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WAY OFF TOPIC, but I would like some help getting my head around this. - Arduino Forum
As i see it.
The dog has no clue where or how far.. The most he can go is half way before he heads out so...
But if the dog had a problem solving brain he would stop at the farthest point eg the middle
so ask yourself this.
What's required to work out how far in? Eg a compass. eg how far have you traveled...
or rough calculations how fast roughly does the dog run, how big is the forest? Distance/time = roughly where dog is if traveling in a straight line.. i personaly woukd just use a gps
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Numerical integration?
August 22nd 2011, 06:48 PM #1
Senior Member
Dec 2010
Numerical integration?
Hello everyone
I have to integrate the definite integral square root(x) using the trapezoidal rule
from x=4 to x=9
I did (9-4)/8
giving me a width of 5/8
then I did
((9-4))/((2n)) giving me 5/16
I did
(4)^(1/2)+2(4.625)^(1/2)+2(5.25)^(1/2)+2(5.875)^(1/2)+ 2(6.5)^(1/2)+(7.125)^(1/2)+2(7.75)^(1/2)+2(8.375)^(1/2)+1(9)^(1/2) times ((5/16))
But what could be wrong
Re: Numerical integration?
There could be lots of things wrong, but you have not shown any such incorrect thing. If you managed an incorrect result, the error appears to be in the final arithmetic. What did you get? I get
12.66395614 or so. That's a good approximation to 38/3.
Re: Numerical integration?
Before I do the times ((5/16)) part I end up getting 40.52 and I checked many times entering the same numbers as above.
August 22nd 2011, 07:22 PM #2
MHF Contributor
Aug 2007
August 23rd 2011, 05:54 AM #3
Senior Member
Dec 2010
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Homework Help
Posted by Sabrina on Tuesday, September 7, 2010 at 8:00pm.
0.38 = (3 X 0.1) + ( X )
My sons paper instructs us to fill in the missing values. We understand that we are to fill in the two values in the second set of parenthesis, but that is all we understand.
Please help...I feel so inadequate because I can't help my child with this problem.
• 5th Grade Math - David, Tuesday, September 7, 2010 at 8:05pm
I'm putting the answer on the right because that's how I'm used to it.
(3*0.1) + (X) = 0.38
First we do the problems in parentheses. Since we are looking to find X we are not going to do that right now.
(3*0.1) = 0.3.
Now we subtract that from the equation.
0.3 + (X) =0.38
0.3 - 0.3 + (X) = 0.38 - 0.3
X = 0.35
• 5th Grade Math - Sabrina, Tuesday, September 7, 2010 at 8:13pm
Thanks for your help but I'm afraid I didn't make the question clear. This is actually asking for two answers.
The x is simply a multiplication symbol and we need a missing value times a missing value. Their is an actual blank to be filled in on either side of the multiplication symbol in the second set
of parenthesis.
• 5th Grade Math - Jen, Tuesday, September 7, 2010 at 9:37pm
0.38 = (3 X 0.1) + ( X )
0.38= .3+x
Subtract .3 from both sides
I don't know why you said it's asking for two answers. I really think this is the only answer.
• 5th Grade Math - Sabrina, Tuesday, September 7, 2010 at 10:15pm
Because in the second set of parenthesis there is an actual black line printed on the page on both sides of the multiplication sign. He must put an answer on both black lines. The instructions
say to fill in the missing values (not value).
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Pre-Calc help needed: Quadratic Functions
November 12th 2006, 05:59 PM #1
Nov 2006
Pre-Calc help needed: Quadratic Functions
These questions are part of a project I am working on for my class. Below is the problem situation. I've been trying to figure this out for hours:
Problem: Maximum Storage Area
A company wants to build an area to store machinery. One side (a length side) borders a river, so fencing will be needed for the other three sides. The company has 528 ft. of chain-link fencing.
Assume that the company wishes to use all of the fencing and the "width" refers to the measure of the two sides that are perp. to the river and "length" refers to the side parl. to the river.
W: 25 50 75 100 125 150 175 200
L : 478 428 378 328 278 228 178 128
A: 11950 21400 28350 32800 34750 34200 31150 25600
Questions I need help with:
1) Let W represent the width. Express the length in terms of W.
2) Write the general formula for the area of a rectangle (I know this one, but it ties into the next question). A = L x W
3) Using the general formula in (2), write the area (A) of the enclosure as a function of W.
Thank you, in advance, for help with this.
*edit: the numbers in the table are a little messed up, sorry.
These questions are part of a project I am working on for my class. Below is the problem situation. I've been trying to figure this out for hours:
Problem: Maximum Storage Area
A company wants to build an area to store machinery. One side (a length side) borders a river, so fencing will be needed for the other three sides. The company has 528 ft. of chain-link fencing.
Assume that the company wishes to use all of the fencing and the "width" refers to the measure of the two sides that are perp. to the river and "length" refers to the side parl. to the river.
W: 25 50 75 100 125 150 175 200
L : 478 428 378 328 278 228 178 128
A: 11950 21400 28350 32800 34750 34200 31150 25600
Questions I need help with:
1) Let W represent the width. Express the length in terms of W.
You know that: $2w+l=528$
Thus: $l=528-2w$
2) Write the general formula for the area of a rectangle (I know this one, but it ties into the next question). A = L x W
3) Using the general formula in (2), write the area (A) of the enclosure as a function of W.
You have $A = wl$
Substitute: $A=w(528-2w)$
Thus: $A=528w-2w^2$
Switch into standard notation: $\boxed{A=-2w^2+528w}$
And that's your answer!
November 12th 2006, 06:20 PM #2
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scilab programmes
i need scilab progam for
1. to obtain fibonacci series
2.to obtain non fibonacci series
3. to find the root of the equation f(x,a)=a*cos(x)-x*e(-a*x) for different values of a∈[1,10]
please reply soon.
it is imporant for my exams
Last edited by prathima (2014-01-01 16:27:06)
Re: scilab programmes
I do not program in Scilab. Best I can do is pseudocode, you will and should write them.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
Re: scilab programmes
Re: scilab programmes
1. to obtain fibonacci series
I guess you mean Fibonacci sequence.
1) x1 = 1;
2) x2 = 1;
3) h = x2;
4) x2 = x1 + x2;
5) x1 = h;
6) Goto 3
Remember to debug it if necessary. I am partying.
2.to obtain non fibonacci series
What is a non Fibonacci sequence specifically?
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
Re: scilab programmes
non fibonacci sequence is 4,6,7,9.10,11,12,14,15,16,17,18,19,20,...
Star Member
Re: scilab programmes
The example for Fibonacci is there: http://hkumath.hku.hk/~nkt/Scilab/IntroToScilab.html
for 3, you can use newton-raphson,
E.g. in python,
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
Re: scilab programmes
i dnt knw hw to insert the condition that a∈[1,10] in newton raphson method
Re: scilab programmes
Is it continuous?
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
Re: scilab programmes
i dont know.
in question it is not clear that a is continous or not
Last edited by prathima (2014-01-02 00:06:38)
Re: scilab programmes
What values can a take? a = 1,2,3,4... integers? Or any value from 1 to 10 like 7.27?
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
Re: scilab programmes
question is
scilab program to find the root of eqn f(x,a)=a*cos(x)-x*e^(-a*x) for different values of a∈[1,10]
Re: scilab programmes
Why not use the code gAr provided for python.
I just changed one line to Input[a]. Now you can enter any a you want.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
Re: scilab programmes
thank you
Re: scilab programmes
scilab program to obtain non fibonacci series
Re: scilab programmes
Generate the fibonacci numbers like I did in the first post and then an array of {1,2,3,4,5....}. When you get a fibonacci number cross it out by zeroing the array element.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
Re: scilab programmes
zeroing the array element means
Re: scilab programmes
Putting a zero in the array element.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
Real Member
Re: scilab programmes
prathima wrote:
it is imporant for my exams
I hope you do not mind me asking but what grade student are you?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Who are you to judge everything?' -Alokananda
Re: scilab programmes
i am not getting
Do you know what an array is?
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
Real Member
Re: scilab programmes
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Who are you to judge everything?' -Alokananda
Real Member
Re: scilab programmes
Hi prathima
Basically, just take the array {1,2,3,4,5,6,...} and put a zero instead all the numbers which are Fibonacci numbers.
Last edited by anonimnystefy (2014-01-02 01:00:47)
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
Re: scilab programmes
He can not do that yet.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
Re: scilab programmes
in scilab array set values in vector form for ex. A=[1 2 3]
Re: scilab programmes
Do you know how to access an individual array element?
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
Re: scilab programmes
What is pg?
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
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Electric field of a spherical cap
I am looking for the electric field caused by a uniformly charged spherical cap.
Actually, I need only the potential inside the sphere. Is there anybody who knows how to do this. Frankly, I do not have a clue. Or could somebody at least give me integral, that I have to solve?
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Excel TRANSPOSE Function
The Excel TRANSPOSE Function
Basic Description
The Excel Transpose function 'transposes' an array of cells (ie. the function copies a horizontal range of cells into a vertical range and vice versa).
Array Formulas:
To input an array formula, you need to first highlight the range of cells for the function result. Type your function into the first cell of the range, and press CTRL-SHIFT-Enter.
Go to the
Excel Array Formulas
page for more details.
The format of the function is :
TRANSPOSE( array )
Where the array argument is a range of Excel spreadsheet cells.
As the transpose function returns an array of values, it must be entered as an Array Formula.
Transpose Function Examples
Example 1
In the example on the right, the simple vertical range of cells A1-A6 is transposed into the horizontal range B1-F1.
The formula for the function can be seen in the formula bar. The curly braces { } show that the function has been input as an Array Formula.
Example 2
In the spreadsheet on the right, the range of cells A1-D2 is transposed into the range F1-G4.
Again the curly braces { } shown in the formula bar indicate that the function has been input as an Array Formula.
More examples of the Excel Transpose function are provided on the Microsoft Office website.
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The Notion of a Rational Convex Program, and an Algorithm for the Arrow-Debreu Nash Bargaining Game
Vijay Vazirani
Abstract: We introduce the notion of a rational convex program (RCP) and we classify the known RCPs into two classes: quadratic and logarithmic. The importance of rationality is that it opens up the
possibility of computing an optimal solution to the program via an algorithm that is either combinatorial or uses an LP-oracle. Next we define a new Nash bargaining game, called ADNB, which is derived
from the linear case of the Arrow-Debreu market model. We show that the convex program for ADNB is a logarithmic RCP, but unlike other known members of this class, it is non-total.
Our main result is a combinatorial, polynomial time algorithm for ADNB. It turns out that the reason for infeasibility of logarithmic RCPs is quite different from that for LPs and quadratic RCPs. We
believe that our ideas for surmounting the new difficulties will be useful for dealing with other non-total RCPs as well. We give an application of our combinatorial algorithm for ADNB to an
important “fair” throughput allocation problem on a wireless channel. Finally, we present a number of interesting questions that the new notion of RCP raises.
Guest: Vijay Vazirani
Host: Zvi Lotker
Podcast: Play in new window | Download
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Public Function RealPart( _
ByVal vX As Variant _
) As Variant
"Real Part"
Return the real part of a complex (or real) number.
Function returns vX unchanged if vX is already a real number.
RealPart(45) = 45
RealPart("23|45") = 23
RealPart("-34.5|12") = -34.5
IsNull(RealPart(Null)) = True
See also:
ImagPart Function
ComplexStringToReals Function
vX: The number whose real part is to be returned. Function returns Null if vX is Null or cannot be fixed up to a real or complex number (as defined by the ComplexStringToReals function). Complex
numbers are represented within strings as "R|I" where R is the real part and I is the imaginary part.
Copyright 1996-1999 Entisoft
Entisoft Tools is a trademark of Entisoft.
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If A^X = B/C, where A, B and C are all known, how on earth do you work out X?
September 8th 2012, 03:40 AM #1
Sep 2012
If A^X = B/C, where A, B and C are all known, how on earth do you work out X?
Right, I should know the answer and I'm ashamed to have to ask for help but this is doing my head in.
Actually trying to use this formula for a spreadsheet but I'm totally flumoxed!
So, if A^X = B/C, how do I work out what X is?
E.g, I know that 1.5^14 = 4379/15, but what if I didn't know that X was 14, how can I work it out?
Re: If A^X = B/C, where A, B and C are all known, how on earth do you work out X?
Tattoo this on your wrist:
if a^p = x then p = LOG(x) / LOG(a)
Re: If A^X = B/C, where A, B and C are all known, how on earth do you work out X?
Many many many thank yous!!!
Re: If A^X = B/C, where A, B and C are all known, how on earth do you work out X?
So you've already got that tattoo?
September 8th 2012, 03:57 AM #2
MHF Contributor
Dec 2007
Ottawa, Canada
September 8th 2012, 04:03 AM #3
Sep 2012
September 8th 2012, 06:11 AM #4
MHF Contributor
Apr 2005
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Posts about Mets on The World's Worst Sports Blog
Posted by tomflesher in Baseball.
Tags: Angels, Bartolo Colon, Baseball, Collin Cowgill, free baseball, John Lannan, Mets
add a comment
You’re trying not to smile, aren’t you?
- My wife on Saturday morning
Although the Dodgers are currently my favorite California team, it’s tough – I’m a huge Angels fan. It all started in 2004, when Josh Paul forgot to tag A.J. Pierzynski …. but I prattle on. Suffice
to say, I was a terrible Mets fan this weekend.
Bartolo Colon took one for the team yesterday, going 5 innings but allowing nine earned runs (four of them home runs). After two extra-inning games, it was nice to get some length out of Colon, even
if it will destroy his stats for the rest of the month. Although this would have been an excellent time to allow professional pinch hitter Ike Davis to show off the stuff that made him Arizona
State’s closer, Terry Collins opted to allow Scott Rice, Jeurys Familia, and John Lannan each toss an inning. Familia was a bright spot, since he doesn’t seem to be taking his loss on Saturday too
I was really pleased to see Lannan used as a potential long man on Saturday night. Although both Lannan and Rice pitched in the night game Saturday and the day game Sunday, Rice had been used in the
left-handed specialist role before being asked to eat up an inning on Sunday. Lannan was finally used in extra innings as a second starter; he ended up only needing to go two innings, but I’m sure
Terry was glad to have a sixth starter on the bench for his second straight extra-innings game. Gonzalez Germen is also doing some excellent work these days. Hopefully we won’t be on the hook for
Kyle Farnsworth in the setup role for too much longer. I’m not sure what kept the Professor out of the high-leverage game on Saturday night – I’m glad, don’t get me wrong, but he had only tossed a
third of an inning the night before, and Terry seems to think he’s useful.
Jose Valverde finally blew a save. It’s been almost a year since he did – he blew three saves in 2013 for Detroit, all within a one-month span starting on May 12th. Of course, June 12th was his last
save opportunity.
Posted by tomflesher in Baseball.
Tags: Baseball, bullpen, game score, Ike Davis, Johnny Cueto, Juan Lagares, Mets, Tough Losses
add a comment
Johnny Cueto is having a tough year so far. In yesterday’s game against the Mets, he pitched to a game score of 65, allowing two earned runs in seven innings; he left with a lead, followed quickly
with a hold by Sam LeCure and a blown save by J.J. Hoover, who surrendered a pinch-hit grand slam to professional pinch hitter Ike Davis^1. 65 is a solid game score; the sabermetric definition of a
quality start is a pitcher who adds value to his team by pitching to a game score above 50. In his first start of the year, Cueto threw seven innings of three-hit ball and struck out eight, pitching
to a 74 game score and surrendering only one run. Unfortunately, that day, Adam Wainwright threw seven innings of three-hit ball and struck out nine, pitching to a 76 game score and surrendering no
runs. Neither bullpen surrendered much, and so Wainwright took the win and dealt Cueto one of the toughest losses we’re likely to see this year.
Let’s give the devil their due – although it’s been easy to criticize the Mets’ bullpen, Scott Rice and Carlos Torres combined for a perfect inning and two thirds yesterday, keeping the score close
enough that Ike was able to knock in the winning home run.
Meanwhile, Juan Lagares‘ slugging percentage is still up at .765, and with 13 total bases on 21 plate appearances he’s averaging about .62 bases every time he steps to the plate. Lagares’ slide into
second yesterday was important for Ike’s hit to be a grand slam; if he’d been out, Ruben Tejada could easily have grounded into a double play and kept Ike out of the batter’s box. Still, Tejada’s OBP
is at .389, and if he can keep that up, a shortstop who gets on base almost eight out of every 20 plate appearances is a valuable person to have on your roster.
^1Davis’s first pinch-hit home run, and, according to Greg Prince via Twitter, the first come-from-behind walk-off grand slam in the history of the Mets.
Posted by tomflesher in Baseball.
Tags: Mets, Nationals, Not the bullpen again, Opening Day, Stuff Gary Cohen Says
add a comment
In the “Stuff Gary Cohen Says” pile, let’s add “When you score six runs, you expect to win the game.” Why he said that, specifically, I’m not sure, since at the time he said it, the score was 5-5.
Offensively, the Mets had a great game yesterday. In any just universe, two homers in regulation giving a five-run score should have won the game; last year, only 308 teams lost in 9 innings or less
with 5 or more runs scored, compared to 1697 teams that won in regulation with at least five. This, of course, isn’t a just universe; it’s Queens.
Dillon Gee had a quality start by game score (53), if not under the official definition, allowing 4 earned runs in 6.2 innings pitched. That was a little long, and the Mets’ commentary team pointed
out that Warthen and Collins seem to plan to let their starters work a little longer this year. Given the bullpen’s performance, I’m not shocked by that – although Jose Valverde pitched a perfect
inning and a third (striking out three), two of the Mets’ relievers walked their only batter faced. Bobby Parnell blew a save, giving up a crucial double to Denard Span in the 9th and showing
velocities that were surprisingly low. Aside from Valverde, the bullpen looked as unreliable as it did last year.
Parnell had an injury-marred season last year. It’s important not to take too much out of a single appearance. That said, I’ve never been a big fan of Parnell. Valverde isn’t the answer – he may not
even be as consistent as Latroy Hawkins was last year, judging by his spring performance – but the Mets have an inexperienced bullpen and they desperately need some consistency from the pen.
Parnell’s neck still raises concerns, as does his seeming inability to handle pressure. There’s no reason the Mets should be relying on Jeurys Familia in the tenth inning on opening day.
It’ll take a few weeks before the system shakes out, of course, and we’ll see whether the Mets’ pen steps up and develops over the early season. That said, the closer position will definitely need
some attention.
Posted by tomflesher in Baseball, Economics.
Tags: Ike Davis, Mets, Pythagorean expectation
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So, Ike Davis was pretty lousy last year. He batted .205/.326/.334 in an injury-shortened season with 106 total bases on 377 plate appearances, meaning he expected to make it to first a bit over a
quarter of the time. Throw in his paltry home run figures and a handful of doubles, and you’re not looking at a major-league first baseman; his 0.2 wins above replacement put him in the company of
Lyle Overbay and Garrett Jones.
Now that that’s out of the way, I’d like to point out that Overbay played 142 games and Jones played 144; Davis definitely presented more bang for your buck than those two, especially since he was
earning $3.125 million. He’ll be getting a 12% raise this year, having re-signed for $3.5 million. Again, his numbers were pretty lousy.
But if you add up all of Davis’s appearances as a starter, you’ll see that the Mets scored 354 runs in those games, and allowed 376, meaning that the Pythagorean expectation for those games is
0.46989 – that corresponds to an expectation of about 76 wins over a 162-game season (or 41 wins over Davis’ tenure). The Mets’ overall winning percentage was .457 (74 wins), and their Pythagorean
expectation was about .45, corresponding to around 73 wins; but without Davis, the team scored 265 runs and allowed 308, leading to an expectation of .425 and around 69 wins on the season.
Additionally, the team actually won only 39 of the 87 games Davis started, for about a .45 winning percentage – right on with their season-long expectation, and two wins below expectation.
Now, there are some caveats. When Davis was active, the team was still doing its best to win, and players like John Buck and Marlon Byrd were still active. Toward the end of the season, the Mets
moved more toward development and away from trying to win every game. It’s therefore entirely possible that the effect of having Davis start the game are wrapped up in the team’s changing fortunes.
Still, the team would have been expected to perform better with Davis in the lineup, at least according to the Pythagorean expectation formula, and actually underperformed.
Posted by tomflesher in Baseball, Economics.
Tags: Bobby Parnell, comparing contracts, Dillon Gee, Mets
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A few days ago, Bobby Parnell and Dillon Gee both re-signed with the Mets; though there are some incentives in Parnell’s deal, he’ll be making $3.7 million to Gee’s $3.625 million. Those numbers were
oddly close (and the contracts similar despite the difference in position), so I decided to check out the players’ recent statistics. Since the players are each negotiating one-year deals, and these
players are neither very old or very young, it seems reasonable to treat the best predictor of future performance as the players’ most recent performance.
Gee started 32 games (almost exactly every fifth game) in 2013 to a 3.62 ERA and a .301 opposing BABIP. The median numbers for starters with 162 or more innings pitched were about 3.51 and .295, so
Gee is performing almost exactly like a full-time starter (and thus presumably a bit better than your average pitcher). Gee’s performance corresponds to 2.2 wins above replacement, a shade below the
median of 3.0 for full-time starters.
I’m not Parnell’s biggest fan, and his season was shortened by an injury (causing him to miss all of August), so I expected the numbers not to operate in his favor. However, his 2.16 ERA is well
below the median of relievers with 40 appearances or more, and his 0.7 WAR is right on the median. Oddly, his BABIP at .268 is much lower than the median of .290, indicating that he’s benefiting, to
some degree, from good fielding behind him. If we restrict the numbers to only pitchers with 15 saves or more (all 32 of them), those medians adjust to 2.645, 1.4, and .277, respectively, keeping him
on the good side of ERA and BABIP but cutting his WAR performance considerably. Let’s see if we can extrapolate – in 104 team games, Parnell played 49, meaning that he played in about 47% of the
team’s games. At that pace, he probably would have been put into about 27 more games, meaning his current stats are about 65% of what his season stats might have been. In that case, let’s hold his
BABIP and ERA constant and extend his WAR to 1.08 (by dividing by .65). That would have ranked him with Huston Street and Addison Reed – much better company than his current competition. It also,
interestingly, would have put him much closer to Gee’s WAR, at a higher-leverage position.
Again, I’m not Parnell’s biggest fan, and I was skeptical about this deal. Assuming that the injury hasn’t harmed him, though, Parnell’s contract really does make sense compared to Gee’s.
Posted by tomflesher in Baseball, Economics.
Tags: annuity, Bobby Bonilla, compound interest, deferred compensation, finance, Mets
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When Bobby Bonilla signed a deferred compensation agreement in 2000, the Mets owed him $5.9 million dollars. Basically, the Mets got to hold on to the $6 million or so (and ended up spending it on
payroll), but they had to pay Bonilla back a bit more in interest. His yearly payments are $1,193,248.20, which means that in absolute terms, the Mets are paying him $35,797,446 in total over the
next 25 years. Of course, the $1.19 million Bonilla gets today is worth much more than the same-size payment he’ll get in 2036.
Bonilla’s arrangement mimics a financial instrument called an annuity, where a constant payment is made at specific time periods after a specific present sum is invested. The annuity formula is:
$Present Value =Payment \times [\frac{1 - \frac{1}{(1 + r)^t}}{r}]$
where r is the annualized interest rate and t is the number of years of payment. Keep in mind, though, that the present value of the annuity isn’t $5.9 million – it’s $5.9 million compounded annually
at some rate of interest agreed to by Bonilla and the team for the ten years between the deal and the first payout. In general, that means
$5900000\times(1 + r)^{10} = Payment \times [\frac{1 - \frac{1}{(1 + r)^t}}{r}]$
Since we know Bonilla’s payout, we can substitute in:
$5900000\times(1 + r)^{10} = 1193248.2 \times [\frac{1 - \frac{1}{(1 + r)^t}}{r}]$
and that solves out neatly to the 8% that the team and Bonilla agreed to. The math checks out so far.
At the time the deal was made, the 8% was 50 basis points (0.5%) below the Prime Rate, the reference rate used by banks in making loans. The average prime rate over the previous year was about 8.16%,
and rates had hovered within 75 basis points since September of 1994*, so while interest rates are expected to move, it was very likely that rates would stay similar, at least in the short term. For
the record, a 30-year fixed rate mortgage would have cost between 8.15% and 8.25%, so taking into account the long maturity of the loan, it wasn’t a bad deal.
Let’s look at how good a prediction it was. Annualizing prime rates, the Mets could have earned a (full prime) rate of return as follows:
$\begin{tabular}{c||cc} Year& Annualized interest rate & Current Value \\ \hline 2000& 0.09233 & 6444766.67 \\ 2001& 0.06922 & 6890851.93 \\ 2002& 0.04675 & 7212999.26 \\ 2003& 0.04123 & 7510355.16 \
\ 2004& 0.04342 & 7836429.74 \\ 2005& 0.06187 & 8321243.53 \\ 2006& 0.08133 & 8998038.00 \\ 2007& 0.08050 & 9722380.06 \\ 2008& 0.05088 & 10217006.15 \\ 2009& 0.03250 & 10549058.85 \\ 2010& 0.03250 &
10891903.26 \\ \end{tabular}$
So, the actual value of the $5.9 million on January 1, 2011, was $10,891,903.26, but the agreement pegged the value at
$5900000*(1.08)^{10} = 12737657.48$
for a difference of about $1.85 million. Bobby’s already better off because historical interest rates didn’t keep up with 8%.
My biggest question is why the Mets agreed to an 8% interest rate then and there to be in effect for the next 35 years. Since I’m not a finance professional, I don’t know whether that’s an industry
standard agreement or not, but it seems like the risk of setting an interest rate that far in the future would be far too high. What if the Mets had agreed to the 8% interest rate for ten years and
then offered Bonilla a menu of financially equivalent options? All of them would rely on the payment formula:
$Payment = \frac{r \times PV}{1 - \frac{1}{(1 + r)^t}}$
where t is the number of periods and r is the newly figured interest rate.
One option would be to take the $12,737,657.48 as a lump sum, although that wouldn’t necessarily be a good idea for the Mets. (We know they’re cash strapped.)
The current prime rate is 3.25%, so if we took the lump sum $12,737,657.48 from the original agreement and reamortized it today at 2.75%, Bobby could receive a payment of $711,270.46 over the next 25
years. Similarly, at 2.75%, $1,047,789.14 per year for 15 years or $2,761,502.75 for five years would be equivalent options. Each has a different total cash outlay, but the discount rate means that
each of them is worth the same $12,737,657.48 in 2011 dollars.
Bringing it all back, that’s why it’s a little silly to talk about the Mets paying $30 million to defer $6 million in compensation. It’s true that they’ll end up putting more dollars into Bonilla’s
hands, but that simply represents Bonilla’s forebearing on the ability to invest that money at current interest rates. It doesn’t matter when you pay him – the money is worth the same amount, and
that’s all that matters.
* Historical prime rates here, thanks to the St. Louis Fed and Federal Reserve Economic Data
Posted by tomflesher in Baseball, Economics.
Tags: Bobby Parnell, closers, Francisco Rodriguez, Jason Isringhausen, Mets, Pedro Beato
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It’s been a while since the Mets traded Francisco Rodriguez, the 1982 model, to the Milwaukee Brewers. Mets manager Terry Collins has indicated that Rule 5 draft pick Pedro Beato, cranky old man
Jason Isringhausen, and veteran Met Bobby Parnell are in competition for the closer role. Rodriguez had a reputation for being unpredictable, and watching him certainly gave that impression – he
pitched wildly and emotionally.
I decided to dig out K-Rod’s stats for this year and figure out what his numbers looked like, using a couple of measures of control: his K/BB ratio (aka ‘control ratio’), his K/9 and BB/9, and then
his batters faced per out (BFPO). If Rodriguez is unpredictable, then he should have a relatively high standard deviation for BFPO. With that in mind, if predictability is an important factor in
selecting a closer, these stats are relevant for Beato, Isringhausen, and Parnell as well. Here they are, for 2011:
The best number overall is bolded. The best from among the three closer candidates is italicized.
$\begin{tabular}{r||rrrrr} Pitcher & KBB & K9 & BB9 & BFPO & SD \\ \hline Rodriguez & \textbf{2.875} & 9.703 & \textbf{0.375} & 1.461 & \textbf{0.476} \\ Beato & 2 & 5.4 & 5.7 & \textit{\textbf
{1.292}} & 0.723 \\ Isringhausen & 1.615 & 6.831 & 4.229 & 1.386 & 0.638 \\ Parnell & \textit{3.2} & \textit{\textbf{11.221}} & \textit{3.506} & 1.442 & \textit{0.503} \\ \end{tabular}$
Rodriguez had the best KBB and BB9, as well as the lowest standard deviation, but his BFPO was the highest in the group. Since he wasn’t walking many batters, that indicates that he was giving up a
lot of hits or otherwise allowing lots of runners. That’s not good – it breeds high-pressure situations, some of which are bound to result in runs.
Beato had the lowest BFPO, but Parnell led all the other categories for current Mets as well as having a better K/9 than Rodriguez as well. Parnell’s BFPO was only .02 below Frankie’s, and was .15
higher than Beato’s (and about .05 greater than Izzy’s). Without a lot more data, it’s hard to compare these numbers meaningfully. However, over the course of 70 innings, that .15 differential adds
up to 31.5 extra baserunners for Parnell above Beato. Parnell’s lower standard deviation means that those runners are going to be spread a bit more evenly than Beato’s, but it’s tough to distinguish
the best choice. Isringhausen has been strong as a setup man, and Beato, as a rookie, is still unpredictable.
Parnell will probably come out of this with the closer’s job, but Collins would be a fool not to leave Isringhausen where he is.
Posted by tomflesher in Baseball, Economics.
Tags: Boone Logan, Daniel Murphy, Hector Noesi, Jason Bay, Mets, Ramiro Pena, RBIs, Scott Hairston, statistics, Subway Series, two-out RBIs, Yankees
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Sunday’s Subway Series game between the Mets and Yankees ended with a bang – Jason Bay hit a single off Hector Noesi that brought home Scott Hairston. The tenth inning should have been over, but
Ramiro Pena committed an error at shortstop that put Daniel Murphy on base for Boone Logan. Hairston’s run was unearned, but no matter – Noesi took the loss and the Mets won the game.
The final score was 3-2, and the interesting thing about the game was that all three of the Mets’ runs came with two outs. (My fiancée, Katie, suggested that this was unusual, and motivated most of
the rest of this post.) In fact, so far, the Mets have had 347 RBIs (of 375 runs scored), and 147 of them have come with two outs. That’s about 42.4% of their RBIs. By contrast, only 1070 of 3274
plate appearances – 32.7% – come with two outs. (Less than a third of plate appearances come with two outs because of the double play, among other reasons.) The majority come with no men out (about
34.8%) with the remainder coming with one out. It seems like the high concentration of 2-out RBIs should be explained by the use of the sacrifice bunt, but the Mets have only had 31 sacrifice bunts
this season – not nearly enough to account for the difference between 32.7% of plate appearances and 42.4% of RBIs.
Is that pattern common across baseball? So far, there have been 10,037 RBIs in Major League Baseball in the 2011 season. 3686 of them – about 36.7% – came with two outs. Excluding the Mets’ numbers,
that’s 3539 out of 9690, or 36.5%. For the National League only, there were 1928 two-out RBIS of 5212 total, or 37%, with 1781 of 4865 (36.6%) of National League RBIs coming with two outs if you
exclude the Mets. (Note that I’m defining ‘in the National League’ as ‘in National League parks,’ since what I’m interested in is whether the Mets’ concentration of RBIs can be partially explained by
the rules requiring pitchers to bat.)
Assume that the Mets’ RBIs are drawn from the same distribution as all others’. Then, 95% of the time, I’d expect the proportion of RBIs that come with two outs to be within two standard errors of
the National League’s proportion, excluding the Mets. (The ‘two standard errors’ comes from the fact that a t-distribution’s critical value for a large number of trials for 95% significance is 1.96.
For less than an infinite number, two standard errors is a handy approximation.) For the Mets’ 347 RBIs, the standard error would be
$\sqrt{\frac{p(1-p)}{n-1}} = \sqrt{\frac{.366(.734)}{346}} = \sqrt{\frac{.232}{346}} = \sqrt{.000671} = .026$
Thus, 95% of the time, the Mets should be within the interval of (.366 – .052, .366+.052), or (.314, .418). Since, again, the Mets’ proportion is .424, the Mets are slightly outside the 95%
confidence interval. That’s pretty close, and certainly could happen by chance, but it’s surprising nonetheless. The question then is whether this is due to some sort of strategy employed by the
Mets’ management or to some sort of clutch playing ability by the Mets. Again, there’s more data to collect and crunch (as always).
Posted by tomflesher in Baseball.
Tags: Angel Pagan, Austin Jackson, Carlos Beltran, David Purcey, Don Kelly, Jason Bay, Justin Turner, Mets, Mike McCoy, position players pitching, Ronnie Paulino, Roy Halladay, Scott Hairston,
Spectrum Club, Super utility dervish, Tigers, utility pitchers, utility player, utilityman, Wilson Valdez
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Super utility dervish Don Kelly is this year’s second inductee into the prestigious* Spectrum Club, which loyal readers if any will recognize as the group of players who have played both pitcher and
designated hitter in a given season. Kelly pitched a perfect third of an inning (for those keeping score at home, that’s one out) against the Mets last night during a 16-9 Tigers loss.
Kelly’s lifetime pitching statistics: 0.1 IP, 0 R, 0 H, 0 E, 0 HR, 0 BB, 0 K, 1 BF. That batter was Scott Hairston, who flied out to Austin Jackson at center.
Kelly came in after David Purcey, the Tigers’ last arm in the bullpen, pitched the last out of the eighth and the first two of the ninth. In his one inning, Purcey gave up five hits, four runs (all
of them earned), two walks (one intentional), and no strikeouts. Purcey’s ninth inning started promisingly when Justin Turner grounded out and Carlos Beltran flied out, but David then gave up a
double to catcher Ronnie Paulino, walked Jason Bay, and then allowed Angel Pagan to double, scoring Paulino. At that point, Jim Leyland called on Kelly, who took care of Hairston to end the inning.
That makes three utility pitchers thus far this year. Of the position players who pitched, Wilson Valdez, Mike McCoy and Don Kelly have each played at least three non-pitching positions. Valdez has
played at second base, third base, and shortstop; McCoy has played second, third, shortstop, center field, and left field; and Kelly has played first, third, left, center, and right. They’re three of
the four pitchers with fifty or more plate appearances. (Roy Halladay is the fourth, with exactly 50 PA this year.)
Over the course of his career, Kelly has been a utility ubermensch, playing every position except catcher. As a lifetime .242/.287/.341 hitter, Kelly needs to be versatile defensively to keep himself
working. That’s essentially the same way Mike McCoy keeps his job. Kelly had never pitched professionally before.
*not a guarantee
Posted by tomflesher in Baseball, Economics.
Tags: Athletics, Brad Ziegler, Charlie Morton, Dane Sardinha, hit by pitch, Jeff Francoeur, Justin Turner, Mariano Rivera, Mets, Oakland As
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The Mets’ Justin Turner quite literally took one for the team last night when he wasn’t trying to get hit, but, oops, managed to get plunked in the bottom of the 13th inning with the bases loaded.
Brad Ziegler was the losing pitcher for Oakland. It was the first game-ending hit by pitch since last year, when Mariano Rivera nailed Jeff Francoeur for the loss in a September game.
In 185 plate appearances this year, Turner has been hit three times. The other two were both by Pittsburgh Pirates pitcher Charlie Morton, eleven days apart; Morton is not especially known for
hitting batters, since he, too, has only been involved in three hit batsmen this year. (The third plunking was Dane Sardinha.) It was the Mets’ only go-ahead HBP this year, and the only one of this
year’s six go-ahead hit batsmen to occur in extra innings.
Turner has a way about him. He’s hit ten go-ahead RBIs this year (and yes, a hit by pitch that forces in a run is an RBI), which accounts for a little over ten percent of the Mets’ 95 go-ahead RBIs.
Only Carlos Beltran, with 13, has more. It’s also the Mets’ only game-ending RBI this year. I guess Turner will take what he can get.
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the definition of voltage
Computing Dictionary
voltage definition
(Or "potential difference", "electro-motive force" (EMF)) A quantity measured as a signed difference between two points in an electrical circuit which, when divided by the
between those points, gives the current flowing between those points in
, according to
Ohm's Law
. Voltage is expressed as a signed number of Volts (V). The voltage gradient in Volts per metre is proportional to the force on a charge.
Voltages are often given relative to "earth" or "ground" which is taken to be at zero Volts. A circuit's earth may or may not be electrically connected to the actual earth.
The voltage between two points is also given by the charge present between those points in
divided by the
. The capacitance in turn depends on the
dielectric constant
of the insulators present.
Yet another law gives the voltage across a piece of circuit as its
multiplied by the rate of change of current flow through it in Amperes per second.
A simple analogy likens voltage to the pressure of water in a pipe. Current is likened to the amount of water (charge) flowing per unit time.
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Past 2000 Seminars
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Past 2000 Seminars
2000 Seminars
3:30 p.m., Friday, January 7, 2000
Mathematics Colloquium
Stuart G. Whittington, Department of Chemistry, University of Toronto
``Coloured self-avoiding walks''
Room Math 100
2:30 p.m., Wednesday, January 12, 2000
Math Biology Seminar
Alexandra Chavez-Ross, Department of Mathematics, UBC
``Follicle Selection Dynamics in the Mammalian Ovary''
Room Math Annex 1102
3:30 p.m., Wednesday, January 12, 2000
Probability Seminar
Rick Durrett, Cornell University
``Single Nucleotide Polymorphisms in the Human Genome:
How many are there? How many will Celera find?''
