisz, Daniel; Bernard, Edouard J.; Cassisi, Santi; Mayer, Lucio; Stetson, Peter; Tolstoy, Eline; Ferguson, Henry
2011-01-01
We present an analysis of the star formation history (SFH) of the transition-type (dIrr/dSph) Local Group galaxy LGS-3 (Pisces) based on deep photometry obtained with the Advanced Camera for Surveys onboard the Hubble Space Telescope. Our observations reach the oldest main-sequence turnoffs at high
1. The ACS LCID Project. V. The Star Formation History of the Dwarf Galaxy LGS-3: Clues to Cosmic Reionization and Feedback
Hidalgo, Sebastian L.; Aparicio, Antonio; Skillman, Evan; Monelli, Matteo; Gallart, Carme; Cole, Andrew; Dolphin, Andrew; Weisz, Daniel; Bernard, Edouard J.; Cassisi, Santi; Mayer, Lucio; Stetson, Peter; Tolstoy, Eline; Ferguson, Henry
We present an analysis of the star formation history (SFH) of the transition-type (dIrr/dSph) Local Group galaxy LGS-3 (Pisces) based on deep photometry obtained with the Advanced Camera for Surveys onboard the Hubble Space Telescope. Our observations reach the oldest main-sequence turnoffs at high
2. Instabilities in Interacting Binary Stars
Andronov, I. L.; Andrych, K. D.; Antoniuk, K. A.; Baklanov, A. V.; Beringer, P.; Breus, V. V.; Burwitz, V.; Chinarova, L. L.; Chochol, D.; Cook, L. M.; Cook, M.; Dubovský, P.; Godlowski, W.; Hegedüs, T.; Hoňková, K.; Hric, L.; Jeon, Y.-B.; Juryšek, J.; Kim, C.-H.; Kim, Y.; Kim, Y.-H.; Kolesnikov, S. V.; Kudashkina, L. S.; Kusakin, A. V.; Marsakova, V. I.; Mason, P. A.; Mašek, M.; Mishevskiy, N.; Nelson, R. H.; Oksanen, A.; Parimucha, S.; Park, J.-W.; Petrík, K.; Quiñones, C.; Reinsch, K.; Robertson, J. W.; Sergey, I. M.; Szpanko, M.; Tkachenko, M. G.; Tkachuk, L. G.; Traulsen, I.; Tremko, J.; Tsehmeystrenko, V. S.; Yoon, J.-N.; Zola, S.; Shakhovskoy, N. M.
2017-07-01
The types of instability in the interacting binary stars are briefly reviewed. The project “Inter-Longitude Astronomy” is a series of smaller projects on concrete stars or groups of stars. It has no special funds, and is supported from resources and grants of participating organizations, when informal working groups are created. This “ILA” project is in some kind similar and complementary to other projects like WET, CBA, UkrVO, VSOLJ, BRNO, MEDUZA, AstroStatistics, where many of us collaborate. Totally we studied 1900+ variable stars of different types, including newly discovered variables. The characteristic timescale is from seconds to decades and (extrapolating) even more. The monitoring of the first star of our sample AM Her was initiated by Prof. V.P. Tsesevich (1907-1983). Since more than 358 ADS papers were published. In this short review, we present some highlights of our photometric and photo-polarimetric monitoring and mathematical modeling of interacting binary stars of different types: classical (AM Her, QQ Vul, V808 Aur = CSS 081231:071126+440405, FL Cet), asynchronous (BY Cam, V1432 Aql), intermediate (V405 Aql, BG CMi, MU Cam, V1343 Her, FO Aqr, AO Psc, RXJ 2123, 2133, 0636, 0704) polars and magnetic dwarf novae (DO Dra) with 25 timescales corresponding to different physical mechanisms and their combinations (part “Polar”); negative and positive superhumpers in nova-like (TT Ari, MV Lyr, V603 Aql, V795 Her) and many dwarf novae stars (“Superhumper”); eclipsing “non-magnetic” cataclysmic variables(BH Lyn, DW UMa, EM Cyg; PX And); symbiotic systems (“Symbiosis”); super-soft sources (SSS, QR And); spotted (and not spotted) eclipsing variables with (and without) evidence for a current mass transfer (“Eclipser”) with a special emphasis on systems with a direct impact of the stream into the gainer star's atmosphere, which we propose to call “Impactor” (short from “Extreme Direct Impactor”), or V361 Lyr-type stars. Other
3. Influence of x-ray energy spectrum, contrasting detail and detector on the signal-to-noise ratio (SNR) and detective quantum efficiency (DQE) in projection radiography
1992-06-01
A lower limit to patient irradiation in diagnostic radiology is set by the fundamental stochastics of the energy imparted to the image receptor (quantum noise). Image quality is investigated here and expressed in terms of the signal-to-noise ratio due to quantum noise. The Monte Carlo method is used to calculate signal-to-noise ratios (SNR{sub {Delta}S}) and detective quantum efficiencies (DQE{sub {Delta}S}) in imaging thin contrasting details of air, fat, bone and iodine within a water phantom using x-ray spectra (40-140 kV) and detectors of CsI, BaFCl and Gd{sub 2}O{sub 2}S. The atomic composition of the contrasting detail influences considerably the values of SNR{sub {Delta}S} due to the different modulations of the energy spectra of primary photons passing beside and through the contrasting detail. (author).
4. Morning Star
Harris, Mark
2010-01-01
Morning Star comprises a group of paintings and drawings whose imagery derives from photographs of 1960s American hippie communes. The paintings are made using oil paint on linen. Their dimensions vary between 180 x 120, and 228 x 217 centimetres. The drawings are in pencil on watercolour paper and are all 56 x 76 centimetres. The work has been exhibited in conventional form, hanging on gallery walls. For Morning Star I made pencil drawings and oil paintings derived from images in Dick Fa...
5. Dust and Gas in the Magellanic Clouds from the HERITAGE Herschel Key Project. II. Gas-to-Dust Ratio Variations across ISM Phases
Roman-Duval, Julia; Meixner, Margaret; Bot, Caroline; Bolatto, Alberto D; Hughes, Annie; Wong, Tony; Babler, Brian; Bernard, Jean-Philippe; Clayton, Geoffrey; Fukui, Yasuo; Galametz, Maud; Galliano, Frederic; Glover, Simon C O; Hony, Sacha; Israel, Frank; Jameson, Katherine; Lebouteiller, Vianney; Lee, Min-Young; Li, Aigen; Madden, Suzanne C; Misselt, Karl; Montiel, Edward; Okumura, K; Onishi, Toshikazu; Panuzzo, Pasquale; Reach, William; Remy-Ruyer, A; Robitaille, Thomas; Rubio, Monica; Sauvage, Marc; Seale, Jonathan; Sewilo, Marta; Staveley-Smith, Lister; Zhukovska, Svitlana
2014-01-01
The spatial variations of the gas-to-dust ratio (GDR) provide constraints on the chemical evolution and lifecycle of dust in galaxies. We examine the relation between dust and gas at 10-50 pc resolution in the Large and Small Magellanic Clouds (LMC and SMC) based on Herschel far-infrared (FIR), H I 21 cm, CO, and Halpha observations. In the diffuse atomic ISM, we derive the gas-to-dust ratio as the slope of the dust-gas relation and find gas-to-dust ratios of 380+250-130 in the LMC, and 1200+1600-420 in the SMC, not including helium. The atomic-to-molecular transition is located at dust surface densities of 0.05 Mo pc-2 in the LMC and 0.03 Mo pc-2 in the SMC, corresponding to AV ~ 0.4 and 0.2, respectively. We investigate the range of CO-to-H2 conversion factor to best account for all the molecular gas in the beam of the observations, and find upper limits on XCO to be 6x1020 cm-2 K-1 km-1 s in the LMC (Z=0.5Zo) at 15 pc resolution, and 4x 1021 cm-2 K-1 km-1 s in the SMC (Z=0.2Zo) at 45 pc resolution. In the ...
6. Asteroseismology of Pulsating Stars
Santosh Joshi; Yogesh C. Joshi
2015-03-01
The success of helioseismology is due to its capability of measuring -mode oscillations in the Sun. This allows us to extract information on the internal structure and rotation of the Sun from the surface to the core. Similarly, asteroseismology is the study of the internal structure of the stars as derived from stellar oscillations. In this review we highlight the progress in the observational asteroseismology, including some basic theoretical aspects. In particular, we discuss our contributions to asteroseismology through the study of chemically peculiar stars under the 'Nainital-Cape Survey' project being conducted at ARIES, Nainital, since 1999. This survey aims to detect new rapidly-pulsating Ap (roAp) stars in the northern hemisphere. We also discuss the contribution of ARIES towards the asteroseismic study of the compact pulsating variables. We comment on the future prospects of our project in the light of the new optical 3.6-m telescope to be installed at Devasthal (ARIES). Finally, we present a preliminary optical design of the high-speed imaging photometers for this telescope.
7. The Carina project. VII. Toward the breaking of the age-metallicity degeneracy of red giant branch stars using the C {sub U,} {sub B,} {sub I} index
Monelli, M.; Milone, A. P.; Gallart, C.; Aparicio, A. [Instituto de Astrofísica de Canarias, Calle Via Lactea s/n, E-38205 La Laguna, Tenerife (Spain); Fabrizio, M.; Cassisi, S.; Buonanno, R. [Istituto Nazionale di Astrofisica-Osservatorio Astronomico Collurania, Via M. Maggini, I-64100 Teramo (Italy); Bono, G. [Dipartimento di Fisica, Universitá di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Rome (Italy); Stetson, P. B. [Dominion Astrophysical Observatory, NRC-Herzberg, 5071 West Saanich Road, Victoria, BC, V9E 2E7 (Canada); Walker, A. R. [Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, Casilla 603, La Serena (Chile); Nonino, M. [Istituto Nazionale di Astrofisica-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, I-40131 Trieste (Italy); Dall' Ora, M. [INAF—Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, I-80131 Napoli (Italy); Ferraro, I.; Iannicola, G.; Pulone, L. [Istituto Nazionale di Astrofisica-Osservatorio Astronomico di Roma, Via Frascati 33, Monte Porzio Catone, I-00044 Rome (Italy); Thévenin, F., E-mail: monelli@iac.es [Université de Nice Sophia-antipolis, CNRS, Observatoire de la Côte d' Azur, Laboratoire Lagrange, BP 4229, F-06304 Nice (France)
2014-12-01
We present an analysis of photometric and spectroscopic data of the Carina dSph galaxy, testing a new approach similar to that used to disentangle multiple populations in Galactic globular clusters (GCs). We show that a proper color combination is able to separate a significant fraction of the red giant branch (RGB) of the two main Carina populations (the old one, ∼12 Gyr, and the intermediate-age one, 4-8 Gyr). In particular, the c {sub U,} {sub B,} {sub I} = (U – B) – (B – I) pseudo-color allows us to follow the RGB of both populations along a relevant portion of the RGB. We find that the oldest stars have a more negative c {sub U,} {sub B,} {sub I} pseudo-color than intermediate-age ones. We correlate the pseudo-color of RGB stars with their chemical properties, finding a significant trend between the iron content and the c {sub U,} {sub B,} {sub I}. Stars belonging to the old population are systematically more metal-poor ([Fe/H] =–2.32 ± 0.08 dex) than the intermediate-age ones ([Fe/H] =–1.82 ± 0.03 dex). This gives solid evidence of the chemical evolution history of this galaxy, and we have a new diagnostic that can allow us to break the age-metallicity degeneracy of H-burning advanced evolutionary phases. We compared the distribution of stars in the c {sub U,} {sub B,} {sub I} plane with theoretical isochrones, finding that no satisfactory agreement can be reached with models developed in a theoretical framework based on standard heavy element distributions. Finally, we discuss possible systematic differences when compared with multiple populations in GCs.
8. The MEGaN project - I. Missing formation of massive nuclear clusters and tidal disruption events by star clusters-massive black hole interactions
Arca-Sedda, M.; Capuzzo-Dolcetta, R.
2017-10-01
We investigated the evolution of a massive galactic nucleus hosting a supermassive black hole (SMBH) with mass MSMBH = 108 M ⊙ surrounded by a population of 42 heavy star clusters (globular clusters, GCs). Using direct N-body modelling, we show here that the assembly of a nuclear star cluster (NSC) through GC orbital decay and merger is efficiently inhibited by the tidal forces exerted from the SMBH. The GC mass-loss induced by tidal forces causes a significant modification of their mass function, leading to a population of low-mass (model. The simulation produced a huge amount of data, which we used to investigate whether the GC debris deposited around the SMBH can enhance the rate of tidal disruption events (TDEs) in our galaxy inner density distribution. Our results suggest that the GC disruption leads to a TDE rate of ∼2 × 10-4 yr-1, about an order of magnitude larger than observed in galactic nuclei with similar density profiles and central SMBH. Our results suggest that the GC disruption shapes the SMBH neighbourhoods, leading to a TDE rate of ∼2 × 10-4 yr-1, a value slightly larger than what expected in previous theoretical modelling of galaxies with similar density profiles and central SMBHs. The simulation presented here is the first of its kind, representing a massive galactic nucleus and its star cluster population on scales ∼100 pc.
9. The IACOB project: IV. New predictions for high-degree non-radial mode instability domains in massive stars and connection with macroturbulent broadening
Godart, M; Herrero, A; Dupret, M A; Grötsch-Noels, A; Salmon, S J A J; Ventura, P
2016-01-01
Asteroseismology is a powerful tool to access the internal structure of stars. Apart from the important impact of theoretical developments, progress in this field has been commonly associated with the analysis of time-resolved observations. Recently, the so-called macroturbulent broadening has been proposed to be a complementary and less expensive way -- in terms of observational time -- to investigate pulsations in massive stars. We assess to what extent this ubiquitous non-rotational broadening component shaping the line profiles of O stars and B supergiants is a spectroscopic signature of pulsation modes driven by a heat mechanism. We compute stellar main sequence and post-main sequence models from 3 to 70Msun with the ATON stellar evolution code and determine the instability domains for heat-driven modes for degrees l=1-20 using the adiabatic and non-adiabatic codes LOSC and MAD. We use the observational material presented in Sim\\'on-D\\'iaz et al. (2016) to investigate possible correlations between the si...
10. The Carina Project VII: Towards the breaking of the age-metallicity degeneracy of red giant branch stars using the c_UBI index
Monelli, M; Fabrizio, M; Bono, G; Stetson, P B; Walker, A R; Cassisi, S; Gallart, C; Nonino, M; Aparicio, A; Buonanno, R; Dall'Ora, M; Ferraro, I; Iannicola, G; Pulone, L; Thévenin, F
2014-01-01
We present an analysis of photometric and spectroscopic data of the Carina dSph galaxy, testing a new approach similar to that used to disentangle multiple populations in Galactic globular clusters (GCs). We show that a proper colour combination is able to separate a significant fraction of the red giant branch (RGB) of the two main Carina populations (the old one, \\sim 12 Gyr, and the intermediate-age one, 4-8 Gyr). In particular, the c_UBI=(U-B)-(B-I) pseudo-colour allows us to follow the RGB of both populations along a relevant portion of the RGB. We find that the oldest stars have more negative c_UBI pseudo-colour than intermediate-age ones. We correlate the pseudo-colour of RGB stars with their chemical properties, finding a significant trend between the iron content and the c_UBI. Stars belonging to the old population are systematically more metal poor ([Fe/H]=-2.32\\pm0.08 dex) than the intermediate-age ones ([Fe/H]=-1.82\\pm0.03 dex). This gives solid evidence on the chemical evolution history of this g...
11. Experimental Design of a Polymeric Solution to Improve the Mobility Ratio in a Reservoir previous implementation of a pilot project of EOR
Vanessa Cuenca
2016-12-01
Full Text Available This paper describes experimental formulations of polymeric solutions through lab evaluations with the objective of finding optimum solution concentration to fluid mobility in reservoirs as previous step before implementing a pilot project of enhanced oil recovery. The polymers, firstly, were selected based on the properties from fluids from reservoir. Two types of polymers were used TCC-330 and EOR909 and the experimental tests were: thermal stability, compatibility, adsorption, salinity, and displacement. The design with the best results was with polymer TCC-330 at 1,500 ppm concentration.
12. Pulsating stars
Catelan, M?rcio
2014-01-01
The most recent and comprehensive book on pulsating stars which ties the observations to our present understanding of stellar pulsation and evolution theory. Written by experienced researchers and authors in the field, this book includes the latest observational results and is valuable reading for astronomers, graduate students, nuclear physicists and high energy physicists.
13. Stars Underground
Jean Leyder
1996-01-01
An imaginary voyage in time where we were witness of the birth of the universe itself, the time of the Big-Bang 15 billion years ago. Particules from the very first moments of time : protons, neutrons and electrons, and also much more energetic one. These particules are preparing to interact collider and generating others which will be the birth to the stars ........
14. STAR Highlights
Masui, Hiroshi; collaboration, for the STAR
2011-01-01
We report selected results from STAR collaboration at RHIC, focusing on jet-hadron and jet-like correlations, quarkonium suppression and collectivity, di-electron spectrum in both p+p and Au+Au, and higher moments of net-protons as well as azimuthal anisotropy from RHIC Beam Energy Scan program.
15. Evolution of Cold Circumstellar Dust Around Solar-Type Stars
Carpenter, J M; Schreyer, K; Launhardt, R; Henning, T; Carpenter, John M.; Wolf, Sebastian; Schreyer, Katharina; Launhardt, Ralf; Henning, Th.
2004-01-01
We present submillimeter (CSO 350um) and millimeter (SEST 1.2 mm, OVRO 3 mm) photometry for 125 solar-type stars from the FEPS Spitzer Legacy program that have masses between ~0.5 and 2.0 Msun and ages from 3 Myr to 3 Gyr. Continuum emission was detected toward four stars with a signal to noise ratio >= 3: the classical T Tauri stars RX J1842.9-3532, RX J1852.3-3700, and PDS 66 with SEST, and the debris disk system HD 107146 with OVRO. RXJ1842.9-3532 and RXJ1852.3-3700 are located in projection nearby the R CrA molecular cloud with estimated ages of ~10 Myr, while PDS66 is a probable member of the 20 Myr old Lower Centaurus-Crux subgroup of the Sco-Cen OB association. The continuum emission toward these three sources is unresolved at the 24'' SEST resolution and likely originates from circumstellar accretion disks, each with estimated dust masses of ~5x10**-5 Msun. Analysis of the visibility data toward HD107146 (age 80-200 Myr) indicates that the 3 mm continuum emission is centered on the star within the as... 16. Pairing mechanisms for binary stars Kouwenhoven, M B N; Goodwin, S P; Zwart, S F Portegies; Kaper, L; 10.1002/asna.200811061 2008-01-01 Knowledge of the binary population in stellar groupings provides important information about the outcome of the star forming process in different environments. Binarity is also a key ingredient in stellar population studies and is a prerequisite to calibrate the binary evolution channels. In these proceedings we present an overview of several commonly used methods to pair individual stars into binary systems, which we refer to as the pairing function. Many pairing functions are frequently used by observers and computational astronomers, either for the mathematical convenience, or because they roughly describe the expected outcome of the star forming process. We discuss the consequences of each pairing function for the interpretation of observations and numerical simulations. The binary fraction and mass ratio distribution generally depend strongly on the selection of the range in primary spectral type in a sample. These quantities, when derived from a binary survey with a mass-limited sample of target stars, ... 17. DURIP-97 Sodium Guide Star Raman Laser 2007-11-02 now been transferred from our laser development laboratory to the astronomical adaptive optics group where it is being modified for practical applications as a guide star laser. This is a project funded by the Air Force. 18. Hierarchical Star Formation Across Galactic Disks Gouliermis, Dimitrios 2016-09-01 Most stars form in clusters. This fact has emerged from the finding that "embedded clusters account for the 70 - 90% fraction of all stars formed in Giant Molecular Clouds (GMCs)." While this is the case at scales of few 10 parsecs, typical for GMCs, a look at star-forming galaxies in the Local Group (LG) shows significant populations of enormous loose complexes of early-type stars extending at scales from few 100 to few 1000 parsecs. The fact that these stellar complexes host extremely large numbers of loosely distributed massive blue stars implies either that stars form also in an unbound fashion or they are immediately dislocated from their original compact birthplaces or both. The Legacy Extra-Galactic UV Survey (LEGUS) has produced remarkable collections of resolved early-type stars in 50 star-forming LG galaxies, suited for testing ideas about recent star formation. I will present results from our ongoing project on star formation across LEGUS disk galaxies. We characterize the global clustering behavior of the massive young stars in order to understand the morphology of star formation over galactic scales. This morphology appears to be self-similar with fractal dimensions comparable to those of the molecular interstellar medium, apparently driven by large-scale turbulence. Our clustering analysis reveals compact stellar systems nested in larger looser concentrations, which themselves are the dense parts of unbound complexes and super-structures, giving evidence of hierarchical star formation up to galactic scales. We investigate the structural and star formation parameters demographics of the star-forming complexes revealed at various levels of compactness. I will discuss the outcome of our correlation and regression analyses on these parameters in an attempt to understand the link between galactic disk dynamics and morphological structure in spiral and ring galaxies of the local universe. 19. Dust, Gas, and Star Formation in the MBM 18--19 High-Latitude Cloud Complex Larson, Kristen A.; Reed, Cyrus M. Projected on the plane of the sky, the MBM 19 molecular cloud extends from the MBM 18 high-latitude cloud toward the Taurus star-forming regions. We present a new CO(J = 1--0) map of MBM 19 that shows clumpy emission with line intensities above 3 K in some regions despite low, relatively smooth 100 micron emission and modest visual extinction. This map complements data that show extremely high polarization efficiency of dust aligned along the bridge axis and low values of the ratio of total-to-selective extinction throughout the complex. In addition, several ongoing searches for spectral signatures of young stars have found evidence for star formation associated with MBM 18--19. We discuss variation in the molecular gas fraction and dust-to-gas ratio estimates, as well as the implications all these data have for understanding star formation in the region. Results of this study and others like it will provide insight into dust and gas of the translucent interstellar medium and star formation at high galactic latitude. This research was supported by the American Astronomical Society's Small Research Grant Program. 20. The Galactic O-Star Spectroscopic Survey (GOSSS). III. 142 Additional O-type Systems. Maíz Apellániz, J.; Sota, A.; Arias, J. I.; Barbá, R. H.; Walborn, N. R.; Simón-Díaz, S.; Negueruela, I.; Marco, A.; Leão, J. R. S.; Herrero, A.; Gamen, R. C.; Alfaro, E. J. 2016-05-01 This is the third installment of the Galactic O-Star Spectroscopic Survey (GOSSS), a massive spectroscopic survey of Galactic O stars, based on new homogeneous, high signal-to-noise ratio, R ˜ 2500 digital observations selected from the Galactic O-Star Catalog. In this paper, we present 142 additional stellar systems with O stars from both hemispheres, bringing the total of O-type systems published within the project to 590. Among the new objects, there are 20 new O stars. We also identify 11 new double-lined spectroscopic binaries, 6 of which are of O+O type and 5 of O+B type, and an additional new tripled-lined spectroscopic binary of O+O+B type. We also revise some of the previous GOSSS classifications, present some egregious examples of stars erroneously classified as O-type in the past, introduce the use of luminosity class IV at spectral types O4-O5.5, and adapt the classification scheme to the work of Arias et al. The GOSSS spectroscopic data in this article were gathered with five facilities: the 1.5 m Telescope at the Observatorio de Sierra Nevada (OSN), the 2.5 m du Pont Telescope at Las Campanas Observatory (LCO), the 3.5 m Telescope at Calar Alto Observatory (CAHA), and the 4.2 m William Herschel Telescope (WHT) and 10.4 m Gran Telescopio Canarias (GTC) at Observatorio del Roque de los Muchachos (ORM). 1. Far-ultraviolet morphology of star-forming filaments in cool core brightest cluster galaxies Tremblay, G. R.; O'Dea, C. P.; Baum, S. A.; Mittal, R.; McDonald, M. A.; Combes, F.; Li, Y.; McNamara, B. R.; Bremer, M. N.; Clarke, T. E.; Donahue, M.; Edge, A. C.; Fabian, A. C.; Hamer, S. L.; Hogan, M. T.; Oonk, J. B. R.; Quillen, A. C.; Sanders, J. S.; Salomé, P.; Voit, G. M. 2015-08-01 We present a multiwavelength morphological analysis of star-forming clouds and filaments in the central (≲50 kpc) regions of 16 low-redshift (z atlas of star formation locales relative to the ambient hot (˜107-8 K) and warm ionized (˜104 K) gas phases, as well as the old stellar population and radio-bright active galactic nucleus (AGN) outflows. Nearly half of the sample possesses kpc-scale filaments that, in projection, extend towards and around radio lobes and/or X-ray cavities. These filaments may have been uplifted by the propagating jet or buoyant X-ray bubble, or may have formed in situ by cloud collapse at the interface of a radio lobe or rapid cooling in a cavity's compressed shell. The morphological diversity of nearly the entire FUV sample is reproduced by recent hydrodynamical simulations in which the AGN powers a self-regulating rain of thermally unstable star-forming clouds that precipitate from the hot atmosphere. In this model, precipitation triggers where the cooling-to-free-fall time ratio is tcool/tff ˜ 10. This condition is roughly met at the maximal projected FUV radius for more than half of our sample, and clustering about this ratio is stronger for sources with higher star formation rates. 2. ESO VLT laser guide star facility Bonaccini, Domenico; Hackenberg, Wolfgang K.; Cullum, Martin J.; Brunetto, Enzo; Ott, Thomas; Quattri, Marco; Allaert, Eric; Dimmler, Martin; Tarenghi, Massimo; Van Kersteren, A.; Di Chirico, C.; Buzzoni, Bernard; Gray, Peter; Tamai, R.; Tapia, M. 2002-02-01 We report in this paper on the design and progress of the ESO Laser Guide Star Facility. The project will create a user facility embedded in UT4, to produce in the Earth's Mesosphere Laser Guide Stars, which extend the sky coverage of Adaptive Optics systems on the VLT UT4 telescope. Embedded into the project are provisions for multiple LGS to cope with second generation MCAO instruments. 3. Double Star Mission Starts Countdown 2003-01-01 @@ As of July, scientists at the CAS Center for Space Science and Applied Research (CSSAR) have been busy modulating and testing the payloads that will be onboard a space exploration satellite, marking the start of the countdown for China's Double Star Project. 4. Simulating the star tracks in the field of view of the Lunar polar telescope of the ILOM project in dependence on the Lunar dynamical figure Petrova, N.; Gusev, A. 2009-04-01 The measurement of the rotation of the Moon is one of techniques to get the information of the internal structure of celestial body. The Lunar Laser Ranging (LLR) has given unprecedented data on the lunar rotation, and gives some proposals of the state of the core. In situ Lunar Orientation Measurement (ILOM) is an experiment to measure the lunar physical librations in situ on the Moon with a small telescope which tracks stars. Simulating the trajectory of stars due to the lunar rotation observed by the ILOM-telescope in the polar region was already made by using numerical theory DE405 (Noda et al., 2008). We have executed calculations of libration tracks of stars on the basis of analytical libration theory (Petrova, 1996; Chapront et al, 1999). It allowed us to do simulating for various models of Lunar gravity field (Lunar dynamical figure). We used dynamical figures constructed on the basis of data received in the current mission Kaguya (SELENE), and then we compared the results with calculations with other dynamic models constructed on the data obtained by the Clementine (GLGM-2) and the Lunar Prospector (LP150Q). The differences between the models GLGM-2, LP150Q and the Kaguya model are larger than 10 milliseconds of arc. This means that proposed accuracy of ILOM observations - 1 millisecond of arc will be enough to improve many parameters of the Lunar interior. In particular, residual estimations will allow to detect small amplitudes of free libration caused by a liquid Lunar core and to estimate its characteristic, first of all - core's ellipticity. All calculation and comparisons, graphic presentation were executed in the VBA environment for MS Excel. The research was supported by the Russian-Japanese grant RFFI-JSPS N 07-02-91212, (2007 - 2009). 5. Stars and Planets Neta, Miguel 2014-05-01 'Estrelas e Planetas' (Stars and Planets) project was developed during the academic year 2009/2010 and was tested on three 3rd grade classes of one school in Quarteira, Portugal. The aim was to encourage the learning of science and the natural and physical phenomena through the construction and manipulation of materials that promote these themes - in this case astronomy. Throughout the project the students built a small book containing three themes of astronomy: differences between stars and planets, the solar system and the phases of the Moon. To each topic was devoted two sessions of about an hour each: the first to teach the theoretical aspects of the theme and the second session to assembly two pages of the book. All materials used (for theoretical sessions and for the construction of the book) and videos of the finished book are available for free use in www.miguelneta.pt/estrelaseplanetas. So far there is only a Portuguese version but soon will be published in English as well. This project won the Excellency Prize 2011 of Casa das Ciências, a portuguese site for teachers supported by the Calouste Gulbenkian Fundation (www.casadasciencias.org). 6. Pulsating Star Mystery Solved 2010-11-01 By discovering the first double star where a pulsating Cepheid variable and another star pass in front of one another, an international team of astronomers has solved a decades-old mystery. The rare alignment of the orbits of the two stars in the double star system has allowed a measurement of the Cepheid mass with unprecedented accuracy. Up to now astronomers had two incompatible theoretical predictions of Cepheid masses. The new result shows that the prediction from stellar pulsation theory is spot on, while the prediction from stellar evolution theory is at odds with the new observations. The new results, from a team led by Grzegorz Pietrzyński (Universidad de Concepción, Chile, Obserwatorium Astronomiczne Uniwersytetu Warszawskiego, Poland), appear in the 25 November 2010 edition of the journal Nature. Grzegorz Pietrzyński introduces this remarkable result: "By using the HARPS instrument on the 3.6-metre telescope at ESO's La Silla Observatory in Chile, along with other telescopes, we have measured the mass of a Cepheid with an accuracy far greater than any earlier estimates. This new result allows us to immediately see which of the two competing theories predicting the masses of Cepheids is correct." Classical Cepheid Variables, usually called just Cepheids, are unstable stars that are larger and much brighter than the Sun [1]. They expand and contract in a regular way, taking anything from a few days to months to complete the cycle. The time taken to brighten and grow fainter again is longer for stars that are more luminous and shorter for the dimmer ones. This remarkably precise relationship makes the study of Cepheids one of the most effective ways to measure the distances to nearby galaxies and from there to map out the scale of the whole Universe [2]. Unfortunately, despite their importance, Cepheids are not fully understood. Predictions of their masses derived from the theory of pulsating stars are 20-30% less than predictions from the theory of the 7. Parsec-scale Variations in the 7Li i/6Li i Isotope Ratio Toward IC 348 and the Perseus OB 2 Association Knauth, D. C.; Taylor, C. J.; Ritchey, A. M.; Federman, S. R.; Lambert, D. L. 2017-01-01 Measurements of the lithium isotopic ratio in the diffuse interstellar medium from high-resolution spectra of the Li i λ6708 resonance doublet have now been reported for a number of lines of sight. The majority of the results for the 7Li/6Li ratio are similar to the solar system ratio of 12.2, but the line of sight toward o Per, a star near the star-forming region IC 348, gave a ratio of about two, the expected value for gas exposed to spallation and fusion reactions driven by cosmic rays. To examine the association of IC 348 with cosmic rays more closely, we measured the lithium isotopic ratio for lines of sight to three stars within a few parsecs of o Per. One star, HD 281159, has 7Li/6Li ≃ 2 confirming production by cosmic rays. The lithium isotopic ratio toward o Per and HD 281159 together with published analyses of the chemistry of interstellar diatomic molecules suggest that the superbubble surrounding IC 348 is the source of the cosmic rays. Based on observations obtained with the Hobby-Eberly Telescope, which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen. 8. Placing Observational Constraints on Massive Star Models Rosenfield, Philip 2011-10-01 The lives and deaths of massive stars are intricately linked to the evolution of galaxies. Yet, despite their integral importance to understanding galaxy evolution, models of massive stars are inconsistent with observations. These uncertainties can be traced to limited observational constraints available for improving massive star models. A sensitive test of the underlying physics of massive stars, e.g., convection, rotation, and mass loss is to measure the ratio of blue core helium burning stars {BHeB} to red core helium burning stars {RHeB}, 5-20Msun stars in the stage evolution immediately following the main sequence. Even the most sophisticated models cannot accurately predict the observed ratio over a range of metallicities, suggesting an insufficient understanding of the underlying physics. However, observational measurements of this ratio over a wide range of environments would provide substantial constraints on the physical parameters governing the evolution of all stars >5 Msun.We propose to place stringent observational constraints on the physics of massive star evolution by uniformly measuring the B/R HeB ratio in a wide range of galaxies. The HST archive contains high quality optical imaging of resolved stellar populations of dozens of nearby galaxies. From the ANGST program, we identified 38 galaxies, spanning 2 dex in metallicity that have significant BHeB and RHeB populations. Using this sample, we will empirically characterize the colors of the BHeB and RHeB sequences as a function of luminosity and metallicity, measure the B/R ratio, and constrain the lifetimes of the BHeB and RHeBs in the Padova stellar evolution models and the Cambridge STARS code. 9. An Analysis of Cesarean Section and Emergency Hernia Ratios as Markers of Surgical Capacity in Low-Income Countries Affected by Humanitarian Emergencies from 2008 – 2014 at Médecins sans Frontières Operations Centre Brussels Projects Stewart, Barclay; Wong, Evan; Papillon-Smith, Jessica; Trelles Centurion, Miguel Antonio; Dominguez, Lynette; Ao, Supongmeren; Jean-Paul, Basimuoneye Kahutsi; Kamal, Mustafa; Helmand, Rahmatullah; Naseer, Aamer; Kushner, Adam L. 2015-01-01 Background: Surgical capacity assessments in low-income countries have demonstrated critical deficiencies. Though vital for planning capacity improvements, these assessments are resource intensive and impractical during the planning phase of a humanitarian crisis. This study aimed to determine cesarean sections to total operations performed (CSR) and emergency herniorrhaphies to all herniorrhaphies performed (EHR) ratios from Médecins Sans Frontières Operations Centre Brussels (MSF-OCB) projects and examine if these established metrics are useful proxies for surgical capacity in low-income countries affected by crisis. Methods: All procedures performed in MSF-OCB operating theatres from July 2008 through June 2014 were reviewed. Projects providing only specialty care, not fully operational or not offering elective surgeries were excluded. Annual CSRs and EHRs were calculated for each project. Their relationship was assessed with linear regression. Results: After applying the exclusion criteria, there were 47,472 cases performed at 13 sites in 8 countries. There were 13,939 CS performed (29% of total cases). Of the 4,632 herniorrhaphies performed (10% of total cases), 30% were emergency procedures. CSRs ranged from 0.06 to 0.65 and EHRs ranged from 0.03 to 1.0. Linear regression of annual ratios at each project did not demonstrate statistical evidence for the CSR to predict EHR [F(2,30)=2.34, p=0.11, R2=0.11]. The regression equation was: EHR = 0.25 + 0.52(CSR) + 0.10(reason for MSF-OCB assistance). Conclusion: Surgical humanitarian assistance projects operate in areas with critical surgical capacity deficiencies that are further disrupted by crisis. Rapid, accurate assessments of surgical capacity are necessary to plan cost- and clinically-effective humanitarian responses to baseline and acute unmet surgical needs in LICs affected by crisis. Though CSR and EHR may meet these criteria in ‘steady-state’ healthcare systems, they may not be useful during 10. Neutron Star Motion in the Disk Galaxy WEI Ying-Chun; A.Taani; PAN Yuan-Yue; WANG Jing; CAI Yan; LIU Gao-Chao; LUO A-Li; ZHANG Hong-Bo; ZHAO Yong-Heng 2010-01-01 @@ The neutron star motions are based on the undisturbed finitely thick galactic disk gravitational potential model.Two initial conditions,I.e.the locations and velocities,are considered.The Monte Carlo method is employed to separate rich diversities of the orbits of neutron stars into several sorts.The Poincaré section has the potential to play an important role in the diagnosis of the neutron star motion.It has been observed that the increasing ratio of the motion range vertical to the galactic plane to that parallel to the galactic plane results in the irregularity of neutron star motion. 11. Wave Star Kramer, Morten; Frigaard, Peter; Brorsen, Michael Nærværende rapport beskriver foreløbige hovedkonklusioner på modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star i perioden 13/9 2004 til 12/11 2004.......Nærværende rapport beskriver foreløbige hovedkonklusioner på modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star i perioden 13/9 2004 til 12/11 2004.... 12. Stars Just Got Bigger - A 300 Solar Mass Star Uncovered 2010-07-01 Using a combination of instruments on ESO's Very Large Telescope, astronomers have discovered the most massive stars to date, one weighing at birth more than 300 times the mass of the Sun, or twice as much as the currently accepted limit of 150 solar masses. The existence of these monsters - millions of times more luminous than the Sun, losing weight through very powerful winds - may provide an answer to the question "how massive can stars be?" A team of astronomers led by Paul Crowther, Professor of Astrophysics at the University of Sheffield, has used ESO's Very Large Telescope (VLT), as well as archival data from the NASA/ESA Hubble Space Telescope, to study two young clusters of stars, NGC 3603 and RMC 136a in detail. NGC 3603 is a cosmic factory where stars form frantically from the nebula's extended clouds of gas and dust, located 22 000 light-years away from the Sun (eso1005). RMC 136a (more often known as R136) is another cluster of young, massive and hot stars, which is located inside the Tarantula Nebula, in one of our neighbouring galaxies, the Large Magellanic Cloud, 165 000 light-years away (eso0613). The team found several stars with surface temperatures over 40 000 degrees, more than seven times hotter than our Sun, and a few tens of times larger and several million times brighter. Comparisons with models imply that several of these stars were born with masses in excess of 150 solar masses. The star R136a1, found in the R136 cluster, is the most massive star ever found, with a current mass of about 265 solar masses and with a birthweight of as much as 320 times that of the Sun. In NGC 3603, the astronomers could also directly measure the masses of two stars that belong to a double star system [1], as a validation of the models used. The stars A1, B and C in this cluster have estimated masses at birth above or close to 150 solar masses. Very massive stars produce very powerful outflows. "Unlike humans, these stars are born heavy and lose weight as 13. Planck stars Rovelli, Carlo 2014-01-01 A star that collapses gravitationally can reach a further stage of its life, where quantum-gravitational pressure counteracts weight. The duration of this stage is very short in the star proper time, yielding a bounce, but extremely long seen from the outside, because of the huge gravitational time dilation. Since the onset of quantum-gravitational effects is governed by energy density --not by size-- the star can be much larger than planckian in this phase. The object emerging at the end of the Hawking evaporation of a black hole can can then be larger than planckian by a factor(m/m_{\\scriptscriptstyle P})^n$, where$m$is the mass fallen into the hole,$m_{\\scriptscriptstyle P}$is the Planck mass, and$n$is positive. The existence of these objects alleviates the black-hole information paradox. More interestingly, these objects could have astrophysical and cosmological interest: they produce a detectable signal, of quantum gravitational origin, around the$10^{-14} cm$wavelength. 14. Discovery and Precise Characterization by the MEarth Project of LP 661-13, an Eclipsing Binary Consisting of Two Fully Convective Low-mass Stars Dittmann, Jason A; Charbonneau, David; Berta-Thompson, Zachory K; Newton, Elisabeth R; Latham, David W; Latham, Christian A; Esquerdo, Gilbert; Berlind, Perry; Calkins, Michael L 2016-01-01 We report the detection of stellar eclipses in the LP 661-13 system. We present the discovery and characterization of this system, including high resolution spectroscopic radial velocities and a photometric solution spanning two observing seasons. LP 661-13 is a low mass binary system with an orbital period of$4.7043512^{+0.0000013}_{-0.0000010}$days at a distance of$24.9 \\pm 1.3$parsecs. LP 661-13A is a$0.30795 \\pm 0.00084M_\\odot$star while LP 661-13B is a$0.19400 \\pm 0.00034M_\\odot$star. The radius of each component is$0.3226 \\pm 0.0033R_\\odot$and$0.2174 \\pm 0.0023R_\\odot$, respectively. We detect out of eclipse modulations at a period slightly shorter than the orbital period, implying that at least one of the components is not rotating synchronously. We find that each component is slightly inflated compared to stellar models, and that this cannot be reconciled through age or metallicity effects. As a nearby eclipsing binary system where both components are near or below the full-conv... 15. Biofluorescent Worlds: Biological fluorescence as a temporal biosignature for flare star worlds O'Malley-James, Jack T.; Kaltenegger, Lisa 2016-01-01 Habitability for planets orbiting active stars has been questioned. Especially, planets in the Habitable Zone (HZ) of M-stars, like our closest star Proxima Centauri, experience temporal high-ultraviolet (UV) radiation. The high fraction of M-stars (75%) within the solar neighborhood, the high occurrence rate of rocky planets around M-stars, and the favorable contrast ratio between the star and a potentially habitable rocky planet, makes such planets interesting targets for upcoming observati... 16. CAOS spectroscopy of Am stars Kepler targets Catanzaro, G; Biazzo, K; Busa', I; Frasca, A; Leone, F; Giarrusso, M; Munari, M; Scuderi, S 2015-01-01 The {\\it Kepler} space mission and its {\\it K2} extension provide photometric time series data with unprecedented accuracy. These data challenge our current understanding of the metallic-lined A stars (Am stars) for what concerns the onset of pulsations in their atmospheres. It turns out that the predictions of current diffusion models do not agree with observations. To understand this discrepancy, it is of crucial importance to obtain ground-based spectroscopic observations of Am stars in the {\\it Kepler} and {\\it K2} fields in order to determine the best estimates of the stellar parameters. In this paper, we present a detailed analysis of high-resolution spectroscopic data for seven stars previously classified as Am stars. We determine the effective temperatures, surface gravities, projected rotational velocities, microturbulent velocities and chemical abundances of these stars using spectral synthesis. These spectra were obtained with {\\it CAOS}, a new instrument recently installed at the observing station... 17. When efficient star formation drives cluster formation Parmentier, G 2008-01-01 We investigate the impact of the star formation efficiency in cluster forming cores on the evolution of the mass in star clusters over the age range 1-100Myr, when star clusters undergo their infant weight-loss/mortality phase. Assuming a constant formation rate of gas-embedded clusters and a weak tidal field, we show that the ratio between the total mass in stars bound to the clusters over that age range and the total mass in stars initially formed in gas-embedded clusters is a strongly increasing function of the averaged local SFE, with little influence from any assumed core mass-radius relation. Our results suggest that, for young starbursts with estimated tidal field strength and known recent star formation history, observed cluster-to-star mass ratios, once corrected for the undetected clusters, constitute promising probes of the local SFE, without the need of resorting to gas mass estimates. Similarly, the mass ratio of stars which remain in bound clusters at the end of the infant mortality/weight-loss ... 18. The Atlas3D project - XIX. Benchmark for early-type galaxies scaling relations from 260 dynamical models: mass-to-light ratio, dark matter, Fundamental Plane and Virial Plane Cappellari, Michele; Alatalo, Katherine; Blitz, Leo; Bois, Maxime; Bournaud, Frederic; Bureau, M; Crocker, Alison F; Davies, Roger L; Davis, Timothy A; de Zeeuw, P T; Duc, Pierre-Alain; Khochfar, Sadegh; Krajnovic, Davor; Kuntschner, Harald; McDermid, Richard M; Morganti, Raffaella; Naab, Thorsten; Oosterloo, Tom; Sarzi, Marc; Serra, Paolo; Weijmans, Anne-Marie; Young, Lisa M 2013-01-01 We study the volume-limited Atlas3D sample of 260 early-type galaxies. We construct detailed axisymmetric dynamical models, which allow for orbital anisotropy, include a dark matter halo, and reproduce in detail both the galaxy images and the high-quality integral-field stellar kinematics out to about 1Re, the projected half-light radius. We derive accurate total (M/L)_e and dark matter fractions f_DM, within a sphere of radius r=Re. We infer masses M_JAM and stellar (M/L)_stars. We find that the thin two-dimensional subset spanned by galaxies in the (M_JAM,sigma_e,R_e^max) coordinates system, which we call the Virial Plane (VP) has an observed rms scatter of 17%, which would imply an intrinsic one of just 4%. The VP satisfies the scalar virial relation M_JAM=5.0*sigma_e^2 R_e^max/G within our tight errors. However, the details of how both Re and sigma_e are determined are critical in defining the precise deviation from this simple virial form. We measure a median dark matter fractions of f_DM=16% in our samp... 19. DUST AND GAS IN THE MAGELLANIC CLOUDS FROM THE HERITAGE HERSCHEL KEY PROJECT. II. GAS-TO-DUST RATIO VARIATIONS ACROSS INTERSTELLAR MEDIUM PHASES Roman-Duval, Julia; Gordon, Karl D.; Meixner, Margaret [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); Bot, Caroline [Observatoire astronomique de Strasbourg, Université de Strasbourg, CNRS, UMR 7550, 11 rue de l' université, F-67000 Strasbourg (France); Bolatto, Alberto; Jameson, Katherine [Department of Astronomy, Lab for Millimeter-wave Astronomy, University of Maryland, College Park, MD 20742-2421 (United States); Hughes, Annie; Hony, Sacha [Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg (Germany); Wong, Tony [University of Illinois at Urbana-Champaign, 1002 W. Green St., Urbana, IL 61801 (United States); Babler, Brian [Department of Astronomy, University of Wisconsin, 475 North Charter St., Madison, WI 53706 (United States); Bernard, Jean-Philippe [CNRS, IRAP, 9 Av. colonel Roche, BP 44346, F-31028 Toulouse Cedex 4 (France); Clayton, Geoffrey C. [Louisiana State University, Department of Physics and Astronomy, 233-A Nicholson Hall, Tower Dr., Baton Rouge, LA 70803-4001 (United States); Fukui, Yasuo [Department of Physics, Nagoya University, Chikusa-ku, Nagoya 464-8602 (Japan); Galametz, Maud [European Southern Observatory, Karl-Schwarzschild-Str 2, D-85748 Garching (Germany); Galliano, Frederic; Lebouteiller, Vianney; Lee, Min-Young [CEA, Laboratoire AIM, Irfu/SAp, Orme des Merisiers, F-91191 Gif-sur-Yvette (France); Glover, Simon [Zentrum für Astronomie, Institut für Theoretische Astrophysik, Universität Heidelberg, Albert-Ueberle Strasse 2, D-69120 Heidelberg (Germany); Israel, Frank [Sterrewacht Leiden, Leiden University, P.O. Box 9513, NL-2300 RA Leiden (Netherlands); Li, Aigen, E-mail: duval@stsci.edu [314 Physics Building, Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211 (United States); and others 2014-12-20 The spatial variations of the gas-to-dust ratio (GDR) provide constraints on the chemical evolution and lifecycle of dust in galaxies. We examine the relation between dust and gas at 10-50 pc resolution in the Large and Small Magellanic Clouds (LMC and SMC) based on Herschel far-infrared (FIR), H I 21 cm, CO, and Hα observations. In the diffuse atomic interstellar medium (ISM), we derive the GDR as the slope of the dust-gas relation and find GDRs of 380{sub −130}{sup +250} ± 3 in the LMC, and 1200{sub −420}{sup +1600} ± 120 in the SMC, not including helium. The atomic-to-molecular transition is located at dust surface densities of 0.05 M {sub ☉} pc{sup –2} in the LMC and 0.03 M {sub ☉} pc{sup –2} in the SMC, corresponding to A {sub V} ∼ 0.4 and 0.2, respectively. We investigate the range of CO-to-H{sub 2} conversion factor to best account for all the molecular gas in the beam of the observations, and find upper limits on X {sub CO} to be 6 × 10{sup 20} cm{sup –2} K{sup –1} km{sup –1} s in the LMC (Z = 0.5 Z {sub ☉}) at 15 pc resolution, and 4 × 10{sup 21} cm{sup –2} K{sup –1} km{sup –1} s in the SMC (Z = 0.2 Z {sub ☉}) at 45 pc resolution. In the LMC, the slope of the dust-gas relation in the dense ISM is lower than in the diffuse ISM by a factor ∼2, even after accounting for the effects of CO-dark H{sub 2} in the translucent envelopes of molecular clouds. Coagulation of dust grains and the subsequent dust emissivity increase in molecular clouds, and/or accretion of gas-phase metals onto dust grains, and the subsequent dust abundance (dust-to-gas ratio) increase in molecular clouds could explain the observations. In the SMC, variations in the dust-gas slope caused by coagulation or accretion are degenerate with the effects of CO-dark H{sub 2}. Within the expected 5-20 times Galactic X {sub CO} range, the dust-gas slope can be either constant or decrease by a factor of several across ISM phases. Further modeling 20. The Transitional Disks Associated With Herbig Stars Grady, C.; Fukagawa, M.; Maruta, Y.; Ohta, Y.; Wisniewski, J.; Lomax, J.; Hashimoto, J.; Currie, T.; Okamoto, Y.; Momose, M.; McElwain, M. 2015-01-01 As part of the Strategic Exploration of Exoplanets and Disks with Subaru YSO survey, we have surveyed a number of Herbig B-F stars mainly at H-band using Polarimetric Differential Imaging + Angular differential imaging. Historically, Herbig stars have been sorted by the shape of the IR SEDs into those which can be fit by power laws over 1-200 micrometers (Meeus et al. 2001, group II), and those which can be interpreted as a power law + a blackbody component (Meeus group I) or as transitional or pre-transitional disks (Maaskant et al. 2013). Meeus group II disks, when imaged with HiCIAO show featureless disks with depolarization along the projection of the disk semi-minor axis (Kusakabe et al. 2012). This is what we had expected to see for the Meeus group I disks, except for the addition of wide gaps or central cavities. Instead we find wild diversity, suggesting that transitional disks are highly perturbed compared to Meeus group II disks. To date, similar structure continues to be observed as higher Strehl ratio imagery becomes available. 1. Variable Star and Exoplanet Section of the Czech Astronomical Society Brát, L.; Zejda, M. 2010-12-01 We present activities of Czech variable star observers organized in the Variable Star and Exoplanet Section of the Czech Astronomical Society. We work in four observing projects: B.R.N.O. - eclipsing binaries, MEDUZA - intrinsic variable stars, TRESCA - transiting exoplanets and candidates, HERO - objects of high energy astrophysics. Detailed information together with O-C gate (database of eclipsing binaries minima timings) and OEJV (Open European Journal on Variable stars) are available on our internet portal http://var.astro.cz. 2. Chemical abundance analysis of 19 barium stars Yang, G C; Spite, M; Chen, Y Q; Zhao, G; Zhang, B; Liu, G Q; Liu, Y J; Liu, N; Deng, L C; Spite, F; Hill, V; Zhang, C X 2016-01-01 We aim at deriving accurate atmospheric parameters and chemical abundances of 19 barium (Ba) stars, including both strong and mild Ba stars, based on the high signal-to-noise ratio and high resolution Echelle spectra obtained from the 2.16 m telescope at Xinglong station of National Astronomical Observatories, Chinese Academy of Sciences. The chemical abundances of the sample stars were obtained from an LTE, plane-parallel and line-blanketed atmospheric model by inputting the atmospheric parameters (effective temperatures, surface gravities, metallicity and microturbulent velocity) and equivalent widths of stellar absorption lines. These samples of Ba stars are giants indicated by atmospheric parameters, metallicities and kinematic analysis about UVW velocity. Chemical abundances of 17 elements were obtained for these Ba stars. Their light elements (O, Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn and Ni) are similar to the solar abundances. Our samples of Ba stars show obvious overabundances of neutron-capture (n-ca... 3. Parametrising Star Formation Histories Simha, Vimal; Conroy, Charlie; Dave, Romeel; Fardal, Mark; Katz, Neal; Oppenheimer, Benjamin D 2014-01-01 We examine the star formation histories (SFHs) of galaxies in smoothed particle hydrodynamics (SPH) simulations, compare them to parametric models that are commonly used in fitting observed galaxy spectral energy distributions, and examine the efficacy of these parametric models as practical tools for recovering the physical parameters of galaxies. The commonly used tau-model, with SFR ~ exp(-t/tau), provides a poor match to the SFH of our SPH galaxies, with a mismatch between early and late star formation that leads to systematic errors in predicting colours and stellar mass-to-light ratios. A one-parameter lin-exp model, with SFR ~ t*exp(-t/tau), is much more successful on average, but it fails to match the late-time behavior of the bluest, most actively star-forming galaxies and the passive, "red and dead" galaxies. We introduce a 4-parameter model, which transitions from lin-exp to a linear ramp after a transition time, which describes our simulated galaxies very well. We test the ability of these paramet... 4. Massive Stars in the Quintuplet Cluster Figer, D F; Morris, M; Figer, Donald F.; Lean, Ian S. Mc 1999-01-01 We present near-infrared photometry and K-band spectra of newly-identified massive stars in the Quintuplet Cluster, one of the three massive clusters projected within 50 pc of the Galactic Center. We find that the cluster contains a variety of massive stars, including more unambiguously identified Wolf-Rayet stars than any cluster in the Galaxy, and over a dozen stars in earlier stages of evolution, i.e., LBV, Ofpe/WN9, and OB supergiants. One newly identified star is the second Luminous Blue Variable'' in the cluster, after the Pistol Star.'' Given the evolutionary stages of the identified stars, the cluster appears to be about 4 \\pm 1 Myr old, assuming coeval formation. The total mass in observed stars is$\\sim 10^3 \\Msun$, and the implied mass is initial mass function. The implied mass density in stars is at least a few thousand$\\Msun pc^{-3}$. The newly-identified stars increase the estimated ionizing flux from this cluster by about an order of magnitude with respect to earlier estimates, to 10^{50.9... 5. STAR FORMATION IN DENSE CLUSTERS Myers, Philip C., E-mail: pmyers@cfa.harvard.edu [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States) 2011-12-10 A model of core-clump accretion with equally likely stopping describes star formation in the dense parts of clusters, where models of isolated collapsing cores may not apply. Each core accretes at a constant rate onto its protostar, while the surrounding clump gas accretes as a power of protostar mass. Short accretion flows resemble Shu accretion and make low-mass stars. Long flows resemble reduced Bondi accretion and make massive stars. Accretion stops due to environmental processes of dynamical ejection, gravitational competition, and gas dispersal by stellar feedback, independent of initial core structure. The model matches the field star initial mass function (IMF) from 0.01 to more than 10 solar masses. The core accretion rate and the mean accretion duration set the peak of the IMF, independent of the local Jeans mass. Massive protostars require the longest accretion durations, up to 0.5 Myr. The maximum protostar luminosity in a cluster indicates the mass and age of its oldest protostar. The distribution of protostar luminosities matches those in active star-forming regions if protostars have a constant birthrate but not if their births are coeval. For constant birthrate, the ratio of young stellar objects to protostars indicates the star-forming age of a cluster, typically {approx}1 Myr. The protostar accretion luminosity is typically less than its steady spherical value by a factor of {approx}2, consistent with models of episodic disk accretion. 6. Measure of the stars Henbest, N. 1984-12-13 The paper concerns the Hertzsprung-Russel (H-R) diagram, which is graph relating the brightness to the surface temperature of the stars. The diagram provides a deep insight into the fundamental properties of the stars. Evolution of the stars; the death of a star; distances; and dating star clusters, are all briefly discussed with reference to the H-R diagram. 7. When stars collide Glebbeek, E.; Pols, O.R. 2007-01-01 When two stars collide and merge they form a new star that can stand out against the background population in a star cluster as a blue straggler. In so called collision runaways many stars can merge and may form a very massive star that eventually forms an intermediate mass blackhole. We have perfor 8. Theoretical Near-IR Spectra for Surface Abundance Studies of Massive Stars Sonneborn, George; Bouret, J. 2011-01-01 We present initial results of a study of abundance and mass loss properties of O-type stars based on theoretical near-IR spectra computed with state-of-the-art stellar atmosphere models. The James Webb Space Telescope (JWST) will be a powerful tool to obtain high signal-to-noise ratio near-IR (1-5 micron) spectra of massive stars in different environments of local galaxies. Our goal is to analyze model near-IR spectra corresponding to those expected from NIRspec on JWST in order to map the wind properties and surface composition across the parameter range of 0 stars and to determine projected rotational velocities. As a massive star evolves, internal coupling, related mixing, and mass loss impact its intrinsic rotation rate. These three parameters form an intricate loop, where enhanced rotation leads to more mixing which in turn changes the mass loss rate, the latter thus affecting the rotation rate. Since the effects of rotation are expected to be much more pronounced at low metallicity, we pay special attention to models for massive stars in the the Small Magellanic Cloud. This galaxy provides a unique opportunity to probe stellar evolution, and the feedback of massive stars on galactic evol.ution in conditions similar to the epoch of maximal star formation. Plain-Language Abstract: We present initial results of a study of abundance and mass loss properties of massive stars based on theoretical near-infrared (1-5 micron) spectra computed with state-of-the-art stellar atmosphere models. This study is to prepare for observations by the James Webb Space Telescope. 9. On the Star Formation-AGN Connection at zeta (is) approximately greater than 0.3 LaMassa, Stephanie M.; Heckman, T. M.; Ptak, Andrew; Urry, C. Megan 2013-01-01 Using the spectra of a sample of approximately 28,000 nearby obscured active galaxies from Data Release 7 of the Sloan Digital Sky Survey (SDSS), we probe the connection between active galactic nucleus (AGN) activity and star formation over a range of radial scales in the host galaxy. We use the extinction-corrected luminosity of the [O iii] 5007A line as a proxy of intrinsic AGN power and supermassive black hole (SMBH) accretion rate. The star formation rates (SFRs) are taken from the MPA-JHU value-added catalog and are measured through the 3 inch SDSS aperture. We construct matched samples of galaxies covering a range in redshifts. With increasing redshift, the projected aperture size encompasses increasing amounts of the host galaxy. This allows us to trace the radial distribution of star formation as a function of AGN luminosity. We find that the star formation becomes more centrally concentrated with increasing AGN luminosity and Eddington ratio. This implies that such circumnuclear star formation is associated with AGN activity, and that it increasingly dominates over omnipresent disk star formation at higher AGN luminosities, placing critical constraints on theoretical models that link host galaxy star formation and SMBH fueling. We parameterize this relationship and find that the star formation on radial scales (is) less than 1.7 kpc, when including a constant disk component, has a sub-linear dependence on SMBH accretion rate: SFR in proportion to solar mass(sup 0.36), suggesting that angular momentum transfer through the disk limits accretion efficiency rather than the supply from stellar mass loss. 10. An infrared study of Be stars based on ISO SWS01 spectra Pin Zhang; Zai-Qi Fu 2009-01-01 The Infrared Space Observatory (ISO) Short-Wavelength Spectrometer (SWS) spectra of 10 Be stars are presented. It can be seen that the Be stars show a diversity in their ISO SWS01 spectral classifications by Kraemer et al., from naked stars, stars associated with dust, stars with warm dust shells, stars with cool dust shells to very red sources. In addition, the Brc/HI(14-6) line flux ratio derived for the sample stars is compared with that of P Cyg, and it is found that the line ratio of Be stars which were investigated show not only lower values as suggested by Waters et al., but also larger values. Therefore, the line ratio cannot he used to judge whether a star is a Be star or not. 11. High T physics at STAR Subhasis Chattopadhyay 2003-05-01 We discuss the capabilities of STAR in exploring the physics at high T in ultrarelativistic heavy-ion colisions from RHIC at$\\sqrt{S_{NN}}=130$GeV. Preliminary results show that the spectra of negatively charged particles get suppressed at larger T in comparison to$p\\overline{p}$data. A strong azimuthal anisotropy observed at large transverse momentum region. A preliminary ratio$\\overline{p}=p$has been measured by STAR-RICH detector. Some ongoing studies and future plans are discussed. 