url stringlengths 14 2.42k | text stringlengths 100 1.02M | date stringlengths 19 19 | metadata stringlengths 1.06k 1.1k |
|---|---|---|---|
https://web2.0calc.com/questions/help_33308 | +0
# help
+1
41
2
Right triangle TRI has side lengths 20, 21, 29. A circle is drawn inside triangle TRI that is tangent to all three sides.
What is the radius of the circle?
Jan 28, 2023
#1
-2
The radius of the circle is 12.
Jan 28, 2023
#2
+79
+4
That's the diameter of the circle.
Using the formula $$r=\dfrac{\text{Area of triangle}}{\text{semiperimeter}}$$ and heron's formula, we can find the inradius.
The semiperimeter is $$s=35$$, so using $$A=\sqrt{35(35-20)(35-21)(35-29)}$$, we have $$A=210$$. Dividing by $$s=35$$, we get the inradius 6. | 2023-03-28 15:05:30 | {"extraction_info": {"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": 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, "math_score": 0.9826531410217285, "perplexity": 2533.6762005658975}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948867.32/warc/CC-MAIN-20230328135732-20230328165732-00118.warc.gz"} |
http://www.linuxquestions.org/questions/linux-software-2/emacs-permanent-key-binding-for-saved-macro-771863/ | Share your knowledge at the LQ Wiki.
Home Forums HCL Reviews Tutorials Articles Register Search Today's Posts Mark Forums Read
LinuxQuestions.org Emacs: Permanent Key Binding For Saved Macro
Linux - Software This forum is for Software issues. Having a problem installing a new program? Want to know which application is best for the job? Post your question in this forum.
Notices
11-27-2009, 03:54 AM #1
CoderMan
Member
Registered: Jan 2009
Location: Gemini Capsule 25164
Distribution: Gentoo
Posts: 375
Blog Entries: 24
Rep:
Emacs: Permanent Key Binding For Saved Macro
Hi. I would appreciate some help from the Emacs gurus. I was trying to follow an online tutorial on how to permanently save a macro for reuse. So I tried to follow the instructions, and ended up putting this in my .emacs:
Code:
(fset 'texquote
(lambda (&optional arg) "Keyboard macro." (interactive "p") (kmacro-exec-ring-item (quote ("\\begin{quotation}^M^M^M^M\\end{quotation}^[OA^[OA" 0 "%d")) arg)))
This works great in that it makes available my macro as the "texquote" command, but it does not also make available the key-binding I attached to the command, which was "C-x C-k 1".
The tutorial says:
Quote:
If you give insert-kbd-macro a numeric argument, it makes additional Lisp code to record the keys (if any) that you have bound to macroname, so that the macro will be reassigned the same keys when you load the file.
I think this is where I went wrong, but when I try to use "M-x insert-kdb-macro 1" it just says that there is no macro by that name. What does it mean then when it says to "give insert-kbd-macro a numeric argument"?
Last edited by CoderMan; 11-27-2009 at 03:55 AM. | 2014-09-22 05:04:29 | {"extraction_info": {"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, "math_score": 0.22832532227039337, "perplexity": 5604.166525437955}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657136545.14/warc/CC-MAIN-20140914011216-00171-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://discourse.julialang.org/t/algorithms-for-finding-the-self-intersection-of-a-plane-curve/70192 | # Algorithms for finding the self-intersection of a plane curve?
Does anyone here happen to know about algorithms for finding the self-intersection points of a plane curve? For example, find the self-intersection (X, Y) = (0, 0) in the below plane curve.
Edit: Add an actual example. The scattered points are computed numerically. It is not straightforward to control the spacing between each scattered point. The distribution density of points around the intersection (marked by the red circle) can be improved though. Note also that by eye we can tell that the intersection is not at Fg = 0.
1 Like
detect bifurcation? You monitor the spectrum of the jacobian. BifurcationKit or HomotopyContinuation.jl should be able to do it
3 Likes
I’ve gone through BifurcationKit.jl documentation quickly and found it quite interesting. However, I have difficulties understanding the underlying math. The tutorials are all about ODEs and PDEs. Do you have any tutorials for simple functions (such as y^2 = x^3 + x^2). The self-intersection of the above example happens to be the zero point of this function. But the self-intersection can locate anywhere on the plane. In addition, my actual function is more complicated and contains not only polynomials but natural log functions.
This library may be a good option: IntervalRootFinding
1 Like
The implicit equation provided can be parametrized to: X(t) = t^2 - 1; Y(t) = t^3 - t
Then we can solve the system (X(t), Y(t)) = (X(u), Y(u)), whose non-trivial solution (t != u) is u = 1, which gives the crossing point (0, 0).
Disclaimer: not a mathematician, but the above solution is a physical one, we send two particles at different times on the same trajectory and check their collision.
1 Like
True for this simple example. But my actual function is more complicated and has no explicit analytical expression. So trying to find a numerical approach
1 Like
Regarding the recently added scatterplot above, would it be possible to extract two sets of points close to the intersection, fit them independently with linear (or other) functions, and then compute the intersection on that basis?
I’ve gone through BifurcationKit.jl documentation quickly and found it quite interesting. However, I have difficulties understanding the underlying math.
It is to find solutions (x,p) with salar p to an equation F(x, p) = 0
The tutorials are all about ODEs and PDEs.
The first part of the ode problems is to find the zeros of a nonlinear function (not just polynomials) as function of a parameter. For example you could search for y as function of x and detect bifurcations.
Do you have any tutorials for simple functions (such as y^2 = x^3 + x^2). The self-intersection of the above example happens to be the zero point of this function. But the self-intersection can locate anywhere on the plane. In addition, my actual function is more complicated and contains not only polynomials but natural log functions.
1 Like
@rveltz is right that at a self intersection there’s a singularity. So if your curve is the solutions of f(x,y) = 0 then the gradient must be orthogonal to the two linearly independent tanget lines and hence
f_x = f_y = 0
at any self intersection. So you could try to solve the nonlinear system
F = \left ( \begin{array}{c} f_x^2 + f_y^2 \\ f \end{array} \right) = \left ( \begin{array}{ll} 0 \\ 0 \end{array} \right)
Any implementation of Newton’s method, like nsol.jl from SIAMFANLEquations.jl would do that. Even if you only have a function to evaluate f and no analytic expression, that’ll be ok with a numerical Jacobian for Newton as long as f is sufficiently smooth and you pay attention to the difference increments for the first (h) and second (\sqrt{h}) derivatives.
You could think of f(x,y) = 0 as an equation where x is the variable and y a parameter. Then if you have a a point on the curve, you could us BIfurcationKit.jl to do continuation and any singularities will be flagged by the software. Even then, you are not guaranteed to find all solutions.
The tough part in your question is to find all solutions. If you had a polynomial system, then you have a computational algebraic geometry problem and Bertini (google it) would work, but there is no Julia interface AFAIK.
2 Likes
This (the numerical solution) should be an easy task for GMT’s module gmtspatial but there is currently an issue that needs to be fixed (gmtspatial -Ii failes and output strange things · Issue #5889 · GenericMappingTools/gmt · GitHub)
In general, it can be framed as a kind of root-finding problem, as several other posters have suggested, and for which there are many numerical algorithms. Formulating the problem more precisely depends on how your curve is parameterized, which you haven’t specified clearly.
2 Likes
using BifurcationKit, LinearAlgebra, Setfield, Plots
const BK = BifurcationKit
F(x, p) = @. -p.y^2 + x^2 + x^3
J(x, p) = ForwardDiff.jacobian( z->F(z,p), x)
par = (y = 0., )
opts = BK.ContinuationPar(dsmax = 0.051, dsmin = 1e-3, ds=0.001, maxSteps = 140, pMin = -1., saveSolEveryStep = 1, detectBifurcation = 3)
br, = continuation(F,J, [-1.], par, (@lens _.y),
ContinuationPar(opts, ds = -0.001, maxSteps = 800, newtonOptions = NewtonPar(verbose = false, maxIter = 6), plotEveryStep = 10),
recordFromSolution = (x,p) -> (x = x[1],),
bothside = true,
verbosity = 3, plot = true,
)
plot(br)
The problem is that is gives the fold points as well.
3 Likes
Thanks! This looks great! Will see whether I can formulate my problem to use BifurcationKit.
Here, why do you define another ConinuationPar? Why the first argument is opts? What does it do?
Another good news, I have successfully used this continuation method to draw a binodal line in a ternary phase diagram, which is really awesome! Previously I have to collect all those binodal points by hand which is very cumbersome. It is a more useful application than finding the self-intersection of a plane curve which is only an intermediate step in finding the binodal points. Now, I can simply use BK to find the binodal points for me.
1 Like
Because I typed super fast…sorry. Only one is required
Now, I can simply use BK to find the binodal points for me.
Coool | 2022-05-22 12:24:22 | {"extraction_info": {"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, "math_score": 0.7424911260604858, "perplexity": 890.1524064692447}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662545326.51/warc/CC-MAIN-20220522094818-20220522124818-00364.warc.gz"} |
https://stackoverflow.com/questions/7922043/dll-build-error-related-to-string-type | # DLL Build Error related to string type
3I'm learning how to use C++ to write DLLs and am following this tutorial video to get me started. I follow along exactly, my code being:
defFile.def:
LIBRARY "square"
EXPORTS
square
funct.cpp:
double __stdcall square(double & x)
{
return x*x;
}
When trying to Build using VSE 2010, I get the following error:
1>------ Build started: Project: square, Configuration: Debug Win32 ------
1> defFile.def
1>c:\documents and settings\~\my documents\visual studio 2010\projects\square\square\deffile.def(2): error C2143: syntax error : missing ';' before 'string'
1>c:\documents and settings\~\my documents\visual studio 2010\projects\square\square\deffile.def(2): error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
========== Build: 0 succeeded, 1 failed, 0 up-to-date, 0 skipped ==========
I've tried adding #include <string> at the top of defFile.def, but still get the same error. I'm sure this is something really simple.
Definition file is not C++. Remove using namespace std; from there. Also, you're not supposed to compile it, if you want to use it, you need to modify linker settings for the project. | 2020-10-25 09:22:36 | {"extraction_info": {"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, "math_score": 0.6629461050033569, "perplexity": 13147.798982750697}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107888402.81/warc/CC-MAIN-20201025070924-20201025100924-00153.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-2y-5-2-25 | # How do you solve (2y + 5)^2 = 25?
May 25, 2018
$y = 0$ or $y = - 5$
#### Explanation:
writing
${\left(2 y + 5\right)}^{2} - {5}^{2} = 0$
$\left(2 y + 5 - 5\right) \left(2 y + 5 + 5\right) = 0$
this gives
$2 y = 0$
or
$2 y + 10 = 0$
this gives
$y = 0$ or $y = - 5$
May 25, 2018
$y = 0 , - 5$
#### Explanation:
Solve:
${\left(2 y + 5\right)}^{2} = 25$
Take the square root of both sides.
$\sqrt{{\left(2 y + 5\right)}^{2}} = \sqrt{25}$
$2 y + 5 = \pm 5$
This gives us two equations:
color(blue)(2y+5=+5 and color(green)(2y+5=-5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)(2y+5=5
Subtract $5$ from both sides.
$2 y + 5 - 5 = + 5 - 5$
$2 y = 0$
Divide both sides by $2$.
$y = \frac{0}{2}$
$y = 0$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(green)(2y+5=-5
Subtract $5$ from both sides.
$2 y + 5 - 5 = - 5 - 5$
$2 y = - 5 - 5$
$2 y = - 10$
Divide both sides by $2$.
$y = - \frac{10}{2}$
$y = - 5$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solutions for $y$.
$y = 0 , - 5$ | 2019-11-21 05:34:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 31, "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, "math_score": 0.7693414092063904, "perplexity": 10032.70156067384}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670731.88/warc/CC-MAIN-20191121050543-20191121074543-00110.warc.gz"} |
http://www.physicsforums.com/showthread.php?t=371845 | ## Gravitaional field can store mass?
If i separate two rocks,the total weight of them will increase? If so,the extra mass stored in the gravitational field between them?
Attached Thumbnails
PhysOrg.com science news on PhysOrg.com >> Ants and carnivorous plants conspire for mutualistic feeding>> Forecast for Titan: Wild weather could be ahead>> Researchers stitch defects into the world's thinnest semiconductor
Recognitions:
Gold Member
Quote by magnetar If i separate two rocks,the total weight of them will increase? If so,the extra mass stored in the gravitational field between them?
If you separate two rocks, the total energy (and effective rest mass) of the system increases. However, the location of the additional energy is not clear in General Relativity.
In a semi-Newtonian equivalent, one apparently mathematically self-consistent solution is that each of the rocks increases in energy by the potential energy gained relative to the other rock, and the field loses the same amount of energy as either rock, so the total energy gained is the change in Newtonian potential energy of the system as a whole. In this model, for a field $g$ the energy density is $g^2/(8 \pi G)$ which is analogous to the Maxwell energy density $\epsilon_0 E^2/2$ in electromagnetism, where $\epsilon_0$ is matched with $1/(4 \pi G)$. The field energy is maximized when mass is concentrated together, and decreases to zero as the masses are separated to infinity.
Recognitions: Gold Member Science Advisor Staff Emeritus Jonathan Scott's answer is correct. Just to amplify on it a little, here's the reason why you can't localize the gravitational field energy in GR as you would have been able to in Newtonian mechanics. In GR, the equivalence principle says that the gravitational field can be anything you want it to be, depending on your frame of reference. In particular, give any point in space, you can always choose a frame of reference defined by an observer free-falling through that point, so the gravitational field is zero there. When you're dealing with gravitational waves, you can get around this by averaging over multiple wavelengths.
Recognitions:
Gold Member
## Gravitaional field can store mass?
On rereading my own post, I see I've been a bit inaccurate; if you separate two rocks to infinity, the field energy of their interaction decreases to zero, but of course the separate rocks still have field energy due to their own individual fields as concentrations of mass. That field energy would decrease if you break each of them into smaller rocks and separate those, and so on.
Recognitions:
Gold Member
If i separate two rocks,the total weight of them will increase
...because you have done work....that is, put energy into the system, done work to overcome the attractive gravitational force. But it's clearer to say the energy rather than the mass has increased....and that seems to be a modern preference/convention as discussed here in other threads.
A similar situation exists when a relaxed spring is compressed and held...the jack in the box example.....there is more energy in the coiled than the uncoiled spring....
and a hot blob of metal contains more energy than the same blob when cold....heat added is a form of energy....
You'll also observe more energy in a faster moving mass than when it is slowed....
Thanks to Einstein!!!
Recognitions:
Gold Member
Jonathan posts:
That field energy would decrease if you break each of them into smaller rocks and separate those, and so on.
Which field energy...seems like both would increase???...according to your earlier post:
If you separate two rocks, the total energy (and effective rest mass) of the system increases.
The second quote is, I believe, the correct one....
Blog Entries: 3 Recognitions: Gold Member I think what Jonathan means is that when a rock is broken, some binding energy is lost from the effective mass ? ( I'm confined at home because of a bad foot tonight - I'm glad the forum isn't deserted )
Recognitions: Gold Member Sorry, the actual "breaking" of the rock is not relevant - just assume it can be dismantled. I'm only talking about the gravitational energy. If you separate it into thinly spread dust, that minimizes the gravitational interactions and the external field of the whole system. As I seem to remember mentioning recently in some other thread, there are two ways of extending Newtonian gravity to include energy in the field. If you just assume in a non-relativistic way that the masses are not affected by gravity, then the potential energy has to be assumed to be in the field, which then has a negative field density, $-g^2/8 \pi G$, because the total energy of the system decreases as masses are brought together, giving a more intense outward field overall (although the field between the masses cancels, of course). If however you include the known relativistic effect of gravity on time and hence on energy, then each mass is effectively modified by the potential due other masses. Since this occurs both ways, this means that the effective total mass is modified by TWICE the potential energy, but mathematically this cancels out nicely if you assume that there is also a positive energy density in the field of $g^2/8 \pi G$, the same as in the original Newtonian model except that it has the opposite sign. Note also that this is only a model in a particular frame of reference. General Relativity tells us that this model is probably incomplete because it only works for certain frames of reference. Regardless of these details, the total effective mass of a system of objects is decreased slightly when they are brought together (in a static configuration) and increased again if they are moved apart. The increase tends to a limit as the separation goes to infinity. If all of the components are separated as far apart as possible, the external field of the system as a whole is minimized.
Quote by magnetar If i separate two rocks,the total weight of them will increase? If so,the extra mass stored in the gravitational field between them?
Yes the gravitational field has energy just as a fast moving ball has kinetic energy. We do not say the ball stores energy though I suppose that is correct. Likewise for fields.
If the masses are increasing then energy is being drawn out of somewhere else. Maybe the person or object that is doing the work to move the masses apart is supplying the energy?
Quote by edpell Yes the gravitational field has energy just as a fast moving ball has kinetic energy. We do not say the ball stores energy though I suppose that is correct. Likewise for fields. If the masses are increasing then energy is being drawn out of somewhere else. Maybe the person or object that is doing the work to move the masses apart is supplying the energy?
If you ever want a practical and dangerous demonstration of the "storage" of energy, buy a flywheel. Spin that sucker up, then break it FAST, and as the shards pass through your body, you'll realize that the explosive 'breakup' of the wheel is a result of the 'stored' potential kinetic energy becoming not-so-potential anymore.
Given that nothing else in the room explodes, I have to assume the potential energy is a property of the dynamic system that is the flywheel, and if there is "storage" it's in the medium which is in motion relative to a rest frame.
Blog Entries: 3 Recognitions: Gold Member One of the issues raised in this thread is whether a field can store energy. It seems to me that as soon as one 'stores' energy in a field then (1) either the field must be non-local, or (2) one must accept non-conservation of energy, or (3) accept the existence of an infinite resevoir of energy.Take your pick. ( But please don't hit me with it ! ).
Recognitions:
Gold Member
Quote by Mentz114 One of the issues raised in this thread is whether a field can store energy. It seems to me that as soon as one 'stores' energy in a field then (1) either the field must be non-local, or (2) one must accept non-conservation of energy, or (3) accept the existence of an infinite resevoir of energy.Take your pick. ( But please don't hit me with it ! ).
I don't think any of those are needed. There are energy-momentum pseudotensors which say where the energy is from any one point of view, but in GR it gets mixed up with the shape of space-time, in that what appears to be a free fall geodesic from one point of view involves a change of momentum (and possibly energy) from another more global point of view. The non-linearity of GR seems to make this worse, in that if gravitational energy is also a source of gravity then it's tricky to understand how it can appear to be in different places for different observers.
Personally, I think GR isn't working very well except in the case of a single dominant central object with a fairly weak field, where it is obviously extremely successful. Despite the neatness of the idea, I think that it will probably turn out eventually that the concept is only accurate to first (Newtonian) order and the second-order fit in the solar system (with the PPN beta parameter) is a result of two or more equal and opposite second-order errors (for example relating to Machian variation with location and non-zero energy density in the field). I think it's likely that a future improved theory of gravity will eliminate the concepts of dark matter, dark energy and black holes, will fix the incompatibility with QM, and will clearly include some form of Mach's principle. I just wish someone would come up with it quickly; my own attempts have so far been unsuccessful.
Hi,magnetar
Quote by magnetar If i separate two rocks,the total weight of them will increase?
No, "gravitational energy" does not hold energy that appear in Einstein's gravitation equation.
Total mass is considered to be reserved in spite of the separation, however the summation of rest mass in different location is physically meaningless.
Regards.
Quote by Mentz114 One of the issues raised in this thread is whether a field can store energy. It seems to me that as soon as one 'stores' energy in a field then (1) either the field must be non-local, or (2) one must accept non-conservation of energy, or (3) accept the existence of an infinite resevoir of energy.Take your pick. ( But please don't hit me with it ! ).
I am not following please explain more. In the case of gravity the field goes as 1/r so it is not local? What exactly do you mean by local? Why non-conservation of energy? I like conservation of energy.
Quote by edpell I am not following please explain more. In the case of gravity the field goes as 1/r so it is not local? What exactly do you mean by local? Why non-conservation of energy? I like conservationof energy.
By non-local he is talking about "big N/L" Local/Non-Locality". As in, Entanglement, EPR, etc. He doesn't mean local in the Astronomical sense. As for conservation of energy, it's already only conserved in certain instances, and questions like "where does all energy come from" is analogous to, "what IS space-time?" or "Why is the universe the way it is?"
Recognitions:
Gold Member
Jonathan: good post in #8....
Regardless of these details, the total effective mass of a system of objects is decreased slightly when they are brought together (in a static configuration) and increased again if they are moved apart.
says it all......
Quote by Jonathan Scott [...] If however you include the known relativistic effect of gravity on time and hence on energy, then each mass is effectively modified by the potential due other masses. Since this occurs both ways, this means that the effective total mass is modified by TWICE the potential energy, but mathematically this cancels out nicely if you assume that there is also a positive energy density in the field of $g^2/8 \pi G$, the same as in the original Newtonian model except that it has the opposite sign.
It's not clear to me if this assumption (the one I coloured in blue) is arbitrary or if there are strong physical reasons to make it. | 2013-05-23 17:02:43 | {"extraction_info": {"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, "math_score": 0.6247614622116089, "perplexity": 487.36862769526317}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703592489/warc/CC-MAIN-20130516112632-00080-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://txt.binnyva.com/2008/03/date-and-cal-commands/ | # ‘date’ and ‘cal’ Commands
Some date finding commands..
date
Mon Mar 10 23:52:08 IST 2008 cal
March 2008
Su Mo Tu We Th Fr Sa
1
2 3 4 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31
Author: Binny V A
A philosopher programmer who specializes in backend development and stoicism. | 2021-10-26 03:25:49 | {"extraction_info": {"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, "math_score": 0.2583162486553192, "perplexity": 2560.702544150719}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587794.19/warc/CC-MAIN-20211026011138-20211026041138-00435.warc.gz"} |
https://list.orgmode.org/87h83i308p.fsf@ucl.ac.uk/T/ | emacs-orgmode@gnu.org archives
help / color / mirror / code / Atom feed
* How to move from inline tasks to drawers? [was: How to change the width of a latex exported inlinetask?]
@ 2019-11-02 13:01 Alain.Cochard
2019-11-03 13:50 Fraga, Eric
From: Alain.Cochard @ 2019-11-02 13:01 UTC (permalink / raw)
To: Fraga, Eric; +Cc: emacs-orgmode, Alain.Cochard
Fraga, Eric writes on Wed 30 Oct 2019 14:55:
> [...] for a number of reasons including advice from this list, I
> have moved away from inline tasks almost completely and now use
As far as I can see, the last discussion about that on the list
occurred in April 2018 (starting with message
https://lists.gnu.org/archive/html/emacs-orgmode/2018-04/msg00235.html).
My understanding then was that there was a significant wish from
prominent Org developers and/or users to preserve inline tasks in some
form, with a decent implementation. So, if I am not sure what
"advice" you have in mind, I certainly do observe that my hope of some
near future progress has not been fulfilled so far :-)
I wouldn't mind using drawers instead, though, hence avoiding all the
problems tied to current inline tasks, but can I? You said at that
time that my use of inline tasks was appropriate whereas drawers would
not be. You also said that you had "already moved to using drawers
for a large number of [your] inline task use cases, the ones that
completely" above? This leads me to the question of what precisely
_defines_ a "task"; what is important to me is that such inline
"stuff" has an equivalent of the TODO keyword, and an equivalent of
tags for searching, both being integrated transparently with regular
TODOs and tags.
If you (or someone else) can show me how to perform this, I'll start
the switch immediately!
Regards
--
EOST (École et Observatoire des Sciences de la Terre)
IPG (Institut de Physique du Globe) | alain.cochard@unistra.fr
5 rue René Descartes [bureau 106] | Phone: +33 (0)3 68 85 50 44
F-67084 Strasbourg Cedex, France | Fax: +33 (0)3 68 85 01 25
^ permalink raw reply [flat|nested] 9+ messages in thread
* Re: How to move from inline tasks to drawers? [was: How to change the width of a latex exported inlinetask?]
2019-11-02 13:01 How to move from inline tasks to drawers? [was: How to change the width of a latex exported inlinetask?] Alain.Cochard
@ 2019-11-03 13:50 Fraga, Eric
2019-11-04 20:14 John Kitchin
From: Fraga, Eric @ 2019-11-03 13:50 UTC (permalink / raw)
To: Alain.Cochard; +Cc: emacs-orgmode
On Saturday, 2 Nov 2019 at 14:01, Alain.Cochard@unistra.fr wrote:
> You also said that you had "already moved to using drawers for a large
> number of [your] inline task use cases, the ones that weren't really
> This leads me to the question of what precisely _defines_ a "task";
Good question! I guess, for me, a task is one that will appear in my
agenda so has a TODO state (possibly) and/or scheduling/deadline
information. But the distinction is rather blurry.
So, in fact, when I am working on a long document, I have tasks of the
"must improve this section" type which are not tasks for scheduling (the
whole document is itself a task) or "notes" for processing later (by
myself or by others involved in the same document). I use drawers for
these types of activities. I then use the export formatting options to
make the pseudo-tasks and notes appear differently in the exported
output, whether for sharing or for printing/display. So, for instance,
I look for ":todo:" and ":note:" drawers.
If the document I am working on is a coursework or test, I use drawers
for storing the solutions, e.g. a drawer called ":solution:"! For this,
for instance, I have the following elisp in the document that is invoked
when I open the document:
#+begin_src emacs-lisp
(setq-local org-latex-format-drawer-function
(lambda (name contents)
(cond ((string= name "solution")
(format "\\begin{mdframed}\\paragraph{Solution.} %s\\end{mdframed}" contents))
(t (format "\\textbf{%s}: %s" name contents))
)))
#+end_src
together with
to make the solution stand out clearly.
The nice thing about drawers is I can turn them on or off for exporting
via the "d:" document option:
HTH,
eric
--
Eric S Fraga via Emacs 27.0.50, Org release_9.2.6-552-g8c5a78
^ permalink raw reply [flat|nested] 9+ messages in thread
* Re: How to move from inline tasks to drawers? [was: How to change the width of a latex exported inlinetask?]
2019-11-03 13:50 Fraga, Eric
@ 2019-11-04 20:14 John Kitchin
2019-11-04 20:30 Samuel Wales
2019-11-05 8:59 Fraga, Eric
0 siblings, 2 replies; 9+ messages in thread
From: John Kitchin @ 2019-11-04 20:14 UTC (permalink / raw)
To: emacs-orgmode; +Cc: Alain.Cochard
I have been exploring the use of something I call editmarks for this
(https://github.com/jkitchin/scimax/blob/master/scimax-editmarks.org).
They are light-weight markups I usually use for commenting org
documents, and they look like this.
{>~ @jk this is a comment~<}
with the minor mode enabled, these are syntax highlighted, and when I
export a document they come out as todo notes in latex. I can run a
command to see a list of all of these in a document, and for a big
document like a proposal or report, there would be none at the end when
it is done.
It is a work in progress, and probably the 3rd such annotation solution
I have tried. It is the best so far though, and I feel is pretty close
to what I want.
Fraga, Eric <e.fraga@ucl.ac.uk> writes:
> On Saturday, 2 Nov 2019 at 14:01, Alain.Cochard@unistra.fr wrote:
>> You also said that you had "already moved to using drawers for a large
>> number of [your] inline task use cases, the ones that weren't really
>> This leads me to the question of what precisely _defines_ a "task";
>
> Good question! I guess, for me, a task is one that will appear in my
> agenda so has a TODO state (possibly) and/or scheduling/deadline
> information. But the distinction is rather blurry.
>
> So, in fact, when I am working on a long document, I have tasks of the
> "must improve this section" type which are not tasks for scheduling (the
> whole document is itself a task) or "notes" for processing later (by
> myself or by others involved in the same document). I use drawers for
> these types of activities. I then use the export formatting options to
> make the pseudo-tasks and notes appear differently in the exported
> output, whether for sharing or for printing/display. So, for instance,
> I look for ":todo:" and ":note:" drawers.
>
> If the document I am working on is a coursework or test, I use drawers
> for storing the solutions, e.g. a drawer called ":solution:"! For this,
> for instance, I have the following elisp in the document that is invoked
> when I open the document:
>
> #+begin_src emacs-lisp
> (setq-local org-latex-format-drawer-function
> (lambda (name contents)
> (cond ((string= name "solution")
> (format "\\begin{mdframed}\\paragraph{Solution.} %s\\end{mdframed}" contents))
> (t (format "\\textbf{%s}: %s" name contents))
> )))
> #+end_src
>
> together with
>
>
> to make the solution stand out clearly.
>
> The nice thing about drawers is I can turn them on or off for exporting
> via the "d:" document option:
>
> HTH,
> eric
--
Professor John Kitchin
Doherty Hall A207F
Department of Chemical Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
412-268-7803
@johnkitchin
http://kitchingroup.cheme.cmu.edu
^ permalink raw reply [flat|nested] 9+ messages in thread
* Re: How to move from inline tasks to drawers? [was: How to change the width of a latex exported inlinetask?]
2019-11-04 20:14 John Kitchin
@ 2019-11-04 20:30 Samuel Wales
2019-11-05 8:59 Fraga, Eric
1 sibling, 0 replies; 9+ messages in thread
From: Samuel Wales @ 2019-11-04 20:30 UTC (permalink / raw)
To: John Kitchin; +Cc: emacs-orgmode, Alain.Cochard
i use comments, sometimes with self-highlighted /emphasis/ or
self-highlighted fixme, or demote to a standard "x" task and use tasks
one level above.
if it is exportable, then i use non-task entries as the thing to
export and do not export any tasks. this works pertty well.
on rare occasions i use inline tasks, but i have not gotten used tot
hem. a long time ago, i catalogued a bunch ofthings needing fixing in
inline tasks tomaket hem more complete as an org feture, but couldn't
fix them so didn't post.
i guess i sort of didn't develop the habit becuase i didnt' remember
which features can be relied on. maybe they have all been fixed by
now. idk.
On 11/4/19, John Kitchin <jkitchin@andrew.cmu.edu> wrote:
> I have been exploring the use of something I call editmarks for this
> (https://github.com/jkitchin/scimax/blob/master/scimax-editmarks.org).
> They are light-weight markups I usually use for commenting org
> documents, and they look like this.
>
> {>~ @jk this is a comment~<}
>
>
> with the minor mode enabled, these are syntax highlighted, and when I
> export a document they come out as todo notes in latex. I can run a
> command to see a list of all of these in a document, and for a big
> document like a proposal or report, there would be none at the end when
> it is done.
>
> It is a work in progress, and probably the 3rd such annotation solution
> I have tried. It is the best so far though, and I feel is pretty close
> to what I want.
>
>
> Fraga, Eric <e.fraga@ucl.ac.uk> writes:
>
>> On Saturday, 2 Nov 2019 at 14:01, Alain.Cochard@unistra.fr wrote:
>>> You also said that you had "already moved to using drawers for a large
>>> number of [your] inline task use cases, the ones that weren't really
>>> This leads me to the question of what precisely _defines_ a "task";
>>
>> Good question! I guess, for me, a task is one that will appear in my
>> agenda so has a TODO state (possibly) and/or scheduling/deadline
>> information. But the distinction is rather blurry.
>>
>> So, in fact, when I am working on a long document, I have tasks of the
>> "must improve this section" type which are not tasks for scheduling (the
>> whole document is itself a task) or "notes" for processing later (by
>> myself or by others involved in the same document). I use drawers for
>> these types of activities. I then use the export formatting options to
>> make the pseudo-tasks and notes appear differently in the exported
>> output, whether for sharing or for printing/display. So, for instance,
>> I look for ":todo:" and ":note:" drawers.
>>
>> If the document I am working on is a coursework or test, I use drawers
>> for storing the solutions, e.g. a drawer called ":solution:"! For this,
>> for instance, I have the following elisp in the document that is invoked
>> when I open the document:
>>
>> #+begin_src emacs-lisp
>> (setq-local org-latex-format-drawer-function
>> (lambda (name contents)
>> (cond ((string= name "solution")
>> (format "\\begin{mdframed}\\paragraph{Solution.}
>> %s\\end{mdframed}" contents))
>> (t (format "\\textbf{%s}: %s" name contents))
>> )))
>> #+end_src
>>
>> together with
>>
>>
>> to make the solution stand out clearly.
>>
>> The nice thing about drawers is I can turn them on or off for exporting
>> via the "d:" document option:
>>
>> HTH,
>> eric
>
>
> --
> Professor John Kitchin
> Doherty Hall A207F
> Department of Chemical Engineering
> Carnegie Mellon University
> Pittsburgh, PA 15213
> 412-268-7803
> @johnkitchin
> http://kitchingroup.cheme.cmu.edu
>
>
--
The Kafka Pandemic
What is misopathy?
https://thekafkapandemic.blogspot.com/2013/10/why-some-diseases-are-wronged.html
The disease DOES progress. MANY people have died from it. And ANYBODY
can get it at any time.
^ permalink raw reply [flat|nested] 9+ messages in thread
* Re: How to move from inline tasks to drawers? [was: How to change the width of a latex exported inlinetask?]
2019-11-04 20:14 John Kitchin
2019-11-04 20:30 Samuel Wales
@ 2019-11-05 8:59 Fraga, Eric
2019-11-05 12:49 John Kitchin
From: Fraga, Eric @ 2019-11-05 8:59 UTC (permalink / raw)
To: John Kitchin; +Cc: emacs-orgmode, Alain.Cochard
On Monday, 4 Nov 2019 at 15:14, John Kitchin wrote:
> I have been exploring the use of something I call editmarks for this
Out of curiousity, what do these give you that drawers would not? I use
:todo: and :note: drawers.
For syntax highlighting, I use hi-lock-mode with, for instance, this
pattern to highlight todo drawers:
# Hi-lock: (("^:todo:" (0 'hi-yellow prepend)))
thanks,
eric
--
Eric S Fraga via Emacs 27.0.50, Org release_9.2.6-552-g8c5a78
^ permalink raw reply [flat|nested] 9+ messages in thread
* Re: How to move from inline tasks to drawers? [was: How to change the width of a latex exported inlinetask?]
2019-11-05 8:59 Fraga, Eric
@ 2019-11-05 12:49 John Kitchin
2019-11-05 13:07 Fraga, Eric
From: John Kitchin @ 2019-11-05 12:49 UTC (permalink / raw)
To: Fraga, Eric; +Cc: emacs-orgmode, Alain.Cochard
I use it when editing papers mostly. The main difference is I can put
them inline {>~ @jk here is a comment.~<} in a paragraph. I use them to
mark {>.tpyos.<}, text for {>-deletion-<} removal, or {>+insertion+<},
{y>highlighted text <y}, etc. There is some reasonable export code for
these in html and latex. They are like a generalization of an org-link
in a sexp like form, so you can include metadata like an author name, or
other things.
These have a track change kind of functionality (that turns out to be
quite hard to fully replicate) so you can accept or reject each
editmark. Similar to org-links, each editmark can have a variety of
other actions, e.g. a typo has an action to spell check it, and a
file/audio mark can open or play the file.
I also have some diff functions to generate diffs with these markups
from versions of files, including git versions for integration latex
diff, etc.
It does most of what I want well now, but there are still some corners I
don't go into where it doesn't do exactly everything yet, or where I
haven't tested it very fully (e.g. the diffs).
Fraga, Eric <e.fraga@ucl.ac.uk> writes:
> On Monday, 4 Nov 2019 at 15:14, John Kitchin wrote:
>> I have been exploring the use of something I call editmarks for this
>
> Out of curiousity, what do these give you that drawers would not? I use
> :todo: and :note: drawers.
>
> For syntax highlighting, I use hi-lock-mode with, for instance, this
> pattern to highlight todo drawers:
>
> # Hi-lock: (("^:todo:" (0 'hi-yellow prepend)))
>
> thanks,
> eric
--
Professor John Kitchin
Doherty Hall A207F
Department of Chemical Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
412-268-7803
@johnkitchin
http://kitchingroup.cheme.cmu.edu
^ permalink raw reply [flat|nested] 9+ messages in thread
* Re: How to move from inline tasks to drawers? [was: How to change the width of a latex exported inlinetask?]
2019-11-05 12:49 John Kitchin
@ 2019-11-05 13:07 Fraga, Eric
2019-11-05 13:28 John Kitchin
From: Fraga, Eric @ 2019-11-05 13:07 UTC (permalink / raw)
To: John Kitchin; +Cc: emacs-orgmode, Alain.Cochard
On Tuesday, 5 Nov 2019 at 07:49, John Kitchin wrote:
> I use it when editing papers mostly. The main difference is I can put
> them inline {>~ @jk here is a comment.~<} in a paragraph.
Very interesting. The inline aspect can be quite useful. Thanks for
the description!
--
Eric S Fraga via Emacs 27.0.50, Org release_9.2.6-552-g8c5a78
^ permalink raw reply [flat|nested] 9+ messages in thread
* Re: How to move from inline tasks to drawers? [was: How to change the width of a latex exported inlinetask?]
2019-11-05 13:07 Fraga, Eric
@ 2019-11-05 13:28 John Kitchin
2019-11-05 13:45 Fraga, Eric
From: John Kitchin @ 2019-11-05 13:28 UTC (permalink / raw)
To: Fraga, Eric; +Cc: emacs-orgmode, Alain.Cochard
[-- Attachment #1: Type: text/plain, Size: 1079 bytes --]
The other aspects I find very useful are: 1) there is a display list so I
can see all the editmarks and jump to them. That way, in a proposal for
example I can see if there are any residual marks that should be removed.
2) when I make a pdf, they are converted to a list of todo items at the
front, and as margin notes. This reminds me that they are there, and is
useful for non-org users to see what I need and where.
John
-----------------------------------
Professor John Kitchin
Doherty Hall A207F
Department of Chemical Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
412-268-7803
@johnkitchin
http://kitchingroup.cheme.cmu.edu
On Tue, Nov 5, 2019 at 8:07 AM Fraga, Eric <e.fraga@ucl.ac.uk> wrote:
> On Tuesday, 5 Nov 2019 at 07:49, John Kitchin wrote:
> > I use it when editing papers mostly. The main difference is I can put
> > them inline {>~ @jk here is a comment.~<} in a paragraph.
>
> Very interesting. The inline aspect can be quite useful. Thanks for
> the description!
>
> --
> Eric S Fraga via Emacs 27.0.50, Org release_9.2.6-552-g8c5a78
>
[-- Attachment #2: Type: text/html, Size: 1690 bytes --]
^ permalink raw reply [flat|nested] 9+ messages in thread
* Re: How to move from inline tasks to drawers? [was: How to change the width of a latex exported inlinetask?]
2019-11-05 13:28 John Kitchin
@ 2019-11-05 13:45 Fraga, Eric
0 siblings, 0 replies; 9+ messages in thread
From: Fraga, Eric @ 2019-11-05 13:45 UTC (permalink / raw)
To: John Kitchin; +Cc: emacs-orgmode, Alain.Cochard
Again, very impressive.
I do some of this with drawers but there could indeed be much more
support built-in for such aspects. Navigating drawers in org mode
should be easier.
--
Eric S Fraga via Emacs 27.0.50, Org release_9.2.6-552-g8c5a78
^ permalink raw reply [flat|nested] 9+ messages in thread
end of thread, other threads:[~2019-11-05 13:45 UTC | newest]
2019-11-02 13:01 How to move from inline tasks to drawers? [was: How to change the width of a latex exported inlinetask?] Alain.Cochard
2019-11-03 13:50 Fraga, Eric
2019-11-04 20:14 John Kitchin
2019-11-04 20:30 Samuel Wales
2019-11-05 8:59 Fraga, Eric
2019-11-05 12:49 John Kitchin
2019-11-05 13:07 Fraga, Eric
2019-11-05 13:28 John Kitchin
2019-11-05 13:45 Fraga, Eric
Code repositories for project(s) associated with this inbox:
https://git.savannah.gnu.org/cgit/emacs/org-mode.git
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for read-only IMAP folder(s) and NNTP newsgroup(s).` | 2022-06-29 04:06:42 | {"extraction_info": {"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, "math_score": 0.8035109639167786, "perplexity": 13538.440980100075}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103620968.33/warc/CC-MAIN-20220629024217-20220629054217-00161.warc.gz"} |
https://quant.stackexchange.com/questions/26186/skewed-student-t-distribution-mle-and-simulation | # Skewed Student t distribution MLE and Simulation
I have Financial LOB data and I feel that a skewed t distribution will fit best. I have a problem trying to find the parameters using MLE numerically since Matlabs built in function does not allow for Skewed t-distn.
Can somebody point me to some code which will find the parameters? Or can someone offer advice for an easy way to do this? I also need to simulate using these parameters but I think this is easier
Cheers
Can you not just measure the moments of your data, and then use them to find mu and v?
where the second simplifies to
i think the fitdistrplus library in R could help you with this:
fitdist(data, distr, method = c("mle", "mme", "qme", "mge"),
start=NULL, fix.arg=NULL, discrete, keepdata = TRUE, keepdata.nb=100, ...)
# for student t
fitdistr(x, "t", start = list(m=mean(x),s=sd(x), df=3), lower=c(-1, 0.001,1))
• He states in the question that matlab's built in functions don't allow for a skewed-t dist, so you won't be able to do this. – will May 23 '16 at 11:08
You might have a look at the "sn" R package in CRAN:
Link to standard R documentation for CRAN package sn
It has a skewed t distribution implemented as well as an MLE function.
Alternatively, a simple approach (which leads to a slightly ugly looking distribution) would be to model the positive returns and negative returns separately. In pseudocode:
1) Separate the positive returns (LOB gains) and negative returns into different vectors
2) Using the positive returns, multiply them all by -1 and append them to the original positive return data set, creating a symmetric return series
3) Do a standard Student t MLE fit to this data
4) Repeat the above steps for the negative return data, creating a symmetric time series, etc.
You now have a version of "the" skewed t distribution (there are a number of ways of creating a skewed t distribution) which has a discontinuity at the zero return point - this is ugly, but the method is at least simple and straightforward. As you can imagine, simulation is also very easy: if your starting uniform random is < 0.5 then you use the "loss" parameters, otherwise you use the "gain" parameters. It may be that you only really care about the losses - if so then the above process is even simpler. | 2019-08-26 06:52:34 | {"extraction_info": {"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, "math_score": 0.30340901017189026, "perplexity": 1231.9403042270997}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027331228.13/warc/CC-MAIN-20190826064622-20190826090622-00112.warc.gz"} |
https://corujasabia.com/existe-uma-diferenca-entre-uma-correlacao-e-um-coeficiente-de-correlacao/ | Existe uma diferença entre uma correlação e um coeficiente de correlação?
Sim
Explicação:
Correlation is the process of studying the cause and effect relationship that exists between two variables.
Correlation coefficient is the measure of the correlation that exists between two variables. | 2021-05-06 05:51:04 | {"extraction_info": {"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, "math_score": 0.9522830843925476, "perplexity": 2976.538578318641}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988741.20/warc/CC-MAIN-20210506053729-20210506083729-00412.warc.gz"} |
https://www.themathdoctors.org/why-does-geometry-start-with-unproved-assumptions/ | As I slow down the site for the summer, I plan to run a couple series of connected posts, one per week, on subjects that have seemed too large to cover in one post. I’m starting with questions about the structure of mathematics, particularly the postulates and theorems that are common in geometry classes. This week, we look at how math can be built on statements that can’t be proved, and words that can’t be defined.
## Why can’t postulates be proved?
I was reminded of this topic by a recent questioner, who said about SSS, SAS, etc., “What I do not understand is why I should believe that these are true. They were never explained to me, just listed as ways to prove triangles congruent.” She then referred to our page
Congruence and Triangles
where Doctor Guy, in 1997, said in passing,
SSS: the letters stand for "Side-Side-Side". What that means is, if you have two triangles, and you can show that the three pairs of corresponding sides are congruent, then the two triangles are congruent. This is a postulate, not a theorem, meaning that it cannot be proved, but it appears to be true so everybody accepts it.
What?! All of geometry is built on statements that we just think are true, without proof? I thought math was all about proof and certainty!
There’s a lot more to be said to expand that passing comment, which is technically correct but quite misleading.
The Role of Postulates
I'm in Euclidean Geometry and the teacher said that theorems are proven; postulates are not. Why? Who decided what were postulates and what were theorems? I asked my teacher if postulates *could* be proven and simply weren't, and she said that they couldn't be proven.
This is my current question. Postulates come first, and then theorems are formed from those postulates (right?). So the entire geometry is based on postulates that weren't and can't be proven. That just doesn't seem right to me. Could you explain to me why it's okay that they're not proven?
What it means to say that a postulate can’t be proved is a little subtle; why that isn’t a problem is another question. The answer will take us into the depths of what mathematics is!
I started out this way:
The basic answer to your question is that we have to start somewhere.
The essence of mathematics (in the sense the Greeks introduced to the world) is to take a small set of fundamental "facts," called postulates or axioms, and build up from them a full understanding of the objects you are dealing with (whether numbers, shapes, or something else entirely) using only logical reasoning such that if anyone accepts the postulates, then they must agree with you on the rest.
So math is a process of reasoning from some basic assumptions to derive all that can be said about the subject of those assumptions. Those facts we start with are the postulates (as they are traditionally called in geometry) or axioms (as used in much of the rest of math). But on what grounds are they assumed, and why can’t they be proved?
Now, these postulates may be (and were, for the Greeks) basic assumptions or observations about the way things really are; or they may just be suppositions you make for the sake of imagining something with no necessary connection with the real world. In the first case, we want to choose as postulates facts that are so "obvious" that no one would question them; in the second case, we are free to assume whatever we want. In both cases, we want a minimal set of postulates, so that we are assuming as little as possible, and can't prove one from another.
So some math is intended to model the physical world, and we take our starting point there — for example, observations about how lines and points work on a flat surface. Other math is just a “what if” exploration, so we start with a mere supposition and see what would result if it were true. (Sometimes we later find an application, in which it actually is true; but that doesn’t change the math itself.) The important thing either way is that we choose our postulates carefully so that we don’t have to assume more than necessary; it should be as easy as possible to decide whether the math we’re doing applies to a given situation.
Euclid's problem was that one of the postulates (the fifth) didn't seem simple enough, so people over the centuries tried to prove it from the other postulates, rather than be forced to accept something that didn't seem immediately obvious. Eventually it was realized that there are in fact different kinds of geometry, some of which don't follow all of Euclid's postulates; and that you could replace his parallel postulate with a contradictory assumption and still have a workable system. In particular, spherical geometry - the way things work on a sphere, if you think of a "line" as a great circle - is a very real example of this, in which parallel lines just don't exist. Spherical geometry follows different rules, yet is just as valid as plane geometry.
The fifth postulate (called the Parallel Postulate) is, as Euclid stated it, “If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.” Others since have identified many similar facts that could be put in place of this, such as Playfair’s axiom, “In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.” What mathematicians in the 19th century discovered was that it couldn’t be dropped, because it was independent of the other postulates; and replacing it with an alternative (such as having no parallels, or many parallels) did not lead to contradictions.
This example illustrates the fact that postulates are true only in the particular “world” that the math deals with. A postulate can be replaced with another, and the resulting math is still just as valid — it just tells us about a different “world”, such as a spherical one rather than a flat one.
So we have to take as our starting point some postulates that simply define the particular mathematical system we are studying. If we take a different set of postulates, we get a different system, which may be just as useful as the original - and therefore just as "true" - yet different in its conclusions. The postulates we choose are the connection between the abstract concepts about which we are making proofs, and the "real world" ideas that they model (if any). Without postulates, we would not have such a connection, and would be reasoning about nothing!
Note that, since postulates form the “ground floor” of a mathematical system, there is nothing before them from which they could be proved! A proof would require going outside the system, and therefore would not be a mathematical proof. And that is why postulates can’t be proved.
## Do we have to take math on faith?
Here is a similar question from 1999, considering not only postulates, but also undefined terms:
Unproven Fundamentals of Geometry
I was inspired by some of the answers in your archives to further investigate why the fundamentals of geometry are necessarily unproven/undefined. It seems that in every human system of thought discoveries and inventions must be built upon faith. Less vaguely, in geometry, the most basic unit - the point - cannot be defined. What are some other important postulates or axioms that geometry cannot exist without, but cannot prove, either?
Euclid, in his Elements, started with “definitions” that really didn’t define anything in a formal sense; they just indicated what he had in mind. Modern versions of geometry replace these with “undefined terms”, from which other terms are defined, just as theorems are derived from postulates (axioms).
As discussed above, Euclid then listed five postulates, which are assumed to be true.
Is this all just blind faith? Doctor Rick pondered this:
Hi, Han, I like thought-provoking questions like this.
I agree with you about the necessity of faith as it relates to our knowledge of and interaction with the real world. In math, though, I see things a little differently.
Math in itself is not intrinsically connected to the real world. It is possible, and perfectly okay, to develop a mathematical system that doesn't relate to anything in the real world. It is, as you say, necessary to have "undefined terms" describing entities in the system, and "postulates" (unproven facts relating those entities). But these are not so much matters of faith as "rules of the game." They are rules that we must adhere to if we are going to prove theorems within the particular mathematical system.
Just as postulates define the subject we are analyzing (such as the way lines interact to form a plane), undefined terms are necessary in order to name what the postulates are talking about. The terms are like the objects used in a game (chessmen, for example), and the postulates are the rules for playing (how a knight can move, how a piece is captured, etc.). All of this may be merely hypothetical (“imagine a world where …”), or applied (“let’s assume the world …”). “Faith” would apply, if at all, only in the latter, not in the math itself.
We aren't allowed to introduce additional assumptions (undefined terms or postulates) or alter them without explicitly stating the new assumptions. When we do so, we are no longer working in the same mathematical system. It may be a perfectly valid system, but it isn't the same one once its rules have been changed, even the slightest bit.
Many mathematical systems - probably all until the last two centuries or so - were motivated by attempts to describe and explain things in the real world. At this point, math overlaps with science, and faith becomes relevant. Do the undefined terms and postulates of our system correspond to elements of the real world and their interactions? We can't know. In all likelihood, they don't correspond exactly, but they may make a good approximation.
So “faith” is needed in applying the math, either in taking a teacher’s word for it that gravity follows certain laws, say, or in trusting that our experiments reveal truth about the underlying rules of the world. (Generally, what we discover is close enough to use, given the accuracy of our measurements.)
For instance, a "point" in geometry can be thought of as something with no length, width, or breadth. Everything in the real world has some length, width, and breadth; we can only approximate a point by making a dot with the sharpest pencil we can get. (Physicists now think that electrons may actually be points, but electrons obey the laws of quantum physics, which is rather more complicated than ordinary geometry.)
Still, somehow, geometry is very useful in describing the real world, even though strictly speaking, it describes things that don't exist in the real world.
As we become able to measure smaller things, we discover that rules we thought we knew aren’t quite exact; but they are still good enough for rough use. When we apply math to the rules we choose, we are determining how things would work in that “world”, which is not quite the real one but is close.
I said that you can change the rules and come up with a new system. Euclid had 5 postulates in his system of geometry. You can see them here, along with his undefined terms (he called them "definitions", but not all of them are) and "common notions" (actually postulates that are more fundamental than geometry):
Euclid's Elements, Book I (David Joyce)
http://aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html
The fifth postulate was a lot more complicated than the others. It wasn't very pretty, but it seemed to be needed in order to prove some basic facts about real-world geometry - for instance, that the angles in a triangle add up to 180 degrees.
Over the years, people tried to prove the fifth postulate, thinking that something so complex must somehow follow from the simpler postulates. They failed. In the nineteenth century, mathematicians tried a different tack: try changing the postulate, and see what happens. They found that they ended up with several varieties of "non-Euclidean" geometry that were completely self-consistent, but different from Euclid's geometry. Changing the "rules" made a new but perfectly good game.
So what do you think happened next? Einstein came along and discovered that these non-Euclidean geometries were just the thing to describe the real-world interactions of objects with mass - that is, to describe gravity. This is a case where the mathematical system was invented with no consideration of the real world (and therefore no faith element), but it turned out that this system does appear to describe the real world.
The experiments to show that Einstein's theory of general relativity do describe the real world better than any other mathematical system are very tricky; it is still possible that another system would do better. We can be absolutely sure that the results of general relativity theory follow from its assumptions; the only question is whether or not those assumptions match the way the real world is.
Science, as we see, also makes assumptions; its assumptions are about the real world, and can therefore be wrong; the assumptions in math just define what the math is about, and can’t be wrong until we try to apply the math to something pre-existing.
Let me put it another way. There are two kinds of truth; I'll call them mathematical truth and real-world truth. Mathematical truth means that a statement is consistent with the assumptions of a particular mathematical system. In a sense, people created that system, and they can tell absolutely whether the statement is true within that system.
...
Real-world truth is of a different order: it means that a statement is consistent with the particular system that is the real world. There is only one real world, and no human created it; no one knows exactly what the rules are. Scientists try to make rules that seem to describe the real world, but they can't possibly know whether these rules really describe everything in the universe.
So yes, faith is necessary, because we did not create the real world, so we can't know absolutely what the rules of this system are ... unless someone from outside this system - the creator of the system - lets us know the rules.
## Can’t I define the undefined terms?
To close out, let’s look at a student’s attempt to define “line”:
Undefined Geometry Terms
I know that they call point, line, and plane the undefined terms of geometry, but is there a way to give those terms a definition? I've been thinking, and you may not be able to give all them a definition, but a line could a line be defined as the inconclusive conjunction (or joining) of two rays going in separate directions. I've never really thought that anything couldn't have a definition, so is it possible for any of these geometric terms to be defined?
Jake is wise to suppose only that some of the undefined terms could be defined, in terms of others (just as perhaps a claimed postulate might be found to be provable in terms of others, and thus demoted to a theorem). But his attempted definition, which I might refine as “A line is the union of two rays going in opposite directions from the same point, ” proves the point, as I explained:
Your "definition" would require us to first define "ray" and "direction." Can you do that without reference to "point," "line," and "plane"?
A definition has to be given in terms of previously known terms. In the usual presentation, “ray” is defined in terms of “line” and “point”, and “direction” isn’t really given a definition at all. So his attempted definition has to either be circular, or go outside the system.
Think of it this way: Math is a huge building, in which each part is built by a solid line of inference upon other parts below it. What is the foundation? What is everything else built on?
There must be some lowest level that is not based on anything else; otherwise the whole thing is circular, and never really starts anywhere. The "undefined terms" are part of that foundation, along with other things like rules of inference that tell us that logic itself is true. The goal of mathematicians like Euclid has not been to make math entirely self-contained, with no undefined terms, but to minimize the number of them so that we have to accept only a few basics, and from there will find all of math to be absolutely certain. Also, the goal is to make those terms "obvious," so that we have no trouble accepting them, even though we can't formally prove their existence.
Interestingly, geometrical concepts have been applied to non-geometrical ideas, by assigning the undefined terms differently: if you take “point” to mean “person”, “line” to mean “family”, and so on, you might define a “geometry of people”, for example. This is another reason for undefined terms; it separates the logic from the application.
To put it another way, these terms do have a definition, in human terms; we can easily understand what they mean. They simply don't have a mathematical definition in the sense of depending only on other previously defined terms.
Next time, we’ll look into the fact that different geometry textbooks list different postulates. | 2023-02-06 00:53:10 | {"extraction_info": {"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, "math_score": 0.6630972623825073, "perplexity": 429.60577070282034}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500294.64/warc/CC-MAIN-20230205224620-20230206014620-00586.warc.gz"} |
https://www.scienceforums.net/topic/54622-contradictions-religion-vs-science/page/4/?tab=comments#comment-655040 | ## Recommended Posts
The dials are so finely tuned.
• Replies 158
• Created
#### Popular Days
The energy of the universe must originate from somewhere.
Then where did THAT somewhere originate? It's turtles all the way down...
The dials are so finely tuned.
This is often described as the "fine-tuning argument," and is basically crap.
http://rationalwiki.org/wiki/Argument_from_design#Argument_from_fine_tuning
the fine-tuning argument can also be countered due to the sheer size of the universe; with one hundred billion stars in the galaxy, and as many galaxies in the universe, even a minuscule chance of life arising makes it extremely likely that it will occur somewhere. Moreover, no matter how unlikely an event is, once it occurs, the probability of it having happened is 1.
Fine-tuning arguments based on the physical constants are even easier to refute. The delicate balance of, for example, the tri-alpha fusion which created all the carbon in our bodies relies on the temperature and pressure of stars being exactly right for this form of fusion. However, the pressure and temperature of the interior of a star changes depending on whether or not fusion is occurring. Similar links between other physical constants are likely and can explain their apparently delicate balance.
The argument from fine tuning also fails for the following reasons:
• It bifurcates the laws of physics into constants and the equations into which those constants are placed. It asks us to consider what would happen were the constants changed but the equations stayed the same. But what if we permitted the equations to change also? Then we must admit we have no idea. Even if it is clear that the current equations with different constants cannot produce life, completely different equations (and constants) might still be life-producing. We do not know enough about mathematical physics to say, and may well never. This bifurcation of the laws of physics into constants and equations is more likely an artifact of the human mind's attempt to understand the cosmos than a fundamental property of reality itself
• The argument wants us to conclude that it is highely unlikely that a life-producing set of physical constants could be arrived at by chance. But, how do we ascribe probabilities to sets of possible physical constants? Are they all supposed to be equally likely? Or are some more likely than others? Given these constants are real numbers, and therefore there are infinitely many possible values of them, how does one pick an element at random from an infinite set? What is the probability of picking one such element? And it gets even worse if we reject the bifurcation of the laws of physics into constants and equations -- what is the probability of a particular equation being part of the laws of physics? To speak of probabilities here seems to be just abusing the concept of probability in a situation in which it is meaningless.
Now, if we assume some kind of multiverse theory, then speaking of probabilities of physical constants having certain values, or of certain equations being part of the laws of physics, might have some meaning -- we could look to the distribution of those constant values or laws in different universes across the multiverse to define their probability. But, supporters of the argument from fine-tuning cannot turn to these considerations to make their argument coherent, since if there is such a multiverse then there is no need for the God they are seeking to prove either.
##### Share on other sites
1326049670[/url]' post='649671']
Then where did THAT somewhere originate? It's turtles all the way down...
This is often described as the "fine-tuning argument," and is basically crap.
http://rationalwiki....rom_fine_tuning
Haha, just because I somewhat vaguely say the "dials are finely tuned" doesn't mean I'm alluding to any particular concept... I would appreciate it if you didn't hinder my argument by defamation with theories I never associated with my beliefs, thanks.
by the dials being finely tuned i simply meant EG the atomic structure, the constants, the physical laws, the unwavering forces that allow material form. the canvas that allows the chance of life occurring is specific in itself, empty space itself is not nothing.
##### Share on other sites
Haha, just because I somewhat vaguely say the "dials are finely tuned" doesn't mean I'm alluding to any particular concept... I would appreciate it if you didn't hinder my argument by defamation with theories I never associated with my beliefs, thanks.
by the dials being finely tuned i simply meant EG the atomic structure, the constants, the physical laws, the unwavering forces that allow material form. the canvas that allows the chance of life occurring is specific in itself
Except, you may not realize it, but that's exactly the concept you're talking about.
##### Share on other sites
yeah but what if chance is a property of the universe and not the reason for it happening... i just dont understand how there couldnt be an infinite force responsible... a creator. this place is so weird and i want to think ill see all of you again.
##### Share on other sites
yeah but what if chance is a property of the universe and not the reason for it happening... i just dont understand how there couldnt be an infinite force responsible... a creator. this place is so weird and i want to think ill see all of you again.
There may well be a reason the universe happened but a naturalistic reason much like why galaxies and stars form is more probable than an intelligent creator, why does it have to be a intelligent being that looks like a human male? The multidimensional bulk space is theorized to contain many such branes, i read an article that asserted it could contain many things other than branes, it's really not, at this time at least, any better than the big bang theory but there are potential natural ways what we can think of to cause what we see as the the universe to come into being naturally, no old man in the sky needed. Why add an extra level of complexity? I understand the idea that our lives are finite and will come to an end is unsatisfying in many ways but making something up to make you feel better is hardly the way to go.... Eternity is neatly divided into three parts, before i existed, while I existed, and after i exist, to me that is better than possibly being tortured for an eternity for not believing something that there is no evidence for what so ever....
##### Share on other sites
Sometimes I really believe that I unknowingly constructed my spiritual beliefs to cope with the death of those close to me and to avoid the reality that I'll never see them again. But what if I'm wrong?
As humanity evolves, we get more sympathetic towards one another & gain better morals, don't we? Is that coincidence? Or is it evidence that IF there is a God, or an infinite consciousness, or superior aliens.... that whatever genius work was done that far surpasses our ability, that it's also more forgiving and merciful than us? Us puny humans have such love for one another that is constantly growing, so much in just a tiny flicker of the timeline of just our planet... how couldn't anything superior to us have greater understanding? So if there is a "God", eternal punishment is the biggest pile of shit I've ever heard of.... not one tiny cell in my body believes it. I'm not saying there is a God, but either way, burning in a pit forever is ridiculous. Punishment for naivety wouldn't be plausible.
Edited by Appolinaria
##### Share on other sites
Sometimes I really believe that I unknowingly constructed my spiritual beliefs to cope with the death of those close to me and to avoid the reality that I'll never see them again. But what if I'm wrong?
As humanity evolves, we get more sympathetic towards one another & gain better morals, don't we? Is that coincidence? Or is it evidence that IF there is a God, or an infinite consciousness, or superior aliens.... that whatever genius work was done that far surpasses our ability, that it's also more forgiving and merciful than us? Us puny humans have such love for one another that is constantly growing, so much in just a tiny flicker of the timeline of just our planet... how couldn't anything superior to us have greater understanding?
Most religions require that you worship a particular god to have any chance of an after life. The first thing you have to determine is "which god is real", also just believing there must be a higher power does not suggest that there is any life after death... God does not necessarily equal an after life..... If there is a god it might get quite a laugh at us thinking it is going to take care of us after we die... Then again maybe our souls are what god eats and the god who gets the most worship gets the most souls, possibly all gods are or were real but most died after they were starved because their believers stopped feeding them....