Room Math Annex 1102
3:30 p.m., Friday, January 14, 2000
Mathematics Colloquium
Christian Klingenberg, Applied Mathematics, Wuerzburg University
``Mathematical modelling and numerical simulation in star formation''
Room Math 100
3:30 p.m., Monday, January 17, 2000
IAM-MATH BIO Colloquium
Leonard Sander, Physics Department, University of Michigan
``Scaling and Crossovers in Diffusion Limited Aggregation''
LSK Bldg., Room 301
11:30 a.m., Tuesday, January 18, 2000
Graduate Student Seminar
Nathan Ng, Department of Mathematics, UBC
``Prime Numbers: A Survey''
LSK Bldg., Room 301
1:30 p.m., Wednesday, January 19, 2000
Algebra/Topology Seminar
Bert Wiest, PIMS Postdoctoral Fellow, UBC
``Ordering of mapping class groups after Thurston''
West Mall Annex 216 (PIMS)
3:30 p.m., Wednesday, January 19, 2000
Probability Seminar
Richard Bass, University of Connecticut
``Local times for space-time Brownian motion''
Room Math Annex 1102
3:30 p.m., Friday, January 21, 2000
Mathematics Colloquium
Anne Bourlioux, University of Montreal
``Small scale asymptotic models for large scale simulations
of turbulent premixed flames''
Room Math 100
1:30 p.m., Tuesday, January 25, 2000
Graduate Student Seminar
Abigail Wacher, Department of Mathematics, UBC
``The Modeling of Rapid Thermal Processing in a Chamber''
LSK Bldg. Room 301
1:30 p.m., Wednesday, January 26, 2000
Algebra Topology Seminar
Kee Y. Lam, Department of Mathematics, UBC
``Pseudo-reflection groups and generalized braid groups''
West Mall Annex 216 (PIMS)
2:30 p.m., Wednesday, January 26, 2000
Math Biology Seminar
Michael C. Mackey, McGill University
``Periodic Hematological Diseases:
Insight into the pathology from mathematical modeling''
Math Annex 1102
3:30 p.m., Wednesday, January 26, 2000
Probability Seminar
Ed Perkins, Department of Mathematics, UBC
``Mutually catalytic branching in the plane''
Math Annex 1102
3:30 p.m., Monday, January 31, 2000
Joint IAM-PIMS Distinguished Colloquium
Anne Greenbaum, Department of Mathematics, University of Washington
``Analysis of Krylov Space Methods for Solving Linear Systems''
LSK Bldg., Room 301
4:30 p.m., Monday, January 31, 2000
PDE Seminar
Nassif Ghoussoub, Department of Mathematics, UBC
``Mass transfer, Monge-Ampere equation and Geometric inequalities''
Math Annex 1118
11:30 a.m., Tuesday, February 1, 2000
Graduate Student Seminar
Amy Norris, Department of Mathematics, UBC
LSK Bldg., Room 301
1:30 p.m., Wednesday, February 2, 2000
Algebra Topology Seminar
Kee Lam, Department of Mathematics, UBC
``Pseudo-reflection groups and generalized braid groups''
*note change of speaker (updated Feb. 1st)*
West Mall Annex 216 (PIMS)
3:30 p.m., Wednesday, February 2, 2000
Math Biology Seminar
Michael Dobeli, Departments of Mathematics and Zoology, UBC
``Evolutionary branching and sympatric speciation caused by different types of ecological interactions''
LSK Bldg., Room 301 (IAM seminar room)
*note change of time and location*
3:30 p.m., Wednesday, February 2, 2000
Probability Seminar
Ed Perkins, Department of Mathematics, UBC
``Mutually catalytic branching in the plane II''
Math Annex 1102
3:30 p.m., Friday, February 4, 2000
Mathematics Colloquium
Anna Vainchtein, Division of Mechanics and Computation,
Department of Mechanical Engineering, Stanford University
``Hysteresis and interface dynamics in mathematical models
of phase transitions''
Math 100
4:30 p.m., Monday, February 7, 2000
PDE Seminar
Nassif Ghoussoub, Department of Mathematics, UBC
``Mass transfer, Monge-Ampere equation and Geometric inequalities II''
Math Annex 1118
11:30 a.m., Tuesday, February 8, 2000
Graduate Student Seminar
Stefan Reinker, Department of Mathematics, UBC
``Does the Brain need Mathematics?''
LSK Bldg., Room 301
1:30 p.m., Wednesday, February 9, 2000
Algebra Topology Seminar
Kee Lam, Department of Mathematics, UBC
``Hyperplane arrangements and pseudo-reflection groups''
West Mall Annex 216 (PIMS)
4:30 p.m., Thursday, February 10, 2000
PIMS-MITACS Mathematical Finance Seminar
Yonggan Zhao, Department of Commerce, UBC
``Portfolio selection with a minimum wealth requirement''
West Mall Annex 216 (PIMS)
2:30 p.m., Monday, February 21, 2000
PDE Seminar
Nassif Ghoussoub, Department of Mathematics, UBC
``Continuous Mass Transport, the Euler and the Fokker-Plank equations''
Math Annex 1118
3:30 p.m., Monday, February 21, 2000
IAM-MATH BIO Colloquium
Mark Lewis, Department of Mathematics, University of Utah
``Realistic models for biological invasion''
LSK Bldg., Room 301
1:30 p.m., Wednesday, February 23, 2000
Algebra/Topology Seminar
David Burggraf, Department of Mathematics, UBC
``Group actions on elliptic dessins d'enfants''
West Mall Annex 216 (PIMS)
3:30 p.m., Wednesday, February 23, 2000
Probability Seminar
Gregory F. Lawler, Department of Mathematics, Duke University
``Computing the intersections exponents for planar Brownian motion'''
Math Annex 1102
4:30 p.m., Thursday, February 24, 2000
PIMS-MITACS Mathematical Finance Seminar
Ulrich Haussmann, Department of Mathematics, UBC
``Optimal portfolio selection with limited diversification
(joint work with N. Dokuchaev)''
West Mall Annex 216 (PIMS)
3:30 p.m., Friday, February 25, 2000
Mathematics Colloquium
Gregory F. Lawler, Department of Mathematics, Duke University
``Universality and conformal invariance in two dimensional
statistical physics''
Room Math 100
2:30 p.m., Monday, February 28, 2000
PDE Seminar
Nassif Ghoussoub, Department of Mathematics, UBC
``Continuous Mass Transport, the Euler and
the Fokker-Plank equations, II''
Math Annex 1118
3:30 p.m., Monday, February 28, 2000
Joint IAM-PIMS Distinguished Colloquium
Marc Feldman, Department of Biological Sciences, Stanford
``Mathematics and Statistics of Human DNA Polymorphisms:
Forward and Backward to History''
LSK Bldg., Room 301
11:30 a.m., Tuesday, February 29, 2000
Graduate Student Seminar
Adriana Dawes, Department of Mathematics, UBC
LSK Bldg., Room 301
3:30 p.m., Tuesday, February 29, 2000
Math Biology Seminar
John Pearson, Los Alamos National Laboratory
``Chemical Reaction Diffusion Systems: An Overview''
Math Annex 1102
1:30 p.m., Wednesday, March 1, 2000
Algebra/Topology Seminar
David Burggraf, Department of Mathematics, UBC
``Group actions on elliptic dessins d'enfants, II''
West Mall Annex 216 (PIMS)
2:30 p.m., Wednesday, March 1, 2000
Math Biology Seminar
John Pearson, Los Alamos National Laboratory
``Fire-Diffuse-Fire and the Dynamics of Intracellular Calcium Waves''
Math Annex 1102
3:30 p.m., Wednesday, March 1, 2000
Probability Seminar
N. Dokuchaev, PIMS, UBC
``Stochastic partial differential equations
with a quasi-periodic boundary condition''
Math Annex 1102
9:45--10:45 a.m., Thursday, March 2, 2000
Number Theory Seminar
Nike Vatsal, Department of Mathematics, UBC
``Uniform Distribution of Heegner Points''
Math Annex 1102
11:00 -- 12:00 p.m., Thursday, March 2, 2000
Number Theory Seminar
Christopher M. Skinner, Institute for Advanced Study, Princeton
``Base Change and a Problem of Serre''
Math Annex 1102
4:30 p.m., Thursday, March 2, 2000
PIMS-MITACS Mathematical Finance Seminar
N. Dokuchaev, PIMS, UBC
``Optimal portfolio selection based on historical prices''
West Mall Annex 216 (PIMS)
3:30 p.m., Friday, March 3, 2000
Mathematics Colloquium
Christopher M. Skinner, Institute for Advanced Study, Princeton
``The diophantine equation a^n+b^n=2c^2''
Room Math 100
1:30 p.m., Saturday, March 4, 2000
Northwest Probability Seminar
Christian Borgs, Microsoft Theory Group
``Partition function zeros: A generalized Lee-Yang theorem''
Smith 105, University of Washington
3:30 p.m., Saturday, March 4, 2000
Northwest Probability Seminar
Xiaowen Zhou, Department of Mathematics, UBC
``Sample path continuity of continuous-site stepping-stone models''
Smith 105, University of Washington
3:30 p.m., Monday, March 6, 2000
Applied Mathematics Colloquium
Avner Friedman, Department of Mathematics, University of Minnesota
``Bifurcation of free boundary problems with application
to tumor growth''
LSK Bldg., Room 301
1:30 p.m., Wednesday, March 8, 2000
Algebra/Topology Seminar
Duane Randall, Department of Mathematics & Computer Science,
Loyola University
``A Survey of the Kervaire Invariant Problem''
West Mall Annex 216 (PIMS)
10 a.m., Thursday, March 9, 2000
Special Algebra/Topology Seminar
Stephen Bigelow, UC Berkeley
``Braid groups are linear''
Math Annex 1102
4:30 p.m., Thursday, March 9, 2000
PIMS-MITACS Mathematical Finance Seminar
John Chadam, Pittsburgh University
``The Exercise Boundary for an American Put Option:
Analytical and Numerical Approximations''
West Mall Annex 216 (PIMS)
3:30 p.m., Friday, March 10, 2000
Mathematics Colloquium
John Chadam, University of Pittsburg
``A mathematical model of bioremediation in a porous medium''
Math 100
3:30 p.m., Monday, March 13, 2000
Joint IAM-PIMS Distinguished Colloquium
Alwyn Scott, Department of Mathematics, Univ. of Arizona
and Department of Mathematical Modelling,
Technical University of Denmark
``Nonlinear Science: Past, Present and Future''
LSK Bldg., Room 301
11:30 a.m., Tuesday, March 14, 2000
Graduate Student Seminar
Stefan Reinker, Department of Mathematics, UBC
``Does the Brain need Mathematics?''
LSK Bldg., Room 301
1:30 p.m., Wednesday, March 15, 2000
Algebra/Topology Seminar
Denis Sjerve, Department of Mathematics, UBC
``Automorphisms of prime Galois coverings of the Riemann Sphere''
West Mall Annex 216 (PIMS)
4:30 p.m., Thursday, March 16, 2000
PIMS-MITACS Mathematical Finance Seminar
Jaksa Cvitanic, University of Southern California
``Methods of partial hedging''
West Mall Annex 216 (PIMS)
3:30 p.m., Friday, March 17, 2000
Mathematics Colloquium
Akbar Rhemtulla, Department of Mathematical Sciences,
University of Alberta
``Expressing Elements of the Commutator Subgroup of a Group
as a Product of Least Number of Commutators''
Room Math 100
11:30 a.m., Tuesday, March 21, 2000
Graduate Student Seminar
Ron Ferguson, Department of Mathematics, UBC
``Permutations with low discrepancy k-sums''
LSK Bldg., Room 301
1:30 p.m., Wednesday, March 22, 2000
Algebra/Topology Seminar
Guillermo Moreno, Centro de Investigacion y Estudios
Advanzados del IPN and University of Oregon
``Higher Dimensional Cayley Dickson Algebras''
West Mall Annex 216 (PIMS)
3:30 p.m., Friday, March 24, 2000
Mathematics Colloquium
Andrew J. Sommese, Univ. of Notre Dame
``Numerical Primary Decomposition''
Room Math 100
3:30 p.m., Monday, March 27, 2000
IAM-MATH BIO Colloquium
Jinko Graham, Department of Mathematics & Statistics,
Simon Fraser University
``Fine-Scale Mapping of a Rare Allele via Disequilibrium Likelihoods''
LSK Bldg., Room 301 (formerly Old Computer Sciences Bldg.)
1:30 p.m., Wednesday, March 29, 2000
Algebra/Topology Seminar
Zhongmou Li, UBC
``Immersion of 3-manifolds in 3-space"
West Mall Annex 216 (PIMS)
4:30 p.m., Thursday, March 30, 2000
PIMS-MITACS Mathematical Finance Seminar
Raman Uppal, Commerce and Business Administration, UBC
``Risk Aversion and Optimal Portfolio Policies
in Partial and General Equilibrium Economies''
West Mall Annex 216 (PIMS)
3:30 p.m., Monday, April 3, 2000
Complexity Seminar
Anders Martin Lof, Steve Marion, Cindy Greenwood
``Asymptotics of the Near-Critical Epidemic Process''
Peter Wall Institute Conference Room
11:30 a.m., Tuesday, April 4, 2000
Graduate Student Seminar
Glen Pugh, Department of Mathematics, UBC
``Riemann, Siegel and Turing: Numerical Evidence for the Riemann Hypothesis''
LSK Bldg., Room 301 (formerly Old Computer Science Bldg.)
1:30 p.m., Wednesday, April 5, 2000
Algebra/Topology Seminar
Bert Wiest, Department of Mathematics, UBC
``Quasi-isometries in group theory''
West Mall Annex 216 (PIMS)
3:30 p.m., Wednesday, April 5, 2000
Probability Seminar
Marek Biskup, Microsoft Research
``Rigorous theory of partition function zeros
at first-order phase transitions''
Math Annex 1102
1:30 p.m., Wednesday, June 14, 2000
Special Number Theory Seminar
Hugh Montgomery, University of Michigan
``Greedy sums of distinct squares"
Math Annex 1102
2:30 p.m., Wednesday, September 6, 2000
Topology Seminar
Prof. Youcheng Zhou, Zhejiang University, China
``Effros Property and Homogeniety''
Math Annex 1102
3:30 p.m., Wednesday, September 6, 2000
Probability Seminar
Antal Jarai, PIMS-UBC
``Invasion percolation and the incipient infinite cluster''
Math Annex 1102
3:30 p.m., Wednesday, September 13, 2000
Algebraic Geometry Seminar
Behrang Noohi, Department of Mathematics, UBC
``Fundamental Groups of Algebraic Stacks''
Math Annex 1118
2:30 p.m., Wednesday, September 13, 2000
UBC PIMS Colloquium
Beno Eckmann, ETH Zurich
``The Euler Characteristic -- some Variations and Ramifications''
WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, September 13, 2000
Probability Seminar
Frank den Hollander, University of Nijmegen
``How random is the composition of two random processes?''
Math Annex 1102
3:30 p.m., Wednesday, September 13, 2000
IAM-PIMS Distinguished Colloquium Speaker
Carlo Cercignani, Dipartimento di Matematica,
Politecnico di Milano, Milan, Italy
``Kinetic Models for Granular Materials: An Exact Solution''
LSK Bldg. Room 301
2:30 p.m., Thursday, September 14, 2000
Algebra-Topology Seminar
Beno Eckmann, ETH Zurich
``Projections, Group Algebras, and Geometry of Groups''
WMAX 216
4:30 p.m., Thursday, September 14, 2000
PIMS-MITACS Mathematical Finance Seminar
D. Chan, UBC
``Introduction to Value at Risk''
WMAX 216
3:30 p.m., Friday, September 15, 2000
Mathematics Colloquium/PIMS Distinguished Chair Lecture
David Brydges, PIMS-Department of Mathematics, University of Virginia
``Self Avoiding Walk and Differential Forms''
Math 100
10:00-11:00 a.m., Monday, September 18, 2000
Scientific Computing and Visualization Seminar
Arian Novruzi, PIMS-UBC
``Newton method in shape optimization problems.
Some comments on its parallelization''
CICSR 204, contact Brian Wetton for details
on this seminar series
3:30 p.m., Monday, September 18, 2000
Mathematics Colloquium
Leonid Mytnik, Israel Institute of Technology
``Duality approach to proving uniqueness''
Math 100
4:45 p.m., Monday, September 18, 2000
PIMS-MITACS Mathematical Finance Seminar
Steve Shreve, Carnegie-Mellon Univ.
``Valuation of Exotic Options under Shortselling Constraints''
WMAX 216 (PIMS seminar room)
3:30 p.m., Tuesday, September 19, 2000
PIMS Distinguished Chair at UBC Lecture
David Brydges, PIMS-Department of Mathematics and Physics,
University of Virginia
``Mehler's Formula and the Renormalization Group"
(Lecture 2 in the series)
Math 104
2:30 p.m., Wednesday, September 20, 2000
Algebra-Topology Seminar
Kee Lam, Mathematics, UBC
``Rational homotopy theory''
WMAX 216
3:30 p.m., Wednesday, September 20, 2000
Algebraic Geometry Seminar
Behrang Noohi, Mathematics, UBC
``Fundamental Groups of Algebraic Stacks, II''
WMAX 216 (previously announced for 2:30 in Math Annex 1118)
3:30 p.m., Wednesday, September 20, 2000
Institute of Applied Mathematics Colloquium
Lionel G. Harrison, Department of Chemistry, UBC
``Branching in Plants: Exploring Reaction-Diffusion:
(1) On the Hemisphere
(2) Interacting with Continuous Morphological Change''
LSK Bldg. Room 301
1:30 p.m., Thursday, September 21, 2000
Mathematics Colloquium
Andrea Fraser, University of New South Wales
Multiplier Operators on the Heisenberg group
Math Annex 1100
4:00 - 5:00 p.m., Thursday, September 21, 2000
PIMS-MITACS Computational Statistics and Data Mining Seminar
Peter J. Rousseeuw, PIMS-Universitaire Instelling Antwerpen (UIA), Belgium
``An Introduction to Regression Depth''
CICSR 208
1:30 - 2:30 p.m., Friday, September 22, 2000
PIMS-MITACS Computational Statistics and Data Mining Seminar
Peter J. Rousseeuw, PIMS-Universitaire Instelling Antwerpen (UIA), Belgium
``Depth Tests of Symmetry and Regression''
LSK 301
3:30 p.m., Friday, September 22, 2000
Mathematics Colloquium
Jacques Hurtubise, CRM and University of Montreal
``Integrable Systems and Surfaces''
Room Math 100
10:00-11:00 a.m., Monday, September 25, 2000
Scientific Computing and Visualization Seminar
Arian Novruzi, PIMS-UBC
``Newton method in shape optimization problems.
Some comments on its parallelization, Part II''
CICSR 204
3:30 p.m., Monday, September 25, 2000
Mathematics Colloquium
Laura Scull, Department of Mathematics, University of Michigan
``Equivariant Homotopy Theory: Classic Constructions in a Modern Setting''
Math 100
10:30 a.m., Tuesday, September 26, 2000
Special Algebra-Topology Seminar
Laura Scull, Department of Mathematics, University of Michigan
``Algebraic Models for Equivariant Homotopy Theory''
Math Annex 1102
1:30 p.m., Tuesday, September 26, 2000
Math Biology Seminar
Israeli Ran & Alexandra Chavez-Ross, UBC
``MITACS progress report: the tinnitus project''
LSK Bldg, Room 301
3:30 p.m., Tuesday, September 26, 2000
PIMS Distinguished Chair at UBC Lecture
David Brydges, PIMS-Department of Mathematics and Physics,
University of Virginia
``Hierarchical Lattices and the Renormalization Group revisited
(Lecture 3 in the series)''
Math 104
3:30 p.m., Wednesday, September 27, 2000
IAM-PIMS Distinguished Colloquium
David Brydges, PIMS-Department of Mathematics and Physics,
University of Virginia
``Gaussian Integrals and Mean Field Theory''
LSK Bldg. Room 301
2:30 p.m., Thursday, September 28, 2000
PDE Seminar
Jingyi Chen, Mathematics, UBC
``Quaternions, Hyperkahler manifolds and a first order system of PDEs''
WMAX 216 (PIMS seminar room)
4:30 p.m., Thursday, September 28, 2000
PIMS-MITACS Mathematical Finance Seminar
Jose Rodriguez, Mathematics, UBC
``More Value at Risk''
WMAX 216
3:30 p.m., Friday, September 29, 2000
Mathematics Colloquium
Ravi Vakil, Department of Mathematics, M.I.T.
``Branched covers of the sphere and the moduli space of curves:
Geometry, physics, representation theory, combinatorics''
Math 100
10:00-11:00 a.m., Monday, October 2, 2000
Scientific Computing and Visualization Seminar
Oliver Dorn, Computer Science, UBC
``The use of level set methods for shape reconstruction
in electromagnetic tomography''
CICSR 204
2:30 p.m., Wednesday, October 4, 2000
Algebra/Topology Seminar
Dale Rolfsen, Mathematics, UBC
``Ordered groups and 3-manifolds''
WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, October 4, 2000
PIMS Distinguished Chair at UBC Lecture
David Brydges, PIMS-Department of Mathematics and Physics,
University of Virginia
``Analysis with the Renormalization Group and Outlook
(Lecture 4 in the series)''
WMAX 216
2:30 p.m., Thursday, October 5, 2000
PDE Seminar
Vitali Vougalter, Mathematics, UBC
``Diamagnetic behavior of sums of Dirichlet eigenvalues''
WMAX 216
3:30 p.m., Friday, October 6, 2000
Mathematics Colloquium
Richard Froese, Mathematics, UBC
``Realizing holonomic constraints in classical and quantum mechanics''
Math 100
1:30 p.m., Tuesday, October 10, 2000
Math Biology Seminar
Susan Anne Baldwin, Bio-Resource Engineering, UBC
``Heat Transfer Model of Thermal Balloon Endometrial Ablation''
LSK Bldg, Room 301
2:30 p.m., Wednesday, October 11, 2000
Algebra/Topology Seminar
Dale Rolfsen, Mathematics, UBC
``Ordered groups and 3-manifolds, II''
WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, October 11, 2000
Institute of Applied Mathematics Colloquium
W. Kendal Bushe, Department of Mechanical Engineering, UBC
``Large Eddy Simulation of Turbulent Reacting Flows''
LSK Bldg. Room 301
3:30 p.m., Wednesday, October 11, 2000
Algebraic Geometry Seminar
Jim Carrell, Mathematics, UBC
``Equivariant cohomology of varieties with a triangular group action''
WMAX 216
3:30 p.m., Wednesday, October 11, 2000
Probability Seminar
Liqing Yan, Mathematics-PIMS, UBC
``The Euler scheme for stochastic differential equations
with irregular coefficients''
Math Annex 1102
2:30 p.m., Thursday, October 12, 2000
PDE Seminar
Christine Chambers, Mathematics, UBC
WMAX 216
4:30 p.m., Thursday, October 12, 2000
PIMS-MITACS Mathematical Finance Seminar
Simon MacNair, Mathematics-PIMS, UBC
``Utility Maximization with Stochastic Factors''
WMAX 216
3:30 p.m., Friday, October 13, 2000
Mathematics Colloquium
Richard Schoen, Department of Mathematics, Stanford University
``A survey of recent progress in general relativity''
Math 100
10:00-11:00 a.m., Monday, October 16, 2000
Scientific Computing and Visualization Seminar
Uri Ascher, Computer Science, UBC
``Grid refinement and scaling for distributed parameter estimation problems''
CICSR 204
2:30 p.m., Wednesday, October 18, 2000
Algebra/Topology Seminar
Bert Wiest, Mathematics-PIMS, UBC
``Ordered groups and 3-manifolds, III''
WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, October 18, 2000
Institute of Applied Mathematics Colloquium
Robert Miura, Mathematics, UBC
``Applications of Excitable Cell Models''
LSK Bldg. Room 301
3:30 p.m., Wednesday, October 18, 2000
Probability Seminar
Siva Athreya, Mathematics-PIMS,UBC
``Long time behaviour of a Brownian flow with jumps''
Math Annex 1102
3:30 p.m., Wednesday, October 18, 2000
Algebraic Geometry Seminar
Jim Carrell, Mathematics, UBC
``Equivariant cohomology of varieties with a triangular group action, II''
WMAX 216
4:30 p.m., Wednesday, October 18, 2000
Student Algebraic Geometry Seminar
Boris Tschirschwitz, Mathematics, UBC
WMAX 216
3:30 p.m., Friday, October 20, 2000
Mathematics Colloquium
Joel Friedman, Mathematics, UBC
``Expanders, Eigenvalues, and Related Topics''
Math 100
a.m.-p.m., Friday, Saturday, October 20-21, 2000
West Coast Optimization Meeting
Speakers: scheduled technical program
Location: University of Washington (Seattle)
For information email Phillip Loewen, loew@math.ubc.ca
10:00-11:00 a.m., Monday, October 23, 2000
Scientific Computing and Visualization Seminar
Uri Ascher, Computer Science, UBC
``Grid refinement and scaling for distributed parameter estimation problems, II''
CICSR 204
2:30 p.m., Wednesday, October 25, 2000
Algebra/Topology Seminar
Zhongmou Li, Mathematics, UBC
``Every orientable 3-manifold with boundary embeds in K_5 join 1''
WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, October 25, 2000
Institute of Applied Mathematics Colloquium
Keith Promislow, Department of Mathematics & Statistics, SFU
``Modulational Stability via Renormalization Methods for Patterns in Forced Dispersive Systems''
LSK Bldg. Room 301
3:30 p.m., Wednesday, October 25, 2000
Probability Seminar
Remco van der Hofstad, Delft University
``Improving performance of third generation mobile phone systems''
Math Annex 1102
3:30 p.m., Wednesday, October 25, 2000
*Postponed til Nov 1st*
Algebraic Geometry Seminar
Jim Carrell, Mathematics, UBC
``Equivariant cohomology of varieties with a triangular group action, III''
WMAX 216
2:30 p.m., Thursday, October 26, 2000
PDE Seminar
Izabella Laba, Mathematics, UBC
``The spectral set conjecture and multiplicative properties of roots of polynomials''
WMAX 216
3:30 p.m., Friday, October 27, 2000
Mathematics Colloquium
Remco van der Hofstad, Delft University
``Recent progress in one-dimensional and high-dimensional
statistical mechanical models''
Math 100
3:30 p.m., Wednesday, November 1, 2000
IAM-PIMS Distinguished Colloquium
Linda Petzold, Departments of Mechanical and Environmental Engineering
and Computer Science, Univ. of California at Santa Barbara
``Algorithms and Software for Dynamic Optimization
with Application to Chemical Vapor Deposition Processes''
LSK Bldg. Room 301
3:30 p.m., Wednesday, November 1, 2000
Probability Seminar
Robert Israel, Mathematics, UBC
``Finding generators from transition matrices''
Math Annex 1102
3:30 p.m., Wednesday, November 1, 2000
Algebraic Geometry Seminar (postponed from 25 Oct)
Jim Carrell, Mathematics, UBC
``Equivariant cohomology of varieties with a triangular group action, III ''
WMAX 216
4:30 p.m., Thursday, November 2, 2000
PIMS-MITACS Mathematical Finance Seminar
P. Laurence, U. Roma and NYU
``American options on multiple assets: bounds via a comparison principle''
WMAX 216
10:00-11:00 a.m., Monday, November 6, 2000
Scientific Computing and Visualization Seminar
Brian Wetton, Mathematics, UBC
``Asymptotic Error Analysis: overview and some unsolved problems''
CICSR 204
3:30 p.m., Wednesday, November 8, 2000
IAM Colloquium
Alejandro Garcia, Department of Physics, San Jose State University, CA
``Stochastic Particle Algorithms: from DSMC to CUBA''
LSK Bldg. Room 301
3:30 p.m., Wednesday, November 8, 2000
Probability Seminar
Xiaowen Zhou, Mathematics, UBC
``A duality formula for multi-type voter model''
Math Annex 1102
3:30 p.m., Wednesday, November 8, 2000
Algebraic Geometry Seminar
Anne O'Halloran, Mathematics, UBC
``The Cohomology of Kontsevich's Stack of Stable Maps to P^n - The Case of Conics"
WMAX 216
10:30 a.m., Thursday, November 9, 2000
Harmonic and Functional Analysis Seminar
Professor Garth Dales, Leeds University
``Amenability and weak amenability for measure algebras''
Math Annex 1102
2:30 p.m., Thursday, November 9, 2000
PDE Seminar
Manfred Salmhofer, ETH -- Zurich
``On the conjecture called `Migdal's Theorem'''
WMAX 216
3:30 p.m., Friday, November 10, 2000
Mathematics Colloquium
Michael Ward, Mathematics, UBC
``The Stability and Dynamics of Spikes for a Reaction-Diffusion System''
Math 100
2:30 p.m., Wednesday, November 15, 2000
Algebra/Topology Seminar
Don Witt, Department of Physics and Astronomy, UBC
``The Smale Conjecture''
WMAX 216
3:30 p.m., Wednesday, November 15, 2000
IAM Colloquium
Roland Stull, Department of Earth and Ocean Sciences, UBC
``A Nonlocal Description of Atmospheric Turbulence''
LSK Bldg. Room 301
3:30 p.m., Wednesday, November 15, 2000
Algebraic Geometry Seminar
Anne O'Halloran, Mathematics, UBC
``The Cohomology of Kontsevich's Stack of Stable Maps to P^n
- The Case of Conics, Part II''
WMAX 216
4:30 p.m., Wednesday, November 15, 2000
Student Algebraic Geometry Seminar
Maciej Mizerski, Mathematics, UBC
``Introduction to Derived Functors (Cohomology)''
Math Annex 1102
4:30 p.m., Wednesday, November 15, 2000
PIMS-MITACS Mathematical Finance Seminar
V. Dion, Mathematics, UBC
``A tutorial on Mortgage Backed Securities''
WMAX 216
2:30 p.m., Thursday, November 16, 2000
PDE Seminar
Arian Novruzi, UBC ``Some results related to free boundary
and shape optimisation problems''
WMAX 216
3:30 p.m., Friday, November 17, 2000
Mathematics Colloquium
Dale Rolfsen, Mathematics, UBC
``Do you want to be a mathematical millionaire?
The Poincare conjecture''
Math 100
10:00-11:00 a.m., Monday, November 20, 2000
Scientific Computing and Visualization Seminar
Radu Bradean, UBC-SFU MITACS PDF
``Transport Phenomena in Porous Fuel Cell Electrodes''
CICSR 204
3:30 p.m., Monday, November 20, 2000
Mathematics Colloquium
Richard Bertram, Institute of Molecular Biophysics,
Florida State University, Tallahassee, Florida
``Mathematical Analysis of Deterministic and Stochastic Models
of Synaptic Transmitter Release''
Math 100
3:30 p.m., Tuesday, November 21, 2000
Math Biology Seminar
Richard Bertram, Institute of Molecular Biophysics,
Florida State University
``Models of Synaptic Transmitter Release and Short-Term Plasticity''
Math 104
3:30 p.m., Wednesday, November 22, 2000
IAM Colloquium
Florin Diacu, Univ. Victoria-PIMS Site Director,
Department of Mathematics and Statistics, Univ. of Victoria
``On the Dynamical Stability of the Helium Atom''
LSK Bldg. Room 301
3:30 p.m., Wednesday, November 22, 2000
Algebraic Geometry Seminar
Kai Behrend, Mathematics, UBC
``Differential Graded Schemes''
WMAX 216
4:30 p.m., Wednesday, November 22, 2000
Student Algebraic Geometry Seminar
Boris Tschirschwitz, Mathematics, UBC
``Derived Functors: Acyclic Resolutions''
WMAX 216
2:30 p.m., Thursday, November 23, 2000
PDE Seminar
Stephen Gustafson, Courant Institute of Mathematical Sciences
``Stability of Localized Solutions of Landau-Lifshitz Equations''
WMAX 216
2:30 p.m., Thursday, November 23, 2000
Special Institute of Applied Mathematics Seminar
Natalia Kouzniak, MITACS PDF, Department of Mathematics, UBC
``Analytical Solutions and Numerical Results in Elasto-plastic
and Elasto-dynamic Problems of Fracture Mechanics''
Math 204
3:30 p.m., Friday, November 24, 2000
Mathematics Colloquium
Stephen Gustafson, Courant Institute
``Some Mathematical Problems in the Ginzburg-Landau
Theory of Superconductivity''
Math 100
3:30 p.m., Monday, November 27, 2000
Mathematics Colloquium
Doug Park, Department of Mathematics & Statistics, McMaster University
``Exotic smooth structures on simply connected 4-dimensional manifolds''
Math 100
Refreshments will be served at 3:15 in the Math Annex
Coffee Lounge, Room 1115.
10:30 a.m., Tuesday, November 28, 2000
Special Topology Seminar
Doug Park, McMaster University
``Gluing formulae for Seiberg-Witten invariant along 3-dimensional torus''
Math Annex 1102
3:30 p.m., Wednesday, November 29, 2000
IAM Colloquium
Ian Frigaard, Department of Mathematics, UBC
``Super-Stable Parallel Flows of Multiple Visco-Plastic Fluids''
LSK Bldg. Room 301
3:30 p.m., Wednesday, November 29, 2000
Algebraic Geometry Seminar (postponed from Nov. 22)
Kai Behrend, Mathematics, UBC
``Differential Graded Schemes''
WMAX 216
2:30 p.m., Thursday, November 30, 2000
PDE Seminar
Martin Bause, University of Erlangen, Nuremberg, Germany
``Numerical approximation schemes for the Poisson-Stokes equations
of compressible viscous flow''
WMAX 216
3:30 p.m., Friday, December 1, 2000
Joint PIMS-MITACS Mathematical Finance Seminar
and Mathematics Colloquium
Darrell Duffie, Stanford University
``Valuation in Dynamic Bargaining Markets''
Math 100
10:00-11:00 a.m., Monday, December 4, 2000
Scientific Computing and Visualization Seminar
Jim Varah, Computer Science, UBC
``Discrete Tomography: Projections, Moments, and Shape Reconstruction''
CICSR 204
3:30 p.m., Monday, December 4, 2000
Mathematics Colloquium
Michael Bennett, Department of Mathematics,
University of Illinois at Urbana-Champaign
``Effective methods for Diophantine problems''
Math 100
1:30 p.m., Tuesday, December 5, 2000
Number Theory Seminar
Michael Bennett, Univ. of Illinois at Urbana-Champaign
``Pillai's conjecture revisited''
Math Annex 1102
3:30 p.m., Friday, December 8, 2000
Special Mathematics Colloquium
Professor Ram Murty, Queen's University
``Riemann Hypothesis: A Status Report''
Math Annex 1100
2000 Seminars
3:30 p.m., Friday, January 7, 2000
Mathematics Colloquium
Stuart G. Whittington, Department of Chemistry, University of Toronto
``Coloured self-avoiding walks''
Room Math 100
2:30 p.m., Wednesday, January 12, 2000
Math Biology Seminar
Alexandra Chavez-Ross, Department of Mathematics, UBC
``Follicle Selection Dynamics in the Mammalian Ovary''
Room Math Annex 1102
3:30 p.m., Wednesday, January 12, 2000
Probability Seminar
Rick Durrett, Cornell University
``Single Nucleotide Polymorphisms in the Human Genome:
How many are there? How many will Celera find?''