12. The role of low-mass star clusters in massive star formation. The Orion Case Rivilla, V M; Jimenez-Serra, I; Rodriguez-Franco, A 2013-01-01 To distinguish between the different theories proposed to explain massive star formation, it is crucial to establish the distribution, the extinction, and the density of low-mass stars in massive star-forming regions. We analyze deep X-ray observations of the Orion massive star-forming region using the Chandra Orion Ultradeep Project (COUP) catalog. We studied the stellar distribution as a function of extinction, with cells of 0.03 pc x 0.03 pc, the typical size of protostellar cores. We derived stellar density maps and calculated cluster stellar densities. We found that low-mass stars cluster toward the three massive star-forming regions: the Trapezium Cluster (TC), the Orion Hot Core (OHC), and OMC1-S. We derived low-mass stellar densities of 10^{5} stars pc^{-3} in the TC and OMC1-S, and of 10^{6} stars pc^{-3} in the OHC. The close association between the low-mass star clusters with massive star cradles supports the role of these clusters in the formation of massive stars. The X-ray observations show for ... 13. Dynamical ejections of massive stars from young star clusters under diverse initial conditions Oh, Seungkyung; Kroupa, Pavel 2016-05-01 segregation. When a large kinematic survey of massive field stars becomes available, for instance through Gaia, our results may be used to constrain the birth configuration of massive stars in star clusters. The results presented here, however, already show that the birth mass-ratio distribution for O-star primaries must be near uniform for mass ratios q ≳ 0.1. 14. The Rb problem in massive AGB stars. Pérez-Mesa, V.; García-Hernández, D. A.; Zamora, O.; Plez, B.; Manchado, A.; Karakas, A. I.; Lugaro, M. 2017-03-01 The asymptotic giant branch (AGB) is formed by low- and intermediate-mass stars (0.8 M_{⊙} develop thermal pulses (TP) and suffer extreme mass loss. AGB stars are the main contributor to the enrichment of the interstellar medium (ISM) and thus to the chemical evolution of galaxies. In particular, the more massive AGB stars (M > 4 M_{⊙}) are expected to produce light (e.g., Li, N) and heavy neutron-rich s-process elements (such as Rb, Zr, Ba, Y, etc.), which are not formed in lower mass AGB stars and Supernova explosions. Classical chemical analyses using hydrostatic atmospheres revealed strong Rb overabundances and high [Rb/Zr] ratios in massive AGB stars of our Galaxy and the Magellanic Clouds (MC), confirming for the first time that the ^{22}Ne neutron source dominates the production of s-process elements in these stars. The extremely high Rb abundances and [Rb/Zr] ratios observed in the most massive stars (specially in the low-metallicity MC stars) uncovered a Rb problem; such extreme Rb and [Rb/Zr] values are not predicted by the s-process AGB models, suggesting fundamental problems in our present understanding of their atmospheres. We present more realistic dynamical model atmospheres that consider a gaseous circumstellar envelope with a radial wind and we re-derive the Rb (and Zr) abundances in massive Galactic AGB stars. The new Rb abundances and [Rb/Zr] ratios derived with these dynamical models significantly resolve the problem of the mismatch between the observations and the theoretical predictions of the more massive AGB stars. 15. Multiplicity in 5 Msun Stars Evans, Nancy Remage 2011-01-01 Multiwavelength opportunities have provided important new insights into the properties of binary/multiple 5 Msun stars. The combination of cool evolved primaries and hot secondaries in Cepheids (geriatric B stars) has yielded detailed information about the distribution of mass ratios. It has also provided a surprisingly high fraction of triple systems. Ground-based radial velocity orbits combined with satellite data from Hubble, FUSE, IUE, and Chandra can provide full information about the systems, including the masses. In particular, X-ray observations can identify low mass companions which are young enough to be physical companions. These multiwavelength observations provide important tests for star formation scenarios including diffenences between high and low mass results and differences between close and wide binaries. 16. The Stars behind the Curtain 2010-02-01 still growing into stars, newborn stars, adult stars and stars nearing the end of their life. All these stars have roughly the same age, a million years, a blink of an eye compared to our five billion year-old Sun and Solar System. The fact that some of the stars have just started their lives while others are already dying is due to their extraordinary range of masses: high-mass stars, being very bright and hot, burn through their existence much faster than their less massive, fainter and cooler counterparts. The newly released image, obtained with the FORS instrument attached to the VLT at Cerro Paranal, Chile, portrays a wide field around the stellar cluster and reveals the rich texture of the surrounding clouds of gas and dust. Notes [1] The star, NGC 3603-A1, is an eclipsing system of two stars orbiting around each other in 3.77 days. The most massive star has an estimated mass of 116 solar masses, while its companion has a mass of 89 solar masses. More information ESO, the European Southern Observatory, is the foremost intergovernmental astronomy organisation in Europe and the world's most productive astronomical observatory. It is supported by 14 countries: Austria, Belgium, the Czech Republic, Denmark, France, Finland, Germany, Italy, the Netherlands, Portugal, Spain, Sweden, Switzerland and the United Kingdom. ESO carries out an ambitious programme focused on the design, construction and operation of powerful ground-based observing facilities enabling astronomers to make important scientific discoveries. ESO also plays a leading role in promoting and organising cooperation in astronomical research. ESO operates three unique world-class observing sites in Chile: La Silla, Paranal and Chajnantor. At Paranal, ESO operates the Very Large Telescope, the world's most advanced visible-light astronomical observatory and VISTA, the largest survey telescope. ESO is the European partner of a revolutionary astronomical telescope ALMA, the largest astronomical project in 17. On the radial profile of gas-phase Fe/α ratio around distant galaxies Zahedy, Fakhri S.; Chen, Hsiao-Wen; Gauthier, Jean-René; Rauch, Michael 2017-04-01 This paper presents a study of the chemical compositions in cool gas around a sample of 27 intermediate-redshift galaxies. The sample comprises 13 massive quiescent galaxies at z = 0.40-0.73 probed by QSO sightlines at projected distances d = 3-400 kpc, and 14 star-forming galaxies at z = 0.10-1.24 probed by QSO sightlines at d = 8-163 kpc. The main goal of this study is to examine the radial profiles of the gas-phase Fe/α ratio in galaxy haloes based on the observed Fe II to Mg II column density ratios. Because Mg+ and Fe+ share similar ionization potentials, the relative ionization correction is small in moderately ionized gas and the observed ionic abundance ratio N(Fe II)/N(Mg II) places a lower limit to the underlying (Fe/Mg) elemental abundance ratio. For quiescent galaxies, a median and dispersion of log _med= -0.06± 0.15 is found at d ≲ 60 kpc, which declines to log _med = -0.25± 0.21 at d ≲ 60 kpc and log = -0.9± 0.4 at larger distances. Including possible differential dust depletion or ionization correction would only increase the inferred (Fe/Mg) ratio. The observed N(Fe II)/N(Mg II) implies supersolar Fe/α ratios in the inner halo of quiescent galaxies. An enhanced Fe abundance indicates a substantial contribution by Type Ia supernovae in the chemical enrichment, which is at least comparable to what is observed in the solar neighbourhood or in intracluster media but differs from young star-forming regions. In the outer haloes of quiescent galaxies and in haloes around star-forming galaxy, however, the observed N(Fe II)/N(Mg II) is consistent with an α-element enhanced enrichment pattern, suggesting a core-collapse supernovae dominated enrichment history. 18. GEOMETRY OF STAR-FORMING GALAXIES FROM SDSS, 3D-HST, AND CANDELS Van der Wel, A.; Chang, Yu-Yen; Rix, H.-W.; Martig, M. [Max-Planck Institut für Astronomie, Königstuhl 17, D-69117, Heidelberg (Germany); Bell, E. F. [Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI 48109 (United States); Holden, B. P.; Koo, D. C.; Mozena, M.; Faber, S. M. [UCO/Lick Observatory, Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064 (United States); Ferguson, H. C.; Brammer, G.; Kassin, S. A. [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); Giavalisco, M. [Astronomy Department, University of Massachusetts, Amherst, MA 01003 (United States); Skelton, R. [South African Astronomical Observatory, P.O. Box 9, Observatory 7935 (South Africa); Whitaker, K. [Astrophysics Science Division, Goddard Space Center, Greenbelt, MD 20771 (United States); Momcheva, I.; Van Dokkum, P. G. [Department of Astronomy, Yale University, New Haven, CT 06511 (United States); Dekel, A. [Center for Astrophysics and Planetary Science, Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel); Ceverino, D. [Department of Theoretical Physics, Universidad Autonoma de Madrid, E-28049 Madrid (Spain); Franx, M., E-mail: vdwel@mpia.de [Leiden Observatory, Leiden University, P.O. Box 9513, NL-2300 AA Leiden (Netherlands); and others 2014-09-01 We determine the intrinsic, three-dimensional shape distribution of star-forming galaxies at 0 < z < 2.5, as inferred from their observed projected axis ratios. In the present-day universe, star-forming galaxies of all masses 10{sup 9}-10{sup 11} M {sub ☉} are predominantly thin, nearly oblate disks, in line with previous studies. We now extend this to higher redshifts, and find that among massive galaxies (M {sub *} > 10{sup 10} M {sub ☉}) disks are the most common geometric shape at all z ≲ 2. Lower-mass galaxies at z > 1 possess a broad range of geometric shapes: the fraction of elongated (prolate) galaxies increases toward higher redshifts and lower masses. Galaxies with stellar mass 10{sup 9} M {sub ☉} (10{sup 10} M {sub ☉}) are a mix of roughly equal numbers of elongated and disk galaxies at z ∼ 1 (z ∼ 2). This suggests that galaxies in this mass range do not yet have disks that are sustained over many orbital periods, implying that galaxies with present-day stellar mass comparable to that of the Milky Way typically first formed such sustained stellar disks at redshift z ∼ 1.5-2. Combined with constraints on the evolution of the star formation rate density and the distribution of star formation over galaxies with different masses, our findings imply that, averaged over cosmic time, the majority of stars formed in disks. 19. The Galactic O-Star Spectroscopic Survey (GOSSS). III. 142 additional O-type systems Apellániz, J Maíz; Arias, J I; Barbá, R H; Walborn, N R; Simón-Díaz, S; Negueruela, I; Marco, A; Leão, J R S; Herrero, A; Gamen, R C; Alfaro, E J 2016-01-01 This is the third installment of GOSSS, a massive spectroscopic survey of Galactic O stars, based on new homogeneous, high signal-to-noise ratio, R~2500 digital observations selected from the Galactic O-Star Catalog (GOSC). In this paper we present 142 additional stellar systems with O stars from both hemispheres, bringing the total of O-type systems published within the project to 590. Among the new objects there are 20 new O stars. We also identify 11 new double-lined spectroscopic binaries (SB2s), of which 6 are of O+O type and 5 of O+B type, and an additional new tripled-lined spectroscopic binary (SB3) of O+O+B type. We also revise some of the previous GOSSS classifications, present some egregious examples of stars erroneously classified as O-type in the past, introduce the use of luminosity class IV at spectral types O4-O5.5, and adapt the classification scheme to the work of Arias et al. (2016). 20. A probable pre-main sequence chemically peculiar star in the open cluster Stock 16 Netopil, M; Paunzen, E; Zwintz, K; Pintado, O I; Bagnulo, S 2014-01-01 We used the Ultraviolet and Visual Echelle Spectrograph of the ESO-Very Large Telescope to obtain a high resolution and high signal-to-noise ratio spectrum of Stock 16-12, an early-type star which previous Delta-a photometric observations suggest being a chemically peculiar (CP) star. We used spectral synthesis to perform a detailed abundance analysis obtaining an effective temperature of 8400 +/- 400 K, a surface gravity of 4.1 +/- 0.4, a microturbulence velocity of 3.4 +0.7/-0.3 km/s, and a projected rotational velocity of 68 +/- 4 km/s. We provide photometric and spectroscopic evidence showing the star is most likely a member of the young Stock 16 open cluster (age 3-8 Myr). The probable cluster membership, the star's position in the Hertzsprung-Russell diagram, and the found infrared excess strongly suggest the star is still in the pre-main-sequence (PMS) phase. We used PMS evolutionary tracks to determine the stellar mass, which ranges between 1.95 and 2.3 Msun, depending upon the adopted spectroscopic o... 1. The lack of carbon stars in the Galactic bulge Zhu Chun-Hua; Lv Guo-Liang; Wang Zhao-Jun; Zhang Jun 2008-01-01 In order to explain the lack of carbon stars in the Galactic bulge, we have made a detailed study of thermal pulseasymptotic giant branch (TP-AGB) stars by using a population synthesis code. The effects of the oxygen overabundance and the mass loss rate on the ratio of the number of carbon stars to that of oxygen stars in the Galactic bulge are discussed. We find that the oxygen overabundance which is about twice as large as that in the solar neighbourhood (close to the present observations) is insufficient to explain the rareness of carbon stars in the bulge. We suggest that the large mass loss rate may serve as a controlling factor in the ratio of the number of carbon stars to that of oxygen stars. 2. Hysteresis Effect in the Activity Indices of the Atmospheres of the Sun and Solar-Type Stars During the Rising and Falling Phases of Cycles Bruevich, E. A.; Yakunina, G. V. 2016-09-01 The hysteresis effect that shows up as a nonunique relationship among the emissions from the photosphere, chromosphere, and corona during the rising and falling phases of solar and stellar activity is analyzed. The following solar indices are analyzed and compared in different phases of the cycle: the radiative flux in the hydrogen Lyman alpha line FLα, radio emission at 10.7 cm F10.7, the sunspot number SSN, the radiative flux in the 530.0 nm green coronal line F530.3, the solar constant TSI, and the relative flux ratio c/w (ratio of the fluxes in the center and in the wings) for the 280 nm Mg II line. In stars with cycles, a hysteresis effect is observed between the CaII chromospheric S-activity index for stars in the Mount Wilson HK project and the photospheric flux Fph for these stars. 3. Ratio of Circulating IFNγ (+) "Th17 Cells" in Memory Th Cells Is Inversely Correlated with the Titer of Anti-CCP Antibodies in Early-Onset Rheumatoid Arthritis Patients Based on Flow Cytometry Methods of the Human Immunology Project. Kotake, Shigeru; Nanke, Yuki; Yago, Toru; Kawamoto, Manabu; Kobashigawa, Tsuyoshi; Yamanaka, Hisashi 2016-01-01 Rheumatoid arthritis (RA) is a systemic autoimmune disease with chronic joint inflammation characterized by activated T cells. IL-17 and Th17 cells play important roles in the pathogenesis of RA. Recently, plasticity in helper T cells has been demonstrated; Th17 cells can convert to Th1 cells. However, it remains to be elucidated whether this conversion occurs in the early phase of RA. Here, we validated the methods of the Human Immunology Project using only the cell-surface marker through measuring the actual expression of IL-17 and IFNγ. We also evaluated the expression of CD161 in human Th17 cells. We then tried to identify Th17 cells, IL-17(+)Th17 cells, and IFNγ (+)Th17 cells in the peripheral blood of early-onset RA patients using the standardized method of the Human Immunology Project. Our findings validated the method and the expression of CD161. The ratio of IFNγ (+)Th17 cells in memory T cells was inversely correlated to the titers of anti-CCP antibodies in the early-onset RA patients. These findings suggest that Th17 cells play important roles in the early phase of RA and that anti-IL-17 antibodies should be administered to patients with early phase RA, especially those with high titers of CCP antibodies. 4. A Vanishing Star Revisited 1999-07-01 during the first partial phase. The star is clearly visible at a constant level all through the total phase at minimum light. It then brightens during the second partial phase and is back to the former level after approximately 10.5 min. The FORS1 instrument was rotated by about 70° to ensure that the trail of NN Ser would not overlap those of the neighbouring stellar images during this special exposure. The field shown measures 2.7 x 2.7 armin 2 and may be compared with that shown in Photo 30a/99; it has the same orientation. Caption to ESO PR Photo 30c/99 : The light-curve of the variable stellar system NN Ser , as extracted from the drift exposure shown in Photo 30b/99 . The count rate is proportional to the brightness of the object; it is about 18,000 counts/pix outside the eclipse and decreases to about 70 counts during the total eclipse (since the full range of the eclipse is shown here, this low level is almost indistinguishable from 0 in this figure). Various properties of the two stars in the NN Ser system may be determined from the shape of the light-curve. The fact that the light-curve is "flat" at the bottom is a clear sign that the eclipse is total , i.e. the hot white dwarf star is completely hidden behind the cool red dwarf star. As ESO PR Photo 30b/99 shows, ANTU and FORS1 did manage this difficult observation! Aided by an excellent seeing of 0.5 arcsec, i.e. a good concentration of the light on each pixel, the recorded signal from NN Ser - although very faint - is well measurable at all times during the eclipse . In the mean, about 70 counts/pixel were registered at the minimum, down from about 18,000 outside the eclipse ( Photo 30c/99 ). The ratio is then about 250, corresponding to just over 6 magnitudes. The measured magnitude during eclipse is 23.0 in the V-band (green-yellow; wavelength 550 nm). Of even greater importance is the fact that the light-curve is found to be perfectly flat at the bottom, i.e. the eclipse is most certainly total . The 5. Q+: characterizing the structure of young star clusters Jaffa, S. E.; Whitworth, A. P.; Lomax, O. 2017-04-01 Many young star clusters appear to be fractal, i.e. they appear to be concentrated in a nested hierarchy of clusters within clusters. We present a new algorithm for statistically analysing the distribution of stars to quantify the level of substructure. We suggest that, even at the simplest level, the internal structure of a fractal cluster requires the specification of three parameters. (i) The 3D fractal dimension, D, measures the extent to which the clusters on one level of the nested hierarchy fill the volume of their parent cluster. (ii) The number of levels, L, reflects the finite ratio between the linear size of the large root-cluster at the top of the hierarchy, and the smallest leaf-clusters at the bottom of the hierarchy. (iii) The volume-density scaling exponent, C = -d ln [δ n]/d ln [L] measures the factor by which the excess density, δn, in a structure of scale L, exceeds that of the background formed by larger structures; it is similar, but not exactly equivalent, to the exponent in Larson's scaling relation between density and size for molecular clouds. We describe an algorithm that can be used to constrain the values of (D,L,C) and apply this method to artificial and observed clusters. We show that this algorithm is able to reliably describe the three-dimensional structure of an artificial star cluster from the two-dimensional projection, and quantify the varied structures observed in real and simulated clusters. 6. Can strange stars mimic dark energy stars? Deb, Debabrata; Guha, B K; Ray, Saibal 2016-01-01 The possibility of strange stars mixed with dark energy to be one of candidates for dark energy stars is the main issue of the present study. Our investigation shows that quark matter is acting as dark energy after certain yet unknown critical condition inside the quark stars. Our proposed model reveals that strange stars mixed with dark energy feature not only a physically acceptable stable model but also mimic characteristics of dark energy stars. The plausible connections are shown through the mass-radius relation as well as the entropy and temperature. We particulary note that two-fluid distribution is the major reason for anisotropic nature of the spherical stellar system. 7. VLT laser guide star facility Bonaccini, Domenico; Allaert, Eric; Araujo, Constanza; Brunetto, Enzo; Buzzoni, Bernard; Comin, Mauro; Cullum, Martin J.; Davies, Richard I.; Dichirico, Canio; Dierickx, Philippe; Dimmler, Martin; Duchateau, Michel; Egedal, Carsten; Hackenberg, Wolfgang K. P.; Hippler, Stefan; Kellner, Stefan; van Kesteren, Arno; Koch, Franz; Neumann, Udo; Ott, Thomas; Quattri, Marco; Quentin, Jutta; Rabien, Sebastian; Tamai, Roberto; Tapia, Mario; Tarenghi, Massimo 2003-02-01 We report on the ongoing VLT Laser Guide Star Facility project, which will allow the ESO UT4 telescope to produce an artificial reference star for the Adaptive Optics systems NAOS-CONICA and SINFONI. A custom developed dye laser producing >10W CW at 589nm is installed on-board of the UT4 telescope, then relayed by means of a single mode optical fiber behind the secondary mirror, where a 500mm diameter lightweight, f/1 launch telescope is projecting the laser beam at 90 km altitude. We described the design tradeoffs and provide some details of the chosen subsystems. This paper is an update including subsystems results, to be read together with our previous paper on LGSF design description. 8. Lifestyles of the Stars. National Aeronautics and Space Administration, Cocoa Beach, FL. John F. Kennedy Space Center. Some general information on stars is provided in this National Aeronautics and Space Administration pamphlet. Topic areas briefly discussed are: (1) the birth of a star; (2) main sequence stars; (3) red giants; (4) white dwarfs; (5) neutron stars; (6) supernovae; (7) pulsars; and (8) black holes. (JN) 9. A new search for R Coronae Borealis stars in the SMC Nikzat, Fatemeh; Catelan, Márcio 2017-09-01 R Coronae Borealis (RCB) stars are rare, and their evolutionary origin is not well understood. Since they are obscured due to formation of carbon dust around the star during their mass loss events, RCB stars can be classified as self-eclipsing variable stars. The purpose of this work is to present a new search for RCB stars in the Small Magellanic Cloud (SMC), by analysing VI data from the OGLE project. 10. Carbon and oxygen isotopic ratios for nearby miras Hinkle, K H; Straniero, O 2016-01-01 C and O isotopic ratios are reported for a sample of 46 Mira and SRa-type variable AGB stars. Vibration-rotation 1st and 2nd overtone CO lines in 1.5 to 2.5$\\mum spectra were measured to derive isotopic ratios for 12C/13C, 16O/17O, and 16O/18O. Comparisons with previous measurements for individual stars and with various samples of evolved stars are discussed. Models for solar composition AGB stars of different initial masses are used to interpret our results. We find that the majority of the M stars had main sequence masses < 2 Msun and have not experienced sizable third dredge-up episodes. The progenitors of the four S-type stars in our sample are slightly more massive. Of the 6 C stars in the sample three have clear evidence relating their origin to the occurrence of the third dredge-up. Comparisons with O-rich presolar grains from AGB stars that lived before the formation of the solar system reveal variations in the interstellar medium chemical composition. The present generation of low-mass AGB stars... 11. Variable Star Astronomy Education & Public Outreach Initiative Young, Donna L. 2008-05-01 The American Association of Variable Star Observers (AAVSO) published a comprehensive variable star curriculum, "Hands-On Astrophysics, Variable Stars in Science, Math, and Computer Education" in 1997. The curriculum, funded by the National Science Foundation, was developed for a comprehensive audience -- amateur astronomers, classroom educators, science fair projects, astronomy clubs, family learning, and anyone interested in learning about variable stars. Some of the activities from the Hands-On Astrophysics curriculum have been incorporated into the educational materials for the Chandra X-Ray Observatory's Educational and Public Outreach (EPO) Office. On two occasions, in 2000 and 2001, triggered by alerts from amateur astronomers, Chandra observed the outburst of the dwarf nova SS Cygni. The cooperation of amateur variable star astronomers and Chandra X-Ray scientists provided proof that the collaboration of amateur and professional astronomers is a powerful tool to study cosmic phenomena. Once again, the Chandra and AAVSO have teamed up -- this time to promote variable star education. The Hands-On Astrophysics curriculum is being re-designed and updated from the original materials to a web-based format. The new version, re-named Variable Star Astronomy, will provide formal and informal educators, and especially amateur astronomers, educational materials to help promote interest in and knowledge of variable stars. 12. On the radial profile of gas-phase Fe/{\\alpha} ratio around distant galaxies Zahedy, Fakhri S; Gauthier, Jean-René; Rauch, Michael 2016-01-01 This paper presents a study of the chemical compositions in cool gas around a sample of 27 intermediate-redshift galaxies. The sample comprises 13 massive quiescent galaxies at z=0.40-0.73 probed by QSO sightlines at projected distances d=3-400 kpc, and 14 star-forming galaxies at z=0.10-1.24 probed by QSO sightlines at d=8-163 kpc. The main goal of this study is to examine the radial profiles of the gas-phase Fe/{\\alpha} ratio in galaxy halos based on the observed Fe II to Mg II column density ratios. Because Mg+ and Fe+ share similar ionization potentials, the relative ionization correction is small in moderately ionized gas and the observed ionic abundance ratio N(Fe II)/N(Mg II) places a lower limit to the underlying (Fe/Mg) elemental abundance ratio. For quiescent galaxies, a median and dispersion of log =-0.06+/-0.15 is found at d ~100 kpc. On the other hand, star-forming galaxies exhibit log =-0.25+/-0.21 at d =-0.9+/-0.4 at larger distances. Including possible differential dust depletion or ionizati... 13. The Cambridge Double Star Atlas MacEvoy, Bruce; Tirion, Wil 2015-12-01 Preface; What are double stars?; The binary orbit; Double star dynamics; Stellar mass and the binary life cycle; The double star population; Detecting double stars; Double star catalogs; Telescope optics; Preparing to observe; Helpful accessories; Viewing challenges; Next steps; Appendices: target list; Useful formulas; Double star orbits; Double star catalogs; The Greek alphabet. 14. Enigma of Runaway Stars Solved 1997-01-01 . In fact, this is one of the most perfect' bow shocks of parabolic form ever observed around an OB-runaway. Moreover, the orientation of the bow shock indicates that the system is moving towards the north; its origin must therefore lie somewhere south of its present position in the sky. It also turns out that the accordingly deduced path of HD77581 crosses a well-known OB-association with the designation Vel OB1 . At the measured distance of Vel OB1 of about 6000 lightyears, the observed proper motion and radial velocity of HD77581 indicate a space velocity of 90 km/sec. With this velocity, it would have taken HD77581 and its compact companion about 2.5 million years to travel the distance between Vel OB1 and its present position. This corresponds exactly to the expected time that has passed since the supernova explosion of the progenitor star of Vela~X-1, as deduced from the observed properties of the binary system. The puzzle comes together Now everything fits! The observation of a bow shock around the OB star HD77581 and its compact companion Vela X-1 supports the scenario originally proposed by Blaauw to create OB-runaway stars by the supernova explosion of the binary companion. Following back the path of the system resulted in the discovery of the place where it was born and from where it escaped after the violent supernova explosion which produced the neutron star that now manifests itself as the strong X-ray source known as Vela X-1. More information about this research project This research project is described in ESO Preprint no.~1199 and will appear shortly as a Letter to the Editor in Astrophysical Journal' (ApJ 475, L37-L40). Notes: [1] Professor Adriaan Blaauw is a well-known Dutch astronomer (Leiden and Groningen). He participated very actively in the build-up of ESO in the 1950's and 60's and he was ESO Director General from 1970 - 1974. He is the author of ESO's Early History - The European Southern Observatory from concept to reality ' (1991). [2 15. Unexplained Brightening of Unusual Star 1997-01-01 particular, with just two exceptions, its orbital period is longer than those of all 150 such systems known. Yet another possibility would be the nova phenomenon which is due to a sudden nuclear explosion in the atmosphere of the white dwarf. But in such cases, the brightness increase is much larger than observed here. Future investigations Consequently, it is at this moment not yet possible to understand the nature of the observed brightening of the AKO 9 binary system. Although it is one of the best observed close binary systems within any globular cluster, the available observations will have to be complemented during future investigations before the responsible mechanism may be identified. More information about this research project A provisional report about this work will be presented on January 15, 1997, at the semi-annual meeting of the American Astronomical Association in Toronto, Canada. Notes: [1] The group consists of Georges Meylan (ESO, Garching, Germany), Dante Minniti (Lawrence Livermore National Laboratory, Livermore, USA), Carlton Pryor (Rutgers Univ., Piscataway, USA), E. Sterl Phinney (Caltech, Pasadena, USA), Bruce Sams (Max-Planck-Institut für Extraterrestrische Physik, Garching, Germany), Chris G. Tinney (Anglo-Australian Observatory, Epping, Australia). [2] The phenomenon of core collapse is reminiscent of the red-giant phase' of stellar evolution when - towards the end of its life - the outer layers of a star begin to expand while its central regions contract. [3] This corresponds to 10 6 stars/pc 3 and 0.1 stars/pc 3 , respectively. How to obtain ESO Press Information ESO Press Information is made available on the World-Wide Web (URL: http://www.eso.org../). ESO Press Photos may be reproduced, if credit is given to the European Southern Observatory. 16. Evolution of Collisionally Merged Massive Stars Suzuki, T K; Baumgardt, H; Ibukiyama, A; Makino, J; Ebisuzaki, & T; Suzuki, Takeru K; Nakasato, Naohito; Baumgardt, Holger; Ibukiyama, Akihiro; Makino, Junichiro 2007-01-01 We investigate the evolution of collisionally merged stars with mass of ~100 Msun which might be formed in dense star clusters. We assumed that massive stars with several tens Msun collide typically after ~1Myr of the formation of the cluster and performed hydrodynamical simulations of several collision events. Our simulations show that after the collisions, merged stars have extended envelopes and their radii are larger than those in the thermal equilibrium states and that their interiors are He-rich because of the stellar evolution of the progenitor stars. We also found that if the mass-ratio of merging stars is far from unity, the interior of the merger product is not well mixed and the elemental abundance is not homogeneous. We then followed the evolution of these collision products by a one dimensional stellar evolution code. After an initial contraction on the Kelvin-Helmholtz (thermal adjustment) timescale (~10^{3-4} yr), the evolution of the merged stars traces that of single homogeneous stars with co... 17. SIRTF autonomous star tracker van Bezooijen, Roelof W. H. 2003-03-01 Two redundant AST-301 autonomous star trackers (AST) serve as the primary attitude sensors for JPL's space infrared telescope facility (SIRTF). These units, which employ a 1553B interface to output their attitude quaternions and uncertainty at a 2 Hz rate, provide a 1 σaccuracy of better than 0.18, 0.18, and 5.1 arcsec about their X, Y, and Z axes, respectively. This is a factor 5.5 better than the accuracy of the flight-proven AST-201 from which the trackers were derived. To obtain this improvement, the field of view (FOV) was reduced to 5 by 5 degrees, the accurate Tycho-1 and ACT catalogs were used for selecting the 71,830 guide stars, star image centroiding was improved to better than 1/50th of a pixel, and optimal attitude estimation was implemented. In addition, the apparent direction to each guide star in the FOV is compensated for proper motion, parallax, velocity aberration, and optical distortion. The AST-301 employs autonomous time-delayed integration (TDI) to achieve image motion compensation (IMC) about its X axis that prevents accuracy degradation, even at rates of 2.1 deg/s, making it actually suitable for use on spinning spacecraft. About the Y axis, a software function called "image motion accommodation" (IMA) processes smeared images to maximize the signal to noise ratio of the resulting synthetic images, which enables robust and accurate tracking at rates tested up to 0.42 deg/s. The AST-301 is capable of acquiring its attitude anywhere in the sky in less than 3 seconds with a 99.98% probability of success, without requiring any a priori attitude knowledge. Following a description of the 7.1 kg AST-301, its operation and IMA, the methodology for translating the night sky test data into performance numbers is presented, while, in addition, the results of tests used to measure alignment stability over temperature are included. 18. Carbon and Oxygen Isotopic Ratios for Nearby Miras Hinkle, Kenneth H.; Lebzelter, Thomas; Straniero, Oscar 2016-07-01 Carbon and oxygen isotopic ratios are reported for a sample of 46 Mira and SRa-type variable asymptotic giant branch (AGB) stars. Vibration-rotation first and second-overtone CO lines in 1.5-2.5 μm spectra were measured to derive isotopic ratios for 12C/13C, 16O/17O, and 16O/18O. Comparisons with previous measurements for individual stars and with various samples of evolved stars, as available in the extant literature, are discussed. Models for solar composition AGB stars of different initial masses are used to interpret our results. We find that the majority of M-stars have main sequence masses ≤2 M ⊙ and have not experienced sizable third dredge-up (TDU) episodes. The progenitors of the four S-type stars in our sample are slightly more massive. Of the six C-stars in the sample three have clear evidence relating their origin to the occurrence of TDU. Comparisons with O-rich presolar grains from AGB stars that lived before the formation of the solar system reveal variations in the interstellar medium chemical composition. The present generation of low-mass AGB stars, as represented by our sample of long period variables (LPVs), shows a large spread of 16O/17O ratios, similar to that of group 1 presolar grains and in agreement with theoretical expectations for the composition of mass 1.2-2 M ⊙ stars after the first dredge-up. In contrast, the 16O/18O ratios of present-day LPVs are definitely smaller than those of group 1 grains. This is most probably a consequence of the the decrease with time of the 16O/18O ratio in the interstellar medium due to the chemical evolution of the Milky Way. One star in our sample has an O composition similar to that of group 2 presolar grains originating in an AGB star undergoing extra-mixing. This may indicate that the extra-mixing process is hampered at high metallicity, or, equivalently, favored at low metallicity. Similarly to O-rich grains, no star in our sample shows evidence of hot bottom burning, which is expected for 19. Spectroscopic observations of active solar-analog stars with high X-ray luminosity, as a proxy of superflare stars Notsu, Yuta; Honda, Satoshi; Maehara, Hiroyuki; Notsu, Shota; Namekata, Kosuke; Nogami, Daisaku; Shibata, Kazunari 2017-02-01 Recent studies of solar-type superflare stars have suggested that even old slowly rotating stars similar to the Sun can have large starspots and superflares. We conducted high-dispersion spectroscopy of 49 nearby solar-analog stars (G-type main-sequence stars with Teff ≈ 5600-6000 K) identified as ROSAT soft X-ray sources, which are not binary stars from previous studies. We expected that these stars could be used as a proxy of bright solar-analog superflare stars, since superflare stars are expected to show strong X-ray luminosity. More than half (37) of the 49 target stars show no evidence of binarity, and their atmospheric parameters (temperature, surface gravity, and metallicity) are within the range of ordinary solar-analog stars. We measured the intensity of Ca II 8542 and Hα lines, which are good indicators of the stellar chromospheric activity. The intensity of these lines indicates that all the target stars have large starspots. We also measured v sin i (projected rotational velocity) and lithium abundance for the target stars. Li abundance is a key to understanding the evolution of the stellar convection zone, which reflects the stellar age, mass and rotational history. We confirmed that many of the target stars rapidly rotate and have high Li abundance, compared with the Sun, as suggested by many previous studies. There are, however, also some target stars that rotate slowly (v sin i = 2-3 km s-1) and have low Li abundance like the Sun. These results support that old and slowly rotating stars similar to the Sun could have high activity levels and large starspots. This is consistent with the results of our previous studies of solar-type superflare stars. In the future, it is important to conduct long-term monitoring observations of these active solar-analog stars in order to investigate detailed properties of large starspots from the viewpoint of stellar dynamo theory. 20. Looking for imprints of the first stellar generations in metal-poor bulge field stars Siqueira-Mello, C.; Chiappini, C.; Barbuy, B.; Freeman, K.; Ness, M.; Depagne, E.; Cantelli, E.; Pignatari, M.; Hirschi, R.; Frischknecht, U.; Meynet, G.; Maeder, A. 2016-09-01 Context. Efforts to look for signatures of the first stars have concentrated on metal-poor halo objects. However, the low end of the bulge metallicity distribution has been shown to host some of the oldest objects in the Milky Way and hence this Galactic component potentially offers interesting targets to look at imprints of the first stellar generations. As a pilot project, we selected bulge field stars already identified in the ARGOS survey as having [Fe/H] ≈-1 and oversolar [α/Fe] ratios, and we used FLAMES-UVES to obtain detailed abundances of key elements that are believed to reveal imprints of the first stellar generations. Aims: The main purpose of this study is to analyse selected ARGOS stars using new high-resolution (R ~ 45 000) and high-signal-to-noise (S/N> 100) spectra. We aim to derive their stellar parameters and elemental ratios, in particular the abundances of C, N, the α-elements O, Mg, Si, Ca, and Ti, the odd-Z elements Na and Al, the neutron-capture s-process dominated elements Y, Zr, La, and Ba, and the r-element Eu. Methods: High-resolution spectra of five field giant stars were obtained at the 8 m VLT UT2-Kueyen telescope with the UVES spectrograph in FLAMES-UVES configuration. Spectroscopic parameters were derived based on the excitation and ionization equilibrium of Fe i and Fe ii. The abundance analysis was performed with a MARCS LTE spherical model atmosphere grid and the Turbospectrum spectrum synthesis code. Results: We confirm that the analysed stars are moderately metal-poor (-1.04 ≤ [Fe/H] ≤-0.43), non-carbon-enhanced (non-CEMP) with [C/Fe] ≤ + 0.2, and α-enhanced. We find that our three most metal-poor stars are nitrogen enhanced. The α-enhancement suggests that these stars were formed from a gas enriched by core-collapse supernovae, and that the values are in agreement with results in the literature for bulge stars in the same metallicity range. No abundance anomalies (Na - O, Al - O, Al - Mg anti-correlations) were 1. "Catch a Star !" 2002-05-01 ESO and EAAE Launch Web-based Educational Programme for Europe's Schools Catch a star!... and discover all its secrets! This is the full title of an innovative educational project, launched today by the European Southern Observatory (ESO) and the European Association for Astronomy Education (EAAE). It welcomes all students in Europe's schools to an exciting web-based programme with a competition. It takes place within the context of the EC-sponsored European Week of Science and Technology (EWST) - 2002 . This unique project revolves around a web-based competition and is centred on astronomy. It is specifically conceived to stimulate the interest of young people in various aspects of this well-known field of science, but will also be of interest to the broad public. What is "Catch a Star!" about? [Go to Catch a Star Website] The programme features useful components from the world of research, but it is specifically tailored to (high-)school students. Younger participants are also welcome. Groups of up to four persons (e.g., three students and one teacher) have to select an astronomical object - a bright star, a distant galaxy, a beautiful comet, a planet or a moon in the solar system, or some other celestial body. Like detectives, they must then endeavour to find as much information as possible about "their" object. This information may be about the position and visibility in the sky, the physical and chemical characteristics, particular historical aspects, related mythology and sky lore, etc. They can use any source available, the web, books, newspaper and magazine articles, CDs etc. for this work. The group members must prepare a (short) summarising report about this investigation and "their" object, with their own ideas and conclusions, and send it to ESO (email address: eduinfo@eso.org). A jury, consisting of specialists from ESO and the EAAE, will carefully evaluate these reports. All projects that are found to fulfill the stipulated requirements, including a 2. Single Star HII Regions in nearby LEGUS Galaxies Kayitesi, Bridget; Lee, Janice C.; Thilker, David A.; LEGUS Team 2017-01-01 It is believed that O stars typically form in clustered environments, however past observations have shown that there are a few O stars in the field that are fairly far from clusters and have low space velocities. The goal of this project is to determine whether these O stars can be born in situ or whether they are runaways ejected from their parent clusters due to binary supernova explosions or other dynamic interactions. To do this, we select candidate hot stars and compute an isolation metric based on distance from other hot stars and clusters. We then deploy Zooniverse citizen scientists to classify the isolated sources and their associated nebulae. The detected presence of an HII region allows us to confirm a candidate as a true O star. We use the Zooniverse classification system to study the morphology of these HII regions and determine the runaway status of the O stars. 3. Abundance analysis of Barium stars Guo-Qing Liu; Yan-Chun Liang; Li-Cai Deng 2009-01-01 We obtain the chemical abundances of six barium stars and two CH subgiant stars based on the high signal-to-noise ratio and high resolution Echelle spectra. The neu- tron capture process elements Y, Zr, Ba, La and Eu show obvious overabundances relative to the Sun, for example, their [Ba/Fe] values are from 0.45 to 1.27. Other elements, in- cluding Na, Mg, A1, Si, Ca, Sc, Ti, V, Cr, Mn and Ni, show comparable abundances to the Solar ones, and their [Fe/H] covers a range from -0.40 to 0.21, which means they belong to the Galactic disk. The predictions of the theoretical model of wind accretion for bi- nary systems can explain the observed abundance patterns of the neutron capture process elements in these stars, which means that their overabundant heavy-elements could be caused by accreting the ejecta of AGB stars, the progenitors of present-day white dwarf companions in binary systems. 4. On stars, galaxies and black holes in massive bigravity Enander, Jonas 2015-01-01 In this paper we study the phenomenology of stars and galaxies in massive bigravity. We give parameter conditions for the existence of viable star solutions when the radius of the star is much smaller than the Compton wavelength of the graviton. If these parameter conditions are not met, we constrain the ratio between the coupling constants of the two metrics, in order to give viable conditions for e.g. neutron stars. For galaxies, we put constraints on both the Compton wavelength of the graviton and the conformal factor and coupling constants of the two metrics. The relationship between black holes and stars, and whether the former can be formed from the latter, is discussed. We argue that the different asymptotic structure of stars and black holes makes it unlikely that black holes form from the gravitational collapse of stars in massive bigravity. 5. Collisions of Dark Matter Axion Stars with Astrophysical Sources Eby, Joshua [Fermilab; Leembruggen, Madelyn [Cincinnati U.; Leeney, Joseph [Cincinnati U.; Suranyi, Peter [Cincinnati U.; Wijewardhana, L. C.R. [Cincinnati U. 2017-01-05 If QCD axions form a large fraction of the total mass of dark matter, then axion stars could be very abundant in galaxies. As a result, collisions with each other, and with other astrophysical bodies, can occur. We calculate the rate and analyze the consequences of three classes of collisions, those occurring between a dilute axion star and: another dilute axion star, an ordinary star, or a neutron star. In all cases we attempt to quantify the most important astrophysical uncertainties; we also pay particular attention to scenarios in which collisions lead to collapse of otherwise stable axion stars, and possible subsequent decay through number changing interactions. Collisions between two axion stars can occur with a high total rate, but the low relative velocity required for collapse to occur leads to a very low total rate of collapses. On the other hand, collisions between an axion star and an ordinary star have a large rate,\\Gamma_\\odot \\sim 3000$collisions/year/galaxy, and for sufficiently heavy axion stars, it is plausible that most or all such collisions lead to collapse. We identify in this case a parameter space which has a stable region and a region in which collision triggers collapse, which depend on the axion number ($N$) in the axion star, and a ratio of mass to radius cubed characterizing the ordinary star ($M_s/R_s^3$). Finally, we revisit the calculation of collision rates between axion stars and neutron stars, improving on previous estimates by taking cylindrical symmetry of the neutron star distribution into account. Collapse and subsequent decay through collision processes, if occurring with a significant rate, can affect dark matter phenomenology and the axion star mass distribution. 6. Be stars in and around young clusters in the Magellanic Clouds Keller, S C; Bessell, M S; Keller, Stefan C; Wood, Peter R; Bessell, Michael S 1998-01-01 We present the results of a search for Be stars in six fields centered on the young clusters NGC 330 and NGC 346 in the SMC, and NGC 1818, NGC 1948, NGC 2004 and NGC 2100 in the LMC. Be stars were identified by differencing R band and narrow-band H$\\alpha$CCD images. Our comparatively large images provide substantial Be star populations both within the clusters and in their surrounding fields. Magnitudes, positions and finding charts are given for the 224 Be stars found. The fraction of Be stars to normal B stars within each cluster is found to vary significantly although the average ratio is similar to the average Be to B star ratio found in the Galaxy. In some clusters, the Be star population is weighted to magnitudes near the main sequence turn-off. The Be stars are redder in$V
7. Undercover Stars Among Exoplanet Candidates
2005-03-01
in solar units. The newly determined, precise values of the mass and radius of OGLE-TR-122b are indicated as the red dot. The blue symbols are values for low-mass stars, while the black symbols on the left represent exoplanets. Note that the "hot Jupiters" - exoplanets orbiting very close to their host star - are larger than OGLE-TR-122b. The various lines represent theoretical models from G. Chabrier, I. Baraffe and colleagues, showing a good agreement between theory and observations. The newly found stellar gnome is the companion of OGLE-TR-122, a rather remote star in the Milky Way galaxy, seen in the direction of the southern constellation Carina. The OGLE programme revealed that OGLE-TR-122 experiences a 1.5 per cent brightness dip once every 7 days 6 hours and 27 minutes, each time lasting just over 3 hours (about 188 min). The FLAMES/UVES measurements, made during 6 nights in March 2004, reveal radial velocity variations of this period with an amplitude of about 20 km/s. This is the clear signature of a very low-mass star, close to the Hydrogen-burning limit, orbiting OGLE-TR-122. This companion received the name OGLE-TR-122b. As François Bouchy of the Observatoire Astronomique Marseille Provence (France) explains: "Combined with the information collected by OGLE, our spectroscopic data now allow us to determine the nature of the more massive star in the system, which appears to be solar-like". This information can then be used to determine the mass and radius of the much smaller companion OGLE-TR-122b. Indeed, the depth (brightness decrease) of the transit gives a direct estimate of the ratio between the radii of the two stars, and the spectroscopic orbit provides a unique value of the mass of the companion, once the mass of the larger star is known. The astronomers find that OGLE-TR-122b weighs one-eleventh of the mass of the Sun and has a diameter that is only one-eighth of the solar one. Thus, although the star is still 96 times as massive as Jupiter, it
8. Massive binary stars as a probe of massive star formation
Kiminki, Daniel C.
2010-10-01
Massive stars are among the largest and most influential objects we know of on a sub-galactic scale. Binary systems, composed of at least one of these stars, may be responsible for several types of phenomena, including type Ib/c supernovae, short and long gamma ray bursts, high-velocity runaway O and B-type stars, and the density of the parent star clusters. Our understanding of these stars has met with limited success, especially in the area of their formation. Current formation theories rely on the accumulated statistics of massive binary systems that are limited because of their sample size or the inhomogeneous environments from which the statistics are collected. The purpose of this work is to provide a higher-level analysis of close massive binary characteristics using the radial velocity information of 113 massive stars (B3 and earlier) and binary orbital properties for the 19 known close massive binaries in the Cygnus OB2 Association. This work provides an analysis using the largest amount of massive star and binary information ever compiled for an O-star rich cluster like Cygnus OB2, and compliments other O-star binary studies such as NGC 6231, NGC 2244, and NGC 6611. I first report the discovery of 73 new O or B-type stars and 13 new massive binaries by this survey. This work involved the use of 75 successful nights of spectroscopic observation at the Wyoming Infrared Observatory in addition to observations obtained using the Hydra multi-object spectrograph at WIYN, the HIRES echelle spectrograph at KECK, and the Hamilton spectrograph at LICK. I use these data to estimate the spectrophotometric distance to the cluster and to measure the mean systemic velocity and the one-sided velocity dispersion of the cluster. Finally, I compare these data to a series of Monte Carlo models, the results of which indicate that the binary fraction of the cluster is 57 +/- 5% and that the indices for the power law distributions, describing the log of the periods, mass-ratios
9. ENERGY STAR Certified Boilers
U.S. Environmental Protection Agency — Certified models meet all ENERGY STAR requirements as listed in the Version 3.0 ENERGY STAR Program Requirements for Boilers that are effective as of October 1,...
10. ENERGY STAR Certified Furnaces
U.S. Environmental Protection Agency — Certified models meet all ENERGY STAR requirements as listed in the Version 4.0 ENERGY STAR Program Requirements for Furnaces that are effective as of February 1,...
11. ENERGY STAR Certified Computers
U.S. Environmental Protection Agency — Certified models meet all ENERGY STAR requirements as listed in the Version 6.1 ENERGY STAR Program Requirements for Computers that are effective as of June 2, 2014....
12. Mass loss from red giant stars. II. Carbon stars
Wannier, P.G.; Sahai, R.; Andersson, B.G.; Johnson, H.R. (JPL, Pasadena, CA (USA) Goteborg Universitet (Sweden) Indiana Univ., Bloomington (USA))
1990-07-01
A millimeter-wave survey has been made of bright relatively unobscured, carbon stars, chosen on the basis of their optical properties. Out of 26 program objects, (J = 2-1)CO emission is detected from 15. Most of these had not been previously detected. There are many differences among the observed objects, but one rather interesting trend emerges: a positive correlation, at moderate IR excesses, between the IR dust emission and the expansion velocity of the dense wind. A similar, positive correlation with the mass-loss rate implies that stars with larger mass fluxes also accelerate them to larger velocities. At high-IR excesses, both correlations break down, and the momentum rate may be limited by the momentum rate of the stellar radiation. All these effects could be ascribed to differences in the gas-to-dust ratio, assuming that radiation pressure initiates and accelerates the wind. 38 refs.
13. Mass loss from red giant stars. II - Carbon stars
Wannier, P. G.; Sahai, R.; Andersson, B.-G.; Johnson, H. R.
1990-01-01
A millimeter-wave survey has been made of bright relatively unobscured, carbon stars, chosen on the basis of their optical properties. Out of 26 program objects, (J = 2-1)CO emission is detected from 15. Most of these had not been previously detected. There are many differences among the observed objects, but one rather interesting trend emerges: a positive correlation, at moderate IR excesses, between the IR dust emission and the expansion velocity of the dense wind. A similar, positive correlation with the mass-loss rate implies that stars with larger mass fluxes also accelerate them to larger velocities. At high-IR excesses, both correlations break down, and the momentum rate may be limited by the momentum rate of the stellar radiation. All these effects could be ascribed to differences in the gas-to-dust ratio, assuming that radiation pressure initiates and accelerates the wind.
14. Chlorine Abundances in Cool Stars
Maas, Z G; Hinkle, K
2016-01-01
Chlorine abundances are reported in 15 evolved giants and one M dwarf in the solar neighborhood. The Cl abundance was measured using the vibration-rotation 1-0 P8 line of H$^{35}$Cl at 3.69851 $\\mu$m. The high resolution L-band spectra were observed using the Phoenix infrared spectrometer on the Kitt Peak Mayall 4m telescope. The average [$^{35}$Cl/Fe] abundance in stars with --0.72$<$[Fe/H]$<$0.20 is [$^{35}$Cl/Fe]=(--0.10$\\pm$0.15) dex. The mean difference between the [$^{35}$Cl/Fe] ratios measured in our stars and chemical evolution model values is (0.16$\\pm$0.15) dex. The [$^{35}$Cl/Ca] ratio has an offset of $\\sim$0.35 dex above model predictions suggesting chemical evolution models are under producing Cl at the high metallicity range. Abundances of C, N, O, Si, and Ca were also measured in our spectral region and are consistent with F and G dwarfs. The Cl versus O abundances from our sample match Cl abundances measured in planetary nebula and \\ion{H}{2} regions. In one star where both H$^{35}$Cl a...
15. Autonomous Star Tracker Algorithms
Betto, Maurizio; Jørgensen, John Leif; Kilsgaard, Søren
1998-01-01
Proposal, in response to an ESA R.f.P., to design algorithms for autonomous star tracker operations.The proposal also included the development of a star tracker breadboard to test the algorithms performances.......Proposal, in response to an ESA R.f.P., to design algorithms for autonomous star tracker operations.The proposal also included the development of a star tracker breadboard to test the algorithms performances....
Davis, Mark J.
2016-01-01
In this digital literacy project, struggling high school readers remixed the "Star Wars" canon through audio storytelling. The "Star Wars" phenomenon motivates adolescents who may be disengaged in the classroom. Students served as actors, Foley artists, and directors in the recording of brief episodes based on the original…
17. From Clouds to Protostars: A Theoretical Framework for the Formation of Wide Multiple Star Systems
Offner, Stella
The majority of stars reside in binary or multiple star systems. Binary formation is determined largely during the earliest stages of star formation, when star forming cores are highly obscured and difficult to probe at high resolution. Exactly why some cores form a single star, while others form a multiple star system, is not understood. The goal of this proposal is to study the physics responsible for stellar multiplicity, with a specific focus on understanding the formation of wide multiple star systems. Theories for binary formation and their properties have strong relevance to NASA science objectives, especially for the Spitzer, Kepler, and JWST missions. Understanding binary formation is crucial for modeling many phenomena that rely on binary properties, ranging from reionization to planet formation. A number of current and planned large-scale surveys aim to probe starless and protostellar cores down to resolutions of approximately 200 AU. These surveys reinforce the timeliness of this project and underscore the pressing need for a predictive and general framework for understanding core fragmentation and the relation between multiplicity and physical conditions. Recently, the PI and co-I have demonstrated that dimensionless parameters can be used in combination with numerical simulations to describe core evolution for (non-idealized) turbulent, non-isothermal cores. They have used simulations to test a new method for characterizing hierarchical structure, which is ideal for identifying and analyzing cores and their incipient substructure. This proposal aims to extend the previous work by running a suite of high-resolution, magneto-hydrodynamic simulations of star-forming molecular clouds. The proposers will then develop an algorithm to track structure (e.g., cores and filaments) as a function of time and assess how well fundamental physical parameters, such as rotational energy, mass-to-flux ratio, and virial parameter, are predictive of stellar multiplicity
18. The ATLAS(3D) project - XV. Benchmark for early-type galaxies scaling relations from 260 dynamical models : mass-to-light ratio, dark matter, Fundamental Plane and Mass Plane
Cappellari, Michele; Scott, Nicholas; Alatalo, Katherine; Blitz, Leo; Bois, Maxime; Bournaud, Frederic; Bureau, M.; Crocker, Alison F.; Davies, Roger L.; Davis, Timothy A.; de Zeeuw, P. T.; Duc, Pierre-Alain; Emsellem, Eric; Khochfar, Sadegh; Krajnovic, Davor; Kuntschner, Harald; McDermid, Richard M.; Morganti, Raffaella; Naab, Thorsten; Oosterloo, Tom; Sarzi, Marc; Serra, Paolo; Weijmans, Anne-Marie; Young, Lisa M.
2013-01-01
We study the volume-limited and nearly mass-selected (stellar mass M-stars greater than or similar to 6 x 10(9) M circle dot) ATLAS(3D) sample of 260 early-type galaxies (ETGs, ellipticals Es and lenticulars S0s). We construct detailed axisymmetric dynamical models (Jeans Anisotropic MGE), which all
19. Star Tracker Performance Estimate with IMU
Aretskin-Hariton, Eliot D.; Swank, Aaron J.
2015-01-01
A software tool for estimating cross-boresight error of a star tracker combined with an inertial measurement unit (IMU) was developed to support trade studies for the Integrated Radio and Optical Communication project (iROC) at the National Aeronautics and Space Administration Glenn Research Center. Typical laser communication systems, such as the Lunar Laser Communication Demonstration (LLCD) and the Laser Communication Relay Demonstration (LCRD), use a beacon to locate ground stations. iROC is investigating the use of beaconless precision laser pointing to enable laser communication at Mars orbits and beyond. Precision attitude knowledge is essential to the iROC mission to enable high-speed steering of the optical link. The preliminary concept to achieve this precision attitude knowledge is to use star trackers combined with an IMU. The Star Tracker Accuracy (STAcc) software was developed to rapidly assess the capabilities of star tracker and IMU configurations. STAcc determines the overall cross-boresight error of a star tracker with an IMU given the characteristic parameters: quantum efficiency, aperture, apparent star magnitude, exposure time, field of view, photon spread, detector pixels, spacecraft slew rate, maximum stars used for quaternion estimation, and IMU angular random walk. This paper discusses the supporting theory used to construct STAcc, verification of the program and sample results.
20. VizieR Online Data Catalog: Spectral classification of O Vz stars from GOSSS (Arias+, 2016)
Arias, J. I.; Walborn, N. R.; Diaz, S. S.; Barba, R. H.; Apellaniz, J. M.; Sabin-Sanjulian, C.; Gamen, R. C.; Morrell, N. I.; Sota, A.; Marco, A.; Negueruela, I.; Leao, J. R. S.; Herrero, A.; Alfaro, E. J.
2016-10-01
All of the observations used in this work come from the Galactic O Star Spectroscopic Survey (GOSSS). Details on the data and analysis procedures are fully discussed in the three papers from the project (Sota et al. 2011, 2014, Cat. III/274; Maiz Apellaniz et al. 2016ApJS..224....4M). GOSSS is a long-term systematic survey of all of the Galactic stars ever classified as O. This project provides moderate resolution (R~2500) spectroscopy in the blue-violet region (approximately 3900-5000Å) with a high signal-to-noise ratio, typically S/N~200-300. The spectral types are available through the latest version of the Galactic O Star Catalog (GOSC; Maiz Apellaniz et al. 2004, Cat. V/116). In this paper, we include 226 O stars from both hemispheres pertaining to the three published GOSSS installments. The categories and numbers that characterize our sample objects are the following: (1) objects that are single lined in the GOSSS spectra and for which no evidence of binarity is known (132 stars listed in Table1); (2) objects that are single lined in the GOSSS spectra but are known to be spectroscopic binaries (SBs) from high-resolution data (45 binaries, Table2); (3) objects that are double lined in the GOSSS spectra (explicit SB2) for which the line separation is sufficiently large to allow measurements of the CDs and EWs of the individual components by the use of deblending methods (23 binaries providing 32 components with spectral types earlier than O9); and (4) explicit SB2 whose spectral components are not sufficiently separated to be measured individually (15 binaries). Binaries belonging to groups (3) and (4) are listed in Table3. (3 data files).
1. The Quest for Identifying BY Draconis Stars within a Data Set of 3,548 Candidate Cepheid Variable Stars (Abstract)
Johnson, J.
2016-06-01
(Abstract only) A spreadsheet of 3,548 automatically classified candidate Cepheid variable stars from the ASAS (All Sky Automated Survey) photometry data was provided to AAVSO (American Association of Variable Star Observers) members for analysis. It was known that the computer filters had significantly overpopulated the list. Patrick Wils originally investigated a small subset of the data using 2MASS, PPMXL, and ROTSE data, and discovered that the vast majority of the 84 candidates he surveyed appeared to have been misidentified, demonstrating the need to reclassify these variables. The most common misidentification seemed to be of BY Draconis stars (K and M spotted dwarfs), which led to an ongoing project to systematically identify BY Draconis stars from this data set. The stars are sorted using the International Variable Star Index (VSX) information and ASAS light curves to search for prior reclassification by other authors in the time since the initial population of the candidate list (e.g. using ROTSE data), along with infrared photometry (2MASS) and proper motion (PPMXL) data. An analysis of light curves and phase plots using the AAVSO software vstar is the final step in identifying potential BY Draconis stars. The goal of this project has been to submit updated identifications for these stars to VSX. This final presentation on this project will identify the last set of reclassified BY Draconis stars and discuss future directions for this research.