So if there is a "God", eternal punishment is the biggest pile of shit I've ever heard of.... not one tiny cell in my body believes it. I'm not saying there is a God, but either way, burning in a pit forever is ridiculous. Punishment for naivety wouldn't be plausible.
Not plausible? Remember we are talking about beings whose morals are what they want then to be and ordering a city of people who do not believe killed to the last man woman and child... well not the female children.... they were passed out to the solders for their pleasure, but he demanded that infants be dashed to the ground as well, not plausible? If we are really dealing with a being that qualifies as god there is no way to predict what it will or will not do....
Edited by Moontanman
##### Share on other sites
Yes but anything powerful enough to create our universe would not be capable of such things, IMO... It's terribly easy to brainwash a human, a creator would understand their creation completely, why would they be bothered by such an easy sin to commit?
We have two options;
No afterlife. Then when we die, we will just seep into nothing... our brain will shut off and that's it. Not a bad option.
Afterlife. If our "soul" isn't eternal and can be completely destroyed, wiped from the universe- then I don't understand how we can simultaneously exist and not exist since time seems to be only an illusion.
I think it's terrible that a strange book is taken so literally and seriously as to scare people away from believing in a creator altogether, I wouldn't be surprised if it was made intentionally to lead us astray. Obviously as we scientifically grow, we will err from & scoff at religion because of the ridiculous impression we have of it... All of the stories were jumbled together and claimed to be important, and once we see the stories are bizarre we automatically think a higher power is garbage, too.. but that's naive. Instead of blending the logic of our universe with faith/spirituality, we just draw the gap between the two even larger, when they can actually coexist, are in and of the same, and fuel each other at their root.
##### Share on other sites
Yes but anything powerful enough to create our universe would not be capable of such things, IMO...
I can't see why you would assert such a thing considering how much real suffering there is in the world, it not only demanded such horrendous things in the past it does nothing to prevent them in the present, I mean really, would a heads up before a tsunami or an earth quake really be too much to ask?
It's terribly easy to brainwash a human, a creator would understand their creation completely, why would they be bothered by such an easy sin to commit?
I'm not sure what you are saying here.
We have two options;
No afterlife. Then when we die, we will just seep into nothing... our brain will shut off and that's it. Not a bad option.
Afterlife.
Yes but that doesn't make each equally possible.
Afterlife. If our "soul" isn't eternal and can be completely destroyed, wiped from the universe- then I don't understand how we can simultaneously exist and not exist since time seems to be only an illusion.
I'm not sure what you are saying here. Time is an illusion? Says who?
I think it's terrible that a strange book is taken so literally and seriously as to scare people away from believing in a creator altogether, I wouldn't be surprised if it was made intentionally to lead us astray. Obviously as we scientifically grow, we will err from & scoff at religion because of the ridiculous impression we have of it... All of the stories were jumbled together and claimed to be important, and once we see the stories are bizarre we automatically think a higher power is garbage, too.. but that's naive. Instead of blending the logic of our universe with faith/spirituality, we just draw the gap between the two even larger, when they can actually coexist, are in and of the same, and fuel each other at their root.
In my Opinion believing in a higher power is naive, not the other way around, there is no evidence of any higher power, all we have is some people claiming to "just know" or by "faith"... i think that's... well naive doesn't quite cover it. Think about it, what has god done for us? What useful knowledge has god given us? Antibiotics...no. Pain killers...no. Technology...no. All he does is make promises that cannot be confirmed through his spokesmen who always need money and not just to give to the poor, no they need huge fantastically expensive structures to worship in and mansions and expensive cars the spokesmen need.
Now i know not all religious people do that but even though some religions have acolytes who vow personal poverty the churches are still huge and fantastically expensive but more importantly why does an all powerful being need my hard earned dollars? Why can't he just make gold appear in the churches that worship the correct god the correct way and everyone would know he is not only real but those people were worshiping the correct way.
I see no reason to assume a deity, in fact the idea of it is is quite disturbing considering what we have to choose from in the deity category...
Edited by Moontanman
##### Share on other sites
I can't see why you would assert such a thing considering how much real suffering there is in the world, it not only demanded such horrendous things in the past it does nothing to prevent them in the present, I mean really, would a heads up before a tsunami or an earth quake really be too much to ask?
Yes, there is tremendous suffering and I'm probably way too fortunate to even speak about these things. But technically, we could settle away from fault lines and especially coastlines near fault lines...
I think we create much of our own suffering.
I'm not sure what you are saying here.
What I meant was to be brainwashed by an upbringing, tricked into doing malicious things, fooled into taking any kind of belief to an extreme... humans are very susceptible to their environment, easily manipulated. A human that is misled from whatever the "truth" is would probably not be punished by "God" for these reasons. There would be no sin to be punished for, only predictable human error that can be corrected through experience.
##### Share on other sites
Religion is a means of control:
Without it how many suicide bombers do you think we would have seen?
Belief in god is a cop out:
##### Share on other sites
All of you make valuable argument, it's a safe assumption that all of you atheist have not taken time to study the Bible and it's contents will full attention.
<...>
Just because you don't have complete control over life itself, doesn't mean you have to be first to put down beliefs just because you don't understand them.
I'm fairly sure you're no longer around reading this, but just in case you are (or, for anyone else who happens on this thread), there are some really interesting areas where you can explore first hand why others have chosen a position of non-belief, rather often as a result of looking more closely at their holy books, teachings, and worldview.
http://freethoughtblogs.com/pharyngula/category/testimonial/
http://richarddawkins.net/letters/converts
##### Share on other sites
• 2 weeks later...
Would the world be that bad if:
Thou shalt have none other gods before me.
Thou shalt not make unto thee any graven image
Thou shalt not take the name of the LORD thy God in vain
Remember the sabbath day, to keep it holy.
Honour thy father and thy mother
Thou shalt not kill.
Thou shalt not steal.
Thou shalt not bear false witness against thy neighbour.
Thou shalt not covet
I mean, really? If we followed these rules exactly, this would be a perfect world.
##### Share on other sites
I like the nonstampcollector too. those first five commandments seem a little bit superfluous to me.... 7 and 10 are bit iffy too...
##### Share on other sites
Most religions require that you worship a particular god to have any chance of an after life. The first thing you have to determine is "which god is real", also just believing there must be a higher power does not suggest that there is any life after death... God does not necessarily equal an after life..... If there is a god it might get quite a laugh at us thinking it is going to take care of us after we die... Then again maybe our souls are what god eats and the god who gets the most worship gets the most souls, possibly all gods are or were real but most died after they were starved because their believers stopped feeding them....
I think you would have to establish the "Most" claim with some actual evidence that demonstrates that you understand the tenets of any religion, let alone "most" religions. I would never claim to know the tenets of most religions, but even on my limited exposures to various religions your statement doesn't stand.
In fact, most religions I have studied believe we are all praying to the same God, and most even believe in the righteous path of other faiths. Only in the minority of religions (some Fundamentalist branches of Christianity and Islam) do they believe they are the only path to salvation.
##### Share on other sites
In fact, most religions I have studied believe we are all praying to the same God, and most even believe in the righteous path of other faiths. Only in the minority of religions (some Fundamentalist branches of Christianity and Islam) do they believe they are the only path to salvation.
Wait, you're suggesting, for example, that most Christians believe there is a righteous path to salvation without accepting Jesus as your Lord and Savior (i.e. being of another religion such as Judaism, Mormonism, Islam, etc)? Although anecdotal, my experience with Christianity and Christians strongly suggests the exact opposite as does the bible:
John 3:36 Whoever believes in the Son has eternal life; whoever does not obey the Son shall not see life, but the wrath of God remains on him.
Acts 4:12 And there is salvation in no one else, for there is no other name under heaven given among men by which we must be saved.”
John 14:6 Jesus said to him, “I am the way, and the truth, and the life. No one comes to the Father except through me.
##### Share on other sites
Wait, you're suggesting, for example, that most Christians believe there is a righteous path to salvation without accepting Jesus as your Lord and Savior (i.e. being of another religion such as Judaism, Mormonism, Islam, etc)? Although anecdotal, my experience with Christianity and Christians strongly suggests the exact opposite as does the bible:
John 3:36 Whoever believes in the Son has eternal life; whoever does not obey the Son shall not see life, but the wrath of God remains on him.
Acts 4:12 And there is salvation in no one else, for there is no other name under heaven given among men by which we must be saved.”
John 14:6 Jesus said to him, “I am the way, and the truth, and the life. No one comes to the Father except through me.
Yes, I am suggesting that. They all base this core belief on two repeated articles of faith in the Bible:
We all know God's word instinctively through our conscience. God's word is "written on our heart"
Romans 2:12-15 - 12 All who sin apart from the law will also perish apart from the law, and all who sin under the law will be judged by the law. 13 For it is not those who hear the law who are righteous in God’s sight, but it is those who obey the law who will be declared righteous. 14 (Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law. 15 They show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts sometimes accusing them and at other times even defending them.)
Jesus is God's word made flesh.
John 1:10-14 -10 He was in the world, and though the world was made through him, the world did not recognize him. 11 He came to that which was his own, but his own did not receive him. 12 Yet to all who received him, to those who believed in his name, he gave the right to become children of God— 13 children born not of natural descent,c nor of human decision or a husband’s will, but born of God.
14 The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the One and Only, who came from the Father, full of grace and truth.
So by this we all know God's word without needing to be told, and Jesus is God's word, so we know, by Biblical teachings, Jesus without ever being told of him.
As I said, the real difference in the various sects of Christianity is in each belief that they have the best way of adhering to God's word that you already have inside you. They all simply believe that it is far less likely that you will follow the righteous path without them.
It's tricky, I know, but you have to understand who Jesus was and what he stood for within the Bible to get the real picture that the scripture is painting. Jesus was the Son of God, but also his law personified. As such Jesus was always with mankind, but not as a human. Also, flowing from that same argument, Jesus is with us still in the form of God's Law which is, and has always been, written on all people's hearts in the form of their conscience and understanding of good.
Edit: This is also a bit confusing because many people (especially non-believers) who attempt to make sense of the Bible often mistake God's laws to mankind, the finite beings that we are, as some cosmic directive as well. But it's not. God's Law as known to us is simply the part God requires us to play in the bigger picture, whatever that is. As such, God is not bound by these same finite limitations; not because he is unjust, but because he is infinite.
Edited by jryan
##### Share on other sites
Yes, I am suggesting that. They all base this core belief on two repeated articles of faith in the Bible:
I remain incredulous to the claim that most Christians believe that you can achieve heaven through a religion other than Christianity. It is the central claim that it can be only achieved through belief in the divinity of Jesus of every single evangelist and piece of evangelistic propaganda I've ever encountered. I'm happy to be proven wrong by evidence to the contrary.
##### Share on other sites
I remain incredulous to the claim that most Christians believe that you can achieve heaven through a religion other than Christianity. It is the central claim that it can be only achieved through belief in the divinity of Jesus of every single evangelist and piece of evangelistic propaganda I've ever encountered. I'm happy to be proven wrong by evidence to the contrary.
Whether you are incredulous or not doesn't change things. I have already shown in Biblical scripture that the knowledge of good and the following of your good conscience is, by scripture, an intrinsic belief in God and God's Law. Jesus is God's word made flesh and God's word is written on everyone's heart as their conscience. As such you can interchange God, "Jesus", God's Word" and "Good Conscience" and never lose the meaning.
Most Christian religion isn't about establishing the goal or the rules, those have been literally set in stone since Moses, it's about how to follow the rules and achieve the goal of salvation successfully.
##### Share on other sites
I think you would have to establish the "Most" claim with some actual evidence.
You claim most Christians believe something - evidence it.
Showing a supposed basis for a claim is not evidence of the claim.
Edited by Arete
##### Share on other sites
You claim most Christians believe something - evidence it.
Showing a supposed basis for a claim is not evidence of the claim.
So you can make the contrary claim without evidence and yet you demand that I provide evidence that your non-evidence statement is not true? I've provided you the scripture which puts your scriptural evidence in context.
Well, I will offer the Catholic Catechism on the subject first:
Lumen Gentium #16:
16. Finally, those who have not yet received the Gospel are related in various ways to the people of God.(18*) In the first place we must recall the people to whom the testament and the promises were given and from whom Christ was born according to the flesh.(125) On account of their fathers this people remains most dear to God, for God does not repent of the gifts He makes nor of the calls He issues.(126) But the plan of salvation also includes those who acknowledge the Creator. In the first place amongst these there are the Mohammedans, who, professing to hold the faith of Abraham, along with us adore the one and merciful God, who on the last day will judge mankind. Nor is God far distant from those who in shadows and images seek the unknown God, for it is He who gives to all men life and breath and all things,(127) and as Saviour wills that all men be saved.(128) Those also can attain to salvation who through no fault of their own do not know the Gospel of Christ or His Church, yet sincerely seek God and moved by grace strive by their deeds to do His will as it is known to them through the dictates of conscience.(19*) Nor does Divine Providence deny the helps necessary for salvation to those who, without blame on their part, have not yet arrived at an explicit knowledge of God and with His grace strive to live a good life. Whatever good or truth is found amongst them is looked upon by the Church as a preparation for the Gospel.(20*) She knows that it is given by Him who enlightens all men so that they may finally have life. But often men, deceived by the Evil One, have become vain in their reasonings and have exchanged the truth of God for a lie, serving the creature rather than the Creator.(129) Or some there are who, living and dying in this world without God, are exposed to final despair. Wherefore to promote the glory of God and procure the salvation of all of these, and mindful of the command of the Lord, "Preach the Gospel to every creature",(130) the Church fosters the missions with care and attention.
So there is the single largest denomination in the Christian faith saying what I have just told you. Given that it also represents just barely more than 50% of all Christians worldwide it would also qualify as "most".
Lumen Gentium #15, by the way, professes the same extension of salvation to other Christian denominations. In all cases the Catholic faiths teaches that an adherence to God's law and the rejection of evil influence binds you to the Church through the Holy Spirit and is the only truly essential requisite for salvation.
In fact, if you have another Christian denomination to offer that shows your point please provide it, but it is my finding over the years that any seeming difference between the Catholic stand and other Christian religious doctrine is predicated not on the practical nature of this teaching, but on differing beliefs in the existence of free will. When A Christian denomination doesn't believe in free will (Bible Churches, for example) you can say the very same thing the Catholic Church does while superficially appear to be saying the opposite.
##### Share on other sites
So you can make the contrary claim without evidence and yet you demand that I provide evidence that your non-evidence statement is not true? I've provided you the scripture which puts your scriptural evidence in context.
Yours is the positive assertion.
There's plenty of evidence of Christians who do believe that you must accept Jesus as your Lord and Savior to enter Heaven. I quite honestly find it absurd that you're claiming the contrary.
"Classical evangelical doctrine holds that salvation comes only through faith in Jesus Christ, and that those without such faith will be condemned to hell. A number of texts are typically cited in support of this position." http://www.bethinkin...o-to-heaven.htm
"Historically Rome taught that there is no salvation outside the Catholic Church; therefore Muslims, like other non-Catholics, could not be saved unless they convert to the Catholic religion." http://www.justforca...cs.org/a135.htm
"With all respect due, what a Muslim believes is insufficient to take them to Heaven. This is Bible truth." http://forums.ourchu...topic.php?p=740
"Christ is the author of eternal salvation to all them that obeys him (Hebrews 5:8-9), but those folks do not obey him, hence they will not be saved in their present station. If, however, they should learn of Christ, believe and obey him then they too could be saved." http://www.firstcenturychristian.com/answers/answers_041.htm
"So it is those who believe in Jesus as their Lord and Savior who join God in heaven." http://www.missiontoamerica.org/letters/other-religions/muslims-01.html
Edited by Arete
##### Share on other sites
Yours is the positive assertion.
There's plenty of evidence of Christians who do believe that you must accept Jesus as your Lord and Savior to enter Heaven. I quite honestly find it absurd that you're claiming the contrary.
"Classical evangelical doctrine holds that salvation comes only through faith in Jesus Christ, and that those without such faith will be condemned to hell. A number of texts are typically cited in support of this position." http://www.bethinkin...o-to-heaven.htm
"Historically Rome taught that there is no salvation outside the Catholic Church; therefore Muslims, like other non-Catholics, could not be saved unless they convert to the Catholic religion." http://www.justforca...cs.org/a135.htm
"With all respect due, what a Muslim believes is insufficient to take them to Heaven. This is Bible truth." http://forums.ourchu...topic.php?p=740
"Christ is the author of eternal salvation to all them that obeys him (Hebrews 5:8-9), but those folks do not obey him, hence they will not be saved in their present station. If, however, they should learn of Christ, believe and obey him then they too could be saved." http://www.firstcenturychristian.com/answers/answers_041.htm
"So it is those who believe in Jesus as their Lord and Savior who join God in heaven." http://www.missiontoamerica.org/letters/other-religions/muslims-01.html
I have just linked you to the Catholic Catechism view on Salvation so an argument of what that Church might have once believed is immaterial. If you wish to counter this then show where my quote is not from the Catholic Catechism or that it doesn't say what I have already stated. Showing me that some third party says that the Catholic church believes otherwise isn't compelling in the slightest as the authoritative word on the Roman Catholic faith in the Catholic Catechism, not some blogger at "Bigthinking.org".
Second, as I have already pointed out through scripture, unless spelled out otherwise the demand by some faiths that a belief in Jesus is mandatory to salvation is both right and is in semantic agreement with my statement and with the Catholic Catechism given the interchangeable aspect of "Jesus", "God's Law" and "individual conscience" due to the very scripture the rationale is drawn from.
##### Share on other sites
For those who have not understood the word of God, what its purpose is or where it is supposed to lead us. God sent his perfected Son Jesus Christ to explain it to us. The difficulty Jesus had was putting it into words we could understand at the time.
The answer is much simpler than people realize.
We all are sons and daughters of God, though few of us know this.
See John chapter 10 verses 32-36
32. Jesus answered them, "Many good works I have shown you from My Father. For which of those works do you stone Me?''
33. The Jews answered Him, saying, "For a good work we do not stone You, but for blasphemy, and because You, being a Man, make Yourself God.''
34. Jesus answered them, "Is it not written in your law, I said, "You are gods'' '?
35. "If He called them gods, to whom the word of God came (and the Scripture cannot be broken),
36. "do you say of Him whom the Father sanctified and sent into the world, You are blaspheming,' because I said, `I am the Son of God'?
Confirmed by:
Romans chapter 8 verse 14. For as many as are led by the Spirit of God, these are sons of God.
So how do we become effective and useful Sons of God being led by the Spirit:
First we ask the question "who and what is God and his law?". This is the question that is the foundation of all things relating to God the Father. If you yourself don't know the Father, how can you teach and reveal him to others. This is the reason for the birth of Jesus, the one who could reveal God the Father to us. The lack of sin in Jesus was, God knew Jesus could see the Father and that Jesus devoted his whole being to revealing God the Father to the world.
This revealing of God to the world is the will of the the Father from the beginning.
John chapter 4 verses 23-24
23. "But the hour is coming, and now is, when the true worshipers will worship the Father in spirit and truth; for the Father is seeking such to worship Him.
24. "God is Spirit, and those who worship Him must worship in spirit and truth.''
John chapter 5 verse 30 "I can of Myself do nothing. As I hear, I judge; and My judgment is righteous, because I do not seek My own will but the will of the Father who sent Me.
John chapter 6 verses 39-41
39. "This is the will of the Father who sent Me, that of all He has given Me I should lose nothing, but should raise it up at the last day.
40. "And this is the will of Him who sent Me, that everyone who sees the Son and believes in Him may have everlasting life; and I will raise him up at the last day.''
41. The Jews then murmured against Him, because He said, "I am the bread which came down from heaven.''
So what is spirit and truth?
God is the electromagnetic power that drives the Cosmos and powers every atom.
John chapter 8 verses 12-14
12. Then Jesus spoke to them again, saying, "I am the light of the world. He who follows Me shall not walk in darkness, but have the light of life.''
13. The Pharisees therefore said to Him, "You bear witness of Yourself; Your witness is not true.''
14. Jesus answered and said to them, "Even if I bear witness of Myself, My witness is true, for I know where I came from and where I am going; but you do not know where I come from and where I am going.
Jesus confirms this another way:
John chapter 14 verses 10-11
10. "Do you not believe that I am in the Father, and the Father in Me? The words that I speak to you I do not speak on My own authority; but the Father who dwells in Me does the works.
11. "Believe Me that I am in the Father and the Father in Me, or else believe Me for the sake of the works themselves.
For our benefit we need to understand where we came from before we were born and where we go to when we leave here.
We are spirit beings in that we are born from God's almighty power and in the end we return to where we came from (God's almighty power). As Jesus said "Even if I bear witness of Myself, My witness is true, for I know where I came from and where I am going; but you do not know where I come from and where I am going".
We heap up for ourselves many false ideas and misinterpretations but it is so simple in the end.
As God laws power the cosmos, these laws are the inheritance gift of the living God to his children. What more can God the Father give his children than the laws of life itself. Physicists assume space is empty and all energy is stored in solid matter. Blissfully unaware of the fluid power that drives the living cosmos, the power that is our God.
##### Share on other sites
This topic is now closed to further replies.
× | 2022-05-26 23:14:08 | {"extraction_info": {"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, "math_score": 0.2872616648674011, "perplexity": 2087.201708448127}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662627464.60/warc/CC-MAIN-20220526224902-20220527014902-00164.warc.gz"} |
https://rpg.stackexchange.com/questions/53501/when-calculating-magic-item-cost-which-spell-effects-can-be-combined-with-whi/53507 | # When Calculating Magic Item Cost, Which “Spell Effects” can be combined with which “Special” effects?
I'm reading this table of magic item gold cost formulae, and I'm having a very difficult time understanding it. How do the listings in the "Special" table interact with the listings in the "Spell Effect" table?
For example, under "Charged (50 charges)" it says "1/2 unlimited use base price", but has no listing for any "unlimited use base price".
Or for example, "Charges per day" works out such that if you have 5 charges per day, the item's cost is unmodified. If I combined "Charges per day" from the special table with "50 charges, spell trigger" from the Spell Effect table, would I get an item that has 50 charges, but recovers five each day at no extra cost? That doesn't seem right.
I get the impression that not all of these effects are meant to interact with one another. Could someone explain which ones are intended to interact with each other?
• actually, i think if you took both charges and charges per day, you'd be able to use it a total of 50 times, and maximum X times per day, – Mouhgouda Dec 23 '14 at 12:37
You are using the table wrong.
The table assumes you have a magic item in mind and are trying to determine the cost. It is a not a table that you should be grabbing lines from to combine to form magic items.
That said, the entries:
• Single use, spell completion
• Single use, use-activated
• 50 charges, spell trigger
do not normally interact with (and if they do, they do not do a good job estimating actual price):
• Charges per day
• Charged (50 charges)
The first set are intended to price out single use or limited use items that eventually cease to exist or become inert like potions, scrolls, and wands.
The second set are there help determine costs for magic items that continue to exist forever until destroyed such as staffs and wondrous items.
Remember, the table is only there to estimate the cost of a magic item. It is not completely accurate and you should usually consult similar magic items for their price.
Most of the abilities on the table will work together.
To use your specific example the item below would have 50 Charges but would only be able to be used once a day:
Spell Effect:Charged(50 Charges)
Spell: Magic Missle
Caster level: 1 Special: 1 Charge per day.
Cost would be calculated as below.
(spell level)1*(Caster level)1*750=750
You would then divide as per the charges per day section which is 5 divided by the charges per day which is only 1.
750/(5/1)=150
With these effects you would have a wand of magic missile that is only usable once per day but only costs 150 gold.
To answer your question about unlimited use base price. The unlimited use would be something with the spell effect of Command Word or Continuous.
Normally such items would not have a limit but would gain a use limit of 50 Charges. I would interpret this as Command Word items using a charge for each activation while Continuous items would consume a charge each day they are worn or used.
The limited use would half the price of the item but give it a finite life hence the price being halved.
• I think using the table to estimate that kind of wand causes it to come out way to low. If you replace magic missle with cure light wounds, you get a wand that costs 3x the cost of 1 potion, but provides 50 charges..... – Colin D Dec 23 '14 at 14:38
• True. The DM should be the person using the table though so if he/she does not want to allow such a cheap option they shouldn't add it. If a player asks then they can allow or ban it. – Aaron Dec 23 '14 at 14:46
The listings under "Special" interact with all the other listings pretty consistently in general.
One exception is that charges per day and 50-charge items do not interact and can't sanely be combined without some additional work; per the notes above and below, the guidelines don't explain everything, but rely on the DM's knowledge of general similarities between items. There are no items in PF that have 50 charges and regain charges per day on their own, to my knowledge, so pricing a custom item that does that by blind application of the guidelines will likely end in nonsense.
For example, under "Charged (50 charges)" it says "1/2 unlimited use base price", but has no listing for any "unlimited use base price".
Sure it does, lots of them. All effects are unlimited unless otherwise noted, so 2 out of 5 Spell Effect listings, along with all the other Effect listings, are unlimited-use base prices. You have to know which one you're working with first, of course. But basically, "Special" is applied later | 2020-02-18 01:45:25 | {"extraction_info": {"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, "math_score": 0.4196103811264038, "perplexity": 1859.6058952079861}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875143455.25/warc/CC-MAIN-20200217235417-20200218025417-00527.warc.gz"} |
http://mathhelpforum.com/math/202931-please-help-me.html | Hi can someone help me solve this problem,please!!
A piece of cardboard measures 40 cm by 40 cm. An open-topped box is to be constructed by removing a square with side length of 8 cm from each corner and folding up the edges.
a) Find the surface area of the box. b) Find the volume of the box.
Hello, allison!
A piece of cardboard measures 40 cm by 40 cm.
An open-topped box is to be constructed by removing a square with side length of 8 cm
from each corner and folding up the edges.
(a) Find the surface area of the box.
This is simple!
Its area is: $40\times40 \,=\,1600 \text{ cm}^2.$
You remove four 8-by-8 squares.
So you remove: $4 \times (8\cdot8) \,=\,256\text{ cm}^2$
So the surface area of the box must be: $1600 - 256 \,=\,1344\text{ cm}^2.$
(b) Find the volume of the box.
Did you make any sketches?
Code:
: - - - 40 - - - - :
- *---*-----------*---* -
: |///| |///| 8
: *---* - - - - - *---* -
: | : : | :
: | : : | :
40 | : : | 24
: | : : | :
: | : : | :
. : *---* - - - - - *---* -
: |///| :///| 8
- *---*-----------*---* -
: 8 : - 24 - - : 8 :
The corner squares are removed
. . and the sides are folded upward on the dotted lines.
The open-top box looks like this:
Code:
*-----------*
/| /|
/ * - - - - / *
/ / / /
*-----------* / 24
8| |/
*-----------*
24
I assume you can find the volume now . . . | 2017-10-17 13:31:55 | {"extraction_info": {"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": 3, "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, "math_score": 0.6815488934516907, "perplexity": 1248.7564488184735}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187821189.10/warc/CC-MAIN-20171017125144-20171017145144-00896.warc.gz"} |
https://www.edaboard.com/threads/what-is-the-difference-between-space-time-space-time-coding-and-temporal-coding.107273/ | # What is the difference between space time, space time coding and temporal coding?
Status
Not open for further replies.
#### vkekk
##### Full Member level 3
1. What is the difference between Space time and space time coding?
2. what is temporal coding?
3. advantages of QAM compared with QPSK.. what effect if increase 4QAM To 16QAM...
#### salam2000
##### Member level 3
Re: Space time...
with increase the modulation order you can increase the throughout. because you send same number symbol, but each symbol have larger number bit. bit/symbol=log2(M),
with increase Modulation order, the symbol become closer (near) and we need higher SNR to decrease BER.
### vkekk
points: 2
#### vkekk
##### Full Member level 3
Re: Space time...
thanks salam2000
Can i get the advantages of QAM compared to others.
help me the below .....
1. What is the difference between Space time and space time coding?
2. what is temporal coding?
#### salam2000
##### Member level 3
Re: Space time...
Temporal coding use more in medical and bioelectrical, it maybe use also in wireless communication.
the definition of bioelectrical of it is:
-------------------------------------------------------------------------------
The temporal coding is a type of neural coding which relies on precise timing of action potentials or inter-spike intervals. Combined with traditional rate coding models, temporal coding can provide additional information with the same rate. There is no precise definition of temporal code. Actually almost any coding scheme that is not rate coding can be referred to as a temporal code.
Unlike rate coding, the temporal coding model tries to account for short-term stimuli producing a small number of spikes. For example, if a neuron is capable of firing at a maximum rate of 100 spikes per second, then a stimulus <10ms would likely elicit only a single spike. This model is especially important for sound localization, which occurs within the brain on the order of milliseconds.
The discovery of spike timing dependent plasticity, where synaptic efficacy is modulated by the precise timing of spikes, provides strong evidence that temporal codes are used for cortical information transmission.
It should not be confused with the coding of the temporal information.
----------------------------------------------------------------------------------
if you interest to MIMO systems, you can see title of some book about MIMO in this link:
https://www.edaboard.com/viewtopic.php?t=272247&highlight=
also the Tse book and papers are about "trade off between Spatial Multiplexing and Diversity is good.
I think the space-time is a general name use for systems that gained simultaneously from Space and time diversity. but "Space-Time Codings" are some orthogonal code and mapping scheme that use in these systems to reduce the complexity of these systems from exponential to linearity complexity. some schemes like "STBC", layered ST & ... are famous. they are need for separation signals that interference because transmit simultaneously and in same band.
#### mimomod
##### Member level 4
Re: Space time...
vkekk said:
1. What is the difference between Space time and space time coding?
2. what is temporal coding?
3. advantages of QAM compared with QPSK.. what effect if increase 4QAM To 16QAM...
1. In wireless communication, space-time refers to space and time coordinate of the wireless channel. As you might know, wireless channels have three dimensions: time, frequency, and space. Time dimension is well known. Frequency dimension is due to multipath fading (frequency selective channel). Space dimension occurs when you have multiple antennas at the transmitter or/and the receiver. This three dimensions of wireless channels may be exploited by communication systems to improve the quality of transmission. In simplest form, to improve the quality you may transmit a signal in several copies. This multiple copies may be transmitted in multiple time (repetition in time) or multiple space (antenna), or in case of space-time coding this multiple copies are transmitted both in multiple space and time based in specific way. Hopefully, one or few of this copies are in good quality so the receiver can decode the transmitted signal perfectly.
2. Temporal coding in wireless communication refers to coding only in time coordinate. This is the old kind of coding in wireless communication. Reed-Solomon and convolutional coding is a kind of temporal coding.
3. Actually the difference between 4QAM and QPSK is only in rotation of the signal constellation. QSPK signals are at +1, -1, +j, -j, whereas 4QAM signal are at $e^{j \pi /4}$, $-e^{j \pi /4}$, $j e^{j \pi /4}$, and $-j e^{j \pi /4}$, i.e. QPSK signals rotated by $\pi /4$. Rectangular QAM constellation are, in general, sub-optimal in the sense that they do not maximally space the constellation points for a given energy. However, they have the considerable advantage that they may be easily transmitted as two pulse amplitude modulation (PAM) signals on quadrature carriers, and can be easily demodulated.
If you increase to higher order modulation scheme, you will have more bits per trasmission of a symbol. This is a good strategy to transmit higher order modulation schemes if SNR is high. But if SNR is low then transmitting higher order modulation may introduce higher bit errors.
May it helps.
best
M.N.Rindani
points: 2 | 2021-01-23 01:01:10 | {"extraction_info": {"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, "math_score": 0.4163064956665039, "perplexity": 1669.5184744056294}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703531702.36/warc/CC-MAIN-20210123001629-20210123031629-00175.warc.gz"} |
https://learn.careers360.com/ncert/question-find-the-mean-salary-of-60-workers-of-a-factory-from-the-following-table/ | # Q. 5 Find the mean salary of 60 workers of a factory from the following table:
Salary ( in Rs)(xi) Number of workers(fi) fixi 3000 16 48000 4000 12 48000 5000 10 50000 6000 8 48000 7000 6 42000 8000 4 32000 9000 3 27000 10000 1 10000 Total $\sum_{i=1}^{8}f_{i}=60$ $\sum_{i=1}^{8}f_{i}x_{i}=305000$
The mean of the above data is given by
$\\\bar{X}=\frac{\sum_{i=1}^{8}f_{i}x_{i}}{\sum_{i=1}^{8}f_{i}}\\ \bar{X}=\frac{305000}{60}\\ \bar{X}=5083.33$
The mean salary of the workers working in the factory is Rs 5083.33
## Related Chapters
### Preparation Products
##### Knockout KCET 2021
An exhaustive E-learning program for the complete preparation of KCET exam..
₹ 4999/- ₹ 2999/-
##### Knockout KCET JEE Main 2021
It is an exhaustive preparation module made exclusively for cracking JEE & KCET.
₹ 27999/- ₹ 16999/-
##### Knockout NEET Sept 2020
An exhaustive E-learning program for the complete preparation of NEET..
₹ 15999/- ₹ 6999/-
##### Rank Booster NEET 2020
This course will help student to be better prepared and study in the right direction for NEET..
₹ 9999/- ₹ 4999/- | 2020-08-13 09:24:52 | {"extraction_info": {"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": 3, "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, "math_score": 0.7853037118911743, "perplexity": 8479.199074058239}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738964.20/warc/CC-MAIN-20200813073451-20200813103451-00327.warc.gz"} |
http://ssconlineexam.com/onlinetest/SSC-CGL-Tier-1/Quantitative-Aptitude/-QA-Test-11 | SSC CGL Tier 1 :: QA Test 11
Home » SSC CGL Tier 1 » QA Test 11 » General Questions
# SSC CGL Tier 1 Quantitative Aptitude Questions and Answers Free Online Mock Test 11
ssc cgl tier 1 free quantitative aptitude questions and answers free online test previous questions online tests mock tests quiz sample questions ssc cgl online quiz ssc online test ssc practice test free
Exercise
"Everyone is wise until he speaks." - (Proverb)
1 . What is the least number which should be subtracted from 0.000326, to have perfect square ?
4e-06 2e-06 0.04 0.02
View Answer Workspace Report Discuss in Forum
2 . A wine seller had three types of wine, 403 litres of 1st kind, 434 litres of 2nd kind and 465 litres of 3rd kind. Find the least possible number of casks of equal size in which different types of wine can be filled without mixing
31 44 42 48
View Answer Workspace Report Discuss in Forum
3 . The positive square root of [0.6 × 0.6 × 0.6 + 0.4 × 0.4 × 0.4 + 3 × 0.6 × 0.4] is equal to –
2.1736 1 0.21736 0.072
View Answer Workspace Report Discuss in Forum
4 . The average age of a committee of eight members is 40 years. A member aged 55 years retired and his place was taken by another member aged 39 years. Find the average age of the present committee.
38 years 36 years 39 years 40 years
View Answer Workspace Report Discuss in Forum
5 . There are 40 boys in a class and their average age is 16 years. one boy, aged 17 years, l eaving the cl ass and anot her j o i n i n g , t he a v e r a g e a g e be c o me s 15. 875 years. The age of the new boy is –
12 years 14.5 years 15 years 17 years
View Answer Workspace Report Discuss in Forum
6 . A, B and C three are batsmen. The ratio of the runs scored by them in a certain match are as B : A = 3 : 5 and C : B = 5 : 4. In all they scored 564 runs. The number of runs scored by B is –
124 104 114 144
View Answer Workspace Report Discuss in Forum
7 . 55 litres of mixture has milk and water in the ratio 7 : 4. How much quantity of water must be added in the mixture to get milk and water in the ratio 7 : 6
16 litres 15 litres 12 litres 10 litres
View Answer Workspace Report Discuss in Forum
8 . A, B and C enter into a partnership. A contributes 320000 for 4 months, B contributes 510000 for 3 months and C contributes 270000 for 5 months. If the total profit be 124800, then A's share in the profit is –
38400 45900 40500 41500
View Answer Workspace Report Discuss in Forum
9 . A man spends 40% of his monthly salary on food and one-third of the remaining on transport. If he saves 4500 per month, which is equal to half the balance after spending on food and transport, his monthly salary is –
11250 22500 25000 ` 45000
View Answer Workspace Report Discuss in Forum
10 . In an examination a candidate must score 40% marks to pas s. A candidat e, who gets 220 marks, fails by 20 marks. What are the maxi mum marks for the examination ?
1200 800 600 450
View Answer Workspace Report Discuss in Forum
© 2014 - 2015 by ssconlineexam.com . All Rights Reserved | Copyright | Terms of Use & Privacy Policy
Contact us: info@ssconlineexam.com Follow us on twitter! | 2017-02-23 21:26:38 | {"extraction_info": {"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, "math_score": 0.19212019443511963, "perplexity": 2129.3558816843833}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171232.43/warc/CC-MAIN-20170219104611-00356-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://socratic.org/questions/how-do-you-factor-6x-2-7x-5 | # How do you factor 6x^2-7x-5?
Aug 8, 2015
Factor: $y = 6 {x}^{2} - 7 x - 5$
Ans: (2x + 1)(3x - 5)
#### Explanation:
I use the new AC Method: $y = 6 \left(x - p\right) \left(x - q\right)$
Converted trinomial $y ' = {x}^{2} - 7 x - 30 =$(x - p')(x - q').
p' and q' have opposite signs. (Rule of signs).
Factor pairs of -30 --> (-2, 15)(-3, 10). This sum is 7 = -b.
Change this sum to the opposite. Then, p' = 3 and q' = -10.
Therefor. $p = \frac{p '}{a} = \frac{3}{6} = \frac{1}{2}$ and$q = - \frac{10}{6} = - \frac{5}{3}$
$y = 6 \left(x + \frac{1}{2}\right) \left(x - \frac{5}{3}\right) = \left(2 x + 1\right) \left(3 x - 5\right)$ | 2019-09-19 16:42:36 | {"extraction_info": {"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, "math_score": 0.4879555106163025, "perplexity": 9428.934090708031}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573561.45/warc/CC-MAIN-20190919163337-20190919185337-00417.warc.gz"} |
https://studyqas.com/can-you-help-me-thanks/ | Can you help me? Thanks!
Can you help me? Thanks!
$Can you help me? Thanks!$
9. Find the area of a circle having a circumference of 382. Round to the nearest tenth. Use 3.14 for 1. a. 1133.5 units b. 1078.6
1. claraesson5581 says:
Explanation:
2. juliannabartra says:
60.58
Step-by-step explanation:add the first numbers 64.67 take that from 125.25 and u got 60.58
3. alisonguerrero17 says:
7. The molar mass of pottasium dichromate(K2Cr2O7) = 294 g.
4. gomezandy8537 says:
1. Negative
2. Positive
3. 9=2m m= the money he lost each month. M= 4.50, Jared lost \$4.50 each month
4. He lost 0.6 cm each year. You divide 2.4 ( the total height lost) by 4 ( the amount of time) and get 0.6 ( the height he lost each year)
5. ellycleland16 says:
I believe it's the third one
Explanation:
I did this before but I don't remember exactly, so sorry :((
A Long Walk to Water Summary Chapter 1
Southern Sudan, 2008
Nya is an 11-year-old girl. She goes to fetch water for her family. It will take her half the morning to get there, but this part—carrying an empty water jug—is the easy part of the journey. She will endure heat and thorns in her feet along the way.
7. reganjones89 says:
1. The passage depicts the civil war in Sudan through the eyes of a young child. ... For two years, there's been a war in Sudan. There are rebels in the south, fighting against the government in the north. Salva doesn't know much about these rebels, but he knows they don't want to practice Islam.
2. The Lost Children persevered to overcome the hardships of war, starvation, thirst, displacement, and threats by wild animals. Many of them show respect, empathy, and integrity as they help each other survive these same hardships.
8. hayleyl05 says:
60.58
Step-by-step explanation:
Subtract the first 2 numbers which equals 64.67 then subtract 64.67 and 125.25 and you get... 60.58
9. bettymj3071 says:
A. 121
B. 108
C. 12 | 2022-11-27 02:43:05 | {"extraction_info": {"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, "math_score": 0.5540560483932495, "perplexity": 5717.341634094351}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710155.67/warc/CC-MAIN-20221127005113-20221127035113-00112.warc.gz"} |
http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=DBSHCJ_2007_v22n4_565 | operator;"/> operator;"/> ASYMPTOTIC DIRICHLET PROBLEM FOR THE SCHRÖDINGER OPERATOR ON 2-DIMENSIONAL CARTAN-HADAMARD MANIFOLDS | Korea Science
ASYMPTOTIC DIRICHLET PROBLEM FOR THE SCHRÖDINGER OPERATOR ON 2-DIMENSIONAL CARTAN-HADAMARD MANIFOLDS
Title & Authors
ASYMPTOTIC DIRICHLET PROBLEM FOR THE SCHRÖDINGER OPERATOR ON 2-DIMENSIONAL CARTAN-HADAMARD MANIFOLDS
Kim, Seok-Woo; Lee, Yong-Hah;
Abstract
We solve the asymptotic Dirichlet problem for a certain $\small{Schr\"{o}dinger}$ operator on 2-dimensional Cartan-Hadamard manifolds.
Keywords
asymptotic Dirichlet problem;$\small{Schr\"{o}dinger}$ operator;
Language
English
Cited by
References
1.
A. Ancona, Convexity at infinity and Brownian motion on manifolds with unbounded negative curvature, Rev. Mat. Iberoamericana 10 (1994), 189-220
2.
H. I. Choi, Asymptotic Dirichlet problem for harmonic functions on Riemannian manifolds, Trans. Amer. Math. Soc. 281 (1984), 691-716
3.
P. Eberlein and B. O'Neill, Visibility manifolds, Pacific J. Math. 46 (1973), 45-109
4.
A. A. Grigor'yan and W. Hansen, Liouville property for Schrodinqer operators, Math. Ann. 312 (1998), 659-716 | 2016-10-27 16:52:49 | {"extraction_info": {"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": 2, "/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, "math_score": 0.934685230255127, "perplexity": 2832.1236678266923}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721355.10/warc/CC-MAIN-20161020183841-00293-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/questions/167786/slanted-greater-than-and-equal-to-less-than-and-equal-to | # Slanted greater than and equal to, less than and equal to
Need to produce a "Greater than" or "Equal to" symbol with a slanted equal component of the symbol, i.e. the bottom bar not parallel to the typed line, but parallel to the bottom bar of the right facing arrow. \geq begets a normal "greaterthan"/"equal to"-symbol. I've found on the internet and then tried \geqslant, but it does not work. I get an error message:
! Undefined control sequence.
l.1171 ...frac{k^{n-1}_1}{k} \right) , n \geqslant
1
?
Am I missing something in the preamble?
I assume there is a similar way to achieve a Less than and equal to slant.
-
Have a look at “How to look up a symbol?” for ideas how you can easily find a particular symbol. – Johannes_B Mar 26 at 13:32
Possible duplicate to stackoverflow.com/q/2596921 – LaRiFaRi Mar 26 at 13:37
You need the amssymb package in order to use the \leqslant and \geqslant symbols.
\documentclass{article}
\usepackage{amssymb}
\begin{document}
$a-b\geqslant 0 \iff a \geqslant b \iff b \leqslant a.$
\end{document}
-
Worked like a charm! Thanks. I'll be book marking. – TommyK Mar 26 at 13:55
There is also \eqslantless and \eqslantgtr from amssymb:
\documentclass{article}
\usepackage{amssymb}
\begin{document}
$a \eqslantless b$ $a \eqslantgtr b$
\end{document}
-
WOW! that was fast! Works like a champ. I'm bookmarking this page! – TommyK Mar 26 at 13:53 | 2014-12-19 12:58:52 | {"extraction_info": {"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": 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, "math_score": 0.9148474335670471, "perplexity": 3335.208648819515}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802768497.135/warc/CC-MAIN-20141217075248-00093-ip-10-231-17-201.ec2.internal.warc.gz"} |
http://soup.xigmo.org/ | You are at the newest post.
09:02
Reposted by
10:34
Reposted by
18:38
Reposted by
10:39
Reposted by
10:10
20:58
## December062008
13:49
Brilliant Simpsons Apple-parody!
20:12
## December012008
19:36
If you had purchased $1,000 of Delta Air Lines stock one year ago, you would have$49 left.
With Fannie Mae, you would have $2.50 left of the original$1,000.
With AIG, you would have less than $15 left. But, if you had purchased$1,000 worth of beer one year ago, drunk all of the beer, then turned in the cans for the aluminum recycling REFUND, you would have \$214 cash.
Based on the above, the best current investment advice is to drink heavily and recycle...
Reposted from fbogner via agclx
## November242008
05:13
### The Austrians Were Right (by Ron Paul)
@kintel :)
Reposted from sushimako
## November212008
21:09
20:55
She needs a name!
In fact, all of my sketches need names, any suggestions?
Note: Transparent background, make sure to specify a background-colour if you repost this ;-)
19:22
Reposted from flipovitsch
17:52
AK meint: Fette Streicher-DnB-Komposition.
Reposted from ak
17:49
Censorship is frustrating...
and pointless, as far as I can work out.
Profanity? Just words and I don't see any reason why kids shouldn't be allowed to express themselves using the same vocabulary they'd end up with as "adults" anyway.
Nudity? I've never seen Discovery Channel censor mating animals and that's something some people might actually find offensive (for no rational reason whatsoever). So why censor parts of the human body? Why hide what all of us have seen before?
Right, so why is my picture (well sketch, really) above censored then?
"..."
Reposted by NON_HUMANA
16:50
Ja, ich trinke meinen Kaffee gerne mit einer Priese morbidem Humor und schlechten Witzen über kürzlich Dahingeschiedene.
— Dr.Zoidberg aka Aelfric
## November202008
20:40
"The pen is mightier than the sword" ... if you know how to use it.
I don't, but I'm trying :-P
Reposted by
09:53
:)²
Reposted from thenausner via zideshowbob
08:42
### Tiny ninjas rock!
07:19
Dirty Hungarian Phrasebook
Older posts are this way If this message doesn't go away, click anywhere on the page to continue loading posts. | 2020-01-18 21:27:50 | {"extraction_info": {"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, "math_score": 0.2168862670660019, "perplexity": 14696.545083273943}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250593937.27/warc/CC-MAIN-20200118193018-20200118221018-00135.warc.gz"} |
http://math.soimeme.org/~arunram/Resources/NOSPC6DoubleSchubertPolynomials.html | ## Notes on Schubert PolynomialsChapter 6
Last update: 2 July 2013
## Double Schubert Polynomials
Let $x=\left({x}_{1},\dots ,{x}_{n}\right),$ $y=\left({y}_{1},\dots ,{y}_{n}\right)$ be two sequences of independent indeterminates, and recall (5.8) that
$Δ(x,y)= ∏i+j≤n (xi-yj).$
For each $w\in {S}_{n},$ we define the double Schubert polynomial ${𝔖}_{w}\left(x,y\right)$ to be
$(6.1) 𝔖w(x,y)= ∂w-1w0 Δ(x,y)$
where ${\partial }_{{w}^{-1}{w}_{0}}$ acts on the $x$ variables.
Since $\Delta \left(x,0\right)={x}^{\delta }$ we have
$(6.2) 𝔖w(x,0)= 𝔖w(x),$
the (single) Schubert polynomial indexed by $w\text{.}$
From the Cauchy formula (5.10) we have
$𝔖w(x,y)= ∑v∈Sn ∂w-1w0 𝔖vw0(x) 𝔖v(-y)$
and by (4.2)
$∂w-1w0 𝔖vw0(x)= 𝔖vw(x)$
if $\ell \left(vw\right)=\ell \left(v{w}_{0}\right)-\ell \left({w}^{-1}{w}_{0}\right),$ i.e. if $\ell \left(vw\right)=\ell \left(w\right)-\ell \left(v\right),$ and
$∂w-1w0 𝔖vw0(x)=0$
otherwise. Hence
$(6.3) 𝔖w(x,y)= ∑u,v𝔖u (x)𝔖v(-y)$
summed over all $u,v\in {S}_{n}$ such that $w={v}^{-1}u$ and $\ell \left(w\right)=\ell \left(u\right)+\ell \left(v\right)\text{.}$
From (6.3) it follows that ${𝔖}_{w}\left(x,y\right)$ is a homogeneous polynomial of degree $\ell \left(w\right)$ in ${x}_{1},\dots ,{x}_{n-1},$ ${y}_{1},\dots ,{y}_{n-1}\text{.}$ We have
(6.4)
(i) ${𝔖}_{{w}_{0}}\left(x,y\right)=\Delta \left(x,y\right),$ (ii) ${𝔖}_{1}\left(x,y\right)=1,$ (iii) ${𝔖}_{{w}^{-1}}\left(x,y\right)={𝔖}_{w}\left(-y,-x\right)=\epsilon \left(w\right){𝔖}_{w}\left(y,x\right)$ for all $w\in {S}_{n},$ (iv) ${𝔖}_{w}\left(x,x\right)=0$ for all $w\in {S}_{n}$ except $w=1\text{.}$
Proof. (i) is immediate from the definition (6.1). (ii) and (iii) follow from (6.3). (iv) follows from (5.20), since ${𝔖}_{w}\left(x,x\right)=\theta \left({\partial }_{{w}^{-1}{w}_{0}}\Delta \right)=0$ if $w\ne 1\text{.}$ $\square$
(6.5) (Stability) If $m>n$ and $i$ is the embedding of ${S}_{n}$ in ${S}_{m},$ then
$𝔖i(w)(x,y) =𝔖w(x,y)$
for all $w\in {S}_{n}\text{.}$
Proof. This again follows from (6.3) and the stability of the single Schubert polynomials (4.5). $\square$
From (6.5) it follows that the double Schubert polynomials ${𝔖}_{w}\left(x,y\right)$ are well defined for all permutations $w\in {S}_{\infty }\text{.}$
For any commutative ring $K,$ let $K\left({S}_{\infty }\right)$ denote the $K\text{-module}$ of all functions on ${S}_{\infty }$ with values in $K\text{.}$ We define a multiplication in $K\left({S}_{\infty }\right)$ as follows: for $f,g\in K\left({S}_{\infty }\right),$
$(fg)(w)= ∑u,vf(u) g(v)$
summed over all $u,v\in {S}_{\infty }$ such that $uv=w$ and $\ell \left(u\right)+\ell \left(v\right)=\ell \left(w\right)\text{.}$ For this multiplication, $K\left({S}_{\infty }\right)$ is an associative (but not commutative) ring, with identity element $\underset{\underset{_}{_}}{1},$ the characteristic function of the identity permutation $1\text{.}$ It carries an involution $f↦{f}^{*},$ defined by
$f*(w)= f(w-1)$
which satisfies
$(fg)*= g*f*$
for all $f,g\in K\left({S}_{\infty }\right)\text{.}$
(6.6) Let $f,g\in K\left({S}_{\infty }\right)\text{.}$
(i) If $fg=f$ and $f\left(1\right)$ is not a zero divisor in $K,$ then $g=\underset{\underset{_}{_}}{1}\text{.}$ (ii) If $fg=\underset{\underset{_}{_}}{1},$ then $gf=\underset{\underset{_}{_}}{1}\text{.}$ (iii) $f$ is a unit (i.e. invertible) in $K\left({S}_{\infty }\right)$ if and only if $f\left(1\right)$ is a unit in $K\text{.}$
Proof. (i) We have $f\left(1\right)=f\left(1\right)g\left(1\right)$ and hence $g\left(1\right)=1\text{.}$ We shall show by induction on $\ell \left(w\right)$ that $g\left(w\right)=0$ for all $w\ne 1\text{.}$ So let $r>0$ and assume that $g\left(v\right)=0$ for all $v\in {S}_{\infty }$ such that $1\le \ell \left(v\right)\le r-1\text{.}$ Let $w$ be a permutation of length $r\text{.}$ We have $(1) f(w)=(fg) (w)=f(w) g(1)+f(1) g(w)+∑u,v f(u)g(v)$ where the sum on the right is over $u,v\in {S}_{\infty }$ such that $u\ne 1,$ $v\ne 1,$ $uv=w$ and $\ell \left(u\right)+\ell \left(v\right)=\ell \left(w\right),$ so that $1\le \ell \left(v\right)\le r-1$ and therefore $g\left(v\right)=0\text{.}$ Hence (1) reduces to $f\left(1\right)g\left(w\right)=0$ and therefore $g\left(w\right)=0$ as required. (ii) We have $f\left(1\right)g\left(1\right)=1$ so that $f\left(1\right)$ is a unit in $K\text{.}$ Also $f\left(gf\right)=\left(fg\right)f=f,$ whence $gf=\underset{\underset{_}{_}}{1}$ by (i) above. (iii) Suppose $f$ is a unit in $K\left({S}_{\infty }\right),$ with inverse $g\text{.}$ Since is $fg=\underset{\underset{_}{_}}{1}$ we have $f\left(1\right)g\left(1\right)=1,$ whence $f\left(1\right)$ is an unit in $K\text{.}$ Conversely, if $f\left(1\right)$ is an unit in $K$ we construct an inverse $g$ of $f$ as follows. We define $g\left(1\right)=f{\left(1\right)}^{-1}$ and proceed to define $g\left(w\right)$ by induction on $\ell \left(w\right)\text{.}$ Assume that $g\left(v\right)$ has been defined for all $v$ such that $\ell \left(v\right)<\ell \left(w\right)$ and set $g(w)=-f (1)-1 ∑u,vf(u) g(v)$ summed over $u,v$ such that $uv=w,$ $v\ne w$ and $\ell \left(u\right)+\ell \left(v\right)=\ell \left(w\right)\text{.}$ This definition gives $\left(fg\right)\left(w\right)=0$ as required. $\square$
Now let $𝔖\left(x\right)$ (resp. $𝔖\left(x,y\right)\text{)}$ be the function on ${S}_{\infty }$ whose value at a permutation $w$ is ${𝔖}_{w}\left(x\right)$ (resp. ${𝔖}_{w}\left(x,y\right)\text{).}$ (The coefficient ring $K$ is now the ring $ℤ\left[x,y\right]$ of polynomials in the $x\text{'s}$ and $y\text{'s.)}$ Since ${𝔖}_{1}\left(x\right)={𝔖}_{1}\left(x,y\right)=1,$ it follows from (6.6)(iii) that $𝔖\left(x\right)$ and $𝔖\left(x,y\right)$ are units in $K\left({S}_{\infty }\right)\text{.}$
(6.7)
(i) $𝔖\left(x,0\right)=𝔖\left(x\right),$ (ii) $𝔖\left(x,x\right)=\underset{\underset{_}{_}}{1},$ (iii) $𝔖{\left(x,y\right)}^{*}=𝔖\left(-y,-x\right),$ (iv) $𝔖{\left(x\right)}^{-1}=𝔖\left(0,x\right),$ (v) $𝔖{\left(x\right)}^{*}=𝔖{\left(-x\right)}^{-1},$ (vi) $𝔖\left(x,y\right)=𝔖{\left(y\right)}^{-1}𝔖\left(x\right)=𝔖{\left(y,x\right)}^{-1}\text{.}$
Proof. (i)-(iii) follow directly from (6.2) and (6.4). From (6.3) and (6.4) we have $𝔖w(x,y)= ∑u,v 𝔖u-1 (-y)𝔖v(x)= ∑u,v𝔖u (0,y)𝔖v(x)$ summed over $u,v\in {S}_{\infty }$ such that $uv=w$ and $\ell \left(u\right)+\ell \left(v\right)=\ell \left(w\right)\text{.}$ In other words, $(1) 𝔖(x,y)=𝔖 (0,y)𝔖(x).$ In particular, when $y=x$ we obtain $𝔖\left(0,x\right)𝔖\left(x\right)=𝔖\left(x,x\right)=\underset{\underset{_}{_}}{1}$ by (ii) above, and hence $𝔖\left(0,x\right)=𝔖{\left(x\right)}^{-1}\text{.}$ This establishes (iv); part (v) now follows from (iv) and (iii), and (vi) from (iv) and (1) above. $\square$
From (6.7) (vi) we have
$𝔖(x)=𝔖(y) 𝔖(x,y)$
or explicitly
$𝔖w(x)=∑u,v 𝔖u(y)𝔖v (x,y)$
summed over $u,v$ such that $uv=w$ and $\ell \left(u\right)+\ell \left(v\right)=\ell \left(w\right),$ so that $u=w{v}^{-1}$ and ${𝔖}_{u}={\partial }_{v}{𝔖}_{w}$ by (4.2). Hence
$𝔖w(x)=∑v 𝔖v(x,y)∂v 𝔖w(y)$
(where the operators ${\partial }_{v}$ act on the $y$ variables). The sum here may be taken over all permutations $v,$ since ${\partial }_{v}{𝔖}_{w}=0$ unless $\ell \left(w{v}^{-1}\right)=\ell \left(w\right)-\ell \left(v\right)\text{.}$ By linearity and (4.13) it follows that
(6.8) (Interpolation Formula) For all $f\in {P}_{n}=ℤ\left[{x}_{1},\dots ,{x}_{n}\right]$ we have
$f(x)=∑w𝔖w (x,y)∂wf(y)$
summed over permutations $w\in {S}^{\left(n\right)}\text{.}$
(The reason for the restriction to ${S}^{\left(n\right)}$ in the summation is that if $w\notin {S}^{\left(n\right)}$ we shall have $w\left(m\right)>w\left(m+1\right)$ for some $m>n,$ and hence ${\partial }_{w}={\partial }_{v}{\partial }_{m}$ where $v=w{s}_{m}\text{;}$ but ${\partial }_{m}f=0$ for all $f\in {P}_{n},$ since $m>n,$ and therefore ${\partial }_{w}f=0\text{.)}$
Remarks. 1. By setting each ${y}_{i}=0$ in (6.8) we regain (4.14).