Room Math Annex 1102
3:30 p.m., Friday, January 14, 2000
Mathematics Colloquium
Christian Klingenberg, Applied Mathematics, Wuerzburg University
``Mathematical modelling and numerical simulation in star formation''
Room Math 100
3:30 p.m., Monday, January 17, 2000
IAM-MATH BIO Colloquium
Leonard Sander, Physics Department, University of Michigan
``Scaling and Crossovers in Diffusion Limited Aggregation''
LSK Bldg., Room 301
11:30 a.m., Tuesday, January 18, 2000
Graduate Student Seminar
Nathan Ng, Department of Mathematics, UBC
``Prime Numbers: A Survey''
LSK Bldg., Room 301
1:30 p.m., Wednesday, January 19, 2000
Algebra/Topology Seminar
Bert Wiest, PIMS Postdoctoral Fellow, UBC
``Ordering of mapping class groups after Thurston''
West Mall Annex 216 (PIMS)
3:30 p.m., Wednesday, January 19, 2000
Probability Seminar
Richard Bass, University of Connecticut
``Local times for space-time Brownian motion''
Room Math Annex 1102
3:30 p.m., Friday, January 21, 2000
Mathematics Colloquium
Anne Bourlioux, University of Montreal
``Small scale asymptotic models for large scale simulations
of turbulent premixed flames''
Room Math 100
1:30 p.m., Tuesday, January 25, 2000
Graduate Student Seminar
Abigail Wacher, Department of Mathematics, UBC
``The Modeling of Rapid Thermal Processing in a Chamber''
LSK Bldg. Room 301
1:30 p.m., Wednesday, January 26, 2000
Algebra Topology Seminar
Kee Y. Lam, Department of Mathematics, UBC
``Pseudo-reflection groups and generalized braid groups''
West Mall Annex 216 (PIMS)
2:30 p.m., Wednesday, January 26, 2000
Math Biology Seminar
Michael C. Mackey, McGill University
``Periodic Hematological Diseases:
Insight into the pathology from mathematical modeling''
Math Annex 1102
3:30 p.m., Wednesday, January 26, 2000
Probability Seminar
Ed Perkins, Department of Mathematics, UBC
``Mutually catalytic branching in the plane''
Math Annex 1102
3:30 p.m., Monday, January 31, 2000
Joint IAM-PIMS Distinguished Colloquium
Anne Greenbaum, Department of Mathematics, University of Washington
``Analysis of Krylov Space Methods for Solving Linear Systems''
LSK Bldg., Room 301
4:30 p.m., Monday, January 31, 2000
PDE Seminar
Nassif Ghoussoub, Department of Mathematics, UBC
``Mass transfer, Monge-Ampere equation and Geometric inequalities''
Math Annex 1118
11:30 a.m., Tuesday, February 1, 2000
Graduate Student Seminar
Amy Norris, Department of Mathematics, UBC
LSK Bldg., Room 301
1:30 p.m., Wednesday, February 2, 2000
Algebra Topology Seminar
Kee Lam, Department of Mathematics, UBC
``Pseudo-reflection groups and generalized braid groups''
*note change of speaker (updated Feb. 1st)*
West Mall Annex 216 (PIMS)
3:30 p.m., Wednesday, February 2, 2000
Math Biology Seminar
Michael Dobeli, Departments of Mathematics and Zoology, UBC
``Evolutionary branching and sympatric speciation caused by different types of ecological interactions''
LSK Bldg., Room 301 (IAM seminar room)
*note change of time and location*
3:30 p.m., Wednesday, February 2, 2000
Probability Seminar
Ed Perkins, Department of Mathematics, UBC
``Mutually catalytic branching in the plane II''
Math Annex 1102
3:30 p.m., Friday, February 4, 2000
Mathematics Colloquium
Anna Vainchtein, Division of Mechanics and Computation,
Department of Mechanical Engineering, Stanford University
``Hysteresis and interface dynamics in mathematical models
of phase transitions''
Math 100
4:30 p.m., Monday, February 7, 2000
PDE Seminar
Nassif Ghoussoub, Department of Mathematics, UBC
``Mass transfer, Monge-Ampere equation and Geometric inequalities II''
Math Annex 1118
11:30 a.m., Tuesday, February 8, 2000
Graduate Student Seminar
Stefan Reinker, Department of Mathematics, UBC
``Does the Brain need Mathematics?''
LSK Bldg., Room 301
1:30 p.m., Wednesday, February 9, 2000
Algebra Topology Seminar
Kee Lam, Department of Mathematics, UBC
``Hyperplane arrangements and pseudo-reflection groups''
West Mall Annex 216 (PIMS)
4:30 p.m., Thursday, February 10, 2000
PIMS-MITACS Mathematical Finance Seminar
Yonggan Zhao, Department of Commerce, UBC
``Portfolio selection with a minimum wealth requirement''
West Mall Annex 216 (PIMS)
2:30 p.m., Monday, February 21, 2000
PDE Seminar
Nassif Ghoussoub, Department of Mathematics, UBC
``Continuous Mass Transport, the Euler and the Fokker-Plank equations''
Math Annex 1118
3:30 p.m., Monday, February 21, 2000
IAM-MATH BIO Colloquium
Mark Lewis, Department of Mathematics, University of Utah
``Realistic models for biological invasion''
LSK Bldg., Room 301
1:30 p.m., Wednesday, February 23, 2000
Algebra/Topology Seminar
David Burggraf, Department of Mathematics, UBC
``Group actions on elliptic dessins d'enfants''
West Mall Annex 216 (PIMS)
3:30 p.m., Wednesday, February 23, 2000
Probability Seminar
Gregory F. Lawler, Department of Mathematics, Duke University
``Computing the intersections exponents for planar Brownian motion'''
Math Annex 1102
4:30 p.m., Thursday, February 24, 2000
PIMS-MITACS Mathematical Finance Seminar
Ulrich Haussmann, Department of Mathematics, UBC
``Optimal portfolio selection with limited diversification
(joint work with N. Dokuchaev)''
West Mall Annex 216 (PIMS)
3:30 p.m., Friday, February 25, 2000
Mathematics Colloquium
Gregory F. Lawler, Department of Mathematics, Duke University
``Universality and conformal invariance in two dimensional
statistical physics''
Room Math 100
2:30 p.m., Monday, February 28, 2000
PDE Seminar
Nassif Ghoussoub, Department of Mathematics, UBC
``Continuous Mass Transport, the Euler and
the Fokker-Plank equations, II''
Math Annex 1118
3:30 p.m., Monday, February 28, 2000
Joint IAM-PIMS Distinguished Colloquium
Marc Feldman, Department of Biological Sciences, Stanford
``Mathematics and Statistics of Human DNA Polymorphisms:
Forward and Backward to History''
LSK Bldg., Room 301
11:30 a.m., Tuesday, February 29, 2000
Graduate Student Seminar
Adriana Dawes, Department of Mathematics, UBC
LSK Bldg., Room 301
3:30 p.m., Tuesday, February 29, 2000
Math Biology Seminar
John Pearson, Los Alamos National Laboratory
``Chemical Reaction Diffusion Systems: An Overview''
Math Annex 1102
1:30 p.m., Wednesday, March 1, 2000
Algebra/Topology Seminar
David Burggraf, Department of Mathematics, UBC
``Group actions on elliptic dessins d'enfants, II''
West Mall Annex 216 (PIMS)
2:30 p.m., Wednesday, March 1, 2000
Math Biology Seminar
John Pearson, Los Alamos National Laboratory
``Fire-Diffuse-Fire and the Dynamics of Intracellular Calcium Waves''
Math Annex 1102
3:30 p.m., Wednesday, March 1, 2000
Probability Seminar
N. Dokuchaev, PIMS, UBC
``Stochastic partial differential equations
with a quasi-periodic boundary condition''
Math Annex 1102
9:45--10:45 a.m., Thursday, March 2, 2000
Number Theory Seminar
Nike Vatsal, Department of Mathematics, UBC
``Uniform Distribution of Heegner Points''
Math Annex 1102
11:00 -- 12:00 p.m., Thursday, March 2, 2000
Number Theory Seminar
Christopher M. Skinner, Institute for Advanced Study, Princeton
``Base Change and a Problem of Serre''
Math Annex 1102
4:30 p.m., Thursday, March 2, 2000
PIMS-MITACS Mathematical Finance Seminar
N. Dokuchaev, PIMS, UBC
``Optimal portfolio selection based on historical prices''
West Mall Annex 216 (PIMS)
3:30 p.m., Friday, March 3, 2000
Mathematics Colloquium
Christopher M. Skinner, Institute for Advanced Study, Princeton
``The diophantine equation a^n+b^n=2c^2''
Room Math 100
1:30 p.m., Saturday, March 4, 2000
Northwest Probability Seminar
Christian Borgs, Microsoft Theory Group
``Partition function zeros: A generalized Lee-Yang theorem''
Smith 105, University of Washington
3:30 p.m., Saturday, March 4, 2000
Northwest Probability Seminar
Xiaowen Zhou, Department of Mathematics, UBC
``Sample path continuity of continuous-site stepping-stone models''
Smith 105, University of Washington
3:30 p.m., Monday, March 6, 2000
Applied Mathematics Colloquium
Avner Friedman, Department of Mathematics, University of Minnesota
``Bifurcation of free boundary problems with application
to tumor growth''
LSK Bldg., Room 301
1:30 p.m., Wednesday, March 8, 2000
Algebra/Topology Seminar
Duane Randall, Department of Mathematics & Computer Science,
Loyola University
``A Survey of the Kervaire Invariant Problem''
West Mall Annex 216 (PIMS)
10 a.m., Thursday, March 9, 2000
Special Algebra/Topology Seminar
Stephen Bigelow, UC Berkeley
``Braid groups are linear''
Math Annex 1102
4:30 p.m., Thursday, March 9, 2000
PIMS-MITACS Mathematical Finance Seminar
John Chadam, Pittsburgh University
``The Exercise Boundary for an American Put Option:
Analytical and Numerical Approximations''
West Mall Annex 216 (PIMS)
3:30 p.m., Friday, March 10, 2000
Mathematics Colloquium
John Chadam, University of Pittsburg
``A mathematical model of bioremediation in a porous medium''
Math 100
3:30 p.m., Monday, March 13, 2000
Joint IAM-PIMS Distinguished Colloquium
Alwyn Scott, Department of Mathematics, Univ. of Arizona
and Department of Mathematical Modelling,
Technical University of Denmark
``Nonlinear Science: Past, Present and Future''
LSK Bldg., Room 301
11:30 a.m., Tuesday, March 14, 2000
Graduate Student Seminar
Stefan Reinker, Department of Mathematics, UBC
``Does the Brain need Mathematics?''
LSK Bldg., Room 301
1:30 p.m., Wednesday, March 15, 2000
Algebra/Topology Seminar
Denis Sjerve, Department of Mathematics, UBC
``Automorphisms of prime Galois coverings of the Riemann Sphere''
West Mall Annex 216 (PIMS)
4:30 p.m., Thursday, March 16, 2000
PIMS-MITACS Mathematical Finance Seminar
Jaksa Cvitanic, University of Southern California
``Methods of partial hedging''
West Mall Annex 216 (PIMS)
3:30 p.m., Friday, March 17, 2000
Mathematics Colloquium
Akbar Rhemtulla, Department of Mathematical Sciences,
University of Alberta
``Expressing Elements of the Commutator Subgroup of a Group
as a Product of Least Number of Commutators''
Room Math 100
11:30 a.m., Tuesday, March 21, 2000
Graduate Student Seminar
Ron Ferguson, Department of Mathematics, UBC
``Permutations with low discrepancy k-sums''
LSK Bldg., Room 301
1:30 p.m., Wednesday, March 22, 2000
Algebra/Topology Seminar
Guillermo Moreno, Centro de Investigacion y Estudios
Advanzados del IPN and University of Oregon
``Higher Dimensional Cayley Dickson Algebras''
West Mall Annex 216 (PIMS)
3:30 p.m., Friday, March 24, 2000
Mathematics Colloquium
Andrew J. Sommese, Univ. of Notre Dame
``Numerical Primary Decomposition''
Room Math 100
3:30 p.m., Monday, March 27, 2000
IAM-MATH BIO Colloquium
Jinko Graham, Department of Mathematics & Statistics,
Simon Fraser University
``Fine-Scale Mapping of a Rare Allele via Disequilibrium Likelihoods''
LSK Bldg., Room 301 (formerly Old Computer Sciences Bldg.)
1:30 p.m., Wednesday, March 29, 2000
Algebra/Topology Seminar
Zhongmou Li, UBC
``Immersion of 3-manifolds in 3-space"
West Mall Annex 216 (PIMS)
4:30 p.m., Thursday, March 30, 2000
PIMS-MITACS Mathematical Finance Seminar
Raman Uppal, Commerce and Business Administration, UBC
``Risk Aversion and Optimal Portfolio Policies
in Partial and General Equilibrium Economies''
West Mall Annex 216 (PIMS)
3:30 p.m., Monday, April 3, 2000
Complexity Seminar
Anders Martin Lof, Steve Marion, Cindy Greenwood
``Asymptotics of the Near-Critical Epidemic Process''
Peter Wall Institute Conference Room
11:30 a.m., Tuesday, April 4, 2000
Graduate Student Seminar
Glen Pugh, Department of Mathematics, UBC
``Riemann, Siegel and Turing: Numerical Evidence for the Riemann Hypothesis''
LSK Bldg., Room 301 (formerly Old Computer Science Bldg.)
1:30 p.m., Wednesday, April 5, 2000
Algebra/Topology Seminar
Bert Wiest, Department of Mathematics, UBC
``Quasi-isometries in group theory''
West Mall Annex 216 (PIMS)
3:30 p.m., Wednesday, April 5, 2000
Probability Seminar
Marek Biskup, Microsoft Research
``Rigorous theory of partition function zeros
at first-order phase transitions''
Math Annex 1102
1:30 p.m., Wednesday, June 14, 2000
Special Number Theory Seminar
Hugh Montgomery, University of Michigan
``Greedy sums of distinct squares"
Math Annex 1102
2:30 p.m., Wednesday, September 6, 2000
Topology Seminar
Prof. Youcheng Zhou, Zhejiang University, China
``Effros Property and Homogeniety''
Math Annex 1102
3:30 p.m., Wednesday, September 6, 2000
Probability Seminar
Antal Jarai, PIMS-UBC
``Invasion percolation and the incipient infinite cluster''
Math Annex 1102
3:30 p.m., Wednesday, September 13, 2000
Algebraic Geometry Seminar
Behrang Noohi, Department of Mathematics, UBC
``Fundamental Groups of Algebraic Stacks''
Math Annex 1118
2:30 p.m., Wednesday, September 13, 2000
UBC PIMS Colloquium
Beno Eckmann, ETH Zurich
``The Euler Characteristic -- some Variations and Ramifications''
WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, September 13, 2000
Probability Seminar
Frank den Hollander, University of Nijmegen
``How random is the composition of two random processes?''
Math Annex 1102
3:30 p.m., Wednesday, September 13, 2000
IAM-PIMS Distinguished Colloquium Speaker
Carlo Cercignani, Dipartimento di Matematica,
Politecnico di Milano, Milan, Italy
``Kinetic Models for Granular Materials: An Exact Solution''
LSK Bldg. Room 301
2:30 p.m., Thursday, September 14, 2000
Algebra-Topology Seminar
Beno Eckmann, ETH Zurich
``Projections, Group Algebras, and Geometry of Groups''
WMAX 216
4:30 p.m., Thursday, September 14, 2000
PIMS-MITACS Mathematical Finance Seminar
D. Chan, UBC
``Introduction to Value at Risk''
WMAX 216
3:30 p.m., Friday, September 15, 2000
Mathematics Colloquium/PIMS Distinguished Chair Lecture
David Brydges, PIMS-Department of Mathematics, University of Virginia
``Self Avoiding Walk and Differential Forms''
Math 100
10:00-11:00 a.m., Monday, September 18, 2000
Scientific Computing and Visualization Seminar
Arian Novruzi, PIMS-UBC
``Newton method in shape optimization problems.
Some comments on its parallelization''
CICSR 204, contact Brian Wetton for details
on this seminar series
3:30 p.m., Monday, September 18, 2000
Mathematics Colloquium
Leonid Mytnik, Israel Institute of Technology
``Duality approach to proving uniqueness''
Math 100
4:45 p.m., Monday, September 18, 2000
PIMS-MITACS Mathematical Finance Seminar
Steve Shreve, Carnegie-Mellon Univ.
``Valuation of Exotic Options under Shortselling Constraints''
WMAX 216 (PIMS seminar room)
3:30 p.m., Tuesday, September 19, 2000
PIMS Distinguished Chair at UBC Lecture
David Brydges, PIMS-Department of Mathematics and Physics,
University of Virginia
``Mehler's Formula and the Renormalization Group"
(Lecture 2 in the series)
Math 104
2:30 p.m., Wednesday, September 20, 2000
Algebra-Topology Seminar
Kee Lam, Mathematics, UBC
``Rational homotopy theory''
WMAX 216
3:30 p.m., Wednesday, September 20, 2000
Algebraic Geometry Seminar
Behrang Noohi, Mathematics, UBC
``Fundamental Groups of Algebraic Stacks, II''
WMAX 216 (previously announced for 2:30 in Math Annex 1118)
3:30 p.m., Wednesday, September 20, 2000
Institute of Applied Mathematics Colloquium
Lionel G. Harrison, Department of Chemistry, UBC
``Branching in Plants: Exploring Reaction-Diffusion:
(1) On the Hemisphere
(2) Interacting with Continuous Morphological Change''
LSK Bldg. Room 301
1:30 p.m., Thursday, September 21, 2000
Mathematics Colloquium
Andrea Fraser, University of New South Wales
Multiplier Operators on the Heisenberg group
Math Annex 1100
4:00 - 5:00 p.m., Thursday, September 21, 2000
PIMS-MITACS Computational Statistics and Data Mining Seminar
Peter J. Rousseeuw, PIMS-Universitaire Instelling Antwerpen (UIA), Belgium
``An Introduction to Regression Depth''
CICSR 208
1:30 - 2:30 p.m., Friday, September 22, 2000
PIMS-MITACS Computational Statistics and Data Mining Seminar
Peter J. Rousseeuw, PIMS-Universitaire Instelling Antwerpen (UIA), Belgium
``Depth Tests of Symmetry and Regression''
LSK 301
3:30 p.m., Friday, September 22, 2000
Mathematics Colloquium
Jacques Hurtubise, CRM and University of Montreal
``Integrable Systems and Surfaces''
Room Math 100
10:00-11:00 a.m., Monday, September 25, 2000
Scientific Computing and Visualization Seminar
Arian Novruzi, PIMS-UBC
``Newton method in shape optimization problems.
Some comments on its parallelization, Part II''
CICSR 204
3:30 p.m., Monday, September 25, 2000
Mathematics Colloquium
Laura Scull, Department of Mathematics, University of Michigan
``Equivariant Homotopy Theory: Classic Constructions in a Modern Setting''
Math 100
10:30 a.m., Tuesday, September 26, 2000
Special Algebra-Topology Seminar
Laura Scull, Department of Mathematics, University of Michigan
``Algebraic Models for Equivariant Homotopy Theory''
Math Annex 1102
1:30 p.m., Tuesday, September 26, 2000
Math Biology Seminar
Israeli Ran & Alexandra Chavez-Ross, UBC
``MITACS progress report: the tinnitus project''
LSK Bldg, Room 301
3:30 p.m., Tuesday, September 26, 2000
PIMS Distinguished Chair at UBC Lecture
David Brydges, PIMS-Department of Mathematics and Physics,
University of Virginia
``Hierarchical Lattices and the Renormalization Group revisited
(Lecture 3 in the series)''
Math 104
3:30 p.m., Wednesday, September 27, 2000
IAM-PIMS Distinguished Colloquium
David Brydges, PIMS-Department of Mathematics and Physics,
University of Virginia
``Gaussian Integrals and Mean Field Theory''
LSK Bldg. Room 301
2:30 p.m., Thursday, September 28, 2000
PDE Seminar
Jingyi Chen, Mathematics, UBC
``Quaternions, Hyperkahler manifolds and a first order system of PDEs''
WMAX 216 (PIMS seminar room)
4:30 p.m., Thursday, September 28, 2000
PIMS-MITACS Mathematical Finance Seminar
Jose Rodriguez, Mathematics, UBC
``More Value at Risk''
WMAX 216
3:30 p.m., Friday, September 29, 2000
Mathematics Colloquium
Ravi Vakil, Department of Mathematics, M.I.T.
``Branched covers of the sphere and the moduli space of curves:
Geometry, physics, representation theory, combinatorics''
Math 100
10:00-11:00 a.m., Monday, October 2, 2000
Scientific Computing and Visualization Seminar
Oliver Dorn, Computer Science, UBC
``The use of level set methods for shape reconstruction
in electromagnetic tomography''
CICSR 204
2:30 p.m., Wednesday, October 4, 2000
Algebra/Topology Seminar
Dale Rolfsen, Mathematics, UBC
``Ordered groups and 3-manifolds''
WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, October 4, 2000
PIMS Distinguished Chair at UBC Lecture
David Brydges, PIMS-Department of Mathematics and Physics,
University of Virginia
``Analysis with the Renormalization Group and Outlook
(Lecture 4 in the series)''
WMAX 216
2:30 p.m., Thursday, October 5, 2000
PDE Seminar
Vitali Vougalter, Mathematics, UBC
``Diamagnetic behavior of sums of Dirichlet eigenvalues''
WMAX 216
3:30 p.m., Friday, October 6, 2000
Mathematics Colloquium
Richard Froese, Mathematics, UBC
``Realizing holonomic constraints in classical and quantum mechanics''
Math 100
1:30 p.m., Tuesday, October 10, 2000
Math Biology Seminar
Susan Anne Baldwin, Bio-Resource Engineering, UBC
``Heat Transfer Model of Thermal Balloon Endometrial Ablation''
LSK Bldg, Room 301
2:30 p.m., Wednesday, October 11, 2000
Algebra/Topology Seminar
Dale Rolfsen, Mathematics, UBC
``Ordered groups and 3-manifolds, II''
WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, October 11, 2000
Institute of Applied Mathematics Colloquium
W. Kendal Bushe, Department of Mechanical Engineering, UBC
``Large Eddy Simulation of Turbulent Reacting Flows''
LSK Bldg. Room 301
3:30 p.m., Wednesday, October 11, 2000
Algebraic Geometry Seminar
Jim Carrell, Mathematics, UBC
``Equivariant cohomology of varieties with a triangular group action''
WMAX 216
3:30 p.m., Wednesday, October 11, 2000
Probability Seminar
Liqing Yan, Mathematics-PIMS, UBC
``The Euler scheme for stochastic differential equations
with irregular coefficients''
Math Annex 1102
2:30 p.m., Thursday, October 12, 2000
PDE Seminar
Christine Chambers, Mathematics, UBC
WMAX 216
4:30 p.m., Thursday, October 12, 2000
PIMS-MITACS Mathematical Finance Seminar
Simon MacNair, Mathematics-PIMS, UBC
``Utility Maximization with Stochastic Factors''
WMAX 216
3:30 p.m., Friday, October 13, 2000
Mathematics Colloquium
Richard Schoen, Department of Mathematics, Stanford University
``A survey of recent progress in general relativity''
Math 100
10:00-11:00 a.m., Monday, October 16, 2000
Scientific Computing and Visualization Seminar
Uri Ascher, Computer Science, UBC
``Grid refinement and scaling for distributed parameter estimation problems''
CICSR 204
2:30 p.m., Wednesday, October 18, 2000
Algebra/Topology Seminar
Bert Wiest, Mathematics-PIMS, UBC
``Ordered groups and 3-manifolds, III''
WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, October 18, 2000
Institute of Applied Mathematics Colloquium
Robert Miura, Mathematics, UBC
``Applications of Excitable Cell Models''
LSK Bldg. Room 301
3:30 p.m., Wednesday, October 18, 2000
Probability Seminar
Siva Athreya, Mathematics-PIMS,UBC
``Long time behaviour of a Brownian flow with jumps''
Math Annex 1102
3:30 p.m., Wednesday, October 18, 2000
Algebraic Geometry Seminar
Jim Carrell, Mathematics, UBC
``Equivariant cohomology of varieties with a triangular group action, II''
WMAX 216
4:30 p.m., Wednesday, October 18, 2000
Student Algebraic Geometry Seminar
Boris Tschirschwitz, Mathematics, UBC
WMAX 216
3:30 p.m., Friday, October 20, 2000
Mathematics Colloquium
Joel Friedman, Mathematics, UBC
``Expanders, Eigenvalues, and Related Topics''
Math 100
a.m.-p.m., Friday, Saturday, October 20-21, 2000
West Coast Optimization Meeting
Speakers: scheduled technical program
Location: University of Washington (Seattle)
For information email Phillip Loewen, loew@math.ubc.ca
10:00-11:00 a.m., Monday, October 23, 2000
Scientific Computing and Visualization Seminar
Uri Ascher, Computer Science, UBC
``Grid refinement and scaling for distributed parameter estimation problems, II''
CICSR 204
2:30 p.m., Wednesday, October 25, 2000
Algebra/Topology Seminar
Zhongmou Li, Mathematics, UBC
``Every orientable 3-manifold with boundary embeds in K_5 join 1''
WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, October 25, 2000
Institute of Applied Mathematics Colloquium
Keith Promislow, Department of Mathematics & Statistics, SFU
``Modulational Stability via Renormalization Methods for Patterns in Forced Dispersive Systems''
LSK Bldg. Room 301
3:30 p.m., Wednesday, October 25, 2000
Probability Seminar
Remco van der Hofstad, Delft University
``Improving performance of third generation mobile phone systems''
Math Annex 1102
3:30 p.m., Wednesday, October 25, 2000
*Postponed til Nov 1st*
Algebraic Geometry Seminar
Jim Carrell, Mathematics, UBC
``Equivariant cohomology of varieties with a triangular group action, III''
WMAX 216
2:30 p.m., Thursday, October 26, 2000
PDE Seminar
Izabella Laba, Mathematics, UBC
``The spectral set conjecture and multiplicative properties of roots of polynomials''
WMAX 216
3:30 p.m., Friday, October 27, 2000
Mathematics Colloquium
Remco van der Hofstad, Delft University
``Recent progress in one-dimensional and high-dimensional
statistical mechanical models''
Math 100
3:30 p.m., Wednesday, November 1, 2000
IAM-PIMS Distinguished Colloquium
Linda Petzold, Departments of Mechanical and Environmental Engineering
and Computer Science, Univ. of California at Santa Barbara
``Algorithms and Software for Dynamic Optimization
with Application to Chemical Vapor Deposition Processes''
LSK Bldg. Room 301
3:30 p.m., Wednesday, November 1, 2000
Probability Seminar
Robert Israel, Mathematics, UBC
``Finding generators from transition matrices''
Math Annex 1102
3:30 p.m., Wednesday, November 1, 2000
Algebraic Geometry Seminar (postponed from 25 Oct)
Jim Carrell, Mathematics, UBC
``Equivariant cohomology of varieties with a triangular group action, III ''
WMAX 216
4:30 p.m., Thursday, November 2, 2000
PIMS-MITACS Mathematical Finance Seminar
P. Laurence, U. Roma and NYU
``American options on multiple assets: bounds via a comparison principle''
WMAX 216
10:00-11:00 a.m., Monday, November 6, 2000
Scientific Computing and Visualization Seminar
Brian Wetton, Mathematics, UBC
``Asymptotic Error Analysis: overview and some unsolved problems''
CICSR 204
3:30 p.m., Wednesday, November 8, 2000
IAM Colloquium
Alejandro Garcia, Department of Physics, San Jose State University, CA
``Stochastic Particle Algorithms: from DSMC to CUBA''
LSK Bldg. Room 301
3:30 p.m., Wednesday, November 8, 2000
Probability Seminar
Xiaowen Zhou, Mathematics, UBC
``A duality formula for multi-type voter model''
Math Annex 1102
3:30 p.m., Wednesday, November 8, 2000
Algebraic Geometry Seminar
Anne O'Halloran, Mathematics, UBC
``The Cohomology of Kontsevich's Stack of Stable Maps to P^n - The Case of Conics"
WMAX 216
10:30 a.m., Thursday, November 9, 2000
Harmonic and Functional Analysis Seminar
Professor Garth Dales, Leeds University
``Amenability and weak amenability for measure algebras''
Math Annex 1102
2:30 p.m., Thursday, November 9, 2000
PDE Seminar
Manfred Salmhofer, ETH -- Zurich
``On the conjecture called `Migdal's Theorem'''
WMAX 216
3:30 p.m., Friday, November 10, 2000
Mathematics Colloquium
Michael Ward, Mathematics, UBC
``The Stability and Dynamics of Spikes for a Reaction-Diffusion System''
Math 100
2:30 p.m., Wednesday, November 15, 2000
Algebra/Topology Seminar
Don Witt, Department of Physics and Astronomy, UBC
``The Smale Conjecture''
WMAX 216
3:30 p.m., Wednesday, November 15, 2000
IAM Colloquium
Roland Stull, Department of Earth and Ocean Sciences, UBC
``A Nonlocal Description of Atmospheric Turbulence''
LSK Bldg. Room 301
3:30 p.m., Wednesday, November 15, 2000
Algebraic Geometry Seminar
Anne O'Halloran, Mathematics, UBC
``The Cohomology of Kontsevich's Stack of Stable Maps to P^n
- The Case of Conics, Part II''
WMAX 216
4:30 p.m., Wednesday, November 15, 2000
Student Algebraic Geometry Seminar
Maciej Mizerski, Mathematics, UBC
``Introduction to Derived Functors (Cohomology)''
Math Annex 1102
4:30 p.m., Wednesday, November 15, 2000
PIMS-MITACS Mathematical Finance Seminar
V. Dion, Mathematics, UBC
``A tutorial on Mortgage Backed Securities''
WMAX 216
2:30 p.m., Thursday, November 16, 2000
PDE Seminar
Arian Novruzi, UBC ``Some results related to free boundary
and shape optimisation problems''
WMAX 216
3:30 p.m., Friday, November 17, 2000
Mathematics Colloquium
Dale Rolfsen, Mathematics, UBC
``Do you want to be a mathematical millionaire?
The Poincare conjecture''
Math 100
10:00-11:00 a.m., Monday, November 20, 2000
Scientific Computing and Visualization Seminar
Radu Bradean, UBC-SFU MITACS PDF
``Transport Phenomena in Porous Fuel Cell Electrodes''
CICSR 204
3:30 p.m., Monday, November 20, 2000
Mathematics Colloquium
Richard Bertram, Institute of Molecular Biophysics,
Florida State University, Tallahassee, Florida
``Mathematical Analysis of Deterministic and Stochastic Models
of Synaptic Transmitter Release''
Math 100
3:30 p.m., Tuesday, November 21, 2000
Math Biology Seminar
Richard Bertram, Institute of Molecular Biophysics,
Florida State University
``Models of Synaptic Transmitter Release and Short-Term Plasticity''
Math 104
3:30 p.m., Wednesday, November 22, 2000
IAM Colloquium
Florin Diacu, Univ. Victoria-PIMS Site Director,
Department of Mathematics and Statistics, Univ. of Victoria
``On the Dynamical Stability of the Helium Atom''
LSK Bldg. Room 301
3:30 p.m., Wednesday, November 22, 2000
Algebraic Geometry Seminar
Kai Behrend, Mathematics, UBC
``Differential Graded Schemes''
WMAX 216
4:30 p.m., Wednesday, November 22, 2000
Student Algebraic Geometry Seminar
Boris Tschirschwitz, Mathematics, UBC
``Derived Functors: Acyclic Resolutions''
WMAX 216
2:30 p.m., Thursday, November 23, 2000
PDE Seminar
Stephen Gustafson, Courant Institute of Mathematical Sciences
``Stability of Localized Solutions of Landau-Lifshitz Equations''
WMAX 216
2:30 p.m., Thursday, November 23, 2000
Special Institute of Applied Mathematics Seminar
Natalia Kouzniak, MITACS PDF, Department of Mathematics, UBC
``Analytical Solutions and Numerical Results in Elasto-plastic
and Elasto-dynamic Problems of Fracture Mechanics''
Math 204
3:30 p.m., Friday, November 24, 2000
Mathematics Colloquium
Stephen Gustafson, Courant Institute
``Some Mathematical Problems in the Ginzburg-Landau
Theory of Superconductivity''
Math 100
3:30 p.m., Monday, November 27, 2000
Mathematics Colloquium
Doug Park, Department of Mathematics & Statistics, McMaster University
``Exotic smooth structures on simply connected 4-dimensional manifolds''
Math 100
Refreshments will be served at 3:15 in the Math Annex
Coffee Lounge, Room 1115.
10:30 a.m., Tuesday, November 28, 2000
Special Topology Seminar
Doug Park, McMaster University
``Gluing formulae for Seiberg-Witten invariant along 3-dimensional torus''
Math Annex 1102
3:30 p.m., Wednesday, November 29, 2000
IAM Colloquium
Ian Frigaard, Department of Mathematics, UBC
``Super-Stable Parallel Flows of Multiple Visco-Plastic Fluids''
LSK Bldg. Room 301
3:30 p.m., Wednesday, November 29, 2000
Algebraic Geometry Seminar (postponed from Nov. 22)
Kai Behrend, Mathematics, UBC
``Differential Graded Schemes''
WMAX 216
2:30 p.m., Thursday, November 30, 2000
PDE Seminar
Martin Bause, University of Erlangen, Nuremberg, Germany
``Numerical approximation schemes for the Poisson-Stokes equations
of compressible viscous flow''
WMAX 216
3:30 p.m., Friday, December 1, 2000
Joint PIMS-MITACS Mathematical Finance Seminar
and Mathematics Colloquium
Darrell Duffie, Stanford University
``Valuation in Dynamic Bargaining Markets''
Math 100
10:00-11:00 a.m., Monday, December 4, 2000
Scientific Computing and Visualization Seminar
Jim Varah, Computer Science, UBC
``Discrete Tomography: Projections, Moments, and Shape Reconstruction''
CICSR 204
3:30 p.m., Monday, December 4, 2000
Mathematics Colloquium
Michael Bennett, Department of Mathematics,
University of Illinois at Urbana-Champaign
``Effective methods for Diophantine problems''
Math 100
1:30 p.m., Tuesday, December 5, 2000
Number Theory Seminar
Michael Bennett, Univ. of Illinois at Urbana-Champaign
``Pillai's conjecture revisited''
Math Annex 1102
3:30 p.m., Friday, December 8, 2000
Special Mathematics Colloquium
Professor Ram Murty, Queen's University
``Riemann Hypothesis: A Status Report''
Math Annex 1100
3:30 p.m., Friday, January 7, 2000 Mathematics Colloquium Stuart G. Whittington, Department of Chemistry, University of Toronto ``Coloured self-avoiding walks'' Room Math 100
2:30 p.m., Wednesday, January 12, 2000 Math Biology Seminar Alexandra Chavez-Ross, Department of Mathematics, UBC ``Follicle Selection Dynamics in the Mammalian Ovary'' Room Math Annex 1102
3:30 p.m., Wednesday, January 12, 2000 Probability Seminar Rick Durrett, Cornell University ``Single Nucleotide Polymorphisms in the Human Genome: How many are there? How many will Celera find?''
Room Math Annex 1102
3:30 p.m., Friday, January 14, 2000 Mathematics Colloquium Christian Klingenberg, Applied Mathematics, Wuerzburg University ``Mathematical modelling and numerical simulation in star formation'' Room
Math 100
3:30 p.m., Monday, January 17, 2000 IAM-MATH BIO Colloquium Leonard Sander, Physics Department, University of Michigan ``Scaling and Crossovers in Diffusion Limited Aggregation'' LSK Bldg., Room 301
11:30 a.m., Tuesday, January 18, 2000 Graduate Student Seminar Nathan Ng, Department of Mathematics, UBC ``Prime Numbers: A Survey'' LSK Bldg., Room 301
1:30 p.m., Wednesday, January 19, 2000 Algebra/Topology Seminar Bert Wiest, PIMS Postdoctoral Fellow, UBC ``Ordering of mapping class groups after Thurston'' West Mall Annex 216 (PIMS)
3:30 p.m., Wednesday, January 19, 2000 Probability Seminar Richard Bass, University of Connecticut ``Local times for space-time Brownian motion'' Room Math Annex 1102
3:30 p.m., Friday, January 21, 2000 Mathematics Colloquium Anne Bourlioux, University of Montreal ``Small scale asymptotic models for large scale simulations of turbulent premixed flames'' Room Math
1:30 p.m., Tuesday, January 25, 2000 Graduate Student Seminar Abigail Wacher, Department of Mathematics, UBC ``The Modeling of Rapid Thermal Processing in a Chamber'' LSK Bldg. Room 301
1:30 p.m., Wednesday, January 26, 2000 Algebra Topology Seminar Kee Y. Lam, Department of Mathematics, UBC ``Pseudo-reflection groups and generalized braid groups'' West Mall Annex 216 (PIMS)
2:30 p.m., Wednesday, January 26, 2000 Math Biology Seminar Michael C. Mackey, McGill University ``Periodic Hematological Diseases: Insight into the pathology from mathematical modeling'' Math Annex
3:30 p.m., Monday, January 31, 2000 Joint IAM-PIMS Distinguished Colloquium Anne Greenbaum, Department of Mathematics, University of Washington ``Analysis of Krylov Space Methods for Solving Linear
Systems'' LSK Bldg., Room 301
4:30 p.m., Monday, January 31, 2000 PDE Seminar Nassif Ghoussoub, Department of Mathematics, UBC ``Mass transfer, Monge-Ampere equation and Geometric inequalities'' Math Annex 1118
11:30 a.m., Tuesday, February 1, 2000 Graduate Student Seminar Amy Norris, Department of Mathematics, UBC ``TBA'' LSK Bldg., Room 301
1:30 p.m., Wednesday, February 2, 2000 Algebra Topology Seminar Kee Lam, Department of Mathematics, UBC ``Pseudo-reflection groups and generalized braid groups'' *note change of speaker (updated Feb.