2. Multiplicity of rapidly oscillating Ap stars
Schoeller, M; Hubrig, S; Kurtz, D W
2012-01-01
Rapidly oscillating Ap (roAp) stars have rarely been found in binary or higher order multiple systems. This might have implications for their origin. We intend to study the multiplicity of this type of chemically peculiar stars, looking for visual companions in the range of angular separation between 0.05" and 8". We carried out a survey of 28 roAp stars using diffraction-limited near-infrared imaging with NAOS-CONICA at the VLT. Additionally, we observed three non-oscillating magnetic Ap stars. We detected a total of six companion candidates with low chance projection probabilities. Four of these are new detections, the other two are confirmations. An additional 39 companion candidates are very likely chance projections. We also found one binary system among the non-oscillating magnetic Ap stars. The detected companion candidates have apparent K magnitudes between 6.8 and 19.5 and angular separations ranging from 0.23" to 8.9", corresponding to linear projected separations of 30-2400AU. While our study confi...
3. Covering tree with stars
Baumbach, Jan; Guo, Jian-Ying; Ibragimov, Rashid
2013-01-01
We study the tree edit distance problem with edge deletions and edge insertions as edit operations. We reformulate a special case of this problem as Covering Tree with Stars (CTS): given a tree T and a set of stars, can we connect the stars in by adding edges between them such that the resulting ...
4. Covering tree with stars
Baumbach, Jan; Guo, Jiong; Ibragimov, Rashid
2015-01-01
We study the tree edit distance problem with edge deletions and edge insertions as edit operations. We reformulate a special case of this problem as Covering Tree with Stars (CTS): given a tree T and a set of stars, can we connect the stars in by adding edges between them such that the resulting ...
5. Magnetism in massive stars
Henrichs, H.F.
2012-01-01
Stars with mass more than 8 solar masses end their lives as neutron stars, which we mostly observe as highly magnetized objects. Where does this magnetic field come from? Such a field could be formed during the collapse, or is a (modified) remnant of a fossil field since the birth of the star, or ot
6. Managing the star performer.
Hills, Laura
2013-01-01
Our culture seems to be endlessly fascinated with its stars in entertainment, athletics, politics, and business, and holds fast to the idea that extraordinary talent accounts for an individual's extraordinary performance. At first glance, managing a star performer in your medical practice may seem like it would be an easy task. However, there's much more to managing a star performer than many practice managers realize. The concern is how to keep the star performer happy and functioning at a high level without detriment to the rest of the medical practice team. This article offers tips for practice managers who manage star performers. It explores ways to keep the star performer motivated, while at the same time helping the star performer to meld into the existing medical practice team. This article suggests strategies for redefining the star performer's role, for holding the star performer accountable for his or her behavior, and for coaching the star performer. Finally, this article offers practical tips for keeping the star performer during trying times, for identifying and cultivating new star performers, and for managing medical practice prima donnas.
7. America's Star Libraries
Lyons, Ray; Lance, Keith Curry
2009-01-01
"Library Journal"'s new national rating of public libraries, the "LJ" Index of Public Library Service, identifies 256 "star" libraries. It rates 7,115 public libraries. The top libraries in each group get five, four, or three Michelin guide-like stars. All included libraries, stars or not, can use their scores to learn from their peers and improve…
8. America's Star Libraries
Lyons, Ray; Lance, Keith Curry
2009-01-01
"Library Journal"'s new national rating of public libraries, the "LJ" Index of Public Library Service, identifies 256 "star" libraries. It rates 7,115 public libraries. The top libraries in each group get five, four, or three Michelin guide-like stars. All included libraries, stars or not, can use their scores to learn from their peers and improve…
9. To rescue a star
1996-01-01
Massless neutrinos are exchanged in a neutron star, leading to long range interactions. Many body forces of this type follow and we resum them. Their net contribution to the total energy is negligible as compared to the star mass. The stability of the star is not in danger, contrary to recent assertions.
10. Planets, stars and stellar systems
Bond, Howard; McLean, Ian; Barstow, Martin; Gilmore, Gerard; Keel, William; French, Linda
2013-01-01
This is volume 3 of Planets, Stars and Stellar Systems, a six-volume compendium of modern astronomical research covering subjects of key interest to the main fields of contemporary astronomy. This volume on “Solar and Stellar Planetary Systems” edited by Linda French and Paul Kalas presents accessible review chapters From Disks to Planets, Dynamical Evolution of Planetary Systems, The Terrestrial Planets, Gas and Ice Giant Interiors, Atmospheres of Jovian Planets, Planetary Magnetospheres, Planetary Rings, An Overview of the Asteroids and Meteorites, Dusty Planetary Systems and Exoplanet Detection Methods. All chapters of the handbook were written by practicing professionals. They include sufficient background material and references to the current literature to allow readers to learn enough about a specialty within astronomy, astrophysics and cosmology to get started on their own practical research projects. In the spirit of the series Stars and Stellar Systems published by Chicago University Press in...
11. The origin of very wide binary stars
Kouwenhoven, M B N; Davies, Melvyn B; Parker, Richard J; Kroupa, P; Malmberg, D
2011-01-01
A large population of fragile, wide (> 1000 AU) binary systems exists in the Galactic field and halo. These wide binary stars cannot be primordial because of the high stellar density in star forming regions, while formation by capture in the Galactic field is highly improbable. We propose that these binary systems were formed during the dissolution phase of star clusters (see Kouwenhoven et al. 2010, for details). Stars escaping from a dissolving star cluster can have very similar velocities, which can lead to the formation of a wide binary systems. We carry out N-body simulations to test this hypothesis. The results indicate that this mechanism explains the origin of wide binary systems in the Galaxy. The resulting wide binary fraction and semi-major axis distribution depend on the initial conditions of the dissolving star cluster, while the distributions in eccentricity and mass ratio are universal. Finally, since most stars are formed in (relatively tight) primordial binaries, we predict that a large fract...
12. Analysis of a selected sample of RR Lyrae stars in the LMC from OGLE-Ⅲ
Bing-Qiu Chen; Bi-Wei Jiang; Ming Yang
2013-01-01
A systematic study of RR Lyrae stars is performed using a selected sample of 655 objects in the Large Magellanic Cloud (LMC) with long-term observations and numerous measurements from the Optical Gravitational Lensing Experiment Ⅲ project.The phase dispersion method and linear superposition of the harmonic oscillations are used to derive the pulsation frequency and properties of light variation.Itis found that a dichotomy exists in Oosterhoff Type Ⅰ and Oosterhoff Type Ⅱ for RR Lyrae stars in the LMC.Due to our strict criteria for identifying a frequency,a lower limit for the incidence rate of Blazhko modulation in the LMC is estimated in various subclasses of RR Lyrae stars.For fundamental-mode RR Lyrae stars,the rate of 7.5％ is smaller than the previous result.In the case of the first-overtone RR Lyrae variables,the rate of 9.1％ is relatively high.In addition to the Blazhko variables,15 objects are identified to pulsate in the fundamental/first-overtone double mode.Furthermore,four objects show a period ratio around 0.6,which makes them very likely to be rare pulsators in the fundamental/second-overtone double mode.
13. Simple nonlinear models suggest variable star universality
Lindner, John F; Kia, Behnam; Hippke, Michael; Learned, John G; Ditto, William L
2015-01-01
Dramatically improved data from observatories like the CoRoT and Kepler spacecraft have recently facilitated nonlinear time series analysis and phenomenological modeling of variable stars, including the search for strange (aka fractal) or chaotic dynamics. We recently argued [Lindner et al., Phys. Rev. Lett. 114 (2015) 054101] that the Kepler data includes "golden" stars, whose luminosities vary quasiperiodically with two frequencies nearly in the golden ratio, and whose secondary frequencies exhibit power-law scaling with exponent near -1.5, suggesting strange nonchaotic dynamics and singular spectra. Here we use a series of phenomenological models to make plausible the connection between golden stars and fractal spectra. We thereby suggest that at least some features of variable star dynamics reflect universal nonlinear phenomena common to even simple systems.
14. Equivalent Widths of 15 Extrasolar-Planet Host Stars
2002-01-01
We present the equivalent widths of 15 extrasolar-planet host stars.These data were based on the high-resolution, high signal-to-noise ratio spectra obtained with the 2.16 m telescope at Xinglong station. The error in the Xinglong equivalent width is estimated by a comparison of these data with those given in previous studies of common stars.
15. DIRECT IMAGING DISCOVERY OF A 'SUPER-JUPITER' AROUND THE LATE B-TYPE STAR {kappa} And
Carson, J.; Kozakis, T.; Stevens, L.; Wong, P.; Gainey, K. [Department of Physics and Astronomy, College of Charleston, 58 Coming Street, Charleston, SC 29424 (United States); Thalmann, C.; Bonnefoy, M.; Biller, B.; Schlieder, J.; Henning, T.; Brandner, W.; Feldt, M. [Max-Planck-Institut fuer Astronomie, Koenigstuhl 17, D-69117 Heidelberg (Germany); Janson, M. [Department of Astrophysical Sciences, Princeton University, NJ 08544 (United States); Currie, T.; McElwain, M. [ExoPlanets and Stellar Astrophysics Laboratory, Code 667, Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Goto, M. [Young Stars and Star Formation Universitaets-Sternwarte Muenchen, Ludwig-Maximilians-Universitaet, D-81679 Muenchen (Germany); Kandori, R.; Kuzuhara, M. [National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588 (Japan); Fukagawa, M.; Kuwada, Y. [Department of Earth and Space Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043 (Japan); and others
2013-02-01
We present the direct imaging discovery of an extrasolar planet, or possible low-mass brown dwarf, at a projected separation of 55 {+-} 2 AU (1.''058 {+-} 0.''007) from the B9-type star {kappa} And. The planet was detected with Subaru/HiCIAO during the SEEDS survey and confirmed as a bound companion via common proper motion measurements. Observed near-infrared magnitudes of J = 16.3 {+-} 0.3, H = 15.2 {+-} 0.2, K{sub s} = 14.6 {+-} 0.4, and L' = 13.12 {+-} 0.09 indicate a temperature of {approx}1700 K. The galactic kinematics of the host star are consistent with membership in the Columba Association, implying a corresponding age of 30{sup +20}{sub -10} Myr. The system's age, combined with the companion photometry, points to a model-dependent companion mass {approx}12.8 M{sub Jup}. The host star's estimated mass of 2.4-2.5 M{sub Sun} places it among the most massive stars ever known to harbor an extrasolar planet or low-mass brown dwarf. While the mass of the companion is close to the deuterium burning limit, its mass ratio, orbital separation, and likely planet-like formation scenario imply that it may be best defined as a 'super-Jupiter' with properties similar to other recently discovered companions to massive stars.
16. Djehuty A Code for Modeling Whole Stars in Three Dimensions
Turcotte, S; Castor, J I; Cavallo, R M; Cohl, H S; Cook, K; Dearborn, D S P; Dossa, D D; Eastman, R; Eggleton, P P; Eltgroth, P; Keller, S; Murray, S; Taylor, A
2001-01-01
The DJEHUTY project is an intensive effort at the Lawrence Livermore National Laboratory (LLNL) to produce a general purpose 3-D stellar structure and evolution code to study dynamic processes in whole stars.
17. Variability monitoring of OB stars during the Mons campaign
Morel, T; Eversberg, T; Alves, F; Arnold, W; Bergmann, T; Viegas, N G Correia; Fahed, R; Fernando, A; Carreira, L F Gouveia; Hunger, T; Knapen, J H; Leadbeater, R; Dias, F Marques; Moffat, A F J; Reinecke, N; Ribeiro, J; Romeo, N; Gallego, J Sanchez; Santos, E M dos; Schanne, L; Stahl, O; Stober, Ba; Stober, Be; Vollmann, K; Corcoran, M F; Dougherty, S M; Hamaguchi, K; Pittard, J M; Pollock, A M T; Williams, P M
2010-01-01
We present preliminary results of a 3-month campaign carried out in the framework of the Mons project, where time-resolved Halpha observations are used to study the wind and circumstellar properties of a number of OB stars.
18. How and When Will a Neutron Star Become a Hyperon Star?
贾焕玉; 孙宝玺; 孟杰; 赵恩广
2001-01-01
In the framework of the extended relativistic mean-field theory with hyperons, the properties of neutron star matter have been investigated. It is found that at a density of four to five times that of nuclear matter saturation density po, a neutron star will become a hyperon star. This transition is strongly influenced by the coupling constants of hyperons to mesons and a different parameter set. For a given parameter set, a minimum transition baryon density exists when the hyperon coupling ratios satisfy xHσ = xHω = xHρ = 0.65 or xHσ = xHω = 0.62,xHρ = 0.7.
19. Metal-Rich SX Phe stars in the Kepler Field
Nemec, James M; Murphy, Simon J; Kinemuchi, Karen; Jeon, Young-Beom
2016-01-01
A spectroscopic and photometric analysis has been carried out for thirty-two candidate SX_Phe variable blue straggler stars in the Kepler-field (Balona & Nemec 2012). Radial velocities (RVs), space motions (U,V,W), projected rotation velocities (v sin i), spectral types, and atmospheric characteristics (T_eff, log g, [Fe/H], xi_t, zeta_RT, etc.) are presented for 30 of the 32 stars. Although several stars are metal-weak with extreme halo orbits, the mean [Fe/H] of the sample is near solar, thus the stars are more metal-rich than expected for a typical sample of Pop.II stars, and more like halo metal-rich A-type stars (Perry 1969). Two thirds of the stars are fast rotators with v sin i > 50 km/s, including four stars with v sin i > 200 km/s. Three of the stars have (negative) RVs > 250 km/s, five have retrograde space motions, and 21 have total speeds (relative to the LSR) > 400 km/s. All but one of the 30 stars have positions in a Toomre diagram consistent with the kinematics of bona fide halo stars (the ...
20. The Star Blended with the MOA-2008-BLG-310 Source Is Not the Exoplanet Host Star
Bhattacharya, A.; Bennett, D. P.; Anderson, J.; Bond, I. A.; Gould, A.; Batista, V.; Beaulieu, J. P.; Fouqué, P.; Marquette, J. B.; Pogge, R.
2017-08-01
High-resolution Hubble Space Telescope (HST) image analysis of the MOA-2008-BLG-310 microlens system indicates that the excess flux at the location of the source found in the discovery paper cannot primarily be due to the lens star because it does not match the lens-source relative proper motion, {μ }{rel}, predicted by the microlens models. This excess flux is most likely to be due to an unrelated star that happens to be located in close proximity to the source star. Two epochs of HST observations indicate proper motion for this blend star that is typical of a random bulge star but is not consistent with a companion to the source or lens stars if the flux is dominated by only one star, aside from the lens. We consider models in which the excess flux is due to a combination of an unrelated star and the lens star, and this yields a 95% confidence level upper limit on the lens star brightness of {I}L> 22.44 and {V}L> 23.62. A Bayesian analysis using a standard Galactic model and these magnitude limits yields a host star mass of {M}h={0.21}-0.09+0.21 {M}⊙ and a planet mass of {m}p={23.4}-9.9+23.9 {M}\\oplus at a projected separation of {a}\\perp ={1.12}-0.17+0.16 au. This result illustrates that excess flux in a high-resolution image of a microlens-source system need not be due to the lens. It is important to check that the lens-source relative proper motion is consistent with the microlensing prediction. The high-resolution image analysis techniques developed in this paper can be used to verify the WFIRST exoplanet microlensing survey mass measurements.
1. Nuclear physics of stars
2015-01-01
Most elements are synthesized, or ""cooked"", by thermonuclear reactions in stars. The newly formed elements are released into the interstellar medium during a star's lifetime, and are subsequently incorporated into a new generation of stars, into the planets that form around the stars, and into the life forms that originate on the planets. Moreover, the energy we depend on for life originates from nuclear reactions that occur at the center of the Sun. Synthesis of the elements and nuclear energy production in stars are the topics of nuclear astrophysics, which is the subject of this book
2. Magnetic chemically peculiar stars
Schöller, Markus
2015-01-01
Chemically peculiar (CP) stars are main-sequence A and B stars with abnormally strong or weak lines for certain elements. They generally have magnetic fields and all observables tend to vary with the same period. Chemically peculiar stars provide a wealth of information; they are natural atomic and magnetic laboratories. After a brief historical overview, we discuss the general properties of the magnetic fields in CP stars, describe the oblique rotator model, explain the dependence of the magnetic field strength on the rotation, and concentrate at the end on HgMn stars.
3. Massive Stars in the Quintuplet Cluster
Figer, Donald F.; McLean, Ian S.; Morris, Mark
1999-03-01
We present near-infrared photometry and K-band spectra of newly identified massive stars in the Quintuplet cluster, one of the three massive clusters projected within 50 pc of the Galactic center. We find that the cluster contains a variety of massive stars, including more unambiguously identified Wolf-Rayet stars than any cluster in the Galaxy, and over a dozen stars in earlier stages of evolution, i.e., luminous blue variables (LBVs), Ofpe/WN9, and OB supergiants. One newly identified star is the second luminous blue variable in the cluster, after the Pistol star.'' Although we are unable to provide certain spectral classifications for the five enigmatic Quintuplet-proper members, we tentatively propose that they are extremely dusty versions of the WC stars found elsewhere in the cluster and similar to the dozen or so known examples in the Galaxy. Although the cluster parameters are uncertain because of photometric errors and uncertainties in stellar models, i.e., extrapolating initial masses and estimating ionizing fluxes, we have the following conclusions. Given the evolutionary stages of the identified stars, the cluster appears to be about 4+/-1 Myr old, assuming coeval formation. The total mass in observed stars is ~103 Msolar, and the implied mass is ~104 Msolar, assuming a lower mass cutoff of 1 Msolar and a Salpeter initial mass function. The implied mass density in stars is greater than or similar to a few thousand Msolar pc-3. The newly identified stars increase the estimated ionizing flux from this cluster by about an order of magnitude with respect to earlier estimates, to 1050.9 photons s-1, or roughly what is required to ionize the nearby Sickle'' H II region (G0.18-0.04). The total luminosity from the massive cluster stars is ~107.5 Lsolar, enough to account for the heating of the nearby molecular cloud, M0.20-0.033. We propose a picture that integrates most of the major features in this part of the sky, excepting the nonthermal filaments. We
4. Initial data for black hole-neutron star binaries, with rotating stars
Tacik, Nick; Pfeiffer, Harald P; Muhlberger, Curran; Kidder, Lawrence E; Scheel, Mark A; Szilagyi, Bela
2016-01-01
The coalescence of a neutron star with a black hole is a primary science target of ground-based gravitational wave detectors. Constraining or measuring the neutron star spin directly from gravitational wave observations requires knowledge of the dependence of the emission properties of these systems on the neutron star spin. This paper lays foundations for this task, by developing a numerical method to construct initial data for black hole--neutron star binaries with arbitrary spin on the neutron star. We demonstrate the robustness of the code by constructing initial-data sets in large regions of the parameter space. In addition to varying the neutron star spin-magnitude and spin-direction, we also explore neutron star compactness, mass-ratio, black hole spin, and black hole spin-direction. Specifically, we are able to construct initial data sets with neutron stars spinning near centrifugal break-up, and with black hole spins as large as $S_{\\rm BH}/M_{\\rm BH}^2=0.99$.
5. Preserving chemical signatures of primordial star formation in the first low-mass stars
Ji, Alexander P; Bromm, Volker
2015-01-01
We model early star forming regions and their chemical enrichment by Population III (Pop III) supernovae with nucleosynthetic yields featuring high [C/Fe] ratios and pair-instability supernova (PISN) signatures. We aim to test how well these chemical abundance signatures are preserved in the gas prior to forming the first long-lived low-mass stars (or second-generation stars). Our results show that second-generation stars can retain the nucleosynthetic signature of their Pop III progenitors, even in the presence of nucleosynthetically normal Pop III core-collapse supernovae. We find that carbon-enhanced metal-poor stars are likely second-generation stars that form in minihaloes. Furthermore, it is likely that the majority of Pop III supernovae produce high [C/Fe] yields. In contrast, metals ejected by a PISN are not concentrated in the first star forming haloes, which may explain the absence of observed PISN signatures in metal-poor stars. We also find that unique Pop III abundance signatures in the gas are q...
6. Initial data for black hole–neutron star binaries, with rotating stars
Tacik, Nick; Foucart, Francois; Pfeiffer, Harald P.; Muhlberger, Curran; Kidder, Lawrence E.; Scheel, Mark A.; Szilágyi, Béla
2016-11-01
The coalescence of a neutron star with a black hole is a primary science target of ground-based gravitational wave detectors. Constraining or measuring the neutron star spin directly from gravitational wave observations requires knowledge of the dependence of the emission properties of these systems on the neutron star spin. This paper lays foundations for this task, by developing a numerical method to construct initial data for black hole–neutron star binaries with arbitrary spin on the neutron star. We demonstrate the robustness of the code by constructing initial-data sets in large regions of the parameter space. In addition to varying the neutron star spin-magnitude and spin-direction, we also explore neutron star compactness, mass-ratio, black hole spin, and black hole spin-direction. Specifically, we are able to construct initial data sets with neutron stars spinning near centrifugal break-up, and with black hole spins as large as {S}{BH}/{M}{BH}2=0.99.
7. Pre-supernova mixing in CEMP-no source stars
Choplin, Arthur; Ekström, Sylvia; Meynet, Georges; Maeder, André; Georgy, Cyril; Hirschi, Raphael
2017-09-01
Context. CEMP-no stars are long-lived low-mass stars with a very low iron content, overabundances of carbon and no or minor signs for the presence of s- or r-elements. Although their origin is still a matter of debate, they are often considered as being made of a material ejected by a previous stellar generation (source stars). Aims: We place constraints on the source stars from the observed abundance data of CEMP-no stars. Methods: We computed source star models of 20, 32, and 60 M⊙ at Z = 10-5 with and without fast rotation. For each model we also computed a case with a late mixing event occurring between the hydrogen and helium-burning shell 200 yr before the end of the evolution. This creates a partially CNO-processed zone in the source star. We use the 12C/13C and C/N ratios observed on CEMP-no stars to put constraints on the possible source stars (mass, late mixing or not). Then, we inspect more closely the abundance data of six CEMP-no stars and select their preferred source star(s). Results: Four out of the six CEMP-no stars studied cannot be explained without the late mixing process in the source star. Two of them show nucleosynthetic signatures of a progressive mixing (due e.g. to rotation) in the source star. We also show that a 20 M⊙ source star is preferred compared to one of 60 M⊙ and that likely only the outer layers of the source stars were expelled to reproduce the observed 12C/13C. Conclusions: The results suggest that (1) a late mixing process could operate in some source stars; (2) a progressive mixing, possibly achieved by fast rotation, is at work in several source stars; (3) 20 M⊙ source stars are preferred compared to 60 M⊙ ones; and (4) the source star might have preferentially experienced a low energetic supernova with large fallback.
8. THE FIRST STARS
Daniel J. Whalen
2013-12-01
Full Text Available Pop III stars are the key to the character of primeval galaxies, the first heavy elements, the onset of cosmological reionization, and the seeds of supermassive black holes. Unfortunately, in spite of their increasing sophistication, numerical models of Pop III star formation cannot yet predict the masses of the first stars. Because they also lie at the edge of the observable universe, individual Pop III stars will remain beyond the reach of observatories for decades to come, and so their properties are unknown. However, it will soon be possible to constrain their masses by direct detection of their supernovae, and by reconciling their nucleosynthetic yields to the chemical abundances measured in ancient metal-poor stars in the Galactic halo, some of which may bear the ashes of the first stars. Here, I review the state of the art in numerical simulations of primordial stars and attempts to directly and indirectly constrain their properties.
9. Spectroscopic observations of active solar-analog stars having high X-ray luminosity, as a proxy of superflare stars
Notsu, Yuta; Maehara, Hiroyuki; Notsu, Shota; Namekata, Kosuke; Nogami, Daisaku; Shibata, Kazunari
2016-01-01
Recent studies of solar-type superflare stars have suggested that even old slowly rotating stars similar to the Sun can have large starspots and superflares. We conducted high dispersion spectroscopy of 49 nearby solar-analog stars (G-type main sequence stars with $T_{\\rm{eff}}\\approx5,600\\sim6,000$ K) identified as ROSAT soft X-ray sources, which are not binary stars from the previous studies. We expected that these stars can be used as a proxy of bright solar-analog superflare stars, since superflare stars are expected to show strong X-ray luminosity. More than half (37) of the 49 target stars show no evidence of binarity, and their atmospheric parameters ($T_{\\rm{eff}}$, $\\log g$, and [Fe/H]) are within the range of ordinary solar-analog stars. We measured Ca II 8542 and H$\\alpha$ lines, which are good indicators of the chromospheric activity. The intensity of these lines indicates that all the target stars have large starspots. We also measured $v\\sin i$ (projected rotational velocity) and Lithium abundan...
10. AGB stars and presolar grains
Busso, M.; Trippella, O. [INFN and University of Perugia, Perugia (Italy); Maiorca, E. [INAF - Arcetri Astrophysical Observatory, Firenze, Italy and INFN - Section of Perugia, Perugia (Italy); Palmerini, S. [Departamento de Fìsica Teòrica y del Cosmsos, Universidad de Granada, Granada (Spain)
2014-05-09
Among presolar materials recovered in meteorites, abundant SiC and Al{sub 2}O{sub 3} grains of AGB origins were found. They showed records of C, N, O, {sup 26}Al and s-element isotopic ratios that proved invaluable in constraining the nucleosynthesis models for AGB stars [1, 2]. In particular, when these ratios are measured in SiC grains, they clearly reveal their prevalent origin in cool AGB circumstellar envelopes and provide information on both the local physics and the conditions at the nucleosynthesis site (the H- and He-burning layers deep inside the structure). Among the properties ascertained for the main part of the SiC data (the so-called mainstream ones), we mention a large range of {sup 14}N/{sup 15}N ratios, extending below the solar value [3], and {sup 12}C/{sup 13}C ratios ≳ 30. Other classes of grains, instead, display low carbon isotopic ratios (≳ 10) and a huge dispersion for N isotopes, with cases of large {sup 15}N excess. In the same grains, isotopes currently feeded by slow neutron captures reveal the characteristic pattern expected from this process at an efficiency slightly lower than necessary to explain the solar main s-process component. Complementary constraints can be found in oxide grains, especially Al{sub 2}O{sub 3} crystals. Here, the oxygen isotopes and the content in {sup 26}Al are of a special importance for clarifying the partial mixing processes that are known to affect evolved low-mass stars. Successes in modeling the data, as well as problems in explaining some of the mentioned isotopic ratios through current nucleosynthesis models are briefly outlined.
11. Looking for imprints of the first stellar generations in metal-poor bulge field stars
Siqueira-Mello, C; Barbuy, B; Freeman, K; Ness, M; Depagne, E; Cantelli, E; Pignatari, M; Hirschi, R; Frischknecht, U; Meynet, G; Maeder, A
2016-01-01
Context. Efforts to look for signatures of the first stars have concentrated on metal-poor halo objects. However, the low end of the bulge metallicity distribution has been shown to host some of the oldest objects in the Milky Way and hence this Galactic component potentially offers interesting targets to look at imprints of the first stellar generations. As a pilot project, we selected bulge field stars already identified in the ARGOS survey as having [Fe/H] ~ -1 and oversolar [alpha/Fe] ratios, and we used FLAMES-UVES to obtain detailed abundances of key elements that are believed to reveal imprints of the first stellar generations. Aims. The main purpose of this study is to analyse selected ARGOS stars using new high-resolution (R~45,000) and high-signal-to-noise (S/N >100) spectra. We aim to derive their stellar parameters and elemental ratios, in particular the abundances of C, N, the alpha-elements O, Mg, Si, Ca, and Ti, the odd-Z elements Na and Al, the neutron-capture s-process dominated elements Y, Z...
12. Deuterium Fractionation just after the Star Formation
Shibata, D.; Sakai, N.; Yamamoto, S.
2013-10-01
We have recently conducted a five-point strip observation of the DCO+, H13CO+, DNC, HN13C, and N2H+ lines toward low mass Class I protostar L1551 IRS5, and have evaluated the deuterium fractionation ratios DCO+/HCO+ and DNC/HNC. The DCO+/HCO+ ratio is found to be lower toward the protostar position than those toward the adjacent positions. On the other hand, the DNC/HNC ratio does not show such a decrease toward the protostar position. This suggests that the deuterium fractionation ratio of the neutral species is conserved after the star formation. If so, the deuterium fractionation of the neutral species can be used as a novel tracer to investigate the initial condition of the star formation process.
13. Shocks and star formation in Stephan's Quintet. I. Gemini spectroscopy of Hα-bright knots
Konstantopoulos, I. S.; Cluver, M. E. [Australian Astronomical Observatory, P.O. Box 915, North Ryde NSW 1670 (Australia); Appleton, P. N. [NASA Herschel Science Center (NHSC), California Institute of Technology, Pasadena, CA 91125 (United States); Guillard, P. [Institut d' Astrophysique Spatiale, Université Paris-Sud XI, F-91405 Orsay, Cedex (France); Trancho, G. [Giant Magellan Telescope Organisation, Pasadena, CA 91101 (United States); Bastian, N. [Astrophysics Research Institute, Liverpool John Moores University, Liverpool L3 5RF (United Kingdom); Charlton, J. C. [Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802 (United States); Fedotov, K.; Gallagher, S. C. [Department of Physics and Astronomy, The University of Western Ontario, London, ON N6A 3K7 (Canada); Smith, L. J. [Space Telescope Science Institute and European Space Agency, Baltimore, MD 21218 (United States); Struck, C. J., E-mail: iraklis@aao.gov.au [Department of Physics and Astronomy, Iowa State University, Ames, IA 50011 (United States)
2014-03-20
We present a Gemini-GMOS spectroscopic study of Hubble Space Telescope (HST)-selected Hα-emitting regions in Stephan's Quintet (HCG 92), a nearby compact galaxy group, with the aim of disentangling the processes of shock-induced heating and star formation in its intra-group medium. The ≈40 sources are distributed across the system, but most densely concentrated in the ∼kiloparsec-long shock region. Their spectra neatly divide them into narrow- and broad-line emitters, and we decompose the latter into three or more emission peaks corresponding to spatial elements discernible in HST imaging. The emission-line ratios of the two populations of Hα-emitters confirm their nature as H II regions (90% of the sample) or molecular gas heated by a shock front propagating at ≲300 km s{sup –1}. Their redshift distribution reveals interesting three-dimensional structure with respect to gas-phase baryons, with no H II regions associated with shocked gas, no shocked regions in the intruder galaxy NGC 7318B, and a sharp boundary between shocks and star formation. We conclude that star formation is inhibited substantially, if not entirely, in the shock region. Attributing those H II regions projected against the shock to the intruder, we find a lopsided distribution of star formation in this galaxy, reminiscent of pileup regions in models of interacting galaxies. The Hα luminosities imply mass outputs, star formation rates, and efficiencies similar to nearby star-forming regions. Two large knots are an exception to this, being comparable in stellar output to the prolific 30 Doradus region. We also examine Stephan's Quintet in the context of compact galaxy group evolution, as a paradigm for intermittent star formation histories in the presence of a rich, X-ray-emitting intra-group medium. All spectra are provided as supplemental materials.
14. Sc and neutron-capture abundances in Galactic low- and high-alpha field halo stars
Fishlock, Cherie K.; Yong, D.; Karakas, Amanda I.
2017-01-01
We determine relative abundance ratios for the neutron-capture elements Zr, La, Ce, Nd and Eu for a sample of 27 Galactic dwarf stars with -1.5 <[Fe/H] <-0.8. We also measure the iron-peak element Sc. These stars separate into three populations (low-and high-a halo and thick-disc stars) based on ...
15. High resolution spectroscopy of six new extreme helium stars
Heber, U.; Jones, G.; Drilling, J. S.
1986-01-01
High resolution spectra of six newly discovered extreme helium stars are presented. LSS 5121 is shown to be a spectroscopical twin of the hot extreme helium star HD 160641. A preliminary LTE analysis of LSS 3184 yielded an effective temperature of 22,000 K and a surface gravity of log g = 3.2. Four stars form a new subgroup, classified by sharp-lined He I spectra and pronounced O II spectra, and it is conjectured that these lie close to the Eddington limit. The whole group of extreme helium stars apparently is inhomogeneous with respect to luminosity to mass ratio and chemical composition.
16. SpeedStar: A Stellar Gyroscope Project
National Aeronautics and Space Administration — NASA science and exploration missions will continue to require observation and sensing platforms with enhanced guidance, navigation and control (GN&C)...
17. Precision High Altitude Star Tracker Project
National Aeronautics and Space Administration — Motivation: The long, successful history of scientific ballooning, coupled with tightening budgets, has led to a surge of interest in the scientific potential of...
18. Millisecond X-ray Star Tracker Project
National Aeronautics and Space Administration — CrossTrac Engineering, in cooperation with its subcontractors Dr Suneel Sheikh of ASTER Labs, Inc, and Mr Paul Graven of Cateni, Inc, proposes to develop a next...
19. Multiplicity of massive stars
Preibisch, T; Zinnecker, H; Preibisch, Thomas; Weigelt, Gerd; Zinnecker, Hans
2000-01-01
We discuss the observed multiplicity of massive stars and implications on theories of massive star formation. After a short summary of the literature on massive star multiplicity, we focus on the O- and B-type stars in the Orion Nebula Cluster, which constitute a homogenous sample of very young massive stars. 13 of these stars have recently been the targets of a bispectrum speckle interferometry survey for companions. Considering the visual and also the known spectroscopic companions of these stars, the total number of companions is at least 14. Extrapolation with correction for the unresolved systems suggests that there are at least 1.5 and perhaps as much as 4 companions per primary star on average. This number is clearly higher than the mean number of about 0.5 companions per primary star found for the low-mass stars in the general field population and also in the Orion Nebula cluster. This suggests that a different mechanism is at work in the formation of high-mass multiple systems in the dense Orion Nebu...
20. Dark stars: a review.
Freese, Katherine; Rindler-Daller, Tanja; Spolyar, Douglas; Valluri, Monica
2016-06-01
Dark stars are stellar objects made (almost entirely) of hydrogen and helium, but powered by the heat from dark matter annihilation, rather than by fusion. They are in hydrostatic and thermal equilibrium, but with an unusual power source. Weakly interacting massive particles (WIMPs), among the best candidates for dark matter, can be their own antimatter and can annihilate inside the star, thereby providing a heat source. Although dark matter constitutes only [Formula: see text]0.1% of the stellar mass, this amount is sufficient to power the star for millions to billions of years. Thus, the first phase of stellar evolution in the history of the Universe may have been dark stars. We review how dark stars come into existence, how they grow as long as dark matter fuel persists, and their stellar structure and evolution. The studies were done in two different ways, first assuming polytropic interiors and more recently using the MESA stellar evolution code; the basic results are the same. Dark stars are giant, puffy (∼10 AU) and cool (surface temperatures ∼10 000 K) objects. We follow the evolution of dark stars from their inception at ∼[Formula: see text] as they accrete mass from their surroundings to become supermassive stars, some even reaching masses >[Formula: see text] and luminosities >[Formula: see text], making them detectable with the upcoming James Webb Space Telescope. Once the dark matter runs out and the dark star dies, it may collapse to a black hole; thus dark stars may provide seeds for the supermassive black holes observed throughout the Universe and at early times. Other sites for dark star formation may exist in the Universe today in regions of high dark matter density such as the centers of galaxies. The current review briefly discusses dark stars existing today, but focuses on the early generation of dark stars.
1. Dark stars: a review
Freese, Katherine; Rindler-Daller, Tanja; Spolyar, Douglas; Valluri, Monica
2016-06-01
Dark stars are stellar objects made (almost entirely) of hydrogen and helium, but powered by the heat from dark matter annihilation, rather than by fusion. They are in hydrostatic and thermal equilibrium, but with an unusual power source. Weakly interacting massive particles (WIMPs), among the best candidates for dark matter, can be their own antimatter and can annihilate inside the star, thereby providing a heat source. Although dark matter constitutes only ≲ 0.1% of the stellar mass, this amount is sufficient to power the star for millions to billions of years. Thus, the first phase of stellar evolution in the history of the Universe may have been dark stars. We review how dark stars come into existence, how they grow as long as dark matter fuel persists, and their stellar structure and evolution. The studies were done in two different ways, first assuming polytropic interiors and more recently using the MESA stellar evolution code; the basic results are the same. Dark stars are giant, puffy (˜10 AU) and cool (surface temperatures ˜10 000 K) objects. We follow the evolution of dark stars from their inception at ˜1{{M}⊙} as they accrete mass from their surroundings to become supermassive stars, some even reaching masses >{{10}6}{{M}⊙} and luminosities >{{10}10}{{L}⊙} , making them detectable with the upcoming James Webb Space Telescope. Once the dark matter runs out and the dark star dies, it may collapse to a black hole; thus dark stars may provide seeds for the supermassive black holes observed throughout the Universe and at early times. Other sites for dark star formation may exist in the Universe today in regions of high dark matter density such as the centers of galaxies. The current review briefly discusses dark stars existing today, but focuses on the early generation of dark stars.
2. Star-Branched Polymers (Star Polymers)
Hirao, Akira
2015-09-01
The synthesis of well-defined regular and asymmetric mixed arm (hereinafter miktoarm) star-branched polymers by the living anionic polymerization is reviewed in this chapter. In particular, much attention is being devoted to the synthetic development of miktoarm star polymers since 2000. At the present time, the almost all types of multiarmed and multicomponent miktoarm star polymers have become feasible by using recently developed iterative strategy. For example, the following well-defined stars have been successfully synthesized: 3-arm ABC, 4-arm ABCD, 5-arm ABCDE, 6-arm ABCDEF, 7-arm ABCDEFG, 6-arm ABC, 9-arm ABC, 12-arm ABC, 13-arm ABCD, 9-arm AB, 17-arm AB, 33-arm AB, 7-arm ABC, 15-arm ABCD, and 31-arm ABCDE miktoarm star polymers, most of which are quite new and difficult to synthesize by the end of the 1990s. Several new specialty functional star polymers composed of vinyl polymer segments and rigid rodlike poly(acetylene) arms, helical polypeptide, or helical poly(hexyl isocyanate) arms are introduced.
3. Touchstone Stars: Highlights from the Cool Stars 18 Splinter Session
Mann, Andrew W; Boyajian, Tabetha; Gaidos, Eric; von Braun, Kaspar; Feiden, Gregory A; Metcalfe, Travis; Swift, Jonathan J; Curtis, Jason L; Deacon, Niall R; Filippazzo, Joseph C; Gillen, Ed; Hejazi, Neda; Newton, Elisabeth R
2014-01-01
We present a summary of the splinter session on "touchstone stars" -- stars with directly measured parameters -- that was organized as part of the Cool Stars 18 conference. We discuss several methods to precisely determine cool star properties such as masses and radii from eclipsing binaries, and radii and effective temperatures from interferometry. We highlight recent results in identifying and measuring parameters for touchstone stars, and ongoing efforts to use touchstone stars to determine parameters for other stars. We conclude by comparing the results of touchstone stars with cool star models, noting some unusual patterns in the differences.
4. Chemical analysis of 24 dusty (pre-)main-sequence stars
Acke, B; Acke, Bram; Waelkens, Christoffel
2004-01-01
We have analysed the chemical photospheric composition of 24 Herbig Ae/Be and Vega-type stars in search for the lambda Bootis phenomenon. We present the results of the elemental abundances of the sample stars. Some of the stars were never before studied spectroscopically at optical wavelengths. We have determined the projected rotational velocities of our sample stars. Furthermore, we discuss stars that depict a (selective) depletion pattern in detail. HD 4881 and HD 139614 seem to display an overall deficiency. AB Aur and possibly HD 126367 have subsolar values for the iron abundance, but are almost solar in silicon. HD 100546 is the only clear lambda Bootis star in our sample.
5. Spectroscopic survey of Kepler stars - II. FIES/NOT observations of A- and F-type stars
Niemczura, E.; Polińska, M.; Murphy, S. J.; Smalley, B.; Kołaczkowski, Z.; Jessen-Hansen, J.; Uytterhoeven, K.; Lykke, J. M.; Triviño Hage, A.; Michalska, G.
2017-09-01
We have analysed high-resolution spectra of 28 A and 22 F stars in the Kepler field, observed using the Fibre-Fed Échelle Spectrograph at the Nordic Optical Telescope. We provide spectral types, atmospheric parameters and chemical abundances for 50 stars. Balmer, Fe i and Fe ii lines were used to derive effective temperatures, surface gravities and microturbulent velocities. We determined chemical abundances and projected rotational velocities using a spectrum synthesis technique. Effective temperatures calculated by spectral energy distribution fitting are in good agreement with those determined from the spectral line analysis. The stars analysed include chemically peculiar stars of the Am and λ Boo types, as well as stars with approximately solar chemical abundances. The wide distribution of projected rotational velocity, vsin i, is typical for A and F stars. The microturbulence velocities obtained are typical for stars in the observed temperature and surface gravity ranges. Moreover, we affirm the results of Niemczura et al. that Am stars do not have systematically higher microturbulent velocities than normal stars of the same temperature.
6. Winds of Planet Hosting Stars
Nicholson, B A; Brookshaw, L; Vidotto, A A; Carter, B D; Marsden, S C; Soutter, J; Waite, I A; Horner, J
2015-01-01
The field of exoplanetary science is one of the most rapidly growing areas of astrophysical research. As more planets are discovered around other stars, new techniques have been developed that have allowed astronomers to begin to characterise them. Two of the most important factors in understanding the evolution of these planets, and potentially determining whether they are habitable, are the behaviour of the winds of the host star and the way in which they interact with the planet. The purpose of this project is to reconstruct the magnetic fields of planet hosting stars from spectropolarimetric observations, and to use these magnetic field maps to inform simulations of the stellar winds in those systems using the Block Adaptive Tree Solar-wind Roe Upwind Scheme (BATS-R-US) code. The BATS-R-US code was originally written to investigate the behaviour of the Solar wind, and so has been altered to be used in the context of other stellar systems. These simulations will give information about the velocity, pressur...
7. An equatorial ultra iron-poor star identified in BOSS
Prieto, C Allende; Aguado, D S; Hernandez, J I Gonzalez; Rebolo, R; Lee, Y S; Beers, T C; Rockosi, C M; Ge, J
2015-01-01
We report the discovery of SDSS J131326.89-001941.4, an ultra iron-poor red giant star ([Fe/H] ~ -4.3) with a very high carbon abundance ([C/Fe]~ +2.5). This object is the fifth star in this rare class, and the combination of a fairly low effective temperature (Teff ~ 5300 K), which enhances line absorption, with its brightness (g=16.9), makes it possible to measure the abundances of calcium, carbon and iron using a low-resolution spectrum from the Sloan Digital Sky Survey. We examine the carbon and iron abundance ratios in this star and other similar objects in the light of predicted yields from metal-free massive stars, and conclude that they are consistent. By way of comparison, stars with similarly low iron abundances but lower carbon-to-iron ratios deviate from the theoretical predictions.
8. Applying Machine Learning to Star Cluster Classification
Fedorenko, Kristina; Grasha, Kathryn; Calzetti, Daniela; Mahadevan, Sridhar
2016-01-01
Catalogs describing populations of star clusters are essential in investigating a range of important issues, from star formation to galaxy evolution. Star cluster catalogs are typically created in a two-step process: in the first step, a catalog of sources is automatically produced; in the second step, each of the extracted sources is visually inspected by 3-to-5 human classifiers and assigned a category. Classification by humans is labor-intensive and time consuming, thus it creates a bottleneck, and substantially slows down progress in star cluster research.We seek to automate the process of labeling star clusters (the second step) through applying supervised machine learning techniques. This will provide a fast, objective, and reproducible classification. Our data is HST (WFC3 and ACS) images of galaxies in the distance range of 3.5-12 Mpc, with a few thousand star clusters already classified by humans as a part of the LEGUS (Legacy ExtraGalactic UV Survey) project. The classification is based on 4 labels (Class 1 - symmetric, compact cluster; Class 2 - concentrated object with some degree of asymmetry; Class 3 - multiple peak system, diffuse; and Class 4 - spurious detection). We start by looking at basic machine learning methods such as decision trees. We then proceed to evaluate performance of more advanced techniques, focusing on convolutional neural networks and other Deep Learning methods. We analyze the results, and suggest several directions for further improvement.
9. Nitrogen chronology of massive main sequence stars
Köhler, K; Brott, I; Langer, N; de Koter, A
2012-01-01
Rotational mixing in massive main sequence stars is predicted to monotonically increase their surface nitrogen abundance with time. We use this effect to design a method for constraining the age and the inclination angle of massive main sequence stars, given their observed luminosity, effective temperature, projected rotational velocity and surface nitrogen abundance. This method relies on stellar evolution models for different metallicities, masses and rotation rates. We use the population synthesis code STARMAKER to show the range of applicability of our method. We apply this method to 79 early B-type main sequence stars near the LMC clusters NGC 2004 and N 11 and the SMC clusters NGC 330 and NGC 346. From all stars within the sample, 17 were found to be suitable for an age analysis. For ten of them, which are rapidly rotating stars without a strong nitrogen enhancement, it has been previously concluded that they did not evolve as rotationally mixed single stars. This is confirmed by our analysis, which fla...
10. Rocky Planetesimals as the Origin of Metals in DZ Stars
Farihi, J; Redfield, S; Dufour, P; Hambly, N C
2010-01-01
{Abridged}. An analysis of the calcium and hydrogen abundances, Galactic positions and kinematics of 146 DZ stars from the Sloan Digital Sky Survey demonstrates that interaction with the interstellar medium cannot account for their externally polluted atmospheres. The calcium-to-hydrogen ratios for the 37 DZA stars are dominated by super-solar values, as are the lower limits for the remaining 109 DZ stars. All together their metal-contaminated convective envelopes contain 10^{20+-2} g of calcium, commensurate with the masses of calcium inferred for large asteroids. It is probable that these stars are contaminated by circumstellar matter; the rocky remains of terrestrial planetary systems. In this picture, two predictions emerge: 1) at least 3.5% of all main sequence A- and F-type stars build terrestrial planets; and 2) the DZA stars are externally polluted by both metals and hydrogen, and hence constrain the frequency and mass of water-rich, extrasolar planetesimals.
11. Light Curves for Rapidly-Rotating Neutron Stars
Cadeau, C; Leahy, D; Campbell, S S; Cadeau, Coire; Morsink, Sharon M.; Leahy, Denis; Campbell, Sheldon S.
2006-01-01
We present raytracing computations for light emitted from the surface of a rapidly-rotating neutron star in order to construct light curves for X-ray pulsars and bursters. These calculations are for realistic models of rapidly-rotating neutron stars which take into account both the correct exterior metric and the oblate shape of the star. We find that the most important effect arising from rotation comes from the oblate shape of the rotating star. We find that approximating a rotating neutron star as a sphere introduces serious errors in fitted values of the star's radius and mass if the rotation rate is very large. However, in most cases acceptable fits to the ratio M/R can be obtained with the spherical approximation.
12. Protostellar Outflows and Radiative Feedback from Massive Stars. II. Feedback, Star Formation Efficiency, and Outflow Broadening
Kuiper, Rolf; Yorke, Harold W
2016-01-01
We perform two-dimensional axially symmetric radiation-hydrodynamic simulations to assess the impact of outflows and radiative force feedback from massive protostars by varying when the protostellar outflow starts, the ratio of ejection to accretion rates, and the strength of the wide angle disk wind component. The star formation efficiency, i.e. the ratio of final stellar mass to initial core mass, is dominated by radiative forces and the ratio of outflow to accretion rates. Increasing this ratio has three effects: First, the protostar grows slower with a lower luminosity at any given time, lowering radiative feedback. Second, bipolar cavities cleared by the outflow are larger, further diminishing radiative feedback on disk and core scales. Third, the higher momentum outflow sweeps up more material from the collapsing envelope, decreasing the protostar's potential mass reservoir via entrainment. The star formation efficiency varies with the ratio of ejection to accretion rates from 50% in the case of very we...
13. STAR in CTO PCI: When is STAR not a star?
Hira, Ravi S; Dean, Larry S
2016-04-01
Subintimal tracking and reentry (STAR) has been used as a bailout strategy and involves an uncontrolled dissection and recanalization into the distal lumen to reestablish vessel patency. In the current study, thrombolysis in myocardial infarction (TIMI) flow < 3 was the only variable which they found to be significantly associated with restenosis and reocclusion after stent placement. It may be reasonable to consider second generation drug eluting stent placement in patients receiving STAR that have TIMI 3 flow, however, this should only be done if there is no compromise of major side branches. If unsure, we recommend to perform balloon angioplasty without stenting. © 2016 Wiley Periodicals, Inc.
14. Weighing Ultra-Cool Stars
2004-05-01
Large Ground-Based Telescopes and Hubble Team-Up to Perform First Direct Brown Dwarf Mass Measurement [1] Summary Using ESO's Very Large Telescope at Paranal and a suite of ground- and space-based telescopes in a four-year long study, an international team of astronomers has measured for the first time the mass of an ultra-cool star and its companion brown dwarf. The two stars form a binary system and orbit each other in about 10 years. The team obtained high-resolution near-infrared images; on the ground, they defeated the blurring effect of the terrestrial atmosphere by means of adaptive optics techniques. By precisely determining the orbit projected on the sky, the astronomers were able to measure the total mass of the stars. Additional data and comparison with stellar models then yield the mass of each of the components. The heavier of the two stars has a mass around 8.5% of the mass of the Sun and its brown dwarf companion is even lighter, only 6% of the solar mass. Both objects are relatively young with an age of about 500-1,000 million years. These observations represent a decisive step towards the still missing calibration of stellar evolution models for very-low mass stars. PR Photo 19a/04: Orbit of the ultra-cool stars in 2MASSW J0746425+2000321. PR Photo 19b/04: Animated Gif of the orbital motion. Telephone number star Even though astronomers have found several hundreds of very low mass stars and brown dwarfs, the fundamental properties of these extreme objects, such as masses and surface temperatures, are still not well known. Within the cosmic zoo, these ultra-cool stars represent a class of "intermediate" objects between giant planets - like Jupiter - and "normal" stars less massive than our Sun, and to understand them well is therefore crucial to the field of stellar astrophysics. The problem with these ultra-cool stars is that contrary to normal stars that burn hydrogen in their central core, no unique relation exists between the luminosity of the
15. The First Stars
Yoshida, Naoki
2010-10-01
The standard cosmological model predicts that the first cosmological objects are formed when the age of the universe is a few hundred million years. Recent theoretical studies and numerical simulations consistently suggest that the first objects are very massive primordial stars. We introduce the key physics and explain why the first stars are thought to be massive, rather than to be low-mass stars. The state-of-the-art simulations include all the relevant atomic and molecular physics to follow the thermal evolution of a prestellar gas cloud to very high stellar'' densities. Evolutionary calculations of the primordial stars suggest the formation of massive blackholes in the early universe. Finally, we show the results from high-resolution simulations of star formation in a low-metallicity gas. Vigorous fragmentation is triggered in a star-forming gas cloud at a metallicity of as low as Z = 10-5Zsolar.
16. Star formation history in forming dwarf galaxies
Berczik, P.; Kravchuk, S. G.
The processes of formation and evolution of isolated dwarf galaxies over the Hubble timescale is followed by means of SPH techniques. As an initial protogalaxy perturbation we consider an isolated, uniform, solid -- body rotated sphere involved into the Hubble flow and made of dark and baryonic matter in a 10:1 ratio. The simulations are carried out for the set of models having spin parameters lambda in the range from 0.01 to 0.08 and the total mass of dark matter 1011 M_odot . Our model includes gasdynamics, radiative processes, star formation, supernova feedback and simplified chemistry. The application of modified star formation criterion which accounts for chaotic motions and the time lag between initial development of suitable conditions for star formation and star formation itself (Berczik P.P, Kravchuk S.G. 1997, Ap.Sp.Sci.) provides the realistic description of the process of galaxy formation and evolution. Two parameters: total mass and initial angular momentum of the dwarf protogalaxy play the crucial role in its star formation activity. After the 15 Gyr of the evolution the rapidly rotated dwarf galaxies manifest themselves as an extremly gasrich, heavy element deficient objects showing the initial burst of star formation activity in several spatially separated regions. Slowly rotating objects manifest themselves finally as typical evolved dwarf galaxies.
17. Star Formation History in the Solar Vicinity
Gianpaolo, B; Gianpaolo, Bertelli; Emma, Nasi
2000-01-01
The star formation history in the solar neighbourhood is inferred comparing a sample of field stars from the Hipparcos Catalog with synthetic CMDs. We considered separately the main sequence and the red giant region of the HR diagram. The criteria for our best solutions are based on the $\\chi^{2}$ minimization of star distributions in selected zones of the HR diagram. Our analysis suggests that: a) the solutions are compatible with a Salpeter IMF and with {\\sl a star formation rate increasing, in a broad sense, from the beginning to the present time}; b) the deduced volume mass densities and the corresponding absolute scale of the SFR solutions are strongly influenced by the initial mass function slope of low mass stars (below 0.5 Mo); c) the stellar evolutionary models are not completely adequate: in fact {\\sl the theoretical ratio between the He-burning and MS star numbers is always a factor 1.5 greater than the observational value}. This fact could indicate the need of a more efficient overshoot in the evo...
18. r-Process Enhanced Halo Stars
Cowan, J J; Lawler, J E; Den Hartog, E A
2006-01-01
Abundance observations indicate the presence of rapid-neutron capture (i.e., r-process) elements in old Galactic halo and globular cluster stars. These observations provide insight into the nature of the earliest generations of stars in the Galaxy -- the progenitors of the halo stars -- responsible for neutron-capture synthesis of the heavy elements. The large star-to-star scatter observed in the abundances of neutron-capture element/iron ratios at low metallicities -- which diminishes with increasing metallicity or [Fe/H] -- suggests the formation of these heavy elements (presumably from certain types of supernovae) was rare in the early Galaxy. The stellar abundances also indicate a change from the r-process to the slow neutron capture (i.e., s-) process at higher metallicities in the Galaxy and provide insight into Galactic chemical evolution. Finally, the detection of thorium and uranium in halo and globular cluster stars offers an independent age-dating technique that can put lower limits on the age of t...
19. Faint (and bright) variable stars in the satellites of the Milky Way
Vivas, A. Katherina
2017-09-01
I describe two ongoing projects related with variable stars in the satellites of the MilkyWay. In the first project, we are searching for dwarf Cepheid stars (a.k.a δ Scuti and/or SX Phe) in some of the classical dwarf spheroidal galaxies. Our goal is to characterize the population of these variable stars under different environments (age, metallicity) in order to study their use as standard candles in systems for which the metallicity is not necessarily known. In the second project we search for RR Lyrae stars in the new ultra-faint satellite galaxies that have been discovered around the Milky Way in recent years.
20. Hotspot mitigation in the StarCAVE
Rhee, Jordan
2010-01-27
Rear-projected screens such as those in Digital Light Projection (DLP) televisions suffer from an image quality problem called hot spotting, where the image is brightest at a point dependent on the viewing angle. In rear-projected mulit-screen configurations such as the StarCAVE at Calit2, this causes discontinuities in brightness at the edges where screens meet, and thus in the 3D image perceived by the user. In the StarCAVE we know the viewer\\'s position in 3D space and we have programmable graphics hardware, so we can mitigate this effect by performing post-processing in the inverse of the pattern, yielding a homogenous image at the output. Our implementation improves brightness homogeneity by a factor of 4 while decreasing frame rate by only 1-3 fps.
1. The star cluster - field star connection in nearby spiral galaxies. II. Field star and cluster formation histories and their relation
Silva-Villa, E.; Larsen, S. S.
2011-05-01
Context. Recent studies have started to cast doubt on the assumption that most stars are formed in clusters. Observational studies of field stars and star cluster systems in nearby galaxies can lead to better constraints on the fraction of stars forming in clusters. Ultimately this may lead to a better understanding of star formation in galaxies, and galaxy evolution in general. Aims: We aim to constrain the amount of star formation happening in long-lived clusters for four galaxies through the homogeneous, simultaneous study of field stars and star clusters. Methods: Using HST/ACS and HST/WFPC2 images of the galaxies NGC 45, NGC 1313, NGC 5236, and NGC 7793, we estimate star formation histories by means of the synthetic CMD method. Masses and ages of star clusters are estimated using simple stellar population model fitting. Comparing observed and modeled luminosity functions, we estimate cluster formation rates. By randomly sampling the stellar initial mass function (SIMF), we construct artificial star clusters and quantify how stochastic effects influence cluster detection, integrated colors, and age estimates. Results: Star formation rates appear to be constant over the past 107 - 108 years within the fields covered by our observations. The number of clusters identified per galaxy varies, with a few detected massive clusters (M ≥ 105 M⊙) and a few older than 1 Gyr. Among our sample of galaxies, NGC 5236 and NGC 1313 show high star and cluster formation rates, while NGC 7793 and NGC 45 show lower values. We find that stochastic sampling of the SIMF has a strong impact on the estimation of ages, colors, and completeness for clusters with masses ≤ 103 - 104 M⊙, while the effect is less pronounced for high masses. Stochasticity also makes size measurements highly uncertain at young ages (τ ≲ 108 yr), making it difficult to distinguish between clusters and stars based on sizes. Conclusions: The ratio of star formation happening in clusters (Γ) compared to
2. Interacting binary stars
1978-01-01
Interacting Binary Stars deals with the development, ideas, and problems in the study of interacting binary stars. The book consolidates the information that is scattered over many publications and papers and gives an account of important discoveries with relevant historical background. Chapters are devoted to the presentation and discussion of the different facets of the field, such as historical account of the development in the field of study of binary stars; the Roche equipotential surfaces; methods and techniques in space astronomy; and enumeration of binary star systems that are studied
3. ENERGY STAR Unit Reports
Department of Housing and Urban Development — These quarterly Federal Fiscal Year performance reports track the ENERGY STAR qualified HOME units that Participating Jurisdictions record in HUD's Integrated...
4. Horizontal Branch stars as AmFm/HgMn stars
Michaud, G
2008-01-01
Recent observations and models for horizontal branch stars are briefly described and compared to models for AmFm stars. The limitations of those models are emphasized by a comparison to observations and models for HgMn stars.