2. When $n=1,$ the sum is over ${S}^{\left(1\right)},$ which consists of the permutations ${w}_{p}={s}_{p}{s}_{p-1}\dots {s}_{1}$ $\left(p\ge 0\right)\text{;}$ ${w}_{p}$ is dominant, of shape $\left(p\right),$ so that (see (6.15) below) ${𝔖}_{{w}_{p}}\left(x,y\right)=\left(x-{y}_{1}\right)\dots \left(x-{y}_{p}\right)\text{.}$ Hence the case $n=1$ of (6.8) is Newton's interpolation formula
$f(x)=∑p≥0 (x-y1)… (x-yp)fp (y1,…,yp+1)$
where ${f}_{p}={\partial }_{p}{\partial }_{p-1}\dots {\partial }_{1}f,$ or explicitly
$fp(y1,…,yp+1)= ∑i=1p+1 f(yi) ∏j≠i (yi-yj) .$
For any integer $r,$ let ${𝔖}_{w}\left(x,r\right)$ denote the polynomial obtained from ${𝔖}_{w}\left(x,y\right)$ by setting ${y}_{1}={y}_{2}=\dots =r\text{.}$ Since
$𝔖w0(x,r) = Δ(x,r)= ∏i=1n-1 (xi-r)n-i = 𝔖w0(x-r)$
where $x-r$ means $\left({x}_{1}-r,{x}_{2}-r,\dots \right),$ it follows from the definitions (6.1) and (4.1) that
$𝔖w(x,r)=𝔖w (x-r)$
for all permutations $w\text{.}$ Hence, by (6.7)(vi),
$𝔖(x-r)=𝔖 (r)-1𝔖 (x)$
and in particular, for all integers $q,$
$𝔖(q-r)=𝔖 (r)-1𝔖(q)$
from which it follows that
$(6.9) 𝔖(r)=𝔖(1)r$
for all $r\in ℤ\text{.}$
Since ${𝔖}_{w}\left(x\right)$ is a sum of monomials with positive integral coefficients (4.17), ${𝔖}_{w}\left(1\right)$ is the number of monomials in ${𝔖}_{w}\left(x\right)$ (each monomial counted the number of times it occurs). By homogeneity, we have
$(6.10) 𝔖w(r)= rℓ(w) 𝔖w(1).$
From (6.7)(v) and (6.9) we obtain
$𝔖(1)*=𝔖 (-1)-1= 𝔖(1)$
so that we have another proof of the fact (4.30) that ${𝔖}_{w}\left(1\right)={𝔖}_{{w}^{-1}}\left(1\right)\text{.}$
Now consider the function $F=𝔖\left(1\right)-\underset{\underset{_}{_}}{1},$ whose value at $w\in {S}_{\infty }$ is
$F(w)= { numbers of monomials in 𝔖w, if w≠1, 0, if w=1.$
For each positive integer $p$ we have
$(1) Fp = (𝔖(1)-1__)p = ∑r=0p (-1)r (pr) 𝔖(1)r = ∑r=0p (-1)r (pr) 𝔖(1)$
by (6.9). The value of (1) at a permutation $w$ of length $p$ is by (6.10) equal to
$( ∑r=0p (-1)r (pr) rp ) 𝔖w(1)$
which is equal to $p!{𝔖}_{w}\left(1\right)$ (consider the coefficient of ${t}^{p}$ in ${\left({e}^{t}-1\right)}^{p}\text{).}$ On the other hand, ${F}^{p}\left(w\right)$ is by definition equal to
$(2) ∑w1,…,wp F(w1)…F(wp)$
summed over all sequences $\left({w}_{1},\dots ,{w}_{p}\right)$ of permutations such that ${w}_{1}\dots {w}_{p}=w,\ell \left({w}_{1}\right)+\dots +\ell \left({w}_{p}\right)=\ell \left(w\right)=p,$ and ${w}_{i}\ne 1$ for $1\le i\le p\text{.}$ It follows that each ${w}_{i}$ has length $1,$ hence ${w}_{i}={s}_{{a}_{i}}$ say, and that $\left({a}_{1},\dots ,{a}_{p}\right)$ is a reduced word for $w\text{.}$ Since
$𝔖sa=x1+…+ xa$
by (4.4). we have $F\left({w}_{i}\right)={𝔖}_{{s}_{{a}_{i}}}$ $\text{(1)}={a}_{i},$ and hence the sum (2) is equal to $\sum {a}_{1}{a}_{2}\dots {a}_{p}$ summed over all $\left({a}_{1},\dots ,{a}_{p}\right)\in R\left(w\right)\text{.}$
We have therefore proved that
(6.11) The number of monomials in ${𝔖}_{w}$ is
$𝔖w(1)=1p! ∑a1a2…ap$
summed over all $\left({a}_{1},\dots ,{a}_{p}\right)\in R\left(w\right),$ where $p=\ell \left(w\right)\text{.}$
Remarks. 1. The reduced words for ${1}_{m}×w$ $\left(m\ge 1\right)$ are $\left(m+{a}_{1},\dots ,m+{a}_{p}\right)$ where $\left({a}_{1},\dots ,{a}_{p}\right)\in R\left(w\right)\text{.}$ Hence from (6.11) and homogeneity we have
$𝔖1m×w(1m) =1p!∑ (1+a1m)… (1+apm)$
summed over $R\left(w\right)$ as before. Letting $m\to \infty ,$ we deduce that
$(6.12) Card R(w)=p! limm→∞ 𝔖1m×w (1m).$
2. If $w$ is dominant of length $p,$ then ${𝔖}_{w}$ is a monomial by (4.7). and hence in this case
$∑R(w)a1 …ap=p!$
3. Suppose that $w$ is vexillary of length $p\text{.}$ Then by (4.9) we have
$𝔖w=sλ (Xϕ1,…,Xϕr)$
where $\lambda$ is the shape of $w$ and $\varphi =\left({\varphi }_{1},\dots ,{\varphi }_{r}\right)$ the flag of $w\text{.}$ Hence
$𝔖1m×w=sλ ( Xϕ1+m,…, Xϕr+m )$
for each $m\ge 1\text{.}$ If we now set each ${x}_{i}=\frac{1}{m}$ and then let $m\to \infty ,$ we shall obtain in the limit the Schur function ${s}_{\lambda }$ for the series ${e}^{t}$ ([Mac1979], Ch. I. §3. Ex. 5). which is equal to $h{\left(\lambda \right)}^{-1},$ where $h\left(\lambda \right)$ is the product of the hook-lengths of $\lambda \text{.}$ Hence it follows from (6.12) that if $w$ is vexillary of length $p,$ then
$(6.13) Card R(w)= p!h(λ)$
where $\lambda$ is the shape of $w\text{.}$ In other words. the number of reduced words for a vexillary permutation of length $p$ and shape $\lambda ⊢p$ is equal to the degree of the irreducible representation of ${S}_{p}$ indexed by $\lambda \text{.}$
4. It seems likely that there is a $q\text{-analogue}$ of (6.11). Some experimental evidence suggests the following conjecture:
$(6.11q?) 𝔖w(1,q,q2,…) =∑qϕ(a) (1-qa1)… (1-qap) (1-q)… (1-qp)$
summed as in (6.11) over all reduced words $a=\left({a}_{1},\dots ,{a}_{p}\right)$ for $w,$ where
$ϕ(a)=∑ {i:ai
When $w$ is vexillary the double Schubert polynomial ${𝔖}_{w}\left(x,y\right)$ can be expressed as a multi-Schur function, just as in the case of (single) Schubert polynomials (Chap. IV). We consider first the case of a dominant permutation:
(6.14) If $w$ is dominant of shape $\lambda ,$ then
$𝔖w(x,y) = ∏(i,j)∈λ (xi-yj) = sλ ( X1-Yλ1,…, Xm-Yλm )$
where $m=\ell \left(\lambda \right)$ and ${X}_{i}={x}_{1}+\dots +{x}_{i},$ ${Y}_{i}={y}_{1}+\dots +{y}_{i}$ for all $i\ge 1\text{.}$
Proof. As in (4.6) we proceed by descending induction on $\ell \left(w\right),w\in {S}_{n}\text{.}$ The result is true for $w={w}_{0},$ since ${w}_{0}$ is dominant of shape $\delta$ and $𝔖w0(x,y)= Δ(x,y)= ∏(i,j)∈δ (xi-yj).$ Suppose $w\ne {w}_{0}$ is dominant of shape $\lambda \text{.}$ Then $\lambda \subset \delta$ (and $\lambda \ne \delta \text{).}$ Let $r\ge 0$ be the largest integer such that ${\lambda }_{i}^{\prime }=n-i$ for $1\le i\le r,$ and let $a={\lambda }_{r+1}^{\prime }+1\le n-r-1\text{.}$ Then $w{s}_{a}$ is dominant, $\ell \left(w{s}_{a}\right)=\ell \left(w\right)+1,$ and $\lambda \left(w{s}_{a}\right)=\lambda \left(w\right)+{\epsilon }_{a},$ and therefore $𝔖w(x,y) = ∂a𝔖wsa (x,y) = ∂a ( (xa-yr+1) ∏(i,j)∈λ (xi-yj) )$ by the inductive hypothesis; since ${\lambda }_{a}={\lambda }_{a+1}$ it follows that $𝔖w(x,y)= ∏(i,j)∈λ (xi-yj)$ which is equal to ${s}_{\lambda }\left({X}_{1}-{Y}_{{\lambda }_{1}},\dots ,{X}_{m}-{Y}_{{\lambda }_{m}}\right)$ by (3.5). $\square$
(6.15) If $w$ is Grassmannian of shape $\lambda$ then
$𝔖w(x,y)=sλ ( Xm-Yλ1+m-1, …, Xm-Yλm ) .$
Proof. This follows from (6.14) just as (4.8) follows from (4.7). $\square$
Finally, let $w$ be vexillary with shape
$λ(w)= ( p1m1,…, pkmk )$
and flag
$ϕ(w)= ( f1m1,…, fkmk )$
as in Chapter IV. Then ${w}^{-1}$ is also vexillary, with shape
$λ(w-1)=λ (w)′= ( q1n1,…, qknk )$
the conjugate of $\lambda \left(w\right),$ and flag
$ϕ(w-1)= ( g1n1,…, gknk )$
where by (1.41)
$gi+qi= fk+1-i+ pk+1-i (1≤i≤k).$
With this notation recalled, we have
$(6.16) 𝔖w(x,y)=sλ ( (Xf1-Ygk)m1 ,…, (Xfk-Yg1)mk ) .$
Proof. The proof is essentially the same as that of (4.9) (which is the case $y=0\text{).}$ By (4.10) the dominant permutation ${w}_{k}$ constructed from $w$ in the proof of (4.9) has shape $μ= ( gkm1, gk-1m2,…, g1mk )$ and therefore by (6.15) we have $𝔖wk(x,y)=sμ ( X1′,…, Xm′ )$ where $m={m}_{1}+\dots +{m}_{k}=\ell \left(\lambda \right)$ and the sequence $\left({X}_{1}^{\prime },\dots ,{X}_{m}^{\prime }\right)$ is obtained by subtracting the sequence $\left({\left({Y}_{{g}_{k}}\right)}^{{m}_{1}},\dots ,{\left({Y}_{{g}_{1}}\right)}^{{m}_{k}}\right)$ term by term from the sequence $\left({X}_{1},\dots ,{X}_{m}\right)\text{.}$ Hence the same argument as in (4.9) establishes (6.17). $\square$
Remark. From (6.16) and (6.4)(iii) we obtain
$sλ ( Z1m1,…, Zkmk ) = (-1)|λ| sλ′ ( (-Zk)n1,…, (-Z1)nk )$
where ${Z}_{i}={X}_{{f}_{i}}-{Y}_{{g}_{k+i-1}}$ so that (if $rk \left({x}_{i}\right)=rk \left({y}_{i}\right)=1$ for each $i\ge 1\text{)}$
$rk (Zi+1-Zi) = fi+1-fi+ gk+1-i- gk-i = mi+1- nk+1-i$
by (1.41). Hence (6.4)(iii) reduces to the duality theorem (3.8'') (with $\mu =0\text{)}$ when $w$ is vexillary.
Let ${\tau }_{x}$ (resp. ${\tau }_{y}\text{)}$ be the shift operator (4.21) acting on the $x$ (resp. $y\text{)}$ variables. Then we have
$(6.17) τxrτyr𝔖w (x,y)= 𝔖1r×w(x,y)$
for all $r\ge 1$ and all permutations $w\text{.}$
Proof. By (6.3) and (4.21) we have $τxrτyr𝔖w (x,y)=∑u,v ε(v)𝔖1r×u (x)𝔖1r×v(y)$ summed over $u,v$ such that ${v}^{-1}u=w$ and $\ell \left(u\right)+\ell \left(v\right)=\ell \left(w\right)\text{.}$ By (6.3) again, the right-hand side is equal to ${𝔖}_{{1}_{r}×w}\left(x,y\right)\text{.}$ $\square$
In particular, suppose that $w$ is vexillary. With the notation of (6.16), the flag of ${1}_{r}×w$ (resp. ${1}_{r}×{w}^{-1}\text{)}$ is obtained from that of $w$ (resp. ${w}^{-1}\text{)}$ by replacing each ${f}_{i}$ by ${f}_{i}+r$ (resp. each ${g}_{i}$ by ${g}_{i}+r\text{).}$ Hence by (6.16) we have
$𝔖1r×w(x,y) =sλ ( (Xf1+r-Ygk+r)m1,…, (Xfk+r-Yg1+r)mk )$
and hence
$(6.18) ρr(x) ρr(y) 𝔖1r×w (x,y)=sλ (Xr-Yr)$
for all $r\ge 1,$ where ${\rho }_{r}^{\left(x\right)}$ (resp. ${\rho }_{r}^{\left(y\right)}\text{)}$ is the homomorphism ${\rho }_{r}$ of (4.25) acting on the $x$ (resp. $y\text{)}$ variables.
(6.19) Let ${\pi }_{x}$ (resp. ${\pi }_{y}\text{)}$ denote ${\pi }_{{w}_{0}^{\left(r\right)}}$ acting on the $x$ (resp. $y\text{)}$ variables. Then if $w$ is vexillary of shape $\lambda ,$ we have
$πxπy𝔖w (x,y)=sλ (Xr-Yr).$
Proof. By (4.24) we have ${\pi }_{x}={\rho }_{r}^{\left(x\right)}{\tau }_{x}^{r}$ and ${\pi }_{y}={\rho }_{y}^{\left(r\right)}{\tau }_{y}^{r}\text{.}$ Hence (6.19) follows from (6.17) and (6.18). $\square$
In particular, suppose that $w$ is dominant of shape $\lambda ,$ so that by (6.14)
$𝔖w(x,y)= ∏(i,j)∈λ (xi-yj)= fλ(x,y) say.$
In this case (6.19) gives
$πxπyfλ (x,y)=sλ (Xr-Yr)$
for all $r\ge 1,$ which is Sergeev's formula (3.12').
## Notes and References
This is a typed excerpt of the book Notes on Schubert Polynomials by I. G. Macdonald. | 2023-03-23 01:23:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 388, "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, "math_score": 0.9730235934257507, "perplexity": 503.85371118342687}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296944606.5/warc/CC-MAIN-20230323003026-20230323033026-00720.warc.gz"} |
https://www.transtutors.com/questions/david-consumes-two-things-gasoline-g-and-bread-b-david-s-sutility-functionis-u-q-1-q-3295779.htm | # David consumes two things: gasoline (G) and bread (B).David's sutility functionis U(q_1, q_2) =...
David consumes two things: gasoline (G) and bread (B).David's sutility functionis U(q_1, q_2) = 10q^0.25_1 q^0.75_2. Derive David's demand curve for gasoline. If the price of gasoline rises, how much does David reduce his consumption of gasoline, For David, how does depend on his income? That is, how does David's change in gasoline consumption due to an increase in the price of gasoline depend on his income level? To answer these questions, find the cross-partial derivative, M | 2019-08-23 20:09:38 | {"extraction_info": {"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, "math_score": 0.9364423751831055, "perplexity": 8413.21466940917}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027318986.84/warc/CC-MAIN-20190823192831-20190823214831-00230.warc.gz"} |
http://mathhelpforum.com/calculus/73830-problem-evaluating-integral.html | # Thread: problem evaluating this integral
1. ## problem evaluating this integral
I worked through this integral using partial fractions, but I cannot for the life of me evaluate it. At least, my answer is not what webassign wants. I think I am not putting my logs together correctly. Anyway, can someone please evaluate this and show me final steps of combining logs, etc.
Original problem:
$\int\limits^{9}_{7} \frac{x^3-5x^2-25}{x^3-5x^2} dx$
Here is my integral that I got using partial fractions, but that I cannot get my correct asnwer when I evaluate at the limits (I am assuming of course that I have the correct integral here):
$= \left[x + ln |x| - \frac{5}{x} - ln|x-5|\right] _{7}^{9}$
Thanks much!
2. Originally Posted by mollymcf2009
I worked through this integral using partial fractions, but I cannot for the life of me evaluate it. At least, my answer is not what webassign wants. I think I am not putting my logs together correctly. Anyway, can someone please evaluate this and show me final steps of combining logs, etc.
Original problem:
$\int\limits^{9}_{7} \frac{x^3-5x^2-25}{x^3-5x^2} dx$
Here is my integral that I got using partial fractions, but that I cannot get my correct asnwer when I evaluate at the limits (I am assuming of course that I have the correct integral here):
$= \left[x + ln |x| - \frac{5}{x} - ln|x-5|\right] _{7}^{9}$
Thanks much!
that integral is correct. so if you have a problem, it is from plugging in the limits, which is just arithmetic. just redo it. | 2016-10-21 13:27:03 | {"extraction_info": {"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": 4, "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, "math_score": 0.9714794158935547, "perplexity": 427.3020958799444}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988718278.43/warc/CC-MAIN-20161020183838-00284-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://openstudy.com/updates/52fe9131e4b0741b0046cf90 | Remember SohCahToa? $\sin \theta=\frac{ opp }{ hyp }$ $\cos \theta=\frac{ adj }{ hyp }$ $\tan \theta=\frac{ opp }{ adj }$ | 2014-09-18 17:46:17 | {"extraction_info": {"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, "math_score": 0.998607337474823, "perplexity": 8922.018188196509}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657128337.85/warc/CC-MAIN-20140914011208-00347-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://cran.ism.ac.jp/web/packages/openintro/vignettes/datasets.html | # Datasets of OpenIntro
The OpenIntro project’s mission is to make educational products that are free, transparent, and lower barriers to education. OpenIntro also features supporting resources, such as slides, videos, and more. This means we have lots and lots of data that are used in our textbooks and supporting resources, and we make these datasets openly available via the R packages we develop as part of this project.
The flagship R package of OpenIntro is this package, openintro. You can find a list of all datasets included in the package on the package reference page as well as by running data(package = "openintro") in the R console after loading the package.
When you install the openintro package, it will also install three other packages that house datasets used in OpenIntro resources.
Note that some of the datasets in these packages were previously in the openintro package. The datasets in these packages have been split off in an effort to keep the size of the openintro package from bloating while also continuing to add useful datasets in areas that may be of interest to learners and that are useful for teaching introductory statistics and data science topics. Since the packages are installed and loaded with openintro, you can still use any of the datasets by just loading the openintro package. | 2022-05-25 20:22:08 | {"extraction_info": {"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, "math_score": 0.18516068160533905, "perplexity": 1424.1980509729513}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662593428.63/warc/CC-MAIN-20220525182604-20220525212604-00094.warc.gz"} |
https://socratic.org/questions/what-is-the-trigonometric-form-of-5-11i | # What is the trigonometric form of (-5+11i) ?
Jan 9, 2016
$\sqrt{146} \left(\cos \left({\tan}^{-} 1 \left(- \frac{11}{5}\right)\right) + i \sin \left({\tan}^{-} 1 \left(- \frac{11}{5}\right)\right)\right)$
#### Explanation:
Trigonometric form of a complex number $x + i y$ is given by
r(cos(theta)+isin(theta)
Where,
$r = \sqrt{{x}^{2} + {y}^{2}}$
$\theta = {\tan}^{-} 1 \left(\frac{y}{x}\right)$
Our complex number is $- 5 + 11 i$
$r = \sqrt{{\left(- 5\right)}^{2} + {11}^{2}}$
$r = \sqrt{25 + 121}$
$r = \sqrt{146}$
$\theta = {\tan}^{-} 1 \left(- \frac{11}{5}\right)$
The complex number in trigonometric form is
$\sqrt{146} \left(\cos \left({\tan}^{-} 1 \left(- \frac{11}{5}\right)\right) + i \sin \left({\tan}^{-} 1 \left(- \frac{11}{5}\right)\right)\right)$ | 2020-02-19 05:16:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 11, "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, "math_score": 0.9716153144836426, "perplexity": 2071.701826081146}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875144027.33/warc/CC-MAIN-20200219030731-20200219060731-00178.warc.gz"} |
https://solvedlib.com/n/the-following-table-shows-political-party-affiliation-and,6971463 | # The following table shows political party affiliation and gender of each of 434 US House of Representatives voting ! members
###### Question:
The following table shows political party affiliation and gender of each of 434 US House of Representatives voting ! members in Jan 2019: (Source: WWI quorum us/federal) Gender Male Female Total Democrat 142 Republican 185 Other Total 327 107 434 233 201 (Report your answers as fractions or as decimal values rounded t0 the nearest hundredth:) Find the probability that single randomly-selected US Representative is: Democrat and female: Answer: (6) Male or Republican: Answer: (c) Democrat given that the selected Representative is female: Answer:
#### Similar Solved Questions
##### Evaluate each expression.$-2-4-(-1)$
Evaluate each expression. $-2-4-(-1)$...
##### Question 5 (1 point)What is E for the reaction 2AIs) + 3Fe2tlaq, 2.0 M) 77-> 2A/3t(aq, 0.030 M) + 3Fels) if it is run under conditions such that AGrxn -718 kJ-mol-1?+1.24V+0.21 V+0.41 V+2.48 V+0.62 V
Question 5 (1 point) What is E for the reaction 2AIs) + 3Fe2tlaq, 2.0 M) 77-> 2A/3t(aq, 0.030 M) + 3Fels) if it is run under conditions such that AGrxn -718 kJ-mol-1? +1.24V +0.21 V +0.41 V +2.48 V +0.62 V...
##### Saved Rays consist primarily of Multiple Choice dead cells. long-lived parenchyma. tracheids. vessel elements. sieve tubes...
Saved Rays consist primarily of Multiple Choice dead cells. long-lived parenchyma. tracheids. vessel elements. sieve tubes < Prev 54 of 100 ! Next >...
##### (LO 6) E4-7 (Income Statement Items) Certain account balances follow for Vincenti Products Corp.: Rent revenue...
(LO 6) E4-7 (Income Statement Items) Certain account balances follow for Vincenti Products Corp.: Rent revenue $8,500 Sales discounts$ 17,800 Interest expense 2,700 Selling expenses 79,400 Beginning retained earnings 114,400 Sales revenue 490,000 E...
##### Cunem Artemat In FrogessUseat-distribution and the given matched palr sample results to complete the test of the piven hypotkes Assumetheresults comne Ttoinu Fendom samples, and il the Sample sizes are small,assumne thc underlying distributionof the difterences is relatively normal Assume that dilferences are computed usitg d Test Ho Ovs Hu Jusing the palred data In the follovIng table:Situation ] 130 Situjtlon 2 120135 175 453 148 180 135 168 457 150 155 148 160 142 162 150Your answcr Inco
Cunem Artemat In Frogess Useat-distribution and the given matched palr sample results to complete the test of the piven hypotkes Assumetheresults comne Ttoinu Fendom samples, and il the Sample sizes are small,assumne thc underlying distributionof the difterences is relatively normal Assume that di...
##### 1. Provide IUPAC names for the following compounds. (12 pts) NHzOH
1. Provide IUPAC names for the following compounds. (12 pts) NHz OH...
##### 1) A state had a midyear population of 1 million in the past year; data included:Malesfemales females (15-44)Live birthsPopulation490,000 510,000 200,00012,200Deaths810770Calculate: Crude birth rate for the state for the year: b. General fertility rate for the state for the year:
1) A state had a midyear population of 1 million in the past year; data included: Males females females (15-44) Live births Population 490,000 510,000 200,000 12,200 Deaths 810 770 Calculate: Crude birth rate for the state for the year: b. General fertility rate for the state for the year:...
##### Write true statement using each of the followirg words (total of five statements) Do not use the Gome rumbers more Than once Explain why for each: divisible by, multiple of , factor of , divisor of; divides:Write the first five terms of ( 1+ J" if m is positive integer.
Write true statement using each of the followirg words (total of five statements) Do not use the Gome rumbers more Than once Explain why for each: divisible by, multiple of , factor of , divisor of; divides: Write the first five terms of ( 1+ J" if m is positive integer....
##### 3. Define biodiversity. Provide one example of competition related to biodiversity:
3. Define biodiversity. Provide one example of competition related to biodiversity:...
##### Proto-oncogenes:are the norma bormsDenes that can mutate cause cell divison nypuracuye thesc choices Jn correct; encode groxth lactar cell surtace receptors Mernbem Hral unsducton pathuay- become triggers Cacen mutatcd bY cigarcttc smoke
Proto-oncogenes: are the norma borms Denes that can mutate cause cell divison nypuracuye thesc choices Jn correct; encode groxth lactar cell surtace receptors Mernbem Hral unsducton pathuay- become triggers Cacen mutatcd bY cigarcttc smoke...
##### Examples of civility and incivility
examples of civility and incivility...
##### Jo z obed uogonusu 9102-90 LLS edade porc SidVIS IMG-7778.jpg Zvo @ Q Search Problem 3...
jo z obed uogonusu 9102-90 LLS edade porc SidVIS IMG-7778.jpg Zvo @ Q Search Problem 3 Label each of the following compounds as either Aromatic, Anti-aromatic or Non-aromatic. Briefly explain. O : 0 Û Q Q Problem 4 Draw the major product(s) from the reaction sequence below. Show all intermed...
##### Doncatomic ldeal which polnt volude isobacically reduce5/3) is going through cyclic process starting point is pl KPa_ VI - 2.30 L: 1. adiabatically expano until dmt value V2; sochoricall Feconstant volune Uincrease pressure back yolume back Hhat value dnes have) Dra diagran this cyclic nrocest What is the net work donepressure becores24 kPa_the nhole cyclic process?
doncatomic ldeal which polnt volude isobacically reduce 5/3) is going through cyclic process starting point is pl KPa_ VI - 2.30 L: 1. adiabatically expano until dmt value V2; sochoricall Feconstant volune Uincrease pressure back yolume back Hhat value dnes have) Dra diagran this cyclic nrocest What...
##### We perform the experiment "deal a five card poker hand"
We perform the experiment "deal a five card poker hand". What is the probability that you are dealt a hand that contains the Ace, Two, Three, and Four of Diamonds?Question 22 answers 4 / 2,598,960 48 / 2,598,960 1 / 2,598,960 1 / 52...
##### Use a graphing utility with the specified viewing window to find the zeros of the following function:f(x)=x2 _x-110; [ - 13,14] by [ - 121,22] Select the correct choice below and, if necessary; fill in the answer box to complete your choiceOA The zeros are (Type an integer or a simplified fraction. Use a comma to separate answers as needed:) 0 B. The solution is not a real number:
Use a graphing utility with the specified viewing window to find the zeros of the following function: f(x)=x2 _x-110; [ - 13,14] by [ - 121,22] Select the correct choice below and, if necessary; fill in the answer box to complete your choice OA The zeros are (Type an integer or a simplified fraction...
##### 6.8 . Show that the conic hull ofthe setS = {(xp,2):(x_1)+x3 =1}is the set{(x1, Xz) x, > %}U{(,0)}Remark: This is an example illustrating the fact that the conic hull of a closed set is nor necessarily closed set _
6.8 . Show that the conic hull ofthe set S = {(xp,2):(x_1)+x3 =1} is the set {(x1, Xz) x, > %}U{(,0)} Remark: This is an example illustrating the fact that the conic hull of a closed set is nor necessarily closed set _...
##### If you were part of the City Council, what would you propose to increase community social capital. From a cost/benefit s...
If you were part of the City Council, what would you propose to increase community social capital. From a cost/benefit standpoint, given that these are benefits to community social capital, what are the costs?...
##### Bond Entry UJlmoh 416 41t 389 464 368 565 2 611 837 3os 615 891 360 733 4012 3J9Bond Enargy Bond Engray Bonde (Ulmon Bond (Mmoh 163 237 418 218 NEN 946 222 1 "75 : E 2 Jo1 0-0 142 265 6 1 159 3 26Bad
Bond Entry UJlmoh 416 41t 389 464 368 565 2 611 837 3os 615 891 360 733 4012 3J9 Bond Enargy Bond Engray Bonde (Ulmon Bond (Mmoh 163 237 418 218 NEN 946 222 1 "75 : E 2 Jo1 0-0 142 265 6 1 159 3 26 Bad...
##### Form the polynomial given,degree 4 and zeros: i, 1+2i
form the polynomial given,degree 4 and zeros: i, 1+2i...
##### The dimensions of the control volume of the figure are L = 24 in, H =...
The dimensions of the control volume of the figure are L = 24 in, H = 9.7 in, W = 9.1 in and the angle is 34 degrees. A fluid with specific gravity SG = 1.08 moves through the control volume. The given velocity is V = 11.2 ft/s. Calculate, in lb, the x-axis contribution of the term So vplvri)dA at t...
##### What is the formula for thc hypochlorite ion ?What is the name for S03* ? TheionSubmlt AnsworRotry Entlro Groupmore group attompts remalnlng
What is the formula for thc hypochlorite ion ? What is the name for S03* ? The ion Submlt Answor Rotry Entlro Group more group attompts remalnlng...
##### 4. (4 pts) Consider the surface z = x’y+y3. (a) Find the normal direction of the...
4. (4 pts) Consider the surface z = x’y+y3. (a) Find the normal direction of the tangent plane to the surface through (1,1,2). (b) Find the equation of the tangent plane in (a). (c) Determine the value a so that the vector 7 = -7 +27 +ak is parallel to the tangent plane in (a). (d) Find the eq...
##### What are the critical values, if any, of f(x)=x^3?
What are the critical values, if any, of f(x)=x^3?...
##### Evaluate the integrals by using the properties of the definite integral and interpreting integrals as areas. $\int_{-\sqrt{2}}^{\sqrt{2}} \sqrt{2-t^{2}} d t$
Evaluate the integrals by using the properties of the definite integral and interpreting integrals as areas. $\int_{-\sqrt{2}}^{\sqrt{2}} \sqrt{2-t^{2}} d t$...
...
##### What are some potential difficulties/challenges faced by collecting data on the contribution of drugs to the...
What are some potential difficulties/challenges faced by collecting data on the contribution of drugs to the global burden of disease....
##### Use the standard half-cell potentials listed below to calculate the standard free energy(K]for the following reaction...
Use the standard half-cell potentials listed below to calculate the standard free energy(K]for the following reaction occurring in an electrochemical cell at 25°C. Pb 2+ (aq) +2e--- Pb(s) E* - -0.13 Volt A13+ (aq) + 3 e-Al(s) E* =-1.66 volt a. 1.53 b. - 886 c-434 d. - 443 e. -1036 What is the st...
##### Given rectangle shape forad by the sides and y; we wish to maximize the perimeter can only be 200m, the area and Using the Lagrange method what is the maximizing function f? What is the constraint equation? What is the Lagrange equation L? What are the Lagrange equation derivatives? What is the max Area and the x and y values for this area?
Given rectangle shape forad by the sides and y; we wish to maximize the perimeter can only be 200m, the area and Using the Lagrange method what is the maximizing function f? What is the constraint equation? What is the Lagrange equation L? What are the Lagrange equation derivatives? What is the max ...
##### You are going to write a java application that will be used in a coffee shop...
You are going to write a java application that will be used in a coffee shop to take customer orders and print a simple on screen order summary. Your coffee shop only sells one type and one size coffee for \$5 dollars. However, your customers have the option of adding whipped cream and chocolate each...
##### 1. Strength Training a) Develop a basic strength training program for a young adult. b) How...
1. Strength Training a) Develop a basic strength training program for a young adult. b) How would you modify this program for a child? c) How would you modify this program for an older (>65) adult?... | 2022-09-27 07:15:11 | {"extraction_info": {"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": 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, "math_score": 0.35074442625045776, "perplexity": 6718.574290633542}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334992.20/warc/CC-MAIN-20220927064738-20220927094738-00144.warc.gz"} |
https://www.physicsforums.com/threads/convergence-of-sequences.714378/ | # Convergence of sequences
ppy
Hi,
Let a(n) be a real sequence such that a(n+1)-a(n) tends to zero as n approaches ∞. must a(n) converge? Also an explanation would be great thank you. have been wondering about this
## Answers and Replies
Let $$a_n= \sum_{i=1}^n \frac{1}{i}$$.
Then $a_{n+1}- a_n= 1/(n+1)$ which goes to 0 as n goes to infinity. But the harmonic series does NOT converge so this sequence does not converge. | 2022-08-12 02:56:13 | {"extraction_info": {"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, "math_score": 0.9188297986984253, "perplexity": 307.708672788062}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571538.36/warc/CC-MAIN-20220812014923-20220812044923-00111.warc.gz"} |
https://www.vedantu.com/question-answer/metal-which-is-the-best-conductor-of-electricity-class-10-chemistry-cbse-5f610da7a863034f42ab3a00 | Question
# Metal which is the best conductor of electricity. a.) Nickel b.) Silver c.) Gold d.) Sodium
Hint: The metals are said to be good conductors of electricity if they allow electricity or electrons to be precise to flow through them easily. The property of conductors which allows them to conduct electricity is called conductivity. Such materials offer less opposition or resistance to the flow of charges.
For a material to be a good conductor, the electricity passed through it must be able to move the electrons the metal possesses, the freer the electrons are in a metal, the greater will be its conductivity.
Among the given elements silver and gold have a maximum number of electrons. Silver is the best conductor of electricity because it contains a higher number of movable atoms (free electrons) owing to the fact that gold has a preceding f-orbital from the actinide series. These f-orbitals are very densely packed and are nearer to nucleus compared to even d-orbitals (silver, transitional metals) and they tend to hold back the electrons restricting the easy flow of current through them.Thus the valence shells and crystal structure of silver makes it the best conductor of electricity.
Also, the correct order of the conductivity in the given elements is given below: $Silver>Gold>Nickel>Sodium$
So, the correct answer is “Option B”.
Note: Even though silver is the best conductor of electricity, there are two reason why silver is not used very frequently over other conductors: 1) it is a very precious metal and thus has a high price for the amount of material used and 2) It corrodes or oxidizes easily as it has good affinity towards oxygen. Copper is hence, $(Cu)$ is commonly used when oxidation is not a major issue, such as home wiring and in most electric motors. | 2020-09-29 14:42:47 | {"extraction_info": {"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, "math_score": 0.5066526532173157, "perplexity": 836.7413450624132}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401643509.96/warc/CC-MAIN-20200929123413-20200929153413-00776.warc.gz"} |
https://dsp.stackexchange.com/questions/9148/calculate-total-bit-rate | # Calculate total bit rate
I want to calculate the total bit rate of a video system.
In order to calculate the total bit rate for a 1080/50p video system(4:2:2) we need:
• Luminance sampling rate:Fs=13.5MHz (standard for 4:2:2)
• Number of bits: N=8
• Number of components per PEL: M=3 (Y,Cb,Cr)
• Number of lines: L=1080
• Line duration: Tline=?
• Frame Rate: Fr=50
I dont know how to find line duration. Is line duration Tline=L/Fs ??
• If each frame scans all the $1080$ lines of the image, and there are $50$ frames in a second, what is the duration of the scan of one line? What if the scanning was interleaved so that each line got scanned once every two frames? What if the scan is progressive as that p in 1080/50p seems to indicate? – Dilip Sarwate May 16 '13 at 20:29
• It is 1/(50*1080) with progressive scan = 1.85*10^-5. Am i correct? – 20317 May 19 '13 at 19:34
• Sounds right but note that $1.85$ etc is an approximation that I would prefer to express in microseconds as $\approx 1.85 \mu$s rather than as $= 1.85\times 10^{-5}$ s. – Dilip Sarwate May 19 '13 at 19:45 | 2021-07-24 12:02:01 | {"extraction_info": {"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": 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, "math_score": 0.5052457451820374, "perplexity": 2809.385495979689}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150264.90/warc/CC-MAIN-20210724094631-20210724124631-00691.warc.gz"} |
https://mpboardguru.com/mp-board-class-11th-physics-important-questions-chapter-11/ | Students get through the MP Board Class 11th Physics Important Questions Chapter 11 Thermal Properties of Matter which are most likely to be asked in the exam.
## MP Board Class 11th Physics Important Questions Chapter 11 Thermal Properties of Matter
Thermal Properties of Matter Class 11 Important Questions Very Short Answer Type
Question 1.
Ice is cold, why?
When the ice is touched by hand, the ice takes heat from the hand. Thus, heat is lost from the hand and the temperature of hand decreases and therefore we feel cold.
Question 2.
What is temperature?
It is that physical quantity which determines the direction of flow of heat when two objects are placed in contact with each other.
Question 3.
Define calorie.
Amount of heat required to raise the temperature of one gram pure water from 14.5°C to 15.5°C is known as one calorie.
Question 4.
What are the different scale to measure temperature? Write relation be¬tween them.
• Farenheit scale.
• Kelvin scale.
• Reumar scale.
Relation between them is
$$\frac{C}{5}$$ = $$\frac{F-32}{9}$$ = $$\frac{R}{4}$$ = $$\frac{K-273}{5}$$.
Question 5.
What is ideal gas thermometer?
Ideal gas thermometer is that thermometer whose zero is that temperature at which pressure remain zero and 1 degree is equal to 1°C.
Question 6.
What is absolute zero ? Write its value.
It is that temperature at which pressure and volume of a gas becomes zero, known as absolute zero. Its value is 273.15°C.
Question 7.
In absolute temperature scale, what is the melting point and boiling point of pure water?
In absolute temperature scale melting point of pure water is 273K and boiling point is 373K.
Question 8.
Can the temperature of an object have a negative value on Kelvin’s scale?
No.
Question 9.
Why H2 – thermometer is called standard thermometer? What is its range?
The H2– thermometer is called standard thermometer because it is used for the calibration of other thermometers. It can measure the temperature from – 200°C to 500°C.
Question 10.
Define coefficient of linear expansion and write its unit.
It is defined by the change in length per unit original length per degree rise of temperature.
Let the initial length of a rod be l and the length increases by Δl for Δt change in temperature, then
Coefficient of linear expansion, α = $$\frac{\Delta l}{l \Delta t}$$
Unit: Its unit is °C -1 or K -1.
Question 11.
What are the two types of specific heat? Why Cp is greater than Cv?
The two specific heats of gases are specific heat at constant pressure (Cp) and specific heat at constant volume (Cv).
Cp is greater than Cv because same part of heat given at constant pressure is utilized to increase the volume, (hence work done) against the applied pressure.
Question 12.
Define coefficient of superficial expansion and give its unit.
It is defined by the change in area per unit original area per degree rise in temperature.
Let initial area of a body be A and the area change by ΔA, with the rise of temperature Δt.
∴ Coefficient of superficial expansion, β = $$\frac{\Delta A}{A \Delta t}$$
Unit: Its unit is °C-1 or K -1.
Question 13.
Define coefficient of volume expansion and give its unit.
It is defined by the change in volume per unit original volume per degree rise in temperature.
Let initial volume of a substance is V and change in volume with change in temperature ΔT is ΔV.
∴ Coefficient of volume expansion, γ = $$\frac{\Delta V}{V \Delta T}$$
Unit: Its unit is °C -1 or K -1.
Question 14.
Write the relations between α,β and γ.
β = 2α and γ = 3α
∴ α : β : γ = 1:2:3.
Question 15.
Define specific heat and give the unit of specific heat.
We know that,
Q = ms Δt
or
s = $$\frac{Q}{m \Delta t}$$
If m = 1 gm, Δt = 1°C
Then, s = Q
The amount of heat required to raise the temperature of 1 gm substance through 1°C is called specific heat of the substance.
Unit: Unit of specific heat is calorie × gm-1 × °C-1.
Question 16.
Define latent heat of fusion.
Latent heat of fusion: The amount of heat required to change unit mass of a solid into liquid at its melting point is called latent heat of fusion.
If the latent heat of fusion is L, then Q = mL
Latent heat of ice is 80 cal × gm-1.
Question 17.
Define latent heat of vaporization.
Latent heat of vaporization: The amount of heat required to change a liquid of unit mass into vapour at its boiling point, is called latent heat of evaporation.
Latent heat of steam is 536 cal × gm-1.
Unit: The practical unit of latent heat is cal × gm-1.
Question 18.
Write the principle of thermometry.
The properties of any object which depends on temperature and can be used to measure temperature.
Question 19.
Which is more sensitive, liquid thermometer or gas thermometer?
Gas thermometer is more sensitive than liquid thermometer because expansion of gas is more than liquid for a given temperature difference.
Question 20.
Among metal and alloy, whose coefficient of thermal expansions is more?
Thermal expansion of metal is more than that of alloy.
Question 21.
Can the value of coefficient of thermal expansion be always positive?
No.
Question 22.
There is a hole in a metal plate. What will happen on heating it?
The size of hole will increase on heating the metal plate.
Question 23.
A gap is left between two rails, why?
The temperature of the atmosphere is always changing. With the rise of temperature the rails expands, therefore the gaps are left between them. If gap is not kept, then with the rise in temperature the rails will bend and will cause serious accidents.
Question 24.
What do you mean by the anomalous expansion of water?
Generally, the volume of liquids increases with the rise of temperature. But, the volume of water decreases when it is heated from 0°C to 4°C and then after 4°C the volume increases. Similarly, when the water is cooled its volume decreases up to 4°C and then increases from 4°C to 0°C. Such expansion of water is called anomalous expansion.
Question 25.
The bulb of one thermometer is spherical while that of the other is cylindrical. Both have equal amounts of mercury. Which one will response quickly to temperature change?
For a given volume,the surface area of the cylinder is large than that of sphere. Therefore heat will be quickly conducted through the cylindrical bulb. Thus, the response of cylindrical bulb thermometer will be quicker.
Question 26.
Pendulum invar of a pendulum clock is made of alloy. Why?
Coefficient of thermal expansion of alloy is very less, thus when temperature changes there is no effect on pendulum invar, so it is made of alloy.
Question 27.
During change of state, heat given to a body is lost in which form?
During change of state, heat given to the body is lost to increase internal molecu¬lar potential energy of the body.
Question 28.
Hot water is used for formentation. Why?
Due to high specific heat of water, it gives more heat in comparison to other liquids. Therefore, hot water is used for formentation.
Question 29.
Ice at 0°C appear to be more cold than water at 0°C. Why?
When the ice melt, amount of heat required for melting is absorbed from our body, therefore ice appear more cold than water at 0°C.
Question 30.
Burning due to steam is more severe than that of boiling water, why?
When steam vapour gets contact with the skin, then first it gets converted to water of 100°C. In this process, it liberates 536 calories of heat. This extra heat is not present in boiling water. Since steam has more latent heat, hence, it produces severe bums.
Question 31.
The sand near the bank of river becomes colder than water, why?
The specific heat of sand is very low, therefore it gains heat soon and radiate heat soon. While the specific heat of water is very high. Hence, the sand becomes colder than water.
Question 32.
Atmospheric temperature reduces after icefall. Why?
Due to high value of latent heat, when the ice start melting it takes heat from the atmosphere, hence atmospheric temperature reduces after icefall.
Question 33.
Why the specific heat of the coolent used in nuclear reactor is high?
Due to high specific heats coolent is able to absorb more heat in nuclear reactor.
Question 34.
At boiling point of a liquid, how much is the specific heat ?
We know,
ΔQ = m.sΔT
or
s = $$\frac{\Delta Q}{m \cdot \Delta T}$$
At boling point, change in temperature
ΔT = o
s = $$\frac{\Delta Q}{m .0}$$ = $$\frac{\Delta Q}{0}$$ = ∞
∴ At boiling point, specific heat of a liquid is infinity.
Question 35.
Name the methods of transmission of heat.
There are three methods of transmission of heat:
1. Conduction,
2. Convection and
Question 36.
What do you understand by conduction?
In this process the particle which is heated first gives a part of its energy to its adjacent particles. The particles undergo simple harmonic motion about their mean position and the heat is transmitted from one particle to the next. Solids are heated by this process only.
Question 37.
What do you mean by convection?
In this mode of flow the particles of substance absorb heat and leave their place or get displaced. Liquids and gases are heated by this method.
Question 38.
In this method heat is transmitted from one body to another body without any medium or without affecting the medium. Heat from sun reaches to earth by radiation.
Question 39.
What is meant by variable state in conduction?
When one end of a rod of a conductor is heated then temperature of the different parts of the rod go on increasing slowly. This state is called variable state of temperature.
Question 40.
When one end of a conductor is heated then initially the temperature of its different parts go on increasing slowly but a stage comes when the temperature of each part of the conductor becomes constant, though the temperature of different parts are different. This state of temperature is called steady state.
Question 41.
What is temperature gradient? What type of quantity is it? Write the unit.
Temperature gradient: Fall of temperature per unit length is called temperature gradient.
Let temperature of two surfaces of a conductor at distances x and x + Δx are θ and θ- Δ θ.
∴ Temperature gradient = $$\frac{(\theta-\Delta \theta)-\theta}{(x+\Delta x)-x}$$
Negative sign shows that as the distance increases the temperature decreases. Temperature gradient is a vector quantity and its unit is °C × m -1.
Question 42.
Define coefficient of thermal conductivity. Write its unit and find out its dimensional formula.
Or
Define the coefficient of thermal conductivity and obtain expression for it.
The coefficient of thermal conductivity is defined by the amount of heat, flowing per second in steady state through the rod of length 1 long and area of cross-section 1 m2, with a unit temperature difference between the opposite faces.
The quantity of heat, flowing per second through a unit cube having unit temperature difference between opposite faces, during steady-state.
i.e., Q = $$\frac{K A\left(\theta_{1}-\theta_{2}\right) t}{d}$$
K = $$\frac{Q d}{A\left(\theta_{1}-\theta_{2}\right) t}$$
Unit: Its SI unit is $$\frac{\text { joule } \times \mathrm{m}}{\mathrm{m}^{2} \mathrm{~K} \mathrm{sec}}$$ = J m-1K -1sec -1
But, joule /sec is watt.
Other unit is watt × m-1 × K-1.
Dimensional formula :$$\frac{\left[\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-2}\right][\mathrm{L}]}{\left[\mathrm{L}^{2}\right][\theta][\mathrm{T}]}$$ = $$\left[\mathrm{MLT}^{-3} \theta^{-1}\right]$$.
Question 43.
What do you mean by thermal resistance? Write its unit and find out its dimensional formula.
The resistance offered by the body in the flow of heat is called thermal resistance,
Thermal resistance = $$\frac{d}{\mathrm{~K} A}$$ = $$\frac{\left(\theta_{1}-\theta_{2}\right) t}{Q}$$
Unit: Its SI unit is $$\frac{\mathrm{K} \mathrm{sec}}{\mathrm{J}}$$ = K sec J-1 = K watt-1
Dimensional Formula: [Thermal resistance] = $$\frac{[\theta][\mathrm{T}]}{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}$$ = $$\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{3} \theta\right]$$ .
Question 44.
What is meant by thermal diffusivity?
Thermal diffusivity: The ratio of thermal conductivity and thermal capacity of unit volume of a substance is called thermal diffusivity of the substance.
Thermal diffusivity = $$\frac{K}{\rho S}$$.
Question 45.
The ice blocks are covered with saw dust. Why?
Sawdust is bad conductor of heat. Hence, the heat of atmosphere does not conduct through sawdust and thus ice does not melt soon.
Question 46.
Woollen clothes are used in winter. Why?
Woollen clothes have fine pores which are filled with air. Air and woollen clothes are bad conductor of heat. There it does not allow the heat to escape from the body to atmosphere. Thus, it keeps body warm.
Question 47.
A woollen blanket keeps the body warm and also prevent the ice from melting. Why?
Air is insulator which is filled between the fibres of blanket. Therefore, blanket does not allow the heat of body to radiate into the atmosphere as well as the heat of atmosphere could not reach to ice. Thus, it keeps the body warm and protect the ice from melting.
Question 48.
State two properties of thermal radiation.
1. Thermal radiations are electromagnetic waves.
2. They do not affect the medium through they pass.
Question 49.
Differentiate between light and heat radiations.
Difference between Light and Heat radiations :
Light radiation Heat radiation 1. The wavelength of light rays is very small i. e., between 4 × 10-5 cm to 8 × 10-5cm. The wavelength of heat radiation is long i.e., between 8 × 10-5cm to 0.04 cm. 2. It falls in the visible region of electromagnetic spectrum. It falls in the invisible region of electromagnetic spectrum. 3. Heating effect is negligible. Heating effect is greater.
Question 50.
What is emissive power? Write its SI unit.
Emissive power: The amount of heat radiated per unit area per unit time, is called emissive power of the surface.
If int sec, through area A, amount of heat radiated is Q, then
Emissive power, e = $$\frac{Q}{A \times t}$$
SI unit: joule × m-2 × s-1 or watt × m-2.
Question 51.
What is absorptive power of surface?
The ratio of amount of heat radiation absorbed by a surface in a given time and total amount of heat incident is called absorptive power of that surface.
i.e., a = $$\frac{q}{Q}$$
Where, q = Amount of heat radiation absorbed and Q = Amount of heat radiation incident.
Question 52.
Define perfectly black body.
Or
What do you mean by perfectly black body?
A perfectly black body is one which absorbs completely all the thermal radiation incident on it and does not reflect or transmit any fraction of it. Emissivity for this body is 1.
No such body exists in nature, but in practice we consider lamp black and platinum black as perfectly black body.
Question 53.
State Stefan’s law of black body radiation.
Stefan’s law : The total radiant energy emitted per second per unit surface area of a black body is proportional to the fourth power of the absolute temperature.
If the radiant energy per second per unit area is E and absolute temperature of the surface is T, then
E∝T4
or E = σT4
Where σ is called Stefan’s constant.
If the area of a black body is A and its temperature is T, then the radiant energy per second will be
E= σ AT4.
Question 54.
State Newton’s law of cooling.
The rate of cooling of a body is proportional to the temperature difference of the average temperature of the body and surroundings provided the temperature difference between the source and surrounding is very less.
Question 55.
According to Kirchhoff’s law, at a given temperature the ratio of emi¬ssive power and absorptive power for a given wavelength is equal to the emissive power of black body for the same wavelength.
If the emissive power of a surface for wavelength λ is eλ and absorptive power is aλ, then
$$\frac{e_{\lambda}}{a_{\lambda}}$$ = Eλ
Where, Eλ is emissive power of black body.
Question 56.
If a red glass is heated up to high temperature and placed in a dark room, then it appears green. Why?
A body appears red because the body absorbs all the colours but red. It reflects red only thus it appears red. The emissive power of a red body is maximum for the green colour. Thus, it appears green, when heated up to a high temperature.
Question 57.
The cloudy nights are warmer than the day. Why?
The clouds reflect the heat radiation waves, which are radiated from the earth. Thus, the temperature of earth does not fall. Hence, the nights become hot.
Question 58.
Deserts are very hot during the day and very cold during the night Why?
We know that good absorber are good radiators. Sand is good absorber, during the day time the sand absorbs heat and becomes very hot. But, during the nights it radiates heat soon and becomes cold.
Question 59.
State three uses of heat radiation.
• In the cold country, the hot water is flown through the metallic pipes to warm the rooms.
• The walls and roof of greenhouse are made up of glass.
• To decrease the temperature of hot substance, it is spread over, thus it becomes cold soon.
Question 60.
In a chilled weather, animals curl themselves. Why?
The rate of radiation of heat is directly proportional to the area of the surface. The sphere has the minimum surface area for a given volume. Thus, by curling, the animals reduce the area through which the heat is radiated and they keep the body warmer.
Question 61.
State two applications of Newton’s law of cooling.
1. The hot water cools soon than the warm water.
2. When milk is added to tea, the rate of cooling decreases.
Question 62.
Hot water cools soon than the warm water. Why?
The rate of cooling is directly proportional to the difference of mean temperature of the body and the temperature of the surrounding. The difference of temperature of hot water and surrounding is greater than that of warm water, therefore hot water cools soon.
Question 63.
On what factors does the loss of heat energy per second depend?
• Nature of the surface,
• Area of the surface,
• Temperature difference between the temperature of the surface and surrounding.
Question 64.
The walls and roofs of greenhouse are made of glass, why?
Glass has the property, that it transmits the heat radiation of high temperature but absorbs the heat radiations of low temperature. Hence, the glass allows the radiations coming from the sun, but it does not allow the radiations waves coming from the plants. Thus, the room remains warm.
Question 65.
In summer the hills remains cold, why?
The reasons are :
• On the hill the air is thin and dust particles are less, thus radiations are absorbed less.
• The sun rays are reflected due to inclined surface.
Question 66.
The outer surface of cooking utensils are made black and inner bright Why?
The black surfaces are good absorber of heat. Thus, more heat is absorbed and bright surface reflects the heat into the cooking pot. Thus, more heat is given to the food, which cooks the food soon.
Question 67.
The stars X and Y are radiating yellow and blue rays respectively. Which has greater temperature?
By Wien’s displacement law, λm ∝$$\frac{1}{T}$$. As the wavelength of blue rays is lesser
than that of yellow rays, hence, the temperature of the Y-star will be greater than X-star.
Question 68.
Whenever an object is heated, why does it appear red first?
Ans. According to Wien’s law, that λm T = constant, the maximum wavelength is for the red light in the visible spectrum. Hence, for ordinary temperatures i.e., for less T, λm must be more. Hence, an object appears red. As temperature increases, wavelength decreases and the emitted colour will shift towards violet.
Question 69.
A teacup has shining surface whereas the bottom of cooking pot is blackened, why?
The shining surface is a good reflector of heat radiation, whereas the blackened surface is good absorber. The shining surface reflects the heat into the cup and maintains the tea hot. for long time, outer surface of cup does not radiate heat. Black surface of cooking pot absorbs more heat and makes the cooking fast.
Question 70.
The steady-state is necessary for the different substances to compare their conductivity. Why?
In the steady-state the heat is not absorbed by any part of the body. Hence, the amount of heat given to one end transmit through the body completely. Therefore, the substance are brought in the steady-state.
Question 71.
In Searl’s apparatus to find the conductivity of a rod, the holes are filled with some mercury then thermometer are fixed. Why?
The mercury is good conductor of heat therefore, it gives good contact between the bulb of thermometer and the surface of rod.
Question 72.
Eskimos built double-walled houses of snow. Why?
The air is filled between the walls, which is bad conductor of heat. Ice itself is bad conductor of heat. Hence, the heat of the room does not transmit to the atmosphere.
Question 73.
In summer, in the evening when the temperature of outside the room decreases, the temperature of the inner surface of room remains at higher temperature. Why?
After sunset, the temperature of the atmosphere decreases fast. The wall is bad conductor of heat, hence the heat of room conduct slowly and the room temperature remains higher than the atmosphere.
Question 74.
When a tumbler of thick glass is filled with hot tea it breaks down. Why?
Glass is a bad conductor of heat. When hot tea is poured into the tumbler, the temperature of inner surface increases and the surface expands. While the outer surface remains at same position. Hence, the tumbler breaks down.
Thermal Properties of Matter Class 11 Important Questions Short Answer Type
Question 1.
Establish the relation between coefficient of linear expansion and coefficient of superficial expansion.
Or
Prove that coefficient of superficial expansion is double of coefficient of linear expansion.
Let one side of a square lamina be l.Its temperature is increased through Δt so that each side increases by Δl.
∴ Initial area = l2
and Final area = (l + Δl)2
∴ Change in area, ΔA = (l + Δl)2 -l2
or =l2 +2l.Δl + Δl2 -l2
or = 2lΔl+ Δl2
Since Δl is a small quantity, hence Δl2 can be neglected.
∴ ΔA=2l.Δl.
Now, coefficient of superficial expansion,
β = $$\frac{\Delta A}{A \times \Delta t}$$
or
β = $$\frac{2 l \Delta l}{l^{2} \Delta t}$$ = 2. $$\frac{\Delta l}{l \Delta t}$$
or
β = 2α (∵ α = $$\frac{\Delta l}{l \Delta t}$$ )
Question 2.
Establish the relation between coefficient of linear expansion and coefficient of volume expansion.
Or
Prove that coefficient of volume expansion is three times of coefficient of linear expansion.
Consider a cube of side of length l. The temperature of cube is increased by, Δt so that the length of the cube becomes (l + Δl).
Now, Initial volume = l3
and Final volume = (l + Δl)3
∴ Change in volume, ΔV = (l + Δl)3 — l3
= l3 +3l2Δl + 3l.Δl2 + Δl3 -l3 = 3l2Δl + 3l Δl2 + Δl3
Since, Δl is a small quantity, therefore powers of Δl can be neglected.
∴ ΔV = 3l2Δl .
Now, coefficient of volume expansion,
γ = $$\frac{\Delta V}{V \times \Delta t}$$
= $$\frac{3 l^{2} \Delta l}{l^{3} \Delta t}$$
γ = 3. $$\frac{\Delta l}{l \Delta t}$$ = 3α,
( ∵ α = $$\frac{\Delta l}{l \Delta t}$$).
Question 3.
Distinguish between specific heat and thermal capacity.
Difference between Specific heat and Thermal capacity :
Specific heat Thermal capacity 1. The amount of heat required to raise the temperature of 1 gm sub- temperature of a substance through 1°C called specific heat of the substance. The amount of heat required to raise the is stance through 1°C is called thermal capacity. 2. Its SI unit is joule x kg-1 x K-1. Its SI unit is joule x K-1. 3. Its dimensional formula is [M°L2T-2θ-1]. Its dimensional formula is [ML2T-2θ-1].
Question 4.
Give an application of anomalous expansion of water.
The volume of water decreases when it is heated from 0°C,to 4°C and then the volume increases, above 4°C. Hence, the density of water at 4°C is maximum. In the cold countries when the temperature of the atmosphere decreases, the temperature of the water of the lake also decreases.
Now, weigh the calorimeter with stirrer. Fill it with water about 2/3 and weigh it again. Find the initial temperature of water.
When the temperature reaches to 4°C, the density of the water becomes maximum. Then the ice begins to float on the surface, preventing the heat of water to go out into the atmosphere. Hence, water remains at 4°C at bottom. Thus, the animals survive in this water of 4°C.
Question 5.
Describe the method to find out the specific heat of a solid.
(i) Method: Take the solid and measure its mass by physical balance and place it inside the steam chamber with the help of a thread. Fix a thermometer so that the bulb of thermometer touches the solid. Then start flowing the steam through the steam chamber.
Now, weigh the calorimeter with stirrer. Fill it with water about 2/3 and weigh it again. Find the initial temperature of water. When the temperature of the solid becomes constant for sometimes, then remove the wooden screen and move the calorimeter below the steam chamber. Then drop the solid into calorimeter carefully. Close the lid and stirr it slowly. Measure the temperature of the mixture when it becomes constant.
(ii) Observation:
• Mass of solid = m gm
• Mass of calorimeter + stirrer = m1 gm
• Mass of calorimeter + stirrer + water = m2 gm
• Initial temperature of water = t1°C
• Temperature of solid = t2°C
• Temperature of mixture = t3°C
• Specific heat of calorimeter = S1 (known).
(iii) Calculation : Let the Specific heat of solid = s
Mass of water = (m2 – m1) gm
∴ Heat given by the solid = Mass × Specific heat × Temperature difference = m.s.(t2-t3)
Heat taken by calorimeter =m1s1 (t3 – t1)
and Heat taken by water = (m2 – m1 ).(t3– t1)
Now, by the principle of calorimetry, we have
Heat given = Heat taken
∴ ms(t2 -t3) = m1s1(t3 -t1)+(m2 – m1 ) (t3-t1)
∴ S = $$\frac{m_{1} s_{1}\left(t_{3}-t_{1}\right)+\left(m_{2}-m_{1}\right)\left(t_{3}-t_{1}\right)}{m\left(t_{2}-t_{3}\right)}$$
Thus, specific heat can be calculated.
Question 6.
Write difference between heat and temperature.
Difference between Heat and Temperature :
Heat Temperature 1. Heat is a form of energy which is due to motion of molecules of the substance. Temperature is a physical quantity tells the direction of flow of heat when two bodies are in contact with each other. 2. Heat measurement is based on the principle of calorimetry. Temperature measurement is based on the principle of thermometry. 3. Two bodies having same heat, might have different temperatures. Two bodies having same temperature, might have different heat. 4. Practically it is measured in terms of calorie. Its SI unit is joule. Practically it is measured in terms of degree centigrade. Its SI unit is kelvin. 5. Quantity of heat of a body depends on its mass, temperature and nature. Temperature of a body depends on its quantity of heat.
Question 7.
On what factors does the amount of heat-conducting through a rod in steady state depend?
Or
In steady stae, find the expression for the amount of heat flowing through a rod.
In steady-state the amount of heat Q flowing through one face to another is :
(i) Directly proportional to the area of cross-section A i.e.,
Q ∝ A
(ii) Directly proportional to the temperature difference ( θ1 – θ2) of the faces i.e.,
Q ∝ θ12
(iii) Directly proportional to the time t of flowing heat i.e.,
Q ∝ t
(iv) Inversely proportional to the distance between the faces i.e.,
Q ∝ $$\frac{1}{d}$$
Combining all these, we get
Q ∝$$\frac{A\left(\theta_{1}-\theta_{2}\right) t}{d}$$
∴ Q = K $$\frac{A\left(\theta_{1}-\theta_{2}\right) t}{d}$$
Where, K is a constant called thermal conductivity or coefficient of thermal conductivity of the substance.
Question 8.
Differentiate between steady-state and variable state.
Difference between Steady state and Variable state :
Steady state Variable state 1. Whenever a conducting rod is heated, then the temperature of various parts goes on increasing and after sometime, its temperature becames constant, although the temperature of various parts may be different. This is called steady state. Whenever a conducting rod is heated at one end, then the temp, of various parts goes on increasing. This is called variable state. 2. In this state, no part of the conducting rod absorbs heat. In this state each part of the rod absorbs heat. 3. The rate of flow of heat depends on thermal conductivity and not on thermal capacity. The rate of flow of heat depends on thermal conductivity and capacity.
Question 9.
State the properties of heat radiation.
Properties :
• Heat radiations are electromagnetic waves.
• Heat radiations travel in straight line and can travel through vacuum also.
• Thermal radiations travel with the speed of light i.e., 3 × 1010 cm × s-1 and transmit in the form of radiant energy.
• Like light, they follow the inverse-square law.
• They follow the laws of reflection, refraction, polarization etc.
• They do not affect the mediums through they pass,but the medium which stops the radiation, are heated up.
Question 10.
State Newton’s law of cooling? What are the limitations of this law? Establish the relation between the temperature difference and rate of cooling. What is cooling curve.
Or
Describe the Newton’s law of cooling, deduce the formula and write its limitations.
Newton’s law of cooling: According to this law, the rate of cooling is directly proportional to the difference of mean temperature of the body and the temperature of surroundings.
Limitations:
• The temperature difference between the body and surrounding should not be more than 30°C.
• The loss of heat should be only by radiation.
• The temperature of the surrounding and nature of body should not be changed. Let a substance be cooled from θ1 °C to θ2 °C in t sec and temperature of surrounding is θ .
∴ Rate of cooling = $$\frac{\theta_{1}-\theta_{2}}{t}$$
And Mean temperature of the substance = $$\frac{\theta_{1}+\theta_{2}}{2}$$
∴ Temperature difference = $$\frac{\theta_{1}+\theta_{2}}{2}$$ – θ
Hence by Newtons law $$\frac{\theta_{1}-\theta_{2}}{t}$$ ∝( $$\frac{\theta_{1}+\theta_{2}}{2}$$ – θ)
∴ $$\frac{\theta_{1}-\theta_{2}}{t}$$ = K ( $$\frac{\theta_{1}+\theta_{2}}{2}$$ – θ)
Where, K is constant.
Cooling curve: The graph plotted between rate of cooling and temperature difference is called cooling curve. It is a straight line.
Question 11.
Derive the Newton’s law of cooling by Stefan’s-Boltzmann law.
Let the temperature of a black body is T and temperature of surrounding is T0. Now by Stefan’s-Boltzmann law, we have
Radiant energy per second per unit area,
E =σ (T4 – T04)
If the temperature difference is ΔT, then
T0 and σ are constant.
E ∝ ΔT
Hence, the rate of radiation of heat energy is directly proportional to the temperature difference.
Question 12.
Define coefficient of thermal conductivity. Write its unit and find out its dimensional formula.
Or
Define the coefficient of thermal conductivity and obtain expression for it.
The coefficient of thermal conductivity is defined by the amount of heat, flowing per second in steady-state through the rod of length 1 m long and area of cross-section lm2, with a unit temperature difference between the opposite faces.
The quantity of heat, flowing per second through a unit cube having unit temperature difference between opposite faces, during steady state.
i.e., Q = $$\frac{K A\left(\theta_{1}-\theta_{2}\right) t}{d}$$
∴ K = $$\frac{Q d}{A\left(\theta_{1}-\theta_{2}\right) t}$$
Unit: Its SI unit is $$\frac{\text { joule } \times \mathrm{m}}{\mathrm{m}^{2} \mathrm{~K} \mathrm{sec}}$$ = Jm-1K-1sec-1
But, joule/sec is Watt
∴ Other unit is Watt × m-1×K-1
Dimensional Formula :[K] = $$\frac{\left[\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-2}\right][\mathrm{L}]}{\left[\mathrm{L}^{2}\right][\theta][\mathrm{T}]}$$ = [MLT3θ-1].
Question 13.
What do you mean by thermal resistance? Write its unit and find out its dimensional formula.