1st)* West Mall Annex 216 (PIMS)
3:30 p.m., Wednesday, February 2, 2000 Math Biology Seminar Michael Dobeli, Departments of Mathematics and Zoology, UBC ``Evolutionary branching and sympatric speciation caused by different types of
ecological interactions'' LSK Bldg., Room 301 (IAM seminar room) *note change of time and location*
3:30 p.m., Wednesday, February 2, 2000 Probability Seminar Ed Perkins, Department of Mathematics, UBC ``Mutually catalytic branching in the plane II'' Math Annex 1102
3:30 p.m., Friday, February 4, 2000 Mathematics Colloquium Anna Vainchtein, Division of Mechanics and Computation, Department of Mechanical Engineering, Stanford University ``Hysteresis and interface
dynamics in mathematical models of phase transitions'' Math 100
4:30 p.m., Monday, February 7, 2000 PDE Seminar Nassif Ghoussoub, Department of Mathematics, UBC ``Mass transfer, Monge-Ampere equation and Geometric inequalities II'' Math Annex 1118
11:30 a.m., Tuesday, February 8, 2000 Graduate Student Seminar Stefan Reinker, Department of Mathematics, UBC ``Does the Brain need Mathematics?'' LSK Bldg., Room 301
1:30 p.m., Wednesday, February 9, 2000 Algebra Topology Seminar Kee Lam, Department of Mathematics, UBC ``Hyperplane arrangements and pseudo-reflection groups'' West Mall Annex 216 (PIMS)
4:30 p.m., Thursday, February 10, 2000 PIMS-MITACS Mathematical Finance Seminar Yonggan Zhao, Department of Commerce, UBC ``Portfolio selection with a minimum wealth requirement'' West Mall Annex 216
2:30 p.m., Monday, February 21, 2000 PDE Seminar Nassif Ghoussoub, Department of Mathematics, UBC ``Continuous Mass Transport, the Euler and the Fokker-Plank equations'' Math Annex 1118
3:30 p.m., Monday, February 21, 2000 IAM-MATH BIO Colloquium Mark Lewis, Department of Mathematics, University of Utah ``Realistic models for biological invasion'' LSK Bldg., Room 301
1:30 p.m., Wednesday, February 23, 2000 Algebra/Topology Seminar David Burggraf, Department of Mathematics, UBC ``Group actions on elliptic dessins d'enfants'' West Mall Annex 216 (PIMS)
3:30 p.m., Wednesday, February 23, 2000 Probability Seminar Gregory F. Lawler, Department of Mathematics, Duke University ``Computing the intersections exponents for planar Brownian motion''' Math
Annex 1102
4:30 p.m., Thursday, February 24, 2000 PIMS-MITACS Mathematical Finance Seminar Ulrich Haussmann, Department of Mathematics, UBC ``Optimal portfolio selection with limited diversification (joint work
with N. Dokuchaev)'' West Mall Annex 216 (PIMS)
3:30 p.m., Friday, February 25, 2000 Mathematics Colloquium Gregory F. Lawler, Department of Mathematics, Duke University ``Universality and conformal invariance in two dimensional statistical
physics'' Room Math 100
2:30 p.m., Monday, February 28, 2000 PDE Seminar Nassif Ghoussoub, Department of Mathematics, UBC ``Continuous Mass Transport, the Euler and the Fokker-Plank equations, II'' Math Annex 1118
3:30 p.m., Monday, February 28, 2000 Joint IAM-PIMS Distinguished Colloquium Marc Feldman, Department of Biological Sciences, Stanford ``Mathematics and Statistics of Human DNA Polymorphisms: Forward
and Backward to History'' LSK Bldg., Room 301
11:30 a.m., Tuesday, February 29, 2000 Graduate Student Seminar Adriana Dawes, Department of Mathematics, UBC ``TBA'' LSK Bldg., Room 301
3:30 p.m., Tuesday, February 29, 2000 Math Biology Seminar John Pearson, Los Alamos National Laboratory ``Chemical Reaction Diffusion Systems: An Overview'' Math Annex 1102
1:30 p.m., Wednesday, March 1, 2000 Algebra/Topology Seminar David Burggraf, Department of Mathematics, UBC ``Group actions on elliptic dessins d'enfants, II'' West Mall Annex 216 (PIMS)
2:30 p.m., Wednesday, March 1, 2000 Math Biology Seminar John Pearson, Los Alamos National Laboratory ``Fire-Diffuse-Fire and the Dynamics of Intracellular Calcium Waves'' Math Annex 1102
3:30 p.m., Wednesday, March 1, 2000 Probability Seminar N. Dokuchaev, PIMS, UBC ``Stochastic partial differential equations with a quasi-periodic boundary condition'' Math Annex 1102
9:45--10:45 a.m., Thursday, March 2, 2000 Number Theory Seminar Nike Vatsal, Department of Mathematics, UBC ``Uniform Distribution of Heegner Points'' Math Annex 1102
11:00 -- 12:00 p.m., Thursday, March 2, 2000 Number Theory Seminar Christopher M. Skinner, Institute for Advanced Study, Princeton ``Base Change and a Problem of Serre'' Math Annex 1102
4:30 p.m., Thursday, March 2, 2000 PIMS-MITACS Mathematical Finance Seminar N. Dokuchaev, PIMS, UBC ``Optimal portfolio selection based on historical prices'' West Mall Annex 216 (PIMS)
3:30 p.m., Friday, March 3, 2000 Mathematics Colloquium Christopher M. Skinner, Institute for Advanced Study, Princeton ``The diophantine equation a^n+b^n=2c^2'' Room Math 100
1:30 p.m., Saturday, March 4, 2000 Northwest Probability Seminar Christian Borgs, Microsoft Theory Group ``Partition function zeros: A generalized Lee-Yang theorem'' Smith 105, University of
3:30 p.m., Saturday, March 4, 2000 Northwest Probability Seminar Xiaowen Zhou, Department of Mathematics, UBC ``Sample path continuity of continuous-site stepping-stone models'' Smith 105, University
of Washington
3:30 p.m., Monday, March 6, 2000 Applied Mathematics Colloquium Avner Friedman, Department of Mathematics, University of Minnesota ``Bifurcation of free boundary problems with application to tumor
growth'' LSK Bldg., Room 301
1:30 p.m., Wednesday, March 8, 2000 Algebra/Topology Seminar Duane Randall, Department of Mathematics & Computer Science, Loyola University ``A Survey of the Kervaire Invariant Problem'' West Mall
Annex 216 (PIMS)
10 a.m., Thursday, March 9, 2000 Special Algebra/Topology Seminar Stephen Bigelow, UC Berkeley ``Braid groups are linear'' Math Annex 1102
4:30 p.m., Thursday, March 9, 2000 PIMS-MITACS Mathematical Finance Seminar John Chadam, Pittsburgh University ``The Exercise Boundary for an American Put Option: Analytical and Numerical
Approximations'' West Mall Annex 216 (PIMS)
3:30 p.m., Friday, March 10, 2000 Mathematics Colloquium John Chadam, University of Pittsburg ``A mathematical model of bioremediation in a porous medium'' Math 100
3:30 p.m., Monday, March 13, 2000 Joint IAM-PIMS Distinguished Colloquium Alwyn Scott, Department of Mathematics, Univ. of Arizona and Department of Mathematical Modelling, Technical University of
Denmark ``Nonlinear Science: Past, Present and Future'' LSK Bldg., Room 301
11:30 a.m., Tuesday, March 14, 2000 Graduate Student Seminar Stefan Reinker, Department of Mathematics, UBC ``Does the Brain need Mathematics?'' LSK Bldg., Room 301
1:30 p.m., Wednesday, March 15, 2000 Algebra/Topology Seminar Denis Sjerve, Department of Mathematics, UBC ``Automorphisms of prime Galois coverings of the Riemann Sphere'' West Mall Annex 216 (PIMS)
4:30 p.m., Thursday, March 16, 2000 PIMS-MITACS Mathematical Finance Seminar Jaksa Cvitanic, University of Southern California ``Methods of partial hedging'' West Mall Annex 216 (PIMS)
3:30 p.m., Friday, March 17, 2000 Mathematics Colloquium Akbar Rhemtulla, Department of Mathematical Sciences, University of Alberta ``Expressing Elements of the Commutator Subgroup of a Group as a
Product of Least Number of Commutators'' Room Math 100
11:30 a.m., Tuesday, March 21, 2000 Graduate Student Seminar Ron Ferguson, Department of Mathematics, UBC ``Permutations with low discrepancy k-sums'' LSK Bldg., Room 301
1:30 p.m., Wednesday, March 22, 2000 Algebra/Topology Seminar Guillermo Moreno, Centro de Investigacion y Estudios Advanzados del IPN and University of Oregon ``Higher Dimensional Cayley Dickson
Algebras'' West Mall Annex 216 (PIMS)
3:30 p.m., Friday, March 24, 2000 Mathematics Colloquium Andrew J. Sommese, Univ. of Notre Dame ``Numerical Primary Decomposition'' Room Math 100
3:30 p.m., Monday, March 27, 2000 IAM-MATH BIO Colloquium Jinko Graham, Department of Mathematics & Statistics, Simon Fraser University ``Fine-Scale Mapping of a Rare Allele via Disequilibrium
Likelihoods'' LSK Bldg., Room 301 (formerly Old Computer Sciences Bldg.)
1:30 p.m., Wednesday, March 29, 2000 Algebra/Topology Seminar Zhongmou Li, UBC ``Immersion of 3-manifolds in 3-space" West Mall Annex 216 (PIMS)
4:30 p.m., Thursday, March 30, 2000 PIMS-MITACS Mathematical Finance Seminar Raman Uppal, Commerce and Business Administration, UBC ``Risk Aversion and Optimal Portfolio Policies in Partial and
General Equilibrium Economies'' West Mall Annex 216 (PIMS)
3:30 p.m., Monday, April 3, 2000 Complexity Seminar Anders Martin Lof, Steve Marion, Cindy Greenwood ``Asymptotics of the Near-Critical Epidemic Process'' Peter Wall Institute Conference Room
1:30 p.m., Wednesday, April 5, 2000 Algebra/Topology Seminar Bert Wiest, Department of Mathematics, UBC ``Quasi-isometries in group theory'' West Mall Annex 216 (PIMS)
3:30 p.m., Wednesday, April 5, 2000 Probability Seminar Marek Biskup, Microsoft Research ``Rigorous theory of partition function zeros at first-order phase transitions'' Math Annex 1102
1:30 p.m., Wednesday, June 14, 2000 Special Number Theory Seminar Hugh Montgomery, University of Michigan ``Greedy sums of distinct squares" Math Annex 1102
2:30 p.m., Wednesday, September 6, 2000 Topology Seminar Prof. Youcheng Zhou, Zhejiang University, China ``Effros Property and Homogeniety'' Math Annex 1102
3:30 p.m., Wednesday, September 6, 2000 Probability Seminar Antal Jarai, PIMS-UBC ``Invasion percolation and the incipient infinite cluster'' Math Annex 1102
3:30 p.m., Wednesday, September 13, 2000 Algebraic Geometry Seminar Behrang Noohi, Department of Mathematics, UBC ``Fundamental Groups of Algebraic Stacks'' Math Annex 1118
2:30 p.m., Wednesday, September 13, 2000 UBC PIMS Colloquium Beno Eckmann, ETH Zurich ``The Euler Characteristic -- some Variations and Ramifications'' WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, September 13, 2000 Probability Seminar Frank den Hollander, University of Nijmegen ``How random is the composition of two random processes?'' Math Annex 1102
3:30 p.m., Wednesday, September 13, 2000 IAM-PIMS Distinguished Colloquium Speaker Carlo Cercignani, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy ``Kinetic Models for Granular
Materials: An Exact Solution'' LSK Bldg. Room 301
2:30 p.m., Thursday, September 14, 2000 Algebra-Topology Seminar Beno Eckmann, ETH Zurich ``Projections, Group Algebras, and Geometry of Groups'' WMAX 216
4:30 p.m., Thursday, September 14, 2000 PIMS-MITACS Mathematical Finance Seminar D. Chan, UBC ``Introduction to Value at Risk'' WMAX 216
3:30 p.m., Friday, September 15, 2000 Mathematics Colloquium/PIMS Distinguished Chair Lecture David Brydges, PIMS-Department of Mathematics, University of Virginia ``Self Avoiding Walk and
Differential Forms'' Math 100
10:00-11:00 a.m., Monday, September 18, 2000 Scientific Computing and Visualization Seminar Arian Novruzi, PIMS-UBC ``Newton method in shape optimization problems. Some comments on its
parallelization'' CICSR 204, contact Brian Wetton for details on this seminar series
3:30 p.m., Monday, September 18, 2000 Mathematics Colloquium Leonid Mytnik, Israel Institute of Technology ``Duality approach to proving uniqueness'' Math 100
4:45 p.m., Monday, September 18, 2000 PIMS-MITACS Mathematical Finance Seminar Steve Shreve, Carnegie-Mellon Univ. ``Valuation of Exotic Options under Shortselling Constraints'' WMAX 216 (PIMS
seminar room)
3:30 p.m., Tuesday, September 19, 2000 PIMS Distinguished Chair at UBC Lecture David Brydges, PIMS-Department of Mathematics and Physics, University of Virginia ``Mehler's Formula and the
Renormalization Group" (Lecture 2 in the series) Math 104
2:30 p.m., Wednesday, September 20, 2000 Algebra-Topology Seminar Kee Lam, Mathematics, UBC ``Rational homotopy theory'' WMAX 216
3:30 p.m., Wednesday, September 20, 2000 Algebraic Geometry Seminar Behrang Noohi, Mathematics, UBC ``Fundamental Groups of Algebraic Stacks, II'' WMAX 216 (previously announced for 2:30 in Math
Annex 1118)
3:30 p.m., Wednesday, September 20, 2000 Institute of Applied Mathematics Colloquium Lionel G. Harrison, Department of Chemistry, UBC ``Branching in Plants: Exploring Reaction-Diffusion: (1) On the
Hemisphere (2) Interacting with Continuous Morphological Change'' LSK Bldg. Room 301
1:30 p.m., Thursday, September 21, 2000 Mathematics Colloquium Andrea Fraser, University of New South Wales Multiplier Operators on the Heisenberg group Math Annex 1100
4:00 - 5:00 p.m., Thursday, September 21, 2000 PIMS-MITACS Computational Statistics and Data Mining Seminar Peter J. Rousseeuw, PIMS-Universitaire Instelling Antwerpen (UIA), Belgium ``An
Introduction to Regression Depth'' CICSR 208
1:30 - 2:30 p.m., Friday, September 22, 2000 PIMS-MITACS Computational Statistics and Data Mining Seminar Peter J. Rousseeuw, PIMS-Universitaire Instelling Antwerpen (UIA), Belgium ``Depth Tests of
Symmetry and Regression'' LSK 301
3:30 p.m., Friday, September 22, 2000 Mathematics Colloquium Jacques Hurtubise, CRM and University of Montreal ``Integrable Systems and Surfaces'' Room Math 100
10:00-11:00 a.m., Monday, September 25, 2000 Scientific Computing and Visualization Seminar Arian Novruzi, PIMS-UBC ``Newton method in shape optimization problems. Some comments on its
parallelization, Part II'' CICSR 204
3:30 p.m., Monday, September 25, 2000 Mathematics Colloquium Laura Scull, Department of Mathematics, University of Michigan ``Equivariant Homotopy Theory: Classic Constructions in a Modern Setting''
Math 100
10:30 a.m., Tuesday, September 26, 2000 Special Algebra-Topology Seminar Laura Scull, Department of Mathematics, University of Michigan ``Algebraic Models for Equivariant Homotopy Theory'' Math Annex
1:30 p.m., Tuesday, September 26, 2000 Math Biology Seminar Israeli Ran & Alexandra Chavez-Ross, UBC ``MITACS progress report: the tinnitus project'' LSK Bldg, Room 301
3:30 p.m., Tuesday, September 26, 2000 PIMS Distinguished Chair at UBC Lecture David Brydges, PIMS-Department of Mathematics and Physics, University of Virginia ``Hierarchical Lattices and the
Renormalization Group revisited (Lecture 3 in the series)'' Math 104
3:30 p.m., Wednesday, September 27, 2000 IAM-PIMS Distinguished Colloquium David Brydges, PIMS-Department of Mathematics and Physics, University of Virginia ``Gaussian Integrals and Mean Field
Theory'' LSK Bldg. Room 301
2:30 p.m., Thursday, September 28, 2000 PDE Seminar Jingyi Chen, Mathematics, UBC ``Quaternions, Hyperkahler manifolds and a first order system of PDEs'' WMAX 216 (PIMS seminar room)
4:30 p.m., Thursday, September 28, 2000 PIMS-MITACS Mathematical Finance Seminar Jose Rodriguez, Mathematics, UBC ``More Value at Risk'' WMAX 216
3:30 p.m., Friday, September 29, 2000 Mathematics Colloquium Ravi Vakil, Department of Mathematics, M.I.T. ``Branched covers of the sphere and the moduli space of curves: Geometry, physics,
representation theory, combinatorics'' Math 100
10:00-11:00 a.m., Monday, October 2, 2000 Scientific Computing and Visualization Seminar Oliver Dorn, Computer Science, UBC ``The use of level set methods for shape reconstruction in electromagnetic
tomography'' CICSR 204
2:30 p.m., Wednesday, October 4, 2000 Algebra/Topology Seminar Dale Rolfsen, Mathematics, UBC ``Ordered groups and 3-manifolds'' WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, October 4, 2000 PIMS Distinguished Chair at UBC Lecture David Brydges, PIMS-Department of Mathematics and Physics, University of Virginia ``Analysis with the Renormalization
Group and Outlook (Lecture 4 in the series)'' WMAX 216
2:30 p.m., Thursday, October 5, 2000 PDE Seminar Vitali Vougalter, Mathematics, UBC ``Diamagnetic behavior of sums of Dirichlet eigenvalues'' WMAX 216
3:30 p.m., Friday, October 6, 2000 Mathematics Colloquium Richard Froese, Mathematics, UBC ``Realizing holonomic constraints in classical and quantum mechanics'' Math 100
1:30 p.m., Tuesday, October 10, 2000 Math Biology Seminar Susan Anne Baldwin, Bio-Resource Engineering, UBC ``Heat Transfer Model of Thermal Balloon Endometrial Ablation'' LSK Bldg, Room 301
2:30 p.m., Wednesday, October 11, 2000 Algebra/Topology Seminar Dale Rolfsen, Mathematics, UBC ``Ordered groups and 3-manifolds, II'' WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, October 11, 2000 Institute of Applied Mathematics Colloquium W. Kendal Bushe, Department of Mechanical Engineering, UBC ``Large Eddy Simulation of Turbulent Reacting Flows'' LSK
Bldg. Room 301
3:30 p.m., Wednesday, October 11, 2000 Algebraic Geometry Seminar Jim Carrell, Mathematics, UBC ``Equivariant cohomology of varieties with a triangular group action'' WMAX 216
3:30 p.m., Wednesday, October 11, 2000 Probability Seminar Liqing Yan, Mathematics-PIMS, UBC ``The Euler scheme for stochastic differential equations with irregular coefficients'' Math Annex 1102
2:30 p.m., Thursday, October 12, 2000 PDE Seminar Christine Chambers, Mathematics, UBC ``TBA'' WMAX 216
4:30 p.m., Thursday, October 12, 2000 PIMS-MITACS Mathematical Finance Seminar Simon MacNair, Mathematics-PIMS, UBC ``Utility Maximization with Stochastic Factors'' WMAX 216
3:30 p.m., Friday, October 13, 2000 Mathematics Colloquium Richard Schoen, Department of Mathematics, Stanford University ``A survey of recent progress in general relativity'' Math 100
10:00-11:00 a.m., Monday, October 16, 2000 Scientific Computing and Visualization Seminar Uri Ascher, Computer Science, UBC ``Grid refinement and scaling for distributed parameter estimation
problems'' CICSR 204
2:30 p.m., Wednesday, October 18, 2000 Algebra/Topology Seminar Bert Wiest, Mathematics-PIMS, UBC ``Ordered groups and 3-manifolds, III'' WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, October 18, 2000 Institute of Applied Mathematics Colloquium Robert Miura, Mathematics, UBC ``Applications of Excitable Cell Models'' LSK Bldg. Room 301
3:30 p.m., Wednesday, October 18, 2000 Probability Seminar Siva Athreya, Mathematics-PIMS,UBC ``Long time behaviour of a Brownian flow with jumps'' Math Annex 1102
3:30 p.m., Wednesday, October 18, 2000 Algebraic Geometry Seminar Jim Carrell, Mathematics, UBC ``Equivariant cohomology of varieties with a triangular group action, II'' WMAX 216
4:30 p.m., Wednesday, October 18, 2000 Student Algebraic Geometry Seminar Boris Tschirschwitz, Mathematics, UBC ``Sheaves'' WMAX 216
3:30 p.m., Friday, October 20, 2000 Mathematics Colloquium Joel Friedman, Mathematics, UBC ``Expanders, Eigenvalues, and Related Topics'' Math 100
a.m.-p.m., Friday, Saturday, October 20-21, 2000 West Coast Optimization Meeting Speakers: scheduled technical program Location: University of Washington (Seattle) For information email Phillip
Loewen, loew@math.ubc.ca
10:00-11:00 a.m., Monday, October 23, 2000 Scientific Computing and Visualization Seminar Uri Ascher, Computer Science, UBC ``Grid refinement and scaling for distributed parameter estimation
problems, II'' CICSR 204
2:30 p.m., Wednesday, October 25, 2000 Algebra/Topology Seminar Zhongmou Li, Mathematics, UBC ``Every orientable 3-manifold with boundary embeds in K_5 join 1'' WMAX 216 (PIMS Seminar Room)
3:30 p.m., Wednesday, October 25, 2000 Institute of Applied Mathematics Colloquium Keith Promislow, Department of Mathematics & Statistics, SFU ``Modulational Stability via Renormalization Methods
for Patterns in Forced Dispersive Systems'' LSK Bldg. Room 301
3:30 p.m., Wednesday, October 25, 2000 Probability Seminar Remco van der Hofstad, Delft University ``Improving performance of third generation mobile phone systems'' Math Annex 1102
3:30 p.m., Wednesday, October 25, 2000 *Postponed til Nov 1st* Algebraic Geometry Seminar Jim Carrell, Mathematics, UBC ``Equivariant cohomology of varieties with a triangular group action, III''
WMAX 216
2:30 p.m., Thursday, October 26, 2000 PDE Seminar Izabella Laba, Mathematics, UBC ``The spectral set conjecture and multiplicative properties of roots of polynomials'' WMAX 216
3:30 p.m., Friday, October 27, 2000 Mathematics Colloquium Remco van der Hofstad, Delft University ``Recent progress in one-dimensional and high-dimensional statistical mechanical models'' Math 100
3:30 p.m., Wednesday, November 1, 2000 IAM-PIMS Distinguished Colloquium Linda Petzold, Departments of Mechanical and Environmental Engineering and Computer Science, Univ. of California at Santa
Barbara ``Algorithms and Software for Dynamic Optimization with Application to Chemical Vapor Deposition Processes'' LSK Bldg. Room 301
3:30 p.m., Wednesday, November 1, 2000 Probability Seminar Robert Israel, Mathematics, UBC ``Finding generators from transition matrices'' Math Annex 1102
3:30 p.m., Wednesday, November 1, 2000 Algebraic Geometry Seminar (postponed from 25 Oct) Jim Carrell, Mathematics, UBC ``Equivariant cohomology of varieties with a triangular group action, III ''
WMAX 216
4:30 p.m., Thursday, November 2, 2000 PIMS-MITACS Mathematical Finance Seminar P. Laurence, U. Roma and NYU ``American options on multiple assets: bounds via a comparison principle'' WMAX 216
10:00-11:00 a.m., Monday, November 6, 2000 Scientific Computing and Visualization Seminar Brian Wetton, Mathematics, UBC ``Asymptotic Error Analysis: overview and some unsolved problems'' CICSR 204
3:30 p.m., Wednesday, November 8, 2000 IAM Colloquium Alejandro Garcia, Department of Physics, San Jose State University, CA ``Stochastic Particle Algorithms: from DSMC to CUBA'' LSK Bldg. Room 301
3:30 p.m., Wednesday, November 8, 2000 Probability Seminar Xiaowen Zhou, Mathematics, UBC ``A duality formula for multi-type voter model'' Math Annex 1102
3:30 p.m., Wednesday, November 8, 2000 Algebraic Geometry Seminar Anne O'Halloran, Mathematics, UBC ``The Cohomology of Kontsevich's Stack of Stable Maps to P^n - The Case of Conics" WMAX 216
10:30 a.m., Thursday, November 9, 2000 Harmonic and Functional Analysis Seminar Professor Garth Dales, Leeds University ``Amenability and weak amenability for measure algebras'' Math Annex 1102
2:30 p.m., Thursday, November 9, 2000 PDE Seminar Manfred Salmhofer, ETH -- Zurich ``On the conjecture called `Migdal's Theorem''' WMAX 216
3:30 p.m., Friday, November 10, 2000 Mathematics Colloquium Michael Ward, Mathematics, UBC ``The Stability and Dynamics of Spikes for a Reaction-Diffusion System'' Math 100
2:30 p.m., Wednesday, November 15, 2000 Algebra/Topology Seminar Don Witt, Department of Physics and Astronomy, UBC ``The Smale Conjecture'' WMAX 216
3:30 p.m., Wednesday, November 15, 2000 IAM Colloquium Roland Stull, Department of Earth and Ocean Sciences, UBC ``A Nonlocal Description of Atmospheric Turbulence'' LSK Bldg. Room 301
3:30 p.m., Wednesday, November 15, 2000 Algebraic Geometry Seminar Anne O'Halloran, Mathematics, UBC ``The Cohomology of Kontsevich's Stack of Stable Maps to P^n - The Case of Conics, Part II'' WMAX
4:30 p.m., Wednesday, November 15, 2000 Student Algebraic Geometry Seminar Maciej Mizerski, Mathematics, UBC ``Introduction to Derived Functors (Cohomology)'' Math Annex 1102
4:30 p.m., Wednesday, November 15, 2000 PIMS-MITACS Mathematical Finance Seminar V. Dion, Mathematics, UBC ``A tutorial on Mortgage Backed Securities'' WMAX 216
2:30 p.m., Thursday, November 16, 2000 PDE Seminar Arian Novruzi, UBC ``Some results related to free boundary and shape optimisation problems'' WMAX 216
3:30 p.m., Friday, November 17, 2000 Mathematics Colloquium Dale Rolfsen, Mathematics, UBC ``Do you want to be a mathematical millionaire? The Poincare conjecture'' Math 100
10:00-11:00 a.m., Monday, November 20, 2000 Scientific Computing and Visualization Seminar Radu Bradean, UBC-SFU MITACS PDF ``Transport Phenomena in Porous Fuel Cell Electrodes'' CICSR 204
3:30 p.m., Monday, November 20, 2000 Mathematics Colloquium Richard Bertram, Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida ``Mathematical Analysis of Deterministic
and Stochastic Models of Synaptic Transmitter Release'' Math 100
3:30 p.m., Tuesday, November 21, 2000 Math Biology Seminar Richard Bertram, Institute of Molecular Biophysics, Florida State University ``Models of Synaptic Transmitter Release and Short-Term
Plasticity'' Math 104
3:30 p.m., Wednesday, November 22, 2000 IAM Colloquium Florin Diacu, Univ. Victoria-PIMS Site Director, Department of Mathematics and Statistics, Univ. of Victoria ``On the Dynamical Stability of the
Helium Atom'' LSK Bldg. Room 301
3:30 p.m., Wednesday, November 22, 2000 Algebraic Geometry Seminar Kai Behrend, Mathematics, UBC ``Differential Graded Schemes'' WMAX 216
4:30 p.m., Wednesday, November 22, 2000 Student Algebraic Geometry Seminar Boris Tschirschwitz, Mathematics, UBC ``Derived Functors: Acyclic Resolutions'' WMAX 216
2:30 p.m., Thursday, November 23, 2000 PDE Seminar Stephen Gustafson, Courant Institute of Mathematical Sciences ``Stability of Localized Solutions of Landau-Lifshitz Equations'' WMAX 216
2:30 p.m., Thursday, November 23, 2000 Special Institute of Applied Mathematics Seminar Natalia Kouzniak, MITACS PDF, Department of Mathematics, UBC ``Analytical Solutions and Numerical Results in
Elasto-plastic and Elasto-dynamic Problems of Fracture Mechanics'' Math 204
3:30 p.m., Friday, November 24, 2000 Mathematics Colloquium Stephen Gustafson, Courant Institute ``Some Mathematical Problems in the Ginzburg-Landau Theory of Superconductivity'' Math 100
3:30 p.m., Monday, November 27, 2000 Mathematics Colloquium Doug Park, Department of Mathematics & Statistics, McMaster University ``Exotic smooth structures on simply connected 4-dimensional
manifolds'' Math 100 Refreshments will be served at 3:15 in the Math Annex Coffee Lounge, Room 1115.
10:30 a.m., Tuesday, November 28, 2000 Special Topology Seminar Doug Park, McMaster University ``Gluing formulae for Seiberg-Witten invariant along 3-dimensional torus'' Math Annex 1102
3:30 p.m., Wednesday, November 29, 2000 IAM Colloquium Ian Frigaard, Department of Mathematics, UBC ``Super-Stable Parallel Flows of Multiple Visco-Plastic Fluids'' LSK Bldg. Room 301
3:30 p.m., Wednesday, November 29, 2000 Algebraic Geometry Seminar (postponed from Nov. 22) Kai Behrend, Mathematics, UBC ``Differential Graded Schemes'' WMAX 216
2:30 p.m., Thursday, November 30, 2000 PDE Seminar Martin Bause, University of Erlangen, Nuremberg, Germany ``Numerical approximation schemes for the Poisson-Stokes equations of compressible viscous
flow'' WMAX 216
3:30 p.m., Friday, December 1, 2000 Joint PIMS-MITACS Mathematical Finance Seminar and Mathematics Colloquium Darrell Duffie, Stanford University ``Valuation in Dynamic Bargaining Markets'' Math 100
10:00-11:00 a.m., Monday, December 4, 2000 Scientific Computing and Visualization Seminar Jim Varah, Computer Science, UBC ``Discrete Tomography: Projections, Moments, and Shape Reconstruction''
CICSR 204
3:30 p.m., Monday, December 4, 2000 Mathematics Colloquium Michael Bennett, Department of Mathematics, University of Illinois at Urbana-Champaign ``Effective methods for Diophantine problems'' Math
1:30 p.m., Tuesday, December 5, 2000 Number Theory Seminar Michael Bennett, Univ. of Illinois at Urbana-Champaign ``Pillai's conjecture revisited'' Math Annex 1102
3:30 p.m., Friday, December 8, 2000 Special Mathematics Colloquium Professor Ram Murty, Queen's University ``Riemann Hypothesis: A Status Report'' Math Annex 1100
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[FOM] Formalization Thesis
John Baldwin jbaldwin at uic.edu
Fri Dec 28 22:40:43 EST 2007
I cut from Kutateladze's reply to Chow.
On Fri, 28 Dec 2007, S. S. Kutateladze wrote:
> I explain simply that all branches of mathematics cannot be translated
> fully neither into set theory nor into any unique formal theory.
> Category theory yields an illustration, as well as model theory.
I want first to adopt Catarin's Dutilh's nice distinction between the
expressibility thesis and the provability thesis.
Clearly for the model theory the provability thesis is false for ZFC; thre
are plenty of published examples (e.g. existence of saturated models in
various cardinals; the necessity of the weak GCH to prove categoricity
transfer for L-omega_1, omega etc. etc.
But Kutaleladez seems to have a wider view of model theory than I if
denies the expressibility thesis. To me, model theory is essentially built
on Tarski's formal definition of truth in set theory. And to state a
theorem in model theory is to state one that is expressible in the
langugage of set theory.
I would like
an example of a model theoretic proposition that is not so expressible.
John T. Baldwin
Director, Office of Mathematics Education
Department of Mathematics, Statistics,
and Computer Science M/C 249
jbaldwin at uic.edu
Room 327 Science and Engineering Offices (SEO)
851 S. Morgan
Chicago, IL 60607
Assistant to the director
Jan Nekola: 312-413-3750
More information about the FOM mailing list
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he Goodness-of-Fit Test
10.1: The Goodness-of-Fit Test
Created by: CK-12
Learning Objectives
• Understand the difference between the Chi-Square distribution and the Student’s t-distribution.
• Identify the conditions which must be satisfied when using the Chi-Square test.
• Understand the features of experiments that allow Goodness-of-Fit tests to be used.
• Evaluate an hypothesis using the Goodness-of-Fit test.
In previous lessons, we learned that there are several different tests that we can use to analyze data and test hypotheses. The type of test that we choose depends on the data available and what
question we are trying to answer. For example:
• We analyze simple descriptive statistics such as the mean, median, mode and standard deviation to give us an idea of the distribution and to remove outliers, if necessary;
• We calculate probabilities to determine the likelihood of something happening; and
• We use regression analysis to examine the relationship between two or more continuous variables.
But what test do we run if we are trying to examine patterns between distinct categories such as gender, political candidates, locations or preferences? To analyze patterns like these we use the
Chi-Square test.
The Chi-Square test is a statistical test used to examine patterns in distinct or categorical variables, which we learned about in the earlier chapter entitled Planning and Conducting an Experiment
or Study. This test is used in:
1. Estimating how closely a sample matches the expected distribution (also known as the Goodness-of-Fit test) and
2. Estimating if two random variables are independent of one another (also known as the Test of Independence - see Chapter 9).
In this lesson we will learn more about the Goodness-of-Fit test and how to create and evaluate hypotheses using this test.
The Chi-Square Distribution
The Chi-Square Goodness-of-Fit test is used to compare the observed values of a categorical variable with the expected values of that same variable. For example, we would use this test to analyze
surveys that contained categorical variables (for example, gender, city of origin, or locations that people preferred to visit on vacation) to determine if there are in fact relationships between
certain items.
Example: We would use the Chi-Square Goodness-of-Fit test to evaluate if there was a preference in the types of lunch that $11^{th}$
Research Question: Do $11^{th}$
Using a sample of $11^{th}$
Frequency of Type of School Lunch Chosen by Students
Type of Lunch Observed Frequency Expected Frequency
Salad $21$ $25$
Sub Sandwich $29$ $25$
Daily Special $14$ $25$
Brought Own Lunch $36$ $25$
If there is no difference in which type of lunch is preferred, we would expect the students to prefer each type of lunch equally. To calculate the expected frequency of each category as if school
lunch preferences were distributed equally, we divide the number of observations by the number of categories. Since there are $100$$4$$100/4$$25$
The value that indicates the comparison between the observed and expected frequency is called the Chi-Square statistic. The idea is that if the observed frequency is close to the expected frequency,
then the Chi-Square statistic will be small. Or, if the difference between the two frequencies is big, then we expect the Chi-Square statistic to be large.
To calculate the Chi-Square statistic $(X^2)$
$X^2=\sum_i \frac{(O_i-E_i)^2}{E_i}$
Once calculated, we take this Chi-Square value along with the degrees of freedom (this will be discussed later) and look up the Chi-Square value on a standard Chi-Square distribution table. The
Chi-Square distribution allows us to determine the probability that a sample fits an expected pattern. In contrast, the t-distribution tests how likely it is that the means of two different samples
will differ. Please see the table below for more details.
The Difference Between the Chi-Square and the Student's t-test when Using to Compare Two Sample Means
Type of Tells Us Every Day Example Data Needed to Determine Value
Chi-Square The relationship between two or more categorical variables. Analyzing survey data with categorical variables. Observed and expected frequencies for categorical
variables, degrees of freedom.
Student’s The differences between the means of two groups with respect to Determining if there is a difference in the mean of the SAT The mean values for samples from two populations, degrees
t-Test a continuous variable. scores between schools. of freedom.
Features of the Goodness-of-Fit Test
As mentioned, the Goodness-of-Fit test is used to determine patterns of distinct or categorical variables. As we learned in Lesson 6, a categorical variable is one that is not continuous and has
observations in separate categories. Examples of categorical variables include:
-gender (male or female)
-preferences (agreed, neutral or disagreed)
-behaviors (got sent to the office or didn’t get sent to the office)
-physical traits (straight, wavy or curly hair)
Categorical variables are not the same as measurement or continuous variables. The following are normally not categorical variables:
$& - \text{height} && - \text{distance} \\& - \text{weight} && - \text{income} \\& - \text{test scores}$
It is important to note that most of these continuous variables could in fact be converted to a categorical variable. For example, you could create a categorical variable with two values such as
¨Less that $10 \;\mathrm{miles}$$10 \;\mathrm{miles}$
In addition to categorical variables, a Goodness-of-Fit test also requires:
-data obtained through a random sample
-a calculation of the Chi-Square statistic using the formula explained in the last section
-the calculation of the Degrees of Freedom. For a Chi-Square test, the Degrees of Freedom are equal to the number of categories minus one or $df=c-1$
Using our example about the preferences of types of school lunches, we calculate the $df=3$
$\text{df} & = \#\ \text{of categories} - 1 \\3 & = 4 - 1$
There are many situations that use the Goodness-of-Fit test, including surveys, taste tests and analysis of behaviors. Interestingly, Goodness-of-Fit tests are also used in casinos to determine if
there is cheating in games of chance such as cards and dice. For example, if a certain card or number on a die shows up more than expected (a high observed frequency compared to the expected
frequency), officials use the Goodness-of-Fit test to determine the likelihood that the player may be cheating or the game may not be fair.
Evaluating Hypothesis Using the Goodness-of-Fit Test
Let’s use our original example to create and test a hypothesis using the Goodness-of-Fit Chi-Square test. First, we will need to state the null and alternative hypotheses for our research question.
Since our research question states “Do $11^{th}$no difference between the observed and the expected frequencies. Therefore, our alternative hypothesis would state that there is a significant
difference between the observed and expected frequencies.
Null Hypothesis $(H_0:O)= E$(there is no statistically significant difference between observed and expected frequencies)
Alternative Hypothesis $(H_a:O) eq E$(there is a statistically significant difference between observed and expected frequencies)
Using an alpha level of $.05$$.05$$- 1 = 3$$7.81$$7.81$
Reject$(H_0)$if $X_2 > 7.81$
Using the table from above, we can calculate the Chi-Square statistic with relative ease.