5. IS THERE A METALLICITY CEILING TO FORM CARBON STARS?-A NOVEL TECHNIQUE REVEALS A SCARCITY OF C STARS IN THE INNER M31 DISK
Boyer, M. L. [Observational Cosmology Lab, Code 665, NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Girardi, L. [Osservatorio Astronomico di Padova-INAF, Vicolo dell' Osservatorio 5, I-35122 Padova (Italy); Marigo, P. [Department of Physics and Astronomy G. Galilei, University of Padova, Vicolo dell' Osservatorio 3, I-35122 Padova (Italy); Williams, B. F.; Rosenfield, P.; Dalcanton, J. J.; Weisz, D. R. [Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195 (United States); Aringer, B.; Nowotny, W. [Department of Astrophysics, University of Vienna, Tuerkenschanzstrasse 17, A-1180 Wien (Austria); Dorman, C. E.; Guhathakurta, P. [University of California Observatories/Lick Observatory, University of California, 1156 High Street, Santa Cruz, CA 95064 (United States); Melbourne, J. L. [Caltech Optical Observatories, Division of Physics, Mathematics and Astronomy, Mail Stop 301-17, California Institute of Technology, Pasadena, CA 91125 (United States); Olsen, K. A. G., E-mail: martha.boyer@nasa.gov [National Optical Astronomy Observatory, 950 North Cherry Avenue, Tucson, AZ 85719 (United States)
2013-09-01
We use medium-band near-infrared (NIR) Hubble Space Telescope WFC3 photometry with model NIR spectra of asymptotic giant branch (AGB) stars to develop a new tool for efficiently distinguishing carbon-rich (C-type) AGB stars from oxygen-rich (M-type) AGB stars in galaxies at the edge of and outside the Local Group. We present the results of a test of this method on a region of the inner disk of M31, where we find a surprising lack of C stars, contrary to the findings of previous C star searches in other regions of M31. We find only one candidate C star (plus up to six additional, less certain C star candidates), resulting in an extremely low ratio of C to M stars (C/M= (3.3{sup +20}{sub -0.1}) Multiplication-Sign 10{sup -4}) that is one to two orders of magnitude lower than other C/M estimates in M31. The low C/M ratio is likely due to the high metallicity in this region which impedes stars from achieving C/O > 1 in their atmospheres. These observations provide stringent constraints to evolutionary models of metal-rich AGB stars and suggest that there is a metallicity threshold above which M stars are unable to make the transition to C stars, dramatically affecting AGB mass loss and dust production and, consequently, the observed global properties of metal-rich galaxies.
6. Is There a Metallicity Ceiling to Form Carbon Stars? - A Novel Technique Reveals a Scarcity of C-Stars in the Inner M31 Disk
Boyer, Martha L.; Girardi, L.; Marigo, P.; Williams, B. F.; Aringer, B.; Nowotny, W.; Rosenfield, P.; Dorman, C. E.; Guhathakurta, P.; Dalcanton, J. J.; Melbourne, J. L.; Olsen, K. A. G.; Weisz, D. R.
2013-01-01
We use medium-band near-infrared (NIR) Hubble Space Telescope WFC3 photometry with model NIR spectra of Asymptotic Giant Branch (AGB) stars to develop a new tool for efficiently distinguish- ing carbon-rich (C-type) AGB stars from oxygen-rich (M-type) AGB stars in galaxies at the edge of and outside the Local Group. We present the results of a test of this method on a region of the inner disk of M31, where we nd a surprising lack of C stars, contrary to the ndings of previous C star searches in other regions of M31. We nd only 1 candidate C star (plus up to 6 additional, less certain C stars candidates), resulting in an extremely low ratio of C to M stars (C=M = (3.3(sup +20)(sub - 0.1) x 10(sup -4)) that is 1-2 orders of magnitude lower than other C/M estimates in M31. The low C/M ratio is likely due to the high metallicity in this region which impedes stars from achieving C/O > 1 in their atmospheres. These observations provide stringent constraints to evolutionary models of metal-rich AGB stars and suggest that there is a metallicity threshold above which M stars are unable to make the transition to C stars, dramatically affecting AGB mass loss and dust production and, consequently, the observed global properties of metal-rich galaxies.
7. Spectral Properties of Cool Stars: Extended Abundance Analysis of 1626 Planet Search Stars
Brewer, John M; Valenti, Jeff A; Piskunov, Nikolai
2016-01-01
We present a catalog of uniformly determined stellar properties and abundances for 1626 F, G, and K stars using an automated spectral synthesis modeling procedure. All stars were observed using the HIRES spectrograph at Keck Observatory. Our procedure used a single line list to fit model spectra to observations of all stars to determine effective temperature, surface gravity, metallicity, projected rotational velocity, and the abundances of 15 elements (C, N, O, Na, Mg, Al, Si, Ca, Ti, V, Cr, Mn, Fe, Ni, & Y). Sixty percent of the sample had Hipparcos parallaxes and V-band photometry which we combined with the spectroscopic results to obtain mass, radius, and luminosity. Additionally, we used the luminosity, effective temperature, metallicity and alpha-element enhancement to interpolate in the Yonsei-Yale isochrones to derive mass, radius, gravity, and age ranges for those stars. Finally, we determined new relations between effective temperature and macroturbulence for dwarfs and subgiants. Our analysis a...
8. Black Holes and Neutron Stars in Nearby Galaxies: Insights with NuSTAR
Vulic, Neven; Hornschemeier, Ann E.; Wik, Daniel R.; Yukita, Mihoko; Ptak, Andrew; Zezas, Andreas; Lehmer, Bret
2017-08-01
There are a handful of diagnostics that permit determination of compact object identity in X-ray binaries (XRBs), and most of these are confined to bright Galactic sources for which a large number of photons can be gathered. We report on recent work using sensitive hard X-ray constraints to separate black holes from neutron stars in external galaxies with NuSTAR. Determining the ratio of XRBs that are black holes or neutron stars in different galactic environments reveals critical clues about the formation and evolution of binary systems. We analyze a NuSTAR-selected sample of ≈10 nearby galaxies within 5 Mpc that represent a range of star formation rates (0.1 - 10 M⊙ yr-1) and stellar masses (109-11 M⊙). Using color-color and color-intensity diagnostics we classify sources by their accretion states and compact object types. We analyze the 12-25 keV X-ray luminosity functions (XLFs) of our sample scaled by specific star formation rate and compare with the 0.5-8 keV analogues. Our diagnostic methods allow us to produce black hole-only and neutron star-only extragalactic XLFs for the first time.
9. KELT-9b: A giant planet with the temperature of a red dwarf star transiting an unevolved A0 star
Gaudi, B. Scott; Stassun, Keivan G.; Collins, Karen A.; Beatty, Thomas G.; Zhou, George; Latham, David W.; Bieryla, Allyson; Eastman, Jason D.; Siverd, Robert; Crepp, Justin R.; Gonzales, Erica J.; Stevens, Daniel J.; Buchhave, Lars A.; Pepper, Joshua; Johnson, Marshall C.; Colon, Knicole D.; Jensen, Eric L. N.; Rodriguez, Joseph; KELT and KELT-FUN Collaborations
2017-06-01
We report the discovery of KELT-9b, the hottest, most irradiated known hot Jupiter, with a period of ~1.5 days, and radius and mass of ~1.8 Jupiter radii and ~2.7 Jupiter masses. The host is a massive (~2.3 solar masses), hot (effective temperature of ~9,600 K) rapidly-rotating (projected rotation velocity of ~100 km/s) A0 star. Given the implied planetary equilibrium temperature of ~3800 K and scale height of ~1000 km (assuming zero albedo and no heat redistribution), this system provides one of the best targets for detailed characterization of a hot Jupiter atmosphere under extreme irradiation. The planet has been confirmed via high-precision primary transit observations in multiple bands, a lack of companions in deep AO observations, radial velocity detection of the reflex motion of the star due to the companion, detection of the Doppler tomographic signal, and a detection of the secondary eclipse depth in the far-red optical (z) that implies a brightness temperature of ~4600 K, and thus exceptionally poor heat redistribution to the night side. We find that the planet is on a near-polar orbit, likely resulting in orbital precession that will be detectable within a few years. The brightness of the host, the extreme planet temperature, large planet-to-star radius ratio, large planetary atmospheric scale height, and short orbital period, make this an exceptional target for follow-up studies of the planet's atmosphere, which may exhibit unusual photochemistry due to the extreme amount of incident high-energy radiation.
10. Lithium Abundance of Metal-poor Stars
Hua-Wei Zhang; Gang Zhao
2003-01-01
High-resolution, high signal-to-noise ratio spectra have been obtained for 32 metal-poor stars. The equivalent widths of Li λ6708A were measured and the lithium abundances were derived. The average lithium abundance of 21 stars on the lithium plateau is 2.33±0.02 dex. The Lithium plateau exhibits a marginal trend along metallicity, dA(Li)/d[Fe/H] = 0.12±0.06, and no clear trend with the effective temperature. The trend indicates that the abundance of lithium plateau may not be primordial and that a part of the lithium was produced in Galactic Chemical Evolution (GCE).
11. The ESO Large Programme First Stars
Bonifacio, P; Andrievsky, S; Barbuy, B; Beers, T C; Caffau, E; Cayrel, R; Depagne, E; François, P; Hernandez, J I Gonzalez; Hansen, C J; Herwig, F; Hill, V; Korotin, S A; Ludwig, H -G; Molaro, P; Nordström, B; Plez, B; Primas, F; Sivarani, T; Spite, F; Spite, M
2008-01-01
In ESO period 65 (April-September 2000) the large programme 165.N-0276, led by Roger Cayrel, began making use of UVES at the Kueyen VLT telescope. Known within the Team and outside as First Stars'', it was aimed at obtaining high resolution, high signal-to-noise ratio spectra in the range 320 nm -- 1000 nm for a large sample of extremely metal-poor (EMP) stars identified from the HK objective prism survey.In this contribution we highlight the main results of the large programme.
12. AGB stars and presolar grains
Busso, M; Maiorca, E; Palmerini, S
2013-01-01
Among presolar materials recovered in meteorites, abundant SiC and Al$_{2}$O$_{3}$ grains of AGB origins were found. They showed records of C, N, O, $^{26}$Al and s-element isotopic ratios that proved invaluable in constraining the nucleosynthesis models for AGB stars \\cite{zin,gal}. In particular, when these ratios are measured in SiC grains, they clearly reveal their prevalent origin in cool AGB circumstellar envelopes and provide information on both the local physics and the conditions at the nucleosynthesis site (the H- and He-burning layers deep inside the structure). Among the properties ascertained for the main part of the SiC data (the so-called {\\it mainstream} ones), we mention a large range of $^{14}$N/$^{15}$N ratios, extending below the solar value \\cite{mar}, and $^{12}$C/$^{13}$C ratios $\\gtrsim$ 30. Other classes of grains, instead, display low carbon isotopic ratios ($\\gtrsim 10$) and a huge dispersion for N isotopes, with cases of large $^{15}$N excess. In the same grains, isotopes currently...
13. The Massive Star Population in M101
Grammer, Skyler H.
An increasing number of non-terminal giant eruptions are being observed by modern supernova and transient surveys. Very little is known about the origin of these giant eruptions and their progenitors which are presumably very-massive, evolved stars such as luminous blue variables, hypergiants, and supergiants. Motivated by the small number of progenitors positively associated with these giant eruptions, we have begun a survey of the luminous and evolved massive star populations in several nearby galaxies. We aim to identify the likely progenitors of the giant eruptions, study the spatial variations in the stellar populations, and examine the relationship between massive star populations and their environment. The work presented here is focused on stellar populations in the relatively nearby, giant, spiral galaxy M101 from sixteen archival BVI HST/ACS images. We create a catalog of stars in the direction to M101 with photometric errors history (SFH) for the stellar populations in five 2' wide annuli by fitting the color-magnitude diagrams. Binning the SFH into time frames corresponding to populations traced by Halpha, far ultraviolet (FUV), and near ultraviolet (NUV) emission, we show that the fraction of stellar populations young enough to contribute in Halpha is 15% " 35% in the inner regions, compared to less than 5% in the outer regions. This provides a sufficient explanation for the lack of Halpha emission at large radii. We also model the blue to red supergiant ratio in our five annuli, examine the effects that a metallicity gradient and variable SFH have on the predicted ratios, and compare to the observed values. We find that the radial behavior of our modeled blue to red supergiant ratios is highly sensitive to both spatial variations in the SFH and metallicity. Incorporating the derived SFH into the modeled ratios, we are able to reproduce the observed values at large radii (low metallicity), but at small radii (high metallicity) the modeled and observed
14. Stars and linear dunes on Mars
Edgett, Kenneth S.; Blumberg, Dan G.
1994-01-01
A field containing 11 star and incipient star dunes occurs on Mars at 8.8 deg S, 270.9 deg W. Examples of linear dunes are found in a crater at 59.4 deg S, 343 deg W. While rare, dune varieties that form in bi- and multidirectional wind regimes are not absent from the surface of Mars. The occurence of both of these dune fields offers new insight into the nature of martian wind conditions and sand supply. The linear dunes appears to have formed through modification of a formerly transverse aeolian deposit, suggesting a relatively recent change in local wind direction. The 11 dunes in the star dune locality show a progressive change from barchan to star form as each successive dune has traveled up into a valley, into a more complex wind regime. The star dunes corroborate the model of N. Lancaster (1989), for the formation of star dunes by projection of transverse dunes into a complex, topographically influenced wind regime. The star dunes have dark streaks emanating from them, providing evidence that the dunes were active at or near the time the relevant image was obtained by the Viking 1 orbiter in 1978. The star and linear dunes described here are located in different regions on the martian surface. Unlike most star and linear dunes on Earth, both martian examples are isolated occurrences; neither is part of a major sand sea. Previously published Mars general circulation model results suggest that the region in which the linear dune field occurs should be a bimodal wind regime, while the region in which the star dunes occur should be unimodal. The star dunes are probably the result of localized complication of the wind regime owing to topographic confinement of the dunes. Local topographic influence on wind regime is also evident in the linear dune field, as there are transverse dunes in close proximity to the linear dunes, and their occurrence is best explained by funneling of wind through a topographic gap in the upwind crater wall.
15. Observational Effects of Magnetism in O Stars: Surface Nitrogen Abundances
Martins, F.; Escolano, C.; Wade, G. A.; Donati, J. F.; Bouret, J. C.
2011-01-01
Aims. We investigate the surface nitrogen content of the six magnetic O stars known to date as well as of the early B-type star Tau Sco.. We compare these abundances to predictions of evolutionary models to isolate the effects of magnetic field on the transport of elements in stellar interiors. Methods. We conduct a quantitative spectroscopic analysis of the ample stars with state-of-the-art atmosphere models. We rely on high signal-to-noise ratio, high resolution optical spectra obtained with ESPADONS at CFHT and NARVAL at TBL. Atmosphere models and synthetic spectra are computed with the code CMFGEN. Values of N/H together with their uncertainties are determined and compared to predictions of evolutionary models. Results. We find that the magnetic stars can be divided into two groups: one with stars displaying no N enrichment (one object); and one with stars most likely showing extra N enrichment (5 objects). For one star (Ori C) no robust conclusion can be drawn due to its young age. The star with no N enrichment is the one with the weakest magnetic field, possibly of dynamo origin. It might be a star having experienced strong magnetic braking under the condition of solid body rotation, but its rotational velocity is still relatively large. The five stars with high N content were probably slow rotators on the zero age main sequence, but they have surface N/H typical of normal O stars, indicating that the presence of a (probably fossil) magnetic field leads to extra enrichment. These stars may have a strong differential rotation inducing shear mixing. Our results shOuld be viewed as a basis on which new theoretical simulations can rely to better understand the effect of magnetism on the evolution of massive stars.
16. Star Trek in the Schools
Journal of Aerospace Education, 1977
1977-01-01
Describes specific educational programs for using the Star Trek TV program from kindergarten through college. For each grade level lesson plans, ideas for incorporating Star Trek into future classes, and reports of specific programs utilizing Star Trek are provided. (SL)
17. Binary mass ratios: system mass not primary mass
Goodwin, Simon P
2012-01-01
Binary properties are usually expressed (for good observational reasons) as a function of primary mass. It has been found that the distribution of companion masses -- the mass ratio distribution -- is different for different primary masses. We argue that system mass is the more fundamental physical parameter to use. We show that if system masses are drawn from a log-normal mass function, then the different observed mass ratio distributions as a function of primary mass, from M-dwarfs to A-stars, are all consistent with a universal, flat, system mass ratio distribution. We also show that the brown dwarf mass ratio distribution is not drawn from the same flat distribution, suggesting that the process which decides upon mass ratios is very different in brown dwarfs and stars.
18. Stars and Flowers, Flowers and Stars
Minti, Hari
2012-12-01
The author, a graduated from the Bucharest University (1964), actually living and working in Israel, concerns his book to variable stars and flowers, two domains of his interest. The analogies includes double stars, eclipsing double stars, eclipses, Big Bang. The book contains 34 chapters, each of which concerns various relations between astronomy and other sciences and pseudosciences such as Psychology, Religion, Geology, Computers and Astrology (to which the author is not an adherent). A special part of the book is dedicated to archeoastronomy and ethnoastronomy, as well as to history of astronomy. Between the main points of interest of these parts: ancient sanctuaries in Sarmizegetusa (Dacia), Stone Henge(UK) and other. The last chapter of the book is dedicated to flowers. The book is richly illustrated. It is designed for a wide circle of readers.
19. Hybrid stars that masquerade as neutron stars
Mark Paris; Mark Alford; Matt Braby; Sanjay Reddy
2004-11-01
We show that a hybrid (nuclear + quark matter) star can have a mass-radius relationship very similar to that predicted for a star made of purely nucleonic matter. We show this for a generic parameterization of the quark matter equation of state, and also for an MIT bag model, each including a phenomenological correction based on gluonic corrections to the equation of state. We obtain hybrid stars as heavy as 2 M{sub solar} for reasonable values of the bag model parameters. For nuclear matter, we use the equation of state calculated by Akmal, Pandharipande, and Ravenhall using many-body techniques. Both mixed and homogeneous phases of nuclear and quark matter are considered.
20. Astrophysics of extreme mass ratio inspiral sources
Hopman, C
2007-01-01
Compact remnants on orbits with peri-apses close to the Schwarzschild radius of a massive black hole (MBH) lose orbital energy by emitting gravitational waves (GWs) and spiral in. Scattering with other stars allows successful inspiral of such extreme mass ratio inspiral sources (EMRIs) only within small distances, a < few \\times 0.01 pc from the MBH. The event rate of EMRIs is therefore dominated by the stellar dynamics and content in the inner few \\times 0.01 pc. I discuss the relevant dynamical aspects and resulting estimated event rates of EMRIs. Subjects considered include the loss-cone treatment of inspiral sources; mass segregation; resonant relaxation; and alternative routes to EMRI formation such as tidal binary disruptions, stellar formation in disks and tidal capture of massive main sequence stars. The EMRI event rate is estimated to be of order few \\times 10^2/Gyr per MBH, giving excellent prospects for observation by LISA. | 151,713 | 630,366 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2018-13 | longest | en | 0.852553 |
https://www.springbokcasino.co.za/roulette/how-to-play | 1,601,356,612,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600401624636.80/warc/CC-MAIN-20200929025239-20200929055239-00675.warc.gz | 946,533,712 | 13,221 | Here’s the big secret to winning at Roulette: just guess! Yes, it’s true, no matter how many so-called ‘experts’ offer to sell you a winning strategy, Roulette is simply a game of chance. Every straight bet on the table carries the same house edge, which is 2.7% on the single-zero wheel and 5.3% on the double-zero wheel. No strategy, betting system or lucky underwear will be able to lower the house edge in the long run.
But what about all that advice on ‘Roulette strategy’ that flies around the gambling world? With titles like The Grand Martingale and Cancellation, these systems sound fairly legit to the novice Roulette player. The problem with these and all other betting systems is that they rely on a mistake in thinking called the gambler’s fallacy.
The gambler’s fallacy is the mistaken belief that because a number hasn’t yet appeared in a series of spins, it should come up soon. The problem with this is that, in the long run, after thousands and thousands of spins, every number (including the 0 and 00 in Roulette) will come up roughly an even number of times.
But just because it happens in the long run doesn’t mean these odds are translated to the short run. After sitting at the Roulette table for an hour, the number 1 could come up three times, thirty times, or not at all.
Let’s use that last scenario as an example: there have been forty spins and the number 1 hasn’t come up at all. Does it have a higher chance of coming up on the forty-first spin?
The answer is no. The ball has just as much chance of landing on 1 again, as it did at the beginning of the hour. On a double-zero wheel, this chance is 1/38.
An easy way to understand this would be to say that the ball has no memory. Every ‘event’ (every spin of the wheel), is never influenced by the spins before it. The ball doesn’t know (or care) that it hasn’t landed on 1 in forty spins, because every spin is a brand new event.
Of course, if anybody had really found a strategy to beat the house edge in Roulette, either casinos would go out of business or more than likely change the rules so that the table can't be exploited anymore. Betting systems are simply neat ways to lose money very quickly, as they often risk big losses for small wins.
So when it comes to Roulette strategy, the most you can do is put on your lucky underwear and hope for the best. Good luck! | 538 | 2,363 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2020-40 | longest | en | 0.955494 |
http://www.mathisfunforum.com/viewtopic.php?pid=279049 | 1,398,250,224,000,000,000 | text/html | crawl-data/CC-MAIN-2014-15/segments/1398223202457.0/warc/CC-MAIN-20140423032002-00166-ip-10-147-4-33.ec2.internal.warc.gz | 719,352,442 | 5,215 | Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
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## #1 2013-07-23 00:10:04
barbie19022002
Super Member
Offline
### Weird Physics Problem..
I didn't expect in such a early period of time we will have ch-force and the laws of motion and now I am stuck with it..pls..some one help me..
Two Objects of Masses 100g and 200g are moving along the same line and direction with the velocity of 2 m s-1 and 1 m s-1 respectively. They collide and after collision, the first object moved at the velocity of 1.67 m s-1. Determine the velocity of the second object.
Last edited by barbie19022002 (2013-07-23 17:51:36)
Jake is Alice's father, Jake is the ________ of Alice's father?
Why is T called island letter?
think, think, think and don't get up with a solution...
## #2 2013-07-23 07:38:49
bob bundy
Moderator
Offline
### Re: Weird Physics Problem..
hi barbie19022002
You need to use the equation for conservation of momentum:
let m1 = 100 and m2 = 200
u1 = 2 and u2 = 1
After the collision the masses are the same but the velocities are now v1 (= 1.67 ) and v2
So you can 'plug in' the numbers and work out v2
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
## #3 2013-07-23 14:59:55
barbie19022002
Super Member
Offline
### Re: Weird Physics Problem..
can you explain it to me more nicely...pls
Jake is Alice's father, Jake is the ________ of Alice's father?
Why is T called island letter?
think, think, think and don't get up with a solution...
## #4 2013-07-23 15:40:35
Agnishom
Real Member
Online
### Re: Weird Physics Problem..
Are you aware of the law of conservation of momentum?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Who are you to judge everything?' -Alokananda
## #5 2013-07-23 17:17:47
barbie19022002
Super Member
Offline
### Re: Weird Physics Problem..
Ya..I am...but I don't know I to use it..
Jake is Alice's father, Jake is the ________ of Alice's father?
Why is T called island letter?
think, think, think and don't get up with a solution...
## #6 2013-07-23 17:37:54
bob bundy
Moderator
Offline
### Re: Weird Physics Problem..
hi barbie19022002
If you get hit by a truck it hurts a lot more than if you get hit by a fly. Clearly the mass of a moving object makes a difference.
But the velocity does too. A fly that hits you at 60 mph hurts a lot more than a fly that just gently lands on you.
The momentum of a moving object is a measure of these two:
momentum = mass x velocity
When two objects collide they may swap some momentum. This happens all the time in a game of snooker or pool.
The total momentum before and after the collision is constant. This can enable you to work out how fast an object is moving after the event.
so v2 is given by
Can you finish this now?
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
## #7 2013-07-23 17:52:10
barbie19022002
Super Member
Offline
### Re: Weird Physics Problem..
let me try once in my rough..
And thanks to make me understand more clearly...because in this chapter I was hardly able to understand anything clearly...
Thanks, Bob Bundy....
Last edited by barbie19022002 (2013-07-23 17:55:36)
Jake is Alice's father, Jake is the ________ of Alice's father?
Why is T called island letter?
think, think, think and don't get up with a solution...
## #8 2013-07-23 18:09:55
bob bundy
Moderator
Offline
### Re: Weird Physics Problem..
This page has some great videos on this. I recommend you view the Richard Garriott space video first. (4th one on page)
http://physicsnet.co.uk/a-level-physics … -concepts/
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei | 1,125 | 4,027 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2014-15 | longest | en | 0.884622 |
https://topic.alibabacloud.com/a/xtuoj-a--b-again-find-the-minimum-approximate-number-font-colorredgreaterfont-font-colorredthanfont-m-in-a-number_8_8_31719964.html | 1,686,012,988,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652184.68/warc/CC-MAIN-20230605221713-20230606011713-00044.warc.gz | 635,898,343 | 16,503 | # Xtuoj A + B again (find the minimum approximate number greater than m in a number)
Source: Internet
Author: User
Freshman competition:
Accepted: 15 Submit: 243 Time Limit: 1000 MS Memory limit: 65536 KB
Description
James had a lot of students who didn't like to think about a + B in the last semi-finals. To apologize, James made a simple A + B Question for everyone, I hope you will be happy to answer questions. So, the question is coming !!!
Evaluate the value of X, the smallest positive integer that makes B/(a + x) an integer.
Input
The first line is an integer k (K ≤ 10000), indicating the number of samples. In the following example, each row contains two positive integers, A and B (1 ≤ a, B ≤ 108 ).
Output
Output the result of a sample in each row. If there is no such X, the output is-1.
Sample Input
` 31 21 31 4 `
Sample output
` 121 `
Idea: I started to find out all the prime factor complexity logn of B, and then find the approximate number generated for each prime factor, that is, the prime factor M * (, 3 ...) (The complexity is too high) It is similar to the screening method. In sort, scan and find the minimum approximate number greater than a. The result is t, and the data size of 10 ^ 7 is T. Therefore, you do not need to generate all the approximate numbers. Each prime factor only needs to generate a minimum approximate number greater than, in this way, an approximate number (less than ologn) with the same number as the prime factor is generated, and then sort can be used. The Code is as follows:
`# Include <iostream> # include <cstdio> # include <cstring> # include <string> # include <map> # include <algorithm> # include <set> # include <vector> using namespace STD; int A, B, Su; vector <int> S; vector <int> All; void solve () {int temp = B; if (a> = temp) {cout <"-1" <Endl; return;} // Special Judgment // prime factor: For (INT I = 2; I * I <= temp; I ++) {If (TEMP % I = 0) {S. push_back (I); While (TEMP % I = 0) temp/= I ;}} S. push_back (B); // because bitself may be a prime number, add it to the vector. B. The result is not affected even if it is not a prime number. For (INT I = 0; I <S. Size (); I ++) // generate the S. Size () approx. {Su = s [I]; int M = A/Su + 1; All. push_back (Su * m);} Sort (all. begin (), all. end (); For (INT I = 0; I <all. size (); I ++) if (ALL [I]> A) {cout <all [I]-A <Endl; return ;}} int main () {int _; CIN >>_; while (_ --) {CIN >>> A> B; S. clear (); All. clear (); solve ();} return 0 ;}`
Xtuoj A + B again (find the minimum approximate number greater than m in a number)
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• Alibaba Cloud offers highly flexible support services tailored to meet your exact needs. | 915 | 3,504 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2023-23 | latest | en | 0.869162 |
https://www.hireresearcher.co.uk/finite-mat-106-a-card-is-drawn-at-random-from-a-well-shuffled/ | 1,653,011,774,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662530553.34/warc/CC-MAIN-20220519235259-20220520025259-00240.warc.gz | 869,967,776 | 8,058 | # FINITE MAT 106-A card is drawn at random from a well-shuffled
01 / 10 / 2021 Projects
This paper circulates around the core theme of FINITE MAT 106-A card is drawn at random from a well-shuffled together with its essential aspects. It has been reviewed and purchased by the majority of students thus, this paper is rated 4.8 out of 5 points by the students. In addition to this, the price of this paper commences from £ 99. To get this paper written from the scratch, order this assignment now. 100% confidential, 100% plagiarism-free.
## FINITE MAT 106-A card is drawn at random from a well-shuffled
Find the probability.A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 6?Find the probability.In a family with family with 4 children, excluding multiple births, what is the probability of having 2 girls and 2 boys, in that order? Assume that a boy is as likely as a girl at each birth.Find the probability.If you are dealt two cards successively (with replacement of the first) from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.Use the addition rule to find the following probability.If P (A) = 0.2, P (A or B) = 0.3, and P (A and B) = 0.5, find P (B).Find the probability using combinations. Round to the nearest ten-thousandth when necessary.A bag contains 6 cherry, 3 orange and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability that you have all cherry candies.The graduates at Southern University are shown in the table. Use the conditional probability formula to answer the given question below. A student is selected at random from the graduating class.Find the probability that the student is female, given that the student is receiving an education degree, P (F|E).Find the probability of the independent event.If P (E) = 0.9, P (F ? E) = 0.36, and E and F are independent, find P (F).Find the expected value.An insurance company has written 52 policies of \$50,000, 477 of \$25,000, and 918 of \$10,000 on people of age 20. If the probability that a person will die at age 20 is 0.001, how much can the company expect to pay during the year the policies were written?Find the expected value.A contractor is considering a sale that promises a profit of \$39,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of \$14,000 with a probability of 0.3. What is the expected profit?Use a tree diagram to find the probability.10) A couple plans to have four children. Using a tree diagram, obtain the sample space. Then, find the probability that the family has at least one boy.
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## Supporting Pages
FLAT 25% OFF ON EVERY ORDER. Use "FLAT25" as your promo code during checkout | 842 | 3,297 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2022-21 | latest | en | 0.948052 |
http://math.stackexchange.com/questions/295280/affine-function-definition | 1,469,542,864,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257824994.73/warc/CC-MAIN-20160723071024-00262-ip-10-185-27-174.ec2.internal.warc.gz | 154,884,528 | 17,580 | # affine function definition
If we define the affine function as
$f(\lambda x + (1-\lambda)y) = \lambda f(x) + (1-\lambda)f(y)$ for every $x,y \in R^d$ and $\lambda \in R$
How to show that it is equivalent to the definition
$f(x) = Ax +f(0)$ for some $k\times d$ matrix $A$
Thank you!
-
$(\Longrightarrow)$ Suppose first that $f(\lambda x + (1-\lambda)y) = \lambda f(x) + (1-\lambda) f(y)$ for all $x, y \in \mathbb{R}^d$ and $\lambda \in \mathbb{R}$. Let $$g(x) = f(x) - f(0).$$ We have to show that $g$ is linear. This means that we have to check that
• $g(cx) = cg(x)$ for all $x \in \mathbb{R}^d$ and $c \in \mathbb{R}$.
• $g(x+y) = g(x) + g(y)$ for all $x, y\in \mathbb{R}^d$
For the first point, note that $$g(cx) = f(cx) - f(0)$$ by definition. Also, our hypothesis gives $f(cx) = cf(x) + (1-c)f(0)$ (by taking $\lambda = c$ and $y = 0$). You take it from here.
For the second point, note that $$g(x + y) = f(x+y) - f(0)$$ by definition. Also, our hypothesis gives $f(x+y) = \frac{1}{2}f(2x) + \frac{1}{2}f(2y)$ (why?) and that $f(2x) = 2f(x) - f(0)$ (why?). You take it from here.
$(\Longleftarrow)$ Suppose now that $f(x) = Ax + f(0)$ for some $k \times d$ matrix $A$. If $x,y \in \mathbb{R}^d$ and $\lambda \in \mathbb{R}$, then \begin{align*} f(\lambda x + (1-\lambda)y) & = A(\lambda x + (1-\lambda)y) + f(0) \\ & = \ldots \\ & = \ldots \\ & = \lambda f(x) + (1-\lambda) f(y), \end{align*} where the $\ldots$ means I've left the details for you to fill in.
-
This brings another question: How to show any linear mapping is of the form Ax for some matrix A? Thank you! – Salih Ucan Feb 5 '13 at 9:50
That's basic linear algebra. (Are you taking a linear algebra class?) Any matrix $A$ determines a linear map in the obvious way: that is, $h(x) = Ax$ is linear. Conversely, any linear map $h$ can be represented as a matrix by choosing bases for the domain and target. In particular, if $\{e_1, \ldots, e_d\}$ is a basis for the domain, then we can take $$A = [h(e_1) \cdots h(e_d) ]$$ as the matrix, where each $h(e_i) \in \mathbb{R}^k$ is written as a column. – Jesse Madnick Feb 5 '13 at 9:54
Thank you Jesse! yes i am studying linear algebra now.. – Salih Ucan Feb 5 '13 at 10:03 | 795 | 2,206 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2016-30 | latest | en | 0.761907 |
https://matrixread.com/tree-traversals-preorder-inorder-postorder/ | 1,726,763,919,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652055.62/warc/CC-MAIN-20240919162032-20240919192032-00849.warc.gz | 349,945,991 | 18,733 | # Tree Traversals – Preorder, Inorder, Postorder
• DSA
Tree Traversal: visiting every node of a tree. Unlike other linear data structures, where we traverse through every element in order, it’s not the same with the tree. Trees being non-linear data structures, there will always be more than one way to traverse through a tree. There are three types of Tree Traversals namely, Inorder, Preorder, and Postorder. In this post, I’ll explain briefly all three methods with code.
## Tree Data Structure
A Tree Data Structure contains a root node, and every node can have a left and right child.
## Tree Traversals
• Inorder (Left, Root, Right)
• Preorder (Root, Left, Right)
• Postorder (Left, Right, Root)
Consider the below tree,
## Inorder Traversal
1. Traverse Left Subtree
2. Visit Root Node
3. Traverse Right Subtree
``````Inorder (Left, Root, Right)
Output: 4->2->5->1->6->3->7``````
## Preorder Traversal
1. Visit Root Node
2. Traverse Left Subtree
3. Traverse Right Subtree
``````Preorder (Root, Left, Right)
Output: 1->2->4->5->3->6->7``````
## Postorder Traversal
1. Traverse Left Subtree
2. Traverse Right Subtree
3. Visit Root Node
``````Postorder (Left, Right, Root)
Output:4->5->2->6->7->3->1``````
## Code
``````#include <iostream>
using namespace std;
struct Node
{
int data;
struct Node *left, *right;
Node(int data)
{
this->data = data;
left = right = NULL;
}
};
// Preorder traversal
void preorderTraversal(struct Node *node)
{
if (node == NULL)
return;
cout << node->data <<"->";
preorderTraversal(node->left);
preorderTraversal(node->right);
}
// Postorder traversal
void postorderTraversal(struct Node *node)
{
if (node == NULL)
return;
postorderTraversal(node->left);
postorderTraversal(node->right);
cout << node->data <<"->";
}
// Inorder traversal
void inorderTraversal(struct Node *node)
{
if (node == NULL)
return;
inorderTraversal(node->left);
cout << node->data <<"->";
inorderTraversal(node->right);
}
int main()
{
struct Node *root = new Node(1);
root->left = new Node(2);
root->right = new Node(3);
root->left->left = new Node(4);
root->left->right = new Node(5);
root->right->left = new Node(6);
root->right->right = new Node(7);
cout <<"Inorder traversal" ;
inorderTraversal(root);
cout <<"\nPreorder traversal" ;
preorderTraversal(root);
cout <<"\nPostorder traversal" ;
postorderTraversal(root);
}``````
## Output
``````Inorder traversal 4->2->5->1->6->3->7->
Preorder traversal 1->2->4->5->3->6->7->
Postorder traversal 4->5->2->6->7->3->1->``````
## Conclusion
This post is a part of my #30DaysChallenge to write a blog post every day on what I learn, Happy Coding~ Abhiram Reddy. | 754 | 2,646 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2024-38 | latest | en | 0.486474 |
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# Machine Learning Techniques (ᘤᢈ)
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## Machine Learning Techniques ( 機器學習技巧)
### Lecture 14: Miscellaneous Models
Hsuan-Tien Lin (林軒田) htlin@csie.ntu.edu.tw
(2)
(3)
## Recommender System Revisited
### •
competition held by Netflix in 2006
### j
for j-th movie:{(x
= (i), y
=r
)}
### N n=1 j
—abstract features
= (i)
how to
from allD
?
(4)
## Linear Model for Recommender System
consider
for eachD
={(x
= (i), y
=r
)}
, with a shared
y ≈
(x) =
, to be
### learned
from data, like NNet/RBF Net
then,
=y
overall E
### in
with squared error:
E
({
}, {
}) = P
N
E
(w
,{
}) P
N
= 1
N X
(r
)
how to minimize?
### SGD
by sampling known (i,
(5)
## Matrix Factorization
=
learning:
→ learned
and
### vi
→ unknown rating prediction similar modeling can be used for
(6)
(7)
## Coordinate Descent for Linear Blending
Consider a linear blending problem: forG = {g
},
min
1 N
X
−y
(x
)
!
### •
why exponential error
−y
a
on err
as
### •
how to minimize?
—GD, SGD,. . . if few
### •
what if lots of or
—pick
, and update its
only
pick a good
### coordinate i
(the best one for the next step)
### •
minimize by setting
(8)
## Coordinate Descent View of AdaBoost
Consider a linear blending problem: forG = {g
},
min
1 N
X
−y
(x
)
!
pick a good
### coordinate i
(the best one for the next step)
### •
minimize by setting
pick a
set
### t
after some derivations (ML2012Fall HW7.5):
+
error
(9)
### Miscellaneous Models Gradient Boosted Decision Tree
Consider another linear blending problem:
min
1 N
X
y
(x
)
!
### • best coordinate
at t-th iteration (under assumptions):
min
1 N
X
(y
(x
))
—best
on{(x
,
)}
### • best β `new
: one-dimensional
(GBDT):
above + find
(10)
(11)
## Naive Bayes Model
want: getting
### P(y |x)
(e.g. logistic regression) for classification
Bayes rule:
estimating
=y inD (easy!)
### •
joint distribution
: easier if
=
### P(x 1 |y)P(x 2 |y) · · · p(x d |y)
—conditional independence
### •
marginal distribution
:
### piece-wise discrete, Gaussian, etc.
Naive Bayes model:
h(x) =
### P(x 1 |y)P(x 2 |y) · · · p(x d |y) P(y )
with your choice of distribution families
(12)
find g(x) =
### P(x 1 |y) · · · p(x d |y) P(y )
by ‘good estimate’ of all RHS terms
sign
− 1
= sign
Y
− 1
!
= sign
log
| {z }
+
X
log
| {z }
=sign
+
X
### φ i
(x)
!
—also naive linear model with ‘heuristic/learned’
and
### bias
a simple (heuristic) model, usually
(13)
## IDCM 2006 Top 10 Data Mining Algorithms
### 1
C4.5: decision tree
### 2
K -means: clustering, taught with RBF Network
### 3
SVM: large-margin/kernel
### 4
Apriori: for frequent itemset mining
### 5
in Bayesian learning
PageRank: for
### 8
k -NN: taught very shortly within RBF Network
### 9
Naive Bayes: linear model with heuristic transform
### 10
CART: decision tree personal view of four missing ML competitors:
LinReg, LogReg, Random Forest, NNet
(14)
(15)
## Disclaimer
(16)
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
Theprior
istheprior
### P (h = f | D)
istheposterior
Giventheprior,wehavethefulldistribution
LearningFromData-Le ture18 7/23
(17)
### Miscellaneous Models Bayesian Learning
Exampleofaprior
Consideraper eptron:
isdeterminedby
Apossibleprioron
:Ea h
### w i
isindependent,uniformover
### [ −1, 1]
Thisdeterminesthepriorover
-
Given
,we an ompute
### P ( D | h = f)
Puttingthemtogether,weget
### ∝ P (h = f)P (D | h = f)
LearningFromData-Le ture18 8/23
Exampleofaprior
Consideraper eptron:
isdeterminedby
Apossibleprioron
:Ea h
### w i
isindependent,uniformover
### [ −1, 1]
Thisdeterminesthepriorover
-
Given
,we an ompute
### P ( D | h = f)
Puttingthemtogether,weget
### ∝ P (h = f)P (D | h = f)
LearningFromData-Le ture18 8/23
Exampleofaprior
Consideraper eptron:
isdeterminedby
Apossibleprioron
:Ea h
### w i
isindependent,uniformover
### [ −1, 1]
Thisdeterminesthepriorover
-
Given
,we an ompute
### P ( D | h = f)
Puttingthemtogether,weget
### ∝ P (h = f)P (D | h = f)
LearningFromData-Le ture18 8/23
Exampleofaprior
Consideraper eptron:
isdeterminedby
Apossibleprioron
:Ea h
### w i
isindependent,uniformover
### [ −1, 1]
Thisdeterminesthepriorover
-
Given
,we an ompute
### P ( D | h = f)
Puttingthemtogether,weget
### ∝ P (h = f)P (D | h = f)
LearningFromData-Le ture18 8/23
Exampleofaprior
Consideraper eptron:
isdeterminedby
Apossibleprioron
:Ea h
### w i
isindependent,uniformover
### [ −1, 1]
Thisdeterminesthepriorover
-
Given
,we an ompute
### P ( D | h = f)
Puttingthemtogether,weget
### ∝ P (h = f)P (D | h = f)
LearningFromData-Le ture18 8/23
Exampleofaprior
Consideraper eptron:
isdeterminedby
Apossibleprioron
:Ea h
### w i
isindependent,uniformover
### [ −1, 1]
Thisdeterminesthepriorover
-
Given
,we an ompute
### P ( D | h = f)
Puttingthemtogether,weget
### ∝ P (h = f)P (D | h = f)
LearningFromData-Le ture18 8/23
Exampleofaprior
Consideraper eptron:
isdeterminedby
Apossibleprioron
:Ea h
### w i
isindependent,uniformover
### [ −1, 1]
Thisdeterminesthepriorover
-
Given
,we an ompute
### P ( D | h = f)
Puttingthemtogether,weget
### ∝ P (h = f)P (D | h = f)
LearningFromData-Le ture18 8/23
Exampleofaprior
Consideraper eptron:
isdeterminedby
Apossibleprioron
:Ea h
### w i
isindependent,uniformover
### [ −1, 1]
Thisdeterminesthepriorover
-
Given
,we an ompute
### P ( D | h = f)
Puttingthemtogether,weget
### ∝ P (h = f)P (D | h = f)
LearningFromData-Le ture18 8/23
Exampleofaprior
Consideraper eptron:
isdeterminedby
Apossibleprioron
:Ea h
### w i
isindependent,uniformover
### [ −1, 1]
Thisdeterminesthepriorover
-
Given
,we an ompute
### P ( D | h = f )
Puttingthemtogether,weget
### ∝ P (h = f)P (D | h = f)
LearningFromData-Le ture18 8/23
Exampleofaprior
Consideraper eptron:
isdeterminedby
Apossibleprioron
:Ea h
### w i
isindependent,uniformover
### [ −1, 1]
Thisdeterminesthepriorover
-
Given
,we an ompute
### P ( D | h = f )
Puttingthemtogether,weget
### ∝ P (h = f)P (D | h = f)
LearningFromData-Le ture18 8/23
Exampleofaprior
Consideraper eptron:
isdeterminedby
Apossibleprioron
:Ea h
### w i
isindependent,uniformover
### [ −1, 1]
Thisdeterminesthepriorover
-
Given
,we an ompute
### P ( D | h = f )
Puttingthemtogether,weget
### ∝ P (h = f)P (D | h = f)
LearningFromData-Le ture18 8/23
Exampleofaprior
Consideraper eptron:
isdeterminedby
Apossibleprioron
:Ea h
### w i
isindependent,uniformover
### [ −1, 1]
Thisdeterminesthepriorover
-
Given
,we an ompute
### P ( D | h = f )
Puttingthemtogether,weget
### ∝ P (h = f )P (D | h = f )
LearningFromData-Le ture18 8/23
(18)
### Miscellaneous Models Bayesian Learning
A prior isanassumption
Eventhemostneutralprior:
### Hi Hi
Thetrueequivalentis:
### Hi Hi
LearningFromData-Le ture18 9/23
A prior isanassumption
Eventhemostneutralprior:
### Hi Hi
Thetrueequivalentis:
### Hi Hi
LearningFromData-Le ture18 9/23
A prior isanassumption
Eventhemostneutralprior:
### Hi
Thetrueequivalentis:
### Hi Hi
LearningFromData-Le ture18 9/23
A prior isanassumption
Eventhemostneutralprior:
### Hi Hi
Thetrueequivalentis:
### Hi Hi
LearningFromData-Le ture18 9/23
A prior isanassumption
Eventhemostneutralprior:
### −1 1
Thetrueequivalentis:
### Hi Hi
LearningFromData-Le ture18 9/23
A prior isanassumption
Eventhemostneutralprior:
### −1 1
Thetrueequivalentis:
### Hi Hi
LearningFromData-Le ture18 9/23
A prior isanassumption
Eventhemostneutralprior:
### −1 1
Thetrueequivalentwouldbe:
### Hi Hi
LearningFromData-Le ture18 9/23
A prior isanassumption
Eventhemostneutralprior:
### −1 1
Thetrueequivalentwouldbe:
### δ (x )−a
LearningFromData-Le ture18 9/23
(19)
### Miscellaneous Models Bayesian Learning
If weknewtheprior
we ould ompute
forevery
### = ⇒
we an ndthemostprobable
giventhedata
we anderive
forevery
### x
we anderivetheerrorbarforevery
### x
we anderiveeverythinginaprin ipledway
LearningFromData-Le ture18 10/23
If weknewtheprior
we ould ompute
forevery
### = ⇒
we an ndthemostprobable
giventhedata
we anderive
forevery
### x
we anderivetheerrorbarforevery
### x
we anderiveeverythinginaprin ipledway
LearningFromData-Le ture18 10/23
If weknewtheprior
we ould ompute
forevery
### = ⇒
we an ndthemostprobable
giventhedata
we anderive
forevery
### x
we anderivetheerrorbarforevery
### x
we anderiveeverythinginaprin ipledway
LearningFromData-Le ture18 10/23
If weknewtheprior
we ould ompute
forevery
### = ⇒
we an ndthemostprobable
giventhedata
we anderive
forevery
### x
we anderivetheerrorbarforevery
### x
we anderiveeverythinginaprin ipledway
LearningFromData-Le ture18 10/23
If weknewtheprior
we ould ompute
forevery
### = ⇒
we an ndthemostprobable
giventhedata
we anderive
forevery
### x
we anderivetheerrorbarforevery
### x
we anderiveeverythinginaprin ipledway
LearningFromData-Le ture18 10/23
If weknewtheprior
we ould ompute
forevery
### = ⇒
we an ndthemostprobable
giventhedata
we anderive
forevery
### x
we anderivetheerrorbarforevery
### x
we anderiveeverythinginaprin ipledway
LearningFromData-Le ture18 10/23
If weknewtheprior
we ould ompute
forevery
### = ⇒
we an ndthemostprobable
giventhedata
we anderive
forevery
### x
we anderivetheerrorbarforevery
### x
we anderiveeverythinginaprin ipledway
LearningFromData-Le ture18 10/23
If weknewtheprior
we ould ompute
forevery
### = ⇒
we an ndthemostprobable
giventhedata
we anderive
forevery
### x
we anderivetheerrorbarforevery
### x
we anderiveeverythinginaprin ipledway
LearningFromData-Le ture18 10/23
If weknewtheprior
we ould ompute
forevery
### = ⇒
we an ndthemostprobable
giventhedata
we anderive
forevery
### x
we anderivetheerrorbarforevery
### x
we anderiveeverythinginaprin ipledway
LearningFromData-Le ture18 10/23
(20)
## One Instance of Using Posterior
### •
logistic regression: know how to calculate
=
*
maximize
### posterior
= maximize [log Gaussian+
=
= min
### augmented error
(with iid assumption +
+
= max
*
### likelihood
(with iid assumption +
assumptions)
(21)
### Miscellaneous Models Bayesian Learning
When isBayesian learningjusti ed?
1. Thepriorisvalid
trumpsallothermethods
2. Thepriorisirrelevant
justa omputational atalyst
LearningFromData-Le ture18 11/23
When isBayesian learningjusti ed?
1. Thepriorisvalid
trumpsallothermethods
2. Thepriorisirrelevant
justa omputational atalyst
LearningFromData-Le ture18 11/23
When isBayesian learningjusti ed?
1. Thepriorisvalid
trumpsallothermethods
2. Thepriorisirrelevant
justa omputational atalyst
LearningFromData-Le ture18 11/23
When isBayesian learningjusti ed?
1. Thepriorisvalid
trumpsallothermethods
2. Thepriorisirrelevant
justa omputational atalyst
LearningFromData-Le ture18 11/23
When isBayesian learningjusti ed?
1. Thepriorisvalid
trumpsallothermethods
2. Thepriorisirrelevant
justa omputational atalyst
LearningFromData-Le ture18 11/23
(22)
## My Biased View
in reality:
### •
prior/likelihood mostly
### invalid
(Gaussian, conditional independence, etc.), shooting for computational ease
prior/likelihood
(23)
(24)
## Summary
### Bayesian Learning
Hsuan-Tien Lin (NTU CSIE) Machine Learning Foundations 9/27.. The Learning Problem What is Machine Learning. The Machine
Hsuan-Tien Lin (NTU CSIE) Machine Learning Techniques 2/28.. Linear Support Vector Machine Course Introduction.
Feature Exploitation Techniques Error Optimization Techniques Overfitting Elimination Techniques Machine Learning in Practice... Finale Feature
soft-margin k -means OOB error RBF network probabilistic SVM GBDT PCA random forest matrix factorization Gaussian kernel kernel LogReg large-margin prototype quadratic programming
decision tree: a traditional learning model that realizes conditional aggregation.. Decision Tree Decision Tree Hypothesis.. Disclaimers about
decision tree: a traditional learning model that realizes conditional aggregation.. Disclaimers about Decision
• validation set blending: a special any blending model E test (squared): 519.45 =⇒ 456.24. —helped secure the lead in last
Hsuan-Tien Lin (NTU CSIE) Machine Learning Techniques 21/25.. Gradient Boosted Decision Tree Summary of Aggregation Models. Map of
2 Combining Predictive Features: Aggregation Models Lecture 7: Blending and Bagging.. Motivation of Aggregation
Which of the following aggregation model learns diverse g t by reweighting and calculates linear vote by steepest search?.
3 Distilling Implicit Features: Extraction Models Lecture 14: Radial Basis Function Network. RBF
Lecture 4: Soft-Margin Support Vector Machine allow some margin violations ξ n while penalizing them by C; equivalent to upper-bounding α n by C Lecture 5: Kernel Logistic
Hsuan-Tien Lin (NTU CSIE) Machine Learning Techniques 5/22.. Decision Tree Decision Tree Hypothesis. Disclaimers about
1 Embedding Numerous Features: Kernel Models Lecture 1: Linear Support Vector Machine.. linear SVM: more robust and solvable with quadratic programming Lecture 2: Dual Support
1 Embedding Numerous Features: Kernel Models Lecture 1: Linear Support Vector Machine.
Hsuan-Tien Lin (NTU CSIE) Machine Learning Basics
Hsuan-Tien Lin (NTU CSIE) Machine Learning Techniques 3/24.:. Deep Learning Deep
Hsuan-Tien Lin (NTU CSIE) Machine Learning Techniques 21/22.. Matrix Factorization Summary of Extraction Models.
Hsuan-Tien Lin (NTU CSIE) Machine Learning Foundations 5/25.. Noise and Error Noise and Probabilistic Target.
Lecture 1: Large-Margin Linear Classification Large-Margin Separating Hyperplane Standard Large-Margin Problem Support Vector Machine.. Reasons behind
Lecture 4: Soft-Margin SVM Soft-Margin SVM: Primal Soft-Margin SVM: Dual Soft-Margin SVM: Solution Soft-Margin SVM: Selection.. Soft-Margin SVM Soft-Margin
Hsuan-Tien Lin (NTU CSIE) Machine Learning Foundations 0/26... The
3 Distilling Implicit Features: Extraction Models Lecture 14: Radial Basis Function Network. RBF | 5,038 | 15,983 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2023-50 | latest | en | 0.715882 |
https://lookingfordongxi.com/tourer/how-far-do-you-travel-at-60-mph-in-1-hour.html | 1,660,937,807,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573760.75/warc/CC-MAIN-20220819191655-20220819221655-00289.warc.gz | 333,977,890 | 18,566 | # How far do you travel at 60 mph in 1 hour?
Contents
One hour walking at 1 mph moves you 1 mile. Miles per hour is often used for car speeds. One minute at 60 mph will move you 1 mile.
## How long does it take to travel 60 mph?
60 miles per hour equates to 1 mile per minute. One hour and 40 minutes. Or put another way, 100 minutes. 60 mph is equal to one mile per minute or put another way, 88 feet per second.
## How far is 60 miles in minutes?
Thus, it will take 90 minutes to go 60 miles.
## How far do you travel in one second at 60 mph?
Also, 1 hour = 60 minutes = 3600 seconds. Therefore, it can also be said that the car travels 60 miles in 3600 seconds. Therefore, it can travel 60/3600 miles in 1 second, which is equal to approximately 0.017 miles.
## How long does it take to travel 100 miles by car?
Distance = 100 miles, Time = 4 hours, Therefore the average Speed was 25 mph.
## How long would it take to travel 80 miles?
If you’re driving at 80mph (miles per hour), it will take you one hour to drive 80 miles. If you’re driving slower, it will take you longer to drive 80 miles.
## How long does it take to go 60 miles at 60 mph?
1 hour at a speed of 60mph to cover 60 miles.
## How do you convert mph to hours?
Suppose you travel a distance of 100 miles, and it takes 1 1/2 hours to do it. Your average speed is then 100 miles divided by 1.5 hours which equals 66.67 miles per hour. When calculating miles per hour for distances that take only minutes, you convert the number of minutes to fractions of an hour.
## How many minutes is 40 miles at 60 mph?
Answer: The total time taken to cover 40 miles at 60 mph in 40 minutes.
## How far does a car travel in 1 second at 70 mph?
Now, to remember when driving, 70 mph is 102 2/3 ft/sec.
## How far can a car travel in 3 seconds?
The Three-Second Rule Chart
Three-Second Rule 3 seconds
Speed Distance Traveled Good
25 m.p.h. 37 ft. per second 111 ft.
35 m.p.h. 52 ft. per second 166 ft.
45 m.p.h. 66 ft. per second 198 ft.
## How far do you travel at 65 mph in 1 second?
At 65 mph, keeping one second of following distance means the vehicle is traveling 100 feet behind the vehicle in front. It takes an automobile a minimum of 150 feet to stop. With a 100 foot gap plus the auto’s stopping distance of 150 feet, an impact would occur within 250 feet.
## How long is a 200 mile drive?
How long it takes to travel 200 miles depends on how fast you are going. If you are traveling at 45 mph, it will take 4.4 hours; at 60 mph, 3.3 hours; and at 75mph, 2.67 hours.
## How long is a 10 mile car ride?
10 miles divided by 75 miles per hour (in this calculation I used 60 min) equals 8 minutes. SO to travel 10 miles at 75 miles per hours would take you 8 minutes. | 768 | 2,755 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2022-33 | latest | en | 0.911778 |
https://www.clutchprep.com/physics/practice-problems/141985/consider-the-system-shown-in-the-figure-figure-1-block-a-weighs-46-9-n-and-block | 1,606,465,902,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141191511.46/warc/CC-MAIN-20201127073750-20201127103750-00536.warc.gz | 619,539,248 | 34,648 | Forces in Connected Objects (Systems) Video Lessons
Concept
# Problem: Consider the system shown in the figure (Figure 1). Block A weighs 46.9 N and block B weighs 30.1 N.Once block B is set into downward motion, it descends at a constant speed.a.) Calculate the coefficient of kinetic friction between block A and the tabletop.b.) A cat, also of weight 46.9 N, falls asleep on top of block A. If block B is now set into downward motion, what is its acceleration magnitude?
###### FREE Expert Solution
The kinetic frictional force:
$\overline{){{\mathbf{F}}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{\mu }}}_{{\mathbf{k}}}{\mathbf{N}}}$
The normal force:
$\overline{){\mathbf{N}}{\mathbf{=}}{\mathbf{m}}{\mathbf{g}}}$
a)
The sum of horizontal forces on A is:
ΣFA = T - fA
0 = T - μkmAg
The sum of horizontal forces acting on B:
ΣFB = WB - T
0 = WB - T = mBg - T
84% (288 ratings)
###### Problem Details
Consider the system shown in the figure (Figure 1). Block A weighs 46.9 N and block B weighs 30.1 N.Once block B is set into downward motion, it descends at a constant speed.
a.) Calculate the coefficient of kinetic friction between block A and the tabletop.
b.) A cat, also of weight 46.9 N, falls asleep on top of block A. If block B is now set into downward motion, what is its acceleration magnitude? | 372 | 1,320 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.984375 | 4 | CC-MAIN-2020-50 | longest | en | 0.804802 |
https://archive.lib.msu.edu/crcmath/math/math/n/n119.htm | 1,638,407,744,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964361064.58/warc/CC-MAIN-20211201234046-20211202024046-00527.warc.gz | 166,541,024 | 3,275 | ## Niven's Constant
N.B. A detailed on-line essay by S. Finch was the starting point for this entry.
Given a Positive Integer , let its Prime Factorization be written
(1)
Define the functions and by , , and
(2) (3)
Then
(4)
(5)
where is the Riemann Zeta Function (Niven 1969). Niven (1969) also proved that
(6)
where
(7)
(Sloane's A033150).
The Continued Fraction of Niven's constant is 1, 1, 2, 2, 1, 1, 4, 1, 1, 3, 4, 4, 8, 4, 1, ... (Sloane's A033151). The positions at which the digits 1, 2, ... first occur in the Continued Fraction are 1, 3, 10, 7, 47, 41, 34, 13, 140, 252, 20, ... (Sloane's A033152). The sequence of largest terms in the Continued Fraction is 1, 2, 4, 8, 11, 14, 29, 372, 559, ... (Sloane's A033153), which occur at positions 1, 3, 7, 13, 20, 35, 51, 68, 96, ... (Sloane's A033154).
References
Finch, S. Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/niven/niven.html
Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 41, 1983.
Niven, I. Averages of Exponents in Factoring Integers.'' Proc. Amer. Math. Soc. 22, 356-360, 1969.
Plouffe, S. The Niven Constant.'' http://www.lacim.uqam.ca/piDATA/niven.txt.
Sloane, N. J. A. Sequences A033150, A033151, A033152, A033153, and A033154 in An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html. | 503 | 1,390 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2021-49 | latest | en | 0.701375 |
https://all-learning.com/supervised-machine-learning-a-quick-introduction/ | 1,679,383,282,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296943637.3/warc/CC-MAIN-20230321064400-20230321094400-00455.warc.gz | 123,965,590 | 17,256 | # Supervised Machine Learning – A Quick Introduction With Examples [Latest]
Oct 24, 2022
Hey, readers! In this article, we will be focusing on one of the main type of Machine Learning Algorithms — Supervised Machine Learning Algorithms.
As we all know, Machine Learning is a domain which makes use of various algorithms to perform predictions on various sets of data.
These algorithms yield predictions by learning from the data and then perform predictions on the test data to show relevant patterns.
There are basically three types of Machine Learning Algorithms:
• Supervised ML
• Unsupervised ML
• Reinforcement Learning
Today, we will be focusing on Supervised Machine Learning and its various models in detail.
So, without any further delay, let us begin!
## First, what’s Supervised Machine Learning?
Supervised Machine Learning is a branch of Machine Learning wherein the model learns from the input provided to it handy before the prediction.
That is, we provide historic data or in simple language, we provide the algorithms with the datasets collected through various means such as surveys, analysis, scarping, etc. Further, we feed the data to the model and it learns from the data to analyse and detect patterns into the data.
At last, we analyze the efficiency of the model by feeding the model to the test dataset and make predictions out of it. This makes us understand to what extent the model satisfies the data in terms of efficiency.