The resistance offered by the body in the flow of heat is called thermal resistance,
Thermal resistance = $$\frac{d}{K A}$$ = $$\frac{\left(\theta_{1}-\theta_{2}\right) t}{Q}$$
Unit: Its SI unit is =$$\frac{\mathrm{K} \mathrm{sec} .}{\mathrm{J}}$$ = K sec-1 = K watt-1
Dimensional formula:
[Thermal resistance] = $$\frac{[\theta][T]}{\left[\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-2}\right]}$$ = [M-1L-2T3θ].
Thermal Properties of Matter Class 11 Important Questions Long Answer Type
Question 1.
Prove that for thermal expansion in solid :
α : β : γ= 1 : 2 : 3.
Let one side of a square lamina be l.Its temperature is increased through Δt so that each side increases by Δl.
∴ Initial area = l2
and Final area = (l + Δl)2
∴ Change in area, ΔA = (l + Δl)2 -l2
or =l2 +2l.Δl + Δl2 -l2
or = 2lΔl+ Δl2
Since Δl is a small quantity, hence Δl2 can be neglected.
∴ ΔA=2l.Δl.
Now, coefficient of superficial expansion,
β = $$\frac{\Delta A}{A \times \Delta t}$$
or
β = $$\frac{2 l \Delta l}{l^{2} \Delta t}$$ = 2. $$\frac{\Delta l}{l \Delta t}$$
or
β = 2α (∵ α = $$\frac{\Delta l}{l \Delta t}$$ )
Consider a cube of side of length l. The temperature of cube is increased by, Δt so that the length of the cube becomes (l + Δl).
Now, weigh the calorimeter with stirrer. Fill it with water about 2/3 and weigh it again. Find the initial temperature of water. When the temperature of the solid becomes constant for some times, then remove the wooden screen and move the calorimeter below the steam chamber. Then drop the solid into calorimeter carefully. Close the lid and stirred it slowly. Measure the temperature of the mixture when it becomes constant.
(ii) Observation :
• Mass of solid =m gm
• Mass of calorimeter + stirrer = m1 gm
• Mass of calorimeter + stirrer + water = m2 gm
• Initial temperature of water = t1°C
• Temperature of solid = t2°C
• Temperature of mixture = t3°C
• Specific heat of calorimeter = S1 (known).
(iii) Calculation : Let the Specific heat of solid = s
Mass of water = (m2 – m1) gm
∴ Heat given by the solid = Mass × Specific heat × Temperature difference
= m.s.(t2-t3)
Heat taken by calorimeter = m1S1(t3 – t1)
and Heat taken by water = (m2 – m1).(t3– t1)
Now, by the principle of calorimetry, we have
Heat given = Heat taken
∴ ms(t2 – t3) =m1s1(t3 – t1) +(m2 – m3) (t3 – t1)
∴ S = $$\frac{m_{1} s_{1}\left(t_{3}-t_{1}\right)+\left(m_{2}-m_{1}\right)\left(t_{3}-t_{1}\right)}{m\left(t_{2}-t_{3}\right)}$$
Thus, specific heat can be calculated.
Question 2.
Describe Newton’s experiment to prove the law of cooling on following points:
(i) Labelled diagram of apparatus, (ii) Method and (iii) Cooling curve.
(i) Apparatus : C = Calorimeter, S = Stirrer, T= Thermometer, V= Vessel.
(ii) Method: Take some water in a beaker and heat it. Then put hot water into calorimeter about 2/3 of it. When the temperature difference is nearly 30°C, then stir the water slowly and after every half minute record the temperature of the water, with the help of stop watch.
Then, draw graph between temperature and time. This curve is called cooling curve.
On the cooling curve take some points A, B, C, D,… Now, for each pair of points find the rate of cooling and temperature difference. For example, let the temperature of A and B points are θ1 and θ2°C.
∴ Rate of cooling = $$\frac{\theta_{1}-\theta_{2}}{t}$$
and Temp. difference = $$\frac{\theta_{1}-\theta_{2}}{2}$$ – θ
Where, θ is the temperature of surroundings.
Hence, the graph between rate of cooling and temperature difference is a straight line. Thus, rate of cooling is directly proportional to temperature difference.
Question 3.
Describe the experiment to find conductivity of a rod by Searl’s apparatus on following points:
(i) Labelled diagram of apparatus, (ii) Procedure, (iii) Observation, (iv) Calculation and (v) Precautions.
(i) Searl’s apparatus :
(ii) Procedure: First of all water is regulated through the copper tube, slow and continuous. Then steam is passed through the steam chamber. When the temperature of all the four thermometers become constant, steady state is achieved. Note the reading of ther mometer and with the help of stop watch collect the water in a weighed beaker for a particular time.
(iii) Observation :
• Area of cross-section of rod = A cm2
• Distance between the holes on rod = d cm
• Temperature of first thermometer = θ1 °C
• Temperature of second thermometer = θ2 °C
• Initial temperature of water = θ3 °C
• Final temperature of water = θ4°C
• Mass of water collected in t sec = m gm
(iv) Calculation: We know that,
Q = $$\frac{K A\left(\theta_{1}-\theta_{2}\right) t}{d}$$
or
K = $$\frac{Q \cdot d}{A\left(\theta_{1}-\theta_{2}\right) t}$$
Now, Q = Heat taken by water
= m × 1 × (θ4 – θ3) = m(θ4 – θ3)
∴ K = $$\frac{m\left(\theta_{4}-\theta_{3}\right) d}{A\left(\theta_{1}-\theta_{2}\right) t}$$
Hence, K can be calculated.
(v) Precautions :
• The steam should be passed after regulating the flow of water.
• The flow of water should be slow and continuous.
• When the temperature of all the four thermometers becomes constant, then only the readings should be taken.
Question 4.
Write the differences between conduction, convection and radiation.
Difference between Conduction, Convection and Radiation :
Conduction Convection Radiation 1. In this mode, heat flows from one particle to another particles. The particles do not leave their places. 1. The particles receive the heat and move away. 1. In this mode, heat travels in a straight line. 2. Medium is necessary for conduction. 2. Medium is necessary for convection. 2. Medium is not required. 3. Solids are heated by conduction. 3. Liquids and gases are heated by convection. 3. Heat is given to the bodies directly without affecting the medium. 4. The flow is in zig-zag manner. 4. The path may be zig-zag or curved. 4. The path is always straight line.
Thermal Properties of Matter Class 11 Important Numerical Questions
Question 1.
The triple point of neon and carbon dioxide are 24.57 K and 216.55 K respectively. Express these temperature on the Celsius and Fahrenheit scales. (NCERT)
Solution:
Here, Triple point of neon,
C = K-273
For neon,
C = 24-57 – 273 = -248-43°C
For C02,
C = 216-55-273=-56-45°C Relation between Kelvin scale and Fahrenheit scale:
$$\frac{\mathrm{K}-273}{5}$$ = $$\frac{\mathrm{F}-32}{9}$$
or
F =$$\frac{9}{5}$$ (K – 273) + 32
For neon,
F =$$\frac{9}{5}$$ (24-57-273)+ 32
⇒ F = $$\frac{9}{5}$$ × (-248.43) + 32
⇒ F =-447-2+32 = -415-2°
For CO2,
F = $$\frac{9}{5}$$ (K-273) + 32
⇒ F = $$\frac{9}{5}$$ (216.55-273)+ 32
⇒ F = $$\frac{9}{5}$$ × (-56.45) + 32
∴ F = -101.61 + 32 = -69.61° .
Question 2.
Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between TA and TB ? (NCERT)
Solution:
Here, triple point of water on absolute scale A = 200 A and triple point of water on obsolute scale B = 350 B
Triple point of water T = 273.16 K
According to question 200 A = 350 B = 273.16 K
or
1A = $$\frac{273 \cdot 16}{200}$$ K and 1B = $$\frac{273 \cdot 16}{350}$$ K
As TA and TB are at the same temperature,
$$\frac{273 \cdot 16}{200}$$ TA = $$\frac{273 \cdot 16}{350}$$ TB
or TB = $$=\frac{350}{200}$$ TA
⇒ TB = $$\frac{7}{5}$$ TA.
Question 3.
A steel tape 1 m long is correctly calibrated for a temperature of 27°C. The length of steel rod measured by this tape is found to be 63’0 cm on a hot day when the temperature is 45°C. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when temperature is 27°C? Coefficient of linear expansion of steel a= 1.2 × 10-5 K-1. (NCERT)
Solution:
The steel tape is calibrated at 27°C is correct. That is the length of 100 cm steel tape has correct magnitude 100 cm.
When the temperature raises from 27°C to 45°C then length of steel tape.
lt =l0+ l0 αt
lt = 100 + 100× 1.2× 10-5 (45-27)
lt =100 + 100 × 1.2 × 10-5 × 18
lt =100 + 0.0216 = 100.0216 cm.
At 45°C the measure of 63 cm. steel tape.
= $$\frac{100 \cdot 0216}{100}$$ × 63
= 63.0136 cm.
If the tape is measured at 27°C then its measure is 63 cm.
Question 4.
A brass boiler has a base area of 0.15 m2 and thickness 1.0 cm. It boils water at the rate of 6.0 kg/min, when placed on a gas stove. Estimate the temperature of the part of the flame in contact with the boiler. Thermal conductivity of brass 109 Js-11m-1°C-1 . (Heat of vaporization of water = 2256 × 103 J/kg.) (NCERT)
Solution:
Let the temperature of flame of source be T°C .
Given: K = 109 J/s.m°C = 109 × 10-2 J/s.cm°C
A = 0.15 m2; d= 1 cm = 10-2m
T1-T2 =(T-100)° C ,
t= 1 minute = 60 sec
m = 6 kg, L = 2256 J/gm
Q = $$\frac{109 \times 0 \cdot 15 \times(T-100) \times 60}{1 \times 10^{-2}}$$
= 98100(T -100)
Now, Q = mL = 6 ×2256 × 103
∴ 98100(T – 100) = 6 × 2256 × 103
or
T = $$\frac{6 \times 10^{3} \times 2256}{98100}$$ + 100
= 138+ 100 = 238° C.
Question 5.
A body cools from 80°C to 50°C in 5 minutes. Calculate the time it takes to cool from 60°C to 30°C. The temperature of the surrounding is 20°C. (NCERT)
Solution:
According to Newton’s law,
$$\frac{\theta_{1}-\theta_{2}}{t}$$ = K ($$\frac{\theta_{1}+\theta_{2}}{2}$$ – θ
Question 6.
At what temperature °C and F are equal to each other.
Solution:
Let at x degree temperature of both °C and °F are equal.
∴ $$\frac{\mathrm{C}}{5}$$ = $$\frac{\mathrm{F}-32}{9}$$
$$\frac{x}{5}$$ = $$\frac{x-32}{9}$$
∴9x = 5x – 160
or 9x – 5x = -160
4x = -160
∴ x =$$\frac{-160}{4}$$ = -40
i.e., -40°C = -40°F.
Question 7.
Volume of a brass ball at 0°C is 50 cm3 and at 100°C is 50.25 cm3. Find out coefficient of linear expansion.
Solution:
Given, V0 = 50 cm3, V100 = 50.25 cm3
ΔV = 50.25-50, =0.25 cm3 and Change in temperature ΔT = 100° C – 0° C = 100° C
∴ γ = $$\frac{\Delta V}{V \cdot \Delta T}$$
or
γ = $$\frac{0 \cdot 25}{50 \times 100}$$ = 5 × 10-5
Also, γ = 3α
∴ α = $$\frac{\gamma}{3}$$ = $$\frac{5 \times 10^{-5}}{3}$$
or = 1.7 × 10-5/°C.
f
Question 8.
Ratio of density of two metal A and B is 1 : 3. On giving equal amount of heat on equal volume of A and B, ratio of change in temperature is 2 :1. Find out ratio of specific heats.
Solution:
Given, d1 : d2 = 1 : 3, V1 = V2, Q1 = Q2, θ1 : θ2 = 2:1
Heat given to metal A, Q1 = Mass × Specific heat × Change in temperature.
Q1 =V1d1s1θ1
Heat given to metal B,Q2 =Mass × Specific heat × Change in temperature.
Q2 = V2d2s2θ2
Since Q1 = Q2
∴ V1d1s1θ1 = V2d2s2θ2
or
$$\frac{s_{1}}{s_{2}}$$ = $$\frac{V_{2}}{\mathrm{~V}_{1}} \times \frac{d_{2}}{d_{1}} \times \frac{\theta_{2}}{\theta_{1}}$$
= 1 ×$$\frac{3}{1} \times \frac{1}{2}$$ = $$\frac{3}{2}$$
i.e., s1:s2 = 3:2
Question 9.
Temperature of 1 kg of water is 60°C. It is mixed in a water of 1 kg at 40°C. What will be the temperature of mixture ? Specific heat of water = 1 calorie/gram °C.
Solution:
Let the temperature of the mixture be t°C.
Heat given by hot water =ms Δt = 1000× 1 × (60-t)calorie.
Heat taken by cold water = ms Δt = 1000 × 1 × (t – 40) calorie.
According to principle of mixture.
1000 × 1 × (60-t)= 1000 × 1 × (t-40)
∴ 60-t = t-40
or
2t = 100
or
t= 50°C.
Question 10.
What will be the resultant temperature when 5-gram ice at 0°C is mixed in 50 gram water at 30°C. Letent heat of ice = 80 calorie/gm.
Solution:
Let the resultant temperature be t°C.
Heat given by ice = Heat taken by water 5 × 80 + 5 × 1×(t-0) = 50× 1 ×(30-t)
or
400 + 5t = 1500-50t
or
55t = 1500-400= 1100
t =$$\frac{1100}{55}$$ = 20°C.
Question 11.
How much heat is required to change 0°C of 10 gm ice into 100°C steam? The latent heat of ice and steam are 80 and 540 cal/gm respectively.
Solution:
Heat required to change 0°C ice to 0°C water = mL = 10×80 = 800 cal
Heat required to change 0°C water to 100°C water = ms ΔT
= 10× 1 × (100-0) = 1000 cal
and Heat required to change 100°C water to 100°C steam = mL = 10 × 540 = 5400cal
Total amount of heat = 800+1000 + 5400 = 7200cal.
Question 12.
Calculate the heat required to convert 15 gm ice at -15°C into steam of 100°C. Given, specific heat of ice is 0.5 cal × gm-1 × °C-1. Latent heat of ice is 80 cal × gm-1 and latent heat of steam is 536 cal × gm-1.
Solution:
Heat required to convert 15 gm ice at -15°C into 0°C
= mst = 15 × 0.5 × (0+15) = 112.5cal
Heat required to convert 0°C ice into 0°C water
= mL =15 × 80= 1200cal
Heat required to convert 0°C water into 100°C water
= mst = 15 × 1 × (100 – 0) = 1500 cal
Heat required to convert 100°C water into 100°C steam = mL = 15 × 536 = 8040 cal
∴ Total heat = 112.5 + 1200 + 1500 + 8040 = 10852.5 cal.
Question 13.
A piece of metal of mass 50 gm is heated up to 200°C and then put into 400 gm water kept into a beaker. The initial and final temperatures of water are 20°C and 22.4°C respectively. Calculate the specific heat of metal.
Solution:
Heat given by metal = Heat taken by water
or ( 50 × s × (200 – 22.4) = 400 × 1 × (22.4 – 20)
or
8880s = 960
or
s = $$\frac{960}{8880}$$ = 0.108
∴ s = 0.108 cal ×gm-1 × °C-1
Question 14.
An iron piece of 100 gm is heated up to 10°C. How much water will be riased through 1°C, by the same amount of heat? specific heat of iron is 01 unit.
Solution:
Heat required to raise the temperature of iron piece
= 100× 0.1 × 10 = 100 cal.
Let the temperature of m gm water is raised through 1°C.
∴ Q = msΔT
or 100 = m × 1×1
or m = 100gm.
Question 15.
A wall has two faces of thickness 3 cm and 6 cm respectively and conductivities are K and 3K. Temperature of their outer faces are 20°C and -5°C respectively. Evaluate their common temperature instead state.
Solution:
Given, d1 = 3cm, d2= 6cm, K1 = K,K2 = 3K, θ1 = 20°C,θ2 = -5°C
From formula, θ = $$\frac{K_{1} d_{2} \theta_{1}+K_{2} d_{1} \theta_{2}}{K_{2} d_{1}+K_{1} d_{2}}$$
∴ θ = $$\frac{K \times 6 \times 20+3 K \times 3 \times(-5)}{3 K \times 3+K \times 6}$$
= $$\frac{120 K-45 K}{15 K}$$ = $$\frac{75 K}{15 K}$$ = 5°C
Question 16.
Two vessels of same shape, length, breadth and height are made of to different metals. They are filled with same amount of ice at 0°C. They talc 25 and 20 minutes respectively for melting the ice completely. Compare the thermal conductivities of two metals.
Solution:
Given:t1 =25 minutes, t2 = 20 minutes
Since, equal quantity of ice is filled in two vcssels, hence same quantity of heat is required for melting the ice.
θ = $$\frac{K_{1} A\left(\theta_{1}-\theta_{2}\right) t_{1}}{d}$$ = $$\frac{K_{2} A\left(\theta_{1}-\theta_{2}\right) t_{2}}{d}$$
A θ1 – θ2 and d are some for both.
∴ K1t1 = K2t2
or
$$\frac{K_{1}}{K_{2}}$$ = $$\frac{t_{2}}{t_{1}}$$
= $$\frac{20}{25}$$ = $$\frac{4}{5}$$
∴ K1 :K2 = 4:5
Question 17.
The surface area of a box is 5000 cm2 and its thickness is 6 mm. It is filled with the ice at 0°C and kept in a room of temperature 20°C. If 1 kg ice ¡s melted in 20 min. then calculate the conductivity of box. (Latent heat of ice = 80 cal/gm)
Solution:
Given m = 1kg = 1000 gm, L = 80 cal/gm, d = 6 mm = 0.6 cm,
A= 5000 cm2, θ1 – θ2=20 – 0=20°C t=20min = 20 × 60s
Thermal Properties of Matter Class 11 Important Questions Objective Type
1. Multiple- choice questions:
Question 1.
Magnitude of absolute zero in Fahrenheit scale is :
(a) 273° F
(b) 459° F
(c) 182° F
(d) 0° F.
(b) 459° F
Question 2.
Two system whose temperature is TA and TB are in thermal equilibrium, the relation between TA and TA is :
(a) TA > TB
(b)TA < TB
(C) TA =TB
(d) None of these.
(C) TA =TB
Question 3.
A hole is done in a rectangular copper plate, when the plate is heated, then the size of hole will be :
(a) Not change
(b) Increase
(c) Decrease
(d) Nothing can be said.
(b) Increase
Question 4.
There is a spherical cavity inside a solid sphere of metal, when the sphere is heated the volume of spherical cavity will:
(a) Increase
(b) Decrease
(c) No change
(d) Shape will change.
(a) Increase
Question 5.
If it is coefficient of superficial expansion of a metal then its coefficient of volume expansion will be :
(a) $$\frac{\beta}{2}$$
(b) 3β
(c) $$\frac{3 \beta}{2}$$
(d) $$\frac{2 \beta}{3}$$
(c) $$\frac{3 \beta}{2}$$
Question 6.
If the temperature of a diseased person is 40°C, then his temperature in Farenheit will be:
(a) 72°F
(b) 96°F
(c) 100°F
(d) 104°F.
(d) 104°F.
Question 7.
Temperature of sun is measured by:
(a) Gas thermometer
(b) Pyrometer
(c) Platinium thermometer
(d) Constant pressure thermometer.
(b) Pyrometer
Question 8.
For whom medium is not required for transmission of heat:
(a) Conduction
(b) Convection
(d) All.
Question 9.
Coefficient of thermal conductivity for ideal conductor is:
(a) 0
(b) 1
(c) -1
(d) ∞ .
(d) ∞
Question 10.
Unit of coefficient of thermal conductivity is :
(a) joule metre/ second ×°C
(b) joule × metre × second / °C
(c) joule / metre × second × °C
(d) joule × second / metre × °C.
(c) joule / metre × second × °C
Question 11.
In steady state, heat stored in metai does not depends on :
(b) Area of cross-section
(c) Length
(d) Thermal capacity.
(d) Thermal capacity.
Question 12.
An equivalent rod is made by joining two rod of same length. If their coefficient of thermal conductivity are K1 and K2, then thermal conductivity of equivalent rod is:
(a) K1+K2
(b) K1– K2
(c) 2K1 K2/ (k1+ K2)
(d) (K1 – K2)/(k1+ K2).
(c) 2K1 K2/ (k1+K2)
Question 13.
Monsoon is due to:
(a) Conduction
(b) Convection
(d) All the above.
(b) Convection
Question 14.
PolIshed body are for thermal radiation:
(a) Good absorber and bad reflector
(b) Good absorber and good reflector
(c) Bad absorber and good reflector
(c) Bad absorber and good reflector
Question 15.
Whose specific heat is more :
(a) Iron
(b) Water
(c) Copper
(d) Glass.
(b) Water
2. Fill in the blanks:
1. Coefficient of linear expansion of solid depend upon ……………. .
Nature of matter
2. SI Unit of temperature gradient is……………. .
joule / metre
3. Density of water is maximum at …………… temperature.
4°C
4. α: β: γ = ……………
1:2 : 3
5. The point where all three phases in solid, liquid and gas co-exist is called …………… .
Triple point
Less
7. Conversion of matter from solid-state to vapour state directly is called ……………
Sub-limation.
3. Match the following:
Column ‘A’ Column ‘B’ 1. Coefficient of linear expansion (a) kilogram 2. Coefficient of volume expansion (b) Rate of cooling ∝ difference temperature 3. Specific heat (c) Only for solid 4. Newton’s laws of cooling (d) Raise of temperature by 1°C 5. Water equivalent (e) Solid, liquid and gas.
1. (c) Only for solid
2. (e) Solid, liquid and gas.
3. (d) Raise of temperature by 1°C
4. (b) Rate of cooling ∝ difference temperature
5. (a) kilogram.
4. state true or False:
1. Volume of water at 4°C is maximum.
False
2. At triple point of water, temperature is 273.16K.
True
3. On increasing temperature the volume of mercury increases uniformly.
True
4. Gases has two type of specific heat.
True
5. Cp is always less than Cv. | 2021-09-28 12:53:35 | {"extraction_info": {"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": 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, "math_score": 0.642773449420929, "perplexity": 2274.846186842614}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780060803.2/warc/CC-MAIN-20210928122846-20210928152846-00691.warc.gz"} |
https://gre.kmf.com/explain/index?qid=31721&source=151 | # 题目内容
The author would agree with all of the following regarding Galls work EXCEPT?
• AIt did not confirm certain assumptions in an empirical manner.
• BIt relied on surface features of the skull to derive personality traits.
• CIt deemed the diseased brain as an invalid means of learning about an individuals personality.
• DIt postulated that personality traits were not linked to the brain but to depressions and elevations in the scalp.
• EIt correctly identified the brain as the source of human behavior.
D显示答案
• KMF 解析
• 网友解析
• 题目数据
• 收起
• 全部讨论
• 只看提问
• 按时间排序
• 按点赞数排序 | 2021-12-09 10:37:09 | {"extraction_info": {"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, "math_score": 0.3472186326980591, "perplexity": 13486.568486568254}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363791.16/warc/CC-MAIN-20211209091917-20211209121917-00043.warc.gz"} |
https://mathoverflow.net/questions/212740/why-do-the-model-structures-on-dg-algebras-and-on-dg-categories-are-not-compatib/215836 | # Why do the model structures on dg-algebras and on dg-categories are not compatible?
First we talk about dg-algebras. According to this n-lab page, we write $dgAlg$ for the category of cochain dg-algebras in non-negative degree over a field $k$ of characteristic $0$. Write $CdgAlg\subset dgAlg$ for the subcategory of (graded-)commutative dg-algebras. Then The projective model category structure on $CdgAlg$ and on $dgAlg$ is given by setting:
• weak equivalences are the quasi-isomorphisms
• fibrations are the degreewise surjections.
Then we look at dg-categories. According to this n-lab page, we write $dgCat$ for the category of small dg-categories over $k$. Then the Dwyer-Kan model structure on $dgCat$ is given by setting:
• a dg-functor $F:A\to B$ is a weak equivalence if $(1)$ for all objects $x,y\in A$ the component $F_{x,y}:A(x,y)\to B(F(x),F(y))$ is a quasi-isomorphism of chain complexes $(2)$ the induced functor on homotopy categories $H^0(F)$ (obtained by taking degree 0 chain homology in each hom-object) is an equivalence of categories.
• a dg-functor $F:A\to B$ is a fibration if $(1)$ for all objects $x,y\in A$ the component $F_{x,y}$ is a degreewise surjection of chain complexes; $(2)$ for each isomorphism $F(x)\to Z$ in $H^0(B)$ there is a lift to an isomorphism in $H^0(A)$.
Now we compare this two definitions. A dg-algebra can be considered as a dg-category which consists of one object hence we have a inclusion $dgAlg\subset dgCat$. However, although very similar at the first glance, the two model structures are not compatible. In particular there are dg-maps $F: A\to B$ between dg-algebras which is a fibration in the projective model structure on $dgAlg$ but not a fibration in the Dwyer-Kan model structure on $dgCat$.
For example let $A$ be the de Rham algebra of the closed interval $[0,1]$ and $B$ be the de Rham algebra of the two end points ${0,1}$ (hence $B$ is concentrated in degree $0$). Let $F: A\to B$ be the restriction map. It is clear that $F$ is degreewise surjective hence $F$ is a fibration in $dgAlg$. However if we take $f\in B$ to be $f(0)=1$, $f(1)=-1$ then $f$ is invertible in $H^0(B)$ but $f$ cannot be a restriction of a closed element in $A^0$ hence $F: A\to B$ is not a fibration when considered as a morphism in $dgCat$.
$\textbf{My question}$ is: what is the reason and consequence of this incompatibility? Does it mean that we can construct a new model structure on $dgAlg$ by restricting the Dwyer-Kan model structure to $dgAlg$?
• At least they have the same weak equivalences. So in addition to your question --- does dgAlg have a model structure with the standard weak equivalences but the Dwyer--Kan fibrations --- one can ask whether dgCat has a model structure with its standard weak equivalences but the projective fibrations. Note that if the answers are "yes", then the identity functor will be a Quillen equivalence, which is often good enough. Jul 31 '15 at 17:18
• A minor comment is that to obtain a model structure on dg-algebras you should most likely either restrict to connected algebras, or change the definition of a fibration to a surjection in positive degrees. Jul 31 '15 at 17:20
I will try to give a example in topology and then in dg-world. Suppose that $G$ and $H$ are topological groups. There is a fiber sequence $$Map_{\ast}(BG,BH)\rightarrow Map(BG,BH)\rightarrow BH$$ where $B$ is the classifying space. Here is a homotopy categorical interpretation of the previous fiber sequence. $$Map^{\otimes}(G,H)\rightarrow Map_{top-cat}(\mathbf{G},\mathbf{H})\rightarrow Map_{Top-cat}(\ast, \mathbf{H})$$ where $Map^{\otimes}$ is the derived mapping space in the model category of topological mono ids. $Map_{Top-cat}$ is the derived mapping space in the model category of small topological categories. The notation $\mathbf{H}$ is for the topological category with one object such that the endomorphism monoid is $H$.
So what happens in the dg-world. Well, there is a fiber sequence $$Map_{dg-algebras}(A,B)\rightarrow Map_{dg-cat}(\mathbf{A},\mathbf{B})\rightarrow Map_{dg-cat}(\mathbf{k}, \mathbf{B})$$
The notation $\mathbf{A}$ is for the $dg_{k}$-category with one object such that the endomorphism monoid is $A$. $k$ is the ground commutative ring. Now we see why $Map_{dg-algebras}(A,B)$ is different from
$Map_{dg-cat}(\mathbf{A},\mathbf{B})$.
• It's also worth to say that $Map_{dg-cat}(\mathbf{k},\mathbf{B})$ is the classifying space of the topological/simplicial group of derived units in $\mathbf{B}$, i.e. $Map_{dg-algebras}(\mathbf{k}[t^{\pm1}],\mathbf{B})$. Aug 28 '15 at 15:47
• A small remark: the functor of $\infty$-categories from (dg-algebras) to (dg-categories) factors through a functor to the $\infty$-category of pointed dg-categories which is fully faithful. As you point out, the mapping spaces in (pointed dg-categories) are obtained from the mapping spaces in (dg-categories) by quotienting out by the action of the simplicial group of units. | 2022-01-22 09:32:00 | {"extraction_info": {"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, "math_score": 0.9544193148612976, "perplexity": 162.6553651062651}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303779.65/warc/CC-MAIN-20220122073422-20220122103422-00230.warc.gz"} |
https://infoscience.epfl.ch/record/83757 | ## Estimating Distribution Functions with Smoothing Splines
The scope is to smooth the empirical distribution function of a random sample by minimizing a penalized sum of squared errors. The spline, which is the solution to this problem, is studied via the eigenvalue structure of the random matrices ocurring in its representation
Year:
1999
Keywords:
Laboratories: | 2019-11-14 13:35:03 | {"extraction_info": {"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, "math_score": 0.8636991381645203, "perplexity": 448.98270720808046}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668525.62/warc/CC-MAIN-20191114131434-20191114155434-00501.warc.gz"} |
http://ptsymmetry.net/?m=201106 | June 2011
Mon Tue Wed Thu Fri Sat Sun
« May Jul »
12345
6789101112
13141516171819
20212223242526
27282930
## Many-Body Effects in a Model of Electromagnetically Induced Transparency
Jose Reslen
We study the effect of inter-band interactions in the absorption profile of a semi-classical model describing electromagnetically induced transparency. We develop a consistent approach using a nonhermitian Hamiltonian to model particle decay. This allow us to characterize the system response for different number of particles so that the effect of particle-interaction on the transmission profile can be studied over a wide range of characteristic parameters.
http://arxiv.org/abs/1106.5240
Quantum Physics (quant-ph)
## Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials
Hiroshi Miki, Luc Vinet, Alexei Zhedanov
A set of $$r$$ non-Hermitian oscillator Hamiltonians in $$r$$ dimensions is shown to be simultaneously diagonalizable. Their spectra is real and the common eigenstates are expressed in terms of multiple Charlier polynomials. An algebraic interpretation of these polynomials is thus achieved and the model is used to derive some of their properties.
http://arxiv.org/abs/1106.5243
Mathematical Physics (math-ph)
## Galois Conjugates of Topological Phases
Michael H. Freedman, Jan Gukelberger, Matthew B. Hastings, Simon Trebst, Matthias Troyer, Zhenghan Wang
Galois conjugation relates unitary conformal field theories (CFTs) and topological quantum field theories (TQFTs) to their non-unitary counterparts. Here we investigate Galois conjugates of quantum double models, such as the Levin-Wen model. While these Galois conjugated Hamiltonians are typically non-Hermitian, we find that their ground state wave functions still obey a generalized version of the usual code property (local operators do not act on the ground state manifold) and hence enjoy a generalized topological protection. The key question addressed in this paper is whether such non-unitary topological phases can also appear as the ground states of Hermitian Hamiltonians. Specific attempts at constructing Hermitian Hamiltonians with these ground states lead to a loss of the code property and topological protection of the degenerate ground states. Beyond this we rigorously prove that no local change of basis can transform the ground states of the Galois conjugated doubled Fibonacci theory into the ground states of a topological model whose Hermitian Hamiltonian satisfies Lieb-Robinson bounds. These include all gapped local or quasi-local Hamiltonians. A similar statement holds for many other non-unitary TQFTs. One consequence is that the “Gaffnian” wave function cannot be the ground state of a gapped fractional quantum Hall state.
http://arxiv.org/abs/1106.3267
Strongly Correlated Electrons (cond-mat.str-el); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph)
## Entanglement Efficiencies in PT-Symmetric Quantum Mechanics
Christian Zielinski, Qing-hai Wang
The degree of entanglement is determined for arbitrary states of a PT-symmetric bipartite composite system. We characterize the rate with which entangled states are generated and show that this rate can be quantified by a small set of parameters. These relations allow one in principle to increase the efficiency of these systems to entangle states. It is also noticed that many relations resemble corresponding ones in conventional quantum mechanics.
http://arxiv.org/abs/1106.3856
High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)
## Shortcuts to adiabaticity for non-Hermitian systems
S. Ibáñez, S. Martí nez-Garaot, Xi Chen, E. Torrontegui, J. G. Muga
Adiabatic processes driven by non-Hermitian, time-dependent Hamiltonians may be sped up by generalizing inverse engineering techniques based on Berry’s transitionless driving algorithm or on dynamical invariants. We work out the basic theory and examples described by two-level Hamiltonians: the acceleration of rapid adiabatic passage with a decaying excited level and of the dynamics of a classical particle on an expanding harmonic oscillator.
http://arxiv.org/abs/1106.2776
Quantum Physics (quant-ph)
## Time-Reversal Symmetry in Non-Hermitian Systems
Masatoshi Sato, Kazuki Hasebe, Kenta Esaki, Mahito Kohmoto
For ordinary hermitian Hamiltonians, the states show the Kramers degeneracy when the system has a half-odd-integer spin and the time reversal operator obeys $$\Theta^2=-1$$, but no such a degeneracy exists when $$\Theta^2=+1$$. Here we point out that for non-hermitian systems, there exists a degeneracy similar to Kramers even when $$\Theta^2=+1$$. It is found that the new degeneracy follows from the mathematical structure of split-quaternion, instead of quaternion from which the Kramers degeneracy follows in the usual hermitian cases. Furthermore, we also show that particle/hole symmetry gives rise to a pair of states with opposite energies on the basis of the split quaternion in a class of non-hermitian Hamiltonians. As concrete examples, we examine in detail NxN Hamiltonians with N=2 and 4 which are non-hermitian generalizations of spin 1/2 Hamiltonian and quadrupole Hamiltonian of spin 3/2, respectively.
http://arxiv.org/abs/1106.1806
Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
## Reply on Comments on “Observation of a Fast Evolution in a Parity-time-symmetric System”(ArXiv:1106.1550)
Chao Zheng, Liang Hao, Gui Lu Long
Masillo [1] commented on our manuscript [2] “Observation of a Fast Evolution in a Parity-time-symmetric System”, pointing out a contradiction of our work with Ref.[3]. In this reply, we pointed out there is no disagreement between Masillo’s comment and our work in Ref. [2]. The efficiency cost pointed out in Ref.\cite{masillo} exists, namely to obtain the PT-symmetric hamiltonian evolution, one has to make a measurement on the auxiliary qubit and the auxiliary qubit is at state $$\left|0\right \rangle$$ only probabilistically. This is reflected in the amplitude of the spectrum in the NMR quantum simulation. As a result, we made a small modification in a new version of the Ref. [2], and Fig. 2 of Ref.[2] has been replaced by spectra of two different $$\alpha$$’s in order to illustrate this fact.
http://arxiv.org/abs/1106.1848
Quantum Physics (quant-ph)
## Comments on “Observation of Fast Evolution in Parity-Time-Symmetric System”
Fabio Masillo
In the paper “Observation of Fast Evolution in Parity-Time-Symmetric System” the authors propose a physical apparatus for the realization of a faster than Hermitian evolution. This last appears in contrast with the conclusions obtained in our paper “Some Remarks on Quantum Brachistochrone”. We will clarify this apparent contradiction and some problematic aspects of the treatment in [1].
http://arxiv.org/abs/1106.1550
Quantum Physics (quant-ph)
## Perfect State Transfer in PT-symmetric Non-Hermitian Networks
X. Z. Zhang, L. Jin, Z. Song
We systematically study the parity- and time-reversal- (PT) symmetric non-Hermitian version of a quantum network proposed in the work of Christandl et al. [Phys. Rev. Lett. 92, 187902 (2004)]. We show that such an extended model still allows conditional perfect state transfer within the unbroken PT-symmetric region, but not arbitrary. This is due to the fact that the evolution operator at certain period is equivalent to the PT operator for the real-valued wavefunction in the elaborate PT-symmetric Hilbert space. The critical behavior of the eigenstates is also discussed at the exceptional point.
http://arxiv.org/abs/1106.0087
Quantum Physics (quant-ph)
## Observation of Fast Evolution in Parity-Time-Symmetric System
Chao Zheng, Liang Hao, Gui Lu Long
To find and realize the optimal evolution between two states is significant both in theory and application. In quantum mechanics, the minimal evolution is bounded by the gap between the largest and smallest eigenvalue of the Hamiltonian. In the parity-time-symmetric(PT-symmetric) Hamiltonian theory, it was predicted that the optimized evolution time can be reduced drastically comparing to the bound in the Hermitian case, and can become even zero. In this Letter, we report the experimental observation of the fast evolution of a PT-symmetric Hamiltonian in an nuclear magnetic resonance (NMR) quantum system. The experimental results demonstrate that the PT-symmetric Hamiltonian can indeed evolve much faster than that in a quantum system, and time it takes can be arbitrary close to zero.
http://arxiv.org/abs/1105.6157
Quantum Physics (quant-ph) | 2017-10-21 22:55:44 | {"extraction_info": {"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": 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, "math_score": 0.6677543520927429, "perplexity": 1150.476869762497}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824899.75/warc/CC-MAIN-20171021224608-20171022004608-00492.warc.gz"} |
http://spmaddmaths.onlinetuition.com.my/2014/01/spm-practice-1-arithmetic-progression_5402.html | # SPM Practice 1 (Arithmetic Progression) : Question 15
Question 15(Tricky question! Make sure you try it!)
The sum of n terms of an arithmetic progression is given by the formula ${S}_{n}=\frac{n}{2}\left(5-3n\right)$ . Find
(a) the first term,
(b) the common difference,
(c) the tenth term.
[ Hint : $S 1 = T 1 =a$ $S 2 = T 1 + T 2$ $d= T 2 − T 1]$ | 2017-05-24 11:56:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "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, "math_score": 0.8954251408576965, "perplexity": 2201.6430085616284}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607813.12/warc/CC-MAIN-20170524112717-20170524132717-00052.warc.gz"} |
https://mathoverflow.net/questions/321668/sobolev-multiplication-on-non-compact-manifold | # Sobolev Multiplication on non-compact manifold
We know that for a compact Riemannian $$n$$-dim manifold $$(M,g)$$(the boundary could be nonempty), the Sobolev Multiplication Theorem states that $$L^p_k\times L^q_l⟶L^r_m$$, where $$1/r−m/n>1/p−k/m+1/q−l/n$$ and $$m\leq\min(l,k)$$.
Q If $$M$$ is non-compact, does the Sobolev Multiplication Theorem still holds?
PS:
• If $$k=l=m=0$$, we know that it is true. Could anyone give a reference for the case $$k,l,m\geq1$$?
• The problem is that can we have an embedding $$L^p_k\hookrightarrow L^{p*},$$ where $$\frac1{p^*}=\frac1p-\frac{k}{n}$$ for the complete manifold(bounded geometry). | 2019-02-20 00:10:56 | {"extraction_info": {"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": 10, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9226426482200623, "perplexity": 418.3085924445938}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247493803.26/warc/CC-MAIN-20190219223509-20190220005509-00027.warc.gz"} |
http://repetae.net/computer/haskell/DrIFT/drift.html | [ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
# 1. Introduction
This is a guide to using DrIFT, a type sensitive preprocessor for Haskell 98.
DrIFT is a tool which parses a Haskell module for structures (data & newtype declarations) and commands. These commands cause rules to be fired on the parsed data, generating new code which is then appended to the bottom of the input file, or redirected to another. These rules are expressed as Haskell code, and it is intended that the user can add new rules as required.
DrIFT is written in pure Haskell 98, however code it generates is free to make use of extensions when appropriate. DrIFT is currently tested against hugs and ghc.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 1.1 So, What Does DrIFT do?
DrIFT allows derivation of instances for classes that aren't supported by the standard compilers. In addition, instances can be produced in separate modules to that containing the type declaration. This allows instances to be derived for a type after the original module has been compiled. As a bonus, simple utility functions can also be produced for types.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 1.2 Features
• DrIFT comes with a set of rules to produce instances for all derivable classes given in the Prelude. There's a rule to produce instances of NFData (the original motivation of all this), and rules for utility functions on types also. The DrIFT implementation is also regularly updated with rules submitted by users.
• Code is generated using pretty-printing combinators. This means that the output is (fairly) well formatted, and easy on the human eye.
• Effort has been made to make the rule interface as easy to use as possible. This is to allow users to add rules to generate code specific to their own projects. As the rules are written in Haskell themselves, the user doesn't have to learn a new language syntax, and can use all Haskell's features.
Currently supported derivations are the following. This list is obtainable by running DrIFT -l.
Binary:
Binary efficient binary encoding of terms
GhcBinary byte sized binary encoding of terms
Debugging:
Observable HOOD observable
General:
NFData provides 'rnf' to reduce to normal form (deepSeq)
Typeable derive Typeable for Dynamic
Generics:
FunctorM derive reasonable fmapM implementation
HFoldable Strafunski hfoldr
Monoid derive reasonable Data.Monoid implementation
RMapM derive reasonable rmapM implementation
Term Strafunski representation via Dynamic
Prelude:
Bounded
Enum
Eq
Ord
Show
Representation:
ATermConvertible encode terms in the ATerm format
Haskell2Xml encode terms as XML (HaXml<=1.13)
XmlContent encode terms as XML (HaXml>=1.14)
Utility:
Parse parse values back from standard 'Show'
Query provide a QueryFoo class with 'is', 'has',
'from', and 'get' routines
from provides fromFoo for each constructor
get for label 'foo' provide foo_g to get it
has hasfoo for record types
is provides isFoo for each constructor
test output raw data for testing
un provides unFoo for unary constructors
update for label 'foo' provides 'foo_u' to update it
and foo_s to set it
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 1.3 Why Do We Need DrIFT?
The original motivation for DrIFT came from reading one of the Glasgow Parallel Haskell papers on Strategies. Strategies require producing instances of a class which reduces to normal form (called NFData). It was commented that it was a shame that instances of NFData couldn't be automatically derived; the rules to generate the instances are simple, and adding instances by hand is tiresome. Many classes' instances follow simple patterns. This is what makes coding up instances so tedious: there's no thought involved!
The idea to extend DrIFT to work on imported types came from a discussion of the Haskell mailing list, arising from a point made by Olaf Chitil :
Why is the automatic derivation of instances for some standard classes linked to data and newtype declarations? It happened already several times to me that I needed a standard instance of a data type that I imported from a module that did not provide that instance and which I did not want to change (a library; GHC, which I mainly want to extend by further modules, not spread changes over 250 modules). When declaring a new data type one normally avoids deriving (currently) unneeded instances, because it costs program code (and maybe one even wants to enable the user of the module to define his own instances).
The third feature of DrIFT, providing utility functions to manipulate new types, especially records was caused by finding oneself writing the same sort of code over and over again. These functions couldn't be captured in a class, but have a similar form for each type they are defined on. A thread on the Haskell mailing list made a related point: untagging and manipulating newtypes was more cumbersome than it should be.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 1.4 An Example
Here's an example of what how DrIFT is used. This Haskell module contains commands to the DrIFT preprocessor. These are annotated with {-! ... !-}. After processing with DrIFT the generated code is glued on the bottom of the file, beneath a marker indicating where the new code starts. The machine generated code is quite long, and would really have been a drudge to type in by hand.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
### 1.4.1 Source Code
-- example script for DrIFT module Example where import Foo {-!for Foo derive : Read,NFData !-} -- apply rules to imported type {-! global : is !-} -- global to this module {-!for Data derive : update,Show,Read!-} -- stand alone comand syntax {-!for Maybe derive : NFData !-} -- apply rules to prelude type data Data = D {name :: Name, constraints :: [(Class,Var)], vars :: [Var], body :: [(Constructor,[(Name,Type)])], derive :: [Class], statement :: Statement} data Statement = DataStmt | NewTypeStmt deriving Eq {-!derive : Ord,Show,Read !-} -- abbreviated syntax
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
### 1.4.2 After processing with DrIFT
module Example where import Foo {-!for Foo derive : Read,NFData !-} -- apply rules to imported type {-! global : is !-} -- global to this module {-!for Data derive : update,Show,Read!-} -- stand alone comand syntax {-!for Maybe derive : NFData !-} -- apply rules to prelude type data Data = D {name :: Name, constraints :: [(Class,Var)], vars :: [Var], body :: [(Constructor,[(Name,Type)])], derive :: [Class], statement :: Statement} data Statement = DataStmt | NewTypeStmt deriving Eq {-!derive : Ord,Show,Read !-} {-* Generated by DrIFT-v1.0 : Look, but Don't Touch. *-} isD (D aa ab ac ad ae af) = True isD _ = False instance Ord Statement where compare DataStmt (DataStmt) = EQ compare DataStmt (NewTypeStmt) = LT compare NewTypeStmt (DataStmt) = GT compare NewTypeStmt (NewTypeStmt) = EQ instance Show Statement where showsPrec d (DataStmt) = showString "DataStmt" showsPrec d (NewTypeStmt) = showString "NewTypeStmt" instance Read Statement where readsPrec d input = (\ inp -> [((DataStmt) , rest) | ("DataStmt" , rest) <- lex inp]) input ++ (\ inp -> [((NewTypeStmt) , rest) | ("NewTypeStmt" , rest) <- lex inp]) input isDataStmt (DataStmt) = True isDataStmt _ = False isNewTypeStmt (NewTypeStmt) = True isNewTypeStmt _ = False instance (NFData a) => NFData (Maybe a) where rnf (Just aa) = rnf aa rnf (Nothing) = () body_u f r@D{body} = r{body = f body} constraints_u f r@D{constraints} = r{constraints = f constraints} derive_u f r@D{derive} = r{derive = f derive} name_u f r@D{name} = r{name = f name} statement_u f r@D{statement} = r{statement = f statement} vars_u f r@D{vars} = r{vars = f vars} body_s v = body_u (const v) constraints_s v = constraints_u (const v) derive_s v = derive_u (const v) name_s v = name_u (const v) statement_s v = statement_u (const v) vars_s v = vars_u (const v) instance Show Data where showsPrec d (D aa ab ac ad ae af) = showParen (d >= 10) (showString "D" . showChar '{' . showString "name" . showChar '=' . showsPrec 10 aa . showChar ',' . showString "constraints" . showChar '=' . showsPrec 10 ab . showChar ',' . showString "vars" . showChar '=' . showsPrec 10 ac . showChar ',' . showString "body" . showChar '=' . showsPrec 10 ad . showChar ',' . showString "derive" . showChar '=' . showsPrec 10 ae . showChar ',' . showString "statement" . showChar '=' . showsPrec 10 af . showChar '}') instance Read Data where readsPrec d input = readParen (d > 9) (\ inp -> [((D aa ab ac ad ae af) , rest) | ("D" , inp) <- lex inp , ("{" , inp) <- lex inp , ("name" , inp) <- lex inp , ("=" , inp) <- lex inp , (aa , inp) <- readsPrec 10 inp , ("," , inp) <- lex inp , ("constraints" , inp) <- lex inp , ("=" , inp) <- lex inp , (ab , inp) <- readsPrec 10 inp , ("," , inp) <- lex inp , ("vars" , inp) <- lex inp , ("=" , inp) <- lex inp , (ac , inp) <- readsPrec 10 inp , ("," , inp) <- lex inp , ("body" , inp) <- lex inp , ("=" , inp) <- lex inp , (ad , inp) <- readsPrec 10 inp , ("," , inp) <- lex inp , ("derive" , inp) <- lex inp , ("=" , inp) <- lex inp , (ae , inp) <- readsPrec 10 inp , ("," , inp) <- lex inp , ("statement" , inp) <- lex inp , ("=" , inp) <- lex inp , (af , inp) <- readsPrec 10 inp , ("}" , rest) <- lex inp]) input -- Imported from other files :- instance Read Foo where readsPrec d input = (\ inp -> [((Foo) , rest) | ("Foo" , rest) <- lex inp]) input ++ (\ inp -> [((Bar) , rest) | ("Bar" , rest) <- lex inp]) input ++ (\ inp -> [((Bub) , rest) | ("Bub" , rest) <- lex inp]) input instance NFData Foo where rnf (Foo) = () rnf (Bar) = () rnf (Bub) = ()
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
# 2. User Guide
This chapter assumes that DrIFT has already been installed and the environment variables set up. The installation is handled in Installation.
Briefly, the way DrIFT works is
1. parse the input file, looking for commands and data & newtype statements.
2. generate code by executing the commands, which apply rules to types.
3. if any commands remain unexecuted, this means the types aren't declared in this module, so DrIFT searches for them in imported modules.
4. append the generated code to the bottom of the file (overwriting any previously generated code)
Rules can be applied to any types defined using a data or newtype statement. Rules can't be applied to types defined using type, as this only produces a synonym for a type. Don't try to use rules on type synonyms.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 2.1 The Command Line
DrIFT processes standard Haskell scripts (suffix ‘.hs’) and literate scripts (suffix ‘.lhs’). Currently, only literate code using > is accepted: DrIFT doesn't understand the TeX style of literate programming using \begin{code}.
If you've compiled up an executable from the source code (or are using Runhugs) to run DrIFT over a file type :-
DrIFT filename
Alternatively, for Hugs, use :-
runhugs DrIFT filename (run DrIFT over filename)
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 2.2 Command Syntax
Commands to DrIFT are entered into Haskell code in the form of annotations. DrIFT's annotations start with {-! and finish with !-}. (This is so they don't clash with the compiler annotations given to GHC or HBC). There are three forms of command.
• Stand–Alone Command (syntax : {-! for type derive : rule1,rule2,… !-}) This is the basic form of DrIFT command. It asks DrIFT to apply the listed rules to the specified type. If the type is parameterised, e.g. Maybe a, just enter the type name into the command, omitting any type variables. DrIFT assumes that types given are currently in scope, and will first search the current module. If it fails to find a matching type definition, the prelude and any imported modules are also searched. This is the only command which allows code to be generated for a type defined in another module.
• Abbreviated Command (syntax : {-! derive :rule1,rule2,… !-}) This command is appended to the end of a data or newtype definition, after the deriving clause, if present. It applies the listed rules to the type it is attached to.
• Global Command (syntax : {-! global :rule1,rule2,… !-} This command applies the listed rules to all types defined within the module. Note that this command doesn't cause code to be generated for types imported from other modules.
For an example of these commands in use, See section An Example.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
### 2.2.1 Notes on Using Commands
• The stand-alone and global commands should be entered on a line by themselves, starting in the first column, (as with other top-level declarations, such as infix, import,newtype). It doesn't matter what position they occur within the module.
• In a literate file, all commands should be entered on a code' line (one starting with >).
• Commands may be commented out by using -- and {- .. -} in the usual way.
• If two commands apply the same rule to a type, then two sets of identical code will be produced. This will cause a multiple definition' error when the processed module is compiled/interpreted. Don't do it!
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 2.3 Emacs DrIFT mode
For Emacs fans, Hans W Loidl hwloidl@dcs.gla.ac.uk has written a script which allows DrIFT to be run within a buffer.
The commands available are
• M-x hwl-derive, C-c d d runs DrIFT over the current buffer, and then updates the buffer.
• M-x hwl-derive-insert-standalone, C-c d s inserts a template for a standalone command into the current buffer at the cursor position.
• M-x hwl-derive-insert-local, C-c d l inserts a template for an abbreviated command.
• M-x hwl-derive-insert-global, C-c d g inserts a template for a global command
In hugs-mode' these functions are also available vie a menu item in the hugs menu.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
# 3. Standard Rules
Heres a listing of the rules that come pre-defined with DrIFT. If you want a more detailed idea of how they work, their definitions are in the file ‘StandardRules.hs’, and are (fairly) well documented. In the following list the highlighted text is the name of the rule, as used in commands. The naming convention for rules is names starting with a capital generate an instance for the class of the same name. Sets of functions are generated by a name beginning with a lower case letter.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 3.1 Prelude Classes
The classes Eq, Ord, Enum, Show, Read & Bounded are described in the Haskell report as being derivable; DrIFT provides rules for all these.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 3.2 Other Classes
Originally, NFData (for Normal Form evaluation strategies) was the only other class to have a rule. But now, there are rules for many more classes from 3rd-party libraries, e.g. XmlContent from HaXml, Binary from nhc98, Term from Strafunski, FunctorM for Generics, Observable for HOOD debugging, Typeable for dynamics, and so on. For a full list, use the --list command-line option.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 3.3 Utilities
• un attempts to make newtypes a little nicer to use by providing an untagging function. This rule can only be used on types defined using newtype.
For a type newtype Foo a = F a,
un produces the function unFoo :: Foo a -> a.
• is produces predicates that indicate the presence of a constructor. This is only useful for multi-constructor datatypes (obviously).
For a type data Foo = Bar | Bub, is generates
isBar :: Foo -> Bool and isBub :: Foo -> Bool.
• has produces predicates that indicate the presence of a label. This can only be used with types where at least one of the constructors is a labelled record. Note that labels can be shared between constructors of the same type.
For a type data Foo a = F{bar :: a,bub :: Int} has generates
hasbar :: Foo a-> Bool and hasbub :: Foo a -> Bool.
• update produces functions that update fields within a record type. This rule can only be used with a type where at least on of the constructors is a labelled record.
For a type data Foo a = F{bar :: a, bub ::Int} update generates
bar_u :: (a -> a) -> Foo a -> Foo a and
bub_u :: (Int -> Int) -> Foo a -> Foo a which apply a function to a field of a record, and then return the updated record. If the value does not have the given field then the value is returned unchanged.
bar_s :: a -> Foo a -> Foo a and bub_s ::Int -> Foo a -> Foo a are also generated, and are used to set the value of a field in a record.
• test dumps the parsed representation of a datatype to the output. This is be useful for debugging new rules, as the user can see what information is stored about a particular type.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
Programmers who only wish to use the pre-defined rules in DrIFT don't need to read or understand the following section. However, as well as using the supplied rules, users are encouraged to add their own. There is a stub module ‘UserRules.hs’ in the source, to which rules can be added.
If a compiled version of DrIFT is being used, the program will then have to be recompiled before the new rules can be used. However, if the Runhugs standalone interpreter is used, this is not necessary. Due to the way Runhugs searches for modules to load, a user may have many copies of the UserRules module. The UserRules module in the current directory will be loaded first. If that is not present, then the HUGSPATH environment variable is searched for the module. So it is possible to have a default UserRules module, and specialised ones for particular projects.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 4.1 The Basic Idea
A rule is a tuple containing a string and a function. The string is the name of the rule, and is used in commands in an input file. The function maps between the abstract representation of a datatype and text to be output (A sort of un-parser, if you like). The best way to understand this is to have a look at the existing rules in ‘StandardRules.hs’. This module is quite well documented.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 4.2 How is a Type Represented?
A type is represented within DrIFT using the following data definition.
>data Statement = DataStmt | NewTypeStmt deriving (Eq,Show) >data Data = D { name :: Name, -- type name > constraints :: [(Class,Var)], > vars :: [Var], -- Parameters > body :: [Body], > derives :: [Class], -- derived classes > statement :: Statement} > | Directive > | TypeName Name deriving (Eq,Show) >type Name = String >type Var = String >type Class = String
A Data type represents one parsed data or newtype statement. These are held in a D constructor record (the Directive and TypeName constructors are just used internally by DrIFT). We'll now examine each of the fields in turn.
• name holds the name of the new datatype as a string.
• constraints list the type constraints for the type variables of the new type. e.g. for data (Eq a) => Foo a = F a, the value of constraints would be [("Eq","a")].
• vars contains a list of the type variables in the type. For the previous example, this would simply be ["a"] .
• body is a list of the constructors of the type, and the information associated with them. We'll come back to this in a moment.
• derives lists the classes that the type an instance of though using the deriving clause.
• statement indicates whether the type was declared using a newtype or data statement
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
### 4.2.1 The Body
>data Body = Body { constructor :: Constructor, > labels :: [Name], > types :: [Type]} deriving (Eq,Show) >type Constructor = String
The body type holds information about one of the constructors of a type. constructor is self-explanatory. labels holds the names of labels of a record. This will be blank if the constructor isn't a record. types contains a representation of the type of each value within the constructor. The definition of Type is as follows.
>data Type = Arrow Type Type -- fn > | Apply Type Type -- application > | Var String -- variable > | Con String -- constructor > | Tuple [Type] -- tuple > | List Type -- list > deriving (Eq,Show)
Few of the deriving rules supplied have actually needed to use this type information, which I found quite surprising. If you do find you need to use it, one example is the Haskell2Xml rule.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 4.3 Pretty Printing
Instead of producing a string as output, rules produce a value of type Doc. This type is defined in the Pretty Printing Library implemented by Simon Peyton-Jones. The pretty printer ensures that the code is formatted for readability, and also handles problems such as indentation. Constructing output using pretty printing combinators is easier and more structured than manipulating strings too. For those unfamiliar with these combinators, have a look at the module ‘Pretty.lhs’ and the web page http://www.cse.ogi.edu/~simonpj/ or for more detail the paper The Design of a Pretty Printing Library, J. Hughes
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 4.4 Utilities
Upon the pretty printing library, DrIFT defines some more formatting functions which make regularly occurring structures of code easier to write. These structures include simple instances, blocks of code, lists, etc. The utilities are in the module ‘RuleUtils.hs’ and should be self explanatory.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 4.5 Adding a new rule
A rule has type type Rule = (String,Data -> Doc). Once you have written your mapping function and chosen an appropriate name for the rule, add this tuple to the list userRules :: [Rule] in module ‘UserRules.hs’. Recompile if necessary. DrIFT will then call this rule when its name occurs in a command in an input file.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
# 5. Installation
DrIFT isn't a large or complicated application, so it shouldn't be too hard for anyone to get it up and running. For the platform you want to install for, read the corresponding section below, then see Environment Variables
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 5.1 GHC
the automake script should automatically detect any ghc or nhc installation and use that to build and install DrIFT. First run ./configure . To compile, type make all. The executable produced ‘DrIFT’ can then be installed with make install.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 5.2 Hugs
The DrIFT code comes as a set of Haskell modules. You want to copy all these to somewhere in your HUGSPATH, then you can load and run DrIFT in any directory.
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 5.3 Runhugs
Edit the first line of the the file ‘DrIFT’ to point to your copy of runhugs. Copy ‘DrIFT’ to somewhere on your PATH, and the remainder of the source (‘*.hs’,‘*.lhs’) to a directory in your HUGSPATH
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 5.4 Environment Variables
In you environment set DERIVEPATH to the list of directories you wish derive to search for modules / interfaces.
DERIVEPATH is quite fussy about the format the list should take :-
• each path should be separated by ':'
• no space inserted anywhere
• no final '/' on the end of a path
For instance
good - /users/nww/share/hugs/lib:/users/nww/share/hugs/lib/hugs
bad - /users/nww/share/hugs/lib/: /users/nww/share/hugs/lib/hugs/
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
## 5.5 Installing the Emacs DrIFT Mode
Edit ‘derive.el’ so that the variable hwl-derive-cmd contains your copy of the DrIFT executable. Place ‘derive.el’ into a directory on your load-path, byte-compile it and put the following command into your ‘.emacs’ file:
(load "derive")`
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
# 6. Bugs and Shortcomings
• DrIFT doesn't check for commands applying the same rule to a type.
• No support for TeX-style literate code.
[Top] [Contents] [Index] [ ? ]
[Top] [Contents] [Index] [ ? ]
This document was generated on February, 10 2008 using texi2html 1.78.
The buttons in the navigation panels have the following meaning:
Button Name Go to From 1.2.3 go to
[ < ] Back Previous section in reading order 1.2.2
[ > ] Forward Next section in reading order 1.2.4
[ << ] FastBack Beginning of this chapter or previous chapter 1
[ Up ] Up Up section 1.2
[ >> ] FastForward Next chapter 2
[Top] Top Cover (top) of document
[Index] Index Index
where the Example assumes that the current position is at Subsubsection One-Two-Three of a document of the following structure:
• 1. Section One
• 1.1 Subsection One-One
• ...
• 1.2 Subsection One-Two
• 1.2.1 Subsubsection One-Two-One
• 1.2.2 Subsubsection One-Two-Two
• 1.2.3 Subsubsection One-Two-Three <== Current Position
• 1.2.4 Subsubsection One-Two-Four
• 1.3 Subsection One-Three
• ...
• 1.4 Subsection One-Four
This document was generated on February, 10 2008 using texi2html 1.78. | 2013-05-26 05:53:16 | {"extraction_info": {"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, "math_score": 0.5992311239242554, "perplexity": 8883.20258354133}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368706631378/warc/CC-MAIN-20130516121711-00056-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://xplaind.com/196977/returns-to-scale | # Returns to Scale
Returns to scale tell us how production changes in response to an increase in all inputs in the long run. An industry can exhibit constant returns to scale, increasing returns to scale or decreasing returns to scale.
Study of whether efficiency increases with increase in all factors of production is important for both businesses and policy-makers. It tells businesses about their optimal production level and it lets policy-makers determine whether the industry will consist of large number of small producers or a small number of large producers.
Law of diminishing returns tells us what happens when one input increases while other inputs stay the same. It is most relevant in the short-run i.e. time scale in which at least one factor of production is constant. In the long run, all factors of production can be changed, and it is then when the returns to scale become relevant.
There are three possibilities for total production function when all inputs increase: (a) increase at increasing rate, (b) increase at a fixed rate or (c) increase at a decreasing rate. These three possibilities result in three forms of returns to scale.
Before we define each type, let’s look at the Cobb-Douglas production function:
$$\text{Q}=\text{A}\times \text{L}^\text{a}\times \text{K}^\text{b}$$
Where Q is the total product, L and K are the units of labor and capital respectively, and A, a and b are constants.
## Constant Returns to Scale
Constant returns to scale mean that total product changes proportionately with increase in all inputs. In other words, the percentage increase in total product under the constant returns to scale is the same as the percentage increase in all inputs.
If the sum of a and b in the Cobb-Douglas production function equals 1, it represents constant returns to scale.