Frequency Which Student Select Type of School Lunch
Type of Lunch Observed Frequency Expected Frequency $(O-E)^2 /E$
Salad $21$ $25$ $0.64$
Sub Sandwich $29$ $25$ $0.64$
Daily Special $14$ $25$ $4.84$
Brought Own Lunch $36$ $25$ $4.84$
Total (chi-square) $10.96$
$X^2=\sum \frac{(0-E)^2}{E} = 0.64 + 0.64 + 4.84 + 4.84 = 10.96$
Since our Chi-Square statistic of $10.96$$7.81$$11^{th}$
As review, we follow the following steps to formulate and evaluate hypothesis:
1. State the null and alternative hypothesis for the research question.
2. Select the significance level and use the Chi-Square distribution table to write a rule for rejecting the null hypothesis.
3. Calculate the value of the Chi-Square statistic.
4. Determine whether to reject or fail to reject the null hypothesis and write a summary statement based on the results.
Lesson Summary
1. We use the Chi-Square test to examine patterns between categorical variables such as gender, political candidates, locations or preferences.
2. There are two types of Chi-Square tests: the Goodness-of-Fit test and the Test for Independence. We use the Goodness-of-Fit test to estimate how closely a sample matches the expected distribution.
3. To test for significance, it helps to make a table detailing the observed and expected frequencies of the data sample. Using the standard Chi-Square distribution table, we are able to create
criteria for accepting the null or alternative hypotheses for our research questions.
4. To test the null hypothesis it is necessary to calculate the Chi-Square statistic. To calculate the Chi-Square statistic $( x^2)$
$X^2=\sum_i \frac{(0_i-E_i)^2}{E_i}$
$X^2 =$
$O =$
$E =$
5.Using the Chi-Square statistic and the level of significance, we are able to determine whether to reject or fail to reject the null hypothesis and write a summary statement based on these results.
Supplemental Links
Distribution Tables (including the Student’s t-distribution and Chi-Square distribution)
Review Questions
1. What is the name of the statistical test used analyze the patterns between two categorical variables?
1. the Student’s t-test
2. the ANOVA test
3. the Chi-Square test
4. the z-score
2. There are two types of Chi-Square tests. Which type of Chi-Square test estimates how closely a sample matches an expected distribution?
1. the Goodness-of-Fit test
2. the Test for Independence
3. Which of the following is considered a categorical variable:
1. income
2. gender
3. height
4. weight
4. If there were $250$$2$
1. $125$
2. $500$
3. $250$
4. $5$
5. What is the formula for calculating the Chi-Square statistic? The principal is planning a field trip. She samples a group of $100$
Type of Field Trip Number Preferring
Sporting Event $53$
Play $18$
Science Museum $29$
6. What is the observed frequency value for the Science Museum category?
7. What is the expected frequency value for the Sporting Event category?
8. What would be the null hypothesis for the situation above?
1. There is no preference between the types of field trips that students prefer
2. There is a preference between the types of field trips that students prefer
9. What would be the Chi-Square statistic for the research question above?
10. If the estimated Chi-Square level of significance was $5.99$
Review Answers
1. C
2. A
3. B
4. A
5. $X^2=\sum \frac{(0-E)^2}{E}$
6. $29$
7. $33.33$
8. A
9. $20.0$
Type of Field Trip Observed Frequency Expected Frequency Chi-Square
Sporting Event $53$ $33.33$ $12.4$
Play $18$ $33.33$ $7.0$
Science Museum $29$ $33.33$ $0.6$
Chi-Square Total $20.0$
10. Reject the Null Hypothesis
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The traveling salesman problem
The traveling salesman problem, or TSP for short, is this: given a finite number of ``cities'' along with the cost of travel between each pair of them, find the cheapest way of visiting all the
cities and returning to your starting point. (Here, we consider just the symmetric TSP, where traveling from city X to city Y costs the same as traveling from Y to X; the ``way of visiting all the
cities'' is simply the order in which the cities are visited.) To put it differently, the data consist of integer weights assigned to the edges of a finite complete graph; the objective is to find a
hamiltonian cycle (that is, a cycle passing through all the vertices) of the minimum total weight. In this context, hamiltonian cycles are commonly called tours.
TSPLIB is Gerhard Reinelt's library of 110 instances of the traveling salesman problem. Some of these instances arise from the task of drilling holes in printed circuit boards and others have been
constructed artificially. (A popular way of constructing a TSP instance is to choose a set of actual cities and to define the cost of travel from X to Y as the distance between X and Y.) None of them
(with a single exception) is contrived to be hard and none of them is contrived to be easy; some of them have been solved (a few of these are shown here) and others have not.
David Applegate, Robert Bixby, William Cook, and I have written a computer code that solved all but three of the previously unsolved instances from the TSPLIB. One of these is the instance with 225
constructed by Stefan Tschöke and contrived to be hard for its size; the others include and their sizes range from 1,000 to 15,112 cities. (The three TSPLIB instances not solved by Concorde have
18,512 cities, 33,810 cities, and 85,900 cities; these were solved by William Cook, Daniel Espinoza, and Marcos Goycoolea, starting with Concorde and adding various routines for Adam Letchford's
domino-parity constraints; in solving the 85,900-city instance, they also relied on a tour found previously by Keld Helsgaun, which they proved to be optimal.) A few comments on our work are
collected in an interview intended for a general audience and published in 1996. A twelve-page survey intended for a mathematical audience was published in 1998 and awarded the in 2000. Our "local
cuts" are described in there is also a set of eighteen transparencies from my talk on the same subject. Much more can be found on
Our book
was published by Princeton University Press in February 2007 and awarded the
at the INFORMS Awards Ceremony in November 2007. Here is the citation.
Other sites related to the TSP include:
Back to Va ek Chvátal's home page
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modular form Fourier coefficients and associated automorphic representation
up vote 10 down vote favorite
Let $f$ be a cuspidal modular form of some weight and level $N$. Then it determines an irreducible automorphic representation $\pi = \bigotimes'\pi_p$ of $GL_2(\mathbf Q)$. Let $f = \sum_i a_i q^i$
be its fourier expansion. Then it is known that if $p\nmid N$, then $a_p$ determines $\pi_p$ (it is an unramified principal series). Is it true that $a_p$ determines $\pi_p$ in general? And if so,
add comment
2 Answers
active oldest votes
Jared Weinstein and I wrote a paper on how to compute $\pi_p$: see here.
As Olivier says, $a_p$ will often be zero, and in fact if the central character is trivial (or has conductor coprime to $p$) this is always the case when $p^2$ divides the level of $f$.
One can get a bit futher by twisting: you can always twist a newform by Dirichlet characters, and Atkin and Li have shown that $\pi_p$ is principal series or Steinberg at $p$ if and
only if there is some Dirichlet character $\chi$ such that the twist of $f$ by $\chi$ is a newform with nonzero Fourier coefficient at $p$ (or an oldform attached to such a newform).
up vote 10 So that leaves the supercuspidal cases, and here Hecke theory won't help you at all: no matter how you twist your form, the Hecke eigenvalues are all zero. One can actually show (the
down vote "local converse theorem") that $\pi_p$ is uniquely determined by the Atkin-Lehner pseudo-eigenvalues of all of the twists of $f$; but it is not so easy to calculate these, or to
accepted explicitly identify $\pi_p$ from a list of them once you've done so. In my paper with Jared you can find details of a different approach, using Bushnell and Kutzko's theory of "types",
which seems to work quite well.
These algorithms are implemented in recent versions of Magma (and should be in Sage fairly shortly as well, once someone gets around to reviewing my code).
Thanks for your helpful answer, David. – Nicolás Oct 24 '11 at 12:40
add comment
A supercuspidal representation, a Steinberg twisted by a ramified character and a principal series ramified at both characters at $p$ will all have zero $a_{p}$. A reference for this is
up vote 6 Jacquet-Langlands LN 114 Proposition 3.5, 3.6. I am also not sure one can distinguish a priori a simply ramified principal series and a Steinberg twisted by an unramified character purely
down vote using $a_{p}$, you might need to look at the order of the central character at $p$ to do this (in the latter case, the central character is trivial at $p$ while it is not in the former).
2 You can always distinguish unram twists of Steinberg from tamely ramified principal series using $a_p$, because $|a_p|$ will be $p^{(k-1)/2}$ in the former case and $p^{(k-2)/2}$ in the
latter. But you can't recover the inducing characters from $a_p$ in the PS case without knowing the central character as well. – David Loeffler Oct 24 '11 at 10:01
Thanks for your helpful answer, Olivier. – Nicolás Oct 24 '11 at 12:40
add comment
Not the answer you're looking for? Browse other questions tagged modular-forms automorphic-forms nt.number-theory or ask your own question.
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Find the resultant of these two vectors: 2.00 x 10
Number of results: 197,021
Find the resultant of these two vectors: 2.00 * 10^2 units due east and 4.00 * 10^2 units 30.0degrees north of west. please SHOW me how to do this
Thursday, February 5, 2009 at 9:59am by y912f
please help find the resultant of these two vectors: 2.00 * 10^2 units due east and 4.00 * 10^2 units 30.0degrees north of west please show me step by step how to do this thanks for any help!
Friday, February 13, 2009 at 4:22pm by y912f
What is the resultant of two displacement vectors having the same direction? a. The resultant is the sum of the two displacements having the same direction as the original vectors. b. The resultant
is the difference of the two displacements having the same direction as the ...
Tuesday, February 5, 2008 at 4:27pm by Shenay
physical sciences
Two forces of 5N and 7N respectively act on an object. (A)when will the resultant of the two vectors be at a maximum? (B)when will the resultant of the two vectors be at a minimum? (C)what are the
maximum and minimum resultant of the two forces?
Thursday, January 16, 2014 at 2:22pm by fortunate
Two vectors are at right angle to each other as shown. Find the resultant vector (the sum of the two vectors).
Sunday, March 4, 2012 at 4:32pm by Mina
2 displacement vectors of 15 meters and 10 meters are combined. a.Find the magnitude of the minimum possible resultant and the angle between the vectors. b. Find the magnitude of the maximum possible
resultant and the angle between the vectors.
Sunday, September 16, 2007 at 7:37pm by Bailey
physical science
The resultant vector of two particular displacement vectors dose not equal the sum of the magnitudes of the individual vectors. Describe the directions of the two vectors.
Monday, May 2, 2011 at 5:15pm by Becky
physical sciences
Two forces of 5n and 7N respectively act on an object. (A)when will the resultant of the two vectors be at a maximum? (B)when will the resultant of the two vectors be at a minimum? (C)when are the
maximum and minimum resultantof the two forces?
Thursday, January 16, 2014 at 2:37pm by fortunate
Given the displacement vectors A = (7.00 - 1.00 + 3.00 ) m and B = (6.00 + 5.00 - 3.00 ) m, find the magnitudes of the following vectors and express each in terms of its rectangular components. (a) C
= A - B (b) D = 3A + B
Wednesday, September 26, 2012 at 8:20pm by Abraham
Vectors, please check drawing
You have correctly chained the two vectors together. The resultant is the vector that joins the head and tail of the chain, but it is important to note that: "the arrow-head of the resultant and the
chain coincide, and the tails coincide as well" It is not possible to verify ...
Thursday, September 22, 2011 at 9:06pm by MathMate
1) The vector sum of three vectors gives a resultant equal to zero. what can you say about the vectors? 2) Vector is 3.00 units in length and points along the positive x-axis. Vector is 4.00 units in
length and points along the negative y-axis.Use graphical methods to find the...
Thursday, November 19, 2009 at 12:44am by Aman
1) The vector sum of three vectors gives a resultant equal to zero. what can you say about the vectors? 2) Vector is 3.00 units in length and points along the positive x-axis. Vector is 4.00 units in
length and points along the negative y-axis.Use graphical methods to find the...
Thursday, November 19, 2009 at 12:59am by Sandy
Mechanical Engineering Sci.
The paralleogram method is useful if you are doing a graphic solution. Make the two vectors adjacent sides of a parallelogram, complete the other two sides, and draw a diagonal from the corner where
the two vectors touch, to the opposite corner. The diagonal will be the ...
Tuesday, March 15, 2011 at 6:45am by drwls
A football player runs the pattern given in the drawing by the three displacement vectors , , and . The magnitudes of these vectors are A = 6.00 m, B = 13.0 m, and C = 15.0 m. Using the component
method, find the (a) magnitude and (b)direction of the resultant vector + + . ...
Saturday, July 9, 2011 at 9:15pm by Kristi
A football player runs the pattern given in the drawing by the three displacement vectors A ,B ,C and . The magnitudes of these vectors are A = 4.00 m, B = 17.0 m, and C = 19.0 m. Using the component
method, find the (a) magnitude and (b)direction of the resultant vector A + B...
Thursday, July 14, 2011 at 12:47am by Kelli
Two vectors have magnitudes of 3 units and 8 units respectively. The resultant of these two vectors has a magnitude of 8 units. What is the angle between these two vectors?
Friday, March 1, 2013 at 6:58pm by dave
Three vectors are shown in Fig. 3-32 (A = 60.0 , B = 56.0°). Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. (a) Give the resultant in terms of components. (b)
What is the magnitude of the resultant? What is the resultant's angle above ...
Sunday, September 30, 2012 at 6:53pm by joe
Three vectors are shown in Fig. 3-32 (A = 62.0 , B = 58.0°). Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. (a) Give the resultant in terms of components. Rx =
Ry = (b) What is the magnitude of the resultant? What is the resultant's ...
Sunday, September 30, 2012 at 6:39pm by michael
How does the resultant of two vectors change as the angle between the two vectors increase?
Friday, September 30, 2011 at 2:54pm by Lala
How does the resultant of two vectors change as the angle between the two vectors increase?
Sunday, October 2, 2011 at 8:37pm by Lala
7)A car is moving with a uniform speed of 15.0 m/s along a straight path. What is the distance covered by the car in 12.0 minutes? I dont know 8)What is the resultant of two displacement vectors
having the same direction? The resultant is the sum of the two displacements ...
Sunday, March 30, 2008 at 4:21pm by Jon
Discrete Math - Vectors
Can you please help me correct my answers for the following two questions? 1) A tour boat travels 25 km due east and then 15 km S50°E. Represent these displacements in a vector diagram, then
calculate the resultant displacement. ====== My Work: I drew the vectors and connected...
Sunday, February 10, 2008 at 1:32am by Anonymous
2 forces of 5N&7N respectively act on an object. (a) When will the resultant of 2 vectors be at a maximum? (b) When will the resultant of the 2 vectors be at a minimum?
Sunday, January 19, 2014 at 12:33am by Lesed
2 forces of 5N and 7N respectively act on an object.a)When will the resultant of two vectors at a maximum?b)when will the resultant of the two vectors be at a minimum?c)What are the maximum and
minimum resultants of the two forces?d)Draw a diagram to show the maximum and ...
Tuesday, March 25, 2014 at 4:57am by COSMOS
I could write down a bunch of equations but since I cannot draw the triangle for you with the tools we have, it would probably be difficult to explain in words what is going on. Draw the two velocity
vectors end to end. Then close the triangle to get the resultant. The angle ...
Saturday, June 28, 2008 at 3:31pm by drwls
Let A and B be the two vectors of magnitude 10 unit . If they are inclined to X-axis at angle 30 degree and 60 degree respectively. Find the resultant.
Friday, October 14, 2011 at 3:36am by Bablu
Given Vector A with magintude 9.17 feet and Vector B with magnitude of 10.58 feet, what is the resultant of the two vectors added together? Answer: I know it would depend on the direction of the
vector. If in the same line we would add them or if opposite lines we would ...
Tuesday, August 30, 2005 at 11:00am by Nisar
Physics Electric Force
Particle A of charge 2.76 10-4 C is at the origin, particle B of charge -6.54 10-4 C is at (4.00 m, 0), and particle C of charge 1.02 10-4 C is at (0, 3.00 m). We wish to find the net electric force
on C. (a) What is the x component of the electric force exerted by A on C? (b...
Thursday, April 11, 2013 at 2:01pm by Alex
The position vectors, r km, and the velocity vectors, v km/h, of two boats at a certain time are given by ... Boat A:at 10:00 am rA=6i+10j vA=8i–2j Boat B:at 10:30 am rB=8i+5j vB=4i+j ... determine
the time at which boat B should head out so that the two boats do collide.
Thursday, February 7, 2013 at 6:27pm by Molly
Add those two vectors by adding x and y components separately. The equilibrant will have the same magnitude (as the resultant) but be in the opposite direction.
Sunday, December 5, 2010 at 4:15pm by drwls
Physics (vectors)
The way you have described this, A IS the resultant of B and C. If these are indeed three separate vectors then the resultant summing all three is simply 2 times A in the direction of A
Friday, February 15, 2013 at 6:48pm by Damon
make your sketch using the parallelogram property of vectors. The resultant of 8 will be the diagonal of the quadrilateral with sides 3 and 8 let the angle opposite the resultant be Ø by the cosine
law: 8^2 = 8^2 + 3^2 - 2(8)(3)cos∏ 48cosØ = 9 cosØ = 9/48 Ø = 79.163° so ...
Friday, March 1, 2013 at 6:58pm by Reiny
the question does not make sense..the resultant vector is always longer than the two vectors because it is formed by the 90degrees intersection of the smaller forces!!!..so how come the resultant
vector form a 90degree with another smaller vector??? the smaller vectors should ...
Monday, June 3, 2013 at 12:24am by bonjo
So much for the two vectors. Now what is your question? Do they want the magnitude of the resultant? If they want the direction of the resultant, you will have to say more about the direction of
vector 2
Thursday, October 20, 2011 at 11:59am by drwls
if the * is the degrees, then you need to draw the vectors according to their direction. you can use a graph paper and make your own scale: say one unit cube is 10km/hr. then use the protractor to
draw the vectors taking an horizontal line as zero degrees. then draw the ...
Thursday, June 6, 2013 at 3:57am by bonjo
Find the resultant of two vectors 7N and 8N inclined at an angle of 65 degree to each other
Friday, October 14, 2011 at 4:15am by Sunday
Can you help me with this one also? I know how to do it with 3 vectors but I can't seem to draw it with 4 vectors. The magnitudes of the four displacement vectors shown in the drawing are A=16.0 m, B
=11.0 m, C=12.0 m, and D=26.0 m. Determine the (1) magnitude and (2) ...
Sunday, January 23, 2011 at 9:02pm by Brittany
I do not see how the vector D is defined. I have to assume that vector D is the sum of vectors A and B. To find the resultant (sum) of vectors, you would sum the x- and y-components by resolving the
vectors in the x-direction (Pcos(θ)) and y-direction (Psin(θ)). ...
Thursday, September 9, 2010 at 3:46pm by MathMate
Add the two displacement vectors. This will tell you the magnitude and direction of the resultant. If you do not understand how to add vectors, I suggest a review or private tutoring in that subject.
Wednesday, February 16, 2011 at 12:51am by drwls
Mechanics AS (Vectors)
When Studying Vectors, How Would I Go About Answering This Question? In Each of the following Cases, find the magnitude and direction of the resultant vectors of the two given vectors: a) a
displacement of magnitude 26km on a bearing of 175 degrees and a displacement of ...
Tuesday, February 21, 2012 at 1:00pm by Jat
Find the resultant, in magnitude and direction of a force of 40 N which makes an angle with the + X axis of 38o and a force of 20 N acting along the + X axis. Find the x and y components of the
resultant and express them as i and j vectors.
Wednesday, November 7, 2012 at 1:28pm by Anonymous
Yes, but first add the two force vectors. The acceleration will be in the same direction as the resultant force. The magnitude of the resultant force is sqrt [(8.4)^2 + (2.2)^2] = 8.683 N
Sunday, March 2, 2008 at 1:40pm by drwls
Two vectors, A and B, are added by means of vector addition to give a resultant vector R. The magnitudes of A and B are 9 m and 8 m, respectively, and they can have any orientation. What are the
maximum and minimum possible values for the magnitude of R?
Thursday, September 2, 2010 at 12:55pm by Victor
URGENT - Vectors
Two vectors, A and B, are added by means of vector addition to give a resultant vector R. The magnitudes of A and B are 9 m and 8 m, respectively, and they can have any orientation. What are the
maximum and minimum possible values for the magnitude of R?
Thursday, September 2, 2010 at 2:51pm by John
A football player runs the pattern given in the drawing by the three displacement vectors A, B, and C. The magnitudes of these vectors are A = 5.0 m, B= 15 m, and C = 18 m. Using the component
method, find the magnitude and direction è of the resultant vector
Friday, February 8, 2013 at 6:40pm by james
If you want the magnitude of the resultant, use the law of cosines. Drawing a figure will help. The law of sines can get you the sine of any angle of the triangle formed by the two velocity vectors
and the resultant. it's easier using components, but the answer will be the same.
Saturday, June 28, 2008 at 3:31pm by drwls
For your next question on vectors, you will have to brief us as to what you have learned. To combine two vectors, you could use graphical methods or summing components of vectors. In this particular
case, since the two vectors happen to be directed opposite to each other, we ...
Monday, September 7, 2009 at 8:27pm by MathMate
AP Physics
Consider the vectors A = 2.00 i + 7.00 j and B = 3.00 i - 2.00 j. (a) Sketch the vector sum C = A + B and the vector subtraction D = A - B. (b) Find analytical solutions for C and D first in terms of
unit vectors and then in terms of polar coordinates, with angles measured ...
Thursday, August 30, 2012 at 4:55pm by Paige
Three forces of 5 N, 8 N, and 10 N act from the corner of a cube along its edges. Using Cartesian vectors, find the magnitude of the resultant force.
Sunday, May 6, 2012 at 12:06pm by J
Three forces of 5 N, 8 N, and 10 N act from the corner of a cube along its edges. Using Cartesian vectors, find the magnitude of the resultant force.
Monday, May 7, 2012 at 8:28pm by J
COMPONENTS OF VECTORS Vectors are not given all the time in the four directions. For doing calculation more simple sometimes we need to show vectors as in the X, -X and Y, -Y components. components
of vector For example, look at the vector given below, it is in northeast ...
Sunday, October 28, 2007 at 1:24pm by sunday
The cruising speed of a Boeing 767 in still air is 530 mph. Suppose that a 767 is cruising directly east when it encounters an 80 mph wind blowing 40 degrees south of west. Sketch the vectors for the
velocities of the airplane and the wind. Express both vectors in ordered pair...
Monday, February 17, 2014 at 11:34pm by Connie
What should be the angle between two vectors of magnitudes 3.20 and 5.70 units, so that their resultant has a magnitude of 6.10 units?
Monday, January 11, 2010 at 3:11pm by Liza
1 Physical quantities such as length, mass, time and temperature are referred to as vector quantities fundamental quantities scalar quantities derived quantities 2 The following are examples of
vector quantities except displacment velocity accleration speed 3 The addition of ...
Monday, January 28, 2013 at 3:35am by christ
Math: Calculus - Vectors
Two forces of 90 N act on an object. The forces make an angle of 48 degrees to each other. Calculate the resultant force and the force that must be applied to the object to create equilibrium. My
work, using geometric vectors: | r |^2 = 90^2 + 90^2 - 2(90)(90)cos132 | r | = ...
Tuesday, February 19, 2008 at 9:47pm by Anonymous
Well write it out, let 1 represent 10:00 in the x coordinant's position, and let y be the miles out on the course the ship is. Ship 1 10:00 11:00 12:00 1:00 2:00 (1,10);(2,20);(3,30);(4,40);(5,50);
3:00 4:00 5:00 6:00 7:00 (6,60);(7,70);(8,80);(9,90);(10,100) Ship 2 1:00 2:00 ...
Thursday, May 19, 2011 at 11:33pm by Chica
two vectors are defined as a=2i+xj and b=i-4j. find value of x if a) the vectors are parallel b) the vectors are perpendicular
Sunday, November 21, 2010 at 8:12pm by karla
two vectors are defined as a=2i+xj and b=i-4j. find value of x if a) the vectors are parallel b) the vectors are perpendicular
Sunday, November 21, 2010 at 8:50pm by karla
two forces of 5 N respectively act on an object.when will the resultant of the two vectors be at a maximum?
Sunday, January 13, 2013 at 1:56am by katlego
Two forces of 5 N and 7 N respectively act on an object when will the resultant of the two vectors be at a maximum?
Sunday, January 26, 2014 at 1:27pm by Mabeka
two of 5newton and 7newton respectively act on an object.when will the resultant of the two vectors be at a maximum?
Thursday, January 23, 2014 at 3:07pm by pretty
Can a resultant of two vectors be negative?
Sunday, October 14, 2007 at 8:34am by Tom
Use the two force vectors to get it. YOu have a net S force, and a net E force. tHe angle S of east is given by arctan S/E where S and E are the resultant vectors in those directions.
Sunday, October 31, 2010 at 8:32pm by bobpursley
Two forces of 5N and 7N respectively act on an object when will the resultant of the two vectors be at maximum
Tuesday, February 5, 2013 at 12:29pm by Refiloe
two forces 5N and 7N act on an object respectively.When will the resultant of the two vectors be at a maximum?
Thursday, January 16, 2014 at 8:32pm by siphosethu
(a) Add up the four forces as vectors and see if there is an net x component in the resultant vector. If there is, the motion will deviate from the y axis. (b) The answer is called the "equilibrant"
and is equal to the negative of the resultant vector you got in (a). It has ...
Thursday, January 17, 2008 at 5:51pm by drwls
Physics (vectors)
Please help me with this question. I have a triangle that is not a right triangle with sides A, B, and C.(no values).The arrow's heads of A and B are joined and the arrow's head of C is in the tail
of B. How do you find the resultant, the vector equation, and the direction of ...
Friday, February 15, 2013 at 6:48pm by Kathy
TWO FORCES OF 5N AND 7N RESPECTIVELY ACT ON AN OBJECT.WHEN WILL THE RESULTANT OF THE TWO VECTORS BE AT A MAXIMUM?
Thursday, January 17, 2013 at 12:14pm by GOMOLEMO
It is the resultant of the two perpendicular momentum vectors.
Sunday, September 23, 2012 at 6:05am by drwls
The resultant of two vectors is their vector sum.
Wednesday, February 6, 2013 at 12:17pm by Damon
physical sciences
two forces of 5N and 7N respectively act on an object. When will the resultant of the two vectors be at the maximum?
Thursday, January 23, 2014 at 11:26am by patrick sikhosana
physical sciences
two forces of 5n and 7n respectively act on an object. What will the resultant of the two vectors be at maximum??
Tuesday, January 22, 2013 at 2:32am by lusizo mkwelo
Hint: Find the resultant of the two given forces. The third force (which keeps the resultant in equilibrium) is a force which is equal in magnitude to the resultant, but opposite in direction.
Saturday, May 25, 2013 at 8:24am by MathMate
Physics (vectors)
I am stuck with this question.Please help. I have a triangle that is not a right triangle with sides A, B, and C.(no values).The arrow's heads of A and B are joined and the arrow's head of C is in
the tail of B. If the resultant is A,what is the vector equation, and what is ...
Friday, February 15, 2013 at 8:25pm by Kathy
Each charge experiences an attraction to the two nearest corners and a repulsion (half as large) from the farthest corner. When the forces from the two nearest corners are added as vectors, the
resultant is along the diagonal. When you add up the three forces from the other ...
Sunday, January 20, 2008 at 2:08am by drwls
three displacement vectors of a croquet ball are shown in figure p3.49, where |a| = 20.0 units, |b| = 40.0 units, and |c| = 30.0 units. find (a) the resultant in unit–vector notation and (b) the
magnitude and direction of the resultant displacement
Saturday, March 12, 2011 at 3:16am by Anonymous
The position vectors, r km, and velocity vectors, vkm/h, of two boats at a certain time are given by Boat A: 10 am, r(a) = 6i+10j, v(a) = 8i-2j Boat B: 10:30 am, r(b) = 8i+5j, v(b) = 4i+j If the
boats collide, find the time when they collide as well as the position vectors of ...
Monday, January 14, 2013 at 10:14pm by Joel lu
linear algebra
which of the following sets of vectors span R^3? a.){(1, -1, 2), (0, 1, 1)} b.) {1, 2, -1), (6, ,3, 0), (4, -1, 2), (2, -5, 4)} c.) {(2, 2, 3), (-1, -2, 1), (0, 1, 0)} d.) {(1, 0, 0), (0, 1, 0), (0,
0, 1), (1, 1, 1)} can someone show the steps to check for one of them and i ...
Thursday, July 19, 2007 at 2:02pm by chris
Find the magnitude of the resultant of the following two vectors: i) 50 units due east and ii) 100 units 30° north of west. the answer is 62 unit but how it come ?
Monday, October 25, 2010 at 9:59am by meera
Two vectors A and B are added. Show that the magnitude of the resultant cannot be greater than A+B or smaller than l A-B l.
Thursday, September 1, 2011 at 8:41pm by Nar
physical science
when will the resultant of the two(5N ,7N)vectors be at maximum?
Thursday, January 23, 2014 at 4:09am by kolo olothando
A students adds two vectors with magnitude of 200 and 40 , what is the resultant ?!
Thursday, October 17, 2013 at 4:14am by Maryam
Determine whether each statement is true or false. Provide a brief justification. a. Two lines with parallel direction vectors willnot intersect. b. Two linesthat are perpendicularin R3 willhave
perpendicular direction vectors. c. Two linesthat havenon-paralleldirection ...
Wednesday, June 9, 2010 at 5:25pm by Alicia
Multiple Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A = 15.0 m, B = 10.0 m, C = 12.0 m, and D = 29.0 m.
Determine the (a) magnitude and (b) direction for the resultant that occurs ...
Monday, March 10, 2014 at 2:19pm by marah
You don't really even need vectors for this. It takes 2/10 hours to cross the river. In that time, the boat drifts downstream 2/10*4 = 4/5 km. Now, if you want to find the heading needed to get
straight across the river, then you need some vectors.
Monday, March 12, 2012 at 10:45pm by Steve
Two vectors with magnitudes of 6 meters and 8 meters cannot have a resultant of: 48 meters 14 meters 10 meters 2 meters
Friday, August 13, 2010 at 9:18pm by Ronnie
The required plane can be found by: 1. find two distinct points A, B on the line r. 2. Form two vectors from the point P to the two points on the line. These two vectors will lie in the required
plane. 3. find the normal n to the plane by the cross product of the two vectors ...
Friday, March 12, 2010 at 1:36am by MathMate
When you add the two perpendicular vectors, the resultant vector will be the hypotenuse. sqrt[(5^2) + (3.9)^2] = ___
Thursday, January 12, 2012 at 7:52pm by drwls
Summer School Calculus
I would break the two vectors into components N, and E. For instance, the N component of the first is 7cos30. Then, after finding the components, add the N, then the N. Then use trig to find the
resultant. Another way is to use the law of cosines and law of sines, but I dont ...
Saturday, June 28, 2008 at 8:31pm by bobpursley
Math - Geometric Vectors
Find the length and the direction of the resultant of each of the following systems of forces: a) forces of 3 N and 8 N acting at an angle of 60° to each other I'm completely lost. I don't know how
to solve this question using geometric vectors. Please walk me through the ...
Sunday, February 17, 2008 at 2:40pm by Anonymous
Two vectors with magnitudes of 6 meters and 8 meters cannot have a resultant of: 48 meters 14 meters 10 meters 2 meters Please explain. I do not understand how to figure this out!
Sunday, August 9, 2009 at 10:03pm by Hannah
Both velocities are vectors. You could resolve each velocity into it's x- and y- components, which usually coincide with the East and North directions. The velocity relative to water is the
resultant, and the velocity of the ferry is yet unknown. Velocity x-component y-...
Tuesday, September 8, 2009 at 3:52am by MathMate
Both problems involve the adding of two vectors. Get the magnitude of each vector using Coulomb's law. You should make an effort to do these yourself. In problem 2), you end up adding two
perpendicular E-field vectors with magnitudes k*2*10^-9/(1.5)^2 and k*3*10^-9/(1.5)^2 The...
Thursday, February 3, 2011 at 4:59am by drwls
Elementary mechanics
(Q1) 2 forces act on a point object as follows: 100 at 170 and 100 at 50.Find the resultant force (a)110N at 50 (b)110N at 100 (c)100N at 110 (d) 100N at 50 (Q2) given 3 vectors a=-i-4j+2k,b=
3i+2j-2k,c=2i-3j+k,Calculate a-(b-c) (a)-6(b)6(d)9(d)-9 (Q3)The resultant of vectors A...
Friday, July 12, 2013 at 5:21pm by david
Add the two momentum vectors. The resultant vector will have the direction of the coupled cars.
Wednesday, June 22, 2011 at 9:51pm by drwls
two vectors A and B each have magnitude 220 and angle BETWEEN THEM IS 120 WHAT WILL BE RESULTANT?
Thursday, March 20, 2014 at 12:28pm by abdul samad
Discrete Math - Geometric Vectors
Under what conditions will 3 vectors having magnitudes of 7, 24 and 25, respectively, have the zero vector as a resultant? I don't get this question at all.
Saturday, February 9, 2008 at 5:38pm by Anonymous
A football player runs the pattern given in the drawing by the three displacement vectors A, B, and C. The magnitudes of these vectors are A = 5 m, B = 13.0 m, and C = 16.0 m. Using the component
method, find the magnitude and direction è of the resultant vector A + B + C. (...
Wednesday, August 18, 2010 at 10:38pm by yoyoma
given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q are the unit vectors,find the product of vectors p and q?
Tuesday, January 1, 2013 at 6:21am by bhawani
given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q are the unit vectors,find the dot product of vectors p and q?
Wednesday, January 2, 2013 at 1:04am by bhawani
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When diffusion depends on chronology
The Internet, motorways and other transport systems, and many social and biological systems are composed of nodes connected by edges. They can therefore be represented as networks. Scientists
studying diffusion over such networks over time have now identified the temporal characteristics that affect their diffusion pathways. In a paper about to be published in European Physical Journal B,
Renaud Lambiotte and Lionel Tabourier from the University of Namur, Belgium, together with Jean-Charles Delvenne from the Catholic University of Louvain, Belgium, show that one key factor that can
dramatically change a diffusion process is the order in which events take place in complex networks.
Since it is now possible to gather data on the timings at which edges of a complex network are activated or not, network dynamics can now be studied more precisely. Empirical evidence in a variety of
social and biological systems has shown that the time intervals between the activation of edges are such that it occurs in bursts. As a result, there are broad distributions for the times between
these activation events.
So far, a majority of works have relied on computer simulations. However, a purely computational approach is unable to provide a general picture of the problem and to identify important structural
and temporal properties. Instead, the authors developed an analytical model to better understand the properties of time-dependent networks that either accelerate or slow down diffusion.
Their analytical study focused on different classes of popular models for diffusion, namely random walks—which is a mathematical description of a path that consists of a succession of random steps—
and epidemic spread models, and found the way in which the temporal ordering of events matters. They expect these results to help in building more appropriate metrics to understand real-world complex
network data.
More information: R. Lambiotte, and L. Tabourier and J.C. Delvenne (2013), Burstiness and spreading on temporal networks. European Physical Journal B, DOI 10.1140/epjb/e2013-40456-9
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74: Su Doku
Explain xkcd: It's 'cause you're dumb.
Su Doku
Title text: This one is from the Red Belt collection, of 'medium' difficulty
[edit] Explanation
Su Doku (Japanese for "single number", and now usually written as "sudoku") is a type of number puzzle, in which the player must place digits in a matrix field in the correct order. The most common
arrangement is a 9×9 grid subdivided into nine 3×3 grids where no digit is allowed to appear twice in a horizontal or vertical row on that full 9×9 matrix. The number and combination of pre-filled
squares determines the difficulty of the puzzle. When the puzzle is solved each row and column will contain the numbers 1 to 9 in a particular order.
Randall presents just a binary sudoku puzzle. A normal sudoku uses 9 digits, usually 1 to 9, and so fits conveniently into our normal "decimal" counting system (ten digits).
The joke is that the binary system has only two digits (0 and 1), and therefore binary sudoku puzzles would be trivially easy and thus pointless. The puzzle in the comic would be completed by filling
0 in the top-left and 1 in the bottom-left empty box. The only other possible grid would have the 0s and 1s swapped. This fulfills the criteria of having no repeated digits in any row or column.
Square sudoku puzzles can only be formed with a square number of digits (4, 9, 16 ...), on grids with a cube number of positions (8, 27, 64 ...). Thus this is not a completely natural extension of of
the sudoku puzzle to two digits, and could be considered a Latin square problem.
The title text appears to reference a series of published sudoku puzzle books called the "Martial Arts Sudoku". The difficulty of each book is denoted by a martial arts belt color, with each color
representing a certain skill level. Since a red belt is a rather high level (second only to a black belt), the fictional authors of this sudoku collection apparently consider this incredibly simple
puzzle is rather difficult.
[edit] Transcript
[A square divided into 2x2 squares, the top-right one has an 1 in it, the bottom-right one has a 0, the two left ones are empty.]
Binary Su Doku
[edit] Trivia
Some Su Doku puzzles use the hexidecimal system with 16 digits (0-9 and A-F) and a 16x16 grid for more difficulty.
add a comment!
If that puzzle is 4 (i.e. 2x2) domains of 1x1 cells or 1 domain of 4x4 cells then it's actually an impossible puzzle. Sudoku grids for 'n' symbols (ignoring some very interesting variants) need to be
of n² cells in total with n cells in each direction, composed of n 'domains', each of n cells so as to contain one and only one of each symbol in use. That's 81 cells in a traditional 1-9 digit 9x9
format, being 3x3 array of 3x3 individual cells in typical [S:Sudokus:S] [S:Sudokii:S] [S:Sudoka:S] puzzles, but can be irregularly domained instead as long as the domains still have nine cells. In a
12-digit that's often 3x4 cells in each domain, arrayed 4x3 (or 4x3 arrayed 3x4) to make a 12x12 full grid but can be 2x6 6x2s (or <=>) or of irregular, but still equally-sized, subdivisions.