There are more than 100 Supervised Machine Learning algorithms. Let us have a look at some of the most frequently used ML algorithms in detail.
Here we go!!!!! 🙂
## 1. Decision Trees
Decision Tree is a Supervised Machine Learning model that delivers the predictions on the data values in terms of the chances or probabilities based on rules. It develops rules or event of chances of occurrence based on the training data from which it learns the actions.
In a simple language, we can think of a Decision Tree as a flowchart that works on the rules created from the training set based on the chances of the occurrence of events as in if else rules.
Please visit the below link to find a complete package of explanation and implementation of decision trees – Decision Trees – A Practical Approach
## 2. Linear Regression
Linear Regression is a Regression Machine Learning model i.e. it works only for numeric variables. In linear regression, we try to predict the value of the response or target variables from the independent data variables. Thus, the model tries to learn how well the independent variables give accurate information about the response value.
The practical implementation of Linear regression will be out of scope for the topic at hand. But we have you covered. Visit the link below and implement your first Linear regression model in Python – Linear Regression – Practical Implementation
## 3. Logistic Regression
In logistic regression, the model tries to predict the outcome of the binary dependent variable such as true/false, yes/no, male/female, etc using a logit function.
This logit function depends upon the probability and the odds value to predict the value of the binary response variable out of chances or probabilities.
While we are yet to cover a practical implementation of Logistic regression on our website, have a look at the sklearn library’s Logistic regression model module.
## Advantages of Supervised Machine Learning models
• Supervised Machine Learning Algorithms help us predict the values of the test dataset based on the prior evaluations.
• It enables us have a real life solution for problems such as email spam filtering, loan defaulter detection ,etc.
## Limitations faced in Supervised Machine Learning models
• Very less information is available in terms of the class of the object.
• The complexity of the model rises exponentially with increase in the complexity of the data.
## Conclusion
By this, we have come to the end of this topic. Feel free to comment below, in case you come across any question. For more such posts related to Machine Learning in Python, Stay tuned @ Machine Learning with JournalDev, and till then Happy Learning with JournalDev!! 🙂 | 813 | 4,196 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2023-14 | longest | en | 0.917718 |
http://www.jiskha.com/display.cgi?id=1279755432 | 1,493,529,736,000,000,000 | text/html | crawl-data/CC-MAIN-2017-17/segments/1492917124299.47/warc/CC-MAIN-20170423031204-00260-ip-10-145-167-34.ec2.internal.warc.gz | 578,244,900 | 4,121 | # chem 11
posted by on .
if we mix 25 g of sodium bromide with a large amount of potassium chloride, what will our theoretical yield of sodium chloride be?
NaBr+KCL->NaCl+KBr
how do you calculate theoretical yield?
• chem 11 - ,
The stoichiometric amount of NaCl is the theoretical yield.
Convert 25 NaBr to moles. moles = grams/molar mass.
Using the coefficients in the balanced equation, convert moles NaBr to moles NaCl.
Now convert moles NaCl to grams. g = moles x molar mass. This is the theoretical yield.
NOTE: I assume you made up this problem to demonstrate theoretical yield and I have worked the problem accordingly. However, the reaction, in real practice, will NOT take place.
• chem 11 - ,
soooo...would it be like this?
25gx 1mol/103g = 0.2427...
ans.x58
theoretical yield =14.0g
• chem 11 - ,
Yes and no.
Yes, the answer is 14 however, you have mixed up the number of significant figures. If you start with 25 g, the answer may not have more than two; therefore, 14 g is the answer in your problem. | 272 | 1,027 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2017-17 | latest | en | 0.90628 |
https://brainmass.com/physics/stars/light-years-away-distance-traveled-light-years-309532 | 1,620,866,794,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991413.30/warc/CC-MAIN-20210512224016-20210513014016-00123.warc.gz | 164,257,080 | 74,958 | Explore BrainMass
# Light-years away, distance traveled in light years.
Not what you're looking for? Search our solutions OR ask your own Custom question.
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
Part 1
A certain star is 73.3 light-years away. How many years would it take a spacecraft traveling 0.959c to reach that star from Earth, as measured by observers on Earth?
Part 2
How many years would it take to reach that star from Earth, as measured by observers on the spacecraft?
Part 3
What is the distance (in lightyears) traveled according to observers on the spacecraft? Do not enter units.
© BrainMass Inc. brainmass.com March 4, 2021, 10:12 pm ad1c9bdddf
https://brainmass.com/physics/stars/light-years-away-distance-traveled-light-years-309532
#### Solution Preview
Space Travel
Part 1
A certain star is 73.3 light-years away. How many years would it take a spacecraft traveling 0.959c to reach that star from Earth, as measured by observers on Earth?
Part 2
How many ...
#### Solution Summary
The expert examines how far a star is from Earth by measuring the distance traveled in light year.
\$2.49 | 287 | 1,190 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2021-21 | latest | en | 0.954815 |
https://community.tableau.com/message/829964 | 1,576,340,278,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575541281438.51/warc/CC-MAIN-20191214150439-20191214174439-00287.warc.gz | 320,418,821 | 29,833 | 8 Replies Latest reply on Oct 9, 2018 4:20 AM by oscar vicente
# Cut-off Running Sum Mid-Year
Hello. I have a nut that has turned out to be surprisingly hard to crack. See the attached packaged workbook to see the issue. I'm putting together a budget dashboard. In one of the views (second tab of workbook), I want to show a running sum of actuals against a running sum of budget, and show the variance between the two. The problem is that my actuals stop at April, but the budget continues through the rest of the year. So when I put together a running sum the actuals flatline at April, the budget continues to rise, and the variance grows rapidly. I want both the actuals line and the variance bars to end at april. When I try to put together a calculated field (like the one with the exclamation point in the workbook), I get the error that I cannot mix aggregate and non-aggregate results in an if statement.
Any help with this would be much appreciated.
• ###### 1. Re: Cut-off Running Sum Mid-Year
Hi Jmogielnicki, I think the attached workbook works. Instead of going after the date, I wrote calcs to test for SUM([amount])>0, which seems to produce the chart you want. I wrote two new calcs:
Actual (blue line):
IIF(SUM([Amount])>0,RUNNING_SUM(SUM([Amount])), NULL)
Differential (grey bars):
IIF(SUM([Amount])>0,[Actuals minus Budget], NULL)
Here's the chart:
Hope this is what you were looking for.
--Shawn
10 of 10 people found this helpful
• ###### 2. Re: Cut-off Running Sum Mid-Year
Hey Shawn, that is super helpful, and definitely fixed one of the two issues. Was still having trouble getting the running sum of the variance to cut itself off but fixed that with a calculation that referenced one of the calcs that you set up:
IIF(isnull([Actuals minus Budget]), NULL,
RUNNING_SUM(sum((if [Type] = "Actuals" then [Amount] else null end)))-
RUNNING_SUM(sum((if [Type] = "Budget" then [Amount] else null end))))
I'll attach the workbook in case anyone else comes around with a similar issue.
Thanks for the help.
• ###### 3. Re: Cut-off Running Sum Mid-Year
This solution works well if [Amount] is not NULL, but when it is, the running sum will not display, causing discontinuities in the line. For example, if my line is showing cumulative increases by day, and no records are added on weekends, then the line is broken into segments.
I could roll up to by-week instead of by-day, but 'week 1', 'week 2', etc is not as desirable as actual dates.
• ###### 4. Re: Cut-off Running Sum Mid-Year
I have the same problem, I have discontinuities in the lines. Any idea to solve it?
• ###### 5. Re: Cut-off Running Sum Mid-Year
You can try this, Just replace "Actual".
IIF(SUM([Actual])>0,RUNNING_SUM(SUM([Actual])), (SUM([Actual])+ PREVIOUS_VALUE(0)))
• ###### 6. Re: Cut-off Running Sum Mid-Year
In a similar case, i used the LAST function to stop showing the running sum after current date. Here goes my calculated field -
IF LAST()>=(DATEDIFF('week',TODAY(),[End Date],'Monday'))
THEN RUNNING_SUM(SUM([Amount]))
ELSE NULL
END
• ###### 7. Re: Cut-off Running Sum Mid-Year
Hi,
This might be too late for you, but maybe someone else has the same problem and finds it here. I found this article that solved it for me:
Regards,
Willem
1 of 1 people found this helpful | 844 | 3,318 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2019-51 | longest | en | 0.915255 |
https://www.thelaughclub.net/puzzles/most-folks-get-this-wrong-how-many-people-went-for-a-picnic/ | 1,685,594,683,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224647614.56/warc/CC-MAIN-20230601042457-20230601072457-00526.warc.gz | 1,124,686,909 | 30,303 | Most folks get this wrong: How many people went for a picnic?
Most folks get this wrong: How many people went for a picnic?
One of the best ways to pass the time during this lockdown is by solving puzzles and riddles.
Challenges help your brain exercise differently compared to when you are working or watching TV – a simple, yet wonderful method to heal and relax the mind. So you can forget about all your problems for at least a few minutes.
It’s usually hard to take time off to do it, but trust me it is worth it.
Every now and then we share some puzzles or illusions with you – and usually, those articles are well received.
Today’s clever puzzle
Being able to test your skills, challenge the brain and exercise the mind is actually both fun and necessary. Something healthy that feels good is a rare sight, so sitting down to solve a few brainteasers is a win-win situation.
With that said, I wanted to share this super clever puzzle that I came across online with you!
It really makes you think – and lets that problem-solver that you’ve kept inside since school days come out and run free again. They might be a little rusty after all these years – or are your skills polished and ready for any challenge?
Will you find the answer to this riddle?
An elderly couple went on a picnic. They have 5 sons and each son has 3 children. In total, how many people went for a picnic?
How many went for a picnic?
Yes, now it is time to think. Take your time and count everyone, right?
We will report the correct answer below.
So how many people went on this picnic then?
Maybe you think it’s 22 people? Sadly, that’s wrong.
The correct answer is that only 2 people went for a picnic.
At the beginning of the riddle, it says that an elderly couple went on a picnic. However, it was never said that their sons and their children went as well. Since that information was included, it probably made you start counting as you thought it was a math problem – it wasn’t.
The answer was much simpler than most people think.
Did you get the correct answer? Then press that share button below and invite your friends to a fun challenge! | 464 | 2,144 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2023-23 | longest | en | 0.987063 |
https://gmatclub.com/forum/global-ecological-problems-reduce-to-the-problem-of-balancing-supply-a-290473.html | 1,571,051,727,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986653216.3/warc/CC-MAIN-20191014101303-20191014124303-00154.warc.gz | 517,559,796 | 148,284 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
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# Global ecological problems reduce to the problem of balancing supply a
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Global ecological problems reduce to the problem of balancing supply a [#permalink]
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10 Mar 2019, 09:32
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Global ecological problems reduce to the problem of balancing supply and demand. Supply is strictly confined by the earth’s limitations. Demand, however, is essentially unlimited, as there are no limits on the potential demands made by humans. The natural tendency for there to be an imbalance between demand and sustainable supply is the source of these global problems. Therefore, any solutions require reducing current human demand.
Which one of the following is an assumption on which the argument depends?
(A) Supply and demand tend to balance themselves in the long run.
(B) It is possible to determine the limitations of the earth’s sustainable supply.
(C) Actual human demand exceeds the earth’s sustainable supply.
(D) It is never possible to achieve a balance between the environmental supply and human demand.
(E) Human consumption does not decrease the environmental supply.
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Re: Global ecological problems reduce to the problem of balancing supply a [#permalink]
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10 Mar 2019, 10:56
IMO C. Because the conclusion is that in order to maintain a balance (i.e., any solutions) require reducing current human demand. This implicitly states that current human demand exceeds the earth’s sustainable supply.
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Re: Global ecological problems reduce to the problem of balancing supply a [#permalink]
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10 Mar 2019, 11:35
The conclusion is that solution should REQUIRE lowering human demands.
Negating Option E tells that consumption actually reduces supply .. so we have a problem at supply itself. Because even if we reduce demands the balance won't come through
Option C just repeats already what is mentioned in the argument.
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Re: Global ecological problems reduce to the problem of balancing supply a [#permalink]
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10 Mar 2019, 17:01
I think it is B. In order to reduce demand, you would have first to know what the current earth supply is. Therefore, it should be "possible to determine the limitations of the earth’s sustainable supply". (B)
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Global ecological problems reduce to the problem of balancing supply a [#permalink]
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Updated on: 10 Mar 2019, 18:25
IMO C.
What is important here is to notice the difference between "potential demand" and "Actual demand".
C fills out the crack.
Originally posted by rickysinghk11 on 10 Mar 2019, 17:53.
Last edited by rickysinghk11 on 10 Mar 2019, 18:25, edited 1 time in total.
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Re: Global ecological problems reduce to the problem of balancing supply a [#permalink]
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30 Mar 2019, 03:55
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Global ecological problems reduce to the problem of balancing supply and demand. Supply is strictly confined by the earth’s limitations. Demand, however, is essentially unlimited, as there are no limits on the potential demands made by humans. The natural tendency for there to be an imbalance between demand and sustainable supply is the source of these global problems. Therefore, any solutions require reducing current human demand.
Which one of the following is an assumption on which the argument depends?
Conclusion : Any solutions require reducing current human demand.
Why? First point comes in mind is due to limited supply and excessive demand.
(A) Supply and demand tend to balance themselves in the long run.
If this is the case then there is no need to discuss the conclusion.
(B) It is possible to determine the limitations of the earth’s sustainable supply.
Possibility of determining limitations of earth's sustainable supply is irrelevant.
(C) Actual human demand exceeds the earth’s sustainable supply.
Correct : If this is negated, the conclusion will not hold true. We can't do anything about supply so try to reduce demand.
(D) It is never possible to achieve a balance between the environmental supply and human demand.
Same as A.
(E) Human consumption does not decrease the environmental supply.
If this is true then it is good. No purpose of writing such conclusion.
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Re: Global ecological problems reduce to the problem of balancing supply a [#permalink]
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30 Mar 2019, 11:25
Global ecological problems reduce to the problem of balancing supply and demand. Supply is strictly confined by the earth’s limitations. Demand, however, is essentially unlimited, as there are no limits on the potential demands made by humans. The natural tendency for there to be an imbalance between demand and sustainable supply is the source of these global problems. Therefore, any solutions require reducing current human demand.
Which one of the following is an assumption on which the argument depends?
(A) Supply and demand tend to balance themselves in the long run.
(B) It is possible to determine the limitations of the earth’s sustainable supply.
(C) Actual human demand exceeds the earth’s sustainable supply.
(D) It is never possible to achieve a balance between the environmental supply and human demand.
(E) Human consumption does not decrease the environmental supply.
Hi Folks,
Author relates Global ecological problems to supply & demand. Further in the argument, Earth is considered a supplier and humans as consumers.
Author claims that supply is confined, whereas demand is unlimited.
Author uses a strong word while drawing his conclusion "ANY" and insists on reducing current demand.
The argument seems to be hanging by authors claim that supply is limited and demand is unlimited.
Hence, it better be valid in order to draw such a strong conclusion.
Correct choice C validates author's claim. It also passes negation test. Logical opposite of choice C would be "Actual human demand does not exceed the earth’s sustainable supply." This clearly refutes Author's claim and conclusion falls apart naturally.
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Re: Global ecological problems reduce to the problem of balancing supply a [#permalink]
### Show Tags
03 Apr 2019, 05:18
1
Quote:
Global ecological problems reduce to the problem of balancing supply and demand. Supply is strictly confined by the earth’s limitations. Demand, however, is essentially unlimited, as there are no limits on the potential demands made by humans. The natural tendency for there to be an imbalance between demand and sustainable supply is the source of these global problems. Therefore, any solutions require reducing current human demand.
Conclusion: Solution for the global problems caused by an imbalance between demand and sustainable supply is to reduce current human demand.
But the premise talks about potential demands.
So, there is the logical gap. Author assumes that just like potential demands are unlimited, current human demands are also unlimited and exceed the supply. Only then the argument holds and that is why, we should reduce the current human demand.
Which one of the following is an assumption on which the argument depends?
Quote:
(A) Supply and demand tend to balance themselves in the long run.
Nothing of that sort is mentioned in the passage. Even if they do balance, is supply increased or demand decreased? We, cannot deduce and hence won't help the conclusion.
Quote:
(B) It is possible to determine the limitations of the earth’s sustainable supply.
If it is possible to determine the limitations of supply, then how is it helping the conclusion that demand should be decreased?
Quote:
(C) Actual human demand exceeds the earth’s sustainable supply.
Correct
Quote:
(D) It is never possible to achieve a balance between the environmental supply and human demand.
If anything, this statement is a weakner.
Quote:
(E) Human consumption does not decrease the environmental supply
It does not matter whether we can increase or decrease the supply. Conclusion is about reducing demand and this statement does not address that issue.
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Re: Global ecological problems reduce to the problem of balancing supply a [#permalink] 03 Apr 2019, 05:18
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# Problem 166. Kaprekar numbers
Solution 785608
Submitted on 29 Nov 2015 by Alberto Comin
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% x = 704; tf_correct = false; assert(isequal(kap(x),tf_correct))
2 Pass
%% x = 9 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 9 tf_correct = 1
3 Pass
%% x = 45 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 45 tf_correct = 1
4 Pass
%% x = 55 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 55 tf_correct = 1
5 Pass
%% x = 99 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 99 tf_correct = 1
6 Pass
%% x = 297 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 297 tf_correct = 1
7 Pass
%% x = 703 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 703 tf_correct = 1
8 Pass
%% x = 999 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 999 tf_correct = 1
9 Pass
%% x = 2223 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 2223 tf_correct = 1
10 Pass
%% x = 2728 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 2728 tf_correct = 1
11 Pass
%% x = 4950 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 4950 tf_correct = 1
12 Pass
%% x = 5050 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 5050 tf_correct = 1
13 Pass
%% x = 7272 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 7272 tf_correct = 1
14 Pass
%% x = 7777 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 7777 tf_correct = 1
15 Pass
%% x = 9999 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 9999 tf_correct = 1
16 Pass
%% x = 17344 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 17344 tf_correct = 1
17 Pass
%% x = 22222 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 22222 tf_correct = 1
18 Pass
%% x = 77778 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 77778 tf_correct = 1
19 Pass
%% x = 82656 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 82656 tf_correct = 1
20 Pass
%% x = 95121 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 95121 tf_correct = 1
21 Pass
%% x = 99999 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 99999 tf_correct = 1
22 Pass
%% x = 142857 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 142857 tf_correct = 1
23 Pass
%% x = 148149 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 148149 tf_correct = 1
24 Pass
%% x = 181819 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 181819 tf_correct = 1
25 Pass
%% x = 187110 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 187110 tf_correct = 1
26 Pass
%% x = 208495 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 208495 tf_correct = 1
27 Pass
%% x = 318682 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 318682 tf_correct = 1
28 Pass
%% x = 329967 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 329967 tf_correct = 1
29 Pass
%% x = 351352 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 351352 tf_correct = 1
30 Pass
%% x = 356643 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 356643 tf_correct = 1
31 Pass
%% x = 390313 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 390313 tf_correct = 1
32 Pass
%% x = 461539 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 461539 tf_correct = 1
33 Pass
%% x = 466830 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 466830 tf_correct = 1
34 Pass
%% x = 499500 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 499500 tf_correct = 1
35 Pass
%% x = 500500 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 500500 tf_correct = 1
36 Pass
%% x = 533170 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 533170 tf_correct = 1
37 Pass
%% x = 538461 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 538461 tf_correct = 1
38 Pass
%% x = 609687 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 609687 tf_correct = 1
39 Pass
%% x = 643357 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 643357 tf_correct = 1
40 Pass
%% x = 648648 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 648648 tf_correct = 1
41 Pass
%% x = 670033 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 670033 tf_correct = 1
42 Pass
%% x = 681318 tf_correct = true assert(isequal(kap(x),tf_correct))
x = 681318 tf_correct = 1
43 Pass
%% x = 681319 tf_correct = false assert(isequal(kap(x),tf_correct))
x = 681319 tf_correct = 0
44 Pass
%% x = 681320 tf_correct = false assert(isequal(kap(x),tf_correct))
x = 681320 tf_correct = 0
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In the coming future, I am going to add more Physics Quiz For Class 12.
I would love to see your valuable comments on the MCQs selection.
## Physics Quiz For Class 12 Quiz Instructions:
• There will be 30 multiple-choice questions in this online test.
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• Question of
## When an object gains electrons it becomes __________
• Neutral
• Positively charged
• Negatively charged
• None
• Question of
## An atom of oxygen has 8 protons and 10 electrons, this means the atom is ____________
• positively charged because it has excess electrons
• negatively charged because it has excess electrons
• positively charged because it has a deficiency of electrons
• negatively charged because it has a deficiency of electrons
• Question of
## After a balloon is rubbed against wool, the two objects will ________ each other because they have ___________ charges
• attract; like
• attract, opposite
• repel; like
• repel; opposite
• Question of
## Which statement is true of a positively charged object?
• Positively charged objects do not contain any electrons.
• Positively charged objects do not contain neutrons or electrons.
• There is a lack of electrons on a positively charged object.
• The protons and the electrons are both positively charged on such objects.
• Question of
## When two objects are rubbed together, there is a transfer of electrons. How do you determine which object acquires the transferred electrons?
• Always transfer from the bigger to the smaller object, to make it even
• Transfer is based on the initial charge of the two objects
• Transfer is based on how much electron affinity that each object has
• Always transfer from the more negative to the more positive object
• Question of
## What is the end result of charging by contact?
• Both object have the same charge, so they will attract one another
• Both object have the same charge, so they will repel one another
• Both object have the opposite charge, so they will attract one another
• Both object have the opposite charge, so they will repel one another
• Question of
## When a charged object contacts another object (one is usually a conductor), there is a transfer of electrons. How do you determine which object acquires the transferred electrons?
• Always transfer from the bigger to the smaller object, to make it even
• Transfer is based on the initial charge of the two objects
• Transfer is based on how much electron affinity that each object has
• Always transfer from the more negative to the more positive object
• Always transfer from the more negative to the more positive object
• Always transfer from the more negative to the more positive object
• Question of
## Why does the child’s hair stick up?
• The boy is grounded since he’s at the bottom of the slide
• He gained a charge from the slide, and since he’s not grounded, his hairs have the same charge so they repel one another
• He gained a charge from the slide, and since he’s not grounded, his hairs have opposite charges so they repel one another
• When hair is neutral, some have a positive side and some have negative side, so they will attract to each other, making it stand up
• Question of
## After grounding, how will objects interact?
• Both will have the same charge, so they attract one another
• Both will be neutral, so they will attract one another
• Both will be neutral, so they will repel one another
• Both will be neutral, so they will not attract nor repel
• Both will be neutral, so they will not attract nor repel
• Question of
## A balloon is rubbed against a student’s hair and then touched to a wall. The balloon sticks to the wall due to
• The balloon is charged neutral, so is the wall, so it attracts to the wall
• The balloon is charged opposite the wall, so it attracts to the wall
• The balloon has a charge, so it attracts the neutral wall
• The wall grounds the balloon, so it sticks
• Question of
## When a plastic rod is rubbed with wool, the wool acquires a positive charge because
• protons are transferred from the wool to the rod
• protons are transferred from the rod to the wool
• electrons are transferred from the rod to the wool
• electrons are transferred from the wool to the rod
• Question of
## Grounding happens when _______.
• A neutral object comes into contact with another neutral object
• A charged object is rubbed against another charged object
• A neutral object touches a MASSIVE conductive object
• A charged object touches a MASSIVE conductive object
• Question of
## Power is defined as:
• the something that enables an object to do work
• how much force an object has
• the rate at which work is done
• energy due to the position of something
• Question of
## Kaylee and Jessica were moving boxes of quiz bowl questions. They each moved 10 boxes. Jessica moved the 10 boxes in 30 minutes, while Kaylee did it in 20 minutes. Assuming the boxes required the same amount of force to move, and they were all moved the same distance, which of the following is true:
• Kaylee did more work than Jessica, because she did it faster.
• Jessica did more work than Kaylee, because she worked longer.
• Jessica did more work than Kaylee, because she worked longer.
• None of the above.
• Question of
• Joule
• Watt
• Newton
• Kelvin
• Question of
## A small motor does 4000J of work in 20 seconds. What is the power of the motor in watts?
• 0.005 Watts
• 200 Watts
• 80,000 Watts
• None of the Above
• None of the Above
• Question of
## A 55 kg person walks up a staircase, and a second 55 kg person runs up the staircase. Who develops more power and why?
• the person who runs up because he takes less time
• the person who walks up because he takes more time, using more energy
• same power for both because both cover the same distance with the same force
• not enough information to determine
• Question of
• 10W
• 50W
• 100W
• 300W
• Question of
• 360 J
• 3600 J
• 36,000 J
• 360,000 J
• Question of
## What is the purpose of this safety sign?
• To make sure students wear a protective apron.
• To make sure students put on gloves.
• To make sure goggles are worn before starting.
• To make sure all directions are read before beginning.
• Question of
## Which procedure below will increase the capacitance of a parallel-plate capacitor?
• Increase the distance of separation between the two plates
• Reduce the surface area of the plate
• Insert an insulator between the two plates
• Insert a conductor between the two plates
• Question of
## A parallel-plate capacitor is charged and then disconnected from the supply. Which of the following will increase the capacitance of the capacitor?
• Reduce the area of the plates
• Move the plates closer to each other
• Insert a conductor between the plates of the capacitor
• Increase the potential difference across the capacitor
• Question of
• 2:5
• 5:2
• 1:4
• 1:2
• Question of
• 2.1nC
• 3.0µC
• 2.75µC
• 3333.1µC
• Question of
## The S.I. unit for electric field is__________
• nC
• μC
• n/C
• none of the above
• Question of
## Electric charges are created ______.
• by gravitational forces.
• separately
• between 2 oppositely charged objects.
• by neutrons.
• Question of
## How can a neutral object become charged?
• by being dipped in water
• by being stuck to the desk with tape
• by allowing gravity to work on it
• by having electrons added or removed
• Question of
## Where can an electric field be found?
• below a force field
• in a gravitational field
• in the space surrounding a charged object
• outside of a magnetic field
• Question of
## If I triple the value of charge of a test charge the electric field will
• Increase by 3
• Increase by 9
• Not change
• Decrease by 9
• Question of
• 1 N/C
• 1 kgm/s
• 1 J/C
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# How to initialize a linear transformation of R^3 in wolfram mathematica?
Posted 10 years ago
Hello guys, I've been trying to solve a linear transformation of R^3 in wolfram mathematica, but i find it difficult to initialize the transformation. Here is the code that i've been trying but it doesn't work. Any suggestions? Off[General::spell1] $TextStyle = {FontFamily -> "Courier-Bold", FontSize -> 18}; ThreeDLinearTransform[M_] := ThreeDLinearTransform[M, {{-2.2, 2.2}, {-2.2, 2.2}, {-2.2, 2.2}}] ThreeDLinearTransform[M_, plotrange_] := Module[{hpairs, vpairs, dpairs, hlines, vlines, dlines, Mhlines,Mvlines, Mdlines, k, n, domain, range}, hpairs = Table[{{0., k, n}, {1., k, n}}, {k, 0, 1, 0.1}, {n, 0,1, 0.1}]; vpairs = Table[{{k, 0., n}, {k, 1., n}}, {k, 0, 1, 0.1}, {n, 0, 1, 0.1}]; dpairs = Table[{{k, n, 0.}, {k, n, 1.}}, {k, 0, 1, 0.1}, {n, 0, 1, 0.1}]; hlines = {RGBColor[0, 0, 1], Thickness[0.006], Line /@ hpairs}; vlines = {RGBColor[1, 0, 0], Thickness[0.006], Line /@ vpairs}; dlines = {RGBColor[0, 1, 0], Thickness[0.006], Line /@ dpairs}; domain = Show[Graphics[hlines], Graphics[vlines], Graphics[dlines], AspectRatio -> Automatic, PlotRange -> plotrange, Axes -> True, Ticks -> {Range[Ceiling[plotrange[[1, 1]]],Floor[plotrange[[1, 2]]]], Range[Ceiling[plotrange[[2, 1]]], Floor[plotrange[[2, 2]]]]},DisplayFunction -> Identity]; Mhlines = {RGBColor[0, 0, 1], Thickness[0.006], Line /@ ({M.#1[[1]], M.#1[[2]]} &) /@ hpairs}; Mvlines = {RGBColor[1, 0, 0], Thickness[0.006], Line /@ ({M.#1[[1]], M.#1[[2]]} &) /@ vpairs}; Mdlines = {RGBColor[0, 1, 0], Thickness[0.006],Line /@ ({M.#1[[1]], M.#1[[2]]} &) /@ dpairs}; range = Show[Graphics[Mhlines], Graphics[Mvlines], AspectRatio -> Automatic, PlotRange -> plotrange, Axes -> True, Ticks -> {Range[Ceiling[plotrange[[1, 1]]], Floor[plotrange[[1, 2]]]], Range[Ceiling[plotrange[[2, 1]]], Floor[plotrange[[2, 2]]]]}, DisplayFunction -> Identity]; Show[GraphicsRow[{domain, range}], DisplayFunction ->$DisplayFunction, ImageSize -> {640, 480}]] and here is the rotation of 45 degrees that I'm trying to do: A = (1/2) {{Sqrt[2], -Sqrt[2], Sqrt[2] }, {Sqrt[2], -Sqrt[2], Sqrt[2]}, {Sqrt[2], -Sqrt[2], Sqrt[2]}}; MatrixForm[A] ThreeDLinearTransform[A]
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Posted 10 years ago
I recommend a different line of attack. Perhaps it will be helpful to extend this example.lines and points originalPoints = Accumulate[RandomReal[{-1, 1}, {20, 3}]] lines = Transpose[ { RandomColor[Length[originalPoints] - 1], Table[Line[{i, i + 1}], {i, 1, Length@originalPoints - 1}] } ] graphics Graphics3D[GraphicsComplex[originalPoints, lines]] graphics with linear transformation rotMat = RotationMatrix[Pi/3, {1, 1, 1}] Graphics3D[ GraphicsComplex[originalPoints /. {x_, y_, z_} :> rotMat.{x, y, z}, lines]] dynamic Manipulate[ Show[ Graphics3D[GraphicsComplex[originalPoints, lines]], With[{rotMat = RotationMatrix[angle Degree, {1, 1, 1}]}, Graphics3D[ GraphicsComplex[ originalPoints /. {x_, y_, z_} :> rotMat.{x, y, z}, lines]] ] ], {angle, 0, 360} ] your transformation A = (1/2) {{Sqrt[2], -Sqrt[2], Sqrt[2]}, {Sqrt[2], -Sqrt[2], Sqrt[2]}, {Sqrt[2], -Sqrt[2], Sqrt[2]}}; Graphics3D[ GraphicsComplex[originalPoints /. {x_, y_, z_} :> A.{x, y, z}, lines]]
Posted 10 years ago
Thank you very much. I've been trying a different approach, so here is what i got by now. I have 3D cube and I need to do linear transformation on it: rotation by 45 degrees, Reflection in the x2-axis, A Contraction, A Dilation, A Vertical Expansion, A Shear. vtc = {{0, 0}, {1, 0}, {1, 1}, {0, 1}};(*VertexTextureCoordinates*) kocka = {{{0, 0, 0}, {0, 1, 0}, {1, 1, 0}, {1, 0, 0}}, {{0, 0, 0}, {1, 0, 0}, {1, 0, 1}, {0, 0, 1}}, {{1, 0, 0}, {1, 1, 0}, {1, 1, 1}, {1, 0, 1}}, {{1, 1, 0}, {0, 1, 0}, {0, 1, 1}, {1, 1, 1}}, {{0, 1, 0}, {0, 0, 0}, {0, 0, 1}, {0, 1, 1}}, {{0, 0, 1}, {1, 0, 1}, {1, 1, 1}, {0, 1, 1}}}; MatrixForm[kocka] Graphics3D[ Table[{Texture[mat[k]], Polygon[kocka[[k]], VertexTextureCoordinates -> vtc]}, {k, 1, 6}], Axes -> True, AxesLabel -> {x, y, z}, PlotRange -> 1]
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Question:
# Question:Q:Finding multiple differences and their averages
Ok so let’s say I’ve got one table with a column of
15
10
12
8
How can I find the differences between each row and it’s neighbor and automatically send the average of all the differences into a separate box in another table? Also this column is likely to get really long since I will be recording data points for several months.
basically do
15 (difference between 15 and 10 is 5)
10 (difference between 10 and 12 is 2)
12 (difference between 12 and 8 is 4)
8 (the average of 5, 2, and 4, is 3.66.....)
but all with formula?
Thank you for your help!
iPad Pro Wi-Fi, iOS 11.1
Posted on
Question marked as Solved
Answer:
Answer:
Hi nor'
Use a column to record the differences.
Find the average of that column.
Formulas:
B3 (and filled down):
B3: IF(AND(LEN(A2)>0,LEN(A3)>0),ABS(A2−A3),"")
C2: AVERAGE(B)
The formula in column B checks the cels in column a one row above its row and on its row. If both contain a value, the diference is calculated, and ABS converts that to an absolute (positive) value. If either test cell is empty, the formula returns a null string, which appears 'blank' and is not included in the 'AVERAGE' calculations.
C2: Returns the mean of all numeric values in column B, an ignores the text values (including the null strings ( "" ) returned by the formula in column B).
Regards,
Barry
Posted on
Page content loaded
Question marked as Solved
Hi nor'
Use a column to record the differences.
Find the average of that column.
Formulas:
B3 (and filled down):
B3: IF(AND(LEN(A2)>0,LEN(A3)>0),ABS(A2−A3),"")
C2: AVERAGE(B)
The formula in column B checks the cels in column a one row above its row and on its row. If both contain a value, the diference is calculated, and ABS converts that to an absolute (positive) value. If either test cell is empty, the formula returns a null string, which appears 'blank' and is not included in the 'AVERAGE' calculations.
C2: Returns the mean of all numeric values in column B, an ignores the text values (including the null strings ( "" ) returned by the formula in column B).
Regards,
Barry
Nov 15, 2017 7:43 PM
User profile for user: nor.support
Question: Finding multiple differences and their averages | 612 | 2,379 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.75 | 4 | CC-MAIN-2018-47 | latest | en | 0.898963 |
http://www.purplemath.com/learning/search.php?author_id=8610&sr=posts | 1,526,921,798,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794864461.53/warc/CC-MAIN-20180521161639-20180521181639-00580.warc.gz | 454,673,773 | 5,187 | ## Search found 3 matches
Sat Nov 21, 2009 5:27 pm
Forum: Trigonometry
Topic: Trig Word Prob: ship goes 62 units at 12 deg, then 111 units
Replies: 3
Views: 2806
### Re: Trig Word Prob: ship goes 62 units at 12 deg, then 111 units
Is this what you mean? If this is the correct diagram, I still can't solve it.
Fri Nov 20, 2009 9:52 pm
Forum: Trigonometry
Topic: Trig Word Prob: ship goes 62 units at 12 deg, then 111 units
Replies: 3
Views: 2806
### Trig Word Prob: ship goes 62 units at 12 deg, then 111 units
A ship travels 62 units on a bearing of 12deg, and then travels on a bearing of 102deg for 111 units. Find the distance from the starting point to the end point. Round to the nearest unit. The answer apparently seems to be 127 units, but I have no idea how to get that. What I'm asking for: A nice d...
Fri Nov 13, 2009 10:46 pm
Forum: Trigonometry
Topic: Need Help with solving a right triangle
Replies: 1
Views: 1684
### Need Help with solving a right triangle
Triangle ABC is a right triangle, with B being the right angle and line CB being the ground. An obtuse triangle is inside triangle ABC. Let's call this obtuse triangle ADC. The diagram should look something like this: http://i646.photobucket.com/albums/uu183/blackhole252/Triangle.jpg Suppose angle A... | 378 | 1,284 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2018-22 | latest | en | 0.849133 |
https://www.mathallstar.org/Practice/Search?Category=TheModMethod | 1,566,215,734,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027314732.59/warc/CC-MAIN-20190819114330-20190819140330-00249.warc.gz | 891,669,112 | 2,532 | #### TheModMethod
###### back to index
Prove there is no integer solutions to $x^2 = y^5 - 4$.
Find all integer solutions to: $x^2 + 3y^2 = 1998x$.
Show the equation $x^2 + y^2-8z^3 = 6$ has no integer solution.
Solve in positive integers the equation $3^x + 4^y = 5^z$ .
Solve in positive integers the equation $8^x + 15^y = 17^z$.
Show that neither $385^{97}$ nor $366^{17}$ can be expressed as the sum of cubes of some consecutive integers.
Show that if there exist integer $x$, $y$, and $z$ such that $3^x + 4^y=5^z$, then both $x$ and $z$ must be even.
Find all ordered integer pairs $(x, y)$ such that $x^3 + y^3=2019$.
Find all the integer pairs $(x, y)$ such that $x^3 = 2^y + 15$.
Determine all positive integer $n$ such that the following equation is solvable in integers: $$x^n + (2+x)^n + (2-x)^n = 0$$ | 287 | 825 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2019-35 | latest | en | 0.752016 |
https://www.physicsforums.com/threads/proving-limit-doesnt-exist.816303/ | 1,508,807,844,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187827662.87/warc/CC-MAIN-20171023235958-20171024015958-00163.warc.gz | 988,157,369 | 17,828 | Proving limit doesn't exist
1. May 28, 2015
NanoMath
1. The problem statement, all variables and given/known data
I have to show that the following function does not have a limit as (x,y) approaches (0,0)
3. The attempt at a solution
I tried taking different paths for example y=x or y=0 and switching to polar coordinates, but I don't get anywhere.
2. May 28, 2015
pasmith
Consider approaching the origin along the line $x = 0$.
3. May 28, 2015
NanoMath
Right so the first term cancels and I am left with: y sin ( 1/ y2 ) + sin ( 1 / y2 ) .
So what do I conclude by taking the limit of this?
y sin ( 1/ y2 ) vanishes since y goes to 0. I am a bit confused on what to do with sin ( 1/y2).
Can I claim that limit doesn't exist because sin ( 1/ y2 ) alternates as y goes to zero and therefore doesn't have unique answer ?
4. May 28, 2015
pasmith
How would you justify that rigorously?
5. May 28, 2015
Zondrina
You can explain the dense oscillations near the origin by recalling $\text{sin}(y) = 0$ for $y = n \pi, n \in \mathbb{Z}$.
So $\text{sin} \left( \frac{1}{y} \right) = 0$ for $y = \frac{1}{n \pi}, n \in \mathbb{Z}, n \neq 0$.
Therefore we can say $\text{sin} \left(\frac{1}{y^2} \right) = 0$ for $y = \frac{1}{\sqrt{n \pi}}, n \in \mathbb{Z}, n \neq 0$.
There is a dense population of these points near zero; think about the interval $(0, \frac{1}{\sqrt{\pi}}]$.
As for showing it formally, you're going to have to squeeze some effort out, and you might need a sandwich to have enough energy.
6. May 28, 2015
NanoMath
Would it be okay to take sequence an = √2/√nπ . Then this sequence obviously converges to zero as n goes to infinity. But f(an) alternates between 1,0,-1,0,...
Last edited: May 28, 2015
7. May 28, 2015
Zondrina
There is infinitely many points approaching zero:
$$\frac{1}{\sqrt{\pi}}, \frac{1}{\sqrt{2 \pi}}, \frac{1}{\sqrt{3\pi}}, \frac{1}{\sqrt{4\pi}}, \frac{1}{\sqrt{5 \pi}}, \frac{1}{\sqrt{6 \pi}}, ...$$
Group these into triplets:
$$\left( \frac{1}{\sqrt{\pi}}, \frac{1}{\sqrt{2 \pi}}, \frac{1}{\sqrt{3\pi}} \right), \left( \frac{1}{\sqrt{4\pi}}, \frac{1}{\sqrt{5 \pi}}, \frac{1}{\sqrt{6 \pi}} \right), ...$$
Notice for each triplet of points inside $(0, \frac{1}{\sqrt{\pi}}]$, the function $\text{sin} \left(\frac{1}{y^2} \right)$ will oscillate from $0$ to $-1$, then to $0$, then to $+1$ and then back to $0$.
The triplets need not be ordered as I've shown. You can group different triplets and the function will oscillate in the same fashion, but potentially in a different order. For example, using:
$$\left( \frac{1}{\sqrt{2 \pi}}, \frac{1}{\sqrt{3\pi}}, \frac{1}{\sqrt{4\pi}} \right)$$
Will produce a different sequence for the oscillation (0,1,0,-1,0), but the behavior will be the same for each triplet. Namely, $\left| \text{sin} \left(\frac{1}{y^2} \right) \right| \leq 1$.
8. May 29, 2015
momoko
Simply speaking, we choose epsilon=0.9, we cannot get a corresponding delta to satisfy the epsilon-delta definition of limit. | 1,016 | 3,001 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.8125 | 4 | CC-MAIN-2017-43 | longest | en | 0.898331 |
https://topic.alibabacloud.com/a/there-are-1-to-font-classtopic-s-color00c1de100font-a-total-of-font-classtopic-s-color00c1de100font-starting-from-1-every-1-2-3--number-take-one-number-and-the-last-few_8_8_31221245.html | 1,679,743,724,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945323.37/warc/CC-MAIN-20230325095252-20230325125252-00425.warc.gz | 652,142,150 | 16,066 | There are 1 to 100 a total of 100, starting from 1, every 1, 2, 3 ... Number take one number and the last few?
Source: Internet
Author: User
Recently find an internship, in doing test assignment encountered such a problem, on the way to record:
Said, there are 1 to 100 a total of 100 numbers, put into a circle. Starting from 1, every 1, 2, 3, 4 ... The number takes a number, keeps looping, and finally leaves a few? Specifically, the beginning (0 numbers) Take 1 away, 1 number (2) to take 3 away, and then 2 number (4, 5) Take 6 away, and then 3 number (7, 8, 9) take 10 away. After the first lap count to 100 and then from 2 onwards, until the last 1 digits left, what are the last remaining? What if it's 1 to n?
`1 Public Static intSelectnumber (intN) {2 3 intresult =-1;4Arraylist<integer> nums =NewArraylist<integer>();5 intindex = 0;//This variable was used to remove numbers from list6 intCount = 0;//count is used to count which numbers should be remove7 intPindex = 0;//This was used to record previous index8 9 //generate a list contains numbers from 1 to nTen for(inti = 1; I <= N; i++) { One Nums.add (i); A } - - while(Nums.size () > 1) { the - while(Index <nums.size ()) { - Nums.remove (index); -count++; +Pindex =index; -Index + =count; + } A atIndex = count-(nums.size ()-pindex); - - while(Index > Nums.size ()-1) { -index = index-nums.size (); - } - } in -result = Nums.get (0); to returnresult; + } - the Public Static voidMain (string[] args) { * intSurviver = Selectnumber (100); \$System.out.println ("The Surviver is:" +surviver);Panax Notoginseng}`
That's my solution, and the last number left is 31.
There are 1 to 100 a total of 100, starting from 1, every 1, 2, 3 ... Number take one number and the last few?
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http://mathhelpforum.com/pre-calculus/213397-writing-complex-number-bi-form.html | 1,529,917,180,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267867579.80/warc/CC-MAIN-20180625072642-20180625092642-00219.warc.gz | 215,361,656 | 10,196 | # Thread: Writing a complex number in a+bi form
1. ## Writing a complex number in a+bi form
Hi guys,
I'm asked to write the number 5/i in the a+bi form. The format is such that I can only enter the values of a and b in the computer. I'm not sure what I should write. Can anyone help me please?
Thanks a lot!
Egoyan
2. ## Re: Writing a complex number in a+bi form
Originally Posted by Egoyan
Hi guys,
I'm asked to write the number 5/i in the a+bi form. The format is such that I can only enter the values of a and b in the computer. I'm not sure what I should write. Can anyone help me please?
Learn this fact, it will save your life in complex numbers.
$\displaystyle (\forall z\in\mathbb{C}\setminus\{0\})\left[\frac{1}{z}=\frac{\overline{z}}{|z|^2}\right]$.
So $\displaystyle \frac{1}{-3+4i}=\frac{-3-4i}{5}$.
This $\displaystyle \frac{5}{i}=\frac{-5i}{1}=-5i$.
3. ## Re: Writing a complex number in a+bi form
Oh my. I did not know that. Heh. Thanks a lot! I won't forget it any time soon now...
4. ## Re: Writing a complex number in a+bi form
More generally, a complex number, a+ bi, multiplied by its "complex conjugate", a- bi, gives a non-negative real number: $\displaystyle (a+ bi)(a- bi)= a^2+ abi - abi- b^2i^2= a^2+ b^2= |a|$. In particular, you can make denominator or a fraction a real number by multiplying the numerator and denominator by the complex conjugate of the denominator:
$\displaystyle \frac{a+ bi}{c+ di}= \frac{a+ bi}{c+ di}\frac{c- di}{c- di}= \frac{(ac+ bd)+ i(bc- ad)}{c^2+ d^2}= \frac{ac+ bd}{c^2+ d^2}+ \frac{bc- ad}{c^2+ d^2}i$. | 517 | 1,575 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2018-26 | latest | en | 0.795497 |
https://www.coursehero.com/file/5247/precept4sol/ | 1,544,537,188,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823621.10/warc/CC-MAIN-20181211125831-20181211151331-00326.warc.gz | 879,368,098 | 66,512 | precept4sol
# precept4sol - Computer Science 340 Reasoning about...
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Computer Science 340 Reasoning about Computation Precept 4 Problem 1 Consider the family of hash functions discussed in class h a,b ( x ) = ( ax + b mod p )( mod n ) where a, b ∈ { 0 , . . . p - 1 } and a = 0. Consider a hash function h a,b drawn uni- formly and at random from this family. For any x 1 , x 2 ∈ { 0 , . . . , p - 1 } , x 1 = x 2 , show that Pr[ h a,b ( x 1 ) = h a,b ( x 2 )] 1 /n. Solution: Let f a,b ( x ) = ( ax + b mod p ). In class, we showed that for any x 1 , x 2 ∈ { 0 , . . . , p - 1 } , x 1 = x 2 , as a, b range over all values in { 0 , . . . p - 1 } , a = 0, the pair ( f a,b ( x 1 ) , f a,b ( x 2 )) ranges over all p ( p - 1) pairs ( y 1 , y 2 ) such that y 1 , y 2 ∈ { 0 , . . . , p - 1 } , y 1 = y 2 . Note that h a,b ( x ) = f a,b ( x ) mod n . Thus the number of h a,b for which h a,b ( x 1 ) = h a,b ( x 2 ) is exactly the number of pairs ( y 1 , y 2 ), y 1 , y 2 ∈ { 0 , . . . , p - 1 } , y 1 = y 2 such that y 1 = y 2 mod n . Let us count the number of such pairs as follows: There are p choices for y 1 . For each choice of y 1 , there are p/n - 1 choices of y 2 such that y 1 = y 2 mod n . Now p/n - 1 ( p + n - 1) /n - 1 = ( p - 1) /n . Hence the number of pairs ( y 1 , y 2 ) such that y 1 = y 2 mod p is at most p ( p - 1) /n . By the above discussion, the number of choices of h a,b such that h a,b ( x 1 ) = h a,b ( x 2 ) is at most p ( p - 1) /n , which is a 1 /n
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# MATH 1630 Homework - Ch_ 2 - From: <Saved by Windows...
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Unformatted text preview: From: <Saved by Windows Internet Explorer 7> Subject: MATH 1630 Homework - Ch. 2 Date: Mon, 7 Sep 2009 16:26:10 -0400 MIME-Version: 1.0 Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Content-Location: http://faculty.cs.weber.edu/brague/MA1630/Assignments/MA1630HwkCh2C.htm X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.5579 X <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML xmlns=3D"http://www.w3.org/TR/REC-html40" xmlns:o =3D=20 "urn:schemas-microsoft-com:office:office" xmlns:w =3D=20 "urn:schemas-microsoft-com:office:word"><HEAD><TITLE>MATH 1630 Homework =- Ch. 2</TITLE> <META http-equiv=3DContent-Type content=3D"text/html; = charset=3Dwindows-1252"> <META content=3DWord.Document name=3DProgId> <META content=3D"MSHTML 6.00.6000.16890" name=3DGENERATOR> <META content=3D"Microsoft Word 11" name=3DOriginator><LINK=20 href=3D"MA1630HwkCh2C_files/filelist.xml" rel=3DFile-List><!--[if gte = mso 9]><xml> <o:DocumentProperties> <o:Author>kirby</o:Author> <o:LastAuthor>Brian Rague</o:LastAuthor> <o:Revision>3</o:Revision> <o:TotalTime>21</o:TotalTime> <o:LastPrinted>2004-02-20T18:45:00Z</o:LastPrinted> <o:Created>2007-09-02T02:07:00Z</o:Created> <o:LastSaved>2009-08-13T00:38:00Z</o:LastSaved> <o:Pages>1</o:Pages> <o:Words>574</o:Words> <o:Characters>3278</o:Characters> <o:Company>Family</o:Company> <o:Lines>27</o:Lines> <o:Paragraphs>7</o:Paragraphs> <o:CharactersWithSpaces>3845</o:CharactersWithSpaces> <o:Version>11.5606</o:Version> </o:DocumentProperties> </xml><![endif]--><!--[if gte mso 9]><xml> <w:WordDocument> <w:SpellingState>Clean</w:SpellingState> <w:GrammarState>Clean</w:GrammarState> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:SelectEntireFieldWithStartOrEnd/> <w:UseWord2002TableStyleRules/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState=3D"false" LatentStyleCount=3D"156"> </w:LatentStyles> </xml><![endif]--> <STYLE>@page Section1 {size: 8.5in 11.0in; margin: 1.0in .7in 1.0in = 1.0in; mso-header-margin: .5in; mso-footer-margin: .5in; = mso-paper-source: 0; } P.MsoNormal { FONT-SIZE: 12pt; MARGIN: 0in 0in 0pt; FONT-FAMILY: "Courier New"; = mso-style-parent: ""; mso-pagination: widow-orphan; = mso-fareast-font-family: "Times New Roman" } LI.MsoNormal { FONT-SIZE: 12pt; MARGIN: 0in 0in 0pt; FONT-FAMILY: "Courier New"; = mso-style-parent: ""; mso-pagination: widow-orphan; = mso-fareast-font-family: "Times New Roman" } DIV.MsoNormal { FONT-SIZE: 12pt; MARGIN: 0in 0in 0pt; FONT-FAMILY: "Courier New"; = mso-style-parent: ""; mso-pagination: widow-orphan; = mso-fareast-font-family: "Times New Roman" } SPAN.SpellE { mso-style-name: ""; mso-spl-e: yes } SPAN.GramE { mso-style-name: ""; mso-gram-e: yes...
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Ask a homework question - tutors are online | 1,269 | 3,643 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2017-13 | longest | en | 0.321313 |
https://www.biggerpockets.com/forums/61/topics/311050-reducing-total-interest-paid-to-your-30-year-mortgage | 1,603,935,998,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107902683.56/warc/CC-MAIN-20201029010437-20201029040437-00554.warc.gz | 640,358,692 | 29,543 | # Reducing total interest paid to your 30 year mortgage
10 Replies
I just got back from day 2 of the Rich Dad seminar taught by Elite Legacy Education. Our instructor Trevor Evans showed us what they call "Double Principal" payments. This is NOT the same as paying two mortgage payments. The premise behind it is that you pay your regular mortgage payment (principal + interest) and you include next month's PRINCIPAL amount. If you pay the principal payment at the beginning of the month you don't get charged with the interest you typically would. If you simply sent in a check and tell them to apply it to principal you will NOT get the same result because you will still be charged the interest in the second month. Your additional payment must match the principal amount of the next month or they won't know what to do with the money. To get that amount you have to create the amortization schedule and skip every other line (diagram below). This is huge if you really understand the concept. The down side is your monthly payment is larger and gets significantly larger as the time goes on because of the flip flop of principal to interest. I found a website who called it modulating payments
Here is their explanation of it
"At the beginning of the loan we owe the most, thus the interest payment we owe is the highest, so the amount of the monthly payment that goes to principal is the lowest. Indeed, in Month 1, next month's principal payment (Month 2) on a 30 year at 6% on \$200,000 is just \$200.10.
So we are budgeted for \$1,688 (the 15 year amount), but let's consider that we pay only the minimum due plus next month's principal: \$1,199 + \$200 = \$1,399. We're under budget!
Now Month 2 arrives. But we've already paid that month's principal. You can just cross a line through that month—interest and all. We would have owed \$999 in interest for that month, but because we paid that month's principal just one month early, that \$999 in interest is completely wiped out. Zero. We spent \$200 one month early and saved \$999. That's a good deal.
It is important to note that the \$999 savings is only realized, non-inflation adjusted, over the full scheduled term of the loan (30 years). If we pay off the loan early and exit the game we won't see the entire savings. We may think that if we pay \$200 thirty days early, then we save only 1/2% of \$200 or \$1. That is the case if we repay the entire loan at the end of that month and then call the whole thing "quits." But for each month we do not pay back the entire loan, the savings accrue. By paying the \$200 thirty days early, the entire loan payment schedule shifts forward one month—so now we will be paid off in 359 months instead of 360 months, etc., etc. That is why in Tip Number Two we think in terms of our total savings, over an entire life's payment span of 15 to 30 years, regardless of the number of mortgages."
I hope someone finds real benefit with this. I know I found it nifty. I also figured out how to calculate it in excel if anyone is interested.
This is very interesting! I'm going to study your link.
Thanks!
Guru Gobledygook, Presuming your mortgage allows prepayment of principal, You can pay any amount towards principal and it will affect the entire amortizations schedule. There is absolutely no magic in paying exactly the amount of principal due in the following payment.
@Ned Carey paying toward the principal versus this strategy is different. Read it closely. Supposedly this cuts out the next month's interest payment. It's what they taught, not something I've done, but I wanted to share.
Joan, Ned is right. We knew all about this 30 years ago. There is no magic the "new innovative spin" they put on it. It's really very simple.....interest is applied every month to your Outstanding Balance. The less outstanding, the less interest charged that month, therefore the more of your payment that goes to principle, which in reality just moves you further along on your amortization schedule. And make no mistake.....paying anything extra toward principle does do Exactly the same thing as paying exactly one month's principle. You and the other people there just didn't know better. And yes, I understand exactly what you were saying, but there is no difference. Next thing you know, they'll being selling a program that predicts what direction the sun will rise in.
To clarify it better maybe, when you make that extra \$200 principle payment you are Not saving the \$999 interest for that month; you will save 4% On That \$200, each month for the life of the loan
I'm glad I posted. I will play around with my Amort schedule in excel and check out the difference, or lack there of. Thanks guys for the clarity.
What is the point in dumping cash into a rental property mortgage. The idea is to get a mortgage at the lowest rate possible. stretch it out as long as possible and have your tenants pay it off while providing you positive cash flow. In addition you hope to realise appreciation which does not change with dumping money onto a mortgage. Think about your ROI.
It also does not, contrary to appearances, increase cash flow on a property.
As others have stated a mortgage is where cash goes to die.
There actually is another way to do this. It has to do with using a non-amortized (simple or compound interest) type of account to pay off the amortized loan. It's the basis of the claims you've seen about paying off a 30-year home loan in around seven years.
I don't have the full details on it, or I'd post something more cogent. I have seen the numbers and I understand why it works, I just don't have the nuts and bolts of it.
In a COBOL programming class many years ago, the class material provided the loan amortization formula and it was up to us to write the code to produce an amortization schedule. Wish I still had that code.
From what I do remember, it's rather more complicated than the more simple "average daily balance" calculation of a non-amortized revolving credit account.
Anyway, that's the basis of debt acceleration. It works because by paying down big chunks of principal the total term of the loan is reduced which, in turn, reduces the total interest paid. You can see that on the amortization schedule the lender provided at closing.
I did find a YouTube link to a webinar about it. It's not short - it's an hour and 36 minutes, but even so, it does NOT spend the whole time selling. It's all info up until about the hour and six minute mark or so.
Hope this helps...
David J Dachtera
@David Dachtera I figured this would get around to the pay off your mortgage in 7 years scam. I wondered it the original pitch @Hoan Thai heard was a set up for selling this. Yes there were some minor advantages to be had by using a second mortgage with a lower interest rate, the float on your account and moving money around from one account to the other but it was a complex scheme with not a lot of advantage.
Most people selling it could not even explain where the savings was coming from. The whole thing was based on having a lot of unused money in your checking account. If you didn't have that, the plan didn't work. What they failed to tell anybody is if you had a 100K mortgage. The only way you could pay it off was by paying at least 100K in seven years.
Although, as you know if you watched the video, it's not a scam. It's probably more the exception than the rule, but the numbers presented back up the claim and illustrate how to do it. It's very real and entirely possible. Most folks are likely to take longer than seven years given the current economy and the toll it has taken on many households. 12 to 15 years (roughly half of a 30-year term) is probably more realistic for most folks.
The video does not recommend using a second-lien (HELOC) type of account, though I suppose that might work if the interest rate is advantageous, rather it recommends an unsecured line of credit. Being a revolving line, the history it builds becomes an advantage in your overall credit history. Being unsecured makes it a positive addition to your types of credit (part of the score calculation in most models). After paying down a couple of "chunks" as the video calls them, I suppose a HELOC with a low utilization might be useful to offset the impact of the "New Checkbook" account on overall credit utilization as the balance fluctuates (as you pay big "chunks" toward the mortgage).
Also, I think you're putting too much focus on the "seven years" thing. Time is not the point, interest reduction by reducing the number of payments is the point. Instead of paying \$230K on an initial loan balance of \$100K after 30 years for example, the point is to aim for paying more like \$130K (no, I didn't work that out on a calculator - it's a guess). THAT is where the savings comes from.
...and yes, the "doesn't work for everyone" part comes from the assumption that your monthly expenses are less than half of your take-home pay for the month. I covered that in my first paragraph in this post.
The whole technique is focused on doing exactly what you said in your last two sentences. So, I don't a problem.
David J Dachtera | 2,040 | 9,200 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2020-45 | latest | en | 0.962239 |
http://kcchao.wikidot.com/permutation | 1,539,881,663,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583511889.43/warc/CC-MAIN-20181018152212-20181018173712-00017.warc.gz | 194,455,609 | 11,742 | Permutation
(1)
\begin{align} p=\left( \begin{array}{cccc} 1 & 2 & 3 & 4 \\ 2 & 3 & 4 & 1 \\ \end{array} \right) \end{align}
(2)
$$P:(1,2,3,4)→(4,1,2,3) not(2,3,4,1)$$
The marble in box 1 moves to box 2, the marble in box 2 moves to box 3, the marble in box 3 moves to box 4, and the marble in box 4 moves to box 1.
page revision: 2, last edited: 27 Dec 2013 09:34 | 164 | 365 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 1, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2018-43 | longest | en | 0.67326 |
https://angeloyeo.github.io/2022/09/28/Mahalanobis_distance_en.html | 1,702,194,322,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679101282.74/warc/CC-MAIN-20231210060949-20231210090949-00037.warc.gz | 123,307,260 | 29,155 | Mahalanobis Distance
※ In this post, vectors are represented using “row vectors” as the default direction. For more detailed explanation of this, please refer to the first section “Data representation using row vectors”.