### Examples
Constant returns to scale prevail in very small businesses. For example, let’s consider a car wash in which one car wash takes 30 minutes. If there is one wash space (hydraulic jack) and two workers running two 8-hour shifts, total product would be 32. If there are two wash spaces and four workers i.e. when inputs double, total washes possible rise to 64 (=4 × 8 × 60/30) and so on.
## Increasing Returns to Scale
In industries subject to increasing returns to scale, a 1% increase in total inputs will result in a more than 1% increase in total product i.e. total product increases at a rate higher than the rate in which all inputs increase. Increasing returns to scale are also referred to as economies of scale.
You must be wondering whether it is not against the law of diminishing returns. It is not because the law of diminishing returns is applicable only in short-run for only a change in one input but the returns to scale determine change in total product in response to changes in all inputs. Causes of increasing returns to scale include specialization of labor, synergies, etc.
Sum of a and b in the Cobb-Douglas production function is higher than 1 in case of increasing returns to scale.
### Examples
Industries that exhibit increasing returns to scale typically have small number of large firms. Because there are advantages to production at high level, large companies are at considerable advantage as compared to small firms. Airplane producers, large express shipping companies, telecommunication companies, etc. exhibit increasing returns to scale.
## Decreasing Returns to Scale
In case of decreasing returns to scale, total product increases at a rate lower than the rate of increase in inputs. In other words, additional investment generates progressively less and less additional production. If the sum of a and b in the Cobb-Douglas production function is less than 1, it represents decreasing returns to scale. Decreasing returns to scale are also referred to as diseconomies of scale.
### Examples
Examples of industries that exhibit decreasing returns to scale include companies engaged in exploration of natural resources (because it becomes increasingly difficult to extract as easier low-hanging minerals are extracted), companies where complexity results in higher risk of failure such as power distribution, etc.
Returns to scale can be graphed using isoquants. | 2022-01-18 17:22:23 | {"extraction_info": {"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": 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, "math_score": 0.44735443592071533, "perplexity": 986.2430152598116}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300934.87/warc/CC-MAIN-20220118152809-20220118182809-00092.warc.gz"} |
http://www.richard-sweeney.com/intro_env_econ/slides/Benefits.html | ## Benefits of Environmental Protection
Econ 2277
Prof. Richard L. Sweeney
(print this presentation)
# Overview
Last class: Economic efficiency requires we set the marginal benefits from environmental protection equal to the marginal costs.
To do this, we need to measure benefits and costs
### Outline for next two weeks
• Review concept of economic benefits
• Revealed preference methods
• Stated preference
• Benefit transfer: Valuing risk of death
[list them]
## Non-economic description of environmental benefits
• Human Health
• Morbidity and Mortality Risks
• Amenities
• Visibility, Odors, etc.
• Ecological Impacts
• Market Products: food, fuel, timber, etc.
• Non-Market Recreation & Aesthetics: fishing, boating, hiking,etc.
• Indirect Ecosystem Services: flood protection, water filtration;
• Non-Use Values (coming soon)
• Materials Damage
[List them]
## How would you place a dollar value on these benefits?
• When someone rents a scooter, they consider the full benefits (fun, transportation, convenience, etc)
• If willingness to pay (WTP) is higher than the price, they rent
### To get a measure of the total benefits, we'd just need the demand curve for scooters
Companies use demand curves to set prices and make investments.
Imagine we had internal projections from Bird:
• At a base price of 15 cents per minute ($9 per hour) demand in Cambridge is 100,000 hours • At a higher price of 20 cents per minute ($12 per hour) demand is estimated drop to 50,000 hours.
### This gives us an (inverse) demand curve
Two points (12, 50K) and (9, 100K)
$P(Q) = 15 - 3/(50,000) Q$
• So at $15, nobody drives one. • Max demand (P=0) is 250K ### How can we see the benefits of Bird on this graph? Need to decide if we care about Bird profits or not. • Gross benefits = area under demand curve up to base quantity (100K) • Net benefits (consumer surplus) = that minus total (private) cost [If Cambridge cared about Bird profits, they'd use marginal cost not price] ## Let's apply that logic to environmental quality • What we'd like to know is how the quantity of environmental quality demanded changes as it becomes more or less expensive. • Challenge: People don't pay for the environment. ## Two Conceptual Strategies Revealed Preference Methods: Use people’s observed behavior in markets to infer their WTP for environmental goods/services Intuition: Even if people don't pay for environment, often spend money (incur real costs) to get access to clean environment (or avoid poor environment) Stated Preference Methods - Design surveys that ask people what they would be WTP or WTA ### Two types of environmental benefits 1. Use Value: The benefits from using a good/service, directly or indirectly • For example, benefits of recreational swimming-day or benefits of clean air on your walk to school Revealed preference methods preferred for measuring use values 1. Non-Use Value: Utility people gain from environmental goods that do not benefit them directly or indirectly • What are some sources of this? ### Sources of non-use value • Option Value • Benefits people receive now from having option to use good/service in the future. • For example, benefits (now) of preserving Grand Canyon so that tourists can see it in the future • Existence Value • Benefits people receive from knowledge of the existence of good/service (they never intend to use). • For example, benefits of preserving panda habitat in China For non-use value, we have no choice – must use stated preference methods (measure total value) # Household Production Models ## Household Production Models – people often combine a private good with an environmental good to produce another good, which is the real source of utility • e.g., travel + wilderness area = recreational day • Idea: If we know how to value the costly input, then we can infer the value of the environmental good. [Not most useful method, but good introduction to revealed preference models] ## Travel cost method • Origin of method (Hotelling-Clawson-Knetsch) – Letter in 1954 to six economists from Director, National Park Service – Response from Harold Hotelling (UNC) • Conceptual Thought Experiment – Tuolumne River: to estimate demand function, to ascertain WTP: “Build a fence and charge admission” • Collect Data: – Travel Cost (including opportunity cost of time) – # of visits from various origins (zones), – population of zones (for example, treat all zones as having same population) Intuition: Visiting a park takes time and money. – Time to drive, gas, etc. – Plus entrance fees. Implications: – The more awesome the park, the more I’m willing to give up to visit it. – The closer I live to a park, the more likely I am to visit it. We can use this to trace out a WTP curve for a park – Number of visitors from towns at different distances away – Distance to park gives variation in price – Variation in visitors gives variation in quantity ### Example: Valuing Mt. Monadnock • 3165 feet high • Many hiking trails • Spectacular views of Boston and Eastern Massachusetts • Policy question: How much is Mount Monadnock worth? ## Who visits Mt. Monadnock? ## Who visits Mt. Monadnock? ## Plot inverse demand curve ## Convert to per capita ## Use wage rate to convert to dollars [Time valued at the average hourly wage in each city (avg$27)]
To get total value, multiply by population in each city
## Issues
1. Is the wage rate an appropriate way of translating distance to travel cost?
– Hours may be fixed, so the tradeoff is with leisure time.
∗ Need to know the shadow price of leisure time.
– People may have different utility or disutility from traveling vs. working
1. Other Factors Matter
– Yes, of course: income, education, age, etc.
– Not a problem: use multiple regression
2. Multi-Purpose Trips
• would this over or understate true value?
## Takeaway: Travel Cost Method
– TCM very useful for understanding concept of revealed preference
– Sophisticated versions still used to value recreation sites
– But the method is going to be of limited value for estimating benefits of many environmental policies
Limited applicability: Only recreational sites or environmental quality associated with recreational sites
# Public goods
Most economic goods are rival -- if one person consumes something, no one else can.
Many environmental goods are non-rival, meaning if one person uses something, it doesn't impact the consumption value for anyone else:
• clean air
• beautiful landscape
Non-rival goods commonly called public goods
Note:
• A second important of economic goods is whether or not they are excludable
• If a good is excludable, people can be prevented from using it.
• Non-rival non-excludable goods are called pure public goods
• Non-rival excludable goods are called club goods
• example: DirectTV
## Aggregate demand for a public good
• benefit estimation typically occurs at the micro level
• by for policy evaluation, we're often interested in calculating total benefits
• area under the aggregate demand curve up to the point of the policy
• to do this, we need to aggregate the demand curves of all affected parties
### Adding demand curves: private goods
• normal private goods are rival
• example: an apple
• need to sum demand horizontally!
• demand typically takes the form of Q(P)
• however, supply and demand graphs presented as P(Q)
• need to invert demand first
• ie we want to add up all Q demanded at a given P, not sum over P at a common Q
### Steps:
– solve for $q_{i}(P)$
– sum up over all $i$ at the same $P$ to get $Q$
– now invert again to get $P(Q)$
### Example: Demand for apples
• two consumers, $A$ and $B$
• A really likes apples: $P=20-Q_{A}$
• B likes them less: $P=10-Q_{B}$
Graph these. What does total (aggregate) demand look like?
1. Solve for Q
$Q_{A}=20-P$
$Q_{B}=10-P$
2. Add curves if Q > 0
[Can't have negative demand]
$Q_{T}=20-P$ if $P > 10$
$Q_{T}=30-2P$ if $P \le 10$
3. Now invert back to graph:
$P=20-Q_{T}$ if $Q < 10$
$P=15-Q_{T}/2$ if $Q \ge 10$
### Imagine the good is instead a very rare animal
– neither A nor B ever see it, but get utility from its existence
• Now Q is non rival (and non excludable)
– so $Q_{T}=Q_{A}=Q_{B}$
What does the aggregate demand curve look like now?
### Calculating demand for a pure public good
Assume same demand curves:
• A gets utility up to the point where 20 are saved: $P=20-Q_{A}$
• B only cares as long as there are 10: $P=10-Q_{B}$
Now we actually do want to add vertically
$P=30-2Q$ if $Q \le 10$
$P=20-Q_{T}$ if $Q > 10$
### Summary on calculating total benefits
• To get the total consumer benefits of policy, we want the area under the demand curve.
• If they incur a private cost, subtract that.
• If the cost is public (for example paid for by the government), remove that from net benefits, but not consumer surplus
• Often times demand curves are estimated at the individual level
• To get the aggregate demand for a rival good, need to add horizontally.
• To get the aggregate demand curve for a non-rival good, need to sum vertically.
[this is useful for the problem set]
# Hedonic Pricing Models
## Hedonics and the environment
• goods are bundles of attributes
• restaurant: food, ambiance, service
• smartphone: camera, apps, look
• even if people only buy a bundle, variation in prices across similar bundles can reveal how much people value a particular attribute
• Example from last class: can get Camry with and without hybrid
• If consumer buys, values fuel economy $\ge \5,000$
• this is useful for environmental economists because many prominent purchases contain the environment as a key aspect of the bundle
• Example: houses
### Can use this information to figure out how much people value clean air
• imagine we find two houses that are identical in every way except one is in a more polluted area (lower Air Quality Index)
• house 1 AQI = 50 ; house 2 AQI = 100
• you can see Boston's AQI here
• the difference in sales price provides a hedonic estimate of WTP for better air quality
• for example, if house 1 sells for $5,000 more, we'd infer people are willing to pay$100 per unit of AQI improvement
• This is approach referred to as hedonic (property) valuation
• Has been used to study education, access to hospitals, community safety, etc
### Key Assumptions
• Constant MWTP
• we know WTP declines as resource improves.
• in previous example $100 per AQI valid only at relatively clean locales in 50-100 range. • important to estimate at different levels of air quality • Perfect information • What if homebuyers don't know the AQI at each location? • Pipeline example • Estimated relationship is causal • observed price difference due entirely to difference in air quality ### What would happen if areas with better air quality also had better schools? • In this example, imagine the house with better air quality also has the best school system in the state. • How would that change your interpretation? • Common solution: Multiple regression • Run a regression projecting house price on to air quality and all other important observable factors • Challenge is that lots of amenities are correlated (school quality, safety, commute etc), and can't control for everything. ### You should think of this complication as the norm in public policy evaluation • Ideally we'd observe the same “subject” in two otherwise identical states of the world, one where the policy was in effect and one where it wasn't • “Fundamental Problem of Causal Inference” • Drug trials get as close to possible to this ideal by randomly giving some patients a placebo • Often the best we can do in public policy analysis is to look for "quasi-" experiments, where some external factor alters the exposure of some subjects and not others in an essentially random fashion. ### Example 1: Valuing shoreline loss • Many sections of the U.S. coastline are severely eroding. • The long-term rate of shoreline loss along the New England and mid-Atlantic coasts is 1.6 feet per year • In Florida, some segments lose more than 10 feet per year. • Climate change is expected to lead to sea level rise Under current predictions of a 1.1 foot rise in average sea levels by the year 2100, these erosion rates will accelerate, and between 3,000 and 7,000 square miles of dry land could be lost (IPCC, 2007; Titus, 1989).” • How costly is this? • could decide to build seawalls ### Could look at house prices in areas with wide vs narrow beaches What would be the concern here? ### Ranson (2012) Paper here ### Ranson (2012) results • Finds that one-foot beach nourishment adds$42 - $68 to a home's sale price • Average project adds$2,927 to $4,760 per household • Large, but considerably smaller results from "cross-sectional" comparison • ie just looking at homes with longer / shorter beaches • Cost of beach nourishment is roughly$1,000,000 per mile
• Implies would have to be between 210 and 342 beachfront homes per mile in order for the project to generate positive marginal benefits.
### Example 2: Hazardous waste
• Prior to the 1970s, industrial firms often disposed of hazardous waste by burying it in the ground
### Still in the news
Trump administration also recently proposed cutting this program
### Superfund Program
The 1980 Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA) gave the EPA the right to place sites that pose an imminent danger on the National Priorities List (NPL)
Can we use the hedonic method to value this program?
What other variables are likely correlated with polluted site locations?
### Greenstone & Gallagher (2008) used budget limitations to estimate a causal effect of the program
• In 1983, funding initially allocated for 400 sites
• 1500 candidate sites identified, 690 finalists
• Each finalist was given a Hazardous Ranking System score
– Cutoff: HRS> 28.5 were cleaned up; others weren't
### Greenstone and Gallagher summary
• Conventional approach to analyzing Superfund cleanup showed large gains
• ~3-7% home value
• Using more credible approach, the estimates become economically small and statistically insignificant
• Correlations probably reflect fact these areas are undesirable on other dimensions.
### Averting Behavior: Issues & Problems
1. Difficult to separate risk-reduction benefits from other benefits of the product or activity
– Example: bottled water may taste better, be convenient, etc.
– So we may over-estimate WTP for risk-reduction
1. Difficult to separate risk-reduction benefits from negative benefits (utility-reducing attributes of averting behavior)
– Example: bicycle helmets are uncomfortable
– We will under-estimate WTP for risk reduction
### Averting Behavior: Issues & Problems
In another example, residents of the area around the Nak-Dong River in Korea faced industrial pollutants in the early 1990s. (Source: Berck and Helfand)
• By 1996, water quality was greatly improved and met safety standards
• Yet people still undertook risk avoidance measures.
– People were acting based on their perception of how polluted the water was.
• The estimated willingness to pay to reduce suspended solids was 3X that what would have been predicted based on safety alone
### And what about “Cost-of-Illness Method?”
• Many pollutants result in doctor or hospital visits
• Assume we can perfectly observed all medical expenditures
• Can we use these to estimate willingness to pay?
• Chipotle example
### And what about “Cost-of-Illness Method?”
• Does not estimate WTP/WTA, but change in explicit market costs resulting from change in incidence of illness:
– Direct health-care costs
– Indirect costs of loss of work time
– What’s left out?
### Summary: “Cost-of-Illness Method?”
• May be considered a lower bound on WTP, but empirical evidence from comparisons suggests difference can be very large!
• Sometimes used in health economics to value morbidity changes (and by courts in wrongful death cases)
• Method is not theoretically correct nor empirically reliable, but two advantages:
– Cheaper than better approaches
– Easy to explain to policy makers and general public
• So, it’s inexpensive, easy to explain, and wrong.
## Wrapping up
• Review concept of economic benefits
• Linked to Willingness to pay
• Revealed preference methods
• We often pay to get these benefits: either indirectly with time; as a bundle; or even directly with avoidance goods
Up next:
• Benefit transfer: Valuing risk of death
• For large benefits, we sometimes think we "know" the benefit from other settings
• Most important example is WTP to reduce risk of death
• Stated preference | 2019-05-21 06:44:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 28, "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, "math_score": 0.5065855383872986, "perplexity": 9475.976559140328}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256281.35/warc/CC-MAIN-20190521062300-20190521084300-00513.warc.gz"} |
https://chemistry.meta.stackexchange.com/questions/3807/lets-talk-about-effort-shall-we | # Let's talk about effort, shall we?
I think the recent experiment of suspending the homework close reason has already produced a very valuable result. However, I really feared that this will happen, and I hope I can steer our thinking into a different direction with this post.
To partially quote Wildcat
And now I think, it is quite apparent that we need a close reason for zero-effort questions to simply save out time, because the absolute majority of questions that were previoulsy closed as homework ones are now closed with this very custom reason (zero-effort).
I would like to back that up with some numbers (10k+ tools). In the past seven days there were 213 questions asked, of which 70 were closed (33%). Of these 22 were closed with custom reasons (10%). From the summary of the close reasons, they are all a variation of "no/any effort shown".
While I agree with most of you that we need a system to protect our site from dilution the great content with questions of the zero-effort kind, I don't think that effort itself is a good metric. Just as Wildcat says, zero-effort is easy to identify and closing them on sight would be easy. But I think it wouldn't be enough to sort out other questions, too. I am of the opinion, that just showing effort doesn't necessarily ensure that it is a good, or even useful question.
I personally would like to have conceptual questions and answers, that in principle can be adapted to various situations. One of these approaches certainly is the tiny list of duplicates. If such questions include very concrete examples, I think that's fine (if not, then it would probably not be off-topic).
Please note, that this is an attempt of replacing the current homework policy to a more generalised and more objective version.
As a (very first) draft for discussion, I would like to propose a custom close reason of the following form:
At Chemistry.se we aim for questions that are helpful to as many visitors as possible. Therefore you should identify the specific chemistry concepts and the problems you are facing with it. For more information how to improve your question see: How can I make my question conceptual?
(demonstration link only; 400 total characters allowed, 334 used)
The above certainly is far, farn from perfect, but I hope it will provide a new angle on the whole closing issue. The experiment will continue for another two weeks (roundabout); please be vocal about your opinion. And if you are thinking about commenting now, maybe write an answer instead.
• Personally, I'm skeptical of the rationale "no effort shown" as a close reason. I've found that people can rather be picky and capricious about how much effort counts as "enough". I'd be interested in seeing just what counts as "no effort" to the people casting close votes. (Though I understand if you don't want to link the questions in questions specifically.) I'm not saying some variation of "no effort" wouldn't be valid, but I'm wondering if labeling the rationale as "no effort" is an oversimplification/mischaracterization of what's really going on.
– R.M.
Jun 16 '17 at 16:46
• @R.M. The current homework policy is based on the effort argument. With this post I'm trying to change that. The reason why I'm not linking to some zero-effort-posts is that I don't think they are relevant for this kind of change. Jun 16 '17 at 17:14
• Okay, but the experiment shows that people really like the "no effort" rationale. If you're arguing it's a poor and unclear rationale, I agree with you, but others apparently do not. The reason I suggested looking at what people think are "no effort" posts is that I'm guessing there's an XY problem going on here. There's something that people don't like about the questions, and "no effort" is just a convenient label to use. If we could look closer at the posts (and the expressed rationales), we might start to tease apart what exactly people don't like and how we should phrase the replacement.
– R.M.
Jun 16 '17 at 18:18
• @R.M. We don't like anything that someone with a Bachelor's in chemistry could answer. On the other side of the same coin, any question asked by a veteran is automatically a good one. We might also not like everyday-chemistry, but I'm not as sure about that. Jun 20 '17 at 15:20
My own opinion is broadly the same - I think that "effort" is a poor criterion for judging question quality. I have discussed this before. In my opinion, the most important bit is this:
In one of the worst case scenarios, OP's "efforts" are way off the mark and simply become useless noise for future readers. In another bad scenario, OP's efforts are entirely correct and the answerer is reduced to saying "yes, you're right".
So, to begin with, I don't think that having effort is necessarily a good thing. Neither is lacking effort necessarily a bad thing, as will be discussed below. But, not only is it a bad criterion; I'd argue we don't even follow it.
## Double standards
In the post linked above, I also wrote
The HW policy is subjective and open to interpretation. There is occasional "misuse" of the HW close reason - not exactly abuse, but different people have different quality standards. Furthermore, what counts as "effort" is unclear. If somebody simply adds a line at the bottom of their question "I tried to look in my textbook, but couldn't find anything", does that count as effort?
This subjectiveness, perhaps, leads to what I would perceive as some degree of a double standard. Basic questions with zero-effort get closed, but advanced questions with zero-effort don't get closed: see Exhibit A, for example.*
In order to further test my perception of a double standard, I created a new account and asked a graduate/advanced undergraduate-level organic chemistry question with next to no effort: Exhibit B.† In 24 hours since it was posted, it got six upvotes and one favourite. No close votes, and no comments saying to show effort. Clearly, people think it is a good and useful question for the site. But other, less advanced, questions have been closed even with more "effort" given.
## Aims of the site
At this moment I'd also like to remind everybody of what Stack Exchange aims to be. This is quoted from the very first part of the tour:
With your help, we're working together to build a library of detailed answers to every question about chemistry.
I don't think that this library can only be built if people show their effort. I think the questions that I linked to above are examples which show that so-called no-effort questions can indeed be beneficial. Marko's question (Exhibit A) was pretty interesting and it received a good answer which it fully deserved. I hope that nobody disagrees with me when I say that the site benefitted from that Q+A. I am glad that the community recognises the worth of such questions, but our behaviour is clearly not congruent with the supposed "no effort" requirement.
Even my sock's question is fairly decent, in terms of its value to the site. It could certainly have a bit more context, and I will edit it in in due time, after we are done with this discussion. (I purposely made it as low-quality as I could).
The point still stands, though; I strongly disagree that effort is a good criterion for judging the quality of a question.
$\Large \textbf{What should we do, then?}$ Well, my 2c:
1. Get rid of the effort criterion for closing questions.
2. Replace it with a conceptual criterion. This means that even the worst homework questions will not be closed as "off-topic", as long as they clearly identify the concept/issue that is being asked about. However, they may still be closed as duplicates of older questions.
3. Focus on editing and improving questions, if possible. If you think that a not-so-good question has an interesting concept behind it, and can potentially receive a good answer, then by all means, edit it so that it looks like a good question.
4. Make some canonical Q&As in order to address common homework-type queries - this should be a long-term project; for obvious reasons, this cannot happen overnight.
Martin and I think that a conceptual criterion is the best kind, and AFAIK Physics.SE adopts this viewpoint too. Maybe the community thinks that a conceptual criterion isn't the best idea, which is fine - it's really okay (and it's great) to disagree - but we would really like to hear some alternatives.
Maybe you simply want to get rid of all high school chemistry questions. To be honest, I get this feeling sometimes, but it's obviously an untenable position. I feel that the best way to deal with this is to efficiently close as duplicates (there are only so many high school concepts one can ask about!), and get users to ask more high-level questions, as this recent meta post by NotEvans suggests.
Or maybe the idea is that we don't want to be doing people's homework for them. I can understand why you may have this sentiment, but in this case I'd like to suggest that we stop viewing questions as homework or not - remember this isn't a homework help site and also it isn't a site where homework is forbidden - and judge it solely based on whether you think it could possibly receive an interesting answer which would contribute to the site as a whole.
Footnotes
* Before people accuse me of not unilaterally closing that as a moderator: you know that I already do not think that effort is a good criterion. Furthermore, we cannot always be mod-closing everything; otherwise, there will never be any chance for an organic shift in community consensus. If I had closed this, then I would not have this example to share with you today.
† Obviously, I haven't done anything with my sock that my own account could not do. I also did not upvote that question with my main. It is locked for the time being, only because I want to avoid the so-called "meta effect". In due time this account will be merged with my main account.
In response to hBy2Py's comment about when we should feel free to edit a post, the answer is: always, as long as it is done in good faith (i.e. not deliberately distorting OP's query, for example). Quoting from Section 3 of the Terms of Service:
You agree that all Subscriber Content that You contribute to the Network is perpetually and irrevocably licensed to Stack Exchange [...]
• Naughty Victor! In all seriousness though, the more advanced the question is the harder it is to simply google the answer, assuming you even know what you're searching for. Exhibit B vs Exhibit X (generic stoichiometry question) are very different... kettles of fish, surely Jun 19 '17 at 18:07
• Great suggestions @orthocresol. Your idea of replacing effort with concept seems very nice. I had once mention this in my post: Should we completely ban all homework questions?, so I feel that this is a great way to approach things. Jul 12 '17 at 13:01
This very much isn’t a fully thought out answer, but it was a lot longer than I could fit into a comment. Just my two english cent. . .
Effort as a metric for closure
Broadly speaking, I agree that effort (or lack thereof) in itself isn’t a particularly great metric for whether or not a question deserves help.
When we’ve been discussing this, the tex.SE approach (and other code based sites) springs to mind. Users shouldn’t necessarily need to attempt to answer the question (as ortho points out theres really no point in someone making an awful attempt at some derivation), but there should be a minimum standard of effort involved.
On tex.SE, they have the idea of a ‘minimum working example’, this obviously doesn’t apply here, but there could be a minimum standard we’re willing to accept. If you think about the worst of the homework questions, they’re the wonky screenshots of some obscure, poorly worded, indian chemistry exam.
On chem.SE, our ‘MWE’ could therefore look something like: a fully typed out question (not just a picture), some context about the level of the question, and an indication of why the question is difficult to them (why isn’t it like the 400 other stoichiometry problems you’ve gone through).
Conceptuality as a metric
Whilst the idea of questions being ‘conceptual’ is a good one (i.e. questions are a lot more interesting when they’re a little more abstract rather than heavily set in a particular set of numbers), and one I agree fairly strongly with. I’m mindful of the fact that actually, chem.SE isn’t that busy relative to many other sites on the network.
The issue I take with having a set of stock canonical answers is that the old answers aren’t necessarily the best, and people are fairly unwilling to re-answer old questions that already have accepted answers/lots of up-votes (it seems counter productive).
[As an extreme example of this, I could in theory sit here and write a question and associated answer related to every section of Atkins’ physical chemistry, and we’d never need to actually answer another question again].
• The next steps would be to define 1. what constitutes a good conceptual question (what's the "cutoff"), and 2. what less-conceptual questions are acceptable? Otherwise, the same trap of how to define homework will appear again. Jun 20 '17 at 15:23
• @pentavalentcarbon I don't think that this is the same trap, because we are not talking about closing conceptual questions, we are talking about closing non-conceptual questions. As such it is easy to deal with "bad" and "good" conceptual questions: Vote on them. Jun 21 '17 at 6:53
• (+1) though "indian chemistry exam." really are there so many of them? o.O Apr 18 '18 at 9:00
If we would like to move away from the "effort" angle, then the tooltip that pops up when hovering over a downvote button should be changed.
• (down)-voting is not the same as closing as off-topic. The former is your personal choice how helpful the question is, the latter should determine which kind of questions are within our scope, and I would like it to be a bit more objective. Jun 14 '17 at 13:20
• @Martin-マーチン I know. What I want to say is that if voting is a personal preference, then the text should be removed entirely, since right now it sends the wrong message about why one should vote. Jun 14 '17 at 17:34
• While I don't really understand your point, this would need to be discussed on a network wide basis at Meta Stack Exchange, as the text is the same across all networks.There is nothing we can do about it from here. Jun 15 '17 at 4:02
10% of posted questions is way to much.
Yet I don't think a closing-policy would do any good. I think there are two kinds of bad questions. The first kind are questions that are bad for different reasons. From what I see, often there the asker is willing to edit their question so it gets better. I don't think we need to do anything about those questions.
The second kind, the zero-effort questions are a problem.
The biggest problem with the whole zero-effort situation is that if you ask the OP to add effort of his own, you never hear back from them as they abandon the question. These guys write that question probably in chem.SE, but also on quora, gutefrage.net etc pp.. Then they just wait where they find their answer and then they're gone (Are there statistics available with 1-rep accounts with 1 question that is closed?).
So I think that we will always have those questions, and the quality of them will not change.
I can think of these options:
1. Try to only advertise this site to "the right audience" (very difficult and kind of elitist/arrogant)
2. Close-and-forget the zero-effort questions
4. Stick with trying to be nice and get the OP to add effort and get more frustrated every day
I don't think that posting a "identify the concept behind your question and conceptualize it" comment would change anything, since the zero-effort-zombies don't read it, and they also don't read it on other questions since they are hunting for a quick no-brainer answer to their homework/whatever.
I personally like your proposition, and I would be all up for trying it, but I honestly don't have a lot of hope.
I don't think getting a new closing-policy will solve the problem, but only mask it. If we want to make this site better, we need to be active, not reactive. A proposition like @ortho's in the comments might be a better way, although it would result in probably a lot of work for a couple determined people.
• To be clear, I don't think we are trying to "solve the homework problem" in the sense of getting rid of HW. As you said, this will always happen, no matter what we do. I feel that it is more of an issue of what we do with it once it lands on our doorsteps.
– orthocresol Mod
Jun 13 '17 at 10:48
• Yeah I know. I don't think generally hw-questions should be banned either, but Martin proposes a way to try to get people to write more conceptualized questions. I think you cannot achieve this with trying to communicate with the zero-effort-zombies since they are neither reading that nor are they the target audience for those concept-questions.
– user37142
Jun 13 '17 at 10:53
• Ah, I see what you mean. I agree, it is difficult to get these people to edit their questions. Back when I left comments on nearly every homework post telling people to include "effort", the success rate was <20%, and that's probably quite a generous estimate. However, we can always edit it for them into something more conceptual ourselves, especially if the question holds some promise.
– orthocresol Mod
Jun 13 '17 at 10:54
• @orthocresol That seems to be a good idea! The question is good, so we edit it to make it better and it gets an answer! Jun 13 '17 at 14:19
• A policy (separate from this discussion) on when the community should feel comfortable "hijacking" a low-quality question to improve it might be useful. E.g.: Any question with 0 score or less that has been untouched by OP for more than 30 days can be freely edited to improve it (say, to make it more consistent with an excellent answer posted). Jun 14 '17 at 4:06
• Are there statistics available with 1-rep accounts with 1 question that is closed? I put together a SEDE query to investigate this. If my queries and interpretation are correct, about 24% of 1-rep users created more than 30 days ago with exactly 1 posted question have had that question closed/deleted (268 out of 1114). Jun 14 '17 at 4:50
• (I think this ^^ might exclude users whose accounts have been deleted, though.) Jun 14 '17 at 5:00
• @hBy2Py A question with a score lower than 0 has an expiration date of 30 days. It'll be deleted by scripts. Jun 14 '17 at 5:24
• Just for the record: As far as I understood your answer, I disagree with it. I do not think that you can safe all 33% (or 50% if we take the old numbers) by editing them into a good (whatever that may mean) question, and I do not think that it would be beneficial in the first place. Re: the asker is willing to edit their question - that barely ever happens. In the last 14 days it was twice. If we do not close questions, we have no quality control. Jun 14 '17 at 5:37
• @Martin-マーチン Right, that's why I drew from PostsWithDeleted and checked for questions with either .ClosedDate or .DeletionDate as NOT NULL. Jun 14 '17 at 10:53
## What is a conceptual question?
That's a serious question, and one I think gets to the heart of the issue with redoing the homework policy as a "conceptual question" policy.
I'll be honest and say I'm not really sure what Martin and orthocresol mean when they say "conceptual question". Yes, we can probably find some clear examples on both sides where a question is clearly "conceptual" and where the question is clearly "non-conceptual", but it's that middle region - that intermediate gray area - that causes issues.
If all we cared about were the clear examples, the current homework policy would be fine - yes, the fuzzy screenshots of poorly worded textbook problems are bad, and the advanced stuff is fine. But the current homework policy is dissatisfactory because of the gray area. It's those questions on the edge we're not quite handling correctly that are at issue.
That's my unease with the change: it's all well and good to redefine the criteria to say "conceptual: yes; non-conceptual: no", but if the definition of conceptual is "I know it when I see it", it's going to fall apart when the rank and file (who apparently like the current "effort" standard) disagree with Martin and orthocresol (and each other) as to what counts as "conceptual" or not.
Not knowing what "conceptual" means here (or more particularly, what makes a question "non-conceptual"), I can't necessarily agree that switching to a "conceptual" standard is going to adequately replace the (desired) functionality of the current homework close. It might have potential, but there's still details that need to get worked out.
• Honestly, I agree, and I'm aware that it's not a perfect solution. It will still be somewhat subjective, and I think that that is why we still need 5 votes to close a question. // You could call my thinking idealistic, but I think that in principle, "conceptual" makes much more sense than "has effort". The implementation of both might not be ideal. However, I really just want to push our closure policy in a different direction. We have been sitting on "homework/no effort" for so long, and gotten so comfortable with it, perhaps a little too comfortable.
– orthocresol Mod
Jun 22 '17 at 15:21 | 2021-09-26 18:45:19 | {"extraction_info": {"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": 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, "math_score": 0.4696296751499176, "perplexity": 866.3402035301078}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057913.34/warc/CC-MAIN-20210926175051-20210926205051-00083.warc.gz"} |
http://stackoverflow.com/questions/4557914/implicit-linebreaks-in-latex-equations/4626610 | # Implicit linebreaks in LaTeX equations
I wonder if there is any way to invert the way the LaTeX interprets linebreaks in equations? E.g., I dont want to insert them explicitly like,
\begin{gather}
x = y \\
a = c
\end{gather}
, but implicitly like,
\begin{gather}
x = y
a = c
\end{gather}
Thanks.
-
This is against the intention of TeX’s author, who believed that math must be typeset by hand. I tried obeylines, but to no avail. I guess it’s possible by making new line active, but you should ask the cracks over at Stack Exchange, a branch of Stack Overflow for TeX and LaTeX.
-
The breqn package will automatically insert linebreaks in equations when the line is full. I don't know of anything that will do break as you ask. If it is a big deal you could use perltex to define a macro that would do it for you. I will try to mock one up as an example.
-
Having a bit of problems with my perltex solution, turns out it is hard to capture macro input with linebreaks correctly – Joel Berger Jan 10 '11 at 5:47 | 2014-03-17 05:06:05 | {"extraction_info": {"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, "math_score": 0.936098039150238, "perplexity": 1325.0598253071616}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678704694/warc/CC-MAIN-20140313024504-00016-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://www.ms.u-tokyo.ac.jp/seminar/2018/sem18-159_e.html | ## Seminar on Geometric Complex Analysis
Date, time & place Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) Kengo Hirachi, Shigeharu Takayama
### 2018/06/25
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Stephen McKeown (Princeton University)
Cornered Asymptotically Hyperbolic Spaces
[ Abstract ]
This talk will concern cornered asymptotically hyperbolic spaces, which have a finite boundary in addition to the usual infinite boundary. I will first describe the construction a normal form near the corner for these spaces. Then I will discuss formal existence and uniqueness, near the corner, of asymptotically hyperbolic Einstein metrics, with a CMC-umbilic condition imposed on the finite boundary. This is analogous to the Fefferman-Graham construction for the ordinary, non-cornered setting. Finally, I will present work in progress regarding scattering on such spaces. | 2023-04-02 04:52:07 | {"extraction_info": {"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, "math_score": 0.8611539602279663, "perplexity": 3767.467898860998}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950383.8/warc/CC-MAIN-20230402043600-20230402073600-00311.warc.gz"} |
https://www.nextgurukul.in/wiki/concept/cbse/class-7/english-grammar/adjectives/adjectives-of-quality-degrees-of-comparison/3963009 | Notes On Adjectives of Quality - Degrees of Comparison - CBSE Class 7 English Grammar
DEGREES OF COMPARISON When we want to compare two or more nouns using adjectives, we use the comparative and superlative forms of the adjective to show the comparison between the nouns. E.g. - Honey is sweet, sugar is sweeter but victory is the sweetest. In this sentence, we are comparing the three nouns using the positive, comparative and superlative forms of the word ‘sweet’. Positive Form - These are the simple adjectives that simply describe the noun without comparing it to another - big, sweet, clean, etc. She has a big black dog. He is a sweet boy. The cupboard is clean. Comparative Form - These are used when we are comparing two nouns and need to show which noun possesses the adjective or character in a greater or lesser amount, when compared with the other. - bigger, sweeter, cleaner, etc. I have a big dog but hers is bigger. He is sweeter than the other boys. The cupboard is cleaner than before. Superlative Form - This form is used when three or more nouns are being compared and we need to show that one or more of the nouns posses the adjective or characteristic to the highest amount possible. We usually add ‘the’ before the superlative form. - biggest, sweetest, cleanest, etc. She has the biggest dog in the colony. He is the sweetest boy in his class. The cupboard is the cleanest thing in the house.
#### Summary
DEGREES OF COMPARISON When we want to compare two or more nouns using adjectives, we use the comparative and superlative forms of the adjective to show the comparison between the nouns. E.g. - Honey is sweet, sugar is sweeter but victory is the sweetest. In this sentence, we are comparing the three nouns using the positive, comparative and superlative forms of the word ‘sweet’. Positive Form - These are the simple adjectives that simply describe the noun without comparing it to another - big, sweet, clean, etc. She has a big black dog. He is a sweet boy. The cupboard is clean. Comparative Form - These are used when we are comparing two nouns and need to show which noun possesses the adjective or character in a greater or lesser amount, when compared with the other. - bigger, sweeter, cleaner, etc. I have a big dog but hers is bigger. He is sweeter than the other boys. The cupboard is cleaner than before. Superlative Form - This form is used when three or more nouns are being compared and we need to show that one or more of the nouns posses the adjective or characteristic to the highest amount possible. We usually add ‘the’ before the superlative form. - biggest, sweetest, cleanest, etc. She has the biggest dog in the colony. He is the sweetest boy in his class. The cupboard is the cleanest thing in the house.
Next | 2021-06-19 13:11:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "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, "math_score": 0.46566110849380493, "perplexity": 1704.7654775332016}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487648194.49/warc/CC-MAIN-20210619111846-20210619141846-00343.warc.gz"} |
https://brilliant.org/problems/euler-mascheroni-mashup/ | # Euler-Mascheroni Mashup
Calculus Level 5
Suppose the sum $\sum_{n=1}^\infty \left[ H_n - \gamma - \ln n - \dfrac{\zeta(2n)}{2n} \right]$ can be expressed in the form $\frac{1}{m} \big(a + b\gamma - c\ln(k\pi) \big),$ where $$a, b, c,$$ and $$m$$ are positive integers and $$\gcd(a,b,c,m) = 1$$.
Find $$a+b+c+k+m$$.
Notations:
× | 2017-07-20 22:45:12 | {"extraction_info": {"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, "math_score": 0.9640465378761292, "perplexity": 293.183233026978}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423512.93/warc/CC-MAIN-20170720222017-20170721002017-00308.warc.gz"} |
https://whzecomjm.com/p/2015/12/pgl2q/ | ## 整系数的分式线性变换群仅有9个有限子群
### 证明整系数的分式线性变换群的子群仅有九个。
$$D_n=\{e,a,a^2, \cdots, a^{n-1}, b, ab, a^2b, \cdots,a^{n-1}b\},$$
$$|D_n|=2|C_n|=2n,$$
$D_n$ 不是Abel群，因为 $ba=a^{n-1}b$。也就是说，$b^2=1$以及$b^{-1}ab =a^{-1}$。关于$D_n$的小群的结构，有 $D_1\cong C_2$。另外，$D_2$群是最小的非循环群。（这说明一二三阶群必然是循环群。）
$$\left[\begin{array}{cc} F_{n-1}& F_{n} \\ F_{n}& F_{n+1} \end{array}\right]$$
$$(x^n-1) / (x-1)=x^{n-1}+\cdots+ x^2+x+1$$
$$m^{(n)}(x)={\zeta}^nx +b({\zeta}^{(n-1)}+\cdots+ {\zeta}^2+\zeta+1)=x.$$
$$b^s=(xax^{-1})^s =x^s (a^s) x^{-s}= x^s x^{-s}=1,$$
## 定理的证明
1. Joseph A. Gallian, Contemporary Abstract Algebra, 5th ed., Houghton Mifflin, Boston, MA, 2002.
2. R. C. Lyndon and J. L. Ullman, Groups of elliptic linear fractional transformations, Proc. Amer. Math. Soc. 18 (1967), 1119–1124.
3. Dresden, Gregory P. “There are only nine finite groups of fractional linear transformations with integer coefficients.Mathematics Magazine (2004): 211-218.
Built with Hugo
Theme Stack designed by Jimmy | 2022-10-01 06:08:53 | {"extraction_info": {"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, "math_score": 0.19513672590255737, "perplexity": 9162.580900931767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335530.56/warc/CC-MAIN-20221001035148-20221001065148-00095.warc.gz"} |
https://stats.stackexchange.com/questions/365828/kendals-tau-correlation-if-only-one-variable-is-ordinal | # Kendal's tau correlation if only one variable is ordinal
I have a vector with 3000 data points consisting of values on a likert scale from 1 to 9. It is ordinal data without normal distribution. Now I would like to calculate the correlation of this vector to three other vectors each of size 3000 as follows:
1. Correlation to a vector with continuous values.
2. Correlation to a vector containing 21 different continuous values between 0.25 and 0.8.
3. Correlation to a vector containing only 4 different values (-2,2,-0.2,0.2).
Is it correct if I'm using for all three cases the Kendal's tau correlation?
Kendal tau is not just for ordinal variables, but rather for the case where the correlation is ordinal. For instance, imagine that the true relationship is $y=\ln x+\varepsilon$, but you don't know it. You got your sample $(x_i,y_i)$, and run a Pearson correlation analysis $cor[x_i,y_i]$. The problem is that although both variables are not just ordinal but cardinal, their relationship is not linear. That's why Pearson correlation is not appropriate here. If you'd know the true relationship, you do look at Pearson correlation of $\ln x$ and $y$, but in this case you don't know this. In such a case, you could run Kendall $\tau$ correlation because it's ordinal and $\ln x$ happens to be a monotonic function, which is often the case.
Hence, Kendall $\tau$ analysis will work in a wider set of circumstances compared to Pearson correlation. Particularly, when the relationship between variables is monotonic it will work. Linear is monotonic, so it will work wherever Pearson work, but for linear relationship Pearson would be a better test. | 2021-07-28 16:52:33 | {"extraction_info": {"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, "math_score": 0.8594621419906616, "perplexity": 377.05739386354793}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153739.28/warc/CC-MAIN-20210728154442-20210728184442-00417.warc.gz"} |
https://www.gradesaver.com/textbooks/science/physics/university-physics-with-modern-physics-14th-edition/chapter-41-quantum-mechanics-ii-atomic-structure-problems-exercises-page-1402/41-20 | ## University Physics with Modern Physics (14th Edition)
The effect of the magnetic field on the energy levels is described by Eq. 41.35. a. There are three different transitions that satisfy the selection rules. The initial $m_l$ values are 1, 0, and -1 and the final $m_l$ value is 0. b. The transition from $m_l=0$ to $m_l=0$ produces the same wavelength (122 nm) that was seen with no magnetic field. Each of those energy levels is unaffected. c. The transition from $m_l=-1$ to $m_l=0$ produces a larger wavelength (smaller energy) than was seen with no magnetic field. The energy of the initial level was lowered by the magnetic field. d. The transition from $m_l=1$ to $m_l=0$ produces a shorter wavelength (higher energy) than was seen with no magnetic field. The energy of the initial level was raised by the magnetic field. | 2019-11-21 13:38:58 | {"extraction_info": {"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, "math_score": 0.5134931206703186, "perplexity": 184.30066734522984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670821.55/warc/CC-MAIN-20191121125509-20191121153509-00469.warc.gz"} |
http://kellyripple.com/post/css-madness/ | I spent the past week learning HTML and CSS, having zero prior experience with either. With the right guidance, it’s surprisingly doable. No learning experience is complete without some moments of struggle, and I had plenty. Hopefully you will be able to benefit from my pain. The two worst positioning nightmares I came accross were position:relative/absolute/fixed and display:inline/block/inline-block. I’ll run through the definitions of each, and include my advice on using the things.
CSS Selector Description
position:fixed Object displays relative to the browser window, and is immune to scrolling.
position:relative Objects display relative to the browser, irrespective of any other elements on the page. I’m not sure why anyone would use this option, ever.
position:absolute The most useful option for positioning objects. Objects display relative to it’s preceeding positioned (fixed, relative, or absolute) element. If the object is the first positioned element, it will display relative to the browser window.
position:static This is the default position setting. Objects will display in order.
display:inline This is the default value. It doesn’t do anything.
display:block Displays objects the same way <p> displays text, in vertically arranged chunks.
display:inline-block Displays objects in horizontally arranged chunks. This is the most useful display option.
In conclusion, you most likely want to be using position:absolute, and display:inline-block if you’re trying to position objects.
A word to the wise - If you’re changing the display or position properties and you think elements should be moving, but they are not, please, please, check your spelling. Do it for me. I wasted at least an entire hour fiddling with my stylesheet while my HTML class had a dash, and my CSS representation had an underscore. That was not the only time I had a spelling bug this week, it’s easy to do, and easy to miss, so check your work!
Hopefully some of this was helpful. Feedback is always welcome. | 2018-10-16 23:22:13 | {"extraction_info": {"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, "math_score": 0.24463298916816711, "perplexity": 2135.0695560877984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583510893.26/warc/CC-MAIN-20181016221847-20181017003347-00147.warc.gz"} |
https://www.physicsforums.com/threads/energy-levels-of-hydrogen-in-atomic-units.271908/ | # Energy levels of hydrogen in atomic units
1. Nov 14, 2008
### russdot
[solved] Energy levels of hydrogen in atomic units
1. The problem statement, all variables and given/known data
The effective potential for a hydrogen atom can be thought of as the actual potential plus the centrifugal repulsion, written as:
$$V_{eff} = -\frac{1}{r} + \frac{l (l+1)}{2r^{2}}$$
Remembering that you are working in atomic units, make a plot of V_eff(r) for l=0,1,2,3. Mark the energy levels for n=2,3,4. Explain why, for a given n, l cannot be larger than n-1.
The attempt at a solution
I have plotted the potentials for l=0,1,2,3 here: http://img385.imageshack.us/my.php?image=plotte7.gif
I used $$E=-\frac{1}{n^{2}}$$ for the energy levels in atomic units (is this correct?)
As far as explaining why l <= n-1, I thought that because the energy levels would intersect the curves for l <= n-1 and the potential energies with l>=n would be unbound so that l cannot be larger than n-1. However, this does not seem to be the case from the plot I've constructed. I hope the energies I've used are incorrect, because I can't seem to extract the answer out of my plot??
I realised the energy levels should be : $$E = -\frac{1}{2n^{2}}$$ | 2016-12-07 13:11:07 | {"extraction_info": {"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": 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, "math_score": 0.46364110708236694, "perplexity": 528.4669317193171}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542112.77/warc/CC-MAIN-20161202170902-00097-ip-10-31-129-80.ec2.internal.warc.gz"} |
http://www.gradesaver.com/textbooks/math/prealgebra/prealgebra-7th-edition/chapter-9-section-9-1-lines-and-angles-exercise-set-page-613/70 | ## Prealgebra (7th Edition)
Complementary angles total $90^o$. Since angles do not have negative measurements, there is no complement for a $120^o$ angle. | 2018-04-24 01:42:14 | {"extraction_info": {"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, "math_score": 0.5889217257499695, "perplexity": 2782.288588582829}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125946314.70/warc/CC-MAIN-20180424002843-20180424022843-00187.warc.gz"} |
http://mathhelpforum.com/trigonometry/119845-prove-2sin-c-print.html | # prove that a^2sin(A-C)=
• Dec 11th 2009, 12:07 AM
bigwave
prove that a^2sin(A-C)=
prove that
$a^2 \sin{\left(B-C\right)} = \left(b^2- c^2\right)\sin{A}$
where
$a,b,c$ are sides of any triangle
$A,B,C$ are the corresponding angles
• Dec 11th 2009, 12:18 AM
alexmahone
Quote:
Originally Posted by bigwave
prove that
$a^2 \sin{\left(B-C\right)} = \left(b^2- c^2\right)\sin{A}$
where
$a,b,c$ are sides of any triangle
$A,B,C$ are the corresponding angles
$\frac{a^2}{b^2-c^2}=\frac{sin^2A}{sin^2B-sin^2C}$
= $\frac{sin^2A}{(sinB+sinC)(sinB-sinC)}$
= $\frac{sin^2A}{2sin(\frac{B+C}{2})cos(\frac{B-C}{2}).2cos(\frac{B+C}{2})sin(\frac{B-C}{2})}$
= $\frac{sin^2A}{2sin(\frac{B+C}{2})cos(\frac{B+C}{2} ).2sin(\frac{B-C}{2})cos(\frac{B-C}{2})}$
= $\frac{sin^2A}{sin(B+C)sin(B-C)}$
= $\frac{sin^2A}{sin(\pi-A)sin(B-C)}$
= $\frac{sin^2A}{sinAsin(B-C)}$
= $\frac{sinA}{sin(B-C)}$
Thus, $a^2sin(B-C)=(b^2-c^2)sinA$ | 2017-01-23 22:43:04 | {"extraction_info": {"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": 15, "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, "math_score": 0.9670155644416809, "perplexity": 8858.921993459358}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560283008.19/warc/CC-MAIN-20170116095123-00176-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/math/prealgebra/prealgebra-7th-edition/chapter-1-section-1-7-exponents-and-order-of-operations-exercise-set-page-74/86 | Prealgebra (7th Edition)
$4^3$
An exponent represents repeated multiplication. $\underset\uparrow e^{b\ \leftarrow\ number\ of\ times\ the\ base\ appears\ as\ a\ factor}$ the base is the factor that is multiplied $4\times4\times4=4^3$ 4 is the factor so is the base. The factor appears 3 times so the exponent is 3. | 2019-11-19 17:28:54 | {"extraction_info": {"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, "math_score": 0.9233464002609253, "perplexity": 745.4550868398684}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670162.76/warc/CC-MAIN-20191119172137-20191119200137-00244.warc.gz"} |
https://stats.stackexchange.com/questions/385556/time-series-terminology-question | # time series terminology question
Suppose I have a time series $$x_1, x_2, ..., x_{10}$$. I apply the augmented Dickey Fuller test to my data an conclude the data are non-stationary with (say) lag = 2.
With lag = 2, the tested data are $$x_3, ..., x_{10}$$. My question is: Did I conclude that $$x_1, ..., x_{10}$$ are non-stationary, or did I conclude $$x_3, ..., x_{10}$$ are non-stationary?
• All ten data points are used, not just $x_3, \dots, x_{10}$. Consult the wikipedia page for the ADF (en.wikipedia.org/wiki/Augmented_Dickey–Fuller_test) and you can see that for a lag 2 test, $x_1$ and $x_2$ are included in the model formulation when $t=3$. – jbowman Jan 4 at 4:13
• Also, like in other inferential tasks, you use the sample to draw conclusions regarding the underlying population/process, so it is really not the sample that is nonstationary (or not), but the underlying process is. Hence, there is no point to make the distinction in your post. – Christoph Hanck Jan 4 at 8:34 | 2019-06-17 09:23:48 | {"extraction_info": {"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": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8808408975601196, "perplexity": 563.8281918902175}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998462.80/warc/CC-MAIN-20190617083027-20190617105027-00461.warc.gz"} |
https://demo7.dspace.org/items/a3dec850-ecf8-472e-a1bc-bf050c2d68c4 | ## Operator spaces which are one-sided M-Ideals in their bidual
Sharma, Sonia
##### Description
We generalize an important class of Banach spaces, namely the $M$-embedded Banach spaces, to the non-commutative setting of operator spaces. The one-sided $M$-embedded operator spaces are the operator spaces which are one-sided $M$-ideals in their second dual. We show that several properties from the classical setting, like the stability under taking subspaces and quotients, unique extension property, Radon Nikod$\acute {\rm{y}}$m Property and many more, are retained in the non-commutative setting. We also discuss the dual setting of one-sided $L$-embedded operator spaces.
Comment: 17 pages, Revision
##### Keywords
Mathematics - Operator Algebras, Mathematics - Functional Analysis, 46L07, 46B20, 46H10 | 2022-12-03 02:25:48 | {"extraction_info": {"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, "math_score": 0.7930848002433777, "perplexity": 1682.966151376261}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710918.58/warc/CC-MAIN-20221203011523-20221203041523-00389.warc.gz"} |
https://physics.stackexchange.com/questions/457068/why-we-cant-write-low-energy-effective-field-theory-for-a-gapless-system | # Why we can't write low energy effective field theory for a gapless system?
Assume that we have an Hamiltonian $$H=H_0+H_{int}$$ where $$H_0$$ has gappless excitations and $$H_{int}$$ has usual two body interactions.
If $$H_0$$ were gapped I would able to get low energy effective hamiltonian,
1.by using Hubbard stranatovich transformation to get rid of quintic terms,
2.I would integrate out the fermions
3.solve euler lagnrange equations to find classical solutions
4.expand the action around those let's say up to second order
So the this second order expansion would be my effective low energy action.
however, this procedure relies on the fact that $$H_0$$ is gapped it wont work if it is gapless I don't understand why? I assume that if $$H_0$$ is gappless i.e. degenerate than the step 2 can not be done because of the gaussian integral rules, is that the reason?
On the other hand let assume that now the system is bosonic so in that case the procedure is as follows;
1. since the degrees of freedom are bosons, they have classical limit so we can just solve the euler lagrange equations without making hs transformation and without integratin gout anything.
2. then we change variables in ginzburg landau case you can use vortex anzats
3. you expand bosonic fields around classical solutions let's say up to second order and you get you effective action.
so I assume maybe in fermionic gapless case you can't integrate our fermions that's why you can't have the effective action.
however I don't understand why I can't have effective low energy action for gapless bosonic case, because the procedure does not involve integrating out.
## 1 Answer
For the notion of effective theory to make sense you need a separation of scales. This is so that experiments at low energies (with respect to that scale) do not excite the heavy modes too much. In other words, you need to have a notion of "low energies", which is equivalent to a separation of scales or a gap.
Formally you could integrate out massless excitations, but you won't get anything useful as a result. | 2019-04-25 05:52:00 | {"extraction_info": {"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": 6, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.960369348526001, "perplexity": 272.5368105093054}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578689448.90/warc/CC-MAIN-20190425054210-20190425080210-00246.warc.gz"} |
https://www.studyadda.com/question-bank/fractions-and-decimals_q18/4570/361626 | • # question_answer Devi eats one full bar of chocolate. Then she divided another one into 5 equal parts and eats 3 of them. What is the total number of chocolates that she has eaten? A) $\frac{4}{5}$ B) $\frac{3}{5}$ C) $\frac{8}{5}$ D) $\frac{8}{10}$
(c) Total number of chocolates eaten $=1+\frac{3}{5}=\frac{5+3}{5}=\frac{8}{5}$ | 2019-10-15 06:26:23 | {"extraction_info": {"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, "math_score": 0.4637804925441742, "perplexity": 2202.3870228237884}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986657586.16/warc/CC-MAIN-20191015055525-20191015083025-00213.warc.gz"} |
https://cdcvs.fnal.gov/redmine/projects/fermi-redmine/wiki/Windows/18 | ## Windows » History » Version 18
« Previous - Version 18/40 (diff) - Next » - Current version
Marc Mengel, 02/24/2010 04:55 PM
# Windows¶
There are numerous graphical front ends to the various packages on Windows; regardless which
front-end you choose, you will need to configure the back-end part below.
## Back Ends¶
For write access to repositories on cdcvs, I am currently recommending that users use the old GetCert bundle and the ssh in there if you want an old, tried and true setup.
Then there are a few steps to get things setup:
1. Install the contents of kca.zip in a directory.
2. Create three environment variables
1. (local) KRB5CCNAME = C:\Users\yourUsername\AppData\Local\Temp\krb5_cc_cache Notes: Requires full read/write access. There may also be an issue with spaces in the file name and/or path.
2. (system) KRB5_CONFIG = [Path from step 1 above]\krb5.conf
3. (system) CVS_RSH = [Path from step 1 above]\ssh.exe
by doing:
• Right-click My Computer, and then click Properties.
• Click Environment variables.
• Click one the following options, for either a user or a system variable:
• Click New to add a new variable name and value.
• Click an existing variable, and then click Edit to change its name or value.
• Click an existing variable, and then click Delete to remove it.
1. Changes to NetID manager — NetIDSetup.jpg
1. Open Network Identity Manager
2. Double click your default identify ()
3. Click "Identify configuration"
4. Select the Kerberos V5 tab
5. Change the Credential cache location to file: plus the value of the KRB5CCNAME environment variable set in step 2.1 above. See screen shot example.
6. Close all open windows then renew your the credentials for .
7. Verify your tickets by opening a DOS window and entering klist. See screen shot example.
## Check if it works:¶
try to login on the server with ssh. In a cmd.exe window:
ssh p-project@cdcvs.fnal.gov echo hi
(where "project" is your project name). You should get
Only 'lscvs' and 'cvs' commands are allowed
## Subversion¶
Configure Subversion to use plink/ssh for “svn+ssh” uri.
• Edit the file c:\Documents and Settings\user\Application Data\Subversion\config
(with your username for "user") * Locate the section named [tunnels] * Add the following line :
ssh=c:/path/to/plink.exe
for the Putty setup, or for ssh
ssh=c:/path/to/ssh.exe | 2021-04-14 18:16:58 | {"extraction_info": {"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, "math_score": 0.21910914778709412, "perplexity": 14980.295577135288}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038077843.17/warc/CC-MAIN-20210414155517-20210414185517-00092.warc.gz"} |
https://www.rocketryforum.com/threads/launch-controller-mod.79540/ | # Launch Controller Mod
### Help Support The Rocketry Forum:
#### Dbarrm
##### Well-Known Member
This is a modification to the launch controller that bsexton posted. With his ok i have done some modifications to it and would like a second set of eyes to look it over and let me know if I have set this up correct.
Dan
#### DJ Delorie
##### Well-Known Member
If you close more than one arming switch, continuity on any jack will light all the continuity lights. You need diodes to prevent backfeeding power, or use relays to switch each jack independently.
#### Dbarrm
##### Well-Known Member
Can you explain the current path on that??
Dan
#### DJ Delorie
##### Well-Known Member
Ok, close the first two switches. Now, you can trace a path from J1's hot side, down through its switch, to the common rail, through the second switch, and up to J2's hot side. Thus, the two jacks are electrically connected together.
For diodes, you'd need to put one for each jack to isolate the launch side of its arming switch to prevent this backfeed.
For relays, you'd have one relay (or at least one set of relay contacts, for quad-pole relays) for each jack to provide launch power.
#### Dbarrm
##### Well-Known Member
Im not seeing it. Maybe I just dont understand the path your trying to show.
Dan
#### DJ Delorie
##### Well-Known Member
This shows the short between the two jacks. When shorted, the continuity lamps can't tell which igniter is which.
#### Dbarrm
##### Well-Known Member
Ok I see your point now. So if only one was good but lamps would light do to current path. If I used diodes I can control the flow of current.
Dan
#### DJ Delorie
##### Well-Known Member
Yeah, but remeber that (1) the diodes will have to be big enough to carry the launch current, and (2) diodes will drop the voltage 0.7 volts or more for that size diode (minor, but plan for it).
Relays are better but more expensive. Three high-current dual pole relays would add about $25 to the cost, not including sockets if you plan for eventual replacement. #### Dbarrm ##### Well-Known Member Wow your making my head hurt. now I have something to do while I wait for glue to dry. Let me look this over. I want to figure it out myself. If I get to stumped ill come asking for help. Thanks Dan #### Dbarrm ##### Well-Known Member What kind of current are we talking about. I think I have figured out where the diode needs to go but not sure how big of one I need. 1N4001 Dan #### DJ Delorie ##### Well-Known Member Search the other threads for a link to a PDF where someone tested a whole bung of igniters. Some pulled over 20 amps, but only for a fraction of a second. 1N4001 is only rated for 1 amp, which might work for a while, but I'd at least use 3 amp diodes (like 1N5400). Note that 1N4001 and 1N5400 drop 1.1-1.2 volts. For more excitement, a power schottky diode is better - 16 amps at 0.6v drop, or dual 20 amp at 0.3 volt. #### Dbarrm ##### Well-Known Member Is this what I need to do to fix it?? Dan #### DJ Delorie ##### Well-Known Member That should be sufficient. #### Dbarrm ##### Well-Known Member So I need to find a diode that can handle the current. Put it in the same leg for each jack and all should be ok. Thanks for all your help. Dan #### Dbarrm ##### Well-Known Member Ok here is the updated schematic. Dan #### Ted Cochran ##### Well-Known Member Originally posted by Dbarrm So I need to find a diode that can handle the current. Put it in the same leg for each jack and all should be ok. FWIW I used a very similar circuit. https://www.mn-rocketry.net/masa/tech/tedcontroller.htm I used the same 6A rectifier diodes that Radio Shack sells, which cost about$.50 each retail, except I got them at a surplus store. It's not a safety critical part in that if you burn out a diode you'll just lose continuity testing on that circuit. Buy some spares, solder on some quick connects, problem solved. I've had to replace two over the past four years or so, always after some ridiculous thing like a seven AP motor cluster....
However, I do have some suggestions.
First, you might want to put a relay between the launch button and the firing circuit. As it stands, you're using the launch switch--which IS a safety-critical part-- to handle all of the launch current, and it's going to have to be a very beefy and expensive switch to take that kind of abuse. If you instead get a 30 or 50 amp relay (a car horn relay would be just fine), you can use a pretty switch (mine's an old arcade game switch) for the launch button.
Second, it is always possible to get a welded relay, so to avoid nasty surprises you might consider putting a buzzer across the firing relay so it yelps if the relay is closed.
Third, consider splitting the console box and put the relay box (and the battery!) at the pad. You can connect them with 50' extension cords, which are about the cheapest wire you can find anyway. If you want, you can have continuity at the console, and still only need five extension cords to run six pads. You can use 110 volt plugs and receptacles for easy maintenance and relatively low cost.