("Killer" variations typically augment the row, column and domain parities with a 'fourth dimension' of unequally-sized irregular domains (no larger than any other domain, containing a maximum of one
of each digit, but possibly zero of some) labelled as having a stated sum total within (more than or equal to m*(m-1)/2 for m cells in that given sum-zone, assuming the lowest digit is 1, and less
than or equal to (n*(n-1)/2)-((n-m)*(n-m-1)/2), if n digits are being used as unique symbols throughout the whole grid), but that's generally in leiu of all pre-existing clue digits, using
Kakuro-like calculations to break ground on the puzzle's answer.)
Realistically, therefore, the comic must be 1x2 domains of 2x1 cells. Or the other way round. Although it's not obvious from the line-weighting which it might be. As each subdivision is the same as
the row-grouping or column-grouping it could effectively be just a 'simpler' puzzle that abandons or considers redundant domains other than the basic rows and columns, given that each possible
domain-type would be congruent with one or other of the two implicit groupings. However, it definitely could not be an "X" variant of the puzzle type (repetition dissallowed across the major
diagonals, as well as across rows and columns), otherwise it reverts to being impossible again...
However, none of what I've just said is particularly entertaining, so please feel free to ignore it and instead try the following Unary Sudoku.... (Hint: its major diagonals are also valid domains to
178.98.31.27 15:07, 24 June 2013 (UTC)
[edit] Major update
I think we even can discus PIxPI grids here at discussion page, but the explain should be simple as possible. Please help on that bad remaining language. AND: Since Randall is from the US we have AE
(American English) here.--Dgbrt (talk) 21:19, 1 July 2013 (UTC)
And Su Doku is only 1 to 9 - thanks for help--Dgbrt (talk) 22:14, 9 July 2013 (UTC)
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1 project tagged "Writing"
Theorem Linker is a program used to visualize references between theorems in a paper written using LaTeX. Using a .tex document (and a .aux file, created by the LaTeX compiler), Theorem Linker will
search through a paper, find theorems, and find references to other theorems within a theorem's "proof". It will then create a digraph in a .dot file (to be opened with programs such as Graphviz or
OmniGraffle) that will display each theorem as a node, with directed edges to describe the relations between the theorems. A path highlighted in red describes the longest path in the graph. Theorem
Linker will also create folders containing graphs to individually show relations of each theorem in a paper.
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Motor Sizing Made Easy
A straightforward procedure can guide designers toward the right motor for common uses.
Authored by:
Norm Ellis
Ellis & Associates CADD/Technical Illustration
Laguna Hills, Calif.
John Brokaw
Motion Control Application Engineer
Baldor Electric Co.
Fort Smith, Ark.
Edited by Leland Teschler
Key points:
• The key to motor selection lies in sizing up the loads and inertia the motor will see.
• First, find the needed velocity and torque. Acceleration needs come from the amount of time needed to reach final velocity.
Baldor Electric Co., www.baldor.com
Ellis & Associates CADD/Technical Illustration, ellis-assoc.com/Contacts.php
Machinery’s Handbook, Industrial Press, tinyurl.com/6yevkoo
There are different ways of selecting electric motors for specific applications. Perhaps the simplest way of approaching motor selection, though, is to ascertain the mechanical or physical
requirements of the job and make the electrical requirements match them. For example, if constrained by space or weight requirements, initially select a motor within those parameters. Then, try to
use mechanical means (pulleys, gears, gear heads, speed reducers, and so forth) to meet the mechanical requirements.
Designers typically first settle on either an ac or dc motor or gearmotor. Gearmotors are ac or dc motors typically used for higher torque and lower rotational speed. Knowing the torque and speed
requirements will help in determining if an ac or dc motor is required.
One of the mechanical limiting factors of electric motors is the bearings. Motors that use bearings will typically last longer than those using bushings. They also typically handle more perpendicular
loading to the shaft (radial load), whether horizontally or vertically.
No matter how much torque the motor can generate, it will eventually hit a crossing point where either torque falls off as speed rises or the motor can only maintain a given torque by rotating more
slowly. Once these torque versus speed qualities have been established, then you can play with the numbers using the aforementioned accessories.
Let us take a concrete example of a Baldor Electric Co. dc motor that generates 11,500 rpm with a 1-in.-pitch-diameter pulley. This configuration will produce a linear speed of 36,128 ipm, or 3,011
fpm, or 602 ips. The pulley size, of course, could be changed to vary the speed or torque. However, some applications might need slower motors with a gearbox. It’s a number game; as the speed
requirement rises, the load capability drops, and vice versa.
Consider the example of applying this motor in a conveyor or tangential drive system. Further assume the need to spray 1 fl oz of material over an 18 × 14-in. area using a spray tip which produces
0.050 gallons/min or 0.1067 fl-oz/sec at 40 psi.
Motor selection starts by first finding the needed speed (or velocity), and torque. Next comes acceleration, determined by establishing the amount of time required for the move and then solving for
shaft speed in rpm.
One determines time in this case by dividing the amount of material to be dispersed by the rate of dispersion, or 1 fl-oz/0.1067 fl-oz/sec = 9.372 sec. To determine linear velocity, divide the length
of material by elapsed time, or 18 in./9.372 sec = 1.9206 ips.
In many cases, velocity is the operational requirement which dictates the motor size and/or type. Examples include the speed with which you can transfer a part from one location to another, the rate
at which you can fill a container or remove material, or a dispersal rate for sprayed fluid.
To find the rotational velocity in rpm corresponding to this linear velocity, we first convert inches/minute to inches/second and then convert to revolutions. In this example the pulley diameter is
1.003 in. That gives 1.9203 ips × 60 sec/min × 1 rev/(1.003 in. × π) = 36.57 rev/min or 0.6 rev/sec.
To determine the angular velocity, acceleration and time, we make a simplifying assumption that it takes 1 linear in. to reach a constant speed. We next determine the associated arc length for a
rotary system, which is 1 in./π = 0.3183 in. The formula for determining arc angle is from the Machinery’s Handbook. To use it, we first determine the pulley radius, 1.003/2 = 0.5015. Using the
pulley radius and associated arc length, we have an arc angle (57.296 × 0.3183)/0.5015 = 36.3655 decimal degrees, or 0.6347 radans. Here, 57.296 is a constant from the Machinery Handbook.
To determine final angular velocity, we divide linear velocity by the pulley radius, 1.9206 ips/0.5915 in. = 3.8297 rad/sec. To determine final angular acceleration, we use the relationship for
a = V^2/2θ
where θ = arc angle and V = linear velocity: (3.8297 rad/sec^2 )/(2 × 0.6347) = 11.5540 rad/sec.^2
The final angular time or time needed to reach velocity comes from the relationship t2 = 2θ/ω. Solving for t gives √((2×0.6347 rad)/11.554 rad/sec^2) = 0.3315 sec.
Of course, the motor must provide more torque if the system needs a higher acceleration rate or a shorter ramp distance. The more torque there is available, the quicker the acceleration to reach the
prescribed velocity.
Next comes the calculation of load inertia. In moving real objects and not just theoretical examples, the load on the motor is more than just the load imposed by the object being moved. It also
consists of the load comprised of pulleys, belts, couplers, shafts, belt-tension devices, and any other object between the motor and the object being moved. To size a motor properly, you must find
the total inertia of all these components as they act on the motor shaft. In this task, it can sometimes be easier to use the actual weight (transformed into mass) of the objects rather than
calculating the inertia requirements.
In our example, say the system consists of: load at 96.0 oz, two pulleys at 1.0 oz each, and a belt at 0.8 oz. Using the general equation for inertia I = mr^2 , where m = mass and r = the distance to
the rotation axis, then the total inertia on the motor, I = (96 oz ×( 0.5015 in.)^2) + (0.8 oz × (0.5015 in.)^2) + ((1 oz × 0.50152 in.) × 2) = 24.8484 oz-in.^2
Next comes friction considerations. Say in this example you are using a common configuration consisting of two slider rails with four carriage pads carrying the load. Each of the four carriage pads
has a coefficient of friction of 0.17. The force due to friction, F = μN, where μ = friction coefficient and N = force perpendicular to the surface. In this case, N = just the mass of the load. So
the relationship reduces to F = (96 oz × (4 × 0.17) = 65.28 oz. This relationship, in turn, is multiplied by the distance to the rotation axis: 65.28 oz × 0.5015 in. = 32.738 oz-in.
To determine total torque, we first determine torque needed for acceleration. The initial step is to convert total inertia from oz-in.2 to oz-in.-sec2. This is a simple conversion that consists of
multiplying total inertia by a factor read from an inertia/torque conversion table, available from a variety of sources: 24.8484 oz-in.^2 × 0.00259 = 0.0643573 oz-in.-sec^2. Next this figure is
multiplied by the angular velocity and divided by the time needed to reach that velocity: (0.0643573 oz-in.-sec^2 × 3.8297 rad/sec)/0.3315 sec = 0.7435 oz-in. Finally, we add the force needed to
overcome friction: 0.7435 oz-in. + 32.738 oz-in. = 33.482 oz-in. Thus, most of the torque for acceleration is needed to overcome friction.
The process for determining torque needed for a constant load is similar. The only difference in the equation is that linear velocity, calculated earlier, is used instead of angular velocity, and
division is by spray time, also calculated earlier, rather than acceleration time. This gives (0.0643573 oz-in.-sec^2 × 1.9206 ips)/9.372 sec = 0.0132 oz-in. To this we once again add the force
needed to overcome friction: 0.0132 oz-in. + 32.738 oz-in. = 32.751 oz-in. Once again, most of the torque goes into overcoming friction. The total torque is just the sum of the torque needed for
acceleration and for handling a constant load: 33.482 + 32.751 = 66.233 oz-in.
A point to note is that torque for acceleration will not always be about the same as torque for constant load, as in this case. Do not assume you can just double the torque for constant load and meet
the total torque requirement.
Determining size
This example didn’t consider deceleration torque. It is not required when solving for maximum torque unless it exceeds the torque needed to accelerate. Another tip: Do not use holding torque to size
the motor. Holding torque shows how much the motor will hold at 0 rpm.
Once this analysis leads to a particular motor, the designer should go back and add the motor-rotor inertia to the calculation and recalculate to verify that the total torque required lies well
inside the torque-versus-speed curve. If not, the situation calls for the next bigger motor size. As long as the required torque and speed are kept below the motor profile (with a safety factor) all
other concerns are not relevant.
Another point to keep in mind: Side load (radial load) and overhang load are established by the motor manufacturer. They must not to be exceeded. Doing so will make the motor fail prematurely.
Finally, with the motor installed, it’s best to empirically measure the actual required torque to move the load and find the side load on the motor.
It is common practice to include a safety factor in motor sizing to account for unseen problems. For example, calculations calling for a 66-oz-in. motor might result in using the next size up, a
100-oz-in. motor, to provide a 1.7 safety factor. Common safety factors are in the 1.5 to 2.0 range.
Empirical measurements can verify calculations. In the above example, a simple fish scale could give a force reading in a pull test to find the amount of force needed to move the load.
One factor that is worth considering is the ratio of load-to-rotor inertia. This entity tends to be important when the motor must accelerate with some precision or stop quickly. It is basically a
ratio of how fast a motor will accelerate or decelerate its own mass. This, in turn, bears on the accuracy of the motor shaft position.
Baldor Electric Co. recommends keeping the load-to-rotor-inertia ratio below 5:1. If there is no accuracy requirement other than for starting or stopping the motor, designers need only make the speed
and torque requirement fall within the speed-versus-torque chart profile with an allowable safety factor. If the rotor-to-load inertia ratio is too high, the problem will be one of overshooting or
undershooting the location of the stop position. The shaft might even oscillate back and forth until settling at the right position.
Thus, the need for precision, or the lack of it, determines whether load-to-rotor inertia must be a significant design parameter. A system with a 1:1 ratio will have optimum precision. A system with
a 2:1 ratio or worse will be less so.
As an example, consider the inertia from the earlier example and a motor having 0.00143 oz-in.-sec^2 rotor inertia. We convert to the same units (using information from widely available tables) to
solve for the ratio: 0.00143 oz-in.-sec^2 × 386 ips^2 = 0.55198 oz-in.^2 Then 24.8484 oz-in.2/0.55198 oz-in.^2 = 45. Thus the ratio is 45:1.
If need be, a simple solution for lowering the ratio is either to use a motor with a larger rotor inertia (bigger shaft) or to add a gearhead to match as closely as possible to the load and rotor
inertia. Use of a gearhead will reduce output shaft speed at the gearhead and boost torque according to the ratio value. One of the many advantages of gearheads is they can handle a higher radial
loading than would be possible by just mounting the device directly to the motor shaft.
Gearboxes offer a significant benefit in that they affect the inertia ratio by a factor of the gearbox ratio squared. Thus to find what gearhead size is needed, we take √(24.8484 oz-in.^2)/(0.55198
oz-in.^2) = 6.7. This indicates a gear ratio of 6.7:1, rounded to 7:1. Recall that with a gearhead, torque rises and output shaft speed drops with the gear ratio. You can now size the gearhead to a
motor by figuring 66 oz-in. × 1.5 (safety factor) = 100 oz-in. of output torque from the gearhead. This gives 100 oz-in./7 = 14 oz-in. from the motor through the gearbox and 37 rpm × 7 = 259 rpm from
the motor.
In this case, the rpm and torque are more than is required. The controller can fine-tune the shaft speed and torque requirements to reach the final values.
Discuss this Article 1
I could not understand about the calculation in paragraph about determining angular velocity, acceleration and time.
as an example: 1in/pi = 0.3183 and t2 = 2 theta / w
Post new comment
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Parametric level set reconstruction methods for hyperspectral diffuse optical tomography
A parametric level set method (PaLS) is implemented for image reconstruction for hyperspectral diffuse optical tomography (DOT). Chromophore concentrations and diffusion amplitude are recovered using
a linearized Born approximation model and employing data from over 100 wavelengths. The images to be recovered are taken to be piecewise constant and a newly introduced, shape-based model is used as
the foundation for reconstruction. The PaLS method significantly reduces the number of unknowns relative to more traditional level-set reconstruction methods and has been show to be particularly well
suited for ill-posed inverse problems such as the one of interest here. We report on reconstructions for multiple chromophores from simulated and experimental data where the PaLS method provides a
more accurate estimation of chromophore concentrations compared to a pixel-based method.
OCIS codes: (170.3010) Image reconstruction techniques, (170.6960) Tomography, (100.3190) Inverse problems, (170.3830) Mammography, (170.3880) Medical and biological imaging, (170.3660) Light
propagation in tissues, (170.5280) Photon migration, (290.1990) Diffusion, (290.7050) Turbid media
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South Pasadena Calculus Tutor
...I love working with students and have experience teaching a wide range of classes from pre-Algebra to Advanced Engineering Mathematics. I am currently at Fuller Seminary in Pasadena preparing
for a career in community work as a pastor. Here is a testimonial from one of my students: “I love this teacher.
9 Subjects: including calculus, geometry, algebra 1, algebra 2
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which advisors were able to help me and which ones were not.
58 Subjects: including calculus, English, reading, writing
...Perhaps the best example of my experience here is when I helped one student get his yearly grade from an F to a B from the end of one semester to the end of the next. I took AP Physics for the
first time in 8th grade, as a student of the only middle school in the country to offer the course, at ...
6 Subjects: including calculus, physics, SAT math, trigonometry
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experience tutoring in Algebra 1 over the past twelve months since I have been tutoring professionally full time.
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...I took a term of differential equations at Caltech. This included ODEs and PDEs, difference equations, dynamical systems, and both qualitative and quantitative analysis of population dynamics
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35 Subjects: including calculus, chemistry, physics, geometry
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charm precut blocks
03-23-2011, 06:09 AM #1
Junior Member
Join Date
Mar 2011
Gainesville Georgia
hi has anyone used the precut charm blocks I have order several packs an would like to know how many it will take for standard quilt and does anyone have a site where can get pattern free for
charm blocks
I've bought them in the past. But it was for a quilt that took a charm pack (or two) and some Jelly Rolls.
Which reminds me, I need to finish that quilt. Ughh!
Good luck in finding your answer.
i like the free patterns from moda
hi has anyone used the precut charm blocks I have order several packs an would like to know how many it will take for standard quilt and does anyone have a site where can get pattern free for
charm blocks
How many quilt squares?
Instructions for figuring how many squares you will need
Figure out the measurements you want for your completed quilt. For new quilters, drawing a large box on a piece of paper helps! For these directions lets say that you are making a lap size quilt
that is 45x60 inches.
Will you be putting a border on your quilt? Draw another box inside of your beginning box. If you will be making a quilt with 2 borders, draw another box inside the second box. I recommend a
quilt with a border because you won't have to deal with all the seam allowances from the squares when you put your binding on.
Mark your measurements inside each box going vertically and horizontally. For instance, your first border is 4 inches, your second border is 3 inches. Most people make the mistake of counting
only 7 inches for the border. BUT, you have 7 inches on both sides which would total 14 inches. So a quilt that is 45x60 is now 45" minus 14" by 60" minus 14", which leaves 31" x 46" area for
your squares.
If you are purchasing 4" squares and use a 1/4 inch seam allowance, you would divide 31" by 3.5 which equals 9 (rounded up) squares across. Divide 46" by 3.5 which equals 13 (rounded down)
squares down.
Multiply the 2 answers 9x13 for a total of 117 4" inch squares. You would need to purchase 3 packages of 40 4" squares. After you sew your squares together you add your borders! When cutting your
strips for your borders, make sure and add 1/2" for seam allowances or your quilt will be smaller than you want it to be!
If you are not using a border you would divide 60" by 3.5 and 45" by 3.5. That would be 17 squares down by 13 across for a total of 221 squares which is 6 packages of 40 squares with some left
over (enough for 2 small 9 patch pillows!)
If you are using 5 inch squares, use the above instructions but use 4.5 instead of 3.5 when calculating. 6 inch squares, use 5.5
Quilts without a border
If you aren't using a border, the following will be helpful in figuring how many 4" squares you need. These sizes are for comforter size quilts, not bedspread size.
Crib size (42" x 50") = 168 squares (12 across by 14 down)
Twin/single size (69" x 90") = 520 squares (20 across by 26 down)
Full/double size (84" x 90") = 624 squares (24 across by 26 down)
Queen size (90" x 96") = 728 squares (26 across by 28 down)
King size (104" x 96") = 840 squares (30 across by 28 down)
thanks all who replied waiting for mail delivery to start
I am making a quilt with the "10 minute block". It takes 5 charms per block. I am using 4 Black & white charms and cutting a fifth out of bright red material for the center diamond. It takes 3
seams to make the block. I did 14 blocks yesterday in between everything else, they are really 10 min. each. http://www.youtube.com/watch?v=ZbTHlGGKMPM. I am using the 5" charms, the lady on the
video uses 10" squares. I get 10 blocks per pack and 2 packs will make 20 blocks so roughly a 50"x70" including sashing and border.
thanks for inf can not wait till i get my charm block package so can start
Purplemem, thanks for that comprehensive explanation. and congrats on your weight loss!!
03-23-2011, 06:11 AM #2
Join Date
Jan 2011
Allen Park, Mi
Blog Entries
03-23-2011, 06:18 AM #3
03-23-2011, 06:23 AM #4
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03-23-2011, 06:25 AM #5
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03-23-2011, 06:50 AM #6
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Gainesville Georgia
03-23-2011, 07:20 AM #7
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Washington DC
Blog Entries
03-23-2011, 07:55 AM #8
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03-23-2011, 02:17 PM #9
Join Date
Mar 2011
western NY formerly MN, FL, NC, SC
Blog Entries
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Results 1 - 10 of 98
- Journal of Artificial Intelligence Research , 1995
"... Multiclass learning problems involve nding a de nition for an unknown function f(x) whose range is a discrete set containing k>2values (i.e., k \classes"). The de nition is acquired by studying
collections of training examples of the form hx i;f(x i)i. Existing approaches to multiclass learning ..."
Cited by 564 (9 self)
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Multiclass learning problems involve nding a de nition for an unknown function f(x) whose range is a discrete set containing k>2values (i.e., k \classes"). The de nition is acquired by studying
collections of training examples of the form hx i;f(x i)i. Existing approaches to multiclass learning problems include direct application of multiclass algorithms such as the decision-tree algorithms
C4.5 and CART, application of binary concept learning algorithms to learn individual binary functions for each of the k classes, and application of binary concept learning algorithms with distributed
output representations. This paper compares these three approaches to a new technique in which error-correcting codes are employed as a distributed output representation. We show that these output
representations improve the generalization performance of both C4.5 and backpropagation on a wide range of multiclass learning tasks. We also demonstrate that this approach is robust with respect to
changes in the size of the training sample, the assignment of distributed representations to particular classes, and the application of over tting avoidance techniques such as decision-tree pruning.
Finally,we show that|like the other methods|the error-correcting code technique can provide reliable class probability estimates. Taken together, these results demonstrate that error-correcting
output codes provide a general-purpose method for improving the performance of inductive learning programs on multiclass problems. 1.
, 1995
"... We present an algorithm for improving the accuracy of algorithms for learning binary concepts. The improvement is achieved by combining a large number of hypotheses, each of which is generated
by training the given learning algorithm on a different set of examples. Our algorithm is based on ideas pr ..."
Cited by 419 (16 self)
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We present an algorithm for improving the accuracy of algorithms for learning binary concepts. The improvement is achieved by combining a large number of hypotheses, each of which is generated by
training the given learning algorithm on a different set of examples. Our algorithm is based on ideas presented by Schapire in his paper "The strength of weak learnability", and represents an
improvement over his results. The analysis of our algorithm provides general upper bounds on the resources required for learning in Valiant's polynomial PAC learning framework, which are the best
general upper bounds known today. We show that the number of hypotheses that are combined by our algorithm is the smallest number possible. Other outcomes of our analysis are results regarding the
representational power of threshold circuits, the relation between learnability and compression, and a method for parallelizing PAC learning algorithms. We provide extensions of our algorithms to
cases in which the conc...
, 1996
"... This is the first of two papers that use off-training set (OTS) error to investigate the assumption -free relationship between learning algorithms. This first paper discusses the senses in which
there are no a priori distinctions between learning algorithms. (The second paper discusses the senses in ..."
Cited by 123 (5 self)
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This is the first of two papers that use off-training set (OTS) error to investigate the assumption -free relationship between learning algorithms. This first paper discusses the senses in which
there are no a priori distinctions between learning algorithms. (The second paper discusses the senses in which there are such distinctions.) In this first paper it is shown, loosely speaking, that
for any two algorithms A and B, there are "as many" targets (or priors over targets) for which A has lower expected OTS error than B as vice-versa, for loss functions like zero-one loss. In
particular, this is true if A is cross-validation and B is "anti-cross-validation" (choose the learning algorithm with largest cross-validation error). This paper ends with a discussion of the
implications of these results for computational learning theory. It is shown that one can not say: if empirical misclassification rate is low; the Vapnik-Chervonenkis dimension of your generalizer is
small; and the trainin...
- Machine Learning , 1995
"... Abstract. The Vapnik-Chervonenkis (V-C) dimension is an important combinatorial tool in the analysis of learning problems in the PAC framework. For polynomial learnability, we seek upper bounds
on the V-C dimension that are polynomial in the syntactic complexity of concepts. Such upper bounds are au ..."
Cited by 91 (1 self)
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Abstract. The Vapnik-Chervonenkis (V-C) dimension is an important combinatorial tool in the analysis of learning problems in the PAC framework. For polynomial learnability, we seek upper bounds on
the V-C dimension that are polynomial in the syntactic complexity of concepts. Such upper bounds are automatic for discrete concept classes, but hitherto little has been known about what general
conditions guarantee polynomial bounds on V-C dimension for classes in which concepts and examples are represented by tuples of real numbers. In this paper, we show that for two general kinds of
concept class the V-C dimension is polynomially bounded in the number of real numbers used to define a problem instance. One is classes where the criterion for membership of an instance in a concept
can be expressed as a formula (in the first-order theory of the reals) with fixed quantification depth and exponentially-bounded length, whose atomic predicates are polynomial inequalities of
exponentially-bounded degree. The other is classes where containment of an instance in a concept is testable in polynomial time, assuming we may compute standard arithmetic operations on reals
exactly in constant time. Our results show that in the continuous case, as in the discrete, the real barrier to efficient learning in the Occam sense is complexity-theoretic and not
information-theoretic. We present examples to show how these results apply to concept classes defined by geometrical figures and neural nets, and derive polynomial bounds on the V-C dimension for
these classes. Keywords: Concept learning, information theory, Vapnik-Chervonenkis dimension, Milnor’s theorem 1.
- Lectures on Parallel Computation , 1993
"... A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of
various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing ..."
Cited by 77 (5 self)
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A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various
aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing [365] demonstrated that, in principle, a single general purpose sequential machine could be
designed which would be capable of efficiently performing any computation which could be performed by a special purpose sequential machine. The importance of this universality result for subsequent
practical developments in computing cannot be overstated. It showed that, for a given computational problem, the additional efficiency advantages which could be gained by designing a special purpose
sequential machine for that problem would not be great. Around 1944, von Neumann produced a proposal [66, 389] for a general purpose storedprogram sequential computer which captured the fundamental
principles of...
- In Proceedings of the 23rd VLDB Conference , 1997
"... We explore how to organize a text database hierarchically to aid better searching and browsing. We propose to exploit the natural hierarchy of topics, or taxonomy, that many corpora,suchas
internet directories, digital libraries, and patent databases enjoy. In our system, the user navigates through ..."
Cited by 76 (5 self)
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We explore how to organize a text database hierarchically to aid better searching and browsing. We propose to exploit the natural hierarchy of topics, or taxonomy, that many corpora,suchas internet
directories, digital libraries, and patent databases enjoy. In our system, the user navigates through the query response not as a at unstructured list, but embedded in the familiar taxonomy, and
annotated with document signatures computed dynamically with respect to where the user is located at any time. Weshowhowto update such databases with new documents with high speed and accuracy. Weuse
techniques from statistical pattern recognition to e ciently separate the feature words or discriminants from the noise words at each node of the taxonomy. Using these, we build a multi-level classi
er. At each node, this classi er can ignore the large number of noise words in a document. Thus the classi er has a small model size and is very fast. However, owing to the use of context-sensitive
features, the classi er is very accurate. We report on experiences with the Reuters newswire benchmark, the US Patent database, and web document samples from Yahoo!. 1
- Artificial Intelligence , 1994
"... We present positive PAC-learning results for the nonmonotonic inductive logic programming setting. In particular, we show that first order range-restricted clausal theories that consist of
clauses with up to k literals of size at most j each are polynomialsample polynomial-time PAC-learnable with on ..."
Cited by 64 (27 self)
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We present positive PAC-learning results for the nonmonotonic inductive logic programming setting. In particular, we show that first order range-restricted clausal theories that consist of clauses
with up to k literals of size at most j each are polynomialsample polynomial-time PAC-learnable with one-sided error from positive examples only. In our framework, concepts are clausal theories and
examples are finite interpretations. We discuss the problems encountered when learning theories which only have infinite non-trivial models and propose a way to avoid these problems using a
representation change called flattening. Finally, we compare our results to PAC-learnability results for the normal inductive logic programming setting. 1
- In , O. Bousquet, U.v. Luxburg, and G. Rsch (Editors , 2004
"... ..."
- Acta Informatica , 1997
"... We consider the problem of measuring the similarity or distance between two finite sets of points in a metric space, and computing the measure. This problem has applications in, e.g.,
computational geometry, philosophy of science, updating or changing theories, and machine learning. We review some o ..."
Cited by 50 (2 self)
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We consider the problem of measuring the similarity or distance between two finite sets of points in a metric space, and computing the measure. This problem has applications in, e.g., computational
geometry, philosophy of science, updating or changing theories, and machine learning. We review some of the distance functions proposed in the literature, among them the minimum distance link
measure, the surjection measure, and the fair surjection measure, and supply polynomial time algorithms for the computation of these measures. Furthermore, we introduce the minimum link measure, a
new distance function which is more appealing than the other distance functions mentioned. We also present a polynomial time algorithm for computing this new measure. We further address the issue of
defining a metric on point sets. We present the metric infimum method that constructs a metric from any distance functions on point sets. In particular, the metric infimum of the minimum link measure
is a quite int...
, 1995
"... Blackbox optimization---optimization in presence of limited knowledge about the objective function---has recently enjoyed a large increase in interest because of the demand from the
practitioners. This has triggered a race for new high performance algorithms for solving large, difficult problems. Si ..."
Cited by 50 (10 self)
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Blackbox optimization---optimization in presence of limited knowledge about the objective function---has recently enjoyed a large increase in interest because of the demand from the practitioners.
This has triggered a race for new high performance algorithms for solving large, difficult problems. Simulated annealing, genetic algorithms, tabu search are some examples. Unfortunately, each of
these algorithms is creating a separate field in itself and their use in practice is often guided by personal discretion rather than scientific reasons. The primary reason behind this confusing
situation is the lack of any comprehensive understanding about blackbox search. This dissertation takes a step toward clearing some of the confusion. The main objectives of this dissertation are: 1.
present SEARCH (Search Envisioned As Relation & Class Hierarchizing)---an alternate perspective of blackbox optimization and its quantitative analysis that lays the foundation essential for
transcending the limits of random enumerative search; 2. design and testing of the fast messy genetic algorithm. SEARCH is a general framework for understanding blackbox optimization in terms of
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Determine the coordinates of the point
May 3rd 2009, 11:02 PM #1
Dec 2008
Determine the coordinates of the point
Show that the line $<br /> 5x+3y+ \lambda x <br />$ = $<br /> 2 \lambda y -6<br />$ always passes from a fixed point . Determine the coordinate of the point.
The equation can be written as
Then $\left\{\begin{array}{ll}x-2y=0\\5x+3y=-6\end{array}\right.$
Now solve the system.
May 4th 2009, 07:28 AM #2
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calc bc (condensed
Posted by APpreciative student on Tuesday, September 14, 2010 at 10:25pm.
is the limit as x approaches 0 of sin3x over 3x equal to zero?
basically this is my problem:
lim [sin 3x / 4x)
x-> 0
~~~~I multiplied& eventually got to
.75* lim (sin 3x / 3x)
x-> 0
~so i figured since (lim (sinx/x)
x-> 0
was equal to zero, then
lim (sin3x/ 3x) also equaled 0
x-> 0
is that right? thank you !!!
(all of the x-> 0 should be under the "lim" -- just in case the text shifts...)
• calc bc (condensed - TutorCat, Tuesday, September 14, 2010 at 10:27pm
see below
• calc bc (condensed - Reiny, Tuesday, September 14, 2010 at 10:40pm
your preliminary steps are correct
lim sin3x/(4x) as x--> 0
= lim (3/4)(sin3x/(3x))
= 3/4(1)
= 3/4
lim sinx/x = 1 not zero
as x-->0
• calc bc (condensed - Reiny, Tuesday, September 14, 2010 at 10:47pm
Here is a simple way to check your limit answers if you have a calculator
pick a value very "close" to your approach value, in this case I would pick x = .001
evaluate using that value, (you are not yet dividing by zero, but close)
for your question I got .749998875, close to 3/4 I would say.
PS. Make sure your calculator is set to Radians
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sheaf theory
After a busy day giving final exams in the MASS program it was nice to learn today that my paper with Paul Siegel about sheaves of C*-algebras has appeared in the Journal of K-Theory. The link for
the published version is
This paper arose from some discussions when Paul was writing his thesis. We were talking about the “lifting and controlling” arguments for Paschke duals that are used in the construction of various
forms of operator-algebraic assembly maps (an early example is the one that appears in my paper with Nigel on the coarse Baum-Connes conjecture, which asserts that the quotient \( D^*(X)/C^*(X) \) of
the “controlled” pseudolocal by the “controlled” locally compact operators does not depend on the assumed “control”). At some point in these discussions I casually remarked that, “of course”, what
is really going on is that the Paschke dual is a sheaf. Some time later I realized that what I had said was, in fact, true. There aren’t any new results here but I hope that there is some
conceptual clarification. (There is an interesting spectral sequence that I’ll try to write about another time, though.)
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MathGroup Archive: May 2004 [00187]
[Date Index] [Thread Index] [Author Index]
Re: UnitStep function leads to very difficult Integration
• To: mathgroup at smc.vnet.net
• Subject: [mg48120] Re: UnitStep function leads to very difficult Integration
• From: astanoff_otez_ceci at yahoo.fr (astanoff)
• Date: Fri, 14 May 2004 00:12:19 -0400 (EDT)
• References: <c7ut4m$q9l$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com
Nathan Moore wrote:
> Hello all,
> I'm trying to evaluate expectation values from joint probability
> distributions which I've had to define in a piecewise manner, ie
> norm = Integrate[G[1,x]G[2,x],{x,0,10}];
> <x^2> = Integrate[G[1,x]G[2,x] x^2,{x,0,10}] * norm
> where the G[k,x] is a set of polynomials defined piecewise on
> intervals, {(0,2),(2,4),(4,6),etc}.
> I assume the most Mathematica-friendly way to define these functions is
> with the UnitStep[] function. This works to varying degree. I was
> able to check the probability normalization this way (integrating only
> one G[k,x]) with an exact result. Unfortunately though Mathematica
> seems unable to find an exact experssion for the expectation when the
> G[k,x] polynomials take sufficiently complex form.
> The integration output starts to look like,
> Integrate[ d^4 ( (d-3)UnitStep[3-d] UnitStep[d-1]/d + UnitStep[1 - d]
> UnitStep[d])^2, {d,0,3}]
This is the way you could get exact rational values :
cv_List(*critical values*),
pd_(*polynomial degree*),
eps_(* epsilon to avoid boundary integration troubles*)
] := Module[{termIntegrate, th, ti},
termIntegrate[{a_, b_}] :=
t=Table[{x, f /. d -> x},{x, a+eps, b-eps, incr}];
tfit = Fit[t,Table[d^n,{n,0,pd}],d] // Chop // Rationalize;
th = Thread[{Drop[cv,-1], Rest[cv]}];
ti = termIntegrate /@ th;
Plus @@ (Integrate[#[[3]],{d, #[[1]]+eps, #[[2]]-eps}]& /@ ti)
(* your example : *)
expr=d^4 ((d-3)UnitStep[3-d] UnitStep[d-1]/d+UnitStep[1-d] UnitStep[d])^2;
0% de pub! Que du bonheur et des vrais adhérents !
Vous aussi inscrivez-vous sans plus tarder!!
Message posté à partir de http://www.gyptis.org, BBS actif depuis 1995.
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Edgemont, PA Prealgebra Tutor
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A cubic polynomial with rational coefficients has the roots 6 + square root 6 and 2/3. Find one additional root.
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Since it has rational coefficients, that means that when you multiply the product of the three roots \[(a)(x-(6+\sqrt{6}))(x-2/3)\] you somehow avoid having an irrational coefficient (something
with a square root). So the big question is What times (x-(6+sqrt(6))) will avoid this issue. I believe there is a parallel problem with complex numbers and they multiply by the complex
conjugate. I suspect something similar here.
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is replying to Can someone tell me what button the professor is hitting...
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.
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Prove that 2n natural numbers is n(2n+1)
If you read the demonstration carefully, you will see right at the beginning the ◊ 'operator' as I define it:
I just reduced your problem to a simpler version. Instead of trying to build an expression for the sum of first 2n naturals, I got the expression for the sum of first N naturals, ◊n. After that you
just plug 2n: ◊(2n) and get the expression.
Think '◊n' as ◊(n) or f(n). There is nothing special about ◊.. It's just a symbol I usually associate with the 'function' that sums the 1st N naturals.
Now read my post 2 or 3 more times and try to catch up with a sheet of paper, line by line.
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S/O What is your least favorite curriculum
May 17, 2013 at 11:57 AM
So the other post got me thinking, What curriculum has completely bombed in your house? Maybe I'm the only one who has changed things up so drastically LOL! I'll tell you, I have gone from
work-booky, to Charlotte Mason, to unschooling, to textbooks, back to work books, and now have figured out what my kids learn best with, and its a mix of all of the above! The ones that bombed the
worst in my house were Heart of Dakota (love the idea of it, hate the actual reality of it) Mystery of History (coma inducing and not enough re-inforcement of ideas) and Horizons for math. So tell
me. What's your biggest curriculum fail? Maybe you'll save another family the trouble.
for us it was the BJU Science and History for first and second grade. The kids hated it.
Bible was a bomb for us this year. I bought it from CBD. It was a good curriculum, it was geared more for 3rd grade than 1st though.
My oldest hated Saxon Math. I hated Saxon Math. We also hate K12's science and history.
We also use different curriculums but Lifepac Science and Lifepac Math, for us, seems to be terrible. We stuck through with the Lifepac Science, but i took one look at the Lifepac Math and sold
We also do not like Abeka Grammar. If my boys had been using it since Kindergarten it may have been okay, but since they came from public school and into 9th grade grammar, it was just too much.
Quoting debramommyof4:
My oldest hated Saxon Math. I hated Saxon Math. We also hate K12's science and history.
I was thinking about getting Saxon math (algebra 2) for my boys. Can you tell me why your oldest hated it so much?
Thank you.
We used it in kindergarten. It was very dry. She loves math but found it very boring.
Quoting starbeck96:
Quoting debramommyof4:
My oldest hated Saxon Math. I hated Saxon Math. We also hate K12's science and history.