Prerequisites
To better understand this post, it is recommended that you be familiar with the following content:
If you need a more detailed explanation of the covariance matrix, please refer to the following post:
Data representation using row vectors
In mathematics, it is more common to view column vectors as the default direction when representing vectors. In other words, a vector $x$ of arbitrary dimension $n$ is usually represented as follows.
$\vec{x}=\begin{bmatrix}x_1 \\ x_2 \\ \vdots \\x_n\end{bmatrix} % Equation (1)$
In this case, the matrix must go to the left of the vector. The product of an arbitrary $n\times n$ dimensional matrix $A$ and an $n$ dimensional column vector $x$ is represented as follows.
$Ax % Equation (2)$
Furthermore, the dot product between column vectors can be expressed using the transpose operator as follows. For any $n$-dimensional vectors $\vec{x}$ and $\vec{y}$,
$dot(\vec x, \vec y)=\vec x^T\vec y % Equation (3)$
However, in data science, for some reason unknown, a single data point is usually treated as a row vector and used. In other words, an arbitrary $d$-dimensional vector $x$ is represented as follows.
$\vec{x}=\begin{bmatrix}x_1 & x_2 & \cdots & x_d\end{bmatrix}% Equation (4)$
In this case, the matrix must go to the right of the vector. The product of an arbitrary $d\times d$ dimensional matrix $R$ and an $d$-dimensional row vector $x$ can be written as follows.
$x R % Equation (5)$
Furthermore, the dot product between row vectors also uses the transpose operation, but the transposed vector is on the right. In other words, for any $d$-dimensional row vectors $\vec{x}$ and $\vec{y}$,
$dot(\vec x, \vec y)=\vec x \vec y^T % Equation (6)$
Going further, in data science, it is common to have a data set $\mathcal D$ with $n$ samples and $d$ features represented as an $n\times d$ dimensional matrix. In other words, if more sample data is added, one row is added. In other words, each data point is treated as a “row vector.”
In this post, the default direction of vectors is set to “row vectors.”
Contextual relative distance
Consider two vectors $\vec x$ and $\vec y$ as shown below.
Figure 1. The distance between two vectors in space can be calculated using the dot product of the vectors.
What formula should be used to calculate the Euclidean distance between an arbitrary point $\vec x$ and $\vec y$? The distance can be calculated using the difference and dot product of the two vectors. This distance is called the Euclidean distance.
$d_E = \sqrt{(\vec x-\vec y)(\vec x-\vec y)^T} % Equation (7)$
However, if we consider other data points in the vicinity, we may need to reconsider whether to use an absolute distance between two points.
Figure 2. The distance between two points, taking into account the context of other data points, may need to be calculated differently.
In the above figure, (a) can be seen as points that are quite away from the distribution of blue data, while (b) is in a relatively less deviated location from the distribution. In other words, considering the “context” of other data points, the distance between the two vectors in Figure 2 (a) may be farther than the distance between the two vectors in Figure 2 (b).
The ambiguous expression “context” can be expressed more mathematically as “standard deviation.” If we can assume that the data is in the form of a normal distribution, we can use the properties of the standard deviation of a normal distribution to see that there is 68, 95, and 99.7% of the data coming in at a distance of 1, 2, and 3 standard deviations away from the mean (center).
Figure 3. How much data is included when moving 1, 2, and 3 standard deviations away from the center in a normal distribution? (68–95–99.7 rule)
In other words, standard deviation contours can be displayed based on the standard deviation, as in the figure below. And these contours become indicators of “contextual” distance.
Figure 4. A contour that represents the distance from the mean in standard deviation units of 68, 95, and 99.7%
And by reducing the ellipsoidal shape in (b) of figure 4 to a unit circle as in (a) of figure 4, we can normalize the standard deviation that represents the “context” of the data. Let’s take a look at the transformation of the vector space using new axes corresponding to standard deviations 1, 2, 3, etc. as shown in figure 5 below.
Figure 5. Representation of the "context" of the data and transformation of the data (vector) space to "normalize" the "context"
This process is performed in the applet at the top of this post. Let’s look at the left of Figure 6. When considering the “context” of the given data, we should judge that the yellow points are farther away than the orange points. This is a complicated task as the Euclidean distance must be calculated while considering the “context”. However, if we normalize the “context” as in the right of Figure 6, the distance between the yellow points is already considered as farther away by simply calculating the Euclidean distance. This is because the original data (vector) space was transformed while taking into account the “context” of the given data in the process of “normalizing” the “context”.
Figure 6. The Euclidean distance measured after "normalizing" the "context" already becomes a distance that takes into account the "context".
Investigating the “context” through the distribution of the given data and normalizing it before calculating the Euclidean distance is the Mahalanobis distance.
$d_M = \sqrt{(\vec x-\vec y)\Sigma^{-1}(\vec x-\vec y)^T} % Equation (8)$
The transformation of the vector space can be represented by a matrix. Specifically, the matrix that represents the “context” of the data is related to the covariance matrix, and the matrix that rotates it back is related to the inverse matrix of the covariance matrix. From now on, let’s try to understand how to grasp the “context” of the data mathematically. Also, let’s examine how to perform “normalization” of the “context” in more detail.
The Meaning of the Covariance Matrix and its Inverse Matrix
Basic Understanding of iid Gaussian Distribution Samples
Before understanding the structure of the data, we first need to understand the properties of iid (independent and identically distributed) normal distribution samples. Although the terminology may seem difficult, there is nothing difficult once we look at it carefully. iid is one of the simplest methodologies for extracting random data samples.
To explain iid, let’s break it down into the following assumptions:
• The extracted data is independently extracted.
• The extracted data is extracted from the same probability distribution.
Furthermore, assuming that the probability distribution extracted here is a normal distribution, the extracted samples can be expressed as “independent and identically distributed normal random variables.”
This time, let’s stack multiple iid normal random variables $z_1, \cdots, z_d$ side by side as $Z\in\mathbb{R}^{n\times d}$. In particular, for convenience of calculation, assume a standard normal distribution.
$Z =\begin{bmatrix} | & | & & |\\ z_1 & z_2 & \cdots & z_d\\ | & | & & |\end{bmatrix} % Equation (9)$ $\text{where } z_1, z_2, \cdots, z_d \text{ are i.i.d. normal random variables with mean 0 and variance 1}\notag$
As we have extracted samples from a standard normal distribution, we can confirm the following. Since the mean of the extracted distribution is 0,
$\mathbb{E}[z_i]=0 \text{ for } i = 1, 2, \cdots, d % Equation (10)$
Moreover, let’s also consider the following given that the variance of the extracted distribution is 1.
$\mathbb{E}\left[Z^TZ\right] = \mathbb{E}\left [\begin{bmatrix} z_1^T z_1 & z_1^T z_2 & \cdots & z_1^Tz_d \\ z_2^T z_1 & z_2^T z_2 & \cdots & z_2^T z_d \\ \vdots & \vdots & \ddots & \vdots \\ z_d^T z_1 & z_d^T z_2 & \cdots & z_d^Tz_d \end{bmatrix}\right ] % 식 (11)$
Here, for $i=1,2,\cdots, d$, $\mathbb{E}\left[z_i^T z_i\right]$ is equal to the sum of $n$ variances of 1, so $\mathbb{E}\left[z_i^T z_i\right]=n$. Furthermore, since $z_i$ is extracted independently, for different $i$ and $j$, $\mathbb E \left[z_i^T z_j \right]=0$.
Therefore, equation (11) can be represented as
$\text{Equation (11)} \Rightarrow \begin{bmatrix} n & 0 & \cdots & 0 \\ 0 & n & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & n \end{bmatrix} = n I$
Here, $I$ is a unit matrix of dimensions $d \times d$.
Another way to understand the given data
Suppose that 1,000 aliens living on Mars were randomly selected and their height and weight were measured. Amazingly, the average height was 10cm and the average weight was 8kg. Suppose that the data is arranged in a table, which roughly looks like the following.
Figure 8. Table summarizing the height and weight of aliens on Mars (rounding up to the 4th alien)
The height and weight data of 1,000 aliens can be found here.
Let’s call the data that arranges the height and weight $\mathcal D$. Also, if the number of aliens sampled is denoted as $n$, and the number of features such as height and weight is represented as $d$, then $\mathcal D$ can also be viewed as the following matrix.
$\mathcal D\in\mathbb{R}^{n\times d}$
Although the data used this time was the height and weight of random 1000 aliens, it is possible to examine the distribution of any data. In order to understand the data distribution from a “new” perspective, let’s move all feature-wise mean values of the dataset to zero. Then, let’s view the new data, for which feature-wise mean values are zero, as data $X$.
If we plot the distributions of $\mathcal D$ and $X$, it is shown as below.
Figure 9. Distribution of height and weight data of aliens on Mars
Now let’s try to understand the data $X$ as a result of linear transformation of raw data $Z$. Here, the reason why the linear transformation matrix $R$ is attached to the right of $Z$ is because we can see the basic direction of the vector as a row vector, as shown in equation (5).
$X = ZR % Equation (14)$ $\text{where }Z \in \mathbb{R}^{n\times d} \text{ and } R \in \mathbb{R}^{d\times d}\notag$
Let’s assume that all columns of $Z$ are datasets extracted from the standard normal distribution of iid (independent and identically distributed).
Figure 10. Understand the given data as $X$ modified from raw data $Z$ linear transformed.
From now on, let’s investigate the similarity between features. By investigating the similarity between features, we can understand the “context” or structural form of the data. That’s because, for example, if feature 1 and feature 2 are very similar, it means that they are highly correlated with each other. To do this, let’s calculate $X^TX$. $X^TX$ will have dimensions of $d \times d$, and it represents the inner product between features. If we calculate $XX^T$, we can expect that this will indicate the similarity between the data. Let’s see the process of calculating $X^TX$ in the figure below.
Figure 11. The process of calculating how similar each data feature is in order to compute the covariance matrix.
Here, using Equation (14) again, we have:
$X^TX = (ZR)^TZR = R^TZ^TZR = R^T(Z^TZ)R % Equation (15)$
Here, according to Equation (12),
$X^TX \approx R^T(nI)R = nR^TR % Equation (16)$
is established. Here, we used “$\approx$” because in actual data, the exact value of the expected value may not come out. And we can confirm the following fact:
$R^TR \approx \frac{1}{n}X^TX % Equation (17)$
What does equation (17) mean in the end? Equation (17) is a way of obtaining the “context” of the data of $X$ or the structural form of the data. This is almost identical to $R^TR$ for the linear transformation $R$ to transform the raw form $Z$ into the given data $X$. And the matrix that expresses the structural form of the equation (17) is called the covariance matrix. Let’s use $\Sigma$ to represent the covariance matrix here.
$\Sigma = \frac{1}{n}X^TX % 식 (18)$
Note that there is also a way to divide by $n-1$ instead of $n$. The resulting covariance matrix obtained by dividing by $n-1$ instead of $n$ is called the sample covariance matrix. The covariance matrix is a useful way to describe the overall structure of the entire dataset and is especially closely related to multivariate normal distribution. If a dataset with two features follows a bivariate normal distribution, as in Figure 12, it can be said to follow one of the three major patterns below.
Figure 12. The three most representative forms of bivariate normal distributions.
Each element of the covariance matrix represents the variance or covariance of each feature. In other words, in the case of two features as in Figure 12, it represents how much data is scattered in the x-axis and y-axis for each feature, as well as how much variation is together between the first and second features.
Figure 13. What each element of the covariance matrix represents.
Inverse matrix and normalization of context
If the given arbitrary data is denoted as $x$ and its primitive form is denoted as $z$, then according to Equation (14), it can be seen that it is possible to restore the “context” of the given data to the form of primitive data by performing the following:
$z=xR^{-1}$
Here, the linear transformation using the inverse matrix is a method of restoring the vector space transformed by the given linear transformation $R$ to its original form. That is, if the process of changing from left to right in Figure 10 is the transformation performed by the original linear transformation $R$, the inverse transformation $R^{-1}$ can be seen as the transformation from right to left in Figure 10.
Figure 14. Linear transformation represented by matrix R and its inverse transformation.
Using Equation (7), we can calculate the distance $d_z$ between the origin and the primitive data vector space as follows:
$d_z=\sqrt{zz^T}=\sqrt{(xR^{-1})(xR^{-1})^T}$ $=\sqrt{xR^{-1}(R^{-1})^Tx^T}=\sqrt{x(R^TR)^{-1}x^T}=\sqrt{x\Sigma^{-1}x^T}$
Here, $\Sigma$ is the covariance matrix of the entire given dataset.
If we perform the same process as above for the distance between arbitrary vectors $x$ and $y$, we can modify the equation as follows, and this is the same as the Mahalanobis distance mentioned earlier:
$\Rightarrow \sqrt{(x-y)\Sigma^{-1}(x-y)^T}$
Contour lines and Principal Axes: Eigenvalues, Eigenvectors
※ The last chapter is somewhat advanced, and it is not necessary to understand it to understand the meaning of Mahalanobis.
※ To better understand the following content, it is recommended to understand the following:
Now let’s add the standard deviation and “contour lines” to understand the “context” of the data, as introduced in Figures 3 and 4. Talking about “contour lines” is one of the most important cores in understanding Mahalanobis distance.
First, let’s take another look at Figure 12. Figure 12 shows three representative forms of bivariate normal distributions that can be found. However, are these three shapes the only possible shapes for the distribution? Probably not. If we express the shape of the distribution with the two factors being how much it has rotated and how much it has been stretched, we can see that there will be countless shapes of the distribution. In other words, any distribution that can be represented by a multivariate normal distribution can be obtained by stretching and rotating a standard normal distribution.
The method of expressing how much the given linear transformation has rotated and how much it has been stretched is called eigenvalue decomposition. The amount of rotation will indicate the direction of the new axis shown on the right in Figure 5, and the amount of stretching will indicate the length of one scale on the new axes. In addition, as discussed in the article on eigen decomposition, the rotation direction is represented by eigenvectors and the amount of stretching is represented by eigenvalues.
Let’s try to eigen-decompose the covariance matrix as follows:
$\Sigma = Q\Lambda Q^{-1}=Q\Lambda Q^T$
Here, since the covariance matrix is always a symmetric matrix, we can replace $Q^{-1}$ with $Q^T$.
Here, $Q$ and $\Lambda$ are matrices with eigenvectors and eigenvalues, respectively.
For example, if we eigen-decompose the covariance matrix of the first image in Figure 12, we can get the following result:
$\begin{bmatrix}1 & 0.5\\0.5 & 1.5\end{bmatrix}=\begin{bmatrix}-0.8507 & 0.5257 \\ 0.5257 & 0.8507\end{bmatrix}\begin{bmatrix}0.6910 & 0 \\ 0 & 1.8090\end{bmatrix}\begin{bmatrix}-0.8507 & 0.5257 \\ 0.5257 & 0.8507\end{bmatrix}^T$
And each column of $Q$ shows how much the standard normal distribution has been rotated, or more precisely, indicates the direction of the principal components (PCs). In addition, the diagonal elements of $\Lambda$ show how much the distribution has been stretched in each principal component direction. Refer to Figure 15 to understand this more visually.
Figure 15. The eigenvalue decomposition of the covariance matrix allows us to represent how much the standard normal distribution has been stretched and rotated as a vector. Here, $\sigma_1$ and $\sigma_2$ represent how much PC1 and PC2 have been stretched, respectively.
To explain this result again, it is a more mathematical representation of the content from Figure 3 to Figure 5. The principal component directions of $Q$ are the two most representative directions for calculating standard deviation, and the diagonal elements of $\Lambda$ indicate the standard deviation in the principal component direction, in other words.
Therefore, if we understand the Mahalanobis distance based on the data on the principal axis (or assume that we project the data onto the principal axis), we can consider the distance as a normalized distance by rotating the principal axis back to the original xy axis and dividing by the standard deviation value obtained from $\Lambda$. | 4,453 | 18,208 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.53125 | 5 | CC-MAIN-2023-50 | latest | en | 0.890394 |
https://www.aqua-calc.com/one-to-one/density/pound-per-metric-teaspoon/stone-per-us-tablespoon/1 | 1,603,908,919,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107900200.97/warc/CC-MAIN-20201028162226-20201028192226-00236.warc.gz | 604,168,459 | 8,963 | # 1 pound per metric teaspoon in stones per US tablespoon
## pounds/metric teaspoon to stone/US tablespoon unit converter
1 pound per metric teaspoon [lb/metric tsp] = 0.21 stone per US tablespoon [st/tbsp]
### pounds per metric teaspoon to stones per US tablespoon density conversion cards
• 1
through
25
pounds per metric teaspoon
• 1 lb/metric tsp to st/tbsp = 0.21 st/tbsp
• 2 lb/metric tsp to st/tbsp = 0.42 st/tbsp
• 3 lb/metric tsp to st/tbsp = 0.63 st/tbsp
• 4 lb/metric tsp to st/tbsp = 0.84 st/tbsp
• 5 lb/metric tsp to st/tbsp = 1.06 st/tbsp
• 6 lb/metric tsp to st/tbsp = 1.27 st/tbsp
• 7 lb/metric tsp to st/tbsp = 1.48 st/tbsp
• 8 lb/metric tsp to st/tbsp = 1.69 st/tbsp
• 9 lb/metric tsp to st/tbsp = 1.9 st/tbsp
• 10 lb/metric tsp to st/tbsp = 2.11 st/tbsp
• 11 lb/metric tsp to st/tbsp = 2.32 st/tbsp
• 12 lb/metric tsp to st/tbsp = 2.53 st/tbsp
• 13 lb/metric tsp to st/tbsp = 2.75 st/tbsp
• 14 lb/metric tsp to st/tbsp = 2.96 st/tbsp
• 15 lb/metric tsp to st/tbsp = 3.17 st/tbsp
• 16 lb/metric tsp to st/tbsp = 3.38 st/tbsp
• 17 lb/metric tsp to st/tbsp = 3.59 st/tbsp
• 18 lb/metric tsp to st/tbsp = 3.8 st/tbsp
• 19 lb/metric tsp to st/tbsp = 4.01 st/tbsp
• 20 lb/metric tsp to st/tbsp = 4.22 st/tbsp
• 21 lb/metric tsp to st/tbsp = 4.44 st/tbsp
• 22 lb/metric tsp to st/tbsp = 4.65 st/tbsp
• 23 lb/metric tsp to st/tbsp = 4.86 st/tbsp
• 24 lb/metric tsp to st/tbsp = 5.07 st/tbsp
• 25 lb/metric tsp to st/tbsp = 5.28 st/tbsp
• 26
through
50
pounds per metric teaspoon
• 26 lb/metric tsp to st/tbsp = 5.49 st/tbsp
• 27 lb/metric tsp to st/tbsp = 5.7 st/tbsp
• 28 lb/metric tsp to st/tbsp = 5.91 st/tbsp
• 29 lb/metric tsp to st/tbsp = 6.13 st/tbsp
• 30 lb/metric tsp to st/tbsp = 6.34 st/tbsp
• 31 lb/metric tsp to st/tbsp = 6.55 st/tbsp
• 32 lb/metric tsp to st/tbsp = 6.76 st/tbsp
• 33 lb/metric tsp to st/tbsp = 6.97 st/tbsp
• 34 lb/metric tsp to st/tbsp = 7.18 st/tbsp
• 35 lb/metric tsp to st/tbsp = 7.39 st/tbsp
• 36 lb/metric tsp to st/tbsp = 7.6 st/tbsp
• 37 lb/metric tsp to st/tbsp = 7.82 st/tbsp
• 38 lb/metric tsp to st/tbsp = 8.03 st/tbsp
• 39 lb/metric tsp to st/tbsp = 8.24 st/tbsp
• 40 lb/metric tsp to st/tbsp = 8.45 st/tbsp
• 41 lb/metric tsp to st/tbsp = 8.66 st/tbsp
• 42 lb/metric tsp to st/tbsp = 8.87 st/tbsp
• 43 lb/metric tsp to st/tbsp = 9.08 st/tbsp
• 44 lb/metric tsp to st/tbsp = 9.29 st/tbsp
• 45 lb/metric tsp to st/tbsp = 9.51 st/tbsp
• 46 lb/metric tsp to st/tbsp = 9.72 st/tbsp
• 47 lb/metric tsp to st/tbsp = 9.93 st/tbsp
• 48 lb/metric tsp to st/tbsp = 10.14 st/tbsp
• 49 lb/metric tsp to st/tbsp = 10.35 st/tbsp
• 50 lb/metric tsp to st/tbsp = 10.56 st/tbsp
• 51
through
75
pounds per metric teaspoon
• 51 lb/metric tsp to st/tbsp = 10.77 st/tbsp
• 52 lb/metric tsp to st/tbsp = 10.98 st/tbsp
• 53 lb/metric tsp to st/tbsp = 11.2 st/tbsp
• 54 lb/metric tsp to st/tbsp = 11.41 st/tbsp
• 55 lb/metric tsp to st/tbsp = 11.62 st/tbsp
• 56 lb/metric tsp to st/tbsp = 11.83 st/tbsp
• 57 lb/metric tsp to st/tbsp = 12.04 st/tbsp
• 58 lb/metric tsp to st/tbsp = 12.25 st/tbsp
• 59 lb/metric tsp to st/tbsp = 12.46 st/tbsp
• 60 lb/metric tsp to st/tbsp = 12.67 st/tbsp
• 61 lb/metric tsp to st/tbsp = 12.89 st/tbsp
• 62 lb/metric tsp to st/tbsp = 13.1 st/tbsp
• 63 lb/metric tsp to st/tbsp = 13.31 st/tbsp
• 64 lb/metric tsp to st/tbsp = 13.52 st/tbsp
• 65 lb/metric tsp to st/tbsp = 13.73 st/tbsp
• 66 lb/metric tsp to st/tbsp = 13.94 st/tbsp
• 67 lb/metric tsp to st/tbsp = 14.15 st/tbsp
• 68 lb/metric tsp to st/tbsp = 14.36 st/tbsp
• 69 lb/metric tsp to st/tbsp = 14.58 st/tbsp
• 70 lb/metric tsp to st/tbsp = 14.79 st/tbsp
• 71 lb/metric tsp to st/tbsp = 15 st/tbsp
• 72 lb/metric tsp to st/tbsp = 15.21 st/tbsp
• 73 lb/metric tsp to st/tbsp = 15.42 st/tbsp
• 74 lb/metric tsp to st/tbsp = 15.63 st/tbsp
• 75 lb/metric tsp to st/tbsp = 15.84 st/tbsp
• 76
through
100
pounds per metric teaspoon
• 76 lb/metric tsp to st/tbsp = 16.05 st/tbsp
• 77 lb/metric tsp to st/tbsp = 16.27 st/tbsp
• 78 lb/metric tsp to st/tbsp = 16.48 st/tbsp
• 79 lb/metric tsp to st/tbsp = 16.69 st/tbsp
• 80 lb/metric tsp to st/tbsp = 16.9 st/tbsp
• 81 lb/metric tsp to st/tbsp = 17.11 st/tbsp
• 82 lb/metric tsp to st/tbsp = 17.32 st/tbsp
• 83 lb/metric tsp to st/tbsp = 17.53 st/tbsp
• 84 lb/metric tsp to st/tbsp = 17.74 st/tbsp
• 85 lb/metric tsp to st/tbsp = 17.96 st/tbsp
• 86 lb/metric tsp to st/tbsp = 18.17 st/tbsp
• 87 lb/metric tsp to st/tbsp = 18.38 st/tbsp
• 88 lb/metric tsp to st/tbsp = 18.59 st/tbsp
• 89 lb/metric tsp to st/tbsp = 18.8 st/tbsp
• 90 lb/metric tsp to st/tbsp = 19.01 st/tbsp
• 91 lb/metric tsp to st/tbsp = 19.22 st/tbsp
• 92 lb/metric tsp to st/tbsp = 19.43 st/tbsp
• 93 lb/metric tsp to st/tbsp = 19.65 st/tbsp
• 94 lb/metric tsp to st/tbsp = 19.86 st/tbsp
• 95 lb/metric tsp to st/tbsp = 20.07 st/tbsp
• 96 lb/metric tsp to st/tbsp = 20.28 st/tbsp
• 97 lb/metric tsp to st/tbsp = 20.49 st/tbsp
• 98 lb/metric tsp to st/tbsp = 20.7 st/tbsp
• 99 lb/metric tsp to st/tbsp = 20.91 st/tbsp
• 100 lb/metric tsp to st/tbsp = 21.12 st/tbsp
• st/tbsp stands for st/US tbsp
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Calculate volume of a hollow cylinder and its surface area | 2,535 | 6,610 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2020-45 | latest | en | 0.539063 |
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plz share quiz 4 here 6-7-12
dear fellows! plz share your today's quiz here.
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Replies to This Discussion
ya sure.. i will share the best one .. solution here.. soon .... of cs502 quiz 4
thanks ..
plz do remember me in ur prayers i will give u 100% solution
umair sid
thanks i pray and waiting
hera all here is the most easy quiz of the cs502 but remember THERE ARE 3 Question which are asked again in that quiz,..
thanks... remember me in ur prayers...
uamir sid
Attachments:
Quiz no# 4 06-07-2012 solved by umair sid 100%
Back edge is
(u,v) where v is an ancestor of u in the tree page # 128
What algorithm technique is used in the implementation of kruskal solution for the MST?
Greedy Technique page #142
in drsigne G=(V,E) ;G has cycle if and only if
The DFS forest has back edge page # 131
Cross edge is :
(u,v) where u and v are not ancestor or descendent of one another page #129
Forword edge is :
(u,v) where v ia a proper decendent of u in the tree. Page # 129
A digraph is strongly connected under what condition ?
A diagraph is strongly connected if for every pair of vertex u,v e v,u can reach v and vice versa. Page #135
You have an adjective list for G, what is the time complexity to computer graph transpose G^T.?
(V + E ) PAGE # 138
Given an adjacency list for G, it is possible to compute G T in Θ(V + E) time.
What is the time complexity to extract a vertex from the priority queue in prim’s algorithm ?
O Log (v) page #152
It takes O(log V) to extract a vertex from the priority queue.
There is relationship between number of back edges and number of cycles in DFS
There is no relationship between back edges and number of cycles
Which is true statement in the following
Kruskal's algorithm (choose best non-cycle edge) is better than Prim's (choose best Tree edge) when the graph has relatively few edges.
Dijkstra’s algorithm :
Has greedy approach to compute single source shortest paths to all other vertices page 154
What is the time complexity to extract a vertex from the priority queue in Prim’s algorithm?
O (log V)
Which is true statement
Breadth first search is shortest path algorithm that works on un-weighted graphs
Depth first search is shortest path algorithm that works on un-weighted graphs.
Both of above are true.
Kruskal's algorithm (choose best non-cycle edge) is better than Prim's (choose best tree edge) when the graph has relatively few edges.
True
thanxxxxxxxxxxx alot..........
pleasure rose... do remember me inur prayers plz thx
dears here is the modified quiz of Umair, plz check it for correctness and comment.
CS502 Quiz no# 4 06-07-2012 Solved by Umair sid 100%
1. Back edge is (u,v) where v is an ancestor of u in the tree page # 128
2. What algorithm technique is used in the implementation of kruskal solution for the MST? Greedy Technique page #142
3. in designe G=(V,E) ;G has cycle if and only if The DFS forest has back edge page # 131
4. Cross edge is : (u,v) where u and v are not ancestor or descendent of one another page #129
5. Forword edge is :(u,v) where v is a proper decendent of u in the tree. Page # 129
6. A digraph is strongly connected if for every pair of vertex u, v Є V, u can reach v and vice versa. Page #135
7. You have an adjacent list for G, what is the time complexity to compute graph transpose G^T.? Θ(V + E ) PAGE # 138
Given an adjacency list for G, it is possible to compute G T in Θ(V + E) time.
1. What is the time complexity to extract a vertex from the priority queue in prim’s algorithm ? O Log (v) page #152
It takes O(log V) to extract a vertex from the priority queue.
1. There is relationship between number of back edges and number of cycles in DFS
There is no relationship between back edges and number of cycles
1. Which is true statement in the following
Kruskal's algorithm (choose best non-cycle edge) is better than Prim's (choose best Tree edge) when the graph has relatively few edges.
Overall time for Kruskal is
Θ(E log E) = Θ(E log V) if the graph is sparse. P-149
True
1. Dijkstra’s algorithm:
Has greedy approach to compute single source shortest paths to all other vertices page 154
1. What is the time complexity to extract a vertex from the priority queue in Prim’s algorithm?
O (log V)
1. Which is true statement
Breadth first search is shortest path algorithm that works on un-weighted graphs
Depth first search is shortest path algorithm that works on un-weighted graphs.
Both of above are true.
thanks a lot
shukar hay zeeshan ap k face pr bhi smile aayi hay
thanks umair
thanks wish u good luck!
thanks
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This is a member-supported website. Your contribution is greatly appreciated! | 1,478 | 5,744 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2020-45 | longest | en | 0.821891 |
http://www.mathcs.emory.edu/~dzb/advice.html | 1,548,063,392,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583771929.47/warc/CC-MAIN-20190121090642-20190121112642-00455.warc.gz | 346,768,799 | 5,534 | Below is a collection of advice that I have written to various Emory and Wisconsin graduate students.
A summary of the advice is the following: learn Algebraic Geometry and Algebraic Number Theory early and repeatedly, read Silverman's AEC I, and half of AEC II, and read the two sets of notes by Poonen (Qpoints and Curves). Qing Lui's book and Ravi Vakil's notes are great, either as an alternative to Hartshorne's book or as a supplement. Read other topics too (with suggestions below).
Your main first priority is to learn algebraic geometry very well and the core material from algebraic number theory. Second is to begin learning more advanced material. (Zeroth is to pass your qualifying exams.) Advice for what someone in NT or algebra (but not analytic number theory) needs to know from algebraic geometry.
My own students: after this I will give you a starter project (something that I have a good idea of how to do but haven't actually tried to do), with the expectation that you will solve it and submit it for publication within a year. As this project nears its end, I will suggest other things for you to read to get a sense of what you are interested in, and will help you form a long term research plan and find other projects to work on.
## Algebraic geometry.
The following is the core material, which typically takes a strong student a (calendar) year to learn well. I personally have needed to carefully learn the rest of Hartshorne for various projects, but the following is a good first pass.
Hart II.1-8, III.1-5,9, and IV.1-3. (Also, know the statement of Serre duality from III.6.)
This is easily a (calendar) year's work of material to learn. Also, its pretty difficult to learn this by just reading Hartshorne. (I had a large department's worth of people to ask questions to, and read lots of other sources too, e.g., "The geometry of schemes" and Eisenbud's commutative algebra book, as well as William Stein's latex'd notes from Hartshorne's 2000 algebraic geometry course.)
There of course is a small bit of healthy disagreement. If I were writing the syllabus for an AG qual, the above would be it. Suresh Venapally suggested a slightly shorter version (Hart II.1-6, III.1-5, and IV.1-2), but with more commutative algebra.
Its also good to know a little bit of chapter 5 (e.g. V.1-2, so being familiar with the intersection pairing on a surface, what a blow up is, and the story of the 27 lines on a cubic surface).
You should of course solicit other opinions. But to support my opinion, 10/13 of Parimala's papers on the arxiv have the word "scheme" in them. (I didn't search the other 3 for "variety" or other geometric terms).
## Algebraic Number Theory.
I consider the first 2 1/2 chapters of Neukirch to contain most of the core material. Neukirch has great exposition, but not too many problems, so I would supplement this with problems from Marcus's Number Fields book (this one has many more problems, especially computational ones). Keith Conrad has quite a few good notes. See also this MO question.
Its also important to know the statements of class field theory and how to apply them in various situations. (The proofs, while beautiful, aren't what I'd consider core background.) On the other hand, you do need to know Galois cohomology, adeles, statements of proofs, etc.
## Emory's qualifying exams
You must take the algebra and analysis exams, and one more. (If you can, take these before arriving at Emory.) If you are hoping to work in algebra, I recommend taking the algebraic geometry exam. There will not always be a course in algebraic geometry; if not, take a year long reading course.
## After this.
Below is an email I sent early on to a Wisconsin graduate student, on what to do to complement learning algebraic geometry.
Here is my running list of advice, which, for now, is geared more for someone who has already been through Hartshorne and Silverman I.
1. I would pick something easy, like Silverman II or one of Serre's old papers (GAGA, FAC)
2. and also pick something hard (e.g., Mazur's Eisenstein paper, or the proof of one of the `big three') to read.
Here are some more detailed suggestions.
A proof of any of the big three is worthwhile to learn:
• Proof of FLT
• Proof of Faltings theorem
• Proof of Weil conjectures
(It is important with these to find a nice balance between learning background and technical details and plowing forward to get a big picture of what is going on and how things fit together. Each of these have lots of `moving parts', and its good to first get a sense of what those parts are before learning each part in isolation. So for instance, it is easy to fall into the trap of spending 6 months just reading about the basics of etale cohomology, without ever reading about any interesting application of it or understanding an overview of the Weil conjectures. OTOH, you should spend some time doing basic exercises about etale morphisms and sites and such.)
Silverman II contains a nice survey of topics, and is lighter reading than the above. Learn about
• Neron models and minimal models of curves,
• CFT of imaginary quadratic etc.
• Tate curve
• There's more stuff too (e.g., modular forms) that I haven't read as carefully.
Papers
• Serre's GAGA and FAC are classics and will really solidify your knowledge.
• Mazur's modular curves papers (Eisenstein ideal, etc). One of Jordan's three favorite papers.
• Another of his favorites is the article mentioned by Deligne in that link.
• Serre-Tate.
If you're looking for more geometric things with less NT content
• Beauville's book "Complex Algebraic Surfaces"
• Harris and Morrison (this is worth spending a lot of time on)
• Deligne and Mumford's Irreducibility of the Moduli space of curves paper | 1,342 | 5,777 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2019-04 | latest | en | 0.967389 |
https://ciannamare.it/python-math-library-absolute-value.html | 1,619,166,432,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039568689.89/warc/CC-MAIN-20210423070953-20210423100953-00293.warc.gz | 273,637,893 | 14,250 | • Is cloralen a disinfectant
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Python is a basic calculator out of the box. Here we consider the most basic mathematical operations: addition, subtraction, multiplication, division and exponenetiation. we use the func:print to get the output.
# Python math library absolute value
• ...the absolut… - examples: Compute the absolute value of every element in an array, Compute the absolute absolute value of each element in `x`. For complex input, ``a + ib``, the absolute value is :math IDE that uses deep learning to provide you with intelligent code completions in Python and...
• The fabs() method in Python number returns the absolute value of x. This method of Python Number has been specified in the math library of Python 2 and Python 3. Thus, Python fabs function refers to one of the Python Math function that is known to return absolute positive value of a specific expression or number.
• The standard math library that comes with Python is quite powerful and useful. Learn how to use it to perform basic mathematical ... This video covers the basic math operators built into Python and the math library, including the modulo operation and rounding ...
• 9.2. math — Mathematical functions¶. This module is always available. Return the natural logarithm of the absolute value of the Gamma function at x. CPython implementation detail: The math module consists mostly of thin wrappers around the platform C math library functions.
• Math Function Summary • The math functions are there when you need them • Unless we are solving complex trigonometry problems or statistics problems - pretty much all we use is the square root >>> import math >>> print math.sqrt(25.0) 5.0
## Southland mall walking hours
• Abs() calculates the absolute value of a given number. Python libraries can cut your development time and reduce your frustration with coding. Familiarize yourself with the library's built-in functions, math modules, and input and output modules.
• Absolute value of a number is the value without considering ... The abs() function of Python's standard library returns the absolute value of the given number.
• lgamma () function is available and compatible with python 3.2 and above versions. This function is a part of python standard math library. Return Value of lgamma () Function in Python lgamma () function returns the natural logarithm of the absolute value of the Gamma function for the given input (x – parameter).
• Python is a basic calculator out of the box. Here we consider the most basic mathematical operations: addition, subtraction, multiplication, division and exponenetiation. we use the func:print to get the output.
• Returns the absolute value of the number. Python's math module also provides some standard mathematical functions and constants. The width is the minimum number of characters reserved for a value and precision refers to the number of characters after the decimal point.
• absolute_value(3) Since we wrote the code in Sublime Text (and saved it as a “abs_val.py” document for instance), we must verify the the outcome using the Terminal. We travel in our terminal to find our “abs_val.py” document.
• Python program uses a for loop and range() function to iterate loop till entered number and calculate the sum, using sum = sum + current number formula. In this article, we are going to write a Python code to calculate the sum and average of the positive numbers starting from 1 to the given number (n)...
• Python Math module provides access to the mathematical functions defined by the C standard. So, we can do many complex mathematical operations with the help of the Python Math functions. fabs() function is used to get the absolute value of the given number. See the example code below.
• NumPy is an extension package in the Python environment that is fundamental for scientific calculation. This is because it adds to the tools that are already available, the typical features of N-dimensional arrays, element-by-element operations, a massive number of mathematical operations in linear algebra, and the ability to integrate and recall source code written in C, C++, and FORTRAN. ...
• Python for maths - check how to solve your mathematics problem with the help of Python math libraries and functions. I am sure your answer will be NO! Don't be shocked, now it is possible to solve all your mathematics problems with the help of Python technology.
• In python, NumPy library has a Linear Algebra module, which has a method named norm(), that takes two arguments to function, first-one being the input vector v, whose norm to be calculated and the second one is the declaration of the norm (i.e. 1 for L1, 2 for L2 and inf for vector max).
• @29834829 https://leetcode.com/problems/maximum-of-absolute-value-expression/discuss/340075/c++-beats-100-(both-time-and-memory)-with-algorithm-and-image.
• absolute value. Euclidean norm. determinant. Numpy is a powerful array programming library, which in python can be interpreted as a domain specific language (DSL). Often this is represented by double-bars to avoid ambiguity with the absolute value notation, but sometimes you may see it...
• It is an overloaded method. It returns the absolute value of an argument. The argument can be of any type such as int, float, double, long, and short. The signature of the method is: public static datatype abs (datatype x) public static datatype abs (datatype x) Where x is an argument whose absolute value is to be determined.
• Mathematical optimization is very … mathematical. If you want performance, it really pays to read the books: Convex Optimization by Boyd and Vandenberghe (pdf available free online). Numerical Optimization, by Nocedal and Wright. Detailed reference on gradient descent methods.
• Learn about math module in Python. It contains scientific mathematics functions such as log, log10, exp, pow etc. Some of the most popular mathematical functions are defined in the math module. These include trigonometric functions, representation functions, logarithmic functions, angle...
• Python abs() is a built-in function available with the standard library of python. It returns the absolute value for the given number. Absolute value of a number is the value without considering its sign. The number can be integer, floating point number or complex number. If the given number is complex...
• lgamma () function is available and compatible with python 3.2 and above versions. This function is a part of python standard math library. Return Value of lgamma () Function in Python lgamma () function returns the natural logarithm of the absolute value of the Gamma function for the given input (x – parameter).
• The Mathematics module in the Python standard library has many features. The simplest use of Python for math is as a calculator. To do this, start Python on the terminal and use the print function. The simple math is available without even activating the math module but beyond addition...
• Time package provides time.perf_counter and time.process_time. The difference here is that perf_counter returns absolute value, which includes time when your Python program process is not running, therefore it might be impacted by machine load.
The absolute value of a real number x is x if x is positive, -x if x is negative. Prototypes for abs, labs and llabs are in stdlib.h; imaxabs is declared in inttypes.h; the fabs functions are declared in math.h; the cabs functions are declared in complex.h.
Python's standard library provides a module namely math for math related functions that wo with all number types except for complex numbers, In order to work with functions of math module, giving statement as follows as the top line of yor import math You need to first import it to your program...
The abs() function in C++ returns the absolute value of the argument. The abs function is identical to fabs() in C++. The function is defined in <cmath> header file.
a positive value with the magnitude of x: abs2(x) the squared magnitude of x: sign(x) indicates the sign of x, returning -1, 0, or +1: signbit(x) indicates whether the sign bit is on (true) or off (false) copysign(x,y) a value with the magnitude of x and the sign of y: flipsign(x,y) a value with the magnitude of x and the sign of x*y
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• Absolute Value in Python & Pandas! Check the Blog Post! Now, we will use Python to get the absolute values from both integers and floats.
3.19. Symbolic math in python. 3.20. Is your ice cream float bigger than mine. 4. Linear algebra. 2.2 Advanced mathematical operators. The primary library we will consider is mod:numpy, which If we provide a default value for an argument, then the argument is called a keyword argument, and it...
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Math skills transparency 34 naming and drawing alkanes | 2,600 | 11,708 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2021-17 | latest | en | 0.76861 |
https://uk.answers.yahoo.com/question/index?qid=20201013123707AAiBPOB | 1,611,641,960,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704798089.76/warc/CC-MAIN-20210126042704-20210126072704-00471.warc.gz | 617,532,497 | 22,798 | # Tax Bracket - best to earn less than next bracket?
Personal Allowance Up to £12,500 0 percent
Basic rate £12,501 to £50,000 20 percent
Higher rate £50,001 to £150,000 40 percent
Additional rate over £150,000 45 percent
Example. Would it make sense to earn £49k rather than £50k because a person on £49k would earn more after tax than being on £50k
Relevance
• Judy
Lv 7
3 months ago
No not at all. Only the amount or the cutoff is taxed at the higher rate.
• 3 months ago
When you get to the 40% tax bracket you keep 60%. If you don't want to do than then quit.
• 3 months ago
Doesn't work like that.
You earn 49k you pay 20% tax.
You earn 51k. You pay 20% tax on everything up to 50k. And 40% on the 1k above that.
So, even with paying 40% tax on a small part of your income, you would still earn more than someone earning 49%.
Like others have said, you have misunderstood how the tax brackets work, and assume you pay the 40% on all your income. You only pay higher rates on the part of your income that falls into that tax bracket.
So let's say you earned 160k a year.
You pay 20% on earnings up to 50k
You will pay 40% on earnings from 50.1k to 150k
And then get hit with 45% tax on the last 10k of your salary.
Hope that makes sense!
• User
Lv 7
3 months ago
Well...what you're concerned about here is "take home pay".
BUT I *think* you might be looking at the chart wrong.
Probably the MEANING is as follows:
first 12,500 - no taxes
amount between 12,500 and 50,000 - 20% tax
amount between 50,000 and 150,000 - 40% tax
etc.
SO
for example
a person making 50,000 would pay
(50,000 - 12,500) x 20% = 7,500
take home = 42,500
while a person making 51,000 would pay
(50,000 - 12,500) x 20% + (51,000 - 50,000) x 40% = 7,900
take home = 43,100
• 3 months ago
No.
You can't fall behind by making more money. Only the amount above the bracket end point is taxed at the higher rate.
For example:
You make £52,000
1) The first £12,500 is at 0%
2) The next £37,500 is at 20% (£50,000 less £12,500)
3) Only the final £2,000 is taxed at 40% (£52,000 less £50,000)
• Anonymous
3 months ago
You're misunderstanding how tax brackets work.
You only pay the higher percentage of tax on the amount you earn that is over the threshold for that bracket.
Meaning if you make 52k, you're only going to pay the higher tax rate on the 2k that's over the 50k cut off. You'll still pay the lower rate for the income that fits into the lower bracket.
The bigger your tax bill, the better off you are. | 767 | 2,541 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2021-04 | latest | en | 0.959177 |
https://www.jiskha.com/questions/1379529/0-100-M-NaOH-in-the-burette-is-titrated-with-25-0-mL-0-120-M-CH3COOH-pKa-4-75 | 1,540,354,020,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583518753.75/warc/CC-MAIN-20181024021948-20181024043448-00116.warc.gz | 949,070,282 | 5,001 | # analytical chemistry
0.100 M NaOH (in the burette) is titrated with 25.0 mL 0.120 M CH3COOH (pKa = 4.75) in a conical flask. Determine the pH of the solution in the flask after 10 mL of the NaOH has been added.
1. 0
2. 0
3. 39
1. millimols CH3COOH = 25.0 x 0.12 = 3.0
millimols NaOH = 10 x 0.1 = 1
..CH3COOH + NaOH ==> CH3COONa + H2O
I...3.0......0........0..........0
C...-1.0....-1.0......+1.0.......
E....2.0......0.......1.0
Substitute the E line into the Henderson-Hasselbalch equation and solve for pH.
pH = pKa + log (base)/(acid)
pH = 4.75 + log (1/35)/(2/35)
1. 0
2. 0
posted by DrBob222
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More Similar Questions | 1,130 | 3,084 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2018-43 | latest | en | 0.742068 |
http://slideplayer.com/slide/4204160/ | 1,529,419,375,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267863043.35/warc/CC-MAIN-20180619134548-20180619154548-00031.warc.gz | 297,562,822 | 24,843 | # Nuclear Reactions, Transmutations, Fission and Fusion
## Presentation on theme: "Nuclear Reactions, Transmutations, Fission and Fusion"— Presentation transcript:
Nuclear Reactions, Transmutations, Fission and Fusion
Till now we have discussed only transmutations of one nuclei to another by emmiting radioactive particle that occur only naturally. Induced (artificial) transmutation This change of one element to another through the bombardment of a nucleus is known as artificial transmutation. Induced transmutation doesn’t mean it can not happen naturally – it means bombarment only example: production of nitrogen from carbon in atmosphere or artificially induced in the lab
● For the nuclear equation : A → C + D or A + B → C + D
● Alpha particle, neutrons, protons, and deuterons …. can be used to produce artificial nuclear reactions. ● The key to understanding these reactions and making predictions about the products of such reactions is being able to balance nuclear equations. ● For the nuclear equation : A → C + D or A + B → C + D ▪ nucleon and proton numbers must balance on each side of the equation. ▪ conservation of total energy (energy + mass) must be satisfied Energy released in nuclear reaction or decay is found the same way as binding energy: first find mass difference Δm = LHS – RHS in u and then E = Δm x (MeV)
Transmutations Examples
Energy released in a decay: A → C + D
spontaneous decay: M > m1 + m2 → binding energy of the decaying nucleus < binding energies of the product nuclei. The daughter is more stable. This is why radioactive decay happens with heavy elements lying to the right of maximum in the binding energy curve. Energy released is in the form of kinetic energy of the products. M > m1 + m2 , but total energy on the left = total energy on the right
a - decay Thorium – 228 decays by a – emission:
Mass of thorium-228 nucleus = u Mass of radium-224 nucleus + a-particle = u u = u Mass difference = u – u = u = 5.49 MeV What happens to this binding energy? It appears mostly as kinetic energy of a – particle. The radium nucleus also recoils slightly (and so momentum is conserved).
b - decay Aluminum – 29 decays by b – emission:
Mass of aluminum-29 nucleus = u Mass of silicon-29 nucleus + b-particle + antineutrino = = u u + 0 = u Mass difference = u – u = u = 3.68 MeV Again this becomes the kinetic energy of the decay products.
Energy released in a nuclear reaction/artificial transmutation
Nuclear reactions A + B → C + D can either 1. release energy if Δm = (mA + mB) – (mC + mD) > 0 The total amount of energy released will be E = Δmc2 in the form of kinetic energy of products. If there was initial kinetic energy, that will be added up to released energy. 2. or requires energy input Nitrogen-14 will decay only if energy is supplied to it – collision with fast moving α particle: u < u Δm = (mA + mB) – (mC + mD) < 0 Famous 1. Rutherford’s induced transmutation: bombarding nitrogen gas with alpha particles from bismuth‑214. α particle must have enough kinetic energy to make up for imbalance in masses, and to provide for kinetic energy of products. This energy is suplied by a particle accelerator used to accelerate the helium nucleus.
Fission ● Fission means splitting up a large nucleus (A > 200) into two smaller nuclei. ● the total BE would increase which means that the daughters are more stable than parent. ● The excess energy is released by the reaction.
● Bombarding the nucleus with neutrons can trigger a fission reaction.
● Spontaneous fission is very rare. Uranium is the largest nucleus found on Earth. Its isotopes will sometimes fission naturally. But half-life for U-235 is 7.04x108 years ● Bombarding the nucleus with neutrons can trigger a fission reaction. ● For example The strong forces that hold the nucleus together only act over a very short distance. When a uranium nucleus absorbs a neutron it knocks the nucleus out of shape. If the nucleus deforms enough, the electrostatic repulsion between the protons in each half becomes greater than the strong force. It then splits in two. The nuclei splits randomly. In the diagram, the fission fragments are shown as isotopes of Ba and Kr. This is just one of the many possible combinations. Fission of a uranium nucleus gives out about 200 MeV of energy.
Chain Reactions ● When the uranium nucleus splits, a number of neutrons are also ejected. ● If each ejected neutron causes another uranium nucleus to undergo fission, we get a chain reaction ● The number of fissions increases rapidly and a huge amount of energy is released. ● Uncontrolled chain reactions are used in nuclear bombs ● The energy they unleash is devastating. ● Nuclear power stations use the heat released in carefully controlled fission reactions to generate electricity. ● They use control rods to absorb some of the neutrons.
Fusion ● Fusion means joining up two small nuclei to form a bigger nucleus. ● When two small nuclei the product of fusion would have more BE per nucleon. ● The increases in binding energy per nucleon are much larger for fusion than for fission reactions, because the graph increases more steeply for light nuclei. ● So fusion gives out more energy per nucleon involved in the reaction than fission.
● Each second, in our Sun, more than 560 million tonnes of hydrogen fuse together to make helium. ● One series of reactions for this is shown here: Each small nucleus has a positive charge so they will repel each other. To make the nuclei come close enough for the strong force to pull them together, they must be thrown together with very igh velocity. For this to take place, the matter must either be heated to temperatures as high as the core of the sun (about 13 million Kelvin) or the particles must be thrown together in a particle accelerator)
● The energy released is radiated by the Sun at a rate of 3
● The energy released is radiated by the Sun at a rate of 3.90 x 1020 MW. ● This is the power output of a million million million large power stations! ● Not surprisingly scientists are keen to develop fusion as a source of power (fusion reactor). ● One possible reaction is the fusion of deuterium and tritium. ● These are isotopes of hydrogen
● Fusion has a number of advantages over fission:
● greater power output per kilogram, ● the raw materials are cheap and readily available, ● no radioactive elements are produced directly, ● irradiation by the neutrons leads to radioactivity in the reactor materials but these have relatively short half lives and only need to be stored safely for a short time. ● So why don't we use fusion in nuclear power stations? ● The JET (Joint European Torus) project was set up to carry out research into fusion power. ● It has yet to generate a self‑sustaining fusion reaction. ● The main problem is getting two nuclei close enough for long enough for them to fuse.
● At this temperature all matter exists as an ionised gas or plasma.
● Each small nucleus has a positive charge so they will repel each other. To make the nuclei come close enough for the strong force to pull them together, they must be thrown together with very igh velocity. For this to take place, the matter must either be heated to temperatures as high as the core of the sun (about 13 million Kelvin) or the particles must be thrown together in a particle accelerator) ● At this temperature all matter exists as an ionised gas or plasma. ● Problem: containment. What can you use to hold something this hot? ● JET (and Princeton) uses magnetic fields in a doughnutshaped chamber called a torus to keep the plasma away from the container walls. ● Unfortunately generating high temperatures and strong magnetic fields uses up more energy than the fusion reaction produces! ● The same problem is with accelerators, the path taken by Japan. ● We are still some years off a fusion power station.
Applying the binding energy curve – checking stability
For example consider the fission reaction Question: has the system become more stable? total binding energy of U-238 = 7.6×238 = 1800 MeV Sr-90 = 8.7×90 = 780 MeV Xe-146 = 8.2×146 = 1200 MeV The sum of the total binding energies of the fission nuclei is greater than the binding energy of the uranium-238 nucleus. Effectively the system has become more stable by losing energy. (KEneutron provided that energy)
Similarly for the fusion reaction
the total binding energy of the helium nucleus is greater than the sum of binding energies of the tritium and deuterium nuclei. So, again as for fission, the system has effectively become more stable by losing energy. total binding energy of H-2 = 1× = 2 MeV total binding energy of H-3 = 2.8×3 = 8.4 MeV total binding energy of He-4 = 4× = 28 MeV
proton neutron nucleus electron
The strong force does not actually occur directly between protons and neutrons in the nucleus, but in the smaller quarks making them up. The force is mediated by fundamental particles called gluons, named for the way they glue quarks together. Each proton or neutron is composed of three quarks. The strong nuclear force between nucleons is the result of the force holding together their constituent quarks. proton neutron nucleus electron | 2,066 | 9,185 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2018-26 | longest | en | 0.904826 |
https://qa.auth.gr/en/class/1/600171055 | 1,713,068,846,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816864.66/warc/CC-MAIN-20240414033458-20240414063458-00500.warc.gz | 445,011,413 | 9,905 | # FLUID MECHANICS I
Title ΜΗΧΑΝΙΚΗ ΡΕΥΣΤΩΝ Ι / FLUID MECHANICS I Code 118 Faculty Engineering School Mechanical Engineering Cycle / Level 1st / Undergraduate Teaching Period Spring Coordinator Kyriakos Yakinthos Common Yes Status Active Course ID 20000338
### Programme of Study: UPS of School of Mechanical Engineering
Registered students: 371
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course426
Academic Year 2020 – 2021 Class Period Spring Faculty Instructors Kyriakos Yakinthos 5hrs Weekly Hours 5 Class ID 600171055
Course Type 2016-2020
• Background
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
• Face to face
Digital Course Content
Language of Instruction
• Greek (Instruction, Examination)
Prerequisites
Required Courses
• 102 PHYSICS
• 113 THERMODYNAMICS I
• 002 Linear Algebra
• 131 LINEAR ALGEBRA
General Prerequisites
Mathematics I, II, III Thermodynamics
Learning Outcomes
Τhe students will have: An understanding of basic Fluid mechanics Be able to choose the appropriate equations to solve a problem Be able to calculate forces in bodies in a flow and pressure losses in a pipe system and apply Fluid mechanics in day t day problems
General Competences
• Apply knowledge in practice
• Retrieve, analyse and synthesise data and information, with the use of necessary technologies
• Advance free, creative and causative thinking
Course Content (Syllabus)
General properties of fluids. Hydrostatic pressure, forces due to it. Description of a flow field: equations of continuity, Euler equations, Bernoulli equation, measurement of flow rate, static and total pressure, instruments. Conservation of momentum, applications. Similarity, non dimensional numbers. Navier –Stokes equations, analytical solutions. Laplace equation for 2-D, steady, incompressible, irrotational flow: velocity potential, stream function, elementary flows. The boundary layer: Prandl’s equation for laminar flow, integral quantities. The boundary layer of a flat plate, boundary layer separation. Transitional and turbulent flow: description of turbulent flow, turbulence quantities, the effect on the flow, introduction to turbulence modeling. Introduction to Computational fluid mechanics. Flow in pipes: Velocity profiles, Pressure drop, Moody diagram. Flow and pressure field in pipe components, nozzles, diffusers, curves, valves. External flow, flow around bodies: cylinders, spheres, prisms of various cross sections, aerodynamic shapes. Compressible flow: Sonic velocity, Mach no, isentropic flow, Laval nozzle, compressible flow in pipes. Water hammer in pipes, and problem alleviation techniques.
Keywords
Fluid mechanics, turbulent flow, forces on bodies, pressure losses, compressible flow
Educational Material Types
• Notes
• Slide presentations
• Multimedia
• Book
Use of Information and Communication Technologies
Use of ICT
• Use of ICT in Course Teaching
• Use of ICT in Communication with Students
Description
Lectures Power point and Video presentations Communication Announcements and other information on e-class Personal communication by e-mail.
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures1775.9
Exams30.1
Total1806
Student Assessment
Description
Final exams at the end of the semester.
Student Assessment methods
• Written Exam with Multiple Choice Questions (Formative, Summative)
• Written Exam with Short Answer Questions (Formative, Summative)
• Written Exam with Extended Answer Questions (Formative, Summative)
• Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Μηχανική Ρευστών, Munson και λοιποί Μηχανική Ρευστών, Elger και λοιποί Μηχανική Ρευστών, Α. Γούλας
Additional bibliography for study
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https://www.jiskha.com/search?query=You+flip+a+coin+20+times+and+get+tails+15+times+you+flip+the+coin+80+more+times.what+do+you+expect+to+happen+to+the+experimental+probability+of+getting+tails+as+you+increase+the+number+of+trials+a.+The+experimental | 1,627,616,062,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153931.11/warc/CC-MAIN-20210730025356-20210730055356-00183.warc.gz | 848,920,625 | 12,458 | # You flip a coin 20 times and get tails 15 times you flip the coin 80 more times.what do you expect to happen to the experimental probability of getting tails as you increase the number of trials a. The experimental
17,321 results
1. ## statistics
1. A random variable X is generated as follows. We flip a coin. With probability p, the result is Heads, and then X is generated according to a PDF fX|H which is uniform on [0,1]. With probability 1−p the result is Tails, and then X is generated
2. ## Math
1. If you flip a fair coin 10 times, what is the probability of a) getting all tails Is it 1/1024? b) getting all heads Is it 1/1024? c) getting at least one tails? Is it 1023/1024? 2. If you roll a pair of fair dice, what is the probability of a) getting
3. ## Maths
When you flip a biased coin the probability of getting a tail is 0.6. How many times would you expect to get tails if you flip the coin 320 times?
4. ## statistics
If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least two tails? A. 1/2 B. 2/3 C. 3/4 D. 4/9 mY ANSWER IS A
5. ## Math
You flip a coin 20 times and get tails 15 times you flip the coin 80 more times.what do you expect to happen to the experimental probability of getting tails as you increase the number of trials a. The experimental probability will get closer to 50% b. The
6. ## algebra
you flip a coin and then roll a fair six-sided die.what is the probability the coin lands heads and the die shows a one.
7. ## math urgent!
You flip a coin 20 times and get tails 15 times. You flip the coin 80 more times. What do you expect to happen to the experimental probability of getting tails as you increase the number of trials? The experimental probability will get closer to 50% The
8. ## Statistics
suppose you flip a fair coin five times. which of these pairs of events are disjoint? (a). you get five heads;you get four heads and a tail (b). the first flip is a head;the second flip is a head (c). you get five heads; the second flip is a tail (d). you
9. ## mathematics
If you flip a coin 10 times, what is the best prediction possible for the number of times it will land on heads?
10. ## math
Jasmine tossed a coin 20 times. It lands on heads 14 times and tails 6 times. What is the relative frequency of landing on tails?
11. ## stats
Suppose you toss a coin 100 times and get 82 heads and 18 tails. Based on these results, what is the probability the next flip will be a tails?
12. ## math
In which scenario do you use geometric distribution to solve? -Find the number of times a tossed coin lands on tails in 10 trials. -Determine the number trials to do to have a tossed coin land on tails 8 times. -Determine the probability of tossed coin and
13. ## mathematics
When you flip a biased coin the probability of getting a tail is 0.3. How many times would you expect to get tails if you flip the coin 320 times?