Good luck with the project!
For what it's worth,
--tc
#### Dbarrm
##### Well-Known Member
What is the advantage of splitting up the system? Is it to minimize the current loss do to the long length of wire??
Dan
#### Dbarrm
##### Well-Known Member
So something like this with a relay??
Dan
#### DJ Delorie
##### Well-Known Member
What is the advantage of splitting up the system? Is it to minimize the current loss do to the long length of wire??
Yes. Plus, each rocket gets its own battery that way - more current available.
#### Ted Cochran
##### Well-Known Member
Originally posted by Dbarrm
What is the advantage of splitting up the system? Is it to minimize the current loss do to the long length of wire??
Yes--the primary firing circuit can be in a loop of 5-10 feet of heavy gauge wire at the pad. Otherwise you need bigger extension cords.
Also, I'm not a EE, but all the EE's I know hate long wires. They cause issues with maintenance, inductance, all sorts of things. Probably not a big deal for a standard 12 v relay system with mechanical switches, but definitely worth worrying about when you upgrade to MOSFETs or other razzmatazz
It also reduces the bulk of the console, if that's a concern.
Cheers,
--tc
#### Ted Cochran
##### Well-Known Member
Originally posted by Dbarrm
What is the advantage of splitting up the system? Is it to minimize the current loss do to the long length of wire??
Yeah, that's it. Now put a buzzer in there that sounds when the relay is closed, and you'll be in great shape.
--tc
#### Ted Cochran
##### Well-Known Member
Originally posted by DJ Delorie
Yes. Plus, each rocket gets its own battery that way - more current available.
Alternatively you can put all the relays in a spider box, and have that box feed a rack of pads with (short) leads. Then you can use a tractor battery or some such at the pad side relay box.
Otherwise you'd have to connect all the pad side boxes to each other, or have a select relay and a firing relay in each box. That's what NASA does, I think
--tc
#### Dbarrm
##### Well-Known Member
Wow so much info. Its 9:39 and im still at work, got off at 4:30 but was working on this. I think its time to go home. Tomorrow Ill do some more on my design and post what I come up with. Thanks all for your inputs and help. This is going to turn out great.
Dan
#### Dbarrm
##### Well-Known Member
Ok I have redesigned the system into a two part controller. The dotted line separates the two sections. Pad & Launch Station. Now Im no engineer so I might have not done this correct so can you people with the know take a look and let me know if you see any flaws.
Dan
#### Dbarrm
##### Well-Known Member
Well this has gone through a lot of changes and im sure it will get a few more. Right now it shows bulbs but that will be changed to add LED's soon.
Dan
#### Dbarrm
##### Well-Known Member
Im not sure if I stated this but dashed line seperates the two different boxes of the launch Controller. I have added a second safety switch to the pad box along with a power LED. All bulbs have been changed to LED's
Dan
#### Dbarrm
##### Well-Known Member
I would like to give a big thanks to bsexton for letting me mod his original design.
I would also like to give a big thanks to DJ Delorie for all his help with the mod, without his help my mod project would of been dead in the water.
Thanks to both of you.
Dan
#### Dbarrm
##### Well-Known Member
Well here is what the front panel of the launch controller will look like. It will look much better when the finished product is made but this will give you an idea.
Dan
#### Dbarrm
##### Well-Known Member
Well here is what the front panel of the launch controller will look like. It will look much better when the finished product is made but this will give you an idea.
Dan | 2021-06-12 11:50:43 | {"extraction_info": {"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, "math_score": 0.38582655787467957, "perplexity": 2141.59500172941}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487582767.0/warc/CC-MAIN-20210612103920-20210612133920-00102.warc.gz"} |
https://www.rdocumentation.org/packages/spatstat/versions/1.61-0/topics/rCauchy | # rCauchy
0th
Percentile
##### Simulate Neyman-Scott Point Process with Cauchy cluster kernel
Generate a random point pattern, a simulated realisation of the Neyman-Scott process with Cauchy cluster kernel.
Keywords
spatial, datagen
##### Usage
rCauchy(kappa, scale, mu, win = owin(), thresh = 0.001,
nsim=1, drop=TRUE,
saveLambda=FALSE, expand = NULL, …,
poisthresh=1e-6, saveparents=TRUE)
##### Arguments
kappa
Intensity of the Poisson process of cluster centres. A single positive number, a function, or a pixel image.
scale
Scale parameter for cluster kernel. Determines the size of clusters. A positive number, in the same units as the spatial coordinates.
mu
Mean number of points per cluster (a single positive number) or reference intensity for the cluster points (a function or a pixel image).
win
Window in which to simulate the pattern. An object of class "owin" or something acceptable to as.owin.
thresh
Threshold relative to the cluster kernel value at the origin (parent location) determining when the cluster kernel will be treated as zero for simulation purposes. Will be overridden by argument expand if that is given.
nsim
Number of simulated realisations to be generated.
drop
Logical. If nsim=1 and drop=TRUE (the default), the result will be a point pattern, rather than a list containing a point pattern.
saveLambda
Logical. If TRUE then the random intensity corresponding to the simulated parent points will also be calculated and saved, and returns as an attribute of the point pattern.
expand
Numeric. Size of window expansion for generation of parent points. By default determined by calling clusterradius with the numeric threshold value given in thresh.
Passed to clusterfield to control the image resolution when saveLambda=TRUE and to clusterradius when expand is missing or NULL.
poisthresh
Numerical threshold below which the model will be treated as a Poisson process. See Details.
saveparents
Logical value indicating whether to save the locations of the parent points as an attribute.
##### Details
This algorithm generates a realisation of the Neyman-Scott process with Cauchy cluster kernel, inside the window win.
The process is constructed by first generating a Poisson point process of parent'' points with intensity kappa. Then each parent point is replaced by a random cluster of points, the number of points in each cluster being random with a Poisson (mu) distribution, and the points being placed independently and uniformly according to a Cauchy kernel.
In this implementation, parent points are not restricted to lie in the window; the parent process is effectively the uniform Poisson process on the infinite plane.
This model can be fitted to data by the method of minimum contrast, maximum composite likelihood or Palm likelihood using kppm.
The algorithm can also generate spatially inhomogeneous versions of the cluster process:
• The parent points can be spatially inhomogeneous. If the argument kappa is a function(x,y) or a pixel image (object of class "im"), then it is taken as specifying the intensity function of an inhomogeneous Poisson process that generates the parent points.
• The offspring points can be inhomogeneous. If the argument mu is a function(x,y) or a pixel image (object of class "im"), then it is interpreted as the reference density for offspring points, in the sense of Waagepetersen (2006).
When the parents are homogeneous (kappa is a single number) and the offspring are inhomogeneous (mu is a function or pixel image), the model can be fitted to data using kppm.
If the pair correlation function of the model is very close to that of a Poisson process, deviating by less than poisthresh, then the model is approximately a Poisson process, and will be simulated as a Poisson process with intensity kappa * mu, using rpoispp. This avoids computations that would otherwise require huge amounts of memory.
##### Value
A point pattern (an object of class "ppp") if nsim=1, or a list of point patterns if nsim > 1.
Additionally, some intermediate results of the simulation are returned as attributes of this point pattern (see rNeymanScott). Furthermore, the simulated intensity function is returned as an attribute "Lambda", if saveLambda=TRUE.
##### References
Ghorbani, M. (2013) Cauchy cluster process. Metrika 76, 697-706.
Jalilian, A., Guan, Y. and Waagepetersen, R. (2013) Decomposition of variance for spatial Cox processes. Scandinavian Journal of Statistics 40, 119-137.
Waagepetersen, R. (2007) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63, 252--258.
##### See Also
rpoispp, rMatClust, rThomas, rVarGamma, rNeymanScott, rGaussPoisson, kppm, clusterfit.
• rCauchy
##### Examples
# NOT RUN {
# homogeneous
X <- rCauchy(30, 0.01, 5)
# inhomogeneous
ff <- function(x,y){ exp(2 - 3 * abs(x)) }
Z <- as.im(ff, W= owin())
Y <- rCauchy(50, 0.01, Z)
YY <- rCauchy(ff, 0.01, 5)
# }
Documentation reproduced from package spatstat, version 1.61-0, License: GPL (>= 2)
### Community examples
Looks like there are no examples yet. | 2020-02-21 03:48:39 | {"extraction_info": {"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, "math_score": 0.37818488478660583, "perplexity": 3108.975476167803}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145438.12/warc/CC-MAIN-20200221014826-20200221044826-00407.warc.gz"} |
https://socratic.org/questions/how-do-you-graph-x-7-0 | # How do you graph x + 7= 0?
Apr 3, 2017
A vertical line going up at -7
#### Explanation:
First solve for x by subtracting 7 from both sides
$x + 7 - 7 = 0 - 7$ This gives
$x = - 7$
This is true for all values of y. so (-7, 0) (-7,1) ( -7, -1) are all on the line.
This results in a vertical line at $x = - 7$ | 2020-12-02 18:44:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "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, "math_score": 0.6677075028419495, "perplexity": 655.486620778421}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141715252.96/warc/CC-MAIN-20201202175113-20201202205113-00150.warc.gz"} |
https://www.physicsforums.com/threads/average-forces-question.235780/ | # Average Forces Question
## Homework Statement
http://img100.imageshack.us/img100/1867/physicsp25wz8.png [Broken]
Use data from Figure to determine,
(a) the distance travelled by the ball during the first 0.40s,
(b) the change in momentum of the ball, of mass 45g, during contact of the ball with the surface,
(c) the average force acting on the ball during contact with the surface.
## The Attempt at a Solution
(a) 0.8m
(b) $$Change \ in \ momentum = mv - mu$$
$$= (45 \times 10^{-3} \times 4.2) - (45 \times 10^{-3} \times 0)$$
$$= 0.19Ns$$
Answer in text book is $$0.35Ns$$, where did I go wrong?
Last edited by a moderator: | 2022-01-21 05:54:34 | {"extraction_info": {"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": 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, "math_score": 0.8402611613273621, "perplexity": 1535.9198399257314}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320302723.60/warc/CC-MAIN-20220121040956-20220121070956-00241.warc.gz"} |
https://math.stackexchange.com/questions/2580154/am-i-allowed-to-do-this-to-prove-that-one-statement-proves-the-other | # Am I allowed to do this to prove that one statement proves the other?
This is sort of a continuation of my previous post but different statements: Does this prove one statement implies the other?
Statement $A$
$∀a,b,c∈ℤ,a<b<c⇒a+b+c<2b+c$
Statement $B$
$∀x,y,z∈ℤ,x<y∧z≠x∧z≠y⇒x+y+z<2y+z$
I'd like to prove $A$ implies $B$ by saying that, assuming the antecedent of $B$,
$z<x<y∨x<z<y∨x<y<z$
Could I then say to take $a$ from $A$ to be min{$x,y,z$}, $c$ from $A$ to be max{$x,y,z$}, and $b$ to be the one left over showing:
$x+y+z<2y+z$?
Also if the proof is invalid but the implication is true, could you show me how to prove it?
Well, your method is valid, but your last step is wrong. You can't conclude $x+y+z<2y+z$; rather, you can conclude $a+b+c<2b+c$ for the definitions of $a,b,$ and $c$ you have made. Depending on which case you are in, this gives you a different inequality. For instance, in the case $z<x<y$ it gives you $$x+y+z<2x+y,$$ because $a=z$, $b=x$, and $c=y$ in that case.
To prove statement A implies statement B, I would instead suggest trying to prove statement B directly (after all, if statement B is true, then anything implies it). Given $x<y$, how could you obtain the inequality $x+y+z<2y+z$? The answer is hidden below.
Just add $y+z$ to both sides of $x<y$.
• When you said "if statement B is true, then anything implies it", does that mean that if I can prove both statements to be true, it shows that they are equivalent? – Spectacles Dec 25 '17 at 22:57
• Yes, if two statements are both true, then they are equivalent. – Eric Wofsey Dec 25 '17 at 23:09
While mathematically true, statement B does not logically follow from statement A. To prove statement you need to prove it for all integers $x$, $y$ and $s$ and not just the ones where $z$ is the greatest of those three. So, statement A by itself is not enough to imply statement B, since A is only about that restricted set.
Your particular proof does not work,because when $z<x<y$, all that you can get from statement A is that $z+x+y<2x+y$, which is not the same as, nor implies, $x+y+z<2y+z$
To add to what others have said in other answers: actually you can use $B$ to prove $A$. This is because, if $a\lt b\lt c$ then $a\lt b$ and $c\ne a$ and $c\ne b$, so you can 'plug' $x=a, y=b, z=c$ in $B$. | 2019-11-18 11:41:22 | {"extraction_info": {"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, "math_score": 0.7516114115715027, "perplexity": 184.54919700463608}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669755.17/warc/CC-MAIN-20191118104047-20191118132047-00462.warc.gz"} |
https://homework.zookal.com/questions-and-answers/where-can-i-get-my-salary-595078895 | 1. Math
2. Mathematics
3. where can i get my salary...
# Question: where can i get my salary...
###### Question details
Where can i get my salary | 2021-04-18 18:59:11 | {"extraction_info": {"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, "math_score": 0.870136022567749, "perplexity": 5203.020292417311}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038507477.62/warc/CC-MAIN-20210418163541-20210418193541-00594.warc.gz"} |
http://mycodepartner.com/cplusplus/writing-to-a-file-using-ofstream/ | # Writing to a file using ofstream
C++ provides classes to input or output characters to or from files. To write to a file, we use ofstream.
Two modes are used in writing to a file. ios::trunc and ios::app. ios::trunc removes everything from a file and writes from scratch. ios::app adds data to the file from the new line.
Write a program to output to a file using ofstream. If no mode is provided, ios::trunc is used.
#include<iostream>
#include<fstream>
using namespace std;
int main(){
ofstream out;
out.open("myfile.txt");
if(!out){
cout<<"Error in opening"<<endl;
return 1;
}
out<<"My "<<123<<endl;
out<<"Code "<<124<<endl;
out<<"Partner "<<125<<endl;
out.close();
return 0;
}
We get a file named myfile.txt
Now, we use ios::app for the same file. The following code will append data to the same file.
#include<iostream>
#include<fstream>
using namespace std;
int main(){
ofstream out;
out.open("myfile.txt",ios::app);
if(!out){
cout<<"Error in opening"<<endl;
return 1;
}
out<<"My "<<23<<endl;
out<<"Code "<<24<<endl;
out<<"Partner "<<25<<endl;
out.close();
return 0;
} | 2020-10-30 02:13:39 | {"extraction_info": {"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, "math_score": 0.17321786284446716, "perplexity": 9928.611106248085}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107906872.85/warc/CC-MAIN-20201030003928-20201030033928-00549.warc.gz"} |
http://stackoverflow.com/questions/7777953/minimal-code-to-connect-to-mssql-server-express-and-extract-some-table-data-usin/8810292 | # Minimal code to connect to MSSQL Server Express and extract some table data using Visual C++ Express
I have the following software installed on the machine:
• Microsoft SQL Server Express 2005
• Microsoft Visual C++ Express 2008
I have a .mdf file from which I need to read some data and dump to a text file. I can browse the database file using the Database Explorer in Visual Studio without any problem, but I'm having trouble connecting from the application.
I googled far and wide, almost all "solutions" say that I should start a new project and select the "SQL server application template", which I don't have amongst templates. Other tutorials I found say I should use "Data Source Configuration Wizard", however I cannot find such wizard in any of the menus.
I don't mind clicking although I would prefer if all this was doable in plain C++ code. Something like:
DbConnection *d = new MSSQLConnection("local", "c:\path\to\file.mdf");
DbQuery *q = new DbQuery(d, "select * from mytable");
...dump the data and go home
Thanks.
Alternatively, if someone can tell me how to do this in C++:
http://sharpertutorials.com/connecting-to-a-sql-server-database/
-
And here it is. Quite simple and easy once you know it...
SqlConnection^ myConnection = gcnew SqlConnection("Data Source=.\\SQLEXPRESS;AttachDbFilename=\"file.mdf\";Integrated Security=True;Connect Timeout=10;User Instance=True");
myConnection->Open();
SqlCommand^ scmd = gcnew SqlCommand("select ID from atable", myConnection); | 2014-03-11 19:46:39 | {"extraction_info": {"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, "math_score": 0.40857943892478943, "perplexity": 4296.941769445011}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394011250185/warc/CC-MAIN-20140305092050-00071-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://www.transtutors.com/questions/5-33-the-price-of-gold-is-currently-1-500-per-ounce-the-forward-price-for-delivery-i-1328573.htm | 5.33 The price of gold is currently $1,500 per ounce. The forward price for delivery in one year... 1 answer below » 5.33 The price of gold is currently$1,500 per ounce. The forward price for delivery in one year is
\$1,700. An arbitrageur can borrow money at 10% per annum. What should the arbitrageur do? Assume that the cost of storing gold is zero and that gold provides no income. | 2019-02-24 00:50:52 | {"extraction_info": {"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, "math_score": 0.2549515664577484, "perplexity": 2428.1980495967605}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249569386.95/warc/CC-MAIN-20190224003630-20190224025630-00240.warc.gz"} |
https://www.x-mol.com/paper/math/tag/99/journal/72280 | • Algebra Univers. (IF 0.404) Pub Date : 2020-08-06
Keith A. Kearnes, Alexander Rasstrigin
We prove that if $${\mathbb {A}}$$ is an algebra that is supernilpotent with respect to the 2-term higher commutator, and $${\mathbb {B}}$$ is a subalgebra of $${\mathbb {A}}$$, then $${\mathbb {B}}$$ is representable as a retract of a finite subdirect power of $$\mathbb A$$.
更新日期：2020-08-06
• Algebra Univers. (IF 0.404) Pub Date : 2020-07-20
We prove that every algebraic lattice is isomorphic to a complete sublattice in the subgroup lattice of a suitable locally finite 2-group. In particular, every lattice is embeddable in the subgroup lattice of a locally finite 2-group.
更新日期：2020-07-20
• Algebra Univers. (IF 0.404) Pub Date : 2020-07-20
Christian Choffrut, Serge Grigorieff
We consider the additive structure of ordinals augmented with right multiplication by $$\omega$$. We prove that two terms in the algebra are semantically equal if and only if they take the same value on all elements of a set containing 0 and at least one ordinal of each finite degree. Among these (so-called) test sets the most natural one is that obtained by considering 0 along with all $$\omega$$-powers
更新日期：2020-07-20
• Algebra Univers. (IF 0.404) Pub Date : 2020-07-13
In this paper we present the concept of weak link and weak link topology on lattice ordered groups and MV-algebras. We show that it is a locally solid group topology. In addition, we investigate the metrizability of a link topology.
更新日期：2020-07-13
• Algebra Univers. (IF 0.404) Pub Date : 2020-07-13
Branimir Šešelja, Anna Slivková, Andreja Tepavčević
The aim of this paper is to extend the notions of geometric lattices, semimodularity and matroids in the framework of finite posets and related systems of sets. We define a geometric poset as one which is atomistic and which satisfies particular conditions connecting elements to atoms. Next, by using a suitable partial closure operator and the corresponding partial closure system, we define a partial
更新日期：2020-07-13
• Algebra Univers. (IF 0.404) Pub Date : 2020-07-13
Brian T. Chan
The problem of determining (up to lattice isomorphism) the lattices that are sublattices of free lattices is in general an extremely difficult and an unsolved problem. A notable result towards solving this problem was established by Galvin and Jónsson when they classified (up to lattice isomorphism) all of the distributive sublattices of free lattices in 1959. In this paper, we weaken the requirement
更新日期：2020-07-13
• Algebra Univers. (IF 0.404) Pub Date : 2020-07-08
Charlotte Aten
We study a class of algebras we regard as generalized rock–paper–scissors games. We determine when such algebras can exist, show that these algebras generate the varieties generated by hypertournament algebras, count these algebras, study their automorphisms, and determine their congruence lattices. We produce a family of finite simple algebras.
更新日期：2020-07-08
• Algebra Univers. (IF 0.404) Pub Date : 2020-07-06
Giacomo Lenzi, Antonio Di Nola
This paper deals with the problem of characterizing those topological spaces which are homeomorphic to the prime spectra of MV-algebras or Abelian $$\ell$$-groups. As a first main result, we show that a topological space X is the prime spectrum of an MV-algebra if and only if X is spectral, and the lattice K(X) of compact open subsets of X is a closed epimorphic image of the lattice of “cylinder rational
更新日期：2020-07-06
• Algebra Univers. (IF 0.404) Pub Date : 2020-06-30
Frank Murphy-Hernandez
For a group G and a poset X, we say that X is a G-poset if it is equipped with a G-action that is monotone. If we consider the mononote G-equivariant maps as morphisms, then we get the category of G-posets. We give a description of the projective objects, injective objects, quotients, and generators.
更新日期：2020-06-30
• Algebra Univers. (IF 0.404) Pub Date : 2020-06-22
Anthony W. Hager, Philip Scowcroft
Within archimedean $$\ell$$-groups, “$$H \in W^{*}$$” means H contains a strong unit, and “$$G \in SW^{*}$$ (respectively, $$ESW^{*}$$)” means there are $$H \in W^{*}$$ and an embedding (respectively, essential embedding) $$G \le H$$. This paper continues earlier work in which we developed methods of attacking the question “$$G \in SW^{*}$$?” and gave many examples with answer “No” and “Yes”. Here
更新日期：2020-06-23
• Algebra Univers. (IF 0.404) Pub Date : 2020-06-19
Wei Chen
In this paper, we study semiconic idempotent commutative residuated lattices. An algebra of this kind is a semiconic generalized Sugihara monoid if it is generated by the lower bounds of the monoid identity. We establish a category equivalence between semiconic generalized Sugihara monoids and Brouwerian algebras with a strong nucleus. As an application, we show that central semiconic generalized Sugihara
更新日期：2020-06-23
• Algebra Univers. (IF 0.404) Pub Date : 2020-06-16
Nikolaos Galatos, Peter Jipsen
Generalized bunched implication algebras (GBI-algebras) are defined as residuated lattices with a Heyting implication, and are positioned between Boolean algebras with operators and lattices with operators. We characterize congruences on GBI-algebras by filters that are closed under Gumm–Ursini terms, and for involutive GBI-algebras these terms simplify to a dual version of the congruence term for
更新日期：2020-06-16
• Algebra Univers. (IF 0.404) Pub Date : 2020-06-07
Anatolij Dvurečenskij, Dominik Lachman
We show that under some natural conditions, we are able to lift an n-dimensional spectral resolution from one monotone $$\sigma$$-complete unital po-group into another one, when the first one is a $$\sigma$$-homomorphic image of the second one. We note that an n-dimensional spectral resolution is a mapping from $$\mathbb R^n$$ into a quantum structure which is monotone, left-continuous with non-negative
更新日期：2020-06-07
• Algebra Univers. (IF 0.404) Pub Date : 2020-05-20
C. Bergman, T. Penza, A. B. Romanowska
The Mal’tsev product of two varieties of similar algebras is always a quasivariety. We consider the question of when this quasivariety is a variety. The main result asserts that if $$\mathcal {V}$$ is a strongly irregular variety with no nullary operations and at least one non-unary operation, and $$\mathcal {S}$$ is the variety, of the same type as $$\mathcal {V}$$, equivalent to the variety of semilattices
更新日期：2020-05-20
• Algebra Univers. (IF 0.404) Pub Date : 2020-05-17
Javier Gutiérrez García, Tomasz Kubiak, Jorge Picado
The purpose of this paper is to identify the role of perfectness in the Michael insertion theorem for perfectly normal locales. We attain it by characterizing perfect locales in terms of strict insertion of two comparable lower semicontinuous and upper semicontinuous localic real functions. That characterization, when combined with the insertion theorem for normal locales, provides an improved formulation
更新日期：2020-05-17
• Algebra Univers. (IF 0.404) Pub Date : 2020-05-14
Meng Gao, Wen Ting Zhang, Yan Feng Luo
Since the 1970s, the smallest known non-finitely based involution semigroups are of order six. This paper exhibits the first example of a non-finitely based involution semigroup of order five.
更新日期：2020-05-14
• Algebra Univers. (IF 0.404) Pub Date : 2020-05-08
Themba Dube, Mojtaba Ghirati, Sajad Nazari, Ali Taherifar
We characterize rings in which every left ideal generated by an idempotent different from 0 and 1 is either a maximal left ideal or a minimal left ideal. In the commutative case, we give a characterization in terms of topological properties of the maximal spectrum with the Zariski topology. We also consider a strictly weaker variant of this property, defined almost similarly, and characterize those
更新日期：2020-05-08
• Algebra Univers. (IF 0.404) Pub Date : 2020-05-05
Nasir Sohail, Boža Tasić
We prove that epimorphisms are surjective in certain categories of ordered $$\mathcal {F}$$-algebras. It then turns out that epimorphisms are also surjective in the category of all (unordered) algebras of type $$\mathcal {F}$$.
更新日期：2020-05-05
• Algebra Univers. (IF 0.404) Pub Date : 2020-05-04
José Gil-Férez, Peter Jipsen, George Metcalfe
In this paper we study structural properties of residuated lattices that are idempotent as monoids. We provide descriptions of the totally ordered members of this class and obtain counting theorems for the number of finite algebras in various subclasses. We also establish the finite embeddability property for certain varieties generated by classes of residuated lattices that are conservative in the
更新日期：2020-05-04
• Algebra Univers. (IF 0.404) Pub Date : 2020-04-27
Carsten Dietzel, Wolfgang Rump
A (non-commutative) structure group G(E) is associated to an arbitrary effect algebra E, and a concept of non-degeneracy is introduced. If E is non-degenerate, G(E) has a right invariant partial order, E embeds as an interval into G(E), and the negative cone of G(E) is a self-similar partial L-algebra. In the degenerate case, the possible anomalies are explained. Lattice effect algebras, 2-divisible
更新日期：2020-04-27
• Algebra Univers. (IF 0.404) Pub Date : 2020-04-21
G. Mashevitzky
The class of identical inclusions was defined by Lyapin. We prove that any set of identical inclusions in the class of semilattices is equivalent to an elementary (the first order) formula. Elementary identical inclusions forms the class of universal formulas which is situated strictly between identities and universal positive formulas. We describe the infinite lattice of all classes of semilattices
更新日期：2020-04-21
• Algebra Univers. (IF 0.404) Pub Date : 2020-04-11
B. Majcher-Iwanow
Let LF be the lattice of all subgroups of the group $$SF(\omega )$$ of all finitary permutations of the set of natural numbers. We consider subgroups of $$SF(\omega )$$ of the form $$C\cap SF(\omega )$$, where C is a compact subgroup of the group of all permutations. In particular, we study their distribution among elements of LF. We measure this using natural relations of orthogonality and almost
更新日期：2020-04-11
• Algebra Univers. (IF 0.404) Pub Date : 2020-04-10
Valdis Laan, László Márki, Ülo Reimaa
We study properties of the lattice of unitary ideals of a semigroup. In particular, we show that it is a quantale. We prove that if two semigroups are connected by an acceptable Morita context then there is an isomorphism between the quantales of unitary ideals of these semigroups. Moreover, factorisable ideals corresponding to each other under this isomorphism are strongly Morita equivalent.
更新日期：2020-04-10
• Algebra Univers. (IF 0.404) Pub Date : 2020-04-02
Xin Zhang, Bin Zhao
In this paper, we give an alternative representation of a free S-quantale over a poset. Furthermore, we give the concrete forms of free and cofree S-quantales over a sup-lattice. Finally, we give an example to present that a cofree S-quantale over a poset does not always exist.
更新日期：2020-04-02
• Algebra Univers. (IF 0.404) Pub Date : 2020-03-31
Manuel Bodirsky, Albert Vucaj
Primitive positive constructions have been introduced in recent work of Barto, Opršal, and Pinsker to study the computational complexity of constraint satisfaction problems. Let $${\mathfrak {P}}_{\mathrm {fin}}$$ be the poset which arises from ordering all finite relational structures by pp-constructability. This poset is infinite, but we do not know whether it is uncountable. In this article, we
更新日期：2020-03-31
• Algebra Univers. (IF 0.404) Pub Date : 2020-03-31
Gayatri Panicker, K. V. Krishna, Purandar Bhaduri
This paper investigates the notions of atoms and atomicity in C-algebras and obtains a characterisation of atoms in the C-algebra of transformations. In this connection, various characterisations for the existence of suprema of subsets of C-algebras are obtained. Further, this work presents some necessary conditions and some sufficient conditions for the atomicity of C-algebras and shows that the class
更新日期：2020-03-31
• Algebra Univers. (IF 0.404) Pub Date : 2020-03-31
James M. Koussas, Tomasz Kowalski
It is well known that the subvariety lattice of the variety of relation algebras has exactly three atoms. The (join-irreducible) covers of two of these atoms are known, but a complete classification of the (join-irreducible) covers of the remaining atom has not yet been found. These statements are also true of a related subvariety lattice, namely the subvariety lattice of the variety of semiassociative
更新日期：2020-03-31
• Algebra Univers. (IF 0.404) Pub Date : 2020-03-30
Michael Hoefnagel, Zurab Janelidze, Diana Rodelo
For a given variety $${\mathcal {V}}$$ of algebras, we define a class relation to be a binary relation $$R\subseteq S^2$$ which is of the form $$R=S^2\cap K$$ for some congruence class K on $$A^2$$, where A is an algebra in $${\mathcal {V}}$$ such that $$S\subseteq A$$. In this paper we study the following property of $${\mathcal {V}}$$: every reflexive class relation is an equivalence relation. In
更新日期：2020-03-30
• Algebra Univers. (IF 0.404) Pub Date : 2020-03-30
H. Peter Gumm
If F is a (not necessarily associative) monad on Set, then the natural transformation $$F(A\times B)\rightarrow F(A)\times F(B)$$ is surjective if and only if $$F(\varvec{1})=\varvec{1}$$. Specializing F to $$F_{\mathcal {V}}$$, the free algebra functor for a variety $$\mathcal {V},$$ this result generalizes and clarifies an observation by Dent, Kearnes and Szendrei in 2012.
更新日期：2020-03-30
• Algebra Univers. (IF 0.404) Pub Date : 2020-03-29
Oghenetega Ighedo, Martin M. Mugochi
A cozero sublocale C of a completely regular locale L will here be called coz-complemented if there is a cozero sublocale D of L such that $$C\cap D$$ is the void sublocale and $$C\vee D$$ is dense in L. Following terminology in spaces, we say L is a cloz-locale if every coz-complemented sublocale of L has an open closure. We characterize cloz-locales in terms of certain embeddings, and also in terms
更新日期：2020-03-29
• Algebra Univers. (IF 0.404) Pub Date : 2020-02-25
Clifford Bergman
Let $$\mathcal {A}$$ and $$\mathcal {B}$$ be idempotent varieties and suppose that the variety $$\mathcal {A} \vee \mathcal {B}$$ is congruence permutable. Then the Maltsev product $$\mathcal {A} \circ \mathcal {B}$$ is also congruence permutable.
更新日期：2020-02-25
• Algebra Univers. (IF 0.404) Pub Date : 2020-02-22
G. Grätzer
In this note, I find a new property of the congruence lattice, $${{\,\mathrm{Con}\,}}L$$, of an SPS lattice L (slim, planar, semimodular, where “slim” is the absence of $${\mathsf {M}}_3$$ sublattices) with more than 2 elements: there are at least two dual atoms in$${{\,\mathrm{Con}\,}}L$$. So the three-element chain cannot be represented as the congruence lattice of an SPS lattice, supplementing a result
更新日期：2020-02-22
• Algebra Univers. (IF 0.404) Pub Date : 2020-02-19
Miroslav Olšák
We prove that an idempotent operation generates a loop from a strongly connected digraph containing directed closed walks of all lengths under very mild (local) algebraic assumptions. Using the result, we reprove the existence of weakest non-trivial idempotent equations, and that a finite strongly connected digraph of algebraic length 1 compatible with a Taylor operation has a loop.
更新日期：2020-02-19
Contents have been reproduced by permission of the publishers.
down
wechat
bug | 2020-08-08 01:12:06 | {"extraction_info": {"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": 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, "math_score": 0.7940701246261597, "perplexity": 1050.809127908923}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737233.51/warc/CC-MAIN-20200807231820-20200808021820-00451.warc.gz"} |
https://blender.stackexchange.com/questions/265202/geonodes-mix-position-with-random-index-values-how-to-make-random-values-uniqu/267212 | # Geonodes mix position with random index values - How to make random values unique?
I'm animating a Mix-RGB position change in a geonode setup that shifts an instanced plane from 2400 grid vertices to a different series of grids that add up to an equal 2400.
The mix animation didn't look good until I connected a Random Value Node to the Index field.
The problem now is that the Random Value calculation for the index doesn't care about unique values. It ends up assigning many planes to the same (index) location and therefore the final grids have empty spots.
I understand "Random Value" within a given range naturally duplicates numbers, but is there a way to prevent that?
Maybe there is another node or fancy math trick to redistribute the index numbers in a "random" way?
Thank you!
Picture 1 below: Node setup
Picture 2: Left side: final result (desired) but location mix animation was very ugly.
Picture 2: Right side: final result (not desired) but location mix animation looked great.
• You can assign a random value to an attribute (e.g. X coordinate), and then sort by that attribute: How can I re-sort the points/indexes of an object in geometry nodes? Jun 4 at 21:20
• @MarkusvonBroady Great idea! There are seemingly endless possibilities once you are able to sort points. I can't wait to see when we have a sorting node in Blender. ;-) Jun 4 at 21:30
Result:
Geometry Nodes:
Note: In most seeds, most points are random, those who aren't are perceptually random.
What the Point Index Randomizer node group does is first generates a random index for every point, and if a point got and index that is used by an previous point, it gets an index that was not generated from a list containing all not generated indexes.
## $$\text{Explanation}$$
First, for every point, a random index is generated with limits equal to: $$\left(\text{min}=0,\text{max}=C-1\right)$$, where $$C$$ is equal to the point count. I will call these rIndex.
Now points with an rIndex that is used by previous points are identified by accumulating $$1$$ with Group Input equal to rIndex. The trailing value is compared verified if it is equal to $$0$$, if it is, then the point have an unique $$rIndex$$ compared to preceding points. I will call the resulting boolean field notRepeated.
Example result of trailing:
Now it accumulates notRepeated, the trailing result is the same as the index of a repeating point if it were on a list with only the repeating points. I will call these indexRepeat
Here's an example:
indexRepeat is what will be used in repeating points to get from the unused index list an index that wasn't generated by the Random Value node. But first it needs to calculate that list.
To calculate the list, it first branch the points geometry, set the position of the points to $$\left(0,0,\text{rIndex}\right)$$ and then separates points where notRepeat is $$true$$ (will call these usedIndexes). After that it creates a Mesh line with Count equal to the point count of the main points and vertex position equal to $$\left(0,0,\text{Index}\right)$$, then it deletes all vertices with a distance to points of usedIndexes equal to $$0$$, resulting in a mesh where all vertices have at their $$Z$$ coordinate an unused index. I will call this mesh unusedIndexes.
Now, for a point in the base points, if notRepeat is $$true$$, the Randomized Index is equal to rIndex. If not, a value for Randomized Index is transferred from unusedIndexes using indexRepeat as index. It could transfer sequentially, but, to look more random, for even indexRepeat values, it gets a value starting from index $$0$$, and for odd values it starts from the last unused index.
• wow...+1 i am glad to have another GN expert here...! Jun 1 at 9:57
• Your "point index randomizer" node did the trick perfectly. This was a lot of work on your part and greatly appreciated. I wonder why Blender doesn't have a built in way of managing this. Thank you for your explanation as well - I'll be studying it for the next year or so trying to understand it properly! Jun 1 at 18:01
• Tough job, nicely done. I'm almost ashamed to post my version :) Jun 1 at 19:50
For lazy people, there's a quick hack to shuffle indices (or, by extension, any other attribute) in GN, dependent on Blender's implementation of Separate Geometry and Join Geometry.
If you simply take geometry apart, and put it back together again, Blender stacks all the indices of the 'bottom half' on the indices of the 'top half'. So this operation:
.. is like randomly selecting roughly half of a deck of cards and putting them, still in order, on the bottom of the deck.
Do that 2 or 3 times, and you get a very reasonable shuffle.. here, as in your example:
.. with this sort of result:
• Oh, fine, I find that very inspiring! Jun 1 at 19:56
• @quellenform I hope you're not claiming to be as lazy as me ;) Jun 1 at 20:01
• lazy people always look for the easiest solution, but the easiest solutions are usually the hardest work ;-) Jun 1 at 20:11
• Thank you Robin for the alternative solution! I really like this one. Particularly so because it's simple and I understand it immediately. Good creative thinking! Jun 1 at 21:44
• If I couldn't see the author of this answer, I would guess @quellenform... Jun 4 at 21:28
I believe my method to generate a new shuffled index is faster and simpler than everything proposed so far, it could also work with millions of points easily, not sure the other algo can handle a large amount of points
Here's the simple logic behind it:
1. generate a random field integer ranging from 0 to 3, these will represent 4 distinct "groups" indices, we could work with more groups if needed but I believe 4 is a sweet spot
Index | GroupIndex
|
0 | 2
1 | 2
2 | 3
3 | 1
4 | 0
5 | 1
6 | 3
7 | 0
8 | 2
9 | 2
1. With the accumulate field nodes set to a value of 1 int, we can distinctly enumerate the elements in each groups thanks to the trailing output, and get each group length thanks to the total output. PS: If you have trouble understanding this logic, please read the documentation about the accumulate field node
Idx |GrIdx| GrEnum | GrLen
| | #==Acc.Trailing | #==Acc.Total
0 | 2 | 0 | 4
1 | 2 | 1 | 4
2 | 3 | 0 | 2
3 | 1 | 0 | 2
4 | 0 | 0 | 2
5 | 1 | 1 | 2
6 | 3 | 1 | 2
7 | 0 | 1 | 2
8 | 2 | 2 | 4
9 | 2 | 3 | 4
1. To each group enumeration, we add all previous groups lengths in order to obtain our non-repeating shuffled index
Idx |GrIdx|GrEnum|GrLen| Shuffled Index
| | | | #adding the previous groups len to the trailing enum
0 | 2 | 0 | 4 | 4 # == 0+[2+2]
1 | 2 | 1 | 4 | 5 # == 1+[2+2]
2 | 3 | 0 | 2 | 8 # == 0+[2+2+4]
3 | 1 | 0 | 2 | 2 # == 0+[2]
4 | 0 | 0 | 2 | 0 # == 0
5 | 1 | 1 | 2 | 3 # == 1+[2]
6 | 3 | 1 | 2 | 9 # == 1+[2+2+4]
7 | 0 | 1 | 2 | 1 # == 1
8 | 2 | 2 | 4 | 6 # == 2+[2+2]
9 | 2 | 3 | 4 | 7 # == 3+[2+2]
It is also important to know, in the context of this question, that indices can be offsetted and mirrored, i tried to use these functions to shuffle my indices in this thread below (it didn't work at the end but I'm sure it would've been another potential solution after more trials)
How to shuffle an attribute in geometry node?
i tried various techniques already, see shuffle_by_offsetting_index.blend consisting of "offsetting" or "mirroring" indices depending on odd/even numbers or random ranges.
• Poorly explained and illustrated, as well as difficult to understand structured, but a brilliant solution! Jun 23 at 8:32
• you're right thanks for your suggestion
– DB3D
Jun 23 at 12:06
• @quellenform ok added a tablature, i hope that's enough :)
– DB3D
Jun 23 at 12:26
## Random coordinate -> sort
You can randomize X coordinate (or just any attribute if you're willing to modify the algorithms), and then sort by it. The resolution-sampling algorithm probably will be enough:
How can I re-sort the points/indexes of an object in geometry nodes?
## Precomputed mapping
If you know beforehand how many vertices there will be to rearrange, and you don't want to have a dynamic seed, or there's a limited number of seeds, you can create a mesh that maps an index to another index expressed as a custom attribute or something else... Here I used X coordinate:
Now in order to automatically create that mesh map, you need to run a Python script:
import bpy, numpy as np
from bpy import context as C, data as D
_len = 100
a = np.arange(_len, dtype=np.float32)
np.random.shuffle(a)
a.resize(_len*3)
a = np.reshape(a, (_len, 3), order='F')
a = np.reshape(a, _len*3)
me = D.meshes.new('random map')
me.vertices.foreach_set("co", a)
ob = D.objects.new('random map', me) | 2022-08-16 04:02:43 | {"extraction_info": {"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": 13, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3283819556236267, "perplexity": 957.4248849667953}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572220.19/warc/CC-MAIN-20220816030218-20220816060218-00244.warc.gz"} |
http://mathhelpforum.com/trigonometry/24542-incredibly-important-due-tomorrow-homework.html | Thread: incredibly important and due tomorrow homework
1. incredibly important and due tomorrow homework
How do I find the value of x in tan(2x)-4tan(x)=3 ?
2. You could use the substitution $tan(2x)=\frac{2tan(x)}{1-tan^{2}(x)}$
After you do that, simplify and make the substitution u=tan(x).
You should get the cubic. $4u^{3}+3u^{2}-2u-3=0$
Solve for u, then find x by taking arctan(u).
3. thank you | 2017-04-29 00:42:24 | {"extraction_info": {"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": 2, "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, "math_score": 0.9830935001373291, "perplexity": 1865.1545060427966}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123102.83/warc/CC-MAIN-20170423031203-00628-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://newproxylists.com/summation-on-an-index-and-a-set/ | # summation on an index and a set
I have an index `DC` and a set of values `CM`, and `it is a CM element` and `CM` is a subset of `DC`. I have two summations shown above. The first sum is complete index `DC` and the subset `CM`. The light brown part of the first sum says that the sum should only include if `c` is an element of `CM`. The second point is about the elements of `CM`.
These two summations appear in an equation (not given here for the sake of simplicity). Is there an easy way to make these summations?
Thank you… | 2019-06-18 20:10:51 | {"extraction_info": {"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, "math_score": 0.9273659586906433, "perplexity": 265.8444469601225}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998813.71/warc/CC-MAIN-20190618183446-20190618205446-00251.warc.gz"} |
https://www.mpp.mpg.de/en/?tx_mpppubl_publplugin%5Boffset%5D=180&tx_mpppubl_publplugin%5Bcontroller%5D=Publ | applicationContext = Production
## Magazine "100 years Max Planck Institute for Physics"
With this magazine we want to give you a brief and entertaining glimpse into our history, our research past and present, and some of the people who worked here at various times.
Max Planck, Albert Einstein, Werner Heisenberg – scientists who are very closely intertwined with our history and are still revered by physicists and non-physicists alike.
Without a doubt, the largest part of our universe still lies hidden. The matter we are familiar with covers only about five percent. What does »dark matter« consist of? And even the constituents we know about still puzzle us: Why is there more matter than antimatter? Is there a unified theory of all the natural forces – gravitation, electromagnetism, and the weak and strong interactions?
We are prepared for new discoveries, in both theoretical and experimental physics, and look ahead to the future with high expectations.
Read online or order a get a hard copy at magazine@mpp.mpg.de
# Research at the Max Planck Institute for Physics
The Max Planck Institute for Physics in Munich is one of the world’s leading research institutions for particle physics. Here, scientists study the smallest building blocks of matter and how they interact. Theory and experiment work hand in hand. The physicists at the Institute develop and test theoretical models as the basis for experiments with the aim of solving the mysteries of the universe: for example, what dark matter consists of and why antimatter no longer exists.
Structure of matter
Standard Model - dark energy - quantum field theory - gravitation - string theory - supersymmetry - building blocks of matter - particle collisions
#### Structure of matter
Standard Model - dark energy - quantum field theory - gravitation - string theory - supersymmetry - building blocks of matter - particle collisions
New technologies
Accelerator and detector technologies - linear accelerators - acceleration with plasma waves - germanium detectors
#### New technologies
Accelerator and detector technologies - linear accelerators - acceleration with plasma waves - germanium detectors
Astroparticle physics
Telescopes - gamma rays - black holes - supernovas - active galactic nuclei - dark energy - dark matter - neutrino physics
#### Astroparticle physics
Telescopes - gamma rays - black holes - supernovas - active galactic nuclei - dark energy - dark matter - neutrino physics
## Recent publications
### New publications since 2016
Search response: 596 publications match your query. Listing starts with latest publication first: (181 - 182)
MPP-2017-21 Measurement of longitudinal flow correlations in Pb+Pb collisions at $\sqrt{s_{\rm{NN}}}$=2.76 and 5.02 TeV with the ATLAS detector, The ATLAS collaboration, ATLAS-CONF-2017-003, (External full text link).
[ATLAS], [Article]
MPP-2017-20 Measurement of jet fragmentation in 5.02 TeV proton-lead and proton-proton collisions with the ATLAS detector, The ATLAS collaboration, ATLAS-CONF-2017-004, (External full text link).
[ATLAS], [Article] | 2017-11-18 10:13:32 | {"extraction_info": {"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, "math_score": 0.28904998302459717, "perplexity": 2497.270762146649}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934804724.3/warc/CC-MAIN-20171118094746-20171118114746-00646.warc.gz"} |
http://www.mathnet.ru/php/archive.phtml?jrnid=im&wshow=issue&year=1959&volume=23&volume_alt=&issue=4&issue_alt=&option_lang=eng | RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB
General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS
Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find
Regular products of modelsA. I. Mal'tsev 489 On null Dirichlet $L$-seriesS. M. Rozin 503 On semi-normed rings with involutionT.-sh. Hsia 509 A theorem on universal coefficients for homology groups of chain complexes without torsionM. F. Bokshtein 529 On properties of sequences of linear aggregates of Jacobi polynomials and their application to the question of the completeness of the system of Jacobi polynomialsA. F. Leont'ev 565 Approximation by entire functions on the exterior of an interval and on a semi-axisYu. A. Brudnyi 595 Contiguity spaces and bicompact extensions of topological spacesV. M. Ivanova, A. A. Ivanov 613 Construction of sequences jointly normal with a given one (erratum)L. P. Starchenko 635 | 2019-10-23 11:28:15 | {"extraction_info": {"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, "math_score": 0.21761454641819, "perplexity": 5507.482796823463}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987833089.90/warc/CC-MAIN-20191023094558-20191023122058-00422.warc.gz"} |
https://stats.stackexchange.com/questions/383355/binary-loss-function | # Binary Loss Function
Currently I am working on Lasso Logistic Regression and in the book by Bulhmann et.al (2011) page 48, it is claimed that the binary loss classification function is given by,
$$\rho(f,y) = log (1+exp(-(-2y-1)f))$$
where $$p(x) = (1+e^-2f)^-1$$
Anyone has managed to solve this because I am not able to solve it, I have tried substituting in
$$y'log(p(x))+(1-y')log(1-p(x)))$$
where $$y'=(y+1)/2$$
• What is the relationship between p(x) and the rho-function. Also what does superscript - mean? Cant find the reference either by googling. – Jesper for President Dec 17 '18 at 10:19
• @JesperHybel the link for the (springer.com/gp/book/9783642201912) for the above mentioned link. So p(x) is the binomial distribution and pho is the loss function for the negative log-likelihood. – Annalise Azzopardi Dec 17 '18 at 18:36 | 2021-05-16 09:12:51 | {"extraction_info": {"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": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8411540389060974, "perplexity": 700.5948399862921}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243992516.56/warc/CC-MAIN-20210516075201-20210516105201-00238.warc.gz"} |
https://physics.stackexchange.com/questions/381153/why-dimensional-analysis-is-never-off-by-more-that-2-pi-pm1 | Why dimensional analysis is never off by more that $(2\pi)^{(\pm1)}$?
I've been reading about dimensions analysis and at one point it mentions that there could be constants that dimensional analysis fails to define and dimensional analysis is never off by more that $(2\pi)^{\pm1}$? why the factor $(2\pi)^{\pm1}$? how does this come about?
because people are saying this is untrue I thought I should link the resource: what I'm reading is here: http://www.physics.drexel.edu/~bob/Chapters/dimensional3.pdf
1 line above example 1b
• This is not true. Your source is probably writing about a specific problem/topic. – valerio Jan 20 '18 at 14:54
• That's totally wrong! You should throw that book in the trash. – knzhou Jan 20 '18 at 14:57
• Factor $2\pi$ is a difference between linear and angular frequency. Or between wavelength and inverse of wavenumber. Maybe thats where this came from. But yes, the statement is too bold. – A.V.S. Jan 20 '18 at 15:02
• The quote is specific to that example, where it's using a pendulum - which relates to the linear vs. angular frequency thing. But note that dimensional analysis normally just tells you dimensions and you're guessing the form based on that. The errors can be arbitrarily large in doing that if you guess the form completely wrong, even if your guess has the right dimensions. – StephenG Jan 20 '18 at 15:16
Counterexample: what is the surface area of a sphere? Dimensional analysis says $r^2$, which is off by $4\pi$.
• I thought dimensional analysis says it goes like $d^2$, which is only off by $\pi$. – JEB Jan 20 '18 at 18:35 | 2019-10-17 00:50:42 | {"extraction_info": {"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, "math_score": 0.6299334168434143, "perplexity": 460.10167612730555}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986672431.45/warc/CC-MAIN-20191016235542-20191017023042-00043.warc.gz"} |
http://mathinsight.org/applet/rotating_sphere_backward_curl | # Math Insight
### Applet: Sphere rotating in opposite direction of macroscopic circulation
When the center of the sphere is fixed, it rotates in a clockwise direction when viewed from the positive $z$-axis, corresponding to a downward pointing curl (green arrow). On the other hand, the counterclockwise macroscopic circulation of the vector field around the $z$-axis is evident from the graph. This example illustrates that one cannot infer curl from the macroscopic circulation of the vector field. Macroscopic and microscopic circulation can be very different. First panel shows the full vector field; second panel shows its projection in the $xy$-plane.
This vector field is $$\dlvf(x,y,z) = \frac{(-y,x,0)}{(x^2+y^2)^{3/2}}$$ for $(x,y) \ne (0,0)$. One can compute that away from the $z$-axis, $$\curl \dlvf(x,y,z) = \frac{(0,0,-1)}{(x^2+y^2)^{3/2}}.$$
The vector field and its curl blow up near the $z$-axis (the vector field arrows would get much longer if we plotted then closer to the $z$-axis). Hence, the sphere spins faster and the curl vector grows longer, the closer you move the sphere to the $z$-axis. | 2017-01-22 14:12:37 | {"extraction_info": {"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, "math_score": 0.8795126080513, "perplexity": 341.102194761411}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281426.63/warc/CC-MAIN-20170116095121-00540-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://www.math.gatech.edu/node/16984 | ## KP hierarchy for the cyclic quiver
Series:
Analysis Seminar
Wednesday, April 9, 2014 - 14:00
1 hour (actually 50 minutes)
Location:
Skiles 005
,
University of Leeds
Organizer:
I will discuss a generalization of the KP hierarchy, which is intimately related to the cyclic quiver and the Calogero-Moser problem for the wreath-product $S_n\wr\mathbb Z/m\mathbb Z$. | 2018-02-18 01:39:08 | {"extraction_info": {"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, "math_score": 0.41299712657928467, "perplexity": 2176.066418496779}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891811243.29/warc/CC-MAIN-20180218003946-20180218023946-00636.warc.gz"} |
https://nforum.ncatlab.org/discussion/3167/ | # Start a new discussion
## Not signed in
Want to take part in these discussions? Sign in if you have an account, or apply for one below
## Discussion Tag Cloud
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeSep 22nd 2011
• (edited Jul 17th 2013)
I have split off spin^c from spin^c structure
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJul 17th 2013
• (edited Jul 17th 2013)
in the section As the homotopy fiber of smooth W3 I have added some more comments and a proposition to make more explicit why the “determinant line” map is given on the canonical $U(1)$-components by multiplication by 2.
• Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
• To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.
• (Help) | 2019-08-24 23:02:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "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, "math_score": 0.889194667339325, "perplexity": 6292.7230072631055}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027321786.95/warc/CC-MAIN-20190824214845-20190825000845-00488.warc.gz"} |
http://www.tug.org/twg/mfg/mail-html/1993-08/msg00204.html | # just another symbol: opm and omp needed?
• To: math-font-discuss@cogs.susx.ac.uk
• Subject: just another symbol: opm and omp needed?
• From: vieth@convex.rz.uni-duesseldorf.de (Ulrik Vieth)
• Date: Wed, 18 Aug 93 12:25:16 +0200
Hello,
Here are some other symbol I once needed: \opm, \omp. Why?
There is \oplus and \ominus and there is +, -, \pm and \mp,
but there's no \opm and \omp.
I once needed them in a context, where \oplus and \ominus were
used as subscripts to indicate symmetric and antisymmetric wave
functions that were normalized. It is easy to specificy formulas
that include both cases using \pm and \mp, but suddenly there
was no \opm and \omp. I constructed symbols using the circle from
the copyright sign, but that was not actually the perfect size.
Does anybody else need these symbols? Judging as an ignorant user,
who never actually designed characters with METAFONT, these symbols
should not be too difficult to make, since all that's needed is
the circle from \oplus and the \pm or \mp in the middle.
But I might be wrong about that ...
Perhaps it would have been better to use encircled + and - instead
of \opm and \omp in that case since \oplus and \ominus weren't use
as binary operators anyway.
Greetings,
Ulrik Vieth. | 2018-06-21 23:54:27 | {"extraction_info": {"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, "math_score": 0.8763698935508728, "perplexity": 8790.262619493256}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864303.32/warc/CC-MAIN-20180621231116-20180622011116-00403.warc.gz"} |
https://www.semanticscholar.org/paper/The-number-of-faces-of-centrally-symmetric-Kalai/7f7cd981fa76a8e90c6057e198d0c0eebd905b7c | # The number of faces of centrally-symmetric polytopes
@article{Kalai1989TheNO,
title={The number of faces of centrally-symmetric polytopes},
author={Gil Kalai},
journal={Graphs and Combinatorics},
year={1989},
volume={5},
pages={389-391}
}
• G. Kalai
• Published 1 December 1989
• Mathematics, Computer Science
• Graphs and Combinatorics
34 Citations
• 2004
s, 22nd Symposium on Fusion Technology, Helsinki, Finland, September 2002, 183 (2002) Darbos. C, et al., Alberti S., Tran M.Q., “Very Long Pulse Operation of the TORE Supra ECRH System“, Book ofExpand
Face Numbers of Centrally Symmetric Polytopes Produced from Split Graphs
• Mathematics, Computer Science
• Electron. J. Comb.
• 2013
This study produces a new family of Hansen polytopes that have only $3^d+16$ nonempty faces, and confirms Kalai's $3D$ conjecture for such poly topes and shows that the Hannerpolytopes among them correspond to threshold graphs. Expand
Polytopal balls arising in optimization
• Mathematics
• 2020
We study a family of polytopes and their duals, that appear in various optimization problems as the unit balls for certain norms. These two families interpolate between the hypercube, the unit ballExpand
15 BASIC PROPERTIES OF CONVEX POLYTOPES
Convex polytopes are fundamental geometric objects that have been investigated since antiquity. The beauty of their theory is nowadays complemented by their importance for many other mathematicalExpand
Constructions and obstructions for extremal polytopes
In the fall of 2001, I was finishing my computer science undergrad studies and Martin Skutella suggested that I take the course " Linear optimization " , a course offered to beginning math gradExpand
Nonexpansive maps with surjective displacement
We investigate necessary and sufficient conditions for a nonexpansive map f on a Banach space X to have surjective displacement, that is, for f − id to map onto X. In particular, we give a computableExpand
Isocanted alcoved polytopes
• Mathematics
• 2020
Through tropical normal idempotent matrices, we introduce isocanted alcoved polytopes, computing their $f$--vectors and checking the validity of the following five conjectures: Barany, unimodality,Expand
A Tale of Centrally Symmetric Polytopes and Spheres
• I. Novik
• Mathematics
• Association for Women in Mathematics Series
• 2019
This paper is a survey of recent advances as well as open problems in the study of face numbers of centrally symmetric simplicial polytopes and spheres. The topics discussed range from neighborlinessExpand
Enumeration of 2-level polytopes
• Mathematics, Computer Science
• Math. Program. Comput.
• 2019
This paper presents the first algorithm for enumerating all combinatorial types of 2-level polytopes of a given dimension d, and provides complete experimental results for d⩽7. Expand
#### References
SHOWING 1-8 OF 8 REFERENCES
On the number of faces of centrally-symmetric simplicial polytopes
• R. Stanley
• Mathematics, Computer Science
• Graphs Comb.
• 1987
The conjectures of Björner are proved and generalizes the result of Bárány-Lovász sincefd−1 =∑ hi, and more strongly that h_i - h_{i - 1} \geqslant \left( {\begin{array}{*{20}c} d \\ i \\ \end{array} } \right) . Expand
Une Caracterisation Volumique de Certains Espaces Normes de Dimension Finie
We give a geometric characterization of finite dimensional normed spacesE, with a 1-unconditional basis, such that their volumetric product is minimal.
Borsuk's theorem and the number of facets of centrally symmetric polytopes
• Mathematics
• 1982
Let C"={x~R": Ix~]<-i i=1 , . . . ,n} be the n-dimensional cube and A be a d-dimensional subspace of R" having no point in common with the ( n d 1 ) dimensional faces of C". We want to find a lowerExpand
The structure of finite dimensional Banach spaces with the 3.2. Intersection property
• Mathematics
• 1981
Let X be a Banach space over the real numbers. Let n and k be integers with 2 ~< k < n. We say tha t X has the n.k. intersection property (n.k.I.P.) if the following holds: Any n balls in X intersectExpand
The dimension of almost spherical sections of convex bodies
• Mathematics
• 1977
© Séminaire analyse fonctionnelle (dit "Maurey-Schwartz") (École Polytechnique), 1975-1976, tous droits réservés. L’accès aux archives du séminaire d’analyse fonctionnelle implique l’accord avec lesExpand | 2021-11-27 00:38:45 | {"extraction_info": {"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": 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, "math_score": 0.8612056374549866, "perplexity": 4112.765007161119}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358074.14/warc/CC-MAIN-20211126224056-20211127014056-00179.warc.gz"} |
https://intelligencemission.com/free-unlimited-electricity-free-energy-symbol.html | The internet is the only reason large corps. cant buy up everything they can get their hands on to stop what’s happening today. @Free Power E. Lassek Bedini has done that many times and continues to build new and better motors. All you have to do is research and understand electronics to understand it. There is Free Power lot of fraud out there but you can get through it by research. With Free Power years in electronics I can see through the BS and see what really works. Build the SG and see for yourself the working model.. A audio transformer Free Power:Free Power ratio has enough windings. Free Power transistor, diode and resistor is all the electronics you need. A Free Energy with magnets attached from Free Electricity″ to however big you want is the last piece. What? Maybe Free Electricity pieces all together? Bedini built one with Free Power Free energy ′ Free Energy and magnets for Free Power convention with hands on from the audience and total explanations to the scientific community. That t is not fraud Harvey1 And why should anyone send you Free Power working motor when you are probably quite able to build one yourself. Or maybe not? Bedini has sent his working models to conventions and let people actually touch them and explained everything to the audience. You obviously haven’t done enough research or understand electronics enough to realize these models actually work.. The SC motor generator is easily duplicated. You can find Free Power:Free Power audio transformers that work quite well for the motor if you look for them and are fortunate enough to find one along with Free Power transistor, diode and resistor and Free Power Free Energy with magnets on it.. There is Free Power lot of fraud but you can actually build the simplest motor with Free Power Free Electricity″ coil of magnet wire with ends sticking out and one side of the ends bared to the couple and Free Power couple paperclips to hold it up and Free Power battery attached to paperclips and Free Power magnet under it.
Meadow’s told Free Power Free Energy’s Free Energy MaCallum Tuesday, “the Free energy people, they want to bring some closure, not just Free Power few sound bites, here or there, so we’re going to be having Free Power hearing this week, not only covering over some of those Free energy pages that you’re talking about, but hearing directly from three whistleblowers that have actually spent the majority of the last two years investigating this. ”
If, in fact, this hearing reveals anything serious like the long-suspected ‘pay-to-play’ strategy of the Free Electricity Foundation–which allegedly sought large donations in return for favors from the Free Electricity-run State Department–then Free Electricity will be in big trouble. The very fact that this hearing is going forward in the manner it is seems to give credence to the idea that the Deep State has just about lost its long-held power to protect its own.
During the early 19th century, the concept of perceptible or free caloric began to be referred to as “free heat” or heat set free. In 1824, for example, the Free Electricity physicist Sadi Carnot, in his famous “Reflections on the Motive Power of Fire”, speaks of quantities of heat ‘absorbed or set free’ in different transformations. In 1882, the Free Energy physicist and physiologist Hermann von Helmholtz coined the phrase ‘free energy ’ for the expression E − TS, in which the change in F (or G) determines the amount of energy ‘free’ for work under the given conditions, specifically constant temperature. [Free Electricity]:Free Power.
How do you gather and retrain the RA? Simple, purchase the biggest Bridge Rectifier (Free Power Free Electricity X Free Electricity Amps.) Connect wires to all four connections, place alligator clips on the other ends (Free Power Free Power!) Connect the ~ connections to the power input at the motor and close as possible. Connect the + cable to the Positive Battery Terminal, the – to the same terminal on the battery. Connect the battery Alligator Clip AFTER the Motor is running full on. That’s it! A moving magnetic field crossing Free Power conductor produces Free Power potential which produces Free Power current that can be used to power Free Power mechanical device. Yes, we often use Free Power prime mover of Free Power traditional form such as steam from fossil fuels or nuclear fission or Free Power prime mover such as wind or water flow but why not use Free Power more efficient means. Take Free Power coil of wire wrapped around Free Power flux conductor such as iron but that is broken into two pieces (such as Free Power U-shaped transformer core closed by Free Power second bar type core) charge the coil for Free Power moment then attempt to pull the to iron cores apart. You will find this takes Free Power lot of your elbow grease (energy) to accomplish this. This is due to the breaking of the flux circuit within the iron core. An example of energy store as magnetic flux. Isn’t this what Free Power permanent magnet is? Transfering one form of energy to another.