I was thinking about getting Saxon math (algebra 2) for my boys. Can you tell me why your oldest hated it so much?
Thank you.
My daughter is older (almost 12) and used an upper level (grade 5) text a couple years ago. It was dry, boring, monotonous... and if appears that the author hates math. I mean, there was no
effort to make it interesting.
Also, it's "algorithm heavy, conceptually weak", in my opinion.
Quoting starbeck96:
Quoting debramommyof4:
My oldest hated Saxon Math. I hated Saxon Math. We also hate K12's science and history.
I was thinking about getting Saxon math (algebra 2) for my boys. Can you tell me why your oldest hated it so much?
Thank you.
Thank you. I will probably look for something else then. I am capable of teaching it myself, but I was really looking for a curriculum that taught it for me to help save me some time.
What about teaching textbooks?
Quoting AutymsMommy:
My daughter is older (almost 12) and used an upper level (grade 5) text a couple years ago. It was dry, boring, monotonous... and if appears that the author hates math. I mean, there was no
effort to make it interesting.
Also, it's "algorithm heavy, conceptually weak", in my opinion.
Quoting starbeck96:
Quoting debramommyof4:
My oldest hated Saxon Math. I hated Saxon Math. We also hate K12's science and history.
I was thinking about getting Saxon math (algebra 2) for my boys. Can you tell me why your oldest hated it so much?
Thank you.
Thank you. My boys do not like math, so I think this would not work for them. We tried Abeka Algebra 1 but it just didn't work, they moved too fast. We are using an older version of BJU and it
seems to be working okay, but the only reason i could afford it is because I got it from someone who was able to purchase the DVDs since it was the old link versions. I just can't afford to spend
400.00 on one subject..
Quoting debrammyof4:
We used it in kindergarten. It was very dry. She loves math but found it very boring.
Quoting starbeck96:
Quoting debramommyof4:
My oldest hated Saxon Math. I hated Saxon Math. We also hate K12's science and history.
I was thinking about getting Saxon math (algebra 2) for my boys. Can you tell me why your oldest hated it so much?
Thank you.
It was also slow for her. We only had it for half a year and she went through the entire book. She did start disliking math at the time though. We have got her love of math back up though. Next
year we are using Khan Academy. I am really interested in Teaching text books but I can not afford it right this secound.
Quoting starbeck96:
Thank you. My boys do not like math, so I think this would not work for them. We tried Abeka Algebra 1 but it just didn't work, they moved too fast. We are using an older version of BJU and
it seems to be working okay, but the only reason i could afford it is because I got it from someone who was able to purchase the DVDs since it was the old link versions. I just can't afford
to spend 400.00 on one subject..
Quoting debrammyof4:
We used it in kindergarten. It was very dry. She loves math but found it very boring.
Quoting starbeck96:
Quoting debramommyof4:
My oldest hated Saxon Math. I hated Saxon Math. We also hate K12's science and history.
I was thinking about getting Saxon math (algebra 2) for my boys. Can you tell me why your oldest hated it so much?
Thank you.
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PC game RNG - diyAudio
diyAudio Moderator Emeritus
Join Date: Oct 2002
Location: Bandung
PC game RNG
This is way off audio. I have this PC game in my old computer (286, with 100Mhz speed). The game is simple. There is 4 blocks that have to be "guessed" to win. The choice is only A or B. We have to
guess it step by step, from block no.1 to the last block.
For example the right answer is A-A-B-A. First we guess the first block. If we guess it right (A), then the game gives green light, we get 25% point, and we can make the guess for the second block.
If again we guess right for the second block (A), it makes our score 50% point. But if we guess wrong for the third block, the game gives red light, and we have this game and continue with other
game. (the game that is wrongly guessed cannot be played anymore). The same case if we already guess wrongly for the first block, then the red light is on and the game is over.
I'm very curious about this game. It is only on the 100Mhz computer. But I think solving this may benefit in many other field. I read in the net that this kind of game is incorporating a RNG (Random
Number Generator) for the computer to make the answers.
Is there any possiblity that we can always knows the answer on such a game? I think about 2 possibilities, but cannot figure out how to do both of it.
1. Nowdays, the computer is 1.5Ghz in speed. How if we make the current PC played this game (on the 100Mhz old PC) so it can collect statistic, so the RNG can be estimated? Is it possible to predict
what an RNG will produce with statistic? Will the faster PC can determine the pattern of RNG produced by slower PC?
2. Is it possible to make such a "Scanner" to determine what will be the next answer? The electronics inside the PC must be making some electromagnetic noise radiance. Is it possible that we can make
such a pocket size scanner, that can determine wheter the next answer will be A or B?
There are many clever guy involved in this website. Maybe some are very familiar with both electronic and computers (and maybe electromagnetic scanners)?
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bout Google?
What About Google?
At this point, maybe you are thinking that Wolfram|Alpha sounds cool, and you might even see some uses for it in your classroom, but you are not yet ready to let go of your Google addiction. Don't
fret, because other geeks have been there already: You can use Goofram for searching with Google and Wolfram|Alpha simultaneously, or you can use heapr to search simultaneously with Google, Wolfram|
Alpha, Twitter, Flickr, and other sites.
[Note: Contents of frame come from google.com or other sites and are not maintained by Loci]
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Did I calculate the 1st and 2nd derivative of this equation correctly??
March 27th 2010, 11:02 AM
Did I calculate the 1st and 2nd derivative of this equation correctly??
question5 on Flickr - Photo Sharing!
The equation is at the link above.
For the 1st derivative I got f' = (49-x^2)^1/2 + (-x)(49-x^2)^-1/2
For the 2nd derivative I got f'' = -98x+x^3 / (49-x^2)^3/2
Are these right?
Thank you(Happy)
March 27th 2010, 11:25 AM
The first derivative is right but I think your second one is wrong.
March 27th 2010, 11:37 AM
question5 on Flickr - Photo Sharing!
The equation is at the link above.
For the 1st derivative I got f' = (49-x^2)^1/2 + (-x)(49-x^2)^-1/2
For the 2nd derivative I got f'' = -98x+x^3 / (49-x^2)^3/2
Are these right?
Thank you(Happy)
Use product rule.. I think your answer has some errors:
$f(x) = x \times \sqrt{{49-x^{2}}}$
$f'(x) = [1 \sqrt{49-x^{2}}] + [x \times \frac{1}{2} \times {(49-x^{2})^\frac{-3}{2}} \times (-2x)] <br /> = [\sqrt{49-x^{2}}] - [{x^2} \times {(49-x^{2})^\frac{-3}{2}}]$
$= \sqrt{49-x^{2}} - \frac{x^2}{\sqrt{49-x^{2}}}$
Now use the product rule to find the second derivative. I am a little too lazy topost the complete solution to find the second derivative. Try doing it yourself and post if you have problems. For
your convenience, the second derivative looks like this:
$2x \times [\frac{{-x}^2}{2(49-x^2)^\frac{3}{2}} -\frac{1}{2 \sqrt{49-x^{2}}}] - \frac{2x}{\sqrt{49-x^{2}}}$
March 28th 2010, 10:36 AM
Hello, and thank you for your responses!
I think I got the right f"
f"=2x^3-147x / (49-x^2)^3/2
I also think I got the inflection points x=0, x=-7, x=7
but now I am having a problem interpreting this into the right answer.
I know it can't be D. I'm pretty sure its not A or B because (0,7) is not on this function. So it is B???? Thank you!!!
March 28th 2010, 11:06 AM
March 28th 2010, 11:38 AM
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|
, 1993
"... This paper presents a general theoretical framework for ensemble methods of constructing significantly improved regression estimates. Given a population of regression estimators, we construct a
hybrid estimator which is as good or better in the MSE sense than any estimator in the population. We argu ..."
Cited by 290 (2 self)
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This paper presents a general theoretical framework for ensemble methods of constructing significantly improved regression estimates. Given a population of regression estimators, we construct a
hybrid estimator which is as good or better in the MSE sense than any estimator in the population. We argue that the ensemble method presented has several properties: 1) It efficiently uses all the
networks of a population - none of the networks need be discarded. 2) It efficiently uses all the available data for training without over-fitting. 3) It inherently performs regularization by
smoothing in functional space which helps to avoid over-fitting. 4) It utilizes local minima to construct improved estimates whereas other neural network algorithms are hindered by local minima. 5)
It is ideally suited for parallel computation. 6) It leads to a very useful and natural measure of the number of distinct estimators in a population. 7) The optimal parameters of the ensemble
estimator are given in clo...
- In Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence , 1995
"... The primary goal of inductive learning is to generalize well -- that is, induce a function that accurately produces the correct output for future inputs. Hansen and Salamon showed that, under
certain assumptions, combining the predictions of several separately trained neural networks will improve ge ..."
Cited by 38 (6 self)
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The primary goal of inductive learning is to generalize well -- that is, induce a function that accurately produces the correct output for future inputs. Hansen and Salamon showed that, under certain
assumptions, combining the predictions of several separately trained neural networks will improve generalization. One of their key assumptions is that the individual networks should be independent in
the errors they produce. In the standard way of performing backpropagation this assumption may be violated, because the standard procedure is to initialize network weights in the region of weight
space near the origin. This means that backpropagation's gradient-descent search may only reach a small subset of the possible local minima. In this paper we present an approach to initializing
neural networks that uses competitive learning to intelligently create networks that are originally located far from the origin of weight space, thereby potentially increasing the set of reachable
local minima....
, 1994
"... ___________________________________ SUPERVISED COMPETITIVE LEARNING: A TECHNOLOGY FOR PEN-BASED ADAPTATION IN REAL TIME by Thomas H. Fuller, Jr.
___________________________________________________________ ADVISOR: Professor Takayuki Dan Kimura ________________________________________________________ ..."
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___________________________________ SUPERVISED COMPETITIVE LEARNING: A TECHNOLOGY FOR PEN-BASED ADAPTATION IN REAL TIME by Thomas H. Fuller, Jr.
___________________________________________________________ ADVISOR: Professor Takayuki Dan Kimura ___________________________________________________________ December, 1994 Saint Louis, Missouri
___________________________________________________________ The advent of affordable, pen-based computers promises wide application in educational and home settings. In such settings, systems will be
regularly employed by a few users (children or students), and occasionally by other users (teachers or parents). The systems must adapt to the writing and gestures of regular users but not lose prior
recognition ability. Furthermore, this adaptation must occur in real time not to frustrate or confuse the user, and not to interfere with the task at hand. It must also provide a reliable measure of
the likelihood of correct recognition. Supervised Competitiv...
"... Neural netsofferanapproachtocomputationthatmimicsbiological nervoussystems. Algorithms based on neural nets have been proposed to address speech recognition tasks which humans perlorm with
little apparent effort. In this paper, neural net classifiers are described and compared with conventional clas ..."
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Neural netsofferanapproachtocomputationthatmimicsbiological nervoussystems. Algorithms based on neural nets have been proposed to address speech recognition tasks which humans perlorm with little
apparent effort. In this paper, neural net classifiers are described and compared with conventional classification algorithms. Perceptron classifiers trained with a new algorithm, called back
propagation, were tested and found to perform roughly as well as conventional classifiers on digit and vowel classification tasks. A new net architecture, called a Viterbi net, which recognizes
time-varying input patterns, provided an accuracyofbetter than 99 % on a large speech data base. Perceptrons and another neural net, the feature map, were implemented in a very large-scale
integration (VLSI) device. Neural nets are highly interconnected networksofrelativelysimpleprocessingelements, or nodes, that operate in parallel. They are designedto mimicthefunction
ofneurobiologicalnetworks. Recentworkonneuralnetworks raises the possibilityofnew approaches to the
"... The primary goal of inductive learning is to generalize well- that is, induce a function that accurately produces the correct output for future inputs. Hansen and Salamon showed that, under
certain assumptions, combining the predictions of several separately trained neural networks will improve gene ..."
Add to MetaCart
The primary goal of inductive learning is to generalize well- that is, induce a function that accurately produces the correct output for future inputs. Hansen and Salamon showed that, under certain
assumptions, combining the predictions of several separately trained neural networks will improve generalization. One of their key assumptions is that the individual networks should be independent in
the errors they produce. In the standard way of performing backpropagation this assumption may be violated, because the standard procedure is to initialize network weights in the region of weight
space near the origin. This means that backpropagation's gradient-descent search may only reach a small subset of the possible local minima. In this paper we present an approach to initializing
neural networks that uses competitive learning to intelligently create networks that are originally located far from the origin of weight space, thereby potentially increasing the set of reachable
local minima. We report experiments on two real-world datasets where combinations of networks initialized with our method generalize better than combinations of networks initialized the traditional
way. 1
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Elizaveta Litvinova
Elizaveta Litvinova
Born in czarist Russia, young Elizaveta’s early education was at a women’s high school in St. Petersburg. In 1866 Elizaveta married Viktor Litvinov and took his last name. Unlike Vladimir Kovalevskii
(Sofia Kovalevskaya’s husband), Litvinov would not allow his wife to travel to Europe to study at the universities there. Litvinova studied with Strannoliubskii (who had also privately tutored
Kovalevskaya). As soon as her husband died, Litvinova went to Zürich and enrolled at a polytechnic institute. In 1873 the Russian czar decreed all Russian women studying in Zürich had to return to
Russia or face the consequences. Litvinova was one of the few to ignore the decree and continue her studies in Zürich. When Litvinova returned to Russia, she was denied university appointments
because she had defied the 1873 recall. She taught at a women’s high school and supplemented her meager income by writing biographies of more famous mathematicians such as Kovalevskaya and Aristotle.
After retiring, it is believed that Litvinova died during the Russian Revolution in 1919.
• 1 A. H. Koblitz “Sofia Vasilevna Kovalevskaia” in Women of Mathematics: A Bibliographic Sourcebook L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 129 - 134
Elizaveta Fedorovna Litvinova, Elizaveta Fedorovna Ivanshkina, Elizaveta Ivanshkina
Mathematics Subject Classification
no label found
no label found
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Re: st: RE: RE: Re: sum across observations until a certain cutpoint
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: st: RE: RE: Re: sum across observations until a certain cutpoint
From Steven Samuels <sjhsamuels@earthlink.net>
To statalist@hsphsun2.harvard.edu
Subject Re: st: RE: RE: Re: sum across observations until a certain cutpoint
Date Sun, 9 Nov 2008 14:31:04 -0500
-reshape- is a Stata command
On Nov 9, 2008, at 1:20 PM, Amanda Botticello wrote:
I want to calculate how many items each subject completed within 60 seconds. And I can't do anything about the data structure, unfortunately.
Amanda L. Botticello, PhD, MPH
Outcomes Research Scientist
Kessler Medical Rehabilitation Research and Education Center
Assistant Professor
Department of Physical Medicine & Rehabilitation
UMDNJ-New Jersey Medical School
1199 Pleasant Valley Way
West Orange, NJ 07052
phone: (973)243-6973
email: abotticello@kmrrec.org
"Nick Cox" <n.j.cox@durham.ac.uk> 11/9/2008 1:14 PM >>>
You've lost me. I don't understand how your data structure copes with
time spent on failed tasks.
Please be clear: Do you want to cumulate times and see how many tasks in
total were completed within a total of 60 seconds, as implied by your
original question, or do you just want to count how many tasks were
individually completed within 60 seconds?
Incidentally, I think you would be better off reshaping this to long.
Amanda Botticello
The data is more like this:
id item1 time1 item2 time2 itmem3 time3
The variable "item" is coded 0,1, where 1 indicates the item was
Time is recorded in number of seconds to complete. If they didn't
complete an item, the time is 0
"Nick Cox" <n.j.cox@durham.ac.uk> 11/9/2008 12:59 PM >>>
Still not very clear to me, but I guess something like this
task1 task2 task3 task4 task5
So that the three individuals above had completed 4, 4, 0 tasks in the
first 60 seconds.
How many within 60 seconds?
gen cumul = 0
gen within60 = 0
qui forval i = 1/5 {
replace cumul = cumul + task`i'
replace within60 = `i' if cumul <= 60
Amanda Botticello PhD, MPH
IT's a "wide" dataset...subjects completed up to 200 items in a task,
and we recorded the number of seconds it took to complete each item. I can create a sum of the total number of items completed and total time;
now I want to find out how many items each individual completed in 60,
90, and 120 seconds. Does that help?
"Martin Weiss" <martin.weiss1@gmx.de> 11/9/2008 11:00 AM >>>
Well, if you want the running sum, look at -help sum()-. But maybe you
give us a peek at your data structure, that would assist in answering
"Amanda Botticello" <abotticello@kmrrec.org>
I have a dataset of test items and the time (in seconds)to complete
item. I need to create a variable that sums the time variables up to a
certain number -- i.e., 60, 90, 120 seconds. Is there a way I can use
egen newvar = rowtot (time*) command to count up to 60 seconds, etc?
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
The information in this transmission is intended for official use of the Kessler Foundation. It is intended for the exclusive use of the persons or entities to which it is addressed. If you are
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this communication, or the use of its contents, is strictly prohibited. If you received this transmission in error, please notify the sender by return e-mail and delete the material from any
* For searches and help try:
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* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
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The International Commission on Mathematical Instruction
Bulletin No. 48
June 2000
The All-Russian Conference on Mathematical Education
Final Announcement of the ICMI Regional Conference
The Organizing Committee for the All-Russian Conference on Mathematical Education (RCME) "Mathematics and Society. Mathematical Education in the New Millennium" is pleased to announce that RCME
will be held in the city of Dubna (near Moscow), Russia, from September 19 to September 22, 2000. This conference is jointly organized by Ministry of Education of Russian Federation, Moscow State
University, Russian Academy of Sciences (Department of Mathematics), Russian Academy of Education, Moscow State Pedagogical University, Russian Association of Teachers of Mathematics, Moscow
Institute for the Development of the Educational Systems, Moscow Center of Continuous Mathematical Education, and has been officially recognized by the Executive Committee of ICMI as an ICMI
Regional Conference.
The three chairpersons of the Organizing Committee are Academician D.V. Anosov, Academician V.A. Sadovnichij, and the well-known teacher from Bieloretsk R.G. Khazankin. The head of the Program
Committee is V.M. Tikhomirov. It is estimated that the number of participants will be about 300. Reviving the traditions of Russian education, the conference will be devoted to the teaching of
mathematics at all levels - from primary school to graduate students. The aim of the conference is to develop the basic concepts of mathematical education in schools and universities in Russia as
a whole, raising its level in accordance with present day requirements.
The following topics will be discussed during the Conference:
□ The role of mathematics and mathematical education for individuals, for Russia and the world at large. Philosophical problems of mathematics;
□ The concept of mathematical education in the twelve school years (problems of education, general concepts, structure and contents of education, teaching plans, number of hours devoted to
mathematics, problems of modernization of education, etc.);
□ Advanced mathematical education. Monitoring professional mathematicians from secondary school to the graduate and PhD track level;
□ The concept of higher mathematical education, its structure and contents;
□ Mathematical education in science, humanities, engineering and economics, the role of fundamental sciences in specialized education. Problems of mathematical education in vocational schools;
□ Perspectives of mathematical education, presentation of achievements of contemporary mathematics in education;
□ Mathematical literature, textbooks and training aids.
The scientific program will consist of plenary and sectional talks and scientific discussions. The plenary speakers are as follows:
□ Acad. Sadovnichij V.A., Mathematical education: current situation and perspectives;
□ Khazankin R.G., Mathematical education in secondary school;
□ Acad. RAE Matrosov V.L. and Smirnov E.I., Problems of mathematical education for teachers;
□ Ass. Acad. Kudryavcev L.D., Common problems of multilevel education;
□ Acad. Anosov D.V., On the education commission of Russian Academy of Sciences;
□ Acad. Arnold V.I., Mathematics and society;
□ Tikhomirov V.M., The concepts of mathematical education;
□ Acad. Zhuravlev Yu.I., Mathematics and computer science.
The conference will work for four full days. Mornings will be devoted to the plenary talks, while in the afternoons participants will be divided according to the following sections and
1. Secondary and vocational schools
□ General mathematical education;
□ Advanced mathematical education (including olympiads and other contests);
□ Mathematical education in vocational schools.
2. Colleges and universities
□ Professional and scientific mathematical education;
□ Mathematical education for engineers and economists;
□ Mathematical education for the students of the humanities;
□ Mathematical education for teachers.
Besides, there will be several round tables with discussions on topical problems of mathematical education. Some of the questions for discussion are:
□ What do you expect from the Conference? What problems in your opinion are the most urgent for mathematical education today?
□ On the standards of mathematical education.
□ Perspectives of mathematics and math education in 21st century.
□ Mathematics and computer science - allies or rivals? Computers in math education.
□ Algebra and geometry in secondary school.
□ Relationship between secondary schools and universities.
□ Testing technologies in the process of education, control and selection.
□ Math education and training of future scientists.
Those interested in participating in the conference and giving a presentation should send a title and a 10-line abstract to conf2000@mccme.ru or should contact the Organizing Committee of the
Conference at the following address:
Contact: Secretariat of RCME
Moscow Center for Continuous Math Education
Bolshoj Vlas'evskij per., d. 11
121002, Moscow, RUSSIA
phone: +7 (095) 241-0500; 241-1237
fax: +7 (095) 291-6501
e-mail: conf2000@mccme.ru
http://www.mccme.ru/conf2000 (main part only in Russian)
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|
Is the length of a side of equilateral triangle E less than
Author Message
Is the length of a side of equilateral triangle E less than [#permalink] 07 Dec 2012, 12:27
This post received
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Kudos [?]: 72 [4] ,
given: 46 Is the length of a side of equilateral triangle E less than the length of a side of square F?
(1) The perimeter of E and the perimeter of F are equal.
(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2.
If anyone find this post helpful plz give+1 kudos
Spoiler: OA
Re: Is the length of a side of equilateral triangle E less than [#permalink] 07 Dec 2012, 12:41
Math Expert
Joined: 02 Sep 2009
This post received
Posts: 17278 KUDOS
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Kudos [?]: 18313 [1
] , given: 2345
Re: Is the length of a side of equilateral triangle E less than [#permalink] 04 Mar 2014, 17:35
bparrish89 Bunuel wrote:
Intern Is the length of a side of equilateral triangle E less than the length of a side of square F?
Joined: 05 Dec 2013 Let x be the length of a side of equilateral triangle E and y be the length of a side of square F.
Question: is x>y?
Posts: 15
(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.
Followers: 0
(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is x\frac{\sqrt{3}}{2} and the diagonal of square F is y\sqrt{2}
Kudos [?]: 6 [0], --> ratio: \frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}} --> x/y=4/3 --> x>y. Sufficient.
given: 1
Answer: D.
Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?
Re: Is the length of a side of equilateral triangle E less than [#permalink] 04 Mar 2014, 20:25
bparrish89 wrote:
Bunuel wrote:
Is the length of a side of equilateral triangle E less than the length of a side of square F?
Let x be the length of a side of equilateral triangle E and y be the length of a side of square F.
Joined: 07 Feb 2011 Question: is x>y?
Posts: 7 (1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.
Followers: 0 (2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is x\frac{\sqrt{3}}{2} and the diagonal of square F is y\sqrt{2}
--> ratio: \frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}} --> x/y=4/3 --> x>y. Sufficient.
Kudos [?]: 0 [0],
given: 5 Answer: D.
Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?
The second statement states the ratio as 2√3 : 3√2 &, the calculated ratio is x√3/2 : y√2. Now if these two ratios are same, we just need to simplify the equation, which gives the
ratio of x:y to 4:3.
Re: Is the length of a side of equilateral triangle E less than [#permalink] 05 Mar 2014, 00:09
Expert's post
bparrish89 wrote:
Bunuel wrote:
Is the length of a side of equilateral triangle E less than the length of a side of square F?
Let x be the length of a side of equilateral triangle E and y be the length of a side of square F.
Question: is x>y?
(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.
(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is x\frac{\sqrt{3}}{2} and the diagonal of square F is y\sqrt{2}
--> ratio: \frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}} --> x/y=4/3 --> x>y. Sufficient.
Answer: D.
Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?
Math Expert
Divide both sides by
Joined: 02 Sep 2009
Posts: 17278
Followers: 2862
Kudos [?]: 18313 [0
], given: 2345 ;
Multiply by 2:
Hope it's clear.
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Re: Is the length of a side of equilateral triangle E less than [#permalink] 05 Mar 2014, 08:07
bparrish89 wrote:
Bunuel wrote:
Is the length of a side of equilateral triangle E less than the length of a side of square F?
sanjoo Let x be the length of a side of equilateral triangle E and y be the length of a side of square F.
Question: is x>y?
Senior Manager
(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.
Joined: 06 Aug 2011
(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is x\frac{\sqrt{3}}{2} and the diagonal of square F is y\sqrt{2}
Posts: 402 --> ratio: \frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}} --> x/y=4/3 --> x>y. Sufficient.
Followers: 2 Answer: D.
Kudos [?]: 41 [0], Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?
given: 81
If equilateral triangle has height 2square root 3.. that means its all sides will be 4..
and if diagonal of square is 3 square root2 that means square has all sides 3.
we got No ! equilateral triangle length is greater than square's length
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !
Re: Is the length of a side of equilateral triangle E less than [#permalink] 05 Mar 2014, 15:05
Bunuel wrote:
bparrish89 wrote:
Bunuel wrote:
Is the length of a side of equilateral triangle E less than the length of a side of square F?
Let x be the length of a side of equilateral triangle E and y be the length of a side of square F.
Question: is x>y?
(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.
(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is x\frac{\sqrt{3}}{2} and the diagonal of square F is y\sqrt{2}
--> ratio: \frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}} --> x/y=4/3 --> x>y. Sufficient.
Answer: D.
Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?
Joined: 05 Dec 2013
Posts: 15
Followers: 0
Kudos [?]: 6 [0],
given: 1 ;
Divide both sides by
Multiply by 2:
Hope it's clear.
That's exactly what I was looking for. Thanks!
Re: Is the length of a side of equilateral triangle E less than [#permalink] 05 Mar 2014, 17:22
Bunuel wrote:
Is the length of a side of equilateral triangle E less than the length of a side of square F?
Joined: 22 Nov 2012
Let x be the length of a side of equilateral triangle E and y be the length of a side of square F.
Posts: 8 Question: is x>y?
GMAT Date: (1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.
(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is x\frac{\sqrt{3}}{2} and the diagonal of square F is y\sqrt{2}
Followers: 0 --> ratio: \frac{(x\frac{\sqrt{3}}{2})}{(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}} --> x/y=4/3 --> x>y. Sufficient.
Kudos [?]: 3 [0], Answer: D.
given: 47
In 2 above, can you tell me how you got y√2?
Re: Is the length of a side of equilateral triangle E less than [#permalink] 05 Mar 2014, 23:58
Expert's post
X017in wrote:
Bunuel wrote:
Is the length of a side of equilateral triangle E less than the length of a side of square F?
Let x be the length of a side of equilateral triangle E and y be the length of a side of square F.
Question: is x>y?
(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.
(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is x\frac{\sqrt{3}}{2} and the diagonal of square F is y\sqrt{2}
--> ratio: \frac{(x\frac{\sqrt{3}}{2})}{(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}} --> x/y=4/3 --> x>y. Sufficient.
Answer: D.
In 2 above, can you tell me how you got y√2?
y is the length of a side of
F. Now, the diagonal of a square is the hypotenuse of a right isosceles triangle made by the sides:
Bunuel Attachment:
Math Expert
square.jpg [ 10.18 KiB | Viewed 182 times ]
Joined: 02 Sep 2009
Therefore by Pythagorean theorem
Posts: 17278
Followers: 2862
Kudos [?]: 18313 [0
], given: 2345 2y^2=diagonal^2
Hope it's clear.
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gmatclubot Re: Is the length of a side of equilateral triangle E less than [#permalink] 05 Mar 2014, 23:58
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The principal pivoting method of quadratic programming
, 1995
"... Recent improvements in the capabilities of complementarity solvers have led to an increased interest in using the complementarity problem framework to address practical problems arising in
mathematical programming, economics, engineering, and the sciences. As a result, increasingly more difficult pr ..."
Cited by 41 (5 self)
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Recent improvements in the capabilities of complementarity solvers have led to an increased interest in using the complementarity problem framework to address practical problems arising in
mathematical programming, economics, engineering, and the sciences. As a result, increasingly more difficult problems are being proposed that exceed the capabilities of even the best algorithms
currently available. There is, therefore, an immediate need to improve the capabilities of complementarity solvers. This thesis addresses this need in two significant ways. First, the thesis proposes
and develops a proximal perturbation strategy that enhances the robustness of Newton-based complementarity solvers. This strategy enables algorithms to reliably find solutions even for problems whose
natural merit functions have strict local minima that are not solutions. Based upon this strategy, three new algorithms are proposed for solving nonlinear mixed complementarity problems that
represent a significant improvement in robustness over previous algorithms. These algorithms have local Q-quadratic convergence behavior, yet depend only on a pseudo-monotonicity assumption to
achieve global convergence from arbitrary starting points. Using the MCPLIB and GAMSLIB test libraries, we perform extensive computational tests that demonstrate the effectiveness of these algorithms
on realistic problems. Second, the thesis extends some previously existing algorithms to solve more general problem classes. Specifically, the NE/SQP method of Pang & Gabriel (1993), the semismooth
equations approach of De Luca, Facchinei & Kanz...
- MATH. OPER. UND STAT. SER. OPTIMIZATION , 1992
"... Three generalizations of the criss-cross method for quadratic programming are presented here. Tucker's, Cottle's and Dantzig's principal pivoting methods are specialized as diagonal and exchange
pivots for the linear complementarity problem obtained from a convex quadratic program. A finite criss- ..."
Cited by 13 (8 self)
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Three generalizations of the criss-cross method for quadratic programming are presented here. Tucker's, Cottle's and Dantzig's principal pivoting methods are specialized as diagonal and exchange
pivots for the linear complementarity problem obtained from a convex quadratic program. A finite criss-cross method, based on least-index resolution, is constructed for solving the LCP. In proving
finiteness, orthogonality properties of pivot tableaus and positive semidefiniteness of quadratic matrices are used. In the last section some special cases and two further variants of the quadratic
criss-cross method are discussed. If the matrix of the LCP has full rank, then a surprisingly simple algorithm follows, which coincides with Murty's `Bard type schema' in the P matrix case.
- Journal of the Operational Research Society of Japan , 1990
"... A combinatorial abstraction of the linear complementarity theory in the setting of oriented matroids was rst considered by M.J. Todd. In this paper, we take a fresh look at this abstraction, and
attempt to give a simple treatment of the combinatorial theory of linear complementarity. We obtain new t ..."
Cited by 12 (8 self)
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A combinatorial abstraction of the linear complementarity theory in the setting of oriented matroids was rst considered by M.J. Todd. In this paper, we take a fresh look at this abstraction, and
attempt to give a simple treatment of the combinatorial theory of linear complementarity. We obtain new theorems, proofs and algorithms in oriented matroids whose specializations to the linear case
are also new. For this, the notion of suciency of square matrices, introduced by Cottle, Pang and Venkateswaran, is extended to oriented matroids. Then, we prove a sort of duality theorem for
oriented matroids, which roughly states: exactly one of the primal and the dual system has a complementary solution if the associated oriented matroid satisfies "weak" sufficiency. We give two
different proofs for this theorem, an elementary inductive proof and an algorithmic proof using the criss-cross method which solves one of the primal or dual problem by using surprisingly simple
pivot rules (without any pertur...
, 1990
"... Specially structured Linear Complementarity Problems (LCP's) and their solution by the criss-cross method are examined in this paper. The criss-cross method is known to be finite for LCP's with
positive semidefinite bisymmetric matrices and with P-matrices. It is also a simple finite algorithm for o ..."
Cited by 6 (4 self)
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Specially structured Linear Complementarity Problems (LCP's) and their solution by the criss-cross method are examined in this paper. The criss-cross method is known to be finite for LCP's with
positive semidefinite bisymmetric matrices and with P-matrices. It is also a simple finite algorithm for oriented matroid programming problems. Recently Cottle, Pang and Venkateswaran identified the
class of (column, row) sufficient matrices. They showed that sufficient matrices are a common generalization of P- and PSD-matrices. Cottle also showed that the principal pivoting method (with a
clever modification) can be applied to row sufficient LCP's. In this paper the finiteness of the criss-cross method for sufficient LCP's is proved. Further it is shown that a matrix is sufficient if
and only if the criss-cross method processes all the LCP's defined by this matrix and all the LCP's defined by the transpose of this matrix and any parameter vector.
"... A splitting method for solving LCP based models of dry frictional contact problems in rigid multibody systems based on box MLCP solver is presented. Since such methods rely on fast and robust
box MLCP solvers, several methods are reviewed and their performance is compared both on random problems and ..."
Cited by 4 (0 self)
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A splitting method for solving LCP based models of dry frictional contact problems in rigid multibody systems based on box MLCP solver is presented. Since such methods rely on fast and robust box
MLCP solvers, several methods are reviewed and their performance is compared both on random problems and on simulation data. We provide data illustrating the convergence rate of the splitting method
which demonstrates that they present a viable alternative to currently available methods.
"... A general framework of nite algorithms is presented here for quadratic programming. This algorithm is a direct generalization of Van der Heyden's algorithm for the linear complementarity problem
and Jensen's `relaxed recursive algorithm', which was proposed for solution of Oriented Matroid programmi ..."
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A general framework of nite algorithms is presented here for quadratic programming. This algorithm is a direct generalization of Van der Heyden's algorithm for the linear complementarity problem and
Jensen's `relaxed recursive algorithm', which was proposed for solution of Oriented Matroid programming problems. The validity of this algorithm is proved the same way as the finiteness of the
criss-cross method is proved. The second part of this paper contains a generalization of Edmonds-Fukuda pivoting rule for quadratic programming. This generalization can be considered as a finite
version of Van de Panne - Whinston algorithm and so it is a simplex method for quadratic programming. These algorithms uses general combinatorial type ideas, so the same methods can be applied for
oriented matroids as well. The generalization of these methods for oriented matroids is a subject of another paper.
"... In this chapter we discuss several methods for solving the LCP based on principal pivot steps. One common feature of these methods is that they do not introduce any arti cial variable. These
methods employ either single or double principal pivot steps, and are guaranteed to process LCPs associated w ..."
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In this chapter we discuss several methods for solving the LCP based on principal pivot steps. One common feature of these methods is that they do not introduce any arti cial variable. These methods
employ either single or double principal pivot steps, and are guaranteed to process LCPs associated with P-matrices or PSD-matrices or both. We consider the LCP (q � M) oforder n, which is the
following in tabular form. w z q I;M q w � z> 0 � w T z =0 (4:1)
"... Abstract — The Linear Complementarity Problem (LCP) is a key problem in robot dynamics, optimization, and simulation. Common experience with dynamic robotic simulations suggests that the
numerical robustness of the LCP solver often determines simulation usability: if the solver fails to find a solut ..."
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Abstract — The Linear Complementarity Problem (LCP) is a key problem in robot dynamics, optimization, and simulation. Common experience with dynamic robotic simulations suggests that the numerical
robustness of the LCP solver often determines simulation usability: if the solver fails to find a solution or finds a solution with significant residual error, interpenetration can result, the
simulation can gain energy, or both. This paper undertakes the first comprehensive evaluation of LCP solvers across the space of multi-rigid body contact problems. We evaluate the performance of
these solvers along the dimensions of solubility, solution quality, and running time. I.
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South Walpole Math Tutor
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47 Subjects: including discrete math, ACT Math, logic, linear algebra
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Homework Help
Posted by Mary jo on Tuesday, April 7, 2009 at 8:40pm.
Solve by the elimination method.
3r 5s =42
is this right.
Decide whteher the pair of line is parallel, perpindular, or n
I said is was parallel. Tell me if this right.
• Math - Reiny, Tuesday, April 7, 2009 at 11:09pm
in your first question, you found only the one variable, you still have to find s
Besides that, you have a typo in the second equation.
in your second problem,
the slope of the first equation is -4/5
the slope of the second one is 5/4
notice they are negative reciprocals of each other.
What did you learn about that situation?
• Math - Latoya Harris, Thursday, February 23, 2012 at 11:54am
can u help me solve this problem
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Vitamin A supplementation and neonatal mortality in the developing world: a meta-regression of cluster-randomized trials
Michael Anthony Rotondi ^a & Nooshin Khobzi ^a
a. University of Western Ontario, Kresge Building (Room K201), London, ON, N6A 5C1, Canada.
Correspondence to Michael Anthony Rotondi (e-mail: mrotondi@uwo.ca).
(Submitted: 31 May 2009 – Revised version received: 04 December 2009 – Accepted: 15 February 2010 – Published online: 16 April 2010.)
Bulletin of the World Health Organization 2010;88:697-702. doi: 10.2471/BLT.09.068080
Vitamin A deficiency is a public health concern in more than half of all countries, and most of the countries affected are in Africa or south-eastern Asia.^1 This deficiency, which is the main cause
of blindness in undernourished children,^2^,^3 contributes to morbidity and mortality from severe infections, including those common in childhood, such as diarrhoeal diseases and measles.^4^,^5
Currently, an estimated 250 million preschool children in the world have vitamin A deficiency, and 250 000 to 500 000 of such children go blind every year. Of the children who go blind, half die
within one year of losing their eyesight.^1 International awareness of the role of vitamin A in improving and maintaining health has led to decades of supplementation being provided to preschool
In children over 6 months of age, vitamin A supplementation has been shown to decrease all-cause mortality.^6^–^10 However, the benefits in children under 6 months of age are still unclear, even
though young infants are especially vulnerable to vitamin A deficiency. In general, all infants are born with low stores of vitamin A and depend on external sources, including breast milk, to build
body stores.^11^,^12 The milk of lactating women in developing countries typically has lower concentrations of vitamin A than that of women in developed countries,^12 which means that neonates may
not obtain their daily requirements.^11 Direct supplementation of neonates and infants younger than 6 months has shown promising results in terms of survival, yet findings have been contradictory.