14. ## Statistics
Suppose Tori has an unfair coin which lands on Tails with probability 0.28 when flipped. If she flips the coin 10 times, find each of the following: Question 5 options: P(No more than 3 Tails) P(Exactly 1 Tail) P(At least 5 Tails) P(Less than or equal to 2
15. ## math
If you flip a coin 12 times, what is the best prediction possible for the number of times it will land on heads?
16. ## pre algebra
you flip a coin and toss a 1-6 number cube. P(not tails and not a 3
17. ## Statistics
You are shown a coin that its owner says is fair in the sense that it will produce the same number of heads and tails when flipped a very large number of times. Suppose you decide to flip a coin 100 times. a. What conclusion would you be likely to draw if
18. ## statistics
Suppose you toss a coin 100 times and get 73heads and 27tails.what is the probability that the next flip is head?
19. ## probability
You flip a fair coin (i.e., the probability of obtaining Heads is 1/2) three times. Assume that all sequences of coin flip results, of length 3, are equally likely. Determine the probability of each of the following events. {HHH}: 3 Heads incorrect {HTH}:
20. ## statistics
air coin is flipped 20 times. a. Determine the probability that the coin comes up tails exactly 15 times. b. Find the probability that the coin comes up tails at least 15 times. c. Find the mean and standard deviation for the random variable X giving the
21. ## Statistics
How many sequences contain exactly three heads when you flip a coin five times? 2 15 10 8 12 my answer was 15 ,but that was incorrect
22. ## Math
A biased coin is tossed 3 times. The probability that the coin will land on heads is 0.6 The probability that the coin will land on tails three times is less than 0.1 Is this correct? Show all your working.
23. ## Math
Flip a fair coin 9 times. Find the probability of getting the following outcome. (Round your answer to six decimal places.) at least 5 heads
24. ## Math
Would you be more likely to get at least 70% tails if you flip a fair coin 10 times or if you flip a fair coin 1000 times? A) You would be more likely to get at least 70% tails if you flip a fair coin 10 times than if you flip a fair coin 1000 times. B)
25. ## Math
If you flip a coin 24 times, what is the best prediction possible for the number of times it will land on tails?
26. ## Math
Arlene wants to randomly chhose one of 12 rows to sit in. how can she do this? A) Roll a number cube. B) Flip a coin. C) Flip a coin twice. D) Flip a coin and roll a number cube. Please help me with this question.
27. ## math
If you flip a coin twice, what is the probability that a head or a tail will land up on the first flip. Express your answers as a percent.
28. ## Statistics
How many sequences contain exactly three heads when you flip a coin five times? my answer was 15 but apparently I am wrong 2 15 10 8 12
29. ## probability with casework
Markov plays a game for three turns. On each turn, he either rolls a fair, six sided die or flips a fair coin. If he rolls a 1 or 2 on the die, he will switch to the coin on the next turn, and if he flips a tails on the coin, he will switch to the die on
30. ## math
A fair coin is flipped 3 times. The probability of getting exactly two heads, given that at least one flip results in a head, can be written as a/b, where a and b are coprime positive integers. What is the value of a+b?
31. ## Math
Suppose you decided to keep flipping a coin until it came up tails. Which of these is most likely? a.flipping the coin 11 times b.flipping the coin 12 times c.flipping the coin 14 times d.flipping the coin 13 times
32. ## probability
Rosencrantz and Guildenstern In the opening scene of Tom Stoppard's play Rosencrantz and Guildenstern Are Dead, about two Elizabethan contemporaries of Hamlet, Guildenstern flips a coin 91 times and gets a head each time. Suppose the coin was balanced. a.
33. ## math
You flip a coin 20 times and get tails 15 times. You flip the coin 80 more times. What do you expect to happen to the experimental probability of getting tails as you increase the number of trials?
34. ## math
What is the theoretical probability of getting tails if you flip a coin 40 times? a)If you did this experimental would you result be the same? Why? b) Is is possible to flip a coin 40 times and get tails each time? Explain.
35. ## math
When you flip a biased coin the probability of getting a tail is 0.6. How many times would you expect to get tails if you flip the coin 320 times?
36. ## math
francisco tossed the coin 10 more times. he got 5 heads and 5 tails. now what i his exrimental probability of getting heads? Wouldn't it depend on the tosses before? 50/50 with each flip. It has no revalence what the last flip or flips were.
37. ## Math
Previously I asked this question below and got an answer with explanation. Arlene wants to randomly chhose one of 12 rows to sit in. how can she do this? A) Roll a number cube. B) Flip a coin. C) Flip a coin twice. D) Flip a coin and roll a number cube.
38. ## Math
A coin is flipped 7 times, what is the probability that the next flip will be tails How do I do this? a- 1/1 b- 1/7 c- 1/8 d- 1/2
39. ## statistics
Suppose that you flip a coin 11 times. What is the probability that you achieve at least 4 tails?
40. ## to bobpursley
In my heads/tails question- why isn't it 1/6? I flip a coin three times, aren't there only 6 possible outcomes?
41. ## Maths
The probability of a biased coin landing on heads is 0.6. I flip the coin 150 times, how many times would the coin land on heads?
42. ## Math
we have 2 coins: coin 1 comes up with the probability of tails of 2/3 while coin 2 comes up with the probability of tails of 1/3 you don't know which is which so you pick one up at random and flip it . If its tails, you guess that the coin you picked up is
43. ## Finite
One coin is fair and one is weighted so that Pr[H] = [ 1/4]. You randomly select one of the two coins, and flip it 3 times, noting the result of each flip. What is the expected number of heads?
44. ## English
Posted by rfvv on Saturday, June 5, 2010 at 5:03am. 1. Flip a coin, and if you get the head, you move one step. If you get the tail, move two steps. Then, using the picture and the words in the circle, make a sentence. 2. Work in pairs. Prepare a coin in
45. ## Math
Zach said he would help Stuart clean his room if Stuart flips a coin 4 times and gets heads all 4 times. What is the probability that Stuart will flip a coin 4 times and get heads all 4 times? Choices- A- 1/16 B- 1/8 C- 1/4 D- 1/2 I am super confused I
46. ## check one question statistic
For the scenario below, determine if the experiment describes a geometric distribution. If it is not a geometric setting, state why. if it is a geometric a) the two outcomes head or not head b) What constitutes one trial Flip a coin constitutes a flip coin
47. ## Easy Stats ?
You decide to flip a fair coin 100 times. What is the variance of this distribution? Also You decide to flip a fair coin 100 times. What is the standard deviation of this distribution?
48. ## Math (Statistics)
Hi! Can someone help me with these two questions? Thanks a bunch! :) 1.) What causes experimental probability to match theoretical probability? In theory heads and tails occur 50/50. 2.) Find a way to estimate the time to flip a coin 10,000 times; 100,000
49. ## Math (Statistics)
Hi! Can someone help me with these two questions? Thanks a bunch! :) 1.) What causes experimental probability to match theoretical probability? In theory heads and tails occur 50/50. 2.) Find a way to estimate the time to flip a coin 10,000 times; 100,000
50. ## math
You flip a fair coin 10,000 times. Approximate the probability that the di fference between the number of heads and number of tails is at most 100.
51. ## statistics
You have two coins that look identical, but one of them is fair and the other is weighted. The weighted coin has a 3/4 chance of flipping heads and a 1/4 chance of flipping tails. Unfortunately, you've forgotten which coin is which! You decide to keep
52. ## maths
Suppose there are 10 coins laid out in front of you. All of the coins are fair (i.e. have an equal chance of heads or tails) except one, which flips to heads every time. You draw one coin at random and flip it 5 times. If each of the 5 flips results in
53. ## probability
We have an infinite collection of biased coins, indexed by the positive integers. Coin i has probability 2−i of being selected. A flip of coin i results in Heads with probability 3−i. We select a coin and flip it. What is the probability that the
54. ## Math
A man comes up to play a game. you flip a coin, if heads you win \$1 and keep playing if heads again you get \$2, if you get heads again, \$4 and so on. If you flip tails you take your money and the game is over. How much should he be willing to pay?
55. ## math
I flip a fair coin seven times in a row. What is the probability that I get at most five heads?
56. ## economics
Suppose you have \$30,000 in wealth and have the choice of two possible gambles: Gamble 1: a single flip of a coin would pay you \$16,000 if it is heads, cost you \$16,000 if it is tails. Gamble2: two coin flips, each payuing you \$8,000 if it is head, each
57. ## MATH
If you flip a coin 9 times and get 9 heads the probability of getting a head on the next toss would be 1/2. Explain how it is 1/2.
58. ## math
You decide to flip a fair coin 100 times. What is the variance of this distribution? and You decide to flip a fair coin 100 times. What is the variance of this distribution?
59. ## Math-Probability
You have a friend who claims to be psychic. You don't believe this so you test your friend by flipping a coin 20 times and having him predict whether each flip is heads or tails. If you are right, and your friend is NOT psychic, the the probability of
60. ## statistics
You have a friend who claims to psychic. You don't believe this so you test your friend by flipping a coin 20 times and having him predict whether each flip is heads of tails. If you are right, and your friend is NOT psychic, then the probability of
61. ## probability
Grace has flipped a coin 500 times and each time is has come up tails. If she flips the coin 500 more times, how many tails should she expect? Why?
62. ## algebra
Jamil tosses a coin 3 times. What is the probability that the coin will land tails up all three times?
63. ## math
Luis draws 1 card from a deck, 39 times. Predict how many times he draws an ace. John and O'Neal are playing a board game in which they roll two number cubes. John needs to get a sum of 8 on the number cubes to win. O'Neal needs a sum of 11, if they take
64. ## physics
if i flip a coin, will the coin stop moving upwards first before it starts to move down? in other words, is there a moment when the coin is not moving at all? why? It stops and has velocity equal to zero at the top. ok.
65. ## Math, Statistics
I know its 1 - P(5/128) but I don't think its correct?? I flip a fair coin seven times in a row. What is the probability that I get at most five heads?
66. ## Math
Find a way to estimate the time to flip a coin 10,000 times; 100,000 times.
67. ## Geometry
A fair coin is flipped 3 times. The probability of getting exactly two heads, given that at least one flip results in a head, can be written as ab, where a and b are coprime positive integers. What is the value of a+b?
68. ## math
A fair coin is flipped 3 times. The probability of getting exactly two heads, given that at least one flip results in a head, can be written as a/b, where a and b are coprime positive integers. What is the value of a+b?
69. ## physics
If you are in a smooth riding bus that is going 50 km/hr and you flip a coin vertically, what is the horizontal velocity of the coin in midair relative to the ground?
70. ## math
Please check my answers Would you be more likely to get at least 70% tails if you flip a fair coin 10 times or if you flip a fair coin 1000 times? same Consider a bowl containing 36 different slips of paper. Ten of the slips of paper each contain one of
71. ## Math
If you flipped a coin once and rolled one die, what is the P(flip a head & roll a 6)? my answer: 1/12 If you did this 36 times, how many times should you expect the outcome to be a head and a 6? my answer: 6 am I right?
72. ## English
1. Flip a coin, and if you get the head, you move one step. If you get the tail, move two steps. Then, using the picture and the words in the circle, make a sentence. 2. Work in pairs. Prepare a coin in each pair. One should flip a coin, and if he gets the
73. ## math
flip a coin 3 times a) what are the odds in favor of getting exactly 2 heads b) what are the odds against getting at most 1 tail i got a) 3/4 b) 7/8 i don't think they are right can someone help
74. ## math
flip a coin 3 times a) what are the odds in favor of getting exactly 2 heads b) what are the odds against getting at most 1 tail
75. ## Math
6. Biased coin Bookmark this page Problem 5. Biased coin 5.0 points possible (graded, results hidden) We are given a biased coin, where the probability of Heads is q. The bias q is itself the realization of a random variable Q which is uniformly
76. ## Probability
You and a friend play the following game: You pay your friend \$3 each turn and then flip a fair coin. It it’s tails, your friend pays you \$(2^n), where n is the number of times you’ve flipped the coin, and the game ends. If it’s heads, you have the
77. ## Math
If you flip a coin 3 times and roll a standard number cube. What is the probability you get 3 heads and roll a 1. Write your answer in a reduced fraction
78. ## math
In a probability experiment, Eric flipped a coin 33 times. The coin landed on heads 22 times. What is the ratio of heads to tails in this experiment?
79. ## math
if freddy tosses a coin three times, what is the probability that the coin will turn up hesds,tails,heads, tails in that order? I came up with 1/2 correct? also the ratio length to the width of the alamo isabout 5to 3 if the width of the alamo is 63ft
80. ## Probability
Rosencrantz and Guildenstern In the opening scene of Tom Stoppard's play Rosencrantz and Guildenstern Are Dead, about two Elizabethan contemporaries of Hamlet, Guildenstern flips a coin 91 times and gets a head each time. Suppose the coin was balanced. a.
81. ## Math
Victoria tossed a coin 30 times and got 17 heads. What is the ratio of heads to coin tosses? What is the ratio of heads to tails? What is the ratio of tails to heads? If victoria tosses the coin 150 times, how many times can she expect to get heads?
82. ## arithmetic
Assume you have an unfair coin - the one that lands heads with probability P (not known beforehand). You have rolled such a coin 20 times and got 16 heads and 4 tails. What is the best estimator of P, Pˆ? (Hint: it is the one based on sample mean.)
83. ## maths : probability
We are given a biased coin, where the probability of Heads is q. The bias q is itself the realization of a random variable Q which is uniformly distributed on the interval [0,1]. We want to estimate the bias of this coin. We flip it 5 times, and define the
84. ## math
You win \$4 if you flip a coin twice and get tails both times. For any other outcome you get nothing. What is the expected value?
85. ## Finite
One coin is fair and one is weighted so that Pr[H]=211. You randomly select one of the two coins, and flip it 5 times, noting the result of each flip. What is the expected number of heads?
86. ## stor
Suppose that you flip a fair coin (P(H)=P(T)=1 2 ) three times and you record if it landed on heads, H, or tails, T. (a) What is the sample space of this experiment? What is the probability of each event? (b) [1 pt] Let X be the number of times that you
87. ## Mathematics
James tossed a coin 20 times. The coin landed on heads 8 times and it landed on tails 12 times. What is the experimental probability for both sides of the coin.
88. ## Probability
What is the probability of flipping a coin two times and getting no heads? If I flip a coin twice and get no heads wouldn't it be 2/2 or 1?
89. ## math
Mr. Carter wants to determine the probabilities for students choosing a hamburger or a hot dog at the school picnic. A. Explain how Mr. Carter could create a simulation for this using a coin. B. Should Mr. Carter flip the coin 5 times or 50 times to get
90. ## math
You flip a coin and toss a 1-6 number cube what is the probabilty of getting a 5 and tails
91. ## math
A fair coin is flipped 3 times. The probability of getting exactly two heads, given that at least one flip results in a head, can be written as a/b, where a and b are coprime positive integers. What is the value of a+b?
92. ## Math
Identify the sampling technique used to obtain this sample: Each person boarding a plane is asked to flip a coin; those showing “tails” have their luggage searched.
93. ## Can someone help me please? MATH
Identify the sampling technique used to obtain this sample: Each person boarding a plane is asked to flip a coin; those showing “tails” have their luggage searched.
94. ## Gr 12 Data
Sarah tosses 5 coins, one after the other. a) How many different outcomes are possible? b) Draw a tree diagram to illustrate the different possibilities. c) In how many ways will the first coin turn up heads and the last coin turn up tails? d) In how many
95. ## math
flip a coin 3 times a) what are the odds in favor of getting exactly 2 heads b) what are the odds against getting at most 1 tail
96. ## probability
Suppose an unfair coin comes up heads 52.2% of the time if it is flipped. If the coin is flipped 26 times, what is the probability that: a) it comes up tails exactly 12 times? b) it comes up heads more than 22 times?
97. ## Conditional Probability
Please refer to the illustration at screenshotsfirefoxcom/jZoizoMJf8a3H0UZ/ds055uzetaobbcloudfrontnet to help answer the following question: Zeb's coin box contains 8 fair, standard coins (heads and tails) and 1 coin which has heads on both sides. He
98. ## MATH
24 1c coins are set out in a row on a table. Then every 2nd coin is replaced by a 2c coin every 3rd coin is replaced by a 5c coin every 4th coin is replaced by a 10c coin every 5th coin is replaced by a 20c coin every 6th coin is replaced by a 50c coin
99. ## statistics and probabilities
You have two coins that look identical, but one of them is fair and the other is weighted. The weighted coin has a 3/4 chance of flipping heads and a 1/4 chance of flipping tails. Unfortunately, you've forgotten which coin is which! You decide to keep
100. ## maths
A coin is biased so that a head is twicw as likely to occur as a tail. Suppose the coin is tossed three times. What is the probality of getting at exactly two tails | 5,687 | 21,890 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2021-31 | latest | en | 0.906316 |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-4-section-4-5-graphs-of-sine-and-cosine-functions-exercise-set-page-598/108 | 1,679,892,619,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296946637.95/warc/CC-MAIN-20230327025922-20230327055922-00001.warc.gz | 882,742,078 | 13,043 | Precalculus (6th Edition) Blitzer
Step 1. Graph the function together with $y=sin(x)$ as shown in the figure. Step 2. We can see that the given function is a very good approximation to $y=sin(x)$ | 56 | 196 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2023-14 | latest | en | 0.90483 |
https://de.maplesoft.com/support/help/addons/view.aspx?path=operators%2Funary | 1,675,849,118,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500758.20/warc/CC-MAIN-20230208092053-20230208122053-00609.warc.gz | 210,802,371 | 26,037 | unary - Maple Help
# Online Help
###### All Products Maple MapleSim
Unary Operators
Description
• The unary operators in Maple are:
+ unary plus (prefix) - unary minus (prefix) ! factorial (postfix) not logical not (prefix) . decimal point (prefix or postfix) \$ sequence operator (prefix) &name neutral operator (prefix)
• Most unary operators can be made to apply element-wise by appending a tilde (~). See operator[elementwise] for details.
Examples
> $3;$$-3$
${3}$
${-3}$ (1)
> $8!$
${40320}$ (2)
> $3.$
${3.}$ (3)
> $0.3$
${0.3}$ (4)
> $\mathrm{}\left(1..10\right)$
${1}{,}{2}{,}{3}{,}{4}{,}{5}{,}{6}{,}{7}{,}{8}{,}{9}{,}{10}$ (5)
> $\mathrm{FAIL}$
${\mathrm{FAIL}}$ (6)
See Also | 240 | 719 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 14, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2023-06 | latest | en | 0.491062 |
https://muster-themes.net/questions/Trigonometry/300148 | 1,716,159,369,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058009.3/warc/CC-MAIN-20240519224339-20240520014339-00845.warc.gz | 377,624,811 | 4,558 | # Find the Exact Value sin(315)
Find the Exact Value sin(315)
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.
The exact value of is .
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Do you know how to Find the Exact Value sin(315)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.
### Name
Name one billion ten million one hundred eighty-one thousand three hundred ninety-six
### Interesting facts
• 1010181396 has 64 divisors, whose sum is 3497800320
• The reverse of 1010181396 is 6931810101
• Previous prime number is 101
### Basic properties
• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 30
• Digital Root 3
### Name
Name twenty million one hundred fifty-one thousand five hundred eighty-five
### Interesting facts
• 20151585 has 8 divisors, whose sum is 22888680
• The reverse of 20151585 is 58515102
• Previous prime number is 9
### Basic properties
• Is Prime? no
• Number parity odd
• Number length 8
• Sum of Digits 27
• Digital Root 9
### Name
Name seven hundred twenty-three million two hundred eighty-three thousand four hundred forty-four
### Interesting facts
• 723283444 has 16 divisors, whose sum is 1631429568
• The reverse of 723283444 is 444382327
• Previous prime number is 403
### Basic properties
• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 37
• Digital Root 1 | 407 | 1,579 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2024-22 | latest | en | 0.725975 |
https://cadabra.science/qa/1746/sign-changed-index-splitting?show=1750 | 1,638,417,463,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964361064.69/warc/CC-MAIN-20211202024322-20211202054322-00289.warc.gz | 228,598,758 | 5,620 | sign changed index splitting
Hello
At first, thank you for inventing this very good tools
i wondering is there other way to split index
if i use split_index command to split index m to \mu and 5,
i get
A^{m} B_{m} = A^{\mu} B_{\mu} + A^{5} A_{5}
but
i want this to be
A^{m} B_{m} = A^{\mu} B_{\mu} - A^{5} A_{5}
Is there any good way?
Thank you
+1 vote
In Cadabra the Einstein index summation convention always means just a plain sum, without sign factors. Did you really mean those indices to one upper, one lower? Or does this sign come from a suppressed metric?
+1 vote
With the version of Cadabra currently on github (2.3.1.5) you can write a small function which examines every term in the expression, counts the number of '5' indices, and flips the sign if there is an odd number of pairs. Starting from
{m,n,p}::Indices(space);
{\mu,\nu}::Indices(subspace, parent=space);
ex:=A^{m n} B_{m n};
split_index(ex, $m, \mu, 5$, repeat=True);
which produces $$A^{\mu \nu} B_{\mu \nu}+A^{\mu 5} B_{\mu 5}+A^{5 \mu} B_{5 \mu}+A^{5 5} B_{5 5},$$ you can define
def flip5(ex):
for node in ex:
for term in node.terms():
cnt=0
for index in term.indices():
if index.name=="1" and index.multiplier==5:
cnt+=1
term.multiplier *= (-1)**(cnt//2)
return ex
and then do
flip5(ex);
to get $$A^{\mu \nu} B_{\mu \nu}-A^{\mu 5} B_{\mu 5}-A^{5 \mu} B_{5 \mu}+A^{5 5} B_{5 5}$$ | 470 | 1,384 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2021-49 | longest | en | 0.700493 |
https://justaaa.com/statistics-and-probability/129482-a-random-sample-of-11-truant-students-produced | 1,721,443,665,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514981.25/warc/CC-MAIN-20240720021925-20240720051925-00420.warc.gz | 292,059,156 | 10,147 | Question
# A random sample of 11 truant students produced the following data, where x is the number...
A random sample of 11 truant students produced the following data, where x is the number of classes missed, and y is the final exam score (out of a maximum of 75 points). The data are presented below in the table of values.
x y
10 54
11 41
12 37
14 36
15 29
16 28
18 28
19 26
22 19
25 19
26 18
What is the equation of the regression line?
yˆ=−1.821x+17.1
yˆ=−1.821x+61.6
yˆ=10.912x+61.6
yˆ=10.912x+17.1
The statistical software output for this problem is:
Hence,
Equation of regression line will be:
y = -1.821x + 61.6
Option B is correct. | 219 | 655 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2024-30 | latest | en | 0.796533 |
https://www.cfd-online.com/Forums/fluent/212033-why-pressure-recovery-less-than-1-smooth-wall-subsonic-compressible-flow.html | 1,675,949,001,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499966.43/warc/CC-MAIN-20230209112510-20230209142510-00834.warc.gz | 705,159,348 | 16,551 | # Why is Pressure Recovery less than 1 for a smooth wall subsonic compressible flow
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November 25, 2018, 12:27 Why is Pressure Recovery less than 1 for a smooth wall subsonic compressible flow #1 Member MWRS Join Date: Apr 2018 Posts: 98 Rep Power: 6 Wall roughness is set to zero. Then why is total pressure in outlet lower than inlet for a compressible flow? I have simulated a simple diverging pipe. What exactly is decreasing the total pressure for a smooth pipe?
November 25, 2018, 12:34 #2 Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,115 Rep Power: 60 Do you still have a wall? I.e. no slip? Smooth is a hydraulic term meaning that the wall roughness is small relative to a specific length scale. A smooth wall does not mean there is no friction (it just means there is no roughness). There will be a total pressure drop. Even if you had slip walls, you still have a viscous flow (navier-stokes) and there would still be a small drop in total pressure. waseeqsiddiqui likes this.
November 25, 2018, 12:35 #3 Member MWRS Join Date: Apr 2018 Posts: 98 Rep Power: 6 yes i have no slip
November 25, 2018, 12:36 #4 Member MWRS Join Date: Apr 2018 Posts: 98 Rep Power: 6 so how would there be a small drop due to viscous flow in a no slip condition?
November 26, 2018, 13:05 #5 Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,115 Rep Power: 60 The fluid has a velocity going into the diffuser. At walls, because of the no-slip condition (for both smooth and rough walls) the fluid adopts the velocity of the wall (presumably 0 m/s). Hence the fluid loses some momentum and this manifests as a total pressure drop. Even if you have slip walls where there is no frictional force induced by the walls. The area is diverging and because of this you have velocity gradients which gives rise to viscous forces. In a newtonian fluid, wherever you have velocity gradients, you have viscous forces. waseeqsiddiqui likes this.
November 26, 2018, 13:06 #6 Member MWRS Join Date: Apr 2018 Posts: 98 Rep Power: 6 Many thanks ! | 575 | 2,161 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2023-06 | latest | en | 0.928434 |
https://www.nichesblog.com/search/multiples-of-6 | 1,643,095,034,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304798.1/warc/CC-MAIN-20220125070039-20220125100039-00604.warc.gz | 948,636,054 | 8,539 | # Keyword Analysis & Research: multiples of 6
## Keyword Research: People who searched multiples of 6 also searched
What are the first 5 multiples of 6?
The first few multiples of 6 are: × 6 = 6 × 6 = 12 × 6 = 18 × 6 = 24 × 6 = 30 × 6 = 36 × 6 = 42 × 6 = 48 × 6 = 54 × 6 = 60 More items...
Which numbers are multiples of 6?
A multiple of six is any number that is divisible by six, such as 12, 24, 360 or 7,907,560,848. If a number is a multiple of two and three, then it is also a multiple of six.
What is the lowest common multiple of 6?
The lowest, or least, common multiple of 4 and 6 is 12. This is the smallest number that is a multiple of both 4 and 6. One way to find the lowest common multiple, or LCM, is to first reduce each number to its prime factors.
Is 54 a multiple of 6?
Multiples of 6 would be 6, 12, 18, 24 and so on. Multiples of 54 would be 54, 108, 162, 216 and so on. Now, compare the two lists to find the smallest number the two lists have in common, which is the Least Common Multiple of 6 and 54. | 323 | 1,032 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2022-05 | latest | en | 0.957858 |
https://freeguruhelpline.com/class-nine-ncert-solutions-chapter-9-areas-of-parallelograms-and-triangles/ | 1,627,561,397,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153857.70/warc/CC-MAIN-20210729105515-20210729135515-00338.warc.gz | 276,193,114 | 10,176 | NEXT
#### Class Nine NCERT Solutions Chapter 9
Chapter 9: Areas of Parallelograms and Triangles (NCERT Solutions)
TEXTBOOK’S EXERCISE – 9.1
1. Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and the two parallels.
Sol. (i) Base DC, parallels DC and AB
(iii) Base QR, parallels QR and PS
TEXTBOOK’S EXERCISE – 9.2
1. In the figure, ABCD is a parallelogram, AE DC and CF AD.
If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.
Sol. Area of parallelogram ABCD
= AB × AE = 16 × 8 cm2 = 128 cm2
Also, area of parallelogram ABCD = AD × FC = (AD × 10) cm2
∴ AD × 10 = 128
⇒ AD = 128/ 10 = 12.8 cm
2. If E, F, G, and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar (EFGH) = 1/2 ar (ABCD).
Sol. Given: A parallelogram ABCD. E, F, G, H are mid-points of sides AB, BC, CD, DA respectively.
To Prove : ar (EFGH) = 1/2 ar (ABCD)
Construction: Join AC and HF.
Proof: In ΔABC,
E is the mid-point of AB.
F is the mid-point of BC.
⇒ EF || AC and EF = 1/2 AC … (i)
Similarly, in ΔADC, we can show that
HG || AC and HG = 1/2 AC … (ii)
From (i) and (ii)
EF || HG and EF = HG
∴ EFGH is a parallelogram.
[One pair of opposite sides is equal and parallel]
HA = FB and HA || FB
[AD = BC ⇒ 12 AD = 1/2 BC ⇒ HA = FB]
∴ ABFH is a parallelogram. [One pair of opposite sides is equal and parallel]
Now, triangle HEF and parallelogram HABF are on the same base HF and between the same parallels
HF and AB.
∴ Area of ΔHEF = 1/2 area of HABF … (iii)
Similarly, area of ΔHGF = 1/2 area of HFCD … (iv)
Area of ΔHEF + area of ΔHGF
= 1/2 (area of HABF + area of HFCD)
⇒ ar (EFGH) = 1/2 ar (ABCD) Proved.
3. P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC).
Sol. Given: A parallelogram ABCD. P and Q are any points on DC and AD respectively.
To prove : ar (APB) = ar (BQC)
Construction : Draw PS || AD and QR || AB.
Proof: In parallelogram ABRQ, BQ is the diagonal.
∴ area of ΔBQR = 1/2 area of ABRQ ………. (i)
In parallelogram CDQR, CQ is diagonal.
∴ area of ΔRQC = 1/2 area of CDQR ……….. (ii)
Adding (i) and (ii), we have
area of ΔBQR + area of ΔRQC
= 12 [area of ABRQ + area of CDQR]
⇒ area of ΔBQC = 1/2 area of ABCD.
Again, in parallelogram DPSA, AP is diagonal.
∴ area of ΔASP = 1/2 area of DPSA ……… (iv)
In parallelogram BCPS, PB is diagonal.
∴ area of ΔBPS = 1/2 area of BCPS ………. (v) | 884 | 2,491 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2021-31 | longest | en | 0.822037 |
https://buzzmath.com/en/blog/using-the-holidays-to-reflect-on-our-greatest-gift-time/ | 1,721,867,726,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518532.61/warc/CC-MAIN-20240724232540-20240725022540-00791.warc.gz | 124,251,713 | 77,962 | Pedagogy
## Using The Holidays To Reflect On Our Greatest Gift: Time
| Publish on December 17, 2018
The movement of time is consistent in our lives. As goes in the old Rolling Stones song, “Time Waits For No One”.
But, how we spend our time varies immensely. The holidays can often become too frenetic, and we overstretch ourselves in doing too much, which leads to a both physical and mental exhaustion during this supposedly slower time.
The idea of time, the quality of it, the need to slow down is not just a concern for our physical health, but our creative health as well. Pondering and reflecting can only be done with others, if we have first given the gift of time to ourselves.
Earlier this month, our company held its annual Holiday party at the office in Montreal. I came up with my family, not only to spend quality time in this lovely city, but to present a “Lunch and Learn” on the day of our party that centered around the idea of…time.
My inspiration for time came from the subject that we all love and share–mathematics. And, it seemed the festive time of the holidays would perhaps allow for deeper and happier reflections as to what does it mean to slow down and not get bogged down in things like performance, checklists, and multitasking. Surprising to most, I used mathematics to illustrate how time gets dwarfed by the creativity and ingenuity often required to solve seemingly simple problems.
Case in point was an idea I presented to my colleagues regarding The Collatz Sequence. This is a sequence generated by picking a random, positive integer and then applying the following rules to it:
Divide it by 2 if it is even, or multiply it by 3 and add 1, if it is odd. So, for example, the number 5 generates the following sequence of numbers.
5, 16, 8, 4, 2, 1
It turns out that all numbers apparently have a cycle that eventually ends back at 1. What is so fascinating about this 88-year-old problem created by Lothar Collatz is not that nobody has proven that this happens for all numbers. No, many things are currently unproven in math. What is remarkable is that it is believed by some in the math community that the mathematics required to tackle this problem isn’t even available!
Even the element of ample time is not enough to solve mathematical mysteries some time. So, it behooves us as educators to give more space and time to our students when they encounter math problems. Thinking mathematically requires not only logic, but patience, persistence, and creativity. These skills are not learned and honed if time is not seen as the most valuable and precious commodity.
The great benefit of slowing down is reclaiming the time and tranquility to make meaningful connections–with people, with culture, with work, with nature, with our own bodies and minds. — Carl Honore —
This holiday season, we hope that yours is filled with warmth and plenty of good cheer. But, beyond all that, is that you spend time with family and friends and celebrate every moment of laughter and conversation. And, that you do it by finding your inner turtle…
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http://www.aspmessageboard.com/showthread.php?178901-help-with-my-2D-array-function | 1,476,995,067,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988717783.68/warc/CC-MAIN-20161020183837-00043-ip-10-171-6-4.ec2.internal.warc.gz | 323,252,255 | 15,602 | help with my 2D array function
Thread: help with my 2D array function
1. Senior Member
Join Date
Dec 1969
Posts
353
help with my 2D array function
This function is for sorting a 2D array which is an array of columns or fields, not records or rows. The problem is that its only sorting one column, not the whole record. I've marked the line which I think is the problem.<BR><BR>[code language="C#"]<BR>function SortTwoDimensionalArray(a,column,order) // a is array, column is column to sort by.<BR>// This is for an unconventional 2 dimensional array, which is an array of columns (fields), not rows (records)<BR>{<BR> var aSorted, aConverter, i, j;<BR> // aSorted will contain the sorted array; aConverter will contain an array for working out<BR> // how to keep records together; i and j are iterators.<BR><BR> aSorted = new Array(a.length);<BR><BR> aSorted[column] = a[column].sort(); // Sort the array containing the column to be sorted by<BR><BR> if (aSorted[column] == a[column])<BR> return a;<BR><BR> // This double loop pattern then matches elements of the sorted array with corresponding elements of the<BR> // origional array, recording the results in a converter array<BR> for (i = 0; i < aSorted[column].length; i++)<BR> {<BR> for (j = 0; j < aSorted[column].length; j++)<BR> {<BR> if (aSorted[i][j] == a[i][0])<BR> {<BR> aConverter[i] = j;<BR> break;<BR> }<BR> }<BR> }<BR><BR> // This double loop uses aConverter to decide which element to assign each value to in aSorted<BR> for (i = 0; i < aSorted.length; i++)<BR> {<BR> if (i != column)<BR> for (i = 0; i < aSorted.length; i++)<BR> aSorted[i][j] = a[i][aConverter[i]]; // I think this is the problem<BR> }<BR><BR> return aSorted;<BR>}<BR>[/code]
2. Senior Member
Join Date
Dec 1969
Posts
19,082
RE: help with my 2D array function
well, for one thing you've nested two loops which use the SAME iterator. shouldn't the inner loop use 'j' as an index as the previous one does?<BR><BR>or is my hangover misleading me again?
3. Senior Member
Join Date
Dec 1969
Posts
353
RE: help with my 2D array function
oh, yes, so I have. Sometimes this sort of thing takes a second pair of eyes. I swithed the i for j, which is what I intended. Its still not working though. This is what I use to test it:<BR><BR>
Code:
`<BR>document.write('<TABLE>');<BR><BR>for (i = 0; i < ArrayToSort[0].length; i++)<BR>{<BR> document.write('<TR><TD>'<BR> + ArrayToSort[0][i] + '</TD><TD>'<BR> + ArrayToSort[1][i] + '</TD><TD>'<BR> + ArrayToSort[2][i] + '</TD><TD>'<BR> + ArrayToSort[3][i] + '</TD></TR>');<BR>}<BR><BR>document.write('<TR><TD COLSPAN=4><BR><BR><BR></TD></TR>');<BR><BR>SortTwoDimensionalArray(ArrayToSort,0);<BR><BR>for (i = 0; i < ArrayToSort[0].length; i++)<BR>{<BR> document.write('<TR><TD>'<BR> + ArrayToSort[0][i] + '</TD><TD>'<BR> + ArrayToSort[1][i] + '</TD><TD>'<BR> + ArrayToSort[2][i] + '</TD><TD>'<BR> + ArrayToSort[3][i] + '</TD></TR>');<BR>}<BR><BR>document.write('</TABLE>');<BR>`
<BR><BR>If it has worked, the first row should read 0 4 8 12, the second 1 5 9 13, and so on.
4. Senior Member
Join Date
Dec 1969
Posts
96,118
Pardon me, but this is *nutso*
You are using JavaScript!<BR><BR>Which has a BUILT IN sort capability for arrays!<BR><BR>And since there isn't any such thing as a "2D array" in JS, you just have to ask it to sort your "array-of-arrays".<BR><BR>And that is *DIRT EASY*.<BR><BR>Here...a working demo...worked first time after I cleaned up 2 typos.<BR><BR>**************<BR><HTML>&# 060;BODY><BR><BR><SCRIPT><BR>var demo = new Array(<BR> new Array( 'Abbie', 'Trent', 27 ),<BR> new Array( 'Bill', 'Smith', 42 ),<BR> new Array( 'Carol', 'Roberts', 33 ),<BR> new Array( 'Dean', 'Quester', 23 ),<BR> new Array( 'Everett', 'Porter', 50 )<BR> );<BR><BR>var sortColumn = 0;<BR><BR>function arraySort( elem1, elem2 )<BR>{<BR> if ( elem1[sortColumn] > elem2[sortColumn] ) return 1;<BR> if ( elem1[sortColumn] < elem2[sortColumn] ) return -1;<BR> return 0;<BR>}<BR><BR>function show( )<BR>{<BR> // have to set a global, unfortunately<BR> sortColumn = parseInt( document.TheForm.column.value );<BR> <BR> var sorted = demo.sort( arraySort );<BR><BR> html = "<TABLE Border=3 CellPadding=8>"<BR> for ( var row = 0; row < sorted.length; ++row )<BR> {<BR> html += "<TR><TD>" + sorted[row].join("</TD><TD>") + "</TD></TR>"<BR> }<BR> html += "</TABLE>";<BR> document.getElementById("showme").innerHTML = html;<BR>}<BR></SCRIPT><BR><BR><FORM Name="TheForm"><BR>Choose a column: <BR><SELECT Name="column"><BR> <OPTION value=0> First name<BR> <OPTION value=1> Last name<BR> <OPTION value=2> Age<BR></SELECT><BR>Then click <INPUT Type=Button Value="HERE" onClick="show();"><BR></FORM><BR><HR><BR><DIV ID="showme"></DIV><BR></BODY></HTML><BR>
5. Senior Member
Join Date
Dec 1969
Posts
96,118
Here's the same thing...
...done fancier, with data from a DB, using an array of objects instead of an array of arrays (though an array *is* an object in JS, so and array of arrays *IS* an array of objects...there will be a quiz Friday).<BR><BR>Oh, and using frames, so that it works even with NS 4 (and, I think NS 3!) browsers.<BR><BR>
6. Senior Member
Join Date
Dec 1969
Posts
96,118
Surprised you didn't...
...catch this one! Why use for loops *at all* to sort any kind of array in JavaScript?<BR><BR><tch/><BR><BR>
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### Topic: How to calculate AC Watts (Read 1 time)previous topic - next topic
#### Lavan
##### Apr 05, 2013, 09:58 pm
Hi There!
I need to buy an 220V AC to 110V AC converter for my Xbox adapter. Only DC power rating is mentioned on the Adapter as 12 V DC @ 9.6 Amps and 5V DC @ 1Amp. If I calculate P=VI, total power is coming to 120 Watts at DC. Will DC wattage is equal to wattage at AC? What wattage of converter I need to buy to hook up this adapter?
#### Grumpy_Mike
#1
##### Apr 05, 2013, 10:02 pm
Quote
Will DC wattage is equal to wattage at AC?
Only if the adapter is 100% efficient at converting the power. Normally they are between 80 and 95% efficient, so allow a bit of margin.
Don't worry about getting one with too much wattage, make sure the voltage and current output are sufficient.
Don't worry about too much current, the device you attach it to will take what current it needs up to the maximum the adapter will supply.
#### Lavan
#2
##### Apr 05, 2013, 10:14 pm
Thank you very much for your quick reply. So a 150 Watt 220 V to 110 V converter is best bet?
#### Grumpy_Mike
#3
##### Apr 05, 2013, 10:20 pm
So a 150 Watt 220 V to 110 V converter is best bet?
Yes if it provides the current and voltage you want either a 150W or 200W converter will do the job.
#4
Thank you!
#### retrolefty
#5
##### Apr 05, 2013, 11:50 pm
Quote
I need to buy an 220V AC to 110V AC converter for my Xbox adapter.
In the old days we would have said "I need a step down transformer 220/110 vac."
Lefty
Go Up | 461 | 1,536 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2017-43 | latest | en | 0.877565 |
http://mathoverflow.net/questions/111537/polycirculant-conjecture?sort=votes | 1,469,462,381,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257824319.59/warc/CC-MAIN-20160723071024-00044-ip-10-185-27-174.ec2.internal.warc.gz | 156,501,319 | 15,622 | # polycirculant conjecture
By the polycirculant conjecture, every vertex-transitive graph is a polycirculant graph (D. Marusic 1981 and D. Jordan 1988). There are two papers that claim to prove this conjecture: 1. A. Golubchik, "On the polycirculant conjecture", available on http://arxiv.org/abs/math.GM/0204209, April 2002. 2. E. Mwambene, "A proof of the polycirculant conjecture", available on http://arxiv.org/abs/math/0506617, Jun 2005. But I find some papers that proved the conjecture in special cases, after 2005. For example (a) Every vertex-transitive graph of valency four is a polycirculant (E. Dobson et.al 2007) (b) All vertex-transitive locally-quasiprimitive graphs have a semiregular automorphism (M. Giudici and J. Xu 2007). (c) Every connected distance-transitive graph admits a semiregular automorphism (K. Kuntar and P.Sparl 2010).
So I want to know that the polycirculat conjecture is proved or not?
-
It is a general policy on MO not to ask about correctness of preprints claiming to prove hard conjectures. The paper math.GM/0204209 is almost surely false for it also claims a simple proof of the Feit-Thompson theorem (in 32 pages!). The paper math/0506617 does not appear to have been published in seven years. But if you want to know if the conjecture is proved or not is I suppose a reasonable, on-topic question. – David Roberts Nov 5 '12 at 9:19
David, I didn't know about this MO policy. I've seen a few questions on MO concerning arXiv preprints and they've often received a very large amount of interest. So long as these questions are asked in a respectful fashion, then it seems to me that MO is a reasonable place for them. (However if there's an official MO policy against such questions, then of course we should abide by that.) – Nick Gill Nov 5 '12 at 11:24
I think David Roberts is referring to various discussions on meta. See tea.mathoverflow.net/discussion/1422/… and the references therein, and also tea.mathoverflow.net/discussion/1447/3/… . – HJRW Nov 5 '12 at 12:48
Lemma 6 of math/0506617 is also false. Any transitive permutation group without a derangement of prime order satisfies the hypotheses and does not contain a semiregular element. (Any semiregular element has a power that is stil semiregular and of prime order.) Such groups exist, such as $M_{11}$ acting on the twelve points.
$A_5$ acting on 10 points is another counterexample. – Michael Giudici Nov 6 '12 at 6:04
Another counterexample: $M_{22}$ on 22 points is a counterexample to Lemma 5 of math.GM/0204209 . (As Gerry Myerson noted, this is overkill. However, I'm interested in the sporadic simple groups and this is a way to use one of them.) – DavidLHarden Nov 10 '12 at 2:20 | 742 | 2,701 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2016-30 | latest | en | 0.9023 |
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# Slides06 - Connected Components, Bipartite Testingsheldon/teaching/mhc... · Logistics Quizzes Quiz...
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Logistics Quizzes Quiz 5: 74% Other quizzes: ~98% I’ll drop lowest 2 quizzes HW HW 2 back: average 44.9/50, 5.2 hours HW 3 due HW 4 out tonight No reading for Thursday Questions?
Transcript
• LogisticsQuizzes
Quiz 5: 74%Other quizzes: ~98%I’ll drop lowest 2 quizzes
HWHW 2 back: average 44.9/50, 5.2 hoursHW 3 dueHW 4 out tonight
Questions?
• Today
BFS/DFS
Connected components
Bipartite testing
Directed Graphs
• Connected Components
Definitions, example, proof on board
• “Meta”-BFS algorithm
while there is an unexplored node s
BFS(s)
end
Example
Running time? argue O(m+n) running time on board
Find all edges incident to u: O(nu)
1
3
5 4
212345
2 4 51 3 42 51 21 3
• Running Time?Set explored[u] to be false for all uA = { s } // set of discovered but not explored nodeswhile A is not empty
Take a node u from Aif explored[u] is false
set explored[u] = truefor each edge (u,v) incident to u
endend
Same reasoning we just did: but now “charge” each line of code to either a node or an edge
O(n)
O(m)
O(m)O(m)
O(n)
• Graph Traversal: Summary
BFS/DFS: O(n+m)Is G connected?Find connected components of GFind distance of every vertex from sourceGet BFS/DFS trees (useful in some other problems)
BFS: explore by distance, layers, queueDFS: explore deeply, recursive, stack
• Application of BFS:Bipartite Testing
• Bipartite GraphsA bipartite graph is an undirected graph G = (V, E) in which the nodes can be colored red or blue such that every edge has one red and one blue end.
is a bipartite graph
is NOT a bipartite graph
Examples? How can we check if a given graph is bipartite?
• Simple Observation: Odd Cycles
Lemma. If G has a cycle of odd length, then G is not bipartite
Proof on board
• BFS and Bipartite GraphsLemma. Let G be a connected graph, and let L0, …, Lk be the layers produced by BFS starting at node s. Exactly one of the following holds:(i) No edge of G joins two nodes of the same layer, and G is
bipartite.(ii) An edge of G joins two nodes of the same layer, and G
contains an odd-length cycle (and hence is not bipartite).
• Layer 1 Layer 2 Layer 3 Layer 4Layer 0
BFS and Bipartite GraphsLemma. Let G be a connected graph, and let L0, …, Lk be the layers produced by BFS starting at node s. Exactly one of the following holds:(i) No edge of G joins two nodes of the same layer, and G is
bipartite.(ii) An edge of G joins two nodes of the same layer, and G
contains an odd-length cycle (and hence is not bipartite).
• BFS and Bipartite Graphs
Layer 1 Layer 2 Layer 3 Layer 4Layer 0
Lemma. Let G be a connected graph, and let L0, …, Lk be the layers produced by BFS starting at node s. Exactly one of the following holds:(i) No edge of G joins two nodes of the same layer, and G is
bipartite.(ii) An edge of G joins two nodes of the same layer, and G
contains an odd-length cycle (and hence is not bipartite).
• Algorithm for Bipartite-Testing
Run BFSCheck each non-tree edge
If any has endpoints in same layer, then G is not bipartiteOtherwise, G is bipartite
Running Time?
Recommended | 980 | 3,382 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2023-14 | latest | en | 0.772699 |
https://vustudents.ning.com/group/mth101calculusandanalyticalgeometry/forum/topics/mth101-calculus-and-analytical-geometry-assignment-no-1?commentId=3783342%3AComment%3A3721292&groupId=3783342%3AGroup%3A59539 | 1,586,027,006,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370524604.46/warc/CC-MAIN-20200404165658-20200404195658-00329.warc.gz | 774,344,905 | 22,271 | We are here with you hands in hands to facilitate your learning & don't appreciate the idea of copying or replicating solutions. Read More>>
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# MTH101 -Calculus and Analytical Geometry Assignment NO #1 Discussion and Solutions Spring Fall 2013 Due date:27 nov 2013
Assignment: # 01 (Fall-2013)
Mth101 (Calculus & Analytical Geometry)
Lecture: 01 – 10
Total Marks = 20
Due date: 27-11-2013
INSTRUCTIONS:-
1. In order to attempt this assignment you should have full command on Lecture# 01 to Lecture # 10
1. Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in Lecture # 01 to Lecture # 10.
2. You should concern recommended books for clarify your concepts if handouts are not sufficient.
3. Try to make solution by yourself and protect your work from other students. If we found the solution files of some students are same then it ‘ll be rewarded zero marks to all those students.
4. You are supposed to submit your assignment in Word format any other formats like scan images, PDF format etc will not be accepted and will be give zero marks.
5. Assignments through e-mail will not be accepted after the due date.If there is any problem in submitting your assignment through LMS, you can send your solution file through email with in due date.
6. You are advised to upload your assignment at least two days before Due date.
Q.1 Marks 5
Solve the inequality and write the solution set in interval form.
Q.2 Marks 5
Find the equation of a circle whose diameter has endpoints (4, -1) and (-6, 7).
Q.3 Marks 5
Evaluate the following limit:
Q.4 Marks 5
If and, then find the composite functions .
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### Replies to This Discussion
phir soluction to send kar do please smajny k bad mein apny method sy kar lo ga please reply
search on google then solve the qs its very easy and simple ...
abbas question no. 2 is sama as like this link.
http://www.algebra.com/algebra/homework/Quadratic-relations-and-con...
Good.....
plz guide me in Q3....
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microsoft mathematics is the best software to solve ur question and also help us to ploting a graph in 2D,3D try MICROSOFT MATHEMATICS u can download from microsoft oficial website its a freeware software
Sir mthtype main square root kaise laity hain?
Some one's answers
tariq bhai mere khayal se question no. 4 g may f ki value dale gi q k osne fog(x) bola hai or apne f may g ki value dali hai ye galat hai,
Ayesha question no. 3 kaise solve kare ge phele ki LCM le ge or upper neche value le ge? or phir limit apply kare ge. or agar LCM le g eto values ye hogi na -x3+3x-2 / x3-xx4-1
ab is may limit apply kare gi
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# Polytope of Type {4,8}
Atlas Canonical Name : {4,8}*64a
Also Known As : {4,8|2}. if this polytope has another name.
Group : SmallGroup(64,128)
Rank : 3
Schlafli Type : {4,8}
Number of vertices, edges, etc : 4, 16, 8
Order of s0s1s2 : 8
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,8,2} of size 128
{4,8,4} of size 256
{4,8,4} of size 256
{4,8,6} of size 384
{4,8,3} of size 384
{4,8,8} of size 512
{4,8,8} of size 512
{4,8,8} of size 512
{4,8,8} of size 512
{4,8,4} of size 512
{4,8,4} of size 512
{4,8,10} of size 640
{4,8,12} of size 768
{4,8,12} of size 768
{4,8,3} of size 768
{4,8,6} of size 768
{4,8,6} of size 768
{4,8,14} of size 896
{4,8,18} of size 1152
{4,8,6} of size 1152
{4,8,9} of size 1152
{4,8,20} of size 1280
{4,8,20} of size 1280
{4,8,3} of size 1344
{4,8,4} of size 1344
{4,8,22} of size 1408
{4,8,26} of size 1664
{4,8,28} of size 1792
{4,8,28} of size 1792
{4,8,30} of size 1920
{4,8,15} of size 1920
{4,8,5} of size 1920
Vertex Figure Of :
{2,4,8} of size 128
{4,4,8} of size 256
{6,4,8} of size 384
{3,4,8} of size 384
{8,4,8} of size 512
{4,4,8} of size 512
{8,4,8} of size 512
{6,4,8} of size 576
{10,4,8} of size 640
{12,4,8} of size 768
{6,4,8} of size 768
{14,4,8} of size 896
{5,4,8} of size 960
{18,4,8} of size 1152
{6,4,8} of size 1152
{4,4,8} of size 1152
{9,4,8} of size 1152
{20,4,8} of size 1280
{22,4,8} of size 1408
{10,4,8} of size 1600
{26,4,8} of size 1664
{6,4,8} of size 1728
{28,4,8} of size 1792
{30,4,8} of size 1920
{15,4,8} of size 1920
{5,4,8} of size 1920
{10,4,8} of size 1920
{10,4,8} of size 1920
{6,4,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,4}*32, {2,8}*32
4-fold quotients : {2,4}*16, {4,2}*16
8-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,8}*128a, {8,8}*128a, {8,8}*128b, {4,16}*128a, {4,16}*128b
3-fold covers : {4,24}*192a, {12,8}*192a
4-fold covers : {8,8}*256a, {4,8}*256a, {8,8}*256c, {4,16}*256a, {4,16}*256b, {16,8}*256a, {16,8}*256b, {8,16}*256c, {8,16}*256d, {16,8}*256d, {8,16}*256e, {8,16}*256f, {16,8}*256f, {4,32}*256a, {4,32}*256b
5-fold covers : {4,40}*320a, {20,8}*320a
6-fold covers : {4,24}*384a, {8,24}*384a, {8,24}*384b, {24,8}*384b, {12,8}*384a, {24,8}*384d, {4,48}*384a, {4,48}*384b, {12,16}*384a, {12,16}*384b
7-fold covers : {4,56}*448a, {28,8}*448a
8-fold covers : {4,16}*512a, {8,16}*512a, {8,16}*512b, {16,16}*512a, {16,16}*512b, {16,16}*512d, {16,16}*512e, {16,16}*512g, {16,16}*512h, {16,16}*512k, {16,16}*512l, {8,16}*512c, {16,8}*512c, {8,16}*512d, {16,8}*512d, {8,16}*512e, {16,8}*512e, {8,16}*512f, {16,8}*512f, {8,8}*512a, {8,8}*512b, {8,8}*512c, {4,8}*512a, {8,8}*512e, {4,16}*512b, {4,8}*512b, {4,8}*512c, {8,8}*512j, {8,8}*512k, {4,16}*512c, {4,16}*512d, {8,8}*512p, {8,8}*512r, {8,16}*512g, {8,16}*512h, {4,32}*512a, {4,32}*512b, {8,32}*512a, {8,32}*512b, {32,8}*512b, {8,32}*512c, {8,32}*512d, {32,8}*512d, {4,64}*512a, {4,64}*512b
9-fold covers : {4,72}*576a, {36,8}*576a, {12,24}*576b, {12,24}*576c, {12,24}*576d, {12,8}*576a, {4,8}*576a, {4,24}*576a
10-fold covers : {4,40}*640a, {8,40}*640a, {8,40}*640b, {40,8}*640b, {20,8}*640a, {40,8}*640d, {4,80}*640a, {4,80}*640b, {20,16}*640a, {20,16}*640b
11-fold covers : {4,88}*704a, {44,8}*704a
12-fold covers : {8,24}*768a, {24,8}*768a, {12,8}*768a, {4,24}*768a, {24,8}*768c, {8,24}*768d, {12,16}*768a, {4,48}*768a, {12,16}*768b, {4,48}*768b, {48,8}*768a, {16,24}*768a, {48,8}*768b, {16,24}*768b, {24,16}*768c, {8,48}*768c, {8,48}*768d, {48,8}*768d, {16,24}*768d, {24,16}*768d, {24,16}*768e, {8,48}*768e, {8,48}*768f, {48,8}*768f, {16,24}*768f, {24,16}*768f, {12,32}*768a, {4,96}*768a, {12,32}*768b, {4,96}*768b, {4,24}*768i, {12,8}*768u, {12,24}*768c
13-fold covers : {4,104}*832a, {52,8}*832a
14-fold covers : {4,56}*896a, {8,56}*896a, {8,56}*896b, {56,8}*896b, {28,8}*896a, {56,8}*896d, {4,112}*896a, {4,112}*896b, {28,16}*896a, {28,16}*896b
15-fold covers : {20,24}*960a, {12,40}*960a, {4,120}*960a, {60,8}*960a
17-fold covers : {68,8}*1088a, {4,136}*1088a
18-fold covers : {36,8}*1152a, {4,72}*1152a, {12,24}*1152a, {12,24}*1152b, {12,24}*1152c, {4,8}*1152a, {4,24}*1152a, {12,8}*1152a, {72,8}*1152a, {8,72}*1152b, {8,72}*1152c, {72,8}*1152c, {24,24}*1152a, {24,24}*1152b, {24,24}*1152d, {24,24}*1152e, {24,24}*1152h, {24,24}*1152i, {8,8}*1152a, {8,24}*1152a, {8,8}*1152c, {8,24}*1152c, {24,8}*1152b, {24,8}*1152c, {36,16}*1152a, {4,144}*1152a, {12,48}*1152a, {12,48}*1152b, {12,48}*1152c, {4,16}*1152a, {4,48}*1152a, {12,16}*1152a, {36,16}*1152b, {4,144}*1152b, {12,48}*1152d, {12,48}*1152e, {12,48}*1152f, {4,16}*1152b, {4,48}*1152b, {12,16}*1152b
19-fold covers : {76,8}*1216a, {4,152}*1216a
20-fold covers : {8,40}*1280a, {40,8}*1280a, {20,8}*1280a, {4,40}*1280a, {40,8}*1280c, {8,40}*1280d, {20,16}*1280a, {4,80}*1280a, {20,16}*1280b, {4,80}*1280b, {80,8}*1280a, {16,40}*1280a, {80,8}*1280b, {16,40}*1280b, {40,16}*1280c, {8,80}*1280c, {8,80}*1280d, {80,8}*1280d, {16,40}*1280d, {40,16}*1280d, {40,16}*1280e, {8,80}*1280e, {8,80}*1280f, {80,8}*1280f, {16,40}*1280f, {40,16}*1280f, {20,32}*1280a, {4,160}*1280a, {20,32}*1280b, {4,160}*1280b
21-fold covers : {28,24}*1344a, {12,56}*1344a, {4,168}*1344a, {84,8}*1344a
22-fold covers : {44,8}*1408a, {4,88}*1408a, {88,8}*1408a, {8,88}*1408b, {8,88}*1408c, {88,8}*1408c, {44,16}*1408a, {4,176}*1408a, {44,16}*1408b, {4,176}*1408b
23-fold covers : {92,8}*1472a, {4,184}*1472a
25-fold covers : {4,200}*1600a, {100,8}*1600a, {20,40}*1600b, {20,40}*1600c, {20,40}*1600d, {20,8}*1600a, {4,8}*1600a, {4,40}*1600a
26-fold covers : {52,8}*1664a, {4,104}*1664a, {104,8}*1664a, {8,104}*1664b, {8,104}*1664c, {104,8}*1664c, {52,16}*1664a, {4,208}*1664a, {52,16}*1664b, {4,208}*1664b
27-fold covers : {4,216}*1728a, {108,8}*1728a, {36,24}*1728b, {12,24}*1728b, {12,72}*1728a, {12,72}*1728b, {36,24}*1728c, {12,24}*1728c, {12,24}*1728d, {12,8}*1728a, {12,24}*1728g, {12,24}*1728h, {4,24}*1728a, {4,24}*1728b, {12,8}*1728b, {12,24}*1728i, {12,24}*1728j, {12,24}*1728o, {4,24}*1728e, {4,24}*1728f, {12,8}*1728e, {12,24}*1728q, {12,8}*1728g, {12,24}*1728s, {12,24}*1728u, {12,24}*1728v
28-fold covers : {8,56}*1792a, {56,8}*1792a, {28,8}*1792a, {4,56}*1792a, {56,8}*1792c, {8,56}*1792d, {28,16}*1792a, {4,112}*1792a, {28,16}*1792b, {4,112}*1792b, {112,8}*1792a, {16,56}*1792a, {112,8}*1792b, {16,56}*1792b, {56,16}*1792c, {8,112}*1792c, {8,112}*1792d, {112,8}*1792d, {16,56}*1792d, {56,16}*1792d, {56,16}*1792e, {8,112}*1792e, {8,112}*1792f, {112,8}*1792f, {16,56}*1792f, {56,16}*1792f, {28,32}*1792a, {4,224}*1792a, {28,32}*1792b, {4,224}*1792b
29-fold covers : {116,8}*1856a, {4,232}*1856a
30-fold covers : {60,8}*1920a, {4,120}*1920a, {12,40}*1920a, {20,24}*1920a, {120,8}*1920a, {8,120}*1920b, {8,120}*1920c, {120,8}*1920c, {24,40}*1920a, {40,24}*1920a, {40,24}*1920b, {24,40}*1920c, {60,16}*1920a, {4,240}*1920a, {12,80}*1920a, {20,48}*1920a, {60,16}*1920b, {4,240}*1920b, {12,80}*1920b, {20,48}*1920b
31-fold covers : {124,8}*1984a, {4,248}*1984a
Permutation Representation (GAP) :
```s0 := ( 2, 4)( 3, 6)(10,13)(12,15);;
s1 := ( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10)(11,13)(12,14)(15,16);;
s2 := ( 2, 3)( 4, 6)( 5, 8)( 9,11)(10,12)(13,15);;
poly := Group([s0,s1,s2]);;
```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
```
Permutation Representation (Magma) :
```s0 := Sym(16)!( 2, 4)( 3, 6)(10,13)(12,15);
s1 := Sym(16)!( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10)(11,13)(12,14)(15,16);
s2 := Sym(16)!( 2, 3)( 4, 6)( 5, 8)( 9,11)(10,12)(13,15);
poly := sub<Sym(16)|s0,s1,s2>;
```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
```
References : None.
to this polytope | 4,560 | 8,109 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2023-40 | latest | en | 0.613891 |
https://brainly.com/question/301857 | 1,484,996,236,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560281069.89/warc/CC-MAIN-20170116095121-00272-ip-10-171-10-70.ec2.internal.warc.gz | 798,808,725 | 9,383 | # Suppose you rent a limousine for a formal reception. The bill for the efenimg evening is \$53.00. A tax of 6% will be added and you want to tip the chuaffer 20% for excellent driving. How much will you pay in total? (please show step by step)
2
by dough
## Answers
2015-02-11T19:54:06-05:00
Okay when doing percentages remember 6% of 100%
so in decimal form it looks like 0.06
0.06 x 53.00
then you would find 20% of 53.00 53.00 x .20
so then add 53 + .2(53) + .06(53) = 65.72
sorry the answer should actually be 66.78.