I looked at what you have for your motor so far and it’s going to be big. Here is my e-mail if you want to send those diagrams, if you know how to do it. [email protected] My name is Free energy MacInnes from Orangeville, On. In regards to perpetual motion energy it already has been proven that (The 2nd law of thermodynamics) which was written by Free Power in 1670 is in fact incorrect as inertia and friction (the two constants affecting surplus energy) are no longer unchangeable rendering the 2nd law obsolete. A secret you need to know is that by reducing input requirements, friction and resistance momentum can be transformed into surplus energy ! Gravity is cancelled out at higher rotation levels and momentum becomes stored energy. The reduction of input requirements is the secret not reveled here but soon will be presented to the world as Free Power free electron generator…electrons are the most plentiful source of energy as they are in all matter. Magnetism and electricity are one and the same and it took Free energy years of research to reach Free Power working design…Canada will lead the world in this new advent of re-engineering engineering methodology…. I really cant see how 12v would make more heat thatn Free Electricity, Free energy or whatever BUT from memeory (I havnt done Free Power fisher and paykel smart drive conversion for about 12months) I think smart drive PMA’s are Free Electricity phase and each circuit can be wired for 12Free Power Therefore you could have all in paralell for 12Free Power Free Electricity in series and then 1in parallel to those Free Electricity for 24Free Power Or Free Electricity in series for 36Free Power Thats on the one single PMA. Free Power, Ya that was me but it was’nt so much the cheep part as it was trying to find Free Power good plan for 48v and i havn’t found anything yet. I e-mailed WindBlue about it and they said it would be very hard to achieve with thiers.
You have proven to everyone here that can read that anything you say just does not matter. After avoiding my direct questions, your tactics of avoiding any real answers are obvious to anyone who reads my questions and your avoidance in response. Not once have you addressed anything that I’ve challenged you on. You have the same old act to follow time after time and you insult everyone here by thinking that even the hard core free energy believers fall for it. Telling everyone that all motors are magnetic when everyone else but you knows that they really mean Free Power permanent magnet motor that requires no external power source. Free Power you really think you’ve pointed out anything? We can see you are just avoiding the real subject and perhaps trying to show off. You are just way off the subject and apparently too stupid to even realize it.
If Free Power reaction is not at equilibrium, it will move spontaneously towards equilibrium, because this allows it to reach Free Power lower-energy , more stable state. This may mean Free Power net movement in the forward direction, converting reactants to products, or in the reverse direction, turning products back into reactants. As the reaction moves towards equilibrium (as the concentrations of products and reactants get closer to the equilibrium ratio), the free energy of the system gets lower and lower. A reaction that is at equilibrium can no longer do any work, because the free energy of the system is as low as possible^Free Electricity. Any change that moves the system away from equilibrium (for instance, adding or removing reactants or products so that the equilibrium ratio is no longer fulfilled) increases the system’s free energy and requires work. Example of how Free Power cell can keep reactions out of equilibrium. The cell expends energy to import the starting molecule of the pathway, A, and export the end product of the pathway, D, using ATP-powered transmembrane transport proteins.
You did not even appear to read or understand my response in the least. I’ve told you several times that I NEVER EXPECTED ANYONE TO SEND ME ONE. You cannot seem to get this. Try to understand this: I HAD TO MAKE UP A DEFINITION CALLED A MAGICAL MAGNETIC MOTOR BECAUSE YOU WOULD NITPICK THE TERM “MAGNETIC MOTOR” BY SAYING THAT ALL MOTORS ARE MAGNETIC. Are you so delusional that you cannot understand what I am saying? Are you too intellectually challenged to understand? Are you knowingly changing the subject again to avoid answering me? Since I have made it painfully clear what I am saying, you have no choice but to stop answering me – just like the rest of the delusional or dishonest believers. In my opinion, your unethical and disingenuous tactics do not make Free Power good case for over unity. You think distracting the sheeple will get them to follow your delusional inventions? Maybe you can scam them out of their money like Free Electricity Free Electricity, the self-proclaimed developer of the Perendev “magnet motor”, who was arrested in kimseymd1Harvey1You need not reply anymore.
One of the reasons it is difficult to prosecute criminals in the system is that it is so deep, complicated, and Free Power lot of disinformation and obfuscation are put out. The idea of elite pedophile rings are still labelled as “conspiracy theories” by establishment media like the Free Energy Free Electricity Times and CNN, who have also been accused of participating in these types of activities. It seems nobody within this realm has Free Power clean sheet, or at least if you’ve done the research it’s very rare. President Trump himself has had suits filed against him for the supposed rape of teenage girls. It is only in working to separate fact from fiction, and actually be willing to look into these matters and consider the possibilities that these crimes are occurring on Free Power massive scale, that we will help to expose what is really going on.
Of course that Free Power such motor (like the one described by you) would not spin at all and is Free Power stupid ideea. The working examples (at least some of them) are working on another principle/phenomenon. They don’t use the attraction and repeling forces of the magnets as all of us know. I repeat: that is Free Power stupid ideea. The magnets whou repel each other would loose their strength in time, anyway. The ideea is that in some configuration of the magnets Free Power scalar energy vortex is created with the role to draw energy from the Ether and this vortex is repsonsible for the extra energy or movement of the rotor. There are scalar energy detectors that can prove that this is happening. You can’t detect scalar energy with conventional tools. The vortex si an ubiquitos thing in nature. But you don’t know that because you are living in an urbanized society and you are lacking the direct interaction with the natural phenomena. Most of the time people like you have no oportunity to observe the Nature all the day and are relying on one of two major fairy-tales to explain this world: religion or mainstream science. The magnetism is more than the attraction and repelling forces. If you would have studied some books related to magnetism (who don’t even talk about free-energy or magnetic motors) you would have known by now that magnetism is such Free Power complex thing and has Free Power lot of application in Free Power wide range of domains.
Take Free Power sheet of plastic that measures Free Power″ x Free Power″ x Free Electricity″ thick and cut Free Power perfect circle measuring Free energy ″ in diameter from the center of it. (You’ll need the Free Electricity″ of extra plastic from the outside later on, so don’t damage it too much. You can make Free Power single cut from the “top” of the sheet to start your cut for the “Free Energy” using Free Power heavy duty jig or saber saw.) Using extreme care, drill the placement holes for the magnets in the edge of the Free Energy, Free Power Free Power/Free Electricity″ diameter, Free Power Free Power/Free Electricity″ deep. Free Energy’t go any deeper, you’ll need to be sure the magnets don’t drop in too far. These holes need to be drill at Free Power Free energy. Free Power degree angle, Free Power trick to do unless you have Free Power large drill press with Free Power swivel head on it.
A very simple understanding of how magnets work would clearly convince the average person that magnetic motors can’t (and don’t work). Pray tell where does the energy come from? The classic response is magnetic energy from when they were made. Or perhaps the magnets tap into zero point energy with the right configuration. What about they harness the earth’s gravitational field. Then there is “science doesn’t know all the answers” and “the laws of physics are outdated”. The list goes on with equally implausible rubbish. When I first heard about magnetic motors of this type I scoffed at the idea. But the more I thought about it the more it made sense and the more I researched it. Using simple plans I found online I built Free Power small (Free Electricity inch diameter) model using regular magnets I had around the shop.
Clausius’s law is overridden by Guth’s law, like 0 J, kg = +n J, kg + −n J, kg, the same cause of the big bang/Hubble flow/inflation and NASA BPP’s diametric drive. There mass and vis are created and destroyed at the same time. The Einstein field equation dictates that Free Power near-flat univers has similar amounts of positive and negative matter; therefore Free Power set of conjugate masses accelerates indefinitely in runaway motion and scales celerity arbitrarily. Free Electricity’s law is overridden by Poincaré’s law, where the microstates at finite temperature are finite so must recur in finite time, or exhibit ergodicity; therefore the finite information and transitions impose Free Power nonMaxwellian population always in nonequilibrium, like in condensed matter’s geometric frustration (“spin ice”), topological conduction (“persistent current” and graphene superconductivity), and in Graeff’s first gravity machine (“Loschmidt’s paradox” and Loschmidt’s refutation of Free Power’s equilibrium in the lapse rate).
The only reason i am looking into this is because Free Power battery company here told me to only build Free Power 48v system because the Free Electricity & 24v systems generate to much heat and power loss. Can i wire Free Power, 12v pma’s or Free Electricity, 24v pma’s together in sieres to add up to 48v? If so i do not know how to do it and will that take care of the heat problem? I am about to just forget it and just build Free Power 12v system. Its not like im going to power my house, just my green house during the winter. Free Electricity, if you do not have wind all the time it will be hard to make anything cheep work. Your wind would have to be pretty constant to keep your voltage from dropping to low, other than that you will need your turbin, rectifire, charge controler, 12v deep cycle battery or two 6v batteries wired together to make one big 12v batt and then Free Power small inverter to change the power from dc to ac to run your battery charger. Thats alot of money verses the amount it puts on your power bill just to charge two AA batteries. Also, you can drive Free Power small dc motor with Free Power fan and produce currently easily. It would just take some rpm experimentation wilth different motor sizes. Kids toys and old VHS video recorders have heaps of dc motors.
The magnitude of G tells us that we don’t have quite as far to go to reach equilibrium. The points at which the straight line in the above figure cross the horizontal and versus axes of this diagram are particularly important. The straight line crosses the vertical axis when the reaction quotient for the system is equal to Free Power. This point therefore describes the standard-state conditions, and the value of G at this point is equal to the standard-state free energy of reaction, Go. The key to understanding the relationship between Go and K is recognizing that the magnitude of Go tells us how far the standard-state is from equilibrium. The smaller the value of Go, the closer the standard-state is to equilibrium. The larger the value of Go, the further the reaction has to go to reach equilibrium. The relationship between Go and the equilibrium constant for Free Power chemical reaction is illustrated by the data in the table below. As the tube is cooled, and the entropy term becomes less important, the net effect is Free Power shift in the equilibrium toward the right. The figure below shows what happens to the intensity of the brown color when Free Power sealed tube containing NO2 gas is immersed in liquid nitrogen. There is Free Power drastic decrease in the amount of NO2 in the tube as it is cooled to -196oC. Free energy is the idea that Free Power low-cost power source can be found that requires little to no input to generate Free Power significant amount of electricity. Such devices can be divided into two basic categories: “over-unity” devices that generate more energy than is provided in fuel to the device, and ambient energy devices that try to extract energy from Free Energy, such as quantum foam in the case of zero-point energy devices. Not all “free energy ” Free Energy are necessarily bunk, and not to be confused with Free Power. There certainly is cheap-ass energy to be had in Free Energy that may be harvested at either zero cost or sustain us for long amounts of time. Solar power is the most obvious form of this energy , providing light for life and heat for weather patterns and convection currents that can be harnessed through wind farms or hydroelectric turbines. In Free Electricity Nokia announced they expect to be able to gather up to Free Electricity milliwatts of power from ambient radio sources such as broadcast TV and cellular networks, enough to slowly recharge Free Power typical mobile phone in standby mode. [Free Electricity] This may be viewed not so much as free energy , but energy that someone else paid for. Similarly, cogeneration of electricity is widely used: the capturing of erstwhile wasted heat to generate electricity. It is important to note that as of today there are no scientifically accepted means of extracting energy from the Casimir effect which demonstrates force but not work. Most such devices are generally found to be unworkable. Of the latter type there are devices that depend on ambient radio waves or subtle geological movements which provide enough energy for extremely low-power applications such as RFID or passive surveillance. [Free Electricity] Free Power’s Demon — Free Power thought experiment raised by Free Energy Clerk Free Power in which Free Power Demon guards Free Power hole in Free Power diaphragm between two containers of gas. Whenever Free Power molecule passes through the hole, the Demon either allows it to pass or blocks the hole depending on its speed. It does so in such Free Power way that hot molecules accumulate on one side and cold molecules on the other. The Demon would decrease the entropy of the system while expending virtually no energy. This would only work if the Demon was not subject to the same laws as the rest of the universe or had Free Power lower temperature than either of the containers. Any real-world implementation of the Demon would be subject to thermal fluctuations, which would cause it to make errors (letting cold molecules to enter the hot container and Free Power versa) and prevent it from decreasing the entropy of the system. In chemistry, Free Power spontaneous processes is one that occurs without the addition of external energy. A spontaneous process may take place quickly or slowly, because spontaneity is not related to kinetics or reaction rate. A classic example is the process of carbon in the form of Free Power diamond turning into graphite, which can be written as the following reaction: Great! So all we have to do is measure the entropy change of the whole universe, right? Unfortunately, using the second law in the above form can be somewhat cumbersome in practice. After all, most of the time chemists are primarily interested in changes within our system, which might be Free Power chemical reaction in Free Power beaker. Free Power we really have to investigate the whole universe, too? (Not that chemists are lazy or anything, but how would we even do that?) When using Free Power free energy to determine the spontaneity of Free Power process, we are only concerned with changes in \text GG, rather than its absolute value. The change in Free Power free energy for Free Power process is thus written as \Delta \text GΔG, which is the difference between \text G_{\text{final}}Gfinal, the Free Power free energy of the products, and \text{G}{\text{initial}}Ginitial, the Free Power free energy of the reactants.
Take Free Power sheet of plastic that measures Free Power″ x Free Power″ x Free Electricity″ thick and cut Free Power perfect circle measuring Free energy ″ in diameter from the center of it. (You’ll need the Free Electricity″ of extra plastic from the outside later on, so don’t damage it too much. You can make Free Power single cut from the “top” of the sheet to start your cut for the “Free Energy” using Free Power heavy duty jig or saber saw.) Using extreme care, drill the placement holes for the magnets in the edge of the Free Energy, Free Power Free Power/Free Electricity″ diameter, Free Power Free Power/Free Electricity″ deep. Free Energy’t go any deeper, you’ll need to be sure the magnets don’t drop in too far. These holes need to be drill at Free Power Free energy. Free Power degree angle, Free Power trick to do unless you have Free Power large drill press with Free Power swivel head on it.
It’s called the reaction– less generator, he also referred to it as the Space Powered Generator. It allows for the production of power with improved efficiency. A prototype has been tested, repeated, and the concept proven in India, as shown above. It’s the answer to cheap electricity anywhere, and it meets to green standard of no fossil fuel usage or Free Energy.
Historically, the term ‘free energy ’ has been used for either quantity. In physics, free energy most often refers to the Helmholtz free energy , denoted by A or F, while in chemistry, free energy most often refers to the Free Power free energy. The values of the two free energies are usually quite similar and the intended free energy function is often implicit in manuscripts and presentations. | 2020-08-10 02:40:37 | {"extraction_info": {"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, "math_score": 0.4708268940448761, "perplexity": 1399.4582082924858}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738603.37/warc/CC-MAIN-20200810012015-20200810042015-00467.warc.gz"} |
https://math.stackexchange.com/questions/852771/element-of-a-singleton-set-with-one-element-notation | # Element of a Singleton (set with one element) notation
I was wondering what the notations are for indicating the element of a singleton (or unit set, or set with cardinality 1). This would be the inverse of set construction:
$$X = \{y\} \tag{1}$$ $$y = \text{? } X \text{ ?} \tag{2}$$
I haven't seen examples of it, but I think using a notation like $X_1$ or $X_0$ is misleading. The general case of $X$ may not even be countable, even though it is obviously countable when $|X|=1$. For example, if $M$ is a set of sets of real numbers:
$$\forall X \in M \,:\,|X|=1 \Rightarrow P(X_0) \tag{3}$$
This seems like a possibility but since all of the $X$ aren't countable it looks misleading.
I found this post that used a notation $$y = \iota X \tag{4}$$
Linguistically it seems similar to the English article "the". I would probably read the above as "y equals the X".
I don't know how commonly used or recognized that notation is. Are there any other notations, possibly more common?
• I don't know of a standard convention, but if it's established that $\lvert X \rvert = 1$, then $y \in X$ is pretty unambiguous. – MartianInvader Jul 1 '14 at 0:01
• I would be careful using notation like $\iota X$ for some kind of definite description. In older works, and in a small corner of modern works, $\iota X$ is just a different notation for $\{X\}$. And if you were using an upright iota for definite descriptions, $\iota X$ is an incomplete fragment of that notation. – Malice Vidrine Jul 1 '14 at 0:16
• It might help to think of the singleton $X$ containing only the element $y$ as being the set such that $\forall a:[a\in X \iff a=y]$. Then, of course, $y\in X$ by the reflexive property of equality. – Dan Christensen Jul 1 '14 at 4:18
• A proposal: Use inverted braces to "unpack" $y$, like so: $\ y=\}X\{\$. – Christian Blatter Jul 1 '14 at 10:00
• @ChristianBlatter Heh that would really make parsing a nightmare. Also I prefer not to introduce new notations, just to build upon what exists. Andreas is about what I would prefer, something simple and obvious like $\text{The}(X)$ – DanielV Jul 1 '14 at 10:07
As Asaf said, in contexts (like ZFC) where everything is a set, you can use $\bigcup X$. Unfortnately, I'd expect that only set theorists will recognize what you're doing without further explanation. I've used the notation $\text{TheUnique}(X)$, but that was in a paper close to computer science, where multi-letter symbols like that are fairly common.
• Sounds a bit too Lord of the Rings for my taste for a notation. – Patrick Da Silva Jul 1 '14 at 1:16
• @Patrick: It's truly a difference in generations. I would think more about Highlander "There can be only one". But I am willing to bet that Andreas hasn't seen either. – Asaf Karagila Jul 1 '14 at 1:39
• @Asaf Well, I once began reading The Lord of The Rings, but never finished even the first volume. This was around 1977, and I remember none of it. – Andreas Blass Jul 1 '14 at 1:46
• But you do know they made a trilogy of movies out of the book, right? – Asaf Karagila Jul 1 '14 at 1:50
• I'm pretty sure Peter Jackson didn't get too far with the books either; that or he really didn't like them. – DanielV Jul 1 '14 at 11:06
If you want to be strict with set theoretic context, then $y=\bigcup\{y\}=\bigcup X$. But this might not work very well outside of set theoretic contexts.
In the case that $X$ is a subset of an ordered set, then $y=\min X=\max X$ as well. There's probably no good, and general notation for this. But I honestly don't see why we would need one.
• Isn't the union of sets also a set? – DanielV Jun 30 '14 at 23:51
• Yes, but what is not a set (and is an element of another set)? :-) – Asaf Karagila Jun 30 '14 at 23:51
I wandered here off the street looking for this answer, and from my further searching, this is the best I've got. The uniqueness quantification is a fairly concise way to show it's a unitary set.
The left hand side might need to be wrapped in an existential quantification. Please edit as necessary; I'm only an engineer, not a mathematician.
$$x = ValueOf(X) \Longleftrightarrow \exists! x : x \in X$$
• I think that as an engineer you should know not to name things "Value Of"...and there really is no advantage of using $\exists !~ x : x \in X$ over just $X = \{x\}$. Also notice that $x$ is bound in the quantifier on the right but onbound on the left, so they can't be referring to the same thing, so it isn't quite right. Thanks for the interest but I think this is not a good direction. – DanielV Jun 7 '18 at 1:31
• My backup plan was closer to.... $$\exists (x = ValueOf(X)) \Longleftrightarrow \exists! x : x \in X$$ but that notation is really dirty – durette Jun 7 '18 at 2:26
• In the relational algebra used to describe databases, it's not uncommon to see $R=\{r\}$ with the understanding that $r$ means every $r$. It's sometimes not very rigorous. The answer to the question above will help me write clearly about an idea... – durette Jun 7 '18 at 4:23 | 2019-07-16 14:01:34 | {"extraction_info": {"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, "math_score": 0.7569277882575989, "perplexity": 609.202006803169}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195524568.14/warc/CC-MAIN-20190716135748-20190716161748-00429.warc.gz"} |
https://blog.appsignal.com/2019/07/09/productive-procrastination-for-programmers.html | appsignal
# Productive Procrastination for Programmers - works for Ruby and Elixir
Stefan Verkerk on
This is a partly-ironic, not-so-serious post on productivity, but increased productivity might actually result from reading it. It is all about the sweetness of procrastination, of pushing away that task you dread, the proverbial frog you need to eat. Take it with a grain of salt.
The reason Productive Procrastination is a superpower is because it allows you to procrastinate, without the guilt associated with it because while you were procrastinating, you were still being productive! At least in the way we define it:
Productive procrastination is delaying your number one priority, but doing some other slightly less important but productive task instead. When done right you haven't actually procrastinated, but you do feel like you did.
It is basically chocolate stroopwafels that make you more fit. With vitamins, to boot.
And now, without further ado, here are our top 5 productive procrastinations.
## 1. Upgrade AppSignal Gem to Get Magic Dashboards
This sounds like self-promotion, but it is not is really how the idea for this blogpost started:
• The catch is that you get a doggy treat (automagically appearing dashboard for things you have in your stack like Sidekiq (or Delayed Job or Resque) or PostgreSQL. Or a zillion more.
• The required 'work' is to do something relatively straightforward, in your comfort zone, yet not too boring (because of the doggy snack). You need to upgrade the AppSignal gem, which is the perfect task for something like this, in our opinion. All it takes is running this:
bundle update appsignal
It may also require you to remove a version lock from the Gemfile, e.g. gem "appsignal", "2.9.2". With a locked version, you can run bundle update appsignal all you want, but it won't upgrade.
For Elixir apps, upgrade by running:
mix deps.update appsignal
## 2. Learn Your Favorite App's Keyboards Shortcuts
Learn the keyboard shortcuts of your most-used apps. Shave off those seconds using the mouse and race through your work.
Here are some general shortcuts that work in most apps:
Basics like how to switch a tab in (almost) every app (browsers, Finder.app, file editors, etc):
• left: cmd + {
• right: cmd + }
Go back and forward in history (the arrows next to the address bar):
• back: cmd + [
• forward: cmd + ]
Switch to a tab using a number in apps with tabs (browsers, iTerm.app, Terminal.app, Finder.app, etc.):
• cmd + 1 switches to tab number 1
• cmd + 2 to tab 2
• cmd + 9 to the last tab regardless of how many tabs there are.
• cmd + l to open the address bar in a browser.
If you want to go further, here's a post on application switching by Tom.
## 3. Tweak Your Mac with Some Terminal Stuff
One of our favorites: Increase the speed of the dock animation!
defaults write com.apple.dock autohide-time-modifier -float 0.25;killall Dock
Or speed up the window animations.
defaults write -g NSWindowResizeTime -float 0.003
Imagine how much time you will save your future self! (Psst, this may be zero, but let's keep the delusion optimism, for now).
## 4. Scan Some Receipts, but Not All of Them. Then Compare Scanning Apps.
Scan just last year's. Here’s another mind trick we play on ourselves: we tell ourselves we don’t have to do something (not all receipts) when in reality we are actually finishing all the 2018 administration. And we put the dangerous procrastination (comparing productivity tools) at the end of the list. Which means we probably won’t get to that. Haha.
## 5. Clean up Your Mac, but Not Completely
One of our favorites as well. Don’t put a lot of thought into it, don’t prepare, just start somewhere, finish that first thing and before you get to finish the second part, when you feel like having a coffee, declare that that subtask is done. Basically, we are playing the same mind trick as in #4. I think you are getting the hang of it.
## 6. Make Sure You Don't Get Paged When on Holiday
Set up a few Anomaly Detection triggers so that bells will go off before sh*t hits the fan. And you can safely be away on holiday with others on Pager Duty. Start with a simple one, like when you hit 90% disk usage on a host:
Here’s how you do that in AppSignal: go to the Triggers screen, add a trigger, and three clicks later you’re done.
Boom. You’ve earned another coffee.
## 7. Read That One (Ruby Magic?) Post, but Only One! The One You Tagged as ‘Read Later’
The one about that thing. That you know will come in handy later in the year when stuff breaks. Or Enumerables? How escaping works in Ruby?
## 8. Don’t Write That One Blogpost, Write the Other One!
Add stuff here. Not done ;-)
## Not Done, but Did It!
See what we did? Maybe we didn't write that blog post we were supposed to. But instead, we wrote this blog post. Which may get people to upgrade their AppSignal gem. This will give them access to features that will make them love AppSignal even more. And helping developers by giving them amazing insights is what we are here for, so we actually made progress towards our vision.
We hope you found this post entertaining and hopefully, productive as well. If you did, then the post has accomplished its goal.
Wait! You said: "here are our top 5 productive procrastinations". And then you wrote 8? (Yes, see how effective the technique is? We were very productive while productively procrastinating, and hopefully, the extra points will help you productively procrastinate as well!)
# Stefan Verkerk
Stefan often shares stories about his Mosaic script-kiddie years. Has been scaling startups since the 90s. Today, he does management and growth things at AppSignal. Has amazing Excel to SQL chops on his customized MacBook.
-> All articles by Stefan Verkerk-> Become an AppSignal author | 2022-11-26 22:52:14 | {"extraction_info": {"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, "math_score": 0.3232191503047943, "perplexity": 4916.864790004174}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446709929.63/warc/CC-MAIN-20221126212945-20221127002945-00831.warc.gz"} |
https://robotology.github.io/robotology-documentation/doc/html/classiCub_1_1iDyn_1_1RigidBodyTransformation.html | iCub-main
iCub::iDyn::RigidBodyTransformation Class Reference
A class for setting a rigid body transformation between iDynLimb and iDynNode. More...
#include <iDynBody.h>
## Public Member Functions
RigidBodyTransformation (iDyn::iDynLimb *_limb, const yarp::sig::Matrix &_H, const std::string &_info, bool _hasSensor=false, const FlowType kin=RBT_NODE_OUT, const FlowType wre=RBT_NODE_IN, const NewEulMode _mode=DYNAMIC, unsigned int verb=iCub::skinDynLib::VERBOSE)
Constructor, defining the limb attached to the node. More...
~RigidBodyTransformation ()
Destructor. More...
bool setRBT (const yarp::sig::Matrix &_H)
Set the roto-translational matrix between the limb and the node, defining the rigid body transformation. More...
bool setKinematic (const yarp::sig::Vector &w0, const yarp::sig::Vector &dw0, const yarp::sig::Vector &ddp0)
Set the kinematic variables (w,dw,ddp) of the limb. More...
bool setKinematicMeasure (const yarp::sig::Vector &w0, const yarp::sig::Vector &dw0, const yarp::sig::Vector &ddp0)
Set the kinematic variables (w,dw,ddp) of the limb, coming from external measurements (ie a sensor). More...
bool setWrench (const yarp::sig::Vector &F0, const yarp::sig::Vector &Mu0)
Set the wrench variables (F,Mu) of the limb. More...
bool setWrenchMeasure (const yarp::sig::Vector &F0, const yarp::sig::Vector &Mu0)
Set the wrench variables (F,Mu) of the limb. More...
bool setWrenchMeasure (iDyn::iDynSensor *sensor, const yarp::sig::Vector &Fsens, const yarp::sig::Vector &Musens)
Set the wrench variables in the sensor. More...
yarp::sig::Matrix getRBT () const
Return the the (4x4) roto-translational matrix defining the rigid body transformation. More...
void getKinematic (yarp::sig::Vector &wNode, yarp::sig::Vector &dwNode, yarp::sig::Vector &ddpNode)
Get the kinematic variables (w,dw,ddp) of the limb, applies the RBT transformation and compute the kinematic variables of the node. More...
void getWrench (yarp::sig::Vector &FNode, yarp::sig::Vector &MuNode)
Get the wrench variables (F,Mu) of the limb, transform it according to the RBT and add it to the node wrench. More...
void setInfoFlow (const FlowType kin, const FlowType wre)
Set the flow of kinematic/wrench information: input to node or output from node. More...
FlowType getKinematicFlow () const
Return the kinematic flow type. More...
FlowType getWrenchFlow () const
return the wrench flow type More...
std::string toString () const
Return some information. More...
bool isSensorized () const
Return a boolean, depending if the limb attached to the RBT has a FT sensor or not. More...
void computeLimbKinematic ()
Calls the compute kinematic of the limb. More...
void computeLimbWrench ()
Calls the compute wrench of the limb. More...
Return the number of links of the limb (N) More...
unsigned int getDOF () const
Return the number of DOF of the limb (DOF <= N) More...
yarp::sig::Matrix getH (const unsigned int i, const bool allLink=false)
Return the i-th roto-translational matrix of the chain. More...
yarp::sig::Matrix getH ()
Return the end-effector roto-translational matrix of the end-effector H of the end-effector. More...
yarp::sig::Vector getEndEffPose (const bool axisRep=true)
Return the end-effector pose: x-y-z Cartesian position and 3/4 angles of orientation. More...
yarp::sig::Matrix computeGeoJacobian (const unsigned int iLink, const yarp::sig::Matrix &Pn, bool rbtRoto=false)
This method is used to compute the Jacobian between two links in two different chains (eg from link 4 in chain_A to link 3 in chain_B. More...
yarp::sig::Matrix computeGeoJacobian (const unsigned int iLink, const yarp::sig::Matrix &Pn, const yarp::sig::Matrix &H0, bool rbtRoto=false)
This method is used to compute the Jacobian between two links in two different chains. More...
yarp::sig::Matrix computeGeoJacobian (const yarp::sig::Matrix &Pn, bool rbtRoto=false)
This method is used to compute the Jacobian between two links in two different chains: in this case it returns the jacobian matrix of the whole chain (from base to end-effector) when Pn is an external vector. More...
yarp::sig::Matrix computeGeoJacobian (const yarp::sig::Matrix &Pn, const yarp::sig::Matrix &H0, bool rbtRoto=false)
This method is used to compute the Jacobian between two links in two different chains: in this case it returns the jacobian matrix of the whole chain (from base to end-effector) when Pn is an external vector, and H0 is an external matrix. More...
yarp::sig::Matrix computeGeoJacobian (bool rbtRoto=false)
yarp::sig::Matrix computeGeoJacobian (const unsigned int iLink, bool rbtRoto=false)
Returns the Jacobian matrix of the limb until the link whose index is iLink in the chain. More...
yarp::sig::Matrix getR6 () const
Return a 6x6 diagonal matrix with the rotational matrix of the RBT. More...
yarp::sig::Matrix getH0 () const
Return the H0 matrix of the limb attached to the RBT. More...
bool setH0 (const yarp::sig::Matrix &_H0)
Set a new H0 matrix in the limb attached to the RBT. More...
yarp::sig::Matrix TESTING_computeCOMJacobian (const unsigned int iLink, bool rbtRoto=false)
Returns the Jacobian matrix of the COM of the selected link (index = iLink) in the chain. More...
yarp::sig::Matrix TESTING_computeCOMJacobian (const unsigned int iLink, const yarp::sig::Matrix &Pn, bool rbtRoto=false)
Returns the Jacobian matrix of the COM of the selected link (index = iLink) in the chain: in this case Pn is an external vector, that happens when multiple limbs are connected. More...
yarp::sig::Matrix TESTING_computeCOMJacobian (const unsigned int iLink, const yarp::sig::Matrix &Pn, const yarp::sig::Matrix &_H0, bool rbtRoto=false)
Returns the Jacobian matrix of the COM of the selected link (index = iLink) in the chain: in this case Pn is an external vector, that happens when multiple limbs are connected. More...
Returns the COM matrix of the selected link (index = iLink) in the chain. More...
## Protected Member Functions
yarp::sig::Matrix getR ()
Return the rotational 3x3 matrix of the RBT. More...
yarp::sig::Vector getr (bool proj=false)
Return the translational part of the RBT matrix. More...
void computeKinematic ()
Basic computations for applying RBT on kinematic variables. More...
void computeWrench ()
Basic computations for applying RBT on wrench variables. More...
## Protected Attributes
iDyn::iDynLimblimb
the limb attached to the RigidBodyTransformation More...
FlowType kinFlow
kinematic flow: in-to/out-from node (RBT_NODE_IN/RBT_NODE_OUT) More...
FlowType wreFlow
wrench flow: in-to/out-from node (RBT_NODE_IN/RBT_NODE_OUT) More...
yarp::sig::Matrix H
the roto-translation between the limb and the node More...
NewEulMode mode
STATIC/DYNAMIC/DYNAMIC_W_ROTOR/DYNAMIC_CORIOLIS_GRAVITY. More...
std::string info
info or useful notes More...
unsigned int verbose
verbosity flag More...
bool hasSensor
flag for sensor or not - only used for setWrenchMeasures() More...
yarp::sig::Vector w
angular velocity More...
yarp::sig::Vector dw
angular acceleration More...
yarp::sig::Vector ddp
linear acceleration More...
yarp::sig::Vector F
force More...
yarp::sig::Vector Mu
moment More...
## Detailed Description
A class for setting a rigid body transformation between iDynLimb and iDynNode.
This class is used by iDynNode to connect two or mutiple limbs and exchanging kinematic and wrench information between limbs.
Definition at line 131 of file iDynBody.h.
## ◆ RigidBodyTransformation()
RigidBodyTransformation::RigidBodyTransformation ( iDyn::iDynLimb * _limb, const yarp::sig::Matrix & _H, const std::string & _info, bool _hasSensor = false, const FlowType kin = RBT_NODE_OUT, const FlowType wre = RBT_NODE_IN, const NewEulMode _mode = DYNAMIC, unsigned int verb = iCub::skinDynLib::VERBOSE )
Constructor, defining the limb attached to the node.
Parameters
_limb pointer to a iDynLimb _H a (4x4) roto-translational matrix defining the rigid body transformation _info a string with information kin the kinematic flow wre the wrench flow _mode the NewEulMode for computations verb verbosity flag
Definition at line 44 of file iDynBody.cpp.
## ◆ ~RigidBodyTransformation()
RigidBodyTransformation::~RigidBodyTransformation ( )
Destructor.
Definition at line 61 of file iDynBody.cpp.
## ◆ computeGeoJacobian() [1/6]
Matrix RigidBodyTransformation::computeGeoJacobian ( bool rbtRoto = false )
Parameters
rbtRoto if false, simply return Jacobian; if true return T * Jacobian, where T is a 6x6 diagonal matrix with the rotational part of the RBT
Returns
the Jacobian matrix of the chain
Definition at line 345 of file iDynBody.cpp.
## ◆ computeGeoJacobian() [2/6]
Matrix RigidBodyTransformation::computeGeoJacobian ( const unsigned int iLink, bool rbtRoto = false )
Returns the Jacobian matrix of the limb until the link whose index is iLink in the chain.
This method basically calls GeoJacobian(iLink) in the iDynChain of the limb.
Parameters
iLink the index of the link, in the chain rbtRoto if false, simply return Jacobian; if true return T * Jacobian, where T is a 6x6 diagonal matrix with the rotational part of the RBT
Returns
the Jacobian matrix of the chain - from the base to the i-th link
Definition at line 353 of file iDynBody.cpp.
## ◆ computeGeoJacobian() [3/6]
yarp::sig::Matrix iCub::iDyn::RigidBodyTransformation::computeGeoJacobian ( const unsigned int iLink, const yarp::sig::Matrix & Pn, bool rbtRoto = false )
This method is used to compute the Jacobian between two links in two different chains (eg from link 4 in chain_A to link 3 in chain_B.
Parameters
iLink the index of the link, in the chain, being the base frame for the Jacobian computation Pn the matrix describing the roto-translational matrix between base and end-effector (in two different limbs) rbtRoto if false, simply return Jacobian; if true return T * Jacobian, where T is a 6x6 diagonal matrix with the rotational part of the RBT
Returns
the Jacobian matrix from the base of the chain until the iLink (e.g. from link 0 to 4)
## ◆ computeGeoJacobian() [4/6]
yarp::sig::Matrix iCub::iDyn::RigidBodyTransformation::computeGeoJacobian ( const unsigned int iLink, const yarp::sig::Matrix & Pn, const yarp::sig::Matrix & H0, bool rbtRoto = false )
This method is used to compute the Jacobian between two links in two different chains.
Parameters
iLink the index of the link, in the chain, being the base frame for the Jacobian computation Pn the matrix describing the roto-translational matrix between base and end-effector (in two different limbs) H0 the H0 matrix of the base to be used for the Jacobian computation rbtRoto if false, simply return Jacobian; if true return T * Jacobian, where T is a 6x6 diagonal matrix with the rotational part of the RBT
Returns
the Jacobian matrix from the iLink of the chain until the base of the chain (ie from link 4 to 0)
## ◆ computeGeoJacobian() [5/6]
yarp::sig::Matrix iCub::iDyn::RigidBodyTransformation::computeGeoJacobian ( const yarp::sig::Matrix & Pn, bool rbtRoto = false )
This method is used to compute the Jacobian between two links in two different chains: in this case it returns the jacobian matrix of the whole chain (from base to end-effector) when Pn is an external vector.
Parameters
Pn the matrix describing the roto-translational matrix between base and end-effector (in two different limbs) rbtRoto if false, simply return Jacobian; if true return T * Jacobian, where T is a 6x6 diagonal matrix with the rotational part of the RBT
Returns
the Jacobian matrix of the chain
## ◆ computeGeoJacobian() [6/6]
yarp::sig::Matrix iCub::iDyn::RigidBodyTransformation::computeGeoJacobian ( const yarp::sig::Matrix & Pn, const yarp::sig::Matrix & H0, bool rbtRoto = false )
This method is used to compute the Jacobian between two links in two different chains: in this case it returns the jacobian matrix of the whole chain (from base to end-effector) when Pn is an external vector, and H0 is an external matrix.
Parameters
Pn the matrix describing the roto-translational matrix between base and end-effector (in two different limbs) H0 the H0 matrix of the base to be used for the Jacobian computation rbtRoto if false, simply return Jacobian; if true return T * Jacobian, where T is a 6x6 diagonal matrix with the rotational part of the RBT
Returns
the Jacobian matrix of the chain
## ◆ computeKinematic()
void RigidBodyTransformation::computeKinematic ( )
protected
Basic computations for applying RBT on kinematic variables.
The computations are similar to the Forward/Backward ones in OneLinkNewtonEuler: compute AngVel/AngAcc/LinAcc. Here they are fastened and adapted to the RBT.
Definition at line 195 of file iDynBody.cpp.
## ◆ computeLimbKinematic()
void RigidBodyTransformation::computeLimbKinematic ( )
Calls the compute kinematic of the limb.
Definition at line 278 of file iDynBody.cpp.
## ◆ computeLimbWrench()
void RigidBodyTransformation::computeLimbWrench ( )
Calls the compute wrench of the limb.
Definition at line 283 of file iDynBody.cpp.
## ◆ computeWrench()
void RigidBodyTransformation::computeWrench ( )
protected
Basic computations for applying RBT on wrench variables.
The computations are similar to the Forward/Backward ones in OneLinkNewtonEuler: compute Force/Moment. Here they are fastened and adapted to the RBT.
Definition at line 246 of file iDynBody.cpp.
## ◆ getDOF()
unsigned int RigidBodyTransformation::getDOF ( ) const
Return the number of DOF of the limb (DOF <= N)
Returns
the number of DOF in the limb
Definition at line 293 of file iDynBody.cpp.
## ◆ getEndEffPose()
Vector RigidBodyTransformation::getEndEffPose ( const bool axisRep = true )
Return the end-effector pose: x-y-z Cartesian position and 3/4 angles of orientation.
Parameters
axisRep a flag for the axis representation
Returns
the end effector pose
Definition at line 308 of file iDynBody.cpp.
## ◆ getH() [1/2]
Matrix RigidBodyTransformation::getH ( )
Return the end-effector roto-translational matrix of the end-effector H of the end-effector.
Definition at line 303 of file iDynBody.cpp.
## ◆ getH() [2/2]
Matrix RigidBodyTransformation::getH ( const unsigned int i, const bool allLink = false )
Return the i-th roto-translational matrix of the chain.
This method basically calls iKinChain::getH(i,allLink). the boolean allLink specifies if all the links are considered, or only the unblocked ones (DOF)
Parameters
i the link index in the chain (0<=i
Returns
Definition at line 298 of file iDynBody.cpp.
## ◆ getH0()
Matrix RigidBodyTransformation::getH0 ( ) const
Return the H0 matrix of the limb attached to the RBT.
Returns
the H0 matrix of the limb attached to the RBT
Definition at line 361 of file iDynBody.cpp.
## ◆ getHCOM()
Matrix RigidBodyTransformation::getHCOM ( unsigned int iLink )
Returns the COM matrix of the selected link (index = iLink) in the chain.
Parameters
Returns
the roto-translational matrix of the selected link COM
Definition at line 401 of file iDynBody.cpp.
## ◆ getKinematic()
void RigidBodyTransformation::getKinematic ( yarp::sig::Vector & wNode, yarp::sig::Vector & dwNode, yarp::sig::Vector & ddpNode )
Get the kinematic variables (w,dw,ddp) of the limb, applies the RBT transformation and compute the kinematic variables of the node.
The variables are stored into the param vectors, which are accessible. This method calls getKinematicNewtonEuler() in the limb, and the limb itself knows whether to get this information in the base or in the end- effector, depending on its iteration mode for kinematics. This method is used by iDynNode to connect two or multiple limbs.
Parameters
wNode the angular velocity of the Node - it is modified! dwNode the angular acceleration of the Node - it is modified! ddpNode the linear acceleration of the Node - it is modified!
Definition at line 152 of file iDynBody.cpp.
## ◆ getKinematicFlow()
FlowType RigidBodyTransformation::getKinematicFlow ( ) const
Return the kinematic flow type.
Returns
the kinematic flow
Definition at line 185 of file iDynBody.cpp.
unsigned int RigidBodyTransformation::getNLinks ( ) const
Return the number of links of the limb (N)
Returns
the number of links in the limb
Definition at line 288 of file iDynBody.cpp.
## ◆ getR()
Matrix RigidBodyTransformation::getR ( )
protected
Return the rotational 3x3 matrix of the RBT.
Returns
the rotational matrix of the RBT
Definition at line 126 of file iDynBody.cpp.
## ◆ getr()
Vector RigidBodyTransformation::getr ( bool proj = false )
protected
Return the translational part of the RBT matrix.
Parameters
proj=true/false
Returns
the distance vector of the RBT
Definition at line 145 of file iDynBody.cpp.
## ◆ getR6()
Matrix RigidBodyTransformation::getR6 ( ) const
Return a 6x6 diagonal matrix with the rotational matrix of the RBT.
Returns
a 6x6 diagonal matrix with the rotational matrix of the RBT
Definition at line 131 of file iDynBody.cpp.
## ◆ getRBT()
Matrix RigidBodyTransformation::getRBT ( ) const
Return the the (4x4) roto-translational matrix defining the rigid body transformation.
Returns
H, the 4x4 matrix of the RBT
Definition at line 121 of file iDynBody.cpp.
## ◆ getWrench()
void RigidBodyTransformation::getWrench ( yarp::sig::Vector & FNode, yarp::sig::Vector & MuNode )
Get the wrench variables (F,Mu) of the limb, transform it according to the RBT and add it to the node wrench.
The variables are stored into the param vectors, which are accessible. This method calls getWrenchNewtonEuler() in the limb, and the limb itself knows whether to get this information in the base ot in the end-effector, depending on its iteration mode for wrenches. This method is used by iDynNode to connect two or multiple limbs.
Parameters
FNode the iDynNode force - it is modified! MuNode the iDynNode moment - it is modified!
Definition at line 166 of file iDynBody.cpp.
## ◆ getWrenchFlow()
FlowType RigidBodyTransformation::getWrenchFlow ( ) const
return the wrench flow type
Returns
the wrench flow
Definition at line 190 of file iDynBody.cpp.
## ◆ isSensorized()
bool RigidBodyTransformation::isSensorized ( ) const
Return a boolean, depending if the limb attached to the RBT has a FT sensor or not.
Returns
true if the limb has a FT sensor, false otherwise
Definition at line 273 of file iDynBody.cpp.
## ◆ setH0()
bool RigidBodyTransformation::setH0 ( const yarp::sig::Matrix & _H0 )
Set a new H0 matrix in the limb attached to the RBT.
Parameters
_H0 the new H0 matrix of the limb attached to the RBT
Returns
true if succeed, false otherwise
Definition at line 366 of file iDynBody.cpp.
## ◆ setInfoFlow()
void RigidBodyTransformation::setInfoFlow ( const FlowType kin, const FlowType wre )
Set the flow of kinematic/wrench information: input to node or output from node.
Parameters
kin the kinematic flow wre the wrench flow
Definition at line 179 of file iDynBody.cpp.
## ◆ setKinematic()
bool RigidBodyTransformation::setKinematic ( const yarp::sig::Vector & w0, const yarp::sig::Vector & dw0, const yarp::sig::Vector & ddp0 )
Set the kinematic variables (w,dw,ddp) of the limb.
This method calls initKinematicNewtonEuler() in the limb, and the limb itself knows whether to set this information in the base or in the end- effector, depending on its iteration mode for kinematics. This method is used by iDynNode to connect two or multiple limbs.
Parameters
w0 the angular velocity dw0 the angular acceleration ddp0 the linear acceleration
Returns
true if succeeds, false otherwise
Definition at line 83 of file iDynBody.cpp.
## ◆ setKinematicMeasure()
bool RigidBodyTransformation::setKinematicMeasure ( const yarp::sig::Vector & w0, const yarp::sig::Vector & dw0, const yarp::sig::Vector & ddp0 )
Set the kinematic variables (w,dw,ddp) of the limb, coming from external measurements (ie a sensor).
This method calls initKinematicNewtonEuler() in the limb, and the limb itself knows whether to set this information in the base or in the end- effector, depending on its iteration mode for kinematics. This method is used by iDynNode to connect two or multiple limbs.
Parameters
w0 the angular velocity dw0 the angular acceleration ddp0 the linear acceleration
Returns
true if succeeds, false otherwise
Definition at line 95 of file iDynBody.cpp.
## ◆ setRBT()
bool RigidBodyTransformation::setRBT ( const yarp::sig::Matrix & _H )
Set the roto-translational matrix between the limb and the node, defining the rigid body transformation.
Parameters
_H a (4x4) roto-translational matrix
Returns
true if succeeds, false otherwise
Definition at line 67 of file iDynBody.cpp.
## ◆ setWrench()
bool RigidBodyTransformation::setWrench ( const yarp::sig::Vector & F0, const yarp::sig::Vector & Mu0 )
Set the wrench variables (F,Mu) of the limb.
This method calls initWrenchNewtonEuler() in the limb, and the limb itself knows whether to set this information in the base ot in the end-effector, depending on its iteration mode for wrenches. This method is used by iDynNode to connect two or multiple limbs.
Parameters
F0 the force Mu0 the moment
Returns
true if succeeds, false otherwise
Definition at line 100 of file iDynBody.cpp.
## ◆ setWrenchMeasure() [1/2]
bool iCub::iDyn::RigidBodyTransformation::setWrenchMeasure ( const yarp::sig::Vector & F0, const yarp::sig::Vector & Mu0 )
Set the wrench variables (F,Mu) of the limb.
This method calls initWrenchNewtonEuler() in the limb, and the limb itself knows whether to set this information in the base ot in the end-effector, depending on its iteration mode for wrenches. This method is used by iDynNode to connect two or multiple limbs.
Parameters
F0 the force Mu0 the moment
Returns
true if succeeds, false otherwise
## ◆ setWrenchMeasure() [2/2]
bool iCub::iDyn::RigidBodyTransformation::setWrenchMeasure ( iDyn::iDynSensor * sensor, const yarp::sig::Vector & Fsens, const yarp::sig::Vector & Musens )
Set the wrench variables in the sensor.
Parameters
sensor the sensor attached to the limb Fsens the force Musens the moment
Returns
true if succeeds, false otherwise
## ◆ TESTING_computeCOMJacobian() [1/3]
Matrix RigidBodyTransformation::TESTING_computeCOMJacobian ( const unsigned int iLink, bool rbtRoto = false )
Returns the Jacobian matrix of the COM of the selected link (index = iLink) in the chain.
Parameters
iLink the index of the link, in the chain rbtRoto if false, simply return Jacobian; if true return T * Jacobian, where T is a 6x6 diagonal matrix with the rotational part of the RBT
Returns
the Jacobian matrix of the selected link COM
Definition at line 377 of file iDynBody.cpp.
## ◆ TESTING_computeCOMJacobian() [2/3]
yarp::sig::Matrix iCub::iDyn::RigidBodyTransformation::TESTING_computeCOMJacobian ( const unsigned int iLink, const yarp::sig::Matrix & Pn, bool rbtRoto = false )
Returns the Jacobian matrix of the COM of the selected link (index = iLink) in the chain: in this case Pn is an external vector, that happens when multiple limbs are connected.
Parameters
Pn the matrix describing the roto-translational matrix between base and end-effector (in two different limbs) iLink the index of the link, in the chain rbtRoto if false, simply return Jacobian; if true return T * Jacobian, where T is a 6x6 diagonal matrix with the rotational part of the RBT
Returns
the Jacobian matrix of the selected link COM
## ◆ TESTING_computeCOMJacobian() [3/3]
yarp::sig::Matrix iCub::iDyn::RigidBodyTransformation::TESTING_computeCOMJacobian ( const unsigned int iLink, const yarp::sig::Matrix & Pn, const yarp::sig::Matrix & _H0, bool rbtRoto = false )
Returns the Jacobian matrix of the COM of the selected link (index = iLink) in the chain: in this case Pn is an external vector, that happens when multiple limbs are connected.
The H0 matrix used to initialize the Jacobian computation is external too.
Parameters
Pn the matrix describing the roto-translational matrix between base and end-effector (in two different limbs) H0 the H0 matrix of the base to be used for the Jacobian computation iLink the index of the link, in the chain rbtRoto if false, simply return Jacobian; if true return T * Jacobian, where T is a 6x6 diagonal matrix with the rotational part of the RBT
Returns
the Jacobian matrix of the selected link COM
## ◆ toString()
std::string iCub::iDyn::RigidBodyTransformation::toString ( ) const
Return some information.
Returns
a string with information
## ◆ ddp
yarp::sig::Vector iCub::iDyn::RigidBodyTransformation::ddp
protected
linear acceleration
Definition at line 167 of file iDynBody.h.
## ◆ dw
yarp::sig::Vector iCub::iDyn::RigidBodyTransformation::dw
protected
angular acceleration
Definition at line 165 of file iDynBody.h.
## ◆ F
yarp::sig::Vector iCub::iDyn::RigidBodyTransformation::F
protected
force
Definition at line 169 of file iDynBody.h.
## ◆ H
yarp::sig::Matrix iCub::iDyn::RigidBodyTransformation::H
protected
the roto-translation between the limb and the node
Definition at line 145 of file iDynBody.h.
## ◆ hasSensor
bool iCub::iDyn::RigidBodyTransformation::hasSensor
protected
flag for sensor or not - only used for setWrenchMeasures()
Definition at line 157 of file iDynBody.h.
## ◆ info
std::string iCub::iDyn::RigidBodyTransformation::info
protected
info or useful notes
Definition at line 151 of file iDynBody.h.
## ◆ kinFlow
FlowType iCub::iDyn::RigidBodyTransformation::kinFlow
protected
kinematic flow: in-to/out-from node (RBT_NODE_IN/RBT_NODE_OUT)
Definition at line 139 of file iDynBody.h.
## ◆ limb
iDyn::iDynLimb* iCub::iDyn::RigidBodyTransformation::limb
protected
the limb attached to the RigidBodyTransformation
Definition at line 136 of file iDynBody.h.
## ◆ mode
NewEulMode iCub::iDyn::RigidBodyTransformation::mode
protected
STATIC/DYNAMIC/DYNAMIC_W_ROTOR/DYNAMIC_CORIOLIS_GRAVITY.
Definition at line 148 of file iDynBody.h.
## ◆ Mu
yarp::sig::Vector iCub::iDyn::RigidBodyTransformation::Mu
protected
moment
Definition at line 171 of file iDynBody.h.
## ◆ verbose
unsigned int iCub::iDyn::RigidBodyTransformation::verbose
protected
verbosity flag
Definition at line 154 of file iDynBody.h.
## ◆ w
yarp::sig::Vector iCub::iDyn::RigidBodyTransformation::w
protected
angular velocity
Definition at line 163 of file iDynBody.h.
## ◆ wreFlow
FlowType iCub::iDyn::RigidBodyTransformation::wreFlow
protected
wrench flow: in-to/out-from node (RBT_NODE_IN/RBT_NODE_OUT)
Definition at line 142 of file iDynBody.h.
The documentation for this class was generated from the following files: | 2022-12-09 13:03:08 | {"extraction_info": {"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, "math_score": 0.28220829367637634, "perplexity": 9869.723225792643}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711396.19/warc/CC-MAIN-20221209112528-20221209142528-00595.warc.gz"} |
http://www.linkhumanitair.org/67hh2uay/11e612-convergence-in-mean | Convergence generally means coming together, while divergence generally means moving apart. Mit Flexionstabellen der verschiedenen Fälle und Zeiten Aussprache und … Convergence definition, an act or instance of converging. Learn more. Also called convergent evolution. In particular, a sequence The internet and digital age have helped fuel this progress, turning a … Convergence definition is - the act of converging and especially moving toward union or uniformity; especially : coordinated movement of the two eyes so that the image of a single point is formed on corresponding retinal areas. One way to define the distance between $X_n$ and $X$ is, where $r \geq 1$ is a fixed number. Therefore, $X_n$ does not converge in the $r$th mean for any $r \geq 1$. Suppose that X1;X2;:::have flnite second moments. Example: Imagine a sequen… on the type of convergence. moments and all exist To show $X_n \ \xrightarrow{p}\ 0$, we can write, for any $\epsilon>0$ https://mathworld.wolfram.com/ConvergenceinMean.html. moments (Karr, 1993, p. 158, Exercise 5.6(a)) Prove that X n q:m:!X)E(X2 n) !E(X2) (Rohatgi, 1976, p. 248, proof of Theorem 8). System response (stress, deformation) will converge to a repeatable solution with decreasing element size. From MathWorld--A Wolfram Web Resource, created by Eric (Note: for convergence in mean, it is usually required that $E|X^{\large r}_n|) The most common choice is$r=2$, in which case it is called the mean-square convergence. How to use convergence in a sentence. Definition - What does Convergence mean? It essentially means that "eventually" a sequence of elements get closer and closer to a single value. X n converges to X in quadratic mean (also called convergence in L2), written X n q:m:! for some measure Convergence in Distribution p 72 Undergraduate version of central limit theorem: Theorem If X 1,...,X n are iid from a population with mean µ and standard deviation σ then n1/2(X¯ −µ)/σ has approximately a normal distribution. Media convergence transforms established industries, services, and work practices and enables entirely new forms of content to emerge. As we have discussed in the lecture entitled Sequences of random variables and their convergence, different concepts of convergence are based on different ways of measuring the distance between two random variables (how "close to each other" two random variables are).. jəns] (anthropology) Independent development of similarities between unrelated cultures. Convergence is the coming together of two different entities, and in the contexts of computing and technology, is the integration of two or more different technologies in a single device or system. converge definition: 1. This refers to convergence in mean. Convergence in probability of a sequence of random variables. If$ X_n \ \xrightarrow{L^{\large s}}\ X$, then$ X_n \ \xrightarrow{L^{\large r}}\ X. \end{align} Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Cesàro means are of particular importance in the study of function spaces. \ &=\infty \qquad (\textrm{sincer \geq 1}). Let be a random variable. Motivation • One of the key questions in statistical signal processing is how to estimate the statistics of a r.v., e.g., its mean, variance, distribution, etc. To compensate for the resulting "excess," vertical motion may result: upward forcing if convergence is at low levels, or downward forcing (subsidence) if convergence is at high levels. is said to converge in the th mean (or in the It erodes long-established media industry and content “silos” and increasingly uncouples content from particular devices, which in turn presents major challenges for public policy and regulation. However, we now prove that convergence in probability does imply convergence in distribution. We do not require that F n(c) converge to 1, since c is not a point of continuity in the limiting distribution function. This condition causes one eye to turn outward instead of inward with the other eye creating double or blurred vision.Convergence insufficiency is usually diagnosed in school-age children and adolescents. ; Nehmen Sie auf wie Sie in ganzen Sätzen 'convergence in mean' sagen, und beobachten Sie sich selbst und hören Sie zu. converge in mean if converges in -norm to a function Hints help you try the next step on your own. How to use convergence in a sentence. The concept of mean-square convergence, or convergence in mean-square, is based on the following intuition: two random variables are "close to each other" if the square of their difference is on average small. \lim_{n \rightarrow \infty} P\big(|X_n-X| \geq \epsilon \big)=0, \qquad \textrm{ for all }\epsilon>0. \end{align}. &= \frac{1}{(r+1) n^{\large r}} \rightarrow 0, \qquad \textrm{ for all }r\geq 1. Convergence in mean implies convergence in probability. Sometimes, however, convergence definition: 1. the fact that two or more things, ideas, etc.X_n$does not converge in the$r$th mean for any$r \geq 1$. From a practical standpoint, technological convergence encompasses two interdependent areas: technical design and functionality. Intuitively, X n is concentrating at 0 so we would like to say that X n !d 0. Convergence in distribution di ers from the other modes of convergence in that it is based not on a direct comparison of the random variables X n with Xbut rather on a comparision of the distributions PfX n 2Ag and PfX2Ag. Precise meaning of statements like “X and Y have approximately the By Chebysjev’s inequality we see that convergence in mean square implies convergence in probability. Since by assumption$\lim \limits_{n \rightarrow \infty} E\left(|X_n-X|^{\large r}\right)=0$, we conclude In functional analysis, "convergence in mean" is most often used as another name for strong Mit Flexionstabellen der verschiedenen Fälle und Zeiten Aussprache und … Convergence in mean: lt;p|>In |probability theory|, there exist several different notions of |convergence of random va... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled. The #1 tool for creating Demonstrations and anything technical. As we mentioned previously, convergence in probability is stronger than convergence in distribution. Consider a sequence of IID random variables, X n, n = 1, 2, 3, …, each with CDF F X n (x) = F X (x) = 1-Q (x-μ σ). value. What is convergence, in general. Theorem 0.2 (Vitali Theorem) Let f n be a sequence of non-negative integrable functions on E. Then Z E f n!0 as n!1if and only if f n!0 in measure and ff ngis uniformly integrable and tight over E. Theorem 0.3 (Fatou’s Lemma) Let f &= \lim_{n \rightarrow \infty} \frac{1}{n}\\ Brechen Sie 'convergence in mean' in Geräusche auf: Sagen Sie es laut und übertreiben Sie die Geräusche, bis Sie sie konsequent produzieren können. (Note: Some authors refer to the case$r=1as convergence in mean.). 7.10. Mean square convergence implies convergence in distribution If a sequence of random variables converges in mean square to a random variable, then also converges in distribution to. It is true that convergence in mean square does not imply convergence almost surely. The formal definition goes something like this: Given (infinite) sequence of real numbers X0, X1, X2, ... Xn ... we say Xn converges to a given number L if for every positive error that you think, there is a Xm such that every element Xn that comes after Xm differs from Lby less than that error. In these contexts, a sequence of random variables Cookies help us deliver our services. W. Weisstein. Its quite rare to actually come across a strictly converging model but convergence is commonly used in a similar manner as convexity is. Again, convergence in quadratic mean is a measure of consistency of any estimator. Learn more. 0 1 \end{align} Converge definition is - to tend or move toward one point or one another : come together : meet. (evolution) Development of similarities between animals or plants of different groups resulting from adaptation to similar habitats. Let be a sequence of random variables defined on a sample space. Consider a sequence\{X_n, n=1,2,3, \cdots \}$such that, The PDF of$X_nis given by ", This entry contributed by Christopher \begin{align}%\label{eq:union-bound} ideas in what follows are \convergence in probability" and \convergence in distribution." E\left(|X_n-0|^{\large r}\right)&=\int_{0}^{\frac{1}{n}} x^{\large r} n \hspace{10pt} dx\\ For example, if we define the distance betweenX_n$and$X$as$P\big(|X_n-X| \geq \epsilon \big)$, we have convergence in probability. and if, where denotes the expectation We have Analysis. 2.2 Convergence in mean square and in probability To verify convergence with probability one we x the outcome !and check whether the corresponding realizations of the random process converge deterministically. An alternative viewpoint is to x the indexing variable iand consider how close the random variable Xe(i) One way of interpreting the convergence of a sequence$X_n$to$X$is to say that the ''distance'' between$X$and$X_n$is getting smaller and smaller. 2 Mean Ergodic Theorem Although the definition of converge in mean square encompasses conver-gence to a random variable, in many applications we shall encounter con- The Solow model predicts unconditional convergence under certain special conditions. In functional analysis, "convergence in mean" is most often used as another name for strong convergence. Field indicates that more air is entering a given area than is leaving that... ' in LEOs Englisch ⇔ Deutsch Wörterbuch almost surely somewhat different convergence almost surely a., is a well defined mathematical term to mean something somewhat different Wolfram. '' is most often used as another name for strong convergence it is true that convergence in mean imply in... A futures contract toward the spot or cash price of a sequence of elements get closer and closer to repeatable... 0 ; 1=n ) global ) with a decreasing trend and closer a... Ganzen Sätzen 'convergence in mean. ) estão 3 dicas que devem ajudá-lo a aperfeiçoar sua pronúncia de... Other words in English definition and synonym dictionary from Reverso mean implies convergence 2nd! ) with a decreasing trend search convergence in distribution., the y... To the case$ r=1 $as convergence in distribution. \xrightarrow { L^ { \large }! N ( 0, \frac { 1 } { n } \right )$ n →d X imply n! R \geq 1 convergence in mean one of the two fundamental theorems of probability, is well... Together, while divergence generally means coming together, while divergence generally means coming together, while generally... Value the limit '' X and y have approximately the divergence vs. an. Another name for strong convergence is most often used as another name for strong convergence $as convergence L2... Converged system B. functional analysis variable has approximately an ( np, np ( −p. For creating Demonstrations and anything technical imply X n » n ( 0, \frac { 1 } n! Estão 3 dicas que devem ajudá-lo a aperfeiçoar sua pronúncia Englisch de in... And synonym dictionary from Reverso Nehmen Sie auf wie Sie in ganzen Sätzen 'convergence in mean to an whenever... Convergence an Overview condition in which your eyes are unable to work together convergence in mean looking nearby... Selbst und hören Sie zu in what follows are \convergence in distribution. in. Practical standpoint, technological convergence is the joining of several distinct technologies one. Distinct technologies into one limit '': come together: 2. the fact that two or things! Converges to X in quadratic mean implies convergence of 2nd lernen Sie die für... Enable different technologies to interoperate efficiently as a converged system { p } \ 0$, for any r. X n is concentrating at 0 so we would like to say that X! 0. Convexity is y = … ideas in what follows are \convergence in distribution. we see convergence! $as convergence in quadratic mean is a measure of consistency of any estimator probability! F n ( t ) definition and synonym dictionary from Reverso this definition is silent convergence! Closer to a repeatable solution with decreasing element size que devem ajudá-lo a aperfeiçoar sua pronúncia Englisch de 'convergence mean. The convergence of 2nd to X in quadratic mean can be given, again, convergence in mean sense... Response ( stress, deformation ) will converge to a repeatable solution with element! To mean something somewhat different, deformation ) will converge to a solution. Sequence of elements get closer and closer to a single set of accounting standards will. Of cookies 3 dicas que devem ajudá-lo a aperfeiçoar sua pronúncia Englisch de 'convergence in convergence in mean is! Again, by the sample mean. ) by Eric W. Weisstein end... Plants of different groups resulting from adaptation to similar habitats mean implies convergence of accounting standards refers to the of.: 2. the fact that… finance and trading, convergence in probability theory there... 1=N ) meaning of statements like “ X and y have approximately the divergence vs. convergence an Overview fact.. X! d c means that eventually '' a sequence of elements get closer and closer to repeatable! Entering a given area than is leaving at that level is entering given! Problems step-by-step from beginning to end is silent about convergence in the$ r $th mean for$... The term is also used in probability most often used as another name for strong convergence limit.! X_N $does not necessarily imply convergence almost surely: have flnite second moments random. Of other words in English definition and synonym dictionary from Reverso coming together, while divergence generally means apart! And synonym dictionary from Reverso what does convergence in quadratic mean implies convergence in mean square sense a. Approximately the divergence vs. convergence an Overview theory, there exist several different of! Convergence generally means moving apart )$ looking at nearby objects a convergence in mean when. X! d 0, see here. ) of cookies of converging convergence in quadratic mean a! Act or instance of converging quadratic mean and thousands of other words in English definition and synonym dictionary from.... F. and Szőkefalvi-Nagy, B. functional analysis, convergence in mean square unconditional convergence under certain special.. A sample space manner as convexity is, they move towards the same point where they join meet…! Standards that convergence in mean be used internationally to emerge Some authors refer to the goal of establishing single! Example, the function y = … ideas in what follows are in... Function y = … ideas in what follows are \convergence in distribution. Sie Übersetzung! The same point where they join or meet… means are of particular importance in the mean square implies in!: 1 have approximately the divergence vs. convergence an Overview often used as another name for strong convergence convergence. Convergence transforms established industries, services, you agree to our use of cookies follows are \convergence probability... The price of a sequence of elements get closer and closer to convergence in mean repeatable with! Over time we would like to say that X n is concentrating at 0 so we would like to that... … definition - what does convergence mean in L2 ), written X n →d X imply X »! Walk through homework problems step-by-step from beginning to end we would like to say that n. Demonstrations and anything technical that X1 ; X2 ;::: have flnite second moments, for any r... … on the type of convergence of 2nd sequence in a normed linear space converges in '! This usage, convergence in mean. ), while divergence generally means moving.... \Large r } } \ 0 $, for any$ r th... Paths Xn ( s ) authors refer to the goal of establishing a single set of accounting refers! Closer to a single set of accounting standards that will be used internationally built-in step-by-step solutions together... Of random variables defined on a sample space that describes the layers of abstraction that enable different to... Integrating against the th Fejer kernel similar or come together: meet }... Be given, again, convergence in mean imply convergence in the $r$ mean! Counterexample that convergence in probability does not necessarily imply convergence in probability '' and \convergence in does... In English definition and synonym dictionary from Reverso sagen, und beobachten Sie sich selbst und hören Sie.... Also Binomial ( n, p ) random variable has approximately an ( np, np ( 1 −p )... Lines, roads, or paths converge, they move towards the same where! Or line ; incline toward each other, as lines that are not.. Coming together, while divergence generally means coming together, while divergence generally means moving apart … -... Of particular importance in the study of function spaces air is entering a given than! ¡X ) 2 closer and closer to a single value entirely new forms of content to emerge normed... ( local or global ) with a decreasing trend several different notions convergence... Mean can be given, again, convergence in distribution. in LEOs Englisch ⇔ Deutsch Wörterbuch decreasing element.! \Geq 1 $and synonym dictionary from Reverso and anything technical ( local or global ) with a trend... To a repeatable solution with decreasing element size, is a term describes! Interdependent areas: technical design and functionality by using our services, you agree to use... And thousands of other words in English definition and synonym dictionary from.... Und Zeiten Aussprache und … definition - what does convergence in probability does imply convergence quadratic... To X in quadratic mean can be given, again, convergence mean. Divergence generally means coming together, while divergence generally means coming together, divergence. Technical design and functionality prove by counterexample that convergence in distribution. that ''! In quadratic mean can be given, again, convergence in quadratic mean can be given,,... Mean square implies convergence in probability does not necessarily imply convergence in mean sense... Content to emerge convergence almost surely mean. )! d c means ! Mean implies convergence of individual sample paths Xn ( s ) same point they. Means moving apart in a normed linear space converges in mean. ) standards refers to the case r=1! If, E ( X n →P X variable has approximately an np... It is true that convergence in mean '' is most often used as another for! Be used internationally th Fejer kernel devem ajudá-lo a aperfeiçoar sua pronúncia Englisch de 'convergence mean. 1 } { n } \right )$ inequality we see that convergence probability. Unable to work together when looking at nearby objects \$ does not imply convergence in mean sense. Special case is called convergence in probability theory, there exist several different notions of convergence in mean is! | 2022-05-18 15:21:55 | {"extraction_info": {"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": 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, "math_score": 0.8620783686637878, "perplexity": 1493.89817669985}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662522284.20/warc/CC-MAIN-20220518151003-20220518181003-00548.warc.gz"} |
https://mc-stan.org/docs/2_29/stan-users-guide/parentheses-and-brackets.html | This is an old version, view current version.
## 35.6 Parentheses and brackets
### Braces for single-statement blocks
Single-statement blocks can be rendered in several ways. The preferred style is fully bracketed with the statement appearing on its own line, as follows.
for (n in 1:N) {
y[n] ~ normal(mu,1);
}
The use of loops and conditionals without brackets can be dangerous. For instance, consider this program.
for (n in 1:N)
z[n] ~ normal(nu,1);
y[n] ~ normal(mu,1);
Because Stan ignores whitespace and the parser completes a statement as eagerly as possible (just as in C++), the previous program is equivalent to the following program.
for (n in 1:N) {
z[n] ~ normal(nu,1);
}
y[n] ~ normal(mu,1);
Therefore, one should prefer to use braces. The only exception is when nesting if-else clauses, where the else branch contains exactly one conditional. Then, it is preferred to place the following if on the same line, as in the following.
if (x) {
// ...
} else if (y) {
// ...
} else {
// ...
}
### Parentheses in nested operator expressions
The preferred style for operators minimizes parentheses. This reduces clutter in code that can actually make it harder to read expressions. For example, the expression a + b * c is preferred to the equivalent a + (b * c) or (a + (b * c)). The operator precedences and associativities follow those of pretty much every programming language including Fortran, C++, R, and Python; full details are provided in the reference manual.
Similarly, comparison operators can usually be written with minimal bracketing, with the form y[n] > 0 || x[n] != 0 preferred to the bracketed form (y[n] > 0) || (x[n] != 0).
### No open brackets on own line
Vertical space is valuable as it controls how much of a program you can see. The preferred Stan style is with the opening brace appearing at the end of a line.
for (n in 1:N) {
y[n] ~ normal(mu,1);
}
This also goes for parameters blocks, transformed data blocks, which should look as follows.
transformed parameters {
real sigma;
// ...
}
The exception to this rule is local blocks which only exist for scoping reasons. The opening brace of these blocks is not associated with any control flow or block structure, so it should appear on its own line. | 2022-08-11 23:11:11 | {"extraction_info": {"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, "math_score": 0.3514856696128845, "perplexity": 2336.2479110099707}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571536.89/warc/CC-MAIN-20220811224716-20220812014716-00473.warc.gz"} |
https://math.stackexchange.com/questions/783266/if-p-lor-q-p-lor-r-can-we-conclude-q-r-what-happens-if-we-use-an | # If $(P \lor Q) = (P \lor R)$ Can we conclude $Q = R$ ? What happens if we use AND instead of the operator OR?
So I am trying to solve this problem and not quite able to figure out the answer. So I'm not sure what two statements I could construct in my truth table to prove these true or false. I believe that $Q$ is not equal to $R$ because OR statements are inclusive. And I believe if we used the AND operators they would be equal. The statement I was thinking about constructing to prove this was if $R \land (P \lor Q) / Q \land (P \lor R)$? Any help would be appreciated
• Doesn't follow, whether you use And or Or. For the Or case, consider the truth-assignment $P \equiv R \equiv \top$ and $Q \equiv \bot$. For the second, consider $P \equiv Q \equiv \bot$ and $R \equiv \top$. May 6, 2014 at 8:42
• @HunanRostomyan You could post that as an answer. May 6, 2014 at 14:08
• Could we say that if we assume Q and R to both be true that when we put them into the "AND" statements it means that P would always have to be true therefore they are not equivalent? Then for the "OR" statements if we assume both Q and R are false then if (P OR Q) is going to be equal to (P OR R) P would always have to be false which we know is also not the case therefore both statements show that Q != R May 6, 2014 at 15:55
If P is true, both P OR Q and P OR R are both true regardless of what Q and R may be. Similarly for the AND case, both are false if P is false.
• @DougSpoonwood How does this contradict what I said? I showed cases where both can be equal without $Q=R$. Which happens to be what the question is about.
– Mike
May 6, 2014 at 16:20 | 2022-05-23 16:02:06 | {"extraction_info": {"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, "math_score": 0.5633374452590942, "perplexity": 226.45424634725453}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662558030.43/warc/CC-MAIN-20220523132100-20220523162100-00505.warc.gz"} |
https://www.physicsforums.com/threads/problem-understanding-relativistic-momentum.156474/ | # Problem understanding relativistic momentum
Many books teaching relativity at the introductory level,go on and say that relativistic momentum cant be described using p=mv
and p=m Dx/Dt(D is Delta)
also
it says the measure Dx is the same as measured by the both people.One who is measuring his own momentum and another who is measuring the moving person's(with respect to him) momentum.
I get confused.how can this be?
Hootenanny
Staff Emeritus
Gold Member
Many books teaching relativity at the introductory level,go on and say that relativistic momentum cant be described using p=mv
and p=m Dx/Dt(D is Delta)
also
it says the measure Dx is the same as measured by the both people.One who is measuring his own momentum and another who is measuring the moving person's(with respect to him) momentum.
I get confused.how can this be?
Perhaps it is meant to say something like the following;
"The above equations assume that the measure[ment] Dx is the same as measured by the both people.One who is measuring his own momentum and another who is measuring the moving person's(with respect to him) momentum."
Why shd they both be the same?As the person will refer to another thing to measure Dx.Like the length of road he covers.But the road will seem contracted to him isnt it?
May be quoting the text would help clear things up.
Hootenanny
Staff Emeritus
Gold Member
Why shd they both be the same?As the person will refer to another thing to measure Dx.Like the length of road he covers.But the road will seem contracted to him isnt it?
They are not the same in special relativity, the quantity dx will indeed be subject to length contraction as described by the lorentz transformations. However, the two equations you have quoted are the equations for classical momentum which are based on the Galilean transformations and hence dx is not subject to length contraction.
Heres the text quoted:
Consider a particle moving with a constant speed v in the positive x direction.Classically it has momentum=mv=mDx/Dt
in which Dx is the distance it travels in time Dt.To find a relativistic expression for momentum,we start with the new definition
p=mDx/Dt(o)
Here,as before Dx is the distance travelled by a moving particle as viewed by the observer watching that particle.However t(o) is the time required to travel that distance,measured by not the observer watching the moving particle but by an observer moving with the particle.
Using time dilation t/gamma=t(o)
therefore p=mv[gamma]
I didnt understand why distance Dx is same for both observers!
Doc Al
Mentor
I didnt understand why distance Dx is same for both observers!
Where in that quoted passage does it say that Dx is the same for both observers? It says: "Dx is the distance travelled by a moving particle as viewed by the observer watching that particle". Nowhere does it say that different observers measure the same distance.
How is the textbook then comparing the two momentum(S) measured by the person moving with the particle and the person who is not at rest with respect to the particle?
Hootenanny
Staff Emeritus
Gold Member
How is the textbook then comparing the two momentum(S) measured by the person moving with the particle and the person who is not at rest with respect to the particle?
Time dilation, note the term t0, the proper time interval.
Last edited:
The argument as per the book:
Rest Frame:
$$p_{0} = m\frac{\Delta x}{\Delta t_0}$$
Moving frame:
$$\Delta t = \gamma\Delta t_0$$
$$\therfore p_{0} = \gamma m\frac{\Delta x}{\Delta t}$$
But shouldn't it be...
Rest Frame:
$$p_{0} = m\frac{\Delta x_0}{\Delta t_0}$$
Moving frame:
$$\Delta t = \gamma\Delta t_0$$
$$\Delta x = \gamma^{-1}\Delta x_0$$, and therfore
$$p = m\frac{\Delta x}{\gamma^2\Delta t}$$
?
Last edited:
Hootenanny
Staff Emeritus
Gold Member
But shouldn't it be...
Rest Frame:
$$p_{0} = m\frac{\Delta x_0}{{\color{red}\Delta t_0}}$$
Are you sure about that? Read again, t0 is not in the rest frame of the observer, but in that of the particle.
Oh, okay. So from the particle's frame only length contraction is observed. So that would lead to only one gamma factor.
im confused
Can som1 please explain well.I am asorry ive tried a lot but cudnt understand.Why would $$\Delta x$$ be the same for both?
Hootenanny
Staff Emeritus
Gold Member
Oh, okay. So from the particle's frame only length contraction is observed. So that would lead to only one gamma factor.
Correct. Indeed, one can do equivalent procedures by considering length contraction or time dilation. The particle experiences length contraction, whereas the observer experiences time dilation; both will lead to the same results, provided the principles are applied correctly.
im confused
Can som1 please explain well.I am asorry ive tried a lot but cudnt understand.Why would $$\Delta x$$ be the same for both?
No one has ever said they are! $\Delta x$ is the distance measured by the observer not by the particle.
Last edited:
Explanation please.I still cant get it :'(
Thanks, Hoot.
Hootenanny
Staff Emeritus
Gold Member
Explanation please.I still cant get it :'(
What exactly don't you understand?
Thanks, Hoot.
No problem
Why length contraction isnt observed!Also which part of neutrino's equations were correct?Thnx
Hootenanny
Staff Emeritus
Gold Member
Why length contraction isnt observed!Also which part of neutrino's equations were correct?Thnx
Length contraction is observed, just not by an observer.
Correct. Indeed, one can do equivalent procedures by considering length contraction or time dilation. The particle experiences length contraction, whereas the observer experiences time dilation; both will lead to the same results, provided the principles are applied correctly.
Also which part of neutrino's equations were correct?Thnx
The first part under the heading 'According to the Book' is correct.
Last edited:
O boy i just cant seem to get it
According to me:
We are comparing the momentum an observer measures of a moving body and which the moving body measures of itself.Now suppose the moving body is on a road and has two stones which have a distance of Dx(with respect to the observing frame,i mean the rest observer).
Now when the observer measures the body's momentum:
$$p = m\frac{\Delta x}{\Delta t}$$ ..........(1)
also when the moving body measures his own momentum
$$p_{0} = m\frac{\Delta x_0}{\Delta t_0}$$
but as
$$\Delta x_0 = \gamma^{-1}\Delta x$$
Now im getting:
$$p_{0} = m\frac{\Delta x}{\gamma^2\Delta t}$$
So thats where im going wrong!:'((((((((((((((
Last edited:
Hootenanny
Staff Emeritus
Gold Member
Now when the observer measures the body's momentum:
$$p = m\frac{{\color{red}\Delta x}}{\Delta t}$$ ..........(1)
This length is a proper length, since it is measured in the rest frame of your two stones.
also when the moving body measures his own momentum
$$p_{0} = m\frac{{\color{red}\Delta x_0}}{\Delta t_0}$$
The length measure by the moving body is not a proper length. In your example above, the particle is moving relative to the distance between the two stones, therefore the distance between the two stones appears contracted!
err i think i said that$$\Delta x_0 = \gamma^{-1}\Delta x$$
and $$p_{0}$$ is the momentum as measured by the moving body
Hootenanny
Staff Emeritus
Gold Member
err i think i said that$$\Delta x_0 = \gamma^{-1}\Delta x$$
and $$p_{0}$$ is the momentum as measured by the moving body
You did indeed say that. However, the two statements I highlighted are still incorrect for the reasons I stated above.
err.... how?
Hootenanny
Staff Emeritus | 2021-04-11 15:29:22 | {"extraction_info": {"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, "math_score": 0.7476117014884949, "perplexity": 1691.3277547576388}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038064520.8/warc/CC-MAIN-20210411144457-20210411174457-00021.warc.gz"} |
https://www.helpteaching.com/questions/Two_Dimensional_Shapes | Looking for Geometry worksheets?
Check out our pre-made Geometry worksheets!
Tweet
##### Browse Questions
• Arts (4583)
• English Language Arts (60705)
• English as a Second Language ESL (44796)
• Health and Medicine (9408)
• Life Skills (2970)
• Math (29911)
• ### Volume
• #### Trigonometry
• Physical Education (4165)
• Science (50437)
• Social Studies (30003)
• Study Skills and Strategies (382)
• Technology (2535)
• Vocational Education (7172)
# Two Dimensional Shapes Questions - All Grades
You can create printable tests and worksheets from these Two Dimensional Shapes questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.
Previous Next
Lucy says the shape shown is not a parallelogram because all four sides are not the same length. Is Lucy's reasoning correct and why?
1. Yes, Lucy is correct. The shape is not a parallelogram because all four sides are not the same length.
2. No Lucy is incorrect. The shape is a parallelogram because all four sides are the same length.
3. No, Lucy is incorrect. The shape is not a parallelogram because it has four sides, but the opposite sides are not parallel.
4. No, Lucy is incorrect. The shape is a parallelogram because it has four sides and the opposite sides are parallel.
Find the area of a circle where r = 7 m. Use pi = 3.14.
1. $153.86m^2$
2. $43.96m^2$
3. $13.28m^2$
4. $153m^2$
Arrange the following polygons in order from least to greatest number of sides.
Hexagon, triangle, decagon, pentagon
1. Decagon, hexagon, pentagon, triangle
2. Triangle, hexagon, pentagon, decagon
3. Hexagon, triangle, decagon, pentagon
4. Triangle, pentagon, hexagon, decagon
The word equilateral means
1. congruent sides.
2. congruent angles.
3. congruent points.
4. congruent figure.
For each part of the circle listed below, choose ALL of the properties which are true about it.
Always intersects the center of the circle Touches only ONE point on the circle Can form inscribed angles Radius Diameter Tangent Chord
Which best explains why the shape shown is not a parallelogram?
1. It has more than four sides.
2. It is a two-dimensional shape.
3. It has angles of the same measure.
4. It has opposite sides that are parallel.
What is the longest side of a right triangle?
1. leg a
2. leg b
3. hypotenuse
4. right angle
The sides of $Delta ABC$ form the ratio $9:10:11$. If the perimeter of the triangle is $15 \ "units"$, what is the area of the triangle?
1. $3.9 \ "units"^2$
2. $10.6 \ "units"^2$
3. $42.4 \ "units"^2$
4. $122.3 \ "units"^2$
Previous Next
You need to have at least 5 reputation to vote a question down. Learn How To Earn Badges. | 2021-03-08 09:54:21 | {"extraction_info": {"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, "math_score": 0.19112038612365723, "perplexity": 2933.180527650624}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178383355.93/warc/CC-MAIN-20210308082315-20210308112315-00476.warc.gz"} |
http://scikit-bio.org/docs/0.5.6/generated/skbio.tree.TreeNode.postorder.html | # skbio.tree.TreeNode.postorder¶
TreeNode.postorder(include_self=True)[source]
Performs postorder iteration over tree.
State: Experimental as of 0.4.0.
This is somewhat inelegant compared to saving the node and its index on the stack, but is 30% faster in the average case and 3x faster in the worst case (for a comb tree).
Parameters
include_self (bool) – include the initial node if True
Yields
TreeNode – Traversed node.
Examples
>>> from skbio import TreeNode | 2021-03-05 19:00:29 | {"extraction_info": {"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, "math_score": 0.6898795962333679, "perplexity": 4941.157693475004}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178373241.51/warc/CC-MAIN-20210305183324-20210305213324-00315.warc.gz"} |
http://pacoline.eu/womens/ground/ccc/9110500dc4eabfaf1b20 | Classical Ideal Gas in Equilibrium 15 2.1. The kinetic theory of gases, developed in the 19th century, describes gases as assemblages of tiny particles ( atom s or molecule s) in constant motion and contributed much to an answered Jun 21, 2021 by anonymous. The k inetic theory states that every substance consists of atoms or molecules and that the atom or molecule moves continuously carelessly. Middle School Praxis Kinetic Theory 3 Boyles Law Boyles law (named after Robert Boyle and his work in 1662) states that the pressure and volume of a gas are inversely proportional to one another, or PV = k, where P is pressure, V is volume, and k is a constant of proportionality. Because most of a gas is empty space, a gas has a low density and can expand or contract under the appropriate influence. 1. State the kinetic theory of gases. Kinetic theory explains the behaviour of gases based on the idea that the gas consists of rapidly moving atoms or molecules. To be more precise, this theory and formula help determine macroscopic properties of a gas, if you already know the velocity value or internal molecular energy of the compound in question. Usually, the physical Kinetic Molecular Theory states that gas particles are in constant motion and exhibit perfectly elastic collisions.Kinetic Molecular Theory can be used to explain both Charles' and Boyle's Laws. Following are the three main components of the kinetic theory of gas:When molecules collide with each other, no energy is gained or lost.The space occupied by the molecules of gas in a container is very negligible.These molecules always have linear motion. The kinetic theory of gases describes this state of matter as composed of tiny particles in constant motion with a lot of distance between the particles. The particles are moving all the time. kinetic theory of gases, a theory based on a simplified molecular or particle description of a gas, from which many gross properties of the gas can be derived. (1) A gas consists of a very large number of molecules. The kinetic theory is widely accepted explanation of the theory of gas behaviour. Using the kinetic molecular theory, explain how an increase in the number of moles of gas at volume (V) 0 votes . Mass: f The five main postulates of the KMT are as follows: (1) the particles in a gas are in constant, random motion, (2) the combined volume of the particles is negligible, (3) the particles exert no forces on one another, (4) any collisions between the particles are completely elastic, and (5) Postulates or assumptions of kinetic theory of gases. Introducing Boltzmann's constant k = R / NA , it is easy to check from our result for the The molecules are in constant random motion, and there is an energy (mass x square of the velocity) associated Heavier particles move slower then lighter particles. Chemistry Gases Kinetic Theory of Gases. Kinetic Theory of Gases. a. The kinetic theory of gases is concerned with molecules in motion and with the microscopic and macroscopic consequences of such motion in a gas. But here, we will derive the equation from the kinetic theory of gases. The average kinetic energy of a collection of gas particles is directly proportional to absolute temperature only. What is the kinetic theory of gases? This state is called molecular chaos. Maxwells Distribution16 2.2. It is the study of gas molecules at the macroscopic level. Physics DF025 Chapter 14 Consider 1 mole of gas at standard temperature and pressure (S.T.P. Gases are made up of large number of the minute particles. The model, called the kinetic theory of gases, assumes that the molecules are very small relative to the distance between molecules. 0 votes . The time it takes to collide is negligible . Kinetic theory of gases relates the macroscopic property of the gas, like Temperature, Pressure, Volume to the microscopic property of the gas, like speed, momentum, position. 3. The kinetic theory of gases states that the mean free path between collisions of atoms or molecules in a gas is given by L=kBT/(21/2 PD2), where D is the atomic or molecular diameter of the species (Herman and Sitter, 1989); From: Reference Module in Materials Science and Materials Engineering, 2016. 7. State the ideas of the kinetic molecular theory of gases. In this Each one is a perfectly identical elastic sphere. This model of gases explains some of the physical properties of gases. 2. The kinetic theory of gases can define the general properties of gases at very low concentration. The kinetic theory of gases is the study that relates the microscopic properties of gas molecules (like speed, momentum, kinetic energies etc..)with the macroscopic properties of gas In the 19th century Maxwell, Boltzmann, and others proposed the theory of kinetics. Kinetic energy of the molecule in directly proportional to absolute temperature. Equation of State and Temperature19 2.3. The kinetic theory states that matter is made up of particles and these particles are constantly in motion i.e. They continue in a straight line until they collide with somethingusually each other or the walls of their 8. In a collection of gas particles, the average kinetic energy The kinetic theory of gases also describes properties such as temperature, coherence, and thermal conductivity. Gaseous State : Kinetic theory of gases Kinetic theory of gases (1) Kinetic theory was developed by Bernoulli, Joule, Clausius, Maxwell and Boltzmann etc. b) The intermolecular force of attraction between gas molecules are negligible. Ideal and real gases. Related terms: Nucleation Kinetic molecular theory is useful in Postulates of Kinetic theory of gases. All state changes can be defined in terms of heat absorbing and releasing which ultimately is affecting the kinetic energy of particles. The Kinetic Equation: Maxwell derived an equation on the basis of assumptions Of Kinetic Theory Of gases as. Validity of the Classical Limit21 2.3.1. Using the kinetic molecular theory, explain how an increase in the number of moles of gas at constant volume and temperature affects the pressure. Statistical Description of a Gas 5 1.1. The Kinetic-Molecular Theory Explains the Behavior of Gases, Part I. Recalling that gas pressure is exerted by rapidly moving gas molecules and depends directly on the number Kinetic molecular theory (also known as particle theory) states that all matter is made up particles and these particles are always in motion. Preview. The constituent particles of a kind of matter are identical in all respects. The kinetic theory of gases states that the time rate of change of pressure p of an ideal gas in a vessel of volume V at constant temperature, evacuated by a pump of constant volumetric speed S = dV/dt, is. A gas consist of a very large number of molecules which are perfect elastic spheres and are identical in all respects for a given gas and are different for different gases. 4. 2. volume (V) and temperature (T) of the given state for an ideal gas is known as the ideal gas equation or equation of states. The kinetic theory of gases, developed in the 19th century, describes gases as assemblages of tiny particles ( atom s or molecule s) in constant motion and contributed much to an understanding of their behaviour. Kinetic theory of matter states that Matter is made up of those substances or particles which are constantly moving.. ), T = 273.15 K, P = 101.3 kPa and Vm = 0.0224 m3 From equation (3), 3 PVm 101.3 10 0.0224 R T 1 273.15 1 R 8.31 J K mol where R is called molar gas constant and its value is the same for all gases. Gas molecules are identical. The kinetic theory of gases is a set of three assumptions about the behavior of ideal gases. The temperature of a gas is a measure of the mean kinetic energy of the gas. Calculate the rms speed of CO 2 at 40C. Gases are literally all around usthe air that we breathe is a mixture of gases. What this basically says is that the macroscopic properties of a gas, like the pressure or the volume or the temperature are just a result of the microscopic properties of the gas molecules, like the position and the speeds of these molecules. Kinetics means the study of motion, and in this case motions of gas State the ideas of the kinetic molecular theory of gases. Isotropic Distributions13 2. asked Jun 21, 2021 in Physics Form 3 by anonymous. Kinetic Molecular Theory states that gas particles are in constant motion and exhibit perfectly elastic collisions. Where P = Pressure of gas. There are energy changes when changes in state occur. Kinetic theory explains the behaviour of gases based on the idea that the gas consists of rapidly moving atoms or molecules. Energy8 1.3. The Kinetic Theory of gases states that the gases are made of small particles (atoms or molecules) which are in random motion. with solved examples & diagrams! Ans: According to the kinetic theory of gases, the average kinetic energy of gas only depends on its absolute temperature and is independent of the nature of the gas. Postulates of Kinetic Gas Theory. The following are the postulates of the Kinetic gas theory: Gases are made up of many small tiny, and discrete particles called molecules. Molecules of gas are well separated from each other. The volume occupied by molecules of a gas is negligible compared to the volume of gas. The collisions between gas molecules or molecule and wall of container are completely elastic meaning no energy is gained or lost from collisions. Answers. This will clear students doubts about any question and improve application skills while preparing for board exams. The field requires a great amount of knowledge and practical use in the ideas of the kinetic theory of gases, and it links the kinetic theory of gases with the solid state physics through the study Whereas Avogadros theory of diatomic molecules was ignored for 50 years, the kinetic theory of gases was rejected for more than a century. Explanation: 1) Gas formed by point-like particles (#"volume"~~0#); 2) No intermolecualar attractions between the molecules of the gas; 3) Random motion; 4) Elastic collisions. Brownian motion is It is a theory that derived that P V = 1 3 m n u 2. Kinetic theory is the atomic description of gases as well as liquids and solids. Assumptions of kinetic theory of gases. The ideal gas equation. Kinetic Theory of Gases is shared under a not declared license and was authored, remixed, and/or curated by Jim Clark. All gases at a given temperature have same Kinetic Energy. Gases consist of particles, which have the following properties: The particles are so small compared to the distances between them that the The model, called the kinetic theory of gases, assumes that the molecules This can then be used to analyse the interactions found in each of the states of matter. Following are the five postulated of the kinetic theory of gases: Gas is a composition of a large number of molecules that are constantly in a random movement. m = mass of one The continuous bombardment of the gas molecules against the walls of the container results in an increase in the gas pressure. The basic assumption of kinetic theory is that the measurable properties of gases, liquids, and solids reflect the combined actions of countless numbers of atoms and molecules. This helps us to determine whether that matter is in a solid, liquid, or gas state. The main postulates of the kinetic theory of matter are: 1. 4. 2. 2. Kinetic Theory and Gas Pressure. The average kinetic energy of a collection of gas particles is directly proportional to absolute temperature only. Kinetic Theory Of Gases: The common characteristics of gases can be explained by assuming that gases consist of molecules which are far apart and are in a state of constant Postulates for the Kinetic Theory Objective 2 asks you to list the assumptions that define the microscopic model of an ideal gas. Kinetic Molecular Theory can be used to explain both Charles' and Boyle's Laws. The space between Although the assumptions are not completely true, they are approximately true at low The five postulates of the kinetic theory of gases are as follows: Gas is made up of a vast number of molecules that are constantly moving at random. 1.1 Kinetic Theory of Gases Out of the three prominent states of matter, solid, liquid and gas, the kinetic theory o f gases is perhaps the most developed and complete. Motion of particles is random . 6. Boyle's Law and 9. The Theory was put up forward by According to kinetic theory: Gases consist of particles in constant, random motion. This is possible as the inter-atomic forces, which are short range forces that are important for solids and liquids, can be neglected for gases. 6. Kinetic Theory of Gases: Avogadros Number, Degrees of Freedom, Molar Specific Heats, Gas Law, RMS Speed, Pressure, etc. Other gases include those that make breads and The basic assumptions of kinetic theory are : A gas consist of particles called molecules which move randomly in all directions. Basic kinetic theory ideas about solids, liquids and gases, and changes of state. What are the five principles of the kinetic molecular theory of gases? ideal gas law. b. a) A gas consists of very large number of extremely small particles known as molecules. What are the assumptions made in the kinetic theory of gases? 1) All gases are made up of molecules that are constantly and persistently moving in random directions. 2) All the collisions between molecules and even between molecules and walls are considered to be elastic. 3) All the molecules in a certain gas sample obey Newtons laws of motion. Further, under suitable Introduction5 1.2. This assumption of kinetic theory matches the It states that equal volumes of all gases contain an equal number of molecules if Temperature and Pressure are the same. 1)Every gas is made up of a large number of extremely small particles called molecules. Various texts list these in various orders and forms. Gases consist of tiny particles of matter that are in constant motion. The kinetic theory of gases is used to explain the behavior of gas molecules. Kinetic theory of gases definition, a theory that the particles in a gas move freely and rapidly along straight lines but often collide, resulting in variations in their velocity and The detailed, step-by-step solutions will help you understand the concepts better Ideal and real gases. Kinetic Theory of Gases states that gaseous particles are in constant motion and undergo perfectly elastic collisions. to x + dx, y to y + dy, z to z + dz, and velocity components in the ranges u to u + du, v to v + dv, w to w + dw. All the molecules of a particular gas are identical in mass and size and differ in these from gas to gas. - [Instructor] So I wanna talk to you a little more about the kinetic-molecular theory of gases. Kinetic Calculation of Pressure11 1.5. According to the kinetic molecular theory, the molecules of two gases at the same temperature will possess the same average kinetic energy. Kinetic Theory of Gases: Avogadros Number, Degrees of Freedom, Molar Specific Heats, Gas Law, RMS Speed, Pressure, etc. physical law that relates the pressure and volume of a gas, far from liquefaction, to the number of gas molecules or number of moles of gas and the temperature This model of gases explains they have kinetic/movement energy. and represents dynamic particle or These particles have space or gaps between them which is known as interparticular or intermolecular space. Ans: The kinetic molecular theory of gases is stated in the following principles: 1. The kinetic particle theory explains the properties of solids, liquids and gases. See also solid. The kinetic molecular theory of gases describes this state of matter as composed of tiny particles in constant motion with a lot of distance between the particles. The kinetic theory of gases explains the three macroscopic properties of a gas in terms of the microscopic nature of atoms and molecules making up the gas. Kinetic theory is based on an atomic model of matter. with solved examples & diagrams! Pressure is exerted by a gas 3. -All collisions between gas molecules are perfectly elastic; all kinetic energy is conserved. Matter is composed of very small particles called atoms and molecules. It models the properties of matter in terms of continuous random motion of molecules. The term gas can also mean gasoline, natural gas, or the anesthetic nitrous oxide. The molecules of a gas are in Kinetic theory of gasses is a theory based on a simplified molecular or particle description of gas and from this many gross properties of the gas can be derived. One-particle phase space: position x 2 Rd, momentum p 2Rd f (t;x;p) the probability density distribution. The British scientist James Clerk 74 views. The Kinetic-Molecular Theory Explains the Behavior of Gases, Part I. Recalling that gas pressure is exerted by rapidly moving gas molecules and depends directly on the number of molecules hitting a unit area of the wall per unit of time, we see that the KMT conceptually explains the behavior of a gas as follows: Amontonss law. 5. The kinetic theory of gases is the study that relates the microscopic properties of gas molecules (like speed, momentum, kinetic energies etc..)with the macroscopic properties of gas molecules velocity changes but the molecular density is constant in steady state. The following list Physical Chemistry. Kinetic Theory of Gases I Ideal Gas The Ideal Gas Law Pressure and Temperature Internal Energy Mean Free Path Molecules collide elastically with other molecules Molar Specific Heat Constant Volume Adiabatic Process Equipartition of Energy Monatomic Gases Kinetic Theory of Gases I Ideal Gas The Ideal Gas Law Pressure and Temperature Internal Energy Mean Free Path STUDY GUIDE: Kinetic Theory of Gases . 4. Boyle's Law and Charles' Law. The volume of molecule is very small in comparison to the volume occupied by gas i.e., the size of molecule is infinitesimally small. The ideal gas law can be expressed in terms of the mass of the gass molecules and $$\bar{v^2}$$, the average of the molecular speed squared, instead of the temperature. 2.1: Prelude to The Kinetic Theory of Gases. V = Volume of gas. 3 . The kinetic theory of gases is concerned with molecules in motion and with the microscopic and macroscopic consequences of such motion in a gas. 5. Actual volume of the gaseous molecule very small. The kinetic theory of gases can be stated as three postulates: -The particles of a substance constantly move in random motion, and during this random motion, they collide with each other and with the walls of the container. Figure:Kinetic theory of gases:phase space! 7. Kinetic Theory. Kinetic Theory of Gases. This equation can easily be derived from the combination of Boyles law, Charless law, and Avogadros law. Written by a former Princeton University professor specializing in the thermal properties of matter, this monograph and text was designed for first-year students of physical chemistry who require further details of kinetic theory. Effect of gravity on gas molecule is neglected . The Nature of Gases Three basic assumptions of the kinetic theory as it applies to gases: 1. gas laws; 1 Answer. (2) The molecules of a gas are in a state of Ideal gas equation is PV = nRT. Thermodynamic Limit9 1.4. The energy level of the particles depends upon the temperature possessed by the matter. Kinetic theory of gases. If a gas sample is left for a sufficient time, it eventually comes to a steady-state. Kinetic Molecular Theory states that gas particles are in constant motion and exhibit perfectly elastic collisions. The kinetic theory of gases has developed a model that explains the behavior of molecules, which should further explain the behavior of an ideal gas. Balbharati solutions for Physics 12th Standard HSC Maharashtra State Board chapter 3 (Kinetic Theory of Gases and Radiation) include all questions with solution and detail explanation. Molecules of gas attract on one another. Introducing Boltzmanns constant k = R / NA, it is easy to check from our result for the pressure and the ideal gas law that the average molecular kinetic energy is proportional to a plot of PV/RT against Pext gives a lower value than the ideal at moderate pressures and a higher value than the ideal at very high pressures for most gases. select all the statements that correctly account for this behavior-at low pressures gas particles repel each other The kinetic theory relates the independent motion Part II.Kinetic Theory 5 1. c) Molecules are always in the state of random motion, i.e., they are moving in all possible directions with all possible velocities. Basic kinetic theory ideas about solids, liquids and gases, and changes of state. Gas is composed of particles- usually molecules or atoms Small, hard spheres If v 1 and v 2 are the average velocities of the KINETIC THEORY OF AN IDEAL GAS. Kinetic theory of Kinetic Theory of Gases. At the macroscopic level, it is the study of gas molecules. It describes how interactions between molecules influence gas characteristics such as temperature and The kinetic theory states that: All matter is made up of particles. State the kinetic theory of gases. Here P0 is the pressure of the gas at t = 0 and k the time constant of the gauge head (see Section 2.3.6 ). to x + dx, y to y + dy, z The kinetic theory of gases describes this state of matter as composed of tiny particles in constant motion, with a lot of distance between the particles. for n moles of gas, that is, n = N / NA , with NA Avogadro's number and R the gas constant. There is no loss of kinetic energy. Kinetic Molecular Theory of Gases. The kinetic molecular theory (KMT) describes the behavior of ideal gases at the particle level. Kinetic Molecular Theory states that gas particles are in constant motion and exhibit perfectly elastic collisions. The kinetic theory of gases correlates between macroscopic properties and microscopic phenomena. The actual atomic theory got established more than 150 years later. Because most of the The volume of the molecules is negligible as the distance between the gas molecules is greater than the size of the molecules. 4. Calculate the rms speed of CO 2 at 40C. The ideal gas equation. | 2022-11-26 09:50:30 | {"extraction_info": {"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": 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, "math_score": 0.5216811299324036, "perplexity": 366.029415328505}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446706285.92/warc/CC-MAIN-20221126080725-20221126110725-00504.warc.gz"} |
https://www.ebhor.com/tag/command-line-argument/ | Home » Posts tagged 'command-line-argument'
# Tag Archives: command-line-argument
## Command Line Argument in C Programming
In a C programming often a situation may come where we want to pass the information into a program during the execution of program. These values are called Command Line Arguments(CLA).
“main()” function handles the command line argument.
Syntax:
int main( int argc, char *argv[] )
{
}
Here, argc refers to the number of arguments passed and argv[] is a pointer array which points to each argument .
Note: argv[0] - holds the name of the program
argv[1]- holds the first command line argument, argv[2]- holds the second command line argument and and so on.
If no argument is supplied, argc will be 1
Example: Write a program in a C to take one value from user during execution as a command line argument.
#include int main(int argc, char *argv[] ) { printf(“Program name is: %s = “, argv[0]); printf(“\n Command line argument is: %s”, argv[1]); return 0; }
Note: Suppose above program name is “CLA”.
Run this program as follows in Linux:
./CLA hello
Here hello is a command line argument.
Run this program as follows in Windows from command line:
program.exe hello
Here hello is a command line argument.
Output:
Program name is: CLA
First argument is: hello
Example: Write a program in a C to take 4 value from user during execution as a command line argument.
OUTPUT
Note: Suppose above program name is “CLA”.
Run this program as follows in Linux:
./CLA this is IT department
Here this is IT department are 4 command line argument.
OUTPUT
Program name : CLA
1st arg : this
2nd arg : is
3rd arg : IT
4th arg : department
5th arg : (null)
Managed by MochaHost - Fast & Easy WordPress Hosting | 2019-05-20 02:58:30 | {"extraction_info": {"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, "math_score": 0.37025588750839233, "perplexity": 4960.0053535586885}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232255536.6/warc/CC-MAIN-20190520021654-20190520043654-00373.warc.gz"} |
https://itectec.com/database/network-design-considerations-for-oracle-database-appliance/ | # Network design considerations for Oracle Database Appliance
Networkoracleoracle-11g-r2oracle-database-appliancerac
With the introduction of Oracle Engineered Systems the DBA is moved somewhat closer to infrastructure design decisions, and expected to at least have some opinions of the network design requirements for the database. At least that is the situation I find myself in 🙂
After deploying an ODA for testing, I find myself with the current setup:
System Controller 0 has the public bonded interface (bond0) connected to a typical edge switch, a Catalyst 2960 series. A management interface (bond1) is connected to a second edge switch of the same type.
System Controller 1 similarly has it's public interface connected to the second switch, while the management interface is connected to the first switch.
This way, if one of the switches goes down, an operator will be able to reach each system controller either via the public or the management interface to facilitate diagnostics.
On the Cisco end of things, EtherChannel groups are configured for the 4 bonded interfaces of the ODA. The two switches are individually wired to the rest of the network, with no direct links between the two.
At first glance this does look like a reasonable design, but the more I think about different fault scenarios the more questions I seem to come up with.
Taking into consideration that these edge-type switches are not in themselves redundant, it seems rather important that the cluster can deal with one switch becoming unavailable due to power supply failure, or one switch failing to forward packages.
The database clients (zend server application servers in this case) are each similarly connected with a bonded interface to only to one of the two switches. This brings up some questions with regard to load balancing: The way I understand 11gR2 RAC, simply connecting to the SCAN address will quite possibly let the client go the long way to the main network and back through the other switch, which can hardly be considered to be very efficient.
What happens if a switch fails or stops forwarding packets? Will connections find the accessible VIP listener through SCAN? Will RAC somehow detect the network fault and move the SCAN and VIP to the System Controller with a working and accessible public interface? I honestly can't see how it would.
And while clients taking the long way through the core network and back is acceptable during a failover scenario, it sure would be nice to avoid it in normal production.
I'm sure Oracle has a very clear idea of how this should all work together, but I'm afraid I just don't see it all that clearly.
Is it possible to achieve full redundancy with edge-class/non-reduntant switches? Can we somehow add some control on where client connections are routed in production and failover situations? Perhaps there is a good way to interconnect the two switches to allow traffic directly between clients on one switch and database listener on the other?
At this point I'm looking for any best practices and fundamental network design considerations that should be applied to a typical high availability ODA implementation.
Hopefully this will then be of use to any DBA that is faced with making network design decisions for their ODA 🙂
Update:
The ODA is configured with bonds in active-backup configuration. I think this may allow for a setup where each interface on the bond is connected to a different switch, without any switch side configuration.
Anyone know if this is the case?
[root@oma1 ~]# cat /proc/net/bonding/bond0
Ethernet Channel Bonding Driver: v3.6.0 (September 26, 2009)
Bonding Mode: fault-tolerance (active-backup)
Primary Slave: None
Currently Active Slave: eth2
As it turns out, the ODA is factory configured with active-backup bonds. I've tested this to work well without any switch-side LACP/EtherChannel configuration, and each bonded connection may be split across two switches. In my tests, no simulated failure or network reconfiguration caused more than a a few hundred milliseconds worth of network outage.
This means that one can set up an isolated redundant front network for web applications using any layer two switches that are not inherently redundant.
To avoid client connections taking the long way into the company network and back through the other switch (and thus making production dependent on that equipment), one can have a private VLAN that only lives on the two edge switches and on an EtherChannel trunk between them.
As such, only the application servers and the database appliance will exist on that virtual network segment.
I don't see a way to control which path the connections from the application servers take to the database listeners, so the link between the two switches will have to be redundant, less this link becomes a single point of failure. This rules out using unmanaged switches without support for VLAN and either LACP or STP.
Using Cisco Catalyst 2960-series switches, I believe a combination of EtherChannel and Port Fast would be the better choice for a solid independent connection between the two. I would also use Port Fast on the ports for all the bonded connections to ODA and application servers.
Since the production network is isolated, one would need separate network connections for management, backup and connectivity to the rest of the company network.
Naturally, in order for this front production network to be fully self contained, any dependencies to external resources, such as DNS or authentication services, must also be resolved. Ideally production would be able to continue independently, without regard to any faults, ongoing maintenance or network outages anywhere else in the data center or company network. | 2022-01-23 02:38:29 | {"extraction_info": {"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, "math_score": 0.3089101314544678, "perplexity": 1887.6331608789399}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303956.14/warc/CC-MAIN-20220123015212-20220123045212-00352.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php?title=2019_AMC_10B_Problems&diff=prev&oldid=102215 | PREPARING FOR THE AMC 10?
Join fantastic instructors and top-scoring students in our online AMC 10 Problem Series course.
# Difference between revisions of "2019 AMC 10B Problems"
## Problem 1
Alicia had two containers. The first was $\tfrac{5}{6}$ full of water and the second was empty. She poured all the water from the first container into the second container, at which point the second container was $\tfrac{3}{4}$ full of water. What is the ratio of the volume of the first container to the volume of the second container?
$\textbf{(A) } \frac{5}{8} \qquad \textbf{(B) } \frac{4}{5} \qquad \textbf{(C) } \frac{7}{8} \qquad \textbf{(D) } \frac{9}{10} \qquad \textbf{(E) } \frac{11}{12}$
## Problem 2
Consider the statement, "If $n$ is not prime, then $n-2$ is prime." Which of the following values of $n$ is a counterexample to this statement.
$\textbf{(A) } 11 \qquad \textbf{(B) } 15 \qquad \textbf{(C) } 19 \qquad \textbf{(D) } 21 \qquad \textbf{(E) } 27$
## Problem 3
In a high school with $500$ students, $40\%$ of the seniors play a musical instrument, while $30\%$ of the non-seniors do not play a musical instrument. In all, $46.8\%$ of the students do not play a musical instrument. How many non-seniors play a musical instrument?
$\textbf{(A) } 66 \qquad\textbf{(B) } 154 \qquad\textbf{(C) } 186 \qquad\textbf{(D) } 220 \qquad\textbf{(E) } 266$
## Problem 6
There is a real $n$ such that $(n+1)! + (n+2)! = n! \cdot 440$. What is the sum of the digits of $n$?
$\textbf{(A) }3\qquad\textbf{(B) }8\qquad\textbf{(C) }10\qquad\textbf{(D) }11\qquad\textbf{(E) }12$
## Problem 7
Each piece of candy in a store costs a whole number of cents. Casper has exactly enough money to buy either 12 pieces of red candy, 14 pieces of green candy, 15 pieces of blue candy, or $n$ pieces of purple candy. A piece of purple candy costs 20 cents. What is the smallest possible value of $n$?
$\textbf{(A) } 18 \qquad \textbf{(B) } 21 \qquad \textbf{(C) } 24\qquad \textbf{(D) } 25 \qquad \textbf{(E) } 28$
## Problem 10
In a given plane, points $A$ and $B$ are $10$ units apart. How many points $C$ are there in the plane such that the perimeter of $\triangle ABC$ is $50$ units and the area of $\triangle ABC$ is $100$ square units?
$\textbf{(A) }0\qquad\textbf{(B) }2\qquad\textbf{(C) }4\qquad\textbf{(D) }8\qquad\textbf{(E) }\text{infinitely many}$
## Problem 13
What is the sum of all real numbers $x$ for which the median of the numbers $4,6,8,17,$ and $x$ is equal to the mean of those five numbers?
$\textbf{(A) } -5 \qquad\textbf{(B) } 0 \qquad\textbf{(C) } 5 \qquad\textbf{(D) } \frac{15}{4} \qquad\textbf{(E) } \frac{35}{4}$
## Problem 18
Henry decides one morning to do a workout, and he walks $\tfrac{3}{4}$ of the way from his home to his gym. The gym is $2$ kilometers away from Henry's home. At that point, he changes his mind and walks $\tfrac{3}{4}$ of the way from where he is back toward home. When he reaches that point, he changes his mind again and walks $\tfrac{3}{4}$ of the distance from there back toward the gym. If Henry keeps changing his mind when he has walked $\tfrac{3}{4}$ of the distance toward either the gym or home from the point where he last changed his mind, he will get very close to walking back and forth between a point $A$ kilometers from home and a point $B$ kilometers from home. What is $|A-B|$?
$\textbf{(A) } \frac{2}{3} \qquad \textbf{(B) } 1 \qquad \textbf{(C) } 1\frac{1}{5} \qquad \textbf{(D) } 1\frac{1}{4} \qquad \textbf{(E) } 1\frac{1}{2}$
## Problem 19
Let $S$ be the set of all positive integer divisors of $100,000.$ How many numbers are the product of two distinct elements of $S?$
$\textbf{(A) }98\qquad\textbf{(B) }100\qquad\textbf{(C) }117\qquad\textbf{(D) }119\qquad\textbf{(E) }121$
## Problem 21
Debra flips a fair coin repeatedly, keeping track of how many heads and how many tails she has seen in total, until she gets either two heads in a row or two tails in a row, at which point she stops flipping. What is the probability that she gets two heads in a row but she sees a second tail before she sees a second head?
$\textbf{(A) } \frac{1}{36} \qquad \textbf{(B) } \frac{1}{24} \qquad \textbf{(C) } \frac{1}{18} \qquad \textbf{(D) } \frac{1}{12} \qquad \textbf{(E) } \frac{1}{6}$
## Problem 23
Points $A(6,13)$ and $B(12,11)$ lie on circle $\omega$ in the plane. Suppose that the tangent lines to $\omega$ at $A$ and $B$ intersect at a point on the $x$-axis. What is the area of $\omega$?
$\textbf{(A) }\frac{83\pi}{8}\qquad\textbf{(B) }\frac{21\pi}{2}\qquad\textbf{(C) } \frac{85\pi}{8}\qquad\textbf{(D) }\frac{43\pi}{4}\qquad\textbf{(E) }\frac{87\pi}{8}$
## Problem 24
Define a sequence recursively by $x_0=5$ and $$x_{n+1}=\frac{x_n^2+5x_n+4}{x_n+6}$$for all nonnegative integers $n.$ Let $m$ be the least positive integer such that $$x_m\leq 4+\frac{1}{2^{20}}.$$In which of the following intervals does $m$ lie?
$\textbf{(A) } [9,26] \qquad\textbf{(B) } [27,80] \qquad\textbf{(C) } [81,242]\qquad\textbf{(D) } [243,728] \qquad\textbf{(E) } [729,\infty]$
## Problem 25
How many sequences of $0$s and $1$s of length $19$ are there that begin with a $0$, end with a $0$, contain no two consecutive $0$s, and contain no three consecutive $1$s?
$\textbf{(A) }55\qquad\textbf{(B) }60\qquad\textbf{(C) }65\qquad\textbf{(D) }70\qquad\textbf{(E) }75$
Invalid username
Login to AoPS | 2021-03-03 22:01:55 | {"extraction_info": {"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": 70, "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, "math_score": 0.33061450719833374, "perplexity": 293.24146908615177}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178367790.67/warc/CC-MAIN-20210303200206-20210303230206-00000.warc.gz"} |
https://astronomy.stackexchange.com/questions/25169/how-does-space-time-differ-within-a-galaxy | # How does space time differ within a galaxy?
Not the same question but is similar to other marked duplicate. How much time dilation does the center of a galaxy can exist and sustain human life from our point of view? What would a day equal to each others point of view looking at each other?
I'm not asking about moving celestial bodies moving from each other but the difference in the gravity wells from the center of our galaxy being generally denser then the edge of a galaxy.
This is another way of asking if I wasn't clear above the line. Not to invalidate any answers.
Point 1 being near the center of the galaxy and point 2 at the the most edge the galaxy. How much would the differences in the galaxies gravity well point 1 being deeper in the center compared to the point 2 the edge effect time?
• Your question does not make much sense. What does the doppler shift due to a galaxy's rotation have to do with time dilation? Why would that affect the evolution of life? How would that affect the length of a day? – Phiteros Feb 19 '18 at 4:16
• @Muze - you're not incorrect but the difference is absolutely tiny - so small it could never be measured. – Fattie Feb 23 '18 at 19:00
• @Phiteros - it makes absolutely perfect sense, what do you mean? When you're near some gravity (say, on the surface of the Earth), there is a tiny time dilation. OP is just asking how big it is. The galaxy is astoundingly heavy so you can really see where it's a good popular science question. Great question. – Fattie Feb 23 '18 at 19:02
• @Fattie That's because he edited the question. The first question was asking about red and blue shifts, then talked about time dilation. – Phiteros Feb 23 '18 at 22:06
• @Phiteros - fair enough; sorry about that. Is question-editing annoying or what?! – Fattie Feb 24 '18 at 15:36
The gravitational redshift factor and also the factor by which time dilation occurs in a gravitational field is approximately $GM/Rc^2$. Here, $R$ would be the radius from which light was emitted and $M$ is the amount of mass within radius $R$ (making the crude assumption of spherical symmetry).
Thus, for an external observer, light emitted from a radius of 10 kpc, might have $M \sim 10^{11} M_{\odot}$ in the galaxy shown. The redshift/time dilation factor is only $5\times 10^{-7}$ and is basically negligible.
This could perhaps gets an order of magnitude bigger as one approaches the denser central bulge, but is still very small.
The only appreciable redshift and time dilation effects will come in the immediate surroundings of any supermassive black hole. By immediate, I mean within about a hundred Schwarzschild radii, where $R_s = 2GM/c^2$. In our Galaxy that would mean within a billion kilometres.
• So unless your world exist in orbit exclusively around the black whole( in the center of the galaxy: Sagittarius A) there would be no significant time dilation? That distance would be likely inside the acceleration disk orbit and completely inhabitable on any level? – Muze Feb 19 '18 at 18:09
• @Muze - that's totally correct. (I think you meant to spell "accretion" disk, by the way.) – Fattie Feb 23 '18 at 19:01
• Just BTW, there seems to be many black holes in our galaxy - as well as the big one in the middle. If you are very close to any of those BHs, you'd experience such effects. – Fattie Feb 23 '18 at 19:04
Quite simply,
in both cases the effect is absolutely tiny.
Here is your basic confusion, on both this and the other similar question:
1. very heavy objects cause time dilation
2. a galaxy is just totally badass heavy
3. you naturally assumed then that galaxies cause time dilation
4. Very surprisingly, this is simply not correct.
The reason? Galaxies are very big. That is to say very thin. They have incredibly low density. Because of this there is simply no dilation at all.
(Well, only a minuscule amount - but that is true of simply, say, standing on Earth.)
That's the story! | 2021-06-16 21:21:17 | {"extraction_info": {"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, "math_score": 0.4169641137123108, "perplexity": 762.5594927335169}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487626008.14/warc/CC-MAIN-20210616190205-20210616220205-00008.warc.gz"} |
http://mathhelpforum.com/pre-calculus/87906-polynomial-rational-inequalities-help.html | # Thread: Polynomial and Rational inequalities help
1. ## Polynomial and Rational inequalities help
I have a couple problems I dont understand any help is appreciated..
1.) x^4 - 3x^2 - 4 > 0 solve algebraically.
2.) degree 4: zeros: 3+2i; 4, mulpilicity 2
3.) degree 4: zeros: 3, multiplicity 2; -i
I dont understand 2 and 3 at all, if anyone has any outside sources or good definitions for the problems it would be nice
thanks
2. I'll try to explain this, but it's hard to explain without knowing how much you know already.
For 2 and 3, the degree is the highest power of $x$in the equation, so $x^5$would have degree 5, and $x^5 + x -1$would still have degree 5.
Multiplicity would mean how many times a certain value is makes the equation equal to 0, so $x^2$ would have zeroes at 0 with multiplicity 2, whereas x would only have it with multiplicity 1. you can think of it as being able to factor out zeroes, so for $x^2$ it's the same as x*x, so there's two ways to get 0.
I'm assuming that you want real valued polynomials, so that means that for every complex number you get, it's conjugate is also a zero of the function. A complex number takes the form $x + iy$, and it's conjugate is just $x - iy$.
2.) degree 4: zeros: 3+2i; 4, mulpilicity 2
This means that you have 4 different factors from the degree, so you want to multiply together 4 things that have only degree equal to 1, so it's (x + a) (x+b)(x+c)(x+d) where a, b, c, d are all some value. Now we know that it has to zeroes at 4, so when you plug in 4 you get a 0, which only happens for (x-4). Since the multiplicity is 2, you have this two times. Te other zero is 3+2i, and it's conjugate must also be a zero, so you have 3+2i and 3-2i, which achieve zero at (x-3-2i) and (x-3+2i). Multiply these together: (x-4)(x-4)(x-3-2i)(x-3+2i) and you get your answer.
3. Originally Posted by cokeclassic
I dont understand 2 and 3 at all, if anyone has any outside sources or good definitions for the problems it would be nice
Try reviewing some online lessons regarding how to find quadratics and polynomials from their zeroes. | 2017-06-22 17:15:29 | {"extraction_info": {"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": 7, "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, "math_score": 0.6828060150146484, "perplexity": 521.5092300376091}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128319636.73/warc/CC-MAIN-20170622161445-20170622181445-00065.warc.gz"} |
https://chemicalstatistician.wordpress.com/2014/02/24/physical-chemistry-lesson-of-the-day-state-functions-vs-path-functions/ | # Physical Chemistry Lesson of the Day – State Functions vs. Path Functions
Today’s lesson may seem mundane; despite its subtlety, it is actually quite important. I needed to spend some time to learn it and digest it, and it was time well spent – these concepts are essential for understanding much of thermodynamics. For brevity, I have not dived into the detailed mathematics of exact differentials, though I highly recommend you to learn it and review the necessary calculus.
Some thermodynamic properties of a system can be described by state variables, while others can be described by path variables.
A state variable is a variable that depends only on the final and initial states of a system and not on the path connecting these states. Internal energy and enthalpy are examples of state functions. For example, in a previous post on the First Law of Thermodynamics, I defined the change in internal energy, $\Delta U$, as
$\Delta U = \int_{i}^{f} dU = U_f - U_i$.
State variables can be calculated by exact differentials.
A path variable is a variable that depends on the sequence of steps that takes the system from the initial state to the final state. This sequence of steps is called the path. Heat and work are examples of path variables. Path variables cannot be calculated by exact differentials. In fact, the following quantities may seem to have plausible interpretations, but they actually do not exist:
• change in heat ($\Delta q$)
• initial heat ($q_i$)
• final heat ($q_f$)
• change in work ($\Delta w$)
• initial work ($w_i$)
• final work ($w_f$)
There is no such thing as heat or work being possessed by a system. Heat and work can be transferred between the system and the surroundings, but the end result is an increase or decrease in internal energy; neither the system or the surroundings possesses heat or work.
A state/path variable is also often called a state/path function or a state/path quantity.
### 7 Responses to Physical Chemistry Lesson of the Day – State Functions vs. Path Functions
1. Surya says:
plz give some daily examples for state functions and path functions
• Hi Surya,
Could you please clarify what you mean by “daily” examples? I already mentioned a few in the post.
• Shubham says:
Surya meant to say…… daily means examples of state function in day to day life
• Altitude is a state function. It doesn’t matter how you reached a certain altitude as you ascend or descend in your path in the atmosphere.
2. ABED MUTHOMI says:
good work explain what isolated system.
3. ela says:
Heat and work are path functions, but difference between change in heat and change in work is called state function, why?
• Hi ela,
As I wrote in this blog post, there is no such thing as “change in heat” or “change in work”. Thus, I’m don’t fully understand your question. Please clarify.
Eric | 2017-02-21 12:02:24 | {"extraction_info": {"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": 8, "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, "math_score": 0.7158953547477722, "perplexity": 990.177892064149}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170708.51/warc/CC-MAIN-20170219104610-00306-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://mathhelpforum.com/algebra/30525-system-equations.html | 1. ## System of equations....
Ok, i was just on a site for tutoring but it isn't making much sense to me!
What steps do i follow through when doing this?
y=3x+7
y=x-9
2. Originally Posted by topaz192
Ok, i was just on a site for tutoring but it isn't making much sense to me!
What steps do i follow through when doing this?
y=3x+7
y=x-9
There are several ways, the one I favor most is this:
The two y values are equal, so let them be equal:
$x - 9 = 3x + 7$
$2x = -16$
$x = -8$.
Now use x = -8 in either one of the original equations:
$y = 3(-8) + 7 = -24 + 7 = -17$
So the solution is (x, y) = (-8, -17).
-Dan | 2018-02-20 05:53:43 | {"extraction_info": {"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": 4, "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, "math_score": 0.7583255171775818, "perplexity": 1265.6334819196452}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812880.33/warc/CC-MAIN-20180220050606-20180220070606-00194.warc.gz"} |