2015-02-11T19:54:37-05:00
\$53 * .06 = \$3.18
\$53 * .2 = \$10.60
Multiply by the percent (per cent, out of 100, 100 being the whole(1) ) so 6% would be .06 and 20% would be .2
add it all together and
\$53 + \$3.18 + \$10.60 = \$66.88 | 291 | 764 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2017-04 | latest | en | 0.868585 |
https://sciencing.com/calculate-many-rings-atom-8550529.html | 1,726,832,236,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652246.93/warc/CC-MAIN-20240920090502-20240920120502-00047.warc.gz | 455,226,341 | 86,466 | # How to Calculate How Many Rings in an Atom
••• Hemera Technologies/PhotoObjects.net/Getty Images
Print
In order to calculate how many rings are in an atom, you need to know how many electrons the atom has. The rings, also known as electron shells, can hold a variable amount of electrons depending on its shell number. For example, the first shell can hold only two electrons. If the atom has more than two electrons, then that atom must have more than one ring. To determine how many electrons a shell can hold, you use a formula that calculates the number of electrons possible in a given shell. You need to fill one shell, starting with shell number one, before filling another. The last shell does not have to be full of electrons.
Find the number of electrons in the atom by using the periodic table. The number of electrons is equal to the atom's atomic number, which is at the top left of the element. For example, assume you want to know how many rings are in the element neon. Neon on the periodic table has an atomic number of 10, so it has 10 electrons.
Square the ring number, then multiply the result by two. Check to see if the ring is full or not. If the ring is full, then move to the next ring. If the ring is not full, then that is how many rings are needed. Starting with the first ring, 1 squared = 1; and 1 x 2 = 2, so that is the maximum number of electrons that ring one can hold. Subtract this from your element's atomic number. Still using neon as an example, you now have eight remaining electrons.
Calculate the number of electrons in the next ring. Using the formula, 2 squared = 4; and 4 x 2 = 8, which indicates that the second ring can hold a maximum of eight electrons. In our example, we had eight remaining electrons, so this ring is full and no electrons remain. Therefore, an atom of neon has two rings. | 419 | 1,846 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2024-38 | latest | en | 0.931305 |
http://www.ams.org/publicoutreach/feature-column/fcarc-199804 | 1,695,351,932,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506320.28/warc/CC-MAIN-20230922002008-20230922032008-00002.warc.gz | 47,494,993 | 11,846 | Let S be the surface which is the graph of
z = f(x,y) = ax2 + 2bxy + ay2.
Equivalently,
f(x,y) = (x,y)A(x,y)t,
where A is the matrix
The character of S depends on the eigenvalues of the matrix A:
If both eigenvalues are positive, S is bowl-shaped, opening up.
If both eigenvalues are negative, S is bowl-shaped, opening down.
If one eigenvalue is positive and the other is negative, S issaddle-shaped.
Here is a picture of S for a particular choice of a andb, together with the eigenvalues of the corresponding matrix A.This picture is a frame from a movie, showing how S changes as Avaries. Clicking on the image will bring up the movie.
This frame and movie are © 1998 Juha Haataja and the Center for ScientificComputing, Finland.
- Steven Weintraub | 198 | 756 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2023-40 | latest | en | 0.898649 |
http://www.reddit.com/r/math/comments/1f2urn/why_is_the_riemann_hypothesis_not_called_the/ca6bstj?context=3 | 1,404,975,324,000,000,000 | text/html | crawl-data/CC-MAIN-2014-23/segments/1404776404630.61/warc/CC-MAIN-20140707234004-00051-ip-10-180-212-248.ec2.internal.warc.gz | 438,767,526 | 14,670 | you are viewing a single comment's thread.
[–] 51 points52 points
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I'm not a number theorist, but I think it's because several theorems have the form, "If the Riemann hypothesis is true, then _________." In other words, it's more interesting for its possible implications -- i.e., as a hypothesis for proving other things -- than merely its own truth or falsity.
[–][S] 6 points7 points
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Assuming that to be true, wouldn't it also have applied to the Poincaré Conjecture before 2002?
[–]Geometry/Topology 6 points7 points
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Why so? What are the major implications of the Poincaré Conjecture for other problems in mathematics?
[–] 0 points1 point
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The poincare conjecture helps with dynamical systems a lot, believe it or not. It's about homeomorphisms, and manifold stability. Basically, its helpful for phase space. At least as far as I've seen.
[–]Geometry/Topology 0 points1 point
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Can you give an example, or a link to an example?
[–] 0 points1 point
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The wikipedia page actually explains it best when explaining how it all came about. I may have been thinking of the Poincare Bendixson theorem, but Poincare's work just shows up literally everywhere in NL dynamics.
Ricci flows were developed, along with a lot of Hamilton's other ideas. Here's the description of how it was proven, which should explain this a bit more:
Perelman proved the conjecture by deforming the manifold using the Ricci flow (which behaves similarly to the heat equation that describes the diffusion of heat through an object). The Ricci flow usually deforms the manifold towards a rounder shape, except for some cases where it stretches the manifold apart from itself towards what are known as singularities. Perelman and Hamilton then chop the manifold at the singularities (a process called "surgery") causing the separate pieces to form into ball-like shapes. Major steps in the proof involve showing how manifolds behave when they are deformed by the Ricci flow, examining what sort of singularities develop, determining whether this surgery process can be completed and establishing that the surgery need not be repeated infinitely many times.
[–]Geometry/Topology 0 points1 point
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I understand the relevance of Poincare-Bendixson theorem for NL dynamics, we used it heavily in my NL dynamics class. However, I don't think the Poincare conjecture is as useful as Poincare-Bendixson. Your reference to the method of proof, using Ricci flows, demonstrates that the techniques developed by Perelman and Hamilton (among others) are very useful, and indeed I know that flows have been used to prove the geometrization and uniformization conjectures. However, this does not mean that the Poincare conjecture is useful per se; Fermat's last theorem isn't particularly useful, but the modularity conjecture is, etc. Contrastingly, the Riemann Hypothesis is directly useful for proving other results in number theory. You could treat RH as a black box, without knowing the proof, and develop a great deal of new results.
[–] 0 points1 point
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Yes, you've raised a very puzzling question. the only reason I said something was that I heard about it while discussing a nl dyn problem with one of my first chaos profs. Now I can't remember what it was though, and its eating at me a great deal.
Now I'm questioning whether or not it was even useful or just interesting when I heard it. im going to look into this actually because I'm really curious now.
The methods being good isn't direct usefulness, I know, that's a bit wishy washy. | 913 | 4,005 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2014-23 | latest | en | 0.969852 |
http://www.dklevine.com/bin/workshops-php/discuss/discuss.php3?showID=76528000000000069 | 1,513,546,258,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948597585.99/warc/CC-MAIN-20171217210620-20171217232620-00375.warc.gz | 345,625,879 | 2,550 | "Inside every small problem is a large problem struggling to get out."
## Thread and Full Text View
Respond to the question: Hawk Dove game?
09/09/2013 08:59 PM by Q-man; Hawk / Dove game
If both players act like hawks they fight til the end where the victor will receive a payoff of 20 and the loser will loose 40 points. The chance of winning for each player is the same.
If both players choose to act Dovish and compromise each player receives 10 points. If one player acts Hawkish when the other chooses to act Dovish then the former receives 30 points while the later gets 0.
Express the above game in strategic form and find all Nash Equilibrium points, Discuss each of these equilibria with respect to their corresponding game values.
My solution gives only one Nash Equilibrium, although the wording of the question implies there is more than one solution.
My payoffs are (player 1, player 2) where H = act Hawkish and D = act Dovish.
(H,H) = (-10,-10)
(H,D) = (30,0)
(D,H) = (0,30)
(D,D) = (10,10)
With (D,D) being my only solution.
[Manage messages] | 273 | 1,065 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2017-51 | latest | en | 0.942826 |
https://www.candlepowerforums.com/threads/the-dangers-of-working-with-a-high-voltage-supply.247663/#post-3152642 | 1,675,030,981,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499768.15/warc/CC-MAIN-20230129211612-20230130001612-00380.warc.gz | 720,829,116 | 34,399 | The Dangers of Working with a High Voltage Supply
D-Dog
Enlightened
I recently acquired a new lab supply which was originally meant for an electrophoresis table. As such it has three modes of output... constant voltage, constant power, constant current. (1000v, 200watts, 400ma)
I understand what constant current and constant voltage are, however, I'm confused by constant power. I'm using the supply to charge a highrate SLA and while 400ma will get the job done (highest it goes on constant current), constant power is adjustable from 0 to 200 watts and being able to charge the battery a little faster would be nice.
I could do constant voltage, however, it is way too hard to modify the voltage with precision being as one pot brings it from 0 all the way to 500/1000 volts... imagine trying to get 13.6 on that
As I figure it, constant power outputs the number of watts you specify regardless of output voltage, however, this sounds just like CC which is why I'm confused.
I think if I select 2 watts then it puts out 500ma at 4 volts or 250ma at 8, however, I don't want to risk anything until I'm sure
Any help is appreciated as I try to figure this out... and yes, 1000volts is dangerous...
Last edited:
ctom
Newly Enlightened
Re: Constant Voltage vs Constant Current vs Constant Power
A constant power power supply will vary the output voltage and current to maintain a constant power level to the load (power = voltage*current) while a constant current supply will only vary the output voltage in an attempt to maintain a constant current to the load. If you can get hold of the manual, it should give you a voltage and current curve for a given power output. Without that information, it would be hard to predict what the voltages and currents will be for a particular power output short of mapping out the output with a variable resistor rated for high power.
As I'm sure you are aware, that power supply can be very dangerous! For example, in the constant current mode, if you were to disconnect the load (battery) from the power supply, the output voltage would most likely rise to the maximum voltage (1000 volts). The insulation on your wire leads may not be rated that high...
D-Dog
Enlightened
Re: Constant Voltage vs Constant Current vs Constant Power
Yep, The unit has two modes, 500v/400ma/200watts and 1000v/200ma/200watts. The wire I use is rated for 2000 volts and even then I keep it on the 500volt max setting figuring every little bit of safety helps
So the question remains if I connect a 12 volt load to the supply in constant power mode will it feed it 2 watts of power continuous at the battery's voltage or at 500v? I will try to look for a manual which may give these curves.
The supply is an ISCO 493 Electrophoresis Power Supply
/Begin Safety Rant
But yea, just reiterating again how dangerous a supply like this can be. I wouldn't want anyone else to try working with this supply unless they really knew what they were doing. Which equation is the one which tells you power through a resistor? I think it's P = V^2 / R The resistance of skin is know so you can see how each little increase in voltage makes the result much more deadly. Or is it just Ohm's Law rearranged I = V / R ? Either way electricity is not something to be taken lightly. A defibrillator pumps 160 Joules or so into you to try to save your heart. The main caps in this supply along can pump out 10x that amount and I'm sure some supply are even more dangerous. It only takes one mistake to end a life... and there is no fuse inside your body to save you (I can't recall how many times I tried measuring voltage on the current mode of my DMM only to see a spark...)
/End Safety Rant
ctom
Newly Enlightened
Re: Constant Voltage vs Constant Current vs Constant Power
Again, without the specifications available (or the circuit schematic), it's hard to predict the output. As an experiment, you could connect an ammeter in series with the battery and power supply. If the supply is outputting 0.167 amps (2 watts/12 volts), you should be OK. A caveat to this method is that you need to check the specs for your battery - if it is a lead acid battery, it may not tolerate a trickle charge rate of 167 ma continuously after the battery is fully charged. Most lead acid batteries are charged with a constant voltage of 13.6 to 13.8 volts with some form of current limit.
D-Dog
Enlightened
Re: Constant Voltage vs Constant Current vs Constant Power
Here is a link to the schematic for my model. If you need to know anything else just ask, I'm sure I can hunt it down
http://www.eisenhower.org/eric/isco/493sch.pdf
PeAK
Enlightened
Re: Constant Voltage vs Constant Current vs Constant Power
I recently acquired a new lab supply .
.
.
.
I understand what constant current and constant voltage are, however, I'm confused by constant power. I'm using the supply to charge a highrate SLA and while 400ma will get the job done (highest it goes on constant current), constant power is adjustable from 0 to 200 watts and being able to charge the battery a little faster would be nice.
Comment:
As P=V*I is finite at 200Watts, the highest current (400mA) will correspond to a voltage of V=P/I=200/0.4=500V. For a 1000V output, this means that the current must drop (to 0.2A).
While it might be possible that your unit can put out higher currents (same power) at lower voltages (examples: 100V at 2A or 25 V at 8A). The max constant current setting often specifies the maximum current available when used in the dual mode as a current source.
D-Dog said:
I could do constant voltage, however, it is way too hard to modify the voltage with precision being as one pot brings it from 0 all the way to 500/1000 volts... imagine trying to get 13.6 on that
As I figure it, constant power outputs the number of watts you specify regardless of output voltage, however, this sounds just like CC which is why I'm confused.
To test how well the power output mode work, you can set the power output to 2 watts and plug different resistor values that differ in ratios of 2 and 4 to see if either voltage changes to put out a different voltage for each resistor value.
Since P=V**2/R, the supply should scale the voltage so that each time the resistor value quadruples; the voltage will double (and the current will reduce at the same time). In this mode, you tax the supply when you add lower resistance values that draw more current. So first you need to do is to calculate the minimum load for the 2 watt setting and the 0.4A current limitation, simultaneously.
Since
Rmin = P/(Imax*Imax) from P=(I**2)/R
=2/(0.4*0.4)=12.5
So try loads of 18 ohms, 36 ohms and 72 ohms to see if the corresponding voltages are
V= sqrt (P*R)= sqrt(2*18)=6V (& 8.4V and 12V)
I think if I select 2 watts then it puts out 500ma at 4 volts or 250ma at 8, however, I don't want to risk anything until I'm sure
Any help is appreciated as I try to figure this out... and yes, 1000volts is dangerous, I know what I'm dealing with
D-Dog
Enlightened
Re: Constant Voltage vs Constant Current vs Constant Power
Remember what I was saying about the dangers of high voltage? Even if you are usually careful?
I'm typing this with one hand because my other one has two second degree burns. I'm quite ok, however, don't ever assume voltage plays nice.
Usually a catastrophic failure is the result of many small mishaps. What follows is what just happened 15 minutes ago.
I had supply set to constant current 300ma charging small AW CR123A cell. It was totally dead to cutoff so I figured on having at least 2 hrs. I went to take a shower and voltage reading 3.9 volts... all good.
Took longer than I thought and got back saw voltage at 12.64 volts (this is 3.7 volt nominal) :-O Must not have been as dead as I thought or because it's old the capacity is lower as it was only on there for an hour)
Not wanting a fire I immediately go to disconnect leads(secured with magnets) to battery. (aka I panic and make stupid mistake in sequencing)
My hands still being wet from shower I see a small spark and feel electrical jolt as I grab negative lead. (I thought the battery circuitry would cutoff all current to prevent overcharge... wrong) Arm retracts and disconnects from source which is now at 500 volts 300ma (remember constant current). I kill power to source and remove battery which is rather warm. I put battery in fridge to contain explosion however, there is none. I remember Where the leads touched me and notice two small white lumps... oh no :-(
So what did I do wrong/right and why am I still alive?
When I saw high voltage condition I panicked (It's 3am here way to late to charge cells)
I'm very tired and reacted without thinking (If I killed the power first no harm done to anything)
I charged a li-ion cell (protected) without being present in room
I had supply set to constant current which will supply 0-500volts at 300ma
incorrectly assuming a 750mah cell would take at least 2 hrs to charge.
Why I'm alive: I followed a bit of common sense and only used one hand, even in my panic. Such rules can save your life and a circuit through your hand is better than one through my heart. I have 2 blister burns but I'm alive, alert, etc... perfectly fine. I've done this once before around 3 years ago and while not fun (330 volts that time), follow the one hand rule and you will live to tell about it. It only takes 40ma through your heart, I had 300ma through my hand.
So now you can all yell at me and tell me how lucky I am to still be posting here... I deserve it. I made sure my leads were rated for 2000 volts, made sure to calculate with headroom how long the cell would take to charge, then went and left the thing there. If I was charging my 18aH SLA all would have been fine as that can bleed heat a lot better than an cr123a. I thought it would be interesting to see if I could charge it on the supply without thinking everything out... I payed...
Anyways, never assume and remember voltage can kill... it doesn't care who you are, what degree you have or what you ate for dinner...
Also remember current takes the path of least resistance. For me that was my middle finger to my thumb. I urge anyone who is working on similar supplies to only use one hand... it may just save your life
-D-Dog aka (Dumb)-Dog
IMSabbel
Enlightened
You have been VERY VERY VERY lucky.
Disregarding the fact that you might be dead, the usage of a PSU of that caliber for tasks like charging a RCR123A is like nuking sparrows.
If _anything_ ever went wrong (and it could, as you used it in absence), you could have easily burned your house down, etc.
PeAK
Enlightened
Re: Constant Voltage vs Constant Current vs Constant Power
D-Dog, good to see you survive the experience and take one for the forum...hope your hand has healed. I had a look at your power supply and do not see any controls to limit the voltage output while in constant current mode:
Remember what I was saying about the dangers of high voltage? Even if you are usually careful?
I'm typing this with one hand ...
.
.
.
So what did I do wrong/right and why am I still alive?
.
.
.
If you provided a path to ground with your feet, the "current" would possibly have travelled from your hand (then through your heart) and then to your foot. The one handed rule means that the path provided will be "local" and the worst that could happen is to lose your hand.
The idea of a safety ground (third pin in a plug) is provide this preferential path (i.e. lower resistance) rather than travel via your heart/foot.
D-Dog said:
I had supply set to constant current which will supply 0-500volts at 300ma
.
.
.
Most units will have a voltage limit control that is set by open circuiting the output and then setting the limit. Remember that a current source functions by raising the voltage until the current desire current is achieved. With an open circuit it tries to raise it to an infinite number.
D-Dog said:
Anyways, never assume and remember voltage can kill...
When I supervised a lab course, I've always told the students that it is the current that kills...the voltage initiates the current, though. So have your current limit on. If the supply does not contain a current limit...throw it away!!!
D-Dog said:
.
.
.
Also remember current takes the path of least resistance. For me that was my middle finger to my thumb. I urge anyone who is working on similar supplies to only use one hand... it may just save your life
.
.
.
Correct...raise one to the "one hand rule" lovecpf
PeAK
D-Dog
Enlightened
Just an update after a night's worth of sleep.
While what I did was undoubtedly stupid, what I did before wasn't. The sad part is that if I hadn't freaked about the voltage (being so tired) and only flipped one switch then there would have been no problem.
Now for the dummy proof (probably why the result wasn't a lot worse)
*You are right, no voltage limit in CC mode, however, I did have a choice between 500v and 1000v and went with 500 for obvious reasons.
*I located the PSU on a table above natural hand height with only enough space to the right of the psu for the battery I'm charging and one hand. This was so even if I forgot the 1hand rule it would be almost impossible to stick two in there.
*The table height is so that if you build a circuit through your hand causing the muscles to contract, the hand pulls back and after the jolt returns to an "at ease" position next to your body. Because of this I suffered no internal burns, only 2 little blisters on the surface... speaking of which...
...back to typing with both hands a mere few hours later... short exposure and 1 hand saved me plus 500v probably helped too although if it was 1000v then the current would have been lower and output power the same.
Oh yea, time to thank AW for putting such a circuit on his battery. The cell read 12.6 volts while chaging but once I took it off and let it cool dropped to 4.3 or so. After I put in the refrig to up the internal resistance it went down to 4.2 Still don't trust it anymore and will buy another but glad the circuit did its job.
Also thinking of putting in a voltage pot even in cc mode because I agree if I had even crude voltage adjustment (lets say I set it for 10 volts) no shock and just a ruined cell If anyone want to help with this it will be appreciated as I have the full schematic, however, don't really have the time right now to look into it.
Last edited:
Armed_Forces
Enlightened
..you're obviously working on a Darwin Award. Hopefully one less in the gene pool. Carry on.
D-Dog
Enlightened
I don't know if the meant "just kidding" or not, however, this is the first time in 5 years I've injured myself to any extent regarding the use of high voltages and it was a lapse in concentration which did it along with trying to fit too much into one day. My point was that it doesn't matter if you are a power engineer or a DIY flashaholic, this sort of accident can happen to anyone (exploding bulbs, exploding cells come to mind right away). Many people don't want to admit to anyone they made a mistake, however, I decided to share mine to hopefully help others also thinking of cutting corners by using a supply not meant for what they are trying to do.
Also, if you were kidding than , however, if you were serious then I don't find it amusing to toy with the idea of my life as "one less in the gene pool"...
I've decided come Monday the supply is going back as I don't have the time to add voltage regulation in CC mode and I have a much safer supply I can use in its place. I'm also using high voltage gloves from now on if I ever use CC mode on another charger which can output more than 50 volts...
The blisters last a week, however, the knowledge gained is for a lifetime, right?
Also, some people I know were talking about their night (or what they remember of it) last night. One puked on her phone, another ran into a light and than fell down a flight of stairs...all in one night while drunk. If anything they are more likely candidates... or at least for a liver transplant than the guy who completed a circuit and got 2 blisters. The guys who fell ended up in the ER while the other wished she was dead... I remained alert enough to remove my hand from the supply, kill the voltage, move the battery to a cool location and then brush my teeth
I don't drink so "alert enough" was in regards to going into shock or the like...
Perhaps I haven't done a great deal putting out what actually happened, however, when I say blisters I mean one the size on the tip of a pencil, the other about 1/3 the surface area of a dime. No skin was charred and my burns" don't look anything like what you see when you search electrical burn on google images. The perception of pain was very similar to a shock pen which leads me to believe the exposure was so short/ the supply turns off if it detects a short. I still don't know how the battery could possibly absorb even half its capacity in an hour at 300ma at lets say 4 volts, however, the volt meter didn't lie and the voltage of the cell was 4.4 volts resting.
Last edited:
LuxLuthor
Flashaholic
D-Dog, I'm glad you are ok. Honestly, I can't imagine someone using that for lithium battery charging...just thinking casually of all the things that can go wrong...especially with magnets!
And with due respect, in your OP, your asking about constant power, and only getting a few responses before using it is not consistent with "... and yes, 1000volts is dangerous, I know what I'm dealing with " I don't believe you understood what you were using, nor the most elementary fundamentals of electricity to have used that PS.
I was like....tell me he didn't touch active, constant output charging leads with wet hands...even as "a being tired mistake." It's up to you, but with those knee-jerk (in a panic) dangerous reactions, I would not only count your blessings as you have....I would make sure to switch to a totally safe setup--no matter how much it costs. No way would I switch to another PS as your charging source which is your apparent next step. Given the plethora of safe lithium battery chargers, what's the point given what happened?
Please don't be offended by my comments, but I'm anticipating there will be another time you are distracted, reacting in a panic, or being forced to deal with a lithium fire, perhaps with wet hands. If for some reason you feel you MUST use a PS, at least switch to safe lithium chemistries as another step.
BVH
Flashaholic
CPF Supporter
Isn't there also a potential of back-feeding into the power supply when the batts are full or near full? Are you using a Schotkey diode to prevent this? Before I knew of this, I blew a \$500 Mastec 30V, 50 Amp PS. Not charging batteries, but by making a "hand connection too slowly" to an HID ballast and missing and re-contacting. The spike backfed the PS and killed it. My new one is protected by a 60 Volt, 80 Amp Schotkey diode.
D-Dog
Enlightened
I won't disagree with anything you said as your 100% right. I was using the supply to charge large SLA batteries and that's where I should have ended it. Those batteries (18aH) can absorb overcharge much better (at 300ma), not to mention have a voltage curve which rises much slower. I would have had a lot of time to react and would have been able to shut of the supply. The use of magnets was equally stupid ... it was because of them coupled with the small battery size that cause me to touch the leads. Also, for clarification, I completed a circuit between the anode of the battery and the conducting lead when the magnet snapped back to the battery, not lead to lead as I only had 1 hand in there
Don't ask why I charged a lithium battery (it was protected at least ) with a CC charger... like I said that was really stupid. I did have a friend in the room at the time who knew to turn off the charger if anything looked fishy (by unplugging it from the wall... not touching the leads ), however, my multimeter shuts off automatically to conserve power and thus the last reading he saw was evidently normal (I think he said 4.15 volts).
My hands were dry when I removed the leads, however, having been in the shower I can imagine the water content of the sub-skin would have been higher. I also have a Pyramid PSU which is 0-15 volts (for the SLA's) so from now on I'm using that, getting rid of this one on Monday.
You right in my stupidity and also in my being naive in terms of electricity. I know the equations and understand schematics, that's what I'm getting my degree in (thesis on the thermal efficiency of variable pulse charging), however, especially with electricity not being something you can visually quantify, until yesterday I hadn't been shocked to any degree for 5 years. That's a while, and in that time I "forgot" just how dangerous the electricity can be (as lame as that sounds). A logger has the spinning blade of a chainsaw to remind him of the danger, a pilot the armed guards and oxygen masks. With electricity you have a high voltage warning and different color wiring. We can't see potential or current, we can't observe electron drift with the naked eye. We know it's there but measuring potential from a DMM gives us a number we plug into an equation, it's not real until the difference is running through you.
Perhaps I thought I had a good enough idea of battery capacity to judge when the charge should be terminated. Perhaps I didn't think of the possibility the magnet woudl try to snap back and my hand would be in the way. Whatever the reason, I made a mistake and payed for it. I'm glad I'm fine and certainly don't understand what I was thinking when I decided to charge one more battery (a small lithium one at that). Like I said, it was a mistake that will stay with me for quite a while.
D-Dog
Enlightened
Isn't there also a potential of back-feeding into the power supply when the batts are full or near full? Are you using a Schotkey diode to prevent this? Before I knew of this, I blew a \$500 Mastec 30V, 50 Amp PS. Not charging batteries, but by making a "hand connection too slowly" to an HID ballast and missing and re-contacting. The spike backfed the PS and killed it. My new one is protected by a 60 Volt, 80 Amp Schotkey diode.
Fairly certain there is a backflow-prevention diode inline with the high voltage output... going to check the schematic now
BVH
Flashaholic
CPF Supporter
Seems to me backflow prevention should be a normally "designed in" and included component in power supplies. Wonder why not in my 1st Mastech.
D-Dog
Enlightened
I actually don't see any main diode although there are ones preventing against reverse polarity and ones protecting most of the vital integrated circuit components. Kinda odd that it isn't present on this either although the age of the supply could be a factor. In fact I don't see over-current either although by now I"m fairly tired (the PSU is unplugged tonight )
LuxLuthor
Flashaholic
D-Dog, again the most important thing is that you are ok, and we appreciate you sharing the event with us. I tried to word my post in a way that would sound "constructively merciful." What really caught my attention, and still does with your last post, is now switching to a 15V Pyramid PS to charge.
Personally, I would never use my various Pyramid PS's to charge Lithium Cobalt cells. Not even my adjustable Mastec 30V 20A. Could I use them for that purpose, and understand how to monitor the charging? Yes. Will I? No. Why? Because "poop" happens. A family member has an emergency. You hear a loud crash upstairs. You see your dog running out the back door about to get skunked. 15, 20, 30+ minutes go by and you suddenly realize you forgot about your charging.
I don't see why you don't error on the side of safety and just use a lithium charger with CC/CV, and 4.2V termination. Then you are not exposing yourself to a distraction/panic situation where you would perhaps again worry about overcharge. Look at the cost effectiveness of being safe.
Obviously, as you progress in your thesis and education you will have more certainty and build in more safeguards. Please see this as me trying to be helpful and keep all of us safe. :wave:
Linger
Flashlight Enthusiast
Theoretical understanding and practical application are very different.
Regardless of the exact cause, this reads a bit like a horror story. Beside the shock thing, the first 'accident' was spiking the cell above 12v. I can't ever see calculating charge times before hand to be a viable, long-term 'free lumens' plan. Maybe I'm too ignorant of this area to see the deeper implications, but i'm completely unconvinced by any of the 'safety' measures described.
Some places engineer for 4 levels of safety, each action in a sequence works to protect you during the subsequent steps. Even if a single step fails completely it is so contained by the previous actions that it is not possible for any harm to come. A person would have to fail three procedures before the next step even exposes them to personal risk. Ideally the system is designed that you may not proceed unless the previous safeguard has been successfuly initiated. In this ideology, you have to perform a complex set of actions to successfully put yourself at risk.
In your current set-up, you have to perform a complicated set of actions to remain safe. | 5,930 | 25,430 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2023-06 | latest | en | 0.95248 |
https://www.convert-measurement-units.com/convert+Millimho+to+Picomho.php | 1,718,461,301,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861594.22/warc/CC-MAIN-20240615124455-20240615154455-00706.warc.gz | 659,347,619 | 13,425 | Convert m℧ to p℧ (Millimho to Picomho)
## Millimho into Picomho
numbers in scientific notation
https://www.convert-measurement-units.com/convert+Millimho+to+Picomho.php
# Convert Millimho to Picomho (m℧ to p℧):
1. Choose the right category from the selection list, in this case 'Electric conductance'.
2. Next enter the value you want to convert. The basic operations of arithmetic: addition (+), subtraction (-), multiplication (*, x), division (/, :, ÷), exponent (^), square root (√), brackets and π (pi) are all permitted at this point.
3. From the selection list, choose the unit that corresponds to the value you want to convert, in this case 'Millimho [m℧]'.
4. Finally choose the unit you want the value to be converted to, in this case 'Picomho [p℧]'.
5. Then, when the result appears, there is still the possibility of rounding it to a specific number of decimal places, whenever it makes sense to do so.
With this calculator, it is possible to enter the value to be converted together with the original measurement unit; for example, '324 Millimho'. In so doing, either the full name of the unit or its abbreviation can be usedas an example, either 'Millimho' or 'm℧'. Then, the calculator determines the category of the measurement unit of measure that is to be converted, in this case 'Electric conductance'. After that, it converts the entered value into all of the appropriate units known to it. In the resulting list, you will be sure also to find the conversion you originally sought. Alternatively, the value to be converted can be entered as follows: '60 m℧ to p℧' or '22 m℧ into p℧' or '92 Millimho -> Picomho' or '37 m℧ = p℧' or '85 Millimho to p℧' or '38 m℧ to Picomho' or '50 Millimho into Picomho'. For this alternative, the calculator also figures out immediately into which unit the original value is specifically to be converted. Regardless which of these possibilities one uses, it saves one the cumbersome search for the appropriate listing in long selection lists with myriad categories and countless supported units. All of that is taken over for us by the calculator and it gets the job done in a fraction of a second.
Furthermore, the calculator makes it possible to use mathematical expressions. As a result, not only can numbers be reckoned with one another, such as, for example, '(11 * 86) m℧'. But different units of measurement can also be coupled with one another directly in the conversion. That could, for example, look like this: '324 Millimho + 972 Picomho' or '95mm x 66cm x 46dm = ? cm^3'. The units of measure combined in this way naturally have to fit together and make sense in the combination in question.
The mathematical functions sin, cos, tan and sqrt can also be used. Example: sin(π/2), cos(pi/2), tan(90°), sin(90) or sqrt(4).
If a check mark has been placed next to 'Numbers in scientific notation', the answer will appear as an exponential. For example, 1.975 308 624 ×1020. For this form of presentation, the number will be segmented into an exponent, here 20, and the actual number, here 1.975 308 624. For devices on which the possibilities for displaying numbers are limited, such as for example, pocket calculators, one also finds the way of writing numbers as 1.975 308 624 E+20. In particular, this makes very large and very small numbers easier to read. If a check mark has not been placed at this spot, then the result is given in the customary way of writing numbers. For the above example, it would then look like this: 197 530 862 400 000 000 000. Independent of the presentation of the results, the maximum precision of this calculator is 14 places. That should be precise enough for most applications. | 907 | 3,685 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2024-26 | latest | en | 0.831987 |
https://socratic.org/questions/how-do-you-write-the-fraction-2-8-in-simplest-form | 1,585,518,269,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370496227.25/warc/CC-MAIN-20200329201741-20200329231741-00535.warc.gz | 718,572,872 | 6,074 | # How do you write the fraction 2/8 in simplest form?
$\frac{1}{4}$
It is $\frac{1}{4}$ because you find a common number that both the numerator and the denominator can be divided by. In this case, it is $2$.
$\frac{2}{2} = 1 \text{ }$ and $\text{ } \frac{8}{2} = 4$
You can't divide $\frac{1}{4}$ anymore so that is the final answer. | 111 | 335 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2020-16 | latest | en | 0.866453 |
https://www.gradesaver.com/textbooks/science/physics/essential-university-physics-volume-1-3rd-edition/chapter-19-exercises-and-problems-page-349/29 | 1,695,823,811,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510300.41/warc/CC-MAIN-20230927135227-20230927165227-00402.warc.gz | 872,158,051 | 12,022 | ## Essential University Physics: Volume 1 (3rd Edition)
(a) $1700MW$ (b)$0.43$ (c) $500K$
(a) We know that $P_c=mc\frac{\Delta T}{dt}$ We plug in the known values to obtain: $P_c=(2.8\times 10^4)(4184)(8.5)=996MW$ and $P_h=P_c+W$ $\implies P_h=996+750=1700MW$ (b) $e=1-\frac{Q_c}{Q_h}$ We plug in the known values to obtain: $e=1-\frac{996}{1746}=0.43$ (c) $e=1-\frac{T_c}{T_h}$ We plug in the known values to obtain: $0.43=1-\frac{273+15}{T_h}$ This simplifies to: $T_h=500K$ | 201 | 477 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2023-40 | latest | en | 0.6883 |
http://booksbw.com/index.php?id1=4&category=mathematical&author=boyce-we&book=2001&page=398 | 1,544,803,063,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376825916.52/warc/CC-MAIN-20181214140721-20181214162221-00455.warc.gz | 42,395,233 | 4,931 | Books in black and white
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# Elementary differential equations 7th edition - Boyce W.E
Boyce W.E Elementary differential equations 7th edition - Wiley publishing , 2001. - 1310 p.
ISBN 0-471-31999-6
Previous << 1 .. 392 393 394 395 396 397 < 398 > 399 400 401 402 403 404 .. 486 >> Next
n n n n
n=1
b = c /(X - u), n = 1,2,... and the desired solution is
n n n *
obtained [after setting 6 (x) = P (x)].
n 2n-1
Section 11.5, Page 666
1a. Since u(x,0) = 0 we have Y(0) = 0. However, since the other two boundaries are given by y = 2x and y = 2(x-2) we cannot separate x and y dependence and thus neither X nor Y satisfy homogeneous B.C. at both end points.
1b. The line y = 2x is transformed into ? = 0 and y = 2(x-2) is transformed into ? = 2. The lines y = 0 and y = 2 are transformed into n = 0 and n = 2 respectively, so the parallelogram is transformed into a square of side 2. From the given equations, we have x = ? + n/2 and y = n. Thus u? = uxx^ + u-yy^ = ux and
un = uxxn + u-yy-n = 1/2ux + uy. Likewise
u^ = uxx - xE, + uxyy^ = uxx un = uxxxn + uxyyn = 1/2uxx + uxy and unn = 1/2uxxxn + 1/2uxyyn + uyxxn + uyyyn = 1/4uxx + uxy + uyy. Therefore,
5/4u^^ - u^n + unn = uxx + uyy = 0.
1c. Substituting u(?,n) = U(?)V(n) into the equation of part b yields 5/4U"V - U'V' + UV" = 0 or upon dividing by UV 5 U" V" U'V'
+ — = ------------, which is not separable. The
4 U V UV
B.C. become U(?,0) = 0, U(?,2) = f(^+1) (since x = ? + n/2), U(0,n) = 0, and U(2,n) = 0.
2. This problem is very similar to the example worked in the text. The fundamental solutions satisfying the P.D.E.(3), the B.C. u(1,t) = 0, t > 0 and the finiteness condition are given by Eqs.(15) and (16). Thus assume u(r,t) is of the form given by Eq.(17). The I.C. require
that u(r,0) = Vc J (X r) = 0 and
n 0 n
n=1
252
Section 11.5
u (r,0) = y1 ak J (1 r) = g(r). From Eq.(26) of
t n n 0 n
n=1
Section 11.4 we obtain c = 0 and
n
1 ka = [1rg(r)J (1 r)dr/ [ 1rJ2(1 r)dr, n = 1,2,... . n n 0 0 n 0 0 n
4. This problem is the same as Problem 22 of Section 10.7.
The periodicity condition requires that p. of that problem be an integer and thus substituting p2 = n2 into the previous results yields the given equations.
5a. Substituting u(r,0,z) = R(r)0(0)Z(z) into Laplace's equation yields R"0Z + R'0Z/r + R0"Z/r2 + R0Z" = 0 or equivalently R"/R + R'/rR + 0"/r20 = - Z"/Z = o. In order to satisfy arbitrary B.C. it can be shown that o must be negative, so assume o = -12, and thus Z" - 12Z = 0 and, after some algebra, it follows that r2R"/R + rR'/R + 12r2 = -0"/0 = a. The periodicity condition 0(0) = 0(2n) requires that "\/~a be an integer n so a = n2. Thus r2R" + rR' + (12r2 - n2)R = 0,
0" + n20 = 0, and Z" - 12Z = 0.
5b. If u(r,0,z) is independent of 0, then the 0"/r20 term
does not appear in the second equation of part a and thus
R"/R + R'/rR = - Z"/Z = -12, from which the desired result
follows.
6. Assuming that u(r,z) = R(r)Z(z) it follows from Problem 5 that R = cJ0(1r) + c2Y0(1r), from Eq.(13), and
Z = k1e-1z + k2e1z. Since u(r,z) is bounded as r ^ 0 and
approaches zero as z ^ ^ we require that c2 = 0, k2 = 0.
The B.C. u(1,z) = 0 requires that J0(1) = 0 leading to an
infinite set of discrete positive eigenvalues 1 ,1 ,...1 ... . The fundamental solutions of the
1 2 n
-1 z
problem are then u (r,z) = J (1 r)e n, n = 1,2,... .
n 0 n
-1 z
Thus assume u(r,z) = 7 c J (1 r)e n . The B.C.
n 0 n n=1
u(r,0) = f(r), 0 < r < 1 requires that u(r,0) = / c J (1 r) = f(r) so
n 0 n n=1
c = [ 1rf(r)J (1 r)dr/[1rJ2(1 r)dr, n = 1,2,... . n J0 0 n J0 0 n
253
7b. Again, 0 periodic of period 2n implies X2 = n2. Thus the solutions to the D.E. are R(r) = c J (kr) + c Y (kr) (note
1 n 2 n
that X and k here are the reverse of Problem 3 of Section
11.4) and 0(0) = d1cosn0 + d2sinn0, n = o,1,2... . For the
solution to remain bounded, c = o and thus
2
v(r,0) = (1/2)coJo(kr) + / Jm(kr)(b sinm0+c cosm0).
m m
m=1
Hence v(c,0) is then a Fourier Series of period 2n and
the coefficients are found as in Section 1o.2, Eqs.(13),
(14) and Problem 27.
9a. Substituting u(p,0,\$) = P(p)0(0)O(^) into Laplace's equation leads to
p2P"/P + 2pP'/P = -(csc2^)0"/0 - O"/O - (cot^)O'/O = o.
In order to satisfy arbitrary B.C. it can be shown that o must be positive, so assume o = p2.
Thus p2P" + 2pP' - p2P = o. Then we have (sin2^)O"/O + (sin^cos^) O'/O + p2sin2^ = - 0"/0 = a.
The periodicity condition 0(o) = 0(2n) requires that "\/~a be an integer X so a = X2. Hence 0" + X 20 = o and (sin2^)O" + (sin^cos^)O' + (p2sin2^ - X2) O = o.
1o. Since u is independent of 0, only the first and third of the Eqs. in 9a hold. The general solution to the Euler equation is
r r I-----
P = c1p 1 + c2p 2 where r1 = (-1 + V 1+4p2 )/2 > o and
r2 = (-1-^/ 1+4p2 ) /2 < o. Since we want u to be bounded
as p ^ o, we set c2 = o. As found in Problem 22 of
Section 5.3, the solutions of Legendre's equation,
Problem 9c, are either singular at 1, at -1, or at both unless p2 = n(n+1), where n is an integer. In this case, one of the two linearly independent solutions is a polynomial denoted by Pn (Problems 23 and 24 of
Section 5.3). Since r1 = (-1 + \J 1+4n(n+1) )/2 = n, the fundamental solutions of this problem satisfying the
n
finiteness condition are un(p,\$) = p P (s) = pnPn(cos^),
Previous << 1 .. 392 393 394 395 396 397 < 398 > 399 400 401 402 403 404 .. 486 >> Next | 2,200 | 5,497 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.921875 | 4 | CC-MAIN-2018-51 | latest | en | 0.81981 |
http://chipznstix.com/epub/301-circuits-practical-electronic-circuits-for-the-home-constructor-1-78 | 1,545,056,192,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376828507.84/warc/CC-MAIN-20181217135323-20181217161323-00294.warc.gz | 58,632,609 | 10,344 | # Download e-book for kindle: 301 circuits Practical electronic circuits for the home by
301 circuit. Vol. 1 КНИГИ ;АППАРАТУРА Название: 301 circuit. Vol. 1Издательство: Elektor Количество страниц: 103 Формат: PDF Размер файла: 20 Mb Язык: EnglishСборник схем журнала Elektor.com zero
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Additional resources for 301 circuits Practical electronic circuits for the home constructor 1-78
Example text
Ing positive or negative increment to x. The area of the graph, enclosed between the two boundaries, is ∆r∆x. e. m + l = ∆R. Consequently D f ( x − ∆x ) = D f ( x ) − l , R f ( x − ∆x ) = R f ( x ) + l . The efficiency of classification in relation to a new boundary at separation is: Ex +∆x = D f ( x) − l Ds ( x) − (l + m) − R f ( x) + l Rs ( x) + (l + m) The resultant equation will now be examined. In this equation, in comparison with the previous equations, the reduction in the numerator and the denominator of the first part of the equation, was added to the numerator and denominator of the second part of the equation, respectively.
Extraction and contamination of the product. These parameters characterise most efficiently the separation process, but the absence of a united criterion complicates comparison of different separation processes. II-2. The characteristics of multiple separation of material with constant extraction. 20 1)ε f1 = 95%, ε c1 = 71% ε f 2 = 89%, ε c2 = 77% 2)ε f = 93%, K f = 18% ε f1 = 86%, K f1 = 11%. If the cost of the initial material is not high, the process is sometimes characterised by the quality of the completed product.
Determination of the optimality conditions. separate between these two products with different degrees of separation. With the known degree of accuracy, the curves N(x); n f (x); n c(x), representing the averaged-out fraction characteristics, can be regarded as continuous and differentiable on the basis of the theorem of the calculation of the sums using integrals. If this assumption appears to be insufficient, then to maintain mathematical strictness in the given derivation the relatively continuous integral should be replaced by the sum sign. | 538 | 2,145 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2018-51 | latest | en | 0.793346 |
https://fourthandsycamore.com/how-to-do-long-multiplication/ | 1,653,588,793,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662619221.81/warc/CC-MAIN-20220526162749-20220526192749-00347.warc.gz | 333,513,434 | 20,489 | ## How can I quickly multiply my mind?
Here’s the trick: Any time you square a two-digit number that ends in 5, the last digits of the answer will be 25 and the digits before that are given by multiplying the first digit of the number by the number that’s one greater.
## At what age should a child know their multiplication tables?
Children can begin to learn their multiplication tables once they have mastered basic addition and subtraction concepts and are familiar with arrays and how to count by 2’s and 5’s, which is usually by age 9. Each student is unique, and some students may be ready to learn multiplication tables earlier than this.
## What is the difference between short and long multiplication?
What is the difference between short and long multiplication? The short multiplication method is the advised route of calculation when someone wants to multiply a 2, 3 or 4 digit number by a 1 digit number. Long multiplication involves the multiplication of a 2, 3 or 4 digit number by a 2 digit number.
## How do you do long multiplication with 3 digits?
To do long multiplication of 3digit numbers, multiply all 3 digits of both numbers together individually. When multiplying by the tens digit of the bottom number, write a 0 on the end of your answer. When multiplying by the hundreds digit of the bottom number, write two 0’s on the end of your answer. | 292 | 1,376 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.28125 | 4 | CC-MAIN-2022-21 | longest | en | 0.907553 |
https://studylib.net/doc/13712247/summer-school---number-theory-for-cryptography-f.-morain | 1,563,609,620,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526489.6/warc/CC-MAIN-20190720070937-20190720092937-00514.warc.gz | 549,440,068 | 42,070 | # Summer School - Number Theory for Cryptography F. Morain
```Summer School - Number Theory for Cryptography
F. Morain
Tutorial, 2013/06/25
1. Implement the AMR test.
2. Find a (probable) family of composite integers N satisfying F (N ) = ϕ(N )/4.
3. Prove Pocklington’s theorem.
4. a) Implement the N − 1 and find proven primes of the form 2 · k! + 1.
b) Same question with the N + 1 test and the family 2 · k! − 1.
4. We consider the equation kϕ(N ) | N − 1 for integers k and N .
a) solve the equation when k = 1.
From now on, fix some k > 1.
b) Give elementary properties of N ’s satisfying the equation.
c) Find non-trivial bounds on the number of prime divisors t of a solution N to the equation.
5. a) Implement the AKS algorithm and prove that 89 is prime.
b) Implement Berrizbeitia’s variant and find some proven primes.
1
```
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11 Cards | 273 | 936 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2019-30 | latest | en | 0.722829 |
https://uk.mathworks.com/matlabcentral/fileexchange?term=financial%20engineering | 1,638,582,572,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362923.11/warc/CC-MAIN-20211204003045-20211204033045-00055.warc.gz | 636,512,101 | 17,764 | 7 results
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sacalar or matrix with elements between 0 and 1 Output: x, an approximation for the inverse normal at uReference: Pau Glasserman, Monte Carlo methods in financial engineering, vol. 53 of applications of | 467 | 2,090 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2021-49 | latest | en | 0.882306 |
https://studymaterialcenter.in/question/let-2-fx-x-x-r-for-any-a-r-define-g-a-r-a-x-fx-if-s-0-4-then-which-one-of-the-following-statements-i/ | 1,659,895,875,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882570692.22/warc/CC-MAIN-20220807181008-20220807211008-00170.warc.gz | 494,862,678 | 24,013 | # Let 2 fx x x () , R = Î . For any A R Í , define g(A) = { R : ( ) A} x fx Î Î . If S = [0, 4], then which one of the following statements is not true ?
Question:
Let $f(x)=x^{2}, x \in \mathrm{R}$. For any $\mathrm{A} \subseteq \mathrm{R}$, define $\mathrm{g}(\mathrm{A})=$ $\{x \in \mathrm{R}: f(x) \in \mathrm{A}\}$. If $\mathrm{S}=[0,4]$, then which one of the following statements is not true?
1. $g(f(S)) \neq S$
2. $f(g(S))=S$
3. $g(f(S))=g(S)$
4. $f(g(S)) \neq f(S)$
Correct Option: 3
JEE Main Previous Year 1 Question of JEE Main from Mathematics Sets, Relations and Functions chapter.
JEE Main Previous Year April 10, 2019 (I)
Solution:
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https://www.physicsforums.com/threads/determining-mass-distribution-for-team-lifting-of-arbitrary-objects.316752/ | 1,582,200,299,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875144722.77/warc/CC-MAIN-20200220100914-20200220130914-00205.warc.gz | 869,561,736 | 18,888 | # Determining mass distribution for team-lifting of arbitrary objects
## Main Question or Discussion Point
Hey all,
New to the forum (obviously, since this is my first post).
I've been scouring the internet trying to find some guidance on a problem I've been having, but have had no luck. Let me just say first off that my physics and math backgrounds are fairly elementary. I have minors in both areas, but it's been years since I've done anything in them.
The problem I need to solve is the following: Let's say I have an arbitrary polygon. This polygon represents the top-down view of an object. We can assume also that it has no hidden surfaces (all faces of the object are either purely horizontal or purely vertical). I know the location of the vertices (in order), as well as the location of the centre of mass (calculated by triangulating the polygon, averaging the centres of the triangles weighted by their size).
I have X number of people lifting this object, at X different points on its boundary. These points are also known. What I need to figure out is exactly what portion of the weight of the object each person is lifting, based on their positions, assuming a uniform density of the object.
I feel as though, intuitively, this should be a relatively simple thing to calculate, but have had no luck in figuring it out or finding a solution....Could really use some guidance here...
Edit: apologies if this is posted in the wrong place. Mods, feel free to move it if necessary (but it's NOT a homework question)
Related Classical Physics News on Phys.org
tiny-tim
Homework Helper
Welcome to PF!
Hi Mikey-D! Welcome to PF!
I don't think there is a solution, if more than 3 people are lifting.
If two people lift a (one-dimensional) bar, you can find the forces, but if three people do, there are infinitely many solutions
(just think … if you're the one in the middle, you could let go completely, and the other two would still support the bar )
Similarly, with a polygon (instead of a bar), you can find the forces for 3 people, but for 4 or more, there are infinitely many solutions.
Interesting...that makes sense. So any more than three people in two dimensions is (arguably) redundant. As long as the triangle formed by those three lifters constrain the CoM, any other lifters are just helping to lighten the load for anyone else on that side of the CoM. Make sense?
ok. So after a little thought, I've come up with the following: obviously, the sum of vertical forces (down from the CoM and up from the three lifting points) must equal zero. Additionally, I should be able to look at the torques applied about any line passing through the CoM from the lifting points, and the torques on one side of the line should be equal to the torques on the other side of the line. By choosing lines passing through the CoM and any two of the lifting points, I should be able to obtain three different equations and solve for the forces applied at each lifting point.
Make sense?
From there, any additional lifters contributing will simply remove a proportional amount of necessary lifting force from lifters on the same side of the CoM as them. How much weight they can remove from others, however, is dependent on the new geometry they form with the original set of lifters. Any triangle which would exclude the CoM cannot bear the full weight, as it would cause the object to be dropped.
tiny-tim
Homework Helper
… Make sense?
Yes … there are only three equations, and so they can't uniquely determine more than three unknowns!
From there, any additional lifters contributing will simply remove a proportional amount of necessary lifting force from lifters on the same side of the CoM as them.
Not proportional … it can be anything.
How much weight they can remove from others, however, is dependent on the new geometry they form with the original set of lifters. Any triangle which would exclude the CoM cannot bear the full weight, as it would cause the object to be dropped.
Sorry, I'm not following this geometrical argument … wherever he is, any force (up or down) by a new lifter can always be compensated for by the others.
Sorry, but I appear to be a bit dense today...
What are the three equations?
1. Sum of vertical forces = 0
2. Sum of torques about an arbitrary axis through the CoM = 0
3. ? (I feel like I'm missing something really obvious here...)
edit: seems my math was off. I can just pick a new arbitrary axis and re-evaluate torques about it, right?
tiny-tim
Homework Helper
Hi Mikey-D!
(sorry to take so long )
Sorry, but I appear to be a bit dense today...
What are the three equations?
1. Sum of vertical forces = 0
2. Sum of torques about an arbitrary axis through the CoM = 0
3. ? (I feel like I'm missing something really obvious here...)
Replace #2 by Sum of torques about an arbitrary point
torque is a vector (which in this case is always horizontal),
so that gives you two equations!
I can just pick a new arbitrary axis and re-evaluate torques about it, right?
No, picking a new point (or a new parallel axis) will give you no new information …
ie no information that you can't get more simply by using (linear) components of force.
Sorry, Tim, but I'm missing something here...
What are my two other equations then (other than sum of force = 0)?
tiny-tim
Homework Helper
Sorry, Tim, but I'm missing something here...
What are my two other equations then (other than sum of force = 0)?
r x F = 0
since all the Fs are vertical and all the rs are horizontal, the r x Fs are horizontal, so that vector equation has two components … ie two equations. | 1,263 | 5,623 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2020-10 | longest | en | 0.971078 |
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## Signals Questions and Answers : Quiz 2
MCQ 6: Analog video signals have their spectra in the range of
1. 4 MHz to 4.5 MHz
2. 20 KHz to 4.5 MHz
3. 20 Hz to 4.5 MHz
4. 0 MHz to 4.5 MHz
MCQ 7: Power amplifier is used to drive
1. Speaker
2. Antenna
3. Fan
4. A and B
MCQ 8: Fourier series is the
1. summation of pure sines
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1. finite y - axis values
2. infinite y - axis values
3. Finite x - axis values
4. Infinite x - axis values and infinite y - axis values | 437 | 1,595 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2024-26 | latest | en | 0.778662 |
https://www.nuclear-power.com/gadolinium-atomic-number-mass-density/ | 1,713,186,644,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816977.38/warc/CC-MAIN-20240415111434-20240415141434-00687.warc.gz | 861,403,512 | 28,224 | # Gadolinium – Atomic Number – Atomic Mass – Density of Gadolinium
Gadolinium is a chemical element with atomic number 64 which means there are 64 protons and 64 electrons in the atomic structure. The chemical symbol for Gadolinium is Gd.
Since the number of electrons is responsible for the chemical behavior of atoms, the atomic number identifies the various chemical elements.
How does the atomic number determine the chemical behavior of atoms?
Atomic mass of Gadolinium is 157.25 u.
Note that each element may contain more isotopes. Therefore this resulting atomic mass is calculated from naturally-occurring isotopes and their abundance.
The unit of measure for mass is the atomic mass unit (amu). One atomic mass unit is equal to 1.66 x 10-24 grams. One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1 g/mol.
For 12C, the atomic mass is exactly 12u, since the atomic mass unit is defined from it. For other isotopes, the isotopic mass usually differs and is usually within 0.1 u of the mass number. For example, 63Cu (29 protons and 34 neutrons) has a mass number of 63, and an isotopic mass in its nuclear ground state is 62.91367 u.
There are two reasons for the difference between mass number and isotopic mass, known as the mass defect:
1. The neutron is slightly heavier than the proton. This increases the mass of nuclei with more neutrons than protons relative to the atomic mass unit scale based on 12C with equal numbers of protons and neutrons.
2. The nuclear binding energy varies between nuclei. A nucleus with greater binding energy has lower total energy, and therefore a lower mass according to Einstein’s mass-energy equivalence relation E = mc2. For 63Cu, the atomic mass is less than 63, so this must be the dominant factor.
The atomic mass number determines especially the atomic mass of atoms. The mass number is different for each different isotope of a chemical element.
How does the atomic mass determine the density of materials?
Typical densities of various substances at atmospheric pressure.
Density is defined as the mass per unit volume. It is an intensive property, which is mathematically defined as mass divided by volume:
ρ = m/V
In other words, the density (ρ) of a substance is the total mass (m) of that substance divided by the total volume (V) occupied by that substance. The standard SI unit is kilograms per cubic meter (kg/m3). The Standard English unit is pounds mass per cubic foot (lbm/ft3).
### Density of Elements in the Periodic Table
Atomic Number 64
Symbol Gd
Element Category Rare Earth Metal
Phase at STP Solid
Atomic Mass [amu] 157.25
Density at STP [g/cm3] 7.901
Electron Configuration [Xe] 4f7 5d1 6s2
Possible Oxidation States +3
Electron Affinity [kJ/mol] 50
Electronegativity [Pauling scale] 1.2
1st Ionization Energy [eV] 6.15
Year of Discovery 1880
Discoverer De Marignac, Charles Galissard
Thermal properties
Melting Point [Celsius scale] 1313
Boiling Point [Celsius scale] 3273
Thermal Conductivity [W/m K] 11
Specific Heat [J/g K] 0.23
Heat of Fusion [kJ/mol] 10.05
Heat of Vaporization [kJ/mol] 359.4 | 814 | 3,176 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2024-18 | latest | en | 0.830013 |
https://www.reference.com/vehicles/measure-exhaust-pipe-size-40275781ef72e80d | 1,481,114,822,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698542112.77/warc/CC-MAIN-20161202170902-00238-ip-10-31-129-80.ec2.internal.warc.gz | 991,675,303 | 20,813 | Q:
# How do you measure an exhaust pipe size?
A:
To measure the size of an exhaust pipe, measure the outside circumference of the pipe and divide it by pi, then subtract the pipe's thickness to determine the inside diameter. Exhaust pipes are sold based off of their inside diameter.
## Keep Learning
When measuring an exhaust pipe without a micrometer or caliper, it is important to make sure that the pipe is measured at a straight section that is at least 4 inches away from any bends.
1. Locate the section of the pipe that will be measured.
2. Find a straight section of the exhaust pipe that will be measured.
3. Find the outside diameter of the pipe.
4. To find the outside diameter of the pipe, first use a tape measure and measure the circumference of the pipe by wrapping the tape measure around the pipe. Take this number and divide it by pi, or 3.14, to find the outer diameter of the pipe.
5. Determine the inner diameter of the pipe.
6. Finally, measure the thickness of the exhaust pipe. Multiply this number by two, because the thickness of the pipe was previously taken into account in two places, and subtract this number from the outside diameter that was found above. The resulting number will be the inside diameter of the pipe.
Sources:
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PEOPLE SEARCH FOR | 435 | 2,072 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2016-50 | longest | en | 0.924006 |
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