Studies conducted in Bangladesh,^13 India^11 and Indonesia^12 have shown reductions in all-cause mortality (15%, 22% and 63%, respectively) in infants who received vitamin A supplementation relative
to controls. Giving neonates vitamin A has also been found to significantly reduce diarrhoea case–fatality rates and the incidence of fever.^14 In contrast, trials in Guinea-Bissau,^15 Nepal^16 and
Zimbabwe^17 suggest a lack of benefit from vitamin A supplementation. The positive findings have led to different recommendations, but these are controversial^15^,^18 and there is much disagreement
throughout the world on the appropriate policy surrounding neonatal vitamin A supplementation.^19^,^20 Clearly, further controlled trials with infants and neonates are needed.
To examine some of the systematic differences in the findings of conflicting studies, we performed a meta-regression analysis in which the logarithm of the relative risk (logRR) of infant death
(measured at either 6 or 12 months of age) was modelled as a function of the prevalence of vitamin A deficiency among pregnant women in the general population. Unlike a simple meta-analysis, a
meta-regression model attempts to explain the variation among studies in terms of a study-level characteristic. A meta-regression analysis is observational in nature and is thus not likely to put an
end to the controversy surrounding neonatal supplementation, but it may provide some insight into effectiveness in subsequent trials, based on the prevalence of vitamin A deficiency. The inclusion of
a cluster-randomized trial^13 in the meta-regression analysis entails a unique application of the proposed method, as discussed later in this paper.
Inclusion criteria
The fundamental question of interest was whether the log(RR) of death among infants who received vitamin A supplements at birth versus placebo or a standard treatment such as vaccination was related
to the level of vitamin A deficiency among pregnant women in the general population. To reconcile the conflicting evidence from different studies, we developed inclusion criteria that took into
account extraneous sources of heterogeneity, such as varying target populations and differences in the time when vitamin A supplementation was administered. The a priori inclusion criteria were that
trials: (i) be randomized; (ii) have an appropriate control group that did not receive any vitamin A supplements; (iii) be administered at the population level (i.e. no supplements provided to
specific subgroups of interest, such as infants or mothers, with or without specific health concerns); and (iv) have the vitamin A supplements administered within the first two days of life. These
criteria were designed to allow for a focused and comprehensive analysis of the efficacy of giving neonates vitamin A supplements in the general population. In addition, the criteria were set to
ensure that the effect of vitamin A supplementation could be extrapolated to the general population by excluding subjects who may have received vitamin A supplements after the first two days of life
or who may have belonged to specific groups treated with vitamin A. This is of primary concern, given the significant variability in vitamin A supplementation trials.
Two studies in Zimbabwe were excluded because their participants were either HIV− or HIV+ mothers only.^17^,^21 A study in Nepal was excluded because it provided vitamin A supplements every four
months and hence was not designed to dose neonates.^16 A fourth trial was excluded because it was designed to measure the efficacy of a smaller dose of vitamin A, rather than the standard dose.^8
Characteristics of the included studies are presented in Table 1.
Statistical analysis
A traditional meta-analysis combines all estimates of an observed treatment effect into a single overall estimate of the efficacy of a particular intervention. In general, the observed treatment
effects are obtained from individually-randomized clinical trials, which ensures that, on average, each estimate of the treatment effect is not confounded by other factors. Nonetheless, observed
treatment effects may lead to differing conclusions stemming from varying inclusion criteria and study populations, variations in the study protocols (e.g. dose or length of follow-up) and random
error. Differences in the observed treatment effects are often the result of between-study heterogeneity, or simply heterogeneity. While attempts to explore the impact of heterogeneity on a
meta-analysis are important, a meta-analysis tacitly accepts heterogeneity by combining different studies in the search for a single underlying treatment effect.^23
The use of cluster-randomized design is becoming more common, and a meta-analysis may be influenced by the inclusion of one or more cluster-randomized trials.^24 The greatest threat to statistical
validity is the failure to incorporate the appropriate design effect in variance calculations.^25 Failing to account for clustering in a meta-analysis will contribute to an underestimation of the
within-study variance, resulting in an unrealistically high weight for that particular treatment effect. Furthermore, care must be taken when combining results from cluster-randomized and
individually-randomized trials, because the intervention itself may interact with the unit of randomization.^26
As explained above, meta-regression analysis attempts to relate the effect size to study-level characteristics. This approach not only acknowledges between-study heterogeneity but also attempts to
explain it at the study level. Similar to a classical meta-analysis, a meta-regression employs weights (typically random effects^27) to account for larger or more accurate studies. Because
meta-regression analysis is observational in nature, rigorous causal associations cannot be directly ascertained.^27
The prevalence of vitamin A deficiency among pregnant women was the main explanatory variable in this meta-regression analysis. While different proxies for vitamin A deficiency^22 exist in the target
infant populations, this measure was deemed the most appropriate because it was obtained by weighting the combined prevalences of low serum retinol and xerophthalmia reported by studies from the
countries of interest. This approach to estimating national prevalences of vitamin A deficiency avoids potential bias resulting from restriction to women who are diagnosed with xerophthalmia, given
that maternal vitamin A deficiency that is less than severe may also have a detrimental effect on infant survival. Estimates of the prevalence of vitamin A deficiency are subject to uncertainty
because of the difficulty of obtaining accurate measurements.^2 As such, prevalence estimates used for our analysis differ from those in other published reports.^28 However, the included values
represent the best estimates of the prevalence of vitamin A deficiency in pregnant women at the time individual subjects were enrolled in each study, while remaining consistent with the literature.^
Infant mortality was the endpoint of interest; thus, RRs < 1 demonstrate the protective effect of vitamin A supplementation on infant mortality. Although vitamin A supplementation was administered to
neonates, mortality was measured at either 6 or 12 months of age. In an attempt to reduce the skewness of the distribution of the RRs, we used the log(RR) as the dependent variable of interest. That
is, we fitted the following weighted linear regression:log(RR[i]) = β[0] + β[1]VAD[i] + ε[i]where VAD[i] corresponds to the prevalence of vitamin A deficiency among pregnant women in study i (i = 1,
2, 3, 4) and ε[i] is an independently and identically distributed normal random variable with zero mean and fixed variance. Within the range of our explanatory variable, β[1] represents the change in
the log(RR) for each percentage increase in the prevalence of vitamin A deficiency among pregnant women and β[0] represents the intercept.
The study weights used in a random effects meta-regression analysis are obtained as the inverse of the sum of the within-trial variance and the residual between-trial variance. By contrast, the fixed
effects meta-regression analysis would simply weight each study by the inverse of its within-study variance. The fixed effects model is a special case of the random effects model in which the
between-trial variance is estimated as zero. Throughout the analysis, we applied the random effects model because it acknowledges the presence of residual heterogeneity.^27 Regardless of the model of
choice, the appropriate weights in a meta-regression analysis should include an adjustment for the effect of clustering. This adjustment is easily incorporated into the within-trial variance by
multiplying the standard estimate of the variance by the design effect, as correctly applied in the Bangladesh trial.^13 In general, failing to adjust for the effect of clustering would result in the
use of inaccurate weights, possibly leading to biases in the estimated covariates and standard errors.
Although unnecessary for the meta-regression analysis, a minor variation of Cochran’s Q statistic for heterogeneity, as well as the I^2 statistic,^29 are required to adjust for the inclusion of a
cluster-randomized trial. Both of these statistics account for the clustering effect in the estimation of the within-study variance for any included cluster-randomized trials.
All statistical analyses were performed using the R software package, with appropriate modifications to account for the incorporation of cluster-randomized trials.^30 The between-study heterogeneity
was estimated using restricted maximum likelihood and empirical Bayes techniques;^27 the residual heterogeneity component was estimated as zero, and this reduced the random effects model to a fixed
effects meta-regression.
As a precursory analysis, a fixed effects meta-analysis model (adjusted for clustering) demonstrated an overall protective effect of vitamin A supplementation with respect to infant death using the
generalized inverse method.^25 The fixed effects RR was 0.85 (95% confidence interval, CI: 0.75–0.95), which indicates a statistically significant overall reduction in mortality. To assess the impact
of study heterogeneity on the meta-analysis, the Q statistic is often used as a basis for deciding between the fixed or random effects meta-analysis model.^29 With this method, the null hypothesis of
study homogeneity is rejected (i.e. the studies are found to be heterogeneous and the fixed effects model is invalidated) if the observed value of Q exceeds the 95% critical value of a χ^2
distribution with degrees of freedom equal to the number of included studies minus one. This value is obtained from statistical tables or software. Within this framework, the Q statistic is
calculated as 6.55, a value that does not exceed the 95% critical value of 7.81 (on three degrees of freedom). A simple method to quantify the between-study heterogeneity is through the I^2
statistic. Using this method, the I^2 value (adjusted for clustering) of 0.54 suggests the presence of moderate heterogeneity, despite the lack of statistical significance of the Q statistic. For the
sake of completeness, the random effects meta-analysis estimates a RR of 0.84 (95% CI: 0.69–1.03), which does not suggest a statistically significant reduction of infant mortality as a result of
neonatal vitamin A supplementation.
The results of the meta-regression analysis are presented graphically in Fig. 1, as well as the fitted meta-regression line and expected 95% confidence bands. Specifically, the intercept (β[0]) is
estimated as 1.66 (95 % CI: 0.20–3.13) and β[1] is estimated as −0.08 (95% CI: −0.15 to −0.02). These findings suggest a statistically significant linear relationship between the prevalence of
vitamin A deficiency among pregnant women in the study population and the observed effectiveness of neonatal vitamin A supplementation in preventing infant death in a given study. The findings
suggest that a study taking place in an area where the prevalence of vitamin A deficiency among pregnant woman is at least 22% would be likely to show a statistically significant, protective effect
of vitamin A supplementation against infant death.
Fig. 1. Meta-regression^a plot of log relative risk of infant death in infants given vitamin A supplements as a function of the prevalence of vitamin A deficiency in pregnant women: log(RR[i]) = β[0]
+ β[1]VAD[i] + ε[i]
Meta-regression analysis aims to relate the size of an effect to one or more characteristics of the studies involved.^27 More specifically, it investigates whether a covariate (potential “effect
modifier”) explains the heterogeneity of treatment effects between studies.^27 In our analysis, the study-level covariate of interest was the prevalence of vitamin A deficiency among pregnant women,
and the outcome variable – overall infant mortality – represented the efficacy of neonatal vitamin A supplementation in developing countries. We found a statistically significant relationship between
the covariate and infant mortality, which suggests that vitamin A supplementation to neonates within the first two days of life confers a benefit in regions where vitamin A deficiency is common. This
is an important finding given the current debate as to whether giving neonates vitamin A supplements helps reduce infant mortality in populations where endemic vitamin A deficiency and high infant
mortality exist.^18^,^31
A recent meta-analysis suggests that there is insufficient evidence to support neonatal supplementation with vitamin A.^32 Although the study is methodologically sound and appropriate, its
application of more general inclusion criteria may limit its ability to ascertain the role of the prevalence of vitamin A deficiency on infant mortality. Furthermore, to calculate the prevalence of
vitamin A deficiency the study employed maternal night blindness as a proxy, but the latter is associated only with the most severe cases of vitamin A deficiency. Also, the prevalence of maternal
night blindness was dichotomized (≥ 5% versus < 5%) and this may have reduced its statistical power.^33 This problem is avoided in the current study through the use of a continuous covariate.
The results of our analyses will be useful in predicting the benefits of providing neonates with vitamin A supplements in certain trials; that is, in trials conducted in regions with a prevalence of
vitamin A deficiency of 22% or more among pregnant women. Some authors have advocated implementation of neonatal vitamin A supplementation in Asia but not in Africa until further trials are carried
out.^18 However, our findings point to another plausible approach to the global problem of nutritional deficiency. In general, vitamin A supplementation may prove beneficial in regions where the
prevalence of vitamin A deficiency among pregnant women is high. Therefore, both Asian and African countries experiencing nutritional deficiencies may benefit from vitamin A supplementation
programmes for infants.
In our meta-regression analysis, we controlled for a significant source of variation between studies (background prevalence of vitamin A deficiency); nevertheless, there is a possibility of residual
heterogeneity.^27 For example, studies may differ with regard to the vitamin A content of supplementary foods, the rate of infant growth and the burden of infectious diseases, all of which may
translate into different requirements or losses of vitamin A.^12^,^31 In addition, we made no distinction between trials employing a single large dose of vitamin A or vitamin A supplements in regular
but smaller amounts – a potentially valuable insight given that a higher-dose regimen has been shown safe but not more efficacious than a lower-dose regimen provided to infants.^34^,^35 Differences
in vaccination coverage among trials may further explain study heterogeneity. The protective effect of neonatal vitamin A supplementation may depend not only on the prevention of vitamin A
deficiency, but also on a synergistic (positive) interaction with routine vaccinations.^5 Vitamin A supplementation may strengthen ongoing immune reactions induced by vaccines; for example, when
given with a live vaccine, vitamin A may further enhance the capacity of the antigen-presenting cells to deliver polarizing signals from helper to non-helper T-cells, an essential component of
cell-mediated immunity.^5 The beneficial effects of vitamin A supplements when given with the vaccines against tuberculosis (bacille Calmette-Guérin or BCG vaccine) and measles can be attributed to
this mechanism. In addition, vitamin A deficiency has been linked to iron and other micronutrient deficiencies.^36^,^37 Thus, there may be a positive interaction between vitamin A supplementation and
overall infant nutritional status.
The Indonesian study^12 was a leverage point in the meta-regression analysis (Fig. 1). Although meta-regression appropriately accounts for the lower precision of this study in comparison to the
others, a sensitivity analysis conducted after removing the Indonesian trial yielded an estimate of β[1] = −0.12 with a two-sided P-value of 0.09. While statistical significance is lost with the
omission of this study, estimates of β[1] remain consistent.
Our study had limitations, particularly owing to the use of meta-regression methods. A meta-regression describes an observational association across trials, even though the original studies may be
randomized.^27 Thus, meta-regression does not have the benefit of randomization to make causal inferences and may introduce bias by confounding. Also, there is the possibility of residual
heterogeneity, as mentioned earlier. However, the prevalence of vitamin A deficiency explains much of the observed heterogeneity (supported by the estimate of zero for the between-study variance).
The observational analysis employed in this paper is unlikely to put an end to the controversy on the effectiveness of neonatal supplementation with vitamin A. However, we hope that it will
contribute to continued debate in the literature and help to focus attention on the role of vitamin A supplementation, micronutrient deficiencies and nutrition in general on infant mortality.
Competing interests:
None declared.
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[Homework] Rational Class
January 13th, 2011, 07:44 PM
burger king
[Homework] Rational Class
Hello, So i am taking a Java class ( I regret it), and I have had alot of labs due, but since i have no clue what is going on in the class, it is really difficult for me to do the labs. I have
done most with half-effort, but on this one i am just completly bewildered. I just need to know how to sart this lab off and stuff so that i can go ahead and do it. Once someone explains to me
how to do part of it, i should understand the rest. If someone is kind enough to help me with this i would Be so so very hapy!
Actual Lab
This lab assignment continues the Rational class that was started with the Lab08MATH02 assignment. Now comes the times to add, subtract, multiply and divide fractions with your nifty Rational
class. This assignment will also be the first unit lab assignment. A unit assignment implies a more challenging assignment that carries greater weight for your average computation. A unit
assignment involves bringing together a greater number of computer skills in one assignment. For instance, the last keyword assignment provided complete main methods, which handled all the GUI
input and output. For this assignment you will need to write the Rational class and also handle most of the code in the main method.
// Lab08MATH03st.java
// The Rational Class Program II
// This is the student, starting version of the Lab08MATH03 assignment.
// There are 5 return methods in the Ration class that have temporary return statements
// which allow the program to compile. Students will need to change these statements.
import javax.swing.JOptionPane;
public class Lab08MATH03st
public static void main (String args[])
String strNum1 = JOptionPane.showInputDialog("Enter Numerator 1");
String strDen1 = JOptionPane.showInputDialog("Enter Denominator 1");
String strNum2 = JOptionPane.showInputDialog("Enter Numerator 2");
String strDen2 = JOptionPane.showInputDialog("Enter Denominator 2");
int num1 = Integer.parseInt(strNum1);
int den1 = Integer.parseInt(strDen1);
int num2 = Integer.parseInt(strNum2);
int den2 = Integer.parseInt(strDen2);
Rational r1 = new Rational(num1,den1);
Rational r2 = new Rational(num2,den2);
Rational r3 = new Rational();
String mul = r1.getOriginal() + " * " + r2.getOriginal() + " = " + r3.getRational();
String div = r1.getOriginal() + " / " + r2.getOriginal() + " = " + r3.getRational();
String add = r1.getOriginal() + " + " + r2.getOriginal() + " = " + r3.getRational();
String sub = r1.getOriginal() + " - " + r2.getOriginal() + " = " + r3.getRational();
String output = mul + "\n" + div + "\n" + add + "\n" + sub;
class Rational
private int firstNum; // entered numerator
private int firstDen; // entered denominator
private int num; // reduced numerator
private int den; // reduceddenominator
public Rational() { }
public Rational(int n, int d) { }
private int getGCF(int n1,int n2)
int rem = 0;
int gcf = 0;
rem = n1 % n2;
if (rem == 0)
gcf = n2;
n1 = n2;
n2 = rem;
while (rem != 0);
return gcf;
private void reduce() { }
public double getDecimal()
return 0.0;
public String getRational()
return "";
public String getOriginal()
return "";
public int getNum()
return 0;
public int getDen()
return 0;
public void multiply(Rational r1, Rational r2) { }
public void divide(Rational r1, Rational r2) { }
public void add(Rational r1, Rational r2) { }
public void subtract(Rational r1, Rational r2) { }
80 Point Version Specifics
This lab assignment starts by doing everything that was required for the Lab08A assignment. You need to write methods Rational, getNum, getDen, getDecimal, getRational, and getOriginal. You will
also need to write methods multiply and divide. Your fractions do not need to be reduced.
80 Point Version Output 1
The execution output will not show the input dialog windows. They are identical to the windows that were used for the Lab08MATH02 assignment. Four separate input dialog windows are used, as is
shown by the provided main method.
Enter these 4 numbers: 2, 5, 5, 7
Note that in the GUI output window above, 4 lines of output are shown. In the 80 and 90 point versions, only the first 2 lines are significant. The sum and difference will appear to be the same
as the quotient.
80 Point Version Output 2
Enter these 4 numbers: 6, 10, 20, 35
90 Point Version Specifics
The 90 point version adds the reduce method. As with Lab08MATH02, you are provided with the getGCF method. Not only do you need to write the reduce method, but you also need to call it in the
appropriate places so that the product and quotient will be displayed in lowest terms.
90 Point Version Output 1
Enter these 4 numbers: 2, 5, 5, 7
NOTE: As with the 80 point version, only the first 2 lines of output are significant.
90 Point Version Output 2
Enter these 4 numbers: 6, 10, 20, 35
100 Point Version Specifics
The 100-point version completes the Rational class with methods add and subtract. The sum and difference also need to be displayed in lowest terms.
100 Point Version Output 1
Enter these 4 numbers: 2, 5, 5, 7
NOTE: Now all 4 lines of output are significant.
ALSO: In the subtraction answer, the negative sign might show up in the numerator.
It also might show up in the denominator. Either way is fine.
100 Point Version Output 2
Enter these 4 numbers: 6, 10, 20, 35
Any help is appreciated!
January 13th, 2011, 08:04 PM
Re: [Homework] Rational Class
1.) I've never heard of "temporary return statements".
2.) Please put code in [highlight=java] [/highlight]
3.) Is that class up there provided for you, or is that your work so far?
4.) Your statements where you read in a value and then take the Integer.parseInt() can be combined.
valueOne = Integer.parseInt(The JOptionPane stuff);
A factor of number n is a value <= n and >-= 1, unless 0, which will have no common factors unless the other int is also 0,
such that n%factor =0.
Two numbers, n1 and n2, would a common factor if
n1%factor = 0 AND n2%factor = 0.
A factor is a greatest common factor if it is the largest factor that n1 and n2 both have in common(or have as factors).
January 13th, 2011, 08:15 PM
Re: [Homework] Rational Class
Why does the Rational class need two parameters?
If it only had 1, say
Code java:
public Rational(int num)
this.num = num;
I could
public int getNum()
return num;
public void add(Rational r1, Rational r2)
setNum((r1.getNum() + r2.getNum());
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[SciPy-dev] Generic polynomials class (was Re: Volunteer for Scipy Project)
[SciPy-dev] Generic polynomials class (was Re: Volunteer for Scipy Project)
Charles R Harris charlesr.harris@gmail....
Fri Oct 9 03:01:39 CDT 2009
On Thu, Oct 8, 2009 at 1:03 PM, Anne Archibald <peridot.faceted@gmail.com>wrote:
> 2009/10/8 Charles R Harris <charlesr.harris@gmail.com>:
> > Hi Anne,
> >
> > On Thu, Oct 8, 2009 at 9:37 AM, Anne Archibald <
> peridot.faceted@gmail.com>
> > wrote:
> >>
> >> 2009/10/7 David Goldsmith <d.l.goldsmith@gmail.com>:
> >> > Thanks for doing that, Anne!
> >>
> >> There is now a rough prototype on github:
> >> http://github.com/aarchiba/scikits.polynomial
> >> It certainly needs more tests and features, but it does support both
> >> the power basis and the Lagrange basis (polynomials represented by
> >> values at Chebyshev points).
> >>
> >
> > Just took a quick look, which is probably all I'll get to for a few days
> as
> > I'm going out of town tomorrow. Anyway, the Chebyshev points there are
> type
> > II, which should probably be distinguished from type I (and III & IV). I
> > also had the impression that the base class could have a few more
> functions
> > and NotImplemented bits. The Polynomial class is implemented as a
> wrapper,
> > it might even make sense to use multiple inheritance (horrors) to get
> > specific polynomial types, but anyway it caught my attention and that
> part
> > of the design might be worth spending some time thinking about. It also
> > might be worth distinguishing series as a separate base because series do
> > admit the division operators //, %, and divmod. Scalar
> > multiplication/division (__truedivision__) should also be built in. I've
> > also been using "from __future__ import division" up at the top to be
> py3k
> > ready. For a series basis I was thinking of using what I've got for
> > Chebyshev but with a bunch of the __foo__ functions raising the
> > NotImplementedError. I've also got a single function for importing the
> > coefficient arrays and doing the type conversions/checking. It's worth
> doing
> > that one way for all the implementations as it makes it easier to
> fix/extend
> > things.
> The polynomial class as a wrapper was a design decision. My reasoning
> was that certain data - roots, integration schemes, weights for
> barycentric interpolation, and so on - are associated with the basis
> rather than any particular polynomial. The various algorithms are also
> associated with the basis, of course (or rather the family of bases).
> So that leaves little in the way of code to be attached to the
> polynomials themselves; basically just adapter code, as you noted.
> This also allows users to stick to working with plain arrays of
> coefficients, as with chebint/chebder/etc. if they prefer. But the
> design is very much open for discussion.
> I agree, there are some good reasons to implement a class for graded
> polynomial bases in which the ith polynomial has degree i. One would
> presumably implement a further class for polynomial bases based on
> orthogonal families specified in terms of recurrence relations.
> Division operators make sense to implement, yes; there are sensible
> notions of division even for polynomials in the Lagrange or Bernstein
> bases. I just hadn't included those functions yet.
> > I've attached the low->high version of the chebyshev.py file just for
> > further reference. The Chebyshev class is at the end.
> Thanks, I'll take a look at it.
I'm thinking that instead of a wrapper class what we want is essentially a
class template replicated with different values for, i.e., multiplication,
division, etc. One way to do that in python is with a class factory. For
In [3]: def cat() : print 'meow'
In [4]: def dog() : print 'woof'
In [31]: def pet_factory(f) :
....: class pet :
....: def talk(self) :
....: print f()
....: return pet
In [32]: DogClass = pet_factory(dog)
In [33]: mydog = DogClass()
In [34]: mydog.talk()
In [35]: CatClass = pet_factory(cat)
In [36]: mycat = CatClass()
In [37]: mycat.talk()
I'm not sure why the None return is printing, but that is the general idea.
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A Guide to the C. Truesdell Papers,
Descriptive Summary
Scope and Contents
Index Terms
Administrative Information
Description of Series
The non-linear field theories of mechanics
Series 2 - Manuscripts of short publications, 1956-1983
Series 3 - Manuscripts of publications and lectures
Series 4 - Lectures on foundations of kinetic theory and statistical mechanics
Series 5 - Notes for Truesdell's courses that did not become the basis of books
Series 6 - Materials connected with the textbook on continuum mechanics (Publications number 183, 196, 211)
Series 7 - Early drafts leading to the book by Truesdell and Bharatha, 1977)
Series 8 - Materials connected with The Tragicomical History of Thermodynamics, 1822-1854, (Publication 225)
Series 9 - Materials connected with 1980
Series 10 - 1973
Series 11 - Unpublished papers and original manuscripts of papers translated or mangled by editors, 1942-1966
Series 12 - Notes taken by Truesdell in courses at the California Institute of Technology (1939-1942), Princeton University (1942-1943) and Indiana University (1950-1953)
Series 13 - Notes on miscellaneous lectures
Series 14 - Biographical and autobiographical material
Series 15 - Published works
Series 16 - Additions
Series 17. Archive for History of Exact Sciences
A Guide to the C. Truesdell Papers, 1939-1989
Creator: Truesdell, C. (Clifford), 1919-
Title: C. Truesdell Papers
Dates: 1921-1989
Abstract: Papers document research of Clifford Ambrose Truesdell III in rational mechanics and its history, and his role in the development of the field since the late 1940s. Included are
correspondence, lecture and course notes, lists of publications and lectures, drafts, galleys and page proofs of publications, grant proposals, reports, reprints, and photographs.
Accession 86-31; 89-4
Extent: 18 ft.; manuscript, typescript, printed, photographic
Laguage: Materials are written in English.
Repository: Dolph Briscoe Center for American History, The University of Texas at Austin
Clifford Ambrose Truesdell III (1919-2000) was born in Los Angeles, California, on February 18, 1919. He was educated at the California Institute of Technology (B.S., mathematics and physics, l941;
M.S., mathematics, 1942), Brown University (Certificate in Mechanics, 1942), and Princeton University (Ph.D., 1943). Truesdell worked briefly at the University of Michigan, the Radiation Laboratory
at the Massachusetts Institute of Technology, and the Naval Ordnance and Research Laboratories, before taking positions at Indiana University (1950-1961) and The Johns Hopkins University (l961-1989).
Truesdell's primary research interest was rational mechanics, a branch of mathematics involving the mathematical formulation and deductive study of the concepts of mechanics. He published numerous
books and papers in several areas of rational mechanics, including continuum mechanics, statistical mechanics, and thermodynamics. Truesdell wrote extensively on the history of rational mechanics,
especially of the eighteenth and nineteenth centuries. He founded three journals: Journal of Rational Mechanics and Analysis (co-founder, 1952), Archive for Rational Mechanics and Analysis (founder,
1957), and Archive for History of Exact Sciences (founder, 1960). Truesdell died on January 14, 2000.
Return to the Table of Contents
Papers are chiefly drafts and proofs of Truesdell's publications, often with several drafts of the same publication. Few publications prior to 1965 are represented; unpublished manuscripts date to
1942. Also included are lists and texts of public lectures and notes on Truesdell's courses, both dating to 1942, and Truesdell's student class notes. Biographical and autobiographical writings and
reminiscences by and about Truesdell are included, along with summaries of Truesdell's correspondence with his associates J. L. Ericksen, W. Noll, and R. A. Toupin. Included are correspondence,
lecture and course notes, lists of publications and lectures, drafts, galley and page proofs, grant proposals, reports, reprints, and photographs. The collection was transferred in l984 from the
American Institute of Physics Niels Bohr Library in New York. The container list was prepared by Truesdell and constitutes a commentary on the papers.
Forms part of the Archives of American Mathematics.
Return to the Table of Contents
Organized by Truesdell into sixteen series:
1. Truesdell & Noll - The Non-linear Field Theories of Mechanics
2. Manuscripts of short publications, 1956-1983
3. Manuscripts of publications and lectures
4. Lectures on foundations of kinetic theory and statistical mechanics
5. Notes for Truesdell's courses that did not become the basis of books
6. Materials connected with the textbook on continuum mechanics
7. Early draughts leading to the book by Truesdell & Bharatha, Concepts and Logic of Classical Thermodynamics as a Theory of Heat Engines, Developed upon the Foundation laid by S. Carnot and F.
8. Materials connected with The Tragicomical History of Thermodynamics, 1822-1854
9. Materials connected with Fundamentals of Maxwell's Kinetic Theory
10. Introduction to Rational Elasticity
11. Unpublished papers and original manuscripts of papers translated or mangled by editors
12. Notes taken by Truesdell in courses at the California Institute of Technology, (1939-1942); Princeton University, (l942-l943); and Indiana University (1950-1953)
13. Notes on miscellaneous lectures
14. Biographical and autobiographical material
15. Published works
16. Additions
17. Items connected with Archive for History of Exact Sciences
Return to the Table of Contents
Access Restrictions
Unrestricted access.
Use Restrictions
These papers are stored remotely at CDL. Contact reference staff for retrieval from offsite storage.
Return to the Table of Contents
Subjects (Persons)
Bharatha, Subramanyam, 1945-
Ericksen, J. L. (Jerald L.), 1924-
Muncaster, R. G.
Noll, W. (Walter), 1925-
Toupin, Richard A., 1926-
Truesdell, C. (Clifford), 1919-
Wang, Chao-cheng, 1938-
Subjects (Organizations)
Archive for History of Exact Sciences
Archive for Rational Mechanics and Analysis
Brown University
California Institute of Technology
Indiana University
Johns Hopkins University
Journal of Rational Mechanics and Analysis
Massachusetts Institute of Technology
Massachusetts Institute of Technology. Radiation Laboratory
Naval Ordnance Laboratory (White Oak, Md.)
Naval Research Laboratory (U. S.)
Princeton University
Continuum mechanics
Mathematics historians
Mechanics, Analytic
Rational mechanics
Science -- History
Statistical mechanics
Return to the Table of Contents
Truesdell's papers were transferred to the Archives of American Mathematics from the American Institute of Physics Center for the History of Physics in 1984.
C. Truesdell Papers, 1939-1989, Archives of American Mathematics, Dolph Briscoe Center for American History, University of Texas at Austin.
Note that this inventory was prepared by Truesdell himself and many entries include personal comments on the materials in his collection.
Return to the Table of Contents
Series 1 - Truesdell and Noll, The non-linear field theories of mechanics, (SP 100)
86-31/1 First complete manuscript:
Part one, paragraphs 1-60, 1960-1963
Part two, paragraphs 61-98, 1960-1963
Part three, paragraphs, 99-117, 1960-1963
86-31/2 First galley proofs, corrected July 1963-January 1965
Second galley proofs, corrected February-May 1965
86-31/3 Manuscript used for typesetting:
Part one, paragraphs 1-41, May 1963-January 1965
Part two, paragraphs 42-78, May 1963-January 1965
86-31/4 Part three, paragraphs 79-103, May 1963-January 1965
Part four, paragraphs 104-130, includes references, May 1963-January 1965
86-31/5 Manuscript, first draft:
Pages 1-499
Pages 500-910, references, pp. B1-B85
86-31/6 Manuscript, revised and supplementary pages, 96 rev-888B, references B78 rev-B82 rev to the first
Manuscript, second revised and supplementary pages, 117 (rev)2-836A(rev), references B57-BR91
Final manuscript:
Pages F0-F399
Pages F400-F720
86-31/7 Pages F721-F999
Pages F1000-F1134, C1-22, P1-P22, Q1-Q45, references BF1-BF98
86-31/8 Revised and supplementary pages
Galley proofs:
Read by K. Zoller
Read by the authors, pages 1-259
86-31/9 Pages 260-458 and supplementary pages read by the authors
Revised proofs
Press proofs
Return to the Table of Contents
Series 2 - Manuscripts of short publications, 1956-1983
86-31/10 Some short manuscripts, 1956-1970:
On the history of the concept of internal pressure, typescript, eighteen pages, condensed version of lecture number 78, 1954, and the English original of the article in German, publication
number 82, 1956
Reactions of late baroque mechanics to success, conjecture, error, and failure in Newton's "Principia," to the Newton Centenary Celebration, University of Texas, Austin, Texas, November 12,
1966. Lecture 360, also used for lectures 375, 384, and 387. First draft of publication 157, 1967, and its revision, chapter 3 of publication 165
Holograph manuscript, twelve pages, or the speech accepting the Panetti Prize, January 1968, publication number 167, 1968
Classical and modern continuum theories, holograph, forty-eight pages, first draft of lecture number 396, 1968, publication number 154L6, 1968
Sulle basi della termodinamica delle miscele I, draft, holograph, seventeen pages, (perhaps written in Pisa in February 1968 while Truesdell was writing Rational Thermodynamics), for
publication number 164, 1968
A precise upper limit for the correctness of the Navier-Stokes Theory with respect to the Kinetic Theory:
First draft, mainly holograph, partly typewritten, fifteen pages, April 8, 1969
Second draft, typescript with many handwritten corrections, twenty-one pages, April 14, 1969, leading to publication number 170, 1969
De pressionibus negativis in sinu et in pariete regionis fluido viscoso moventi impletae schedula, quam conscriptsit C. Truesdell apud Universitatem Johns Hopkins University, Baltimorae et
amico mechanicoque illustrissimo B. Finzi ob diem natalem septuagesimum dedicavit, first draft, holograph, thirty-two pages, December 31, 1969, of publication number 172, 1970
The scholar's workshop and tools:
First draft, holograph, written between six p.m. and eight p.m. for a discussion of historiography that evening, Truesdell was not called upon to speak, Thursday, August 27, 1970
Two pages cancelled from the typescript of a revised draft of the foregoing, which resulted in publication number 187, 1973
The scholar, a species threatened by professions, banquet address to the society for History of Technology and History of Science, Washington D. C., December 29, 1972, first draft of
publication number 203, 1976
Leonard Euler, supreme geometer, lecture number 424 more or less as delivered on April 24, 1971, converted to the first draft of publication number 178, 1972
The efficiency of a homogeneous heat engine, publication number 185, 1973:
Holograph manuscript, forty-six pages, first draft of publication number 185, written during the evening of August 30, 1972
Typescript, second or late draft with final title
Some short manuscripts, 1972-1979:
Theoria de effectibus mechanicis Caloris…, holograph draft, thirty-one pages, October 1, 1972, leading to publication number 184, 1973
Universal flows in the simplest theories of fluids:
First draft, holograph, May 8, 1973
Typescript draft of 1974, leading finally to publication number 212 by Fosdick and Truesdell
A simple example of an initial-value problem with more than one solution, first draft of publication number 195 (1974), holograph, eight pages, May 8, 1973
History of classical mechanics, second draft, typescript, fifty-three pages, with handwritten corrections, March 1975, used to make the third draft of publication number 202, 1976
Address on receipt of a Birkhoff Prize, typescript, eleven pages, as read out on January 5, 1978, leading to publication number 217, 1978
A conceptual outline of thermodynamics for students of mechanics, text as read of lecture number 543, Pisa, May 17, 1978, typescript, thirty pages, resulted in the Italian text, publication
number 221, 1979
The role of mathematics in sciences as exemplified by the work of the Bernoullis and Euler, typescript resulting in publication number 233, 1981, fifty-four pages, text of lecture number
572 read at the Biozentrum, Basel, December 4, 1979
Tradition and history in thermodynamics, holograph, twenty-three pages, begun at six p.m. on September 6, 1979 in Washington D. C., finished at two p.m. September 7 on the plane to Chicago,
text of lecture number 571A, [note: this lecture is one of several sources used to make the Historical Introit of Rational Thermodynamics, second edition, 1984]
Proof that my work estimate implies the Clausius-Planck Inequality:
Second draft, typescript, seventeen pages with handwritten corrections to make the third draft, December 20, 1979
Typescript of third draft with handwritten corrections to make the fourth draft, thirteen pages, January 7, 1980
Final draft, typescript with handwritten corrections, incomplete, eleven pages, leading to publication number 231, 1980
86-31/11 Trois conférences sur la structure conceptuelle de la thermodynamique classique, lectures number 474-476 at Grenoble, December 17 and 18, 1973, resulting finally in publication number 199,
"Les bases axiomatiques de la thermodynamique," 1975:
Brouillon, 1973
Revised text of 3éme Conférence
Moon and Truesdell, Interpretation of adscititious inequalities through the effects pure shear stress produces upon an isotropic elastic solid, publication number 193, 1974, first draft of
this paper was written by Moon, drafts from 1973-1974
Truesdell and Moon, Inequalities sufficient to ensure semi-invertibility of isotropic functions, publication number 197, 1975, drafts from 1973-1974
Improved Estimates of the Efficiencies of irreversible heat engines, publication number 204, 1976:
Holograph manuscript, twenty-seven pages, winter 1974
Typescript of first draft corrected to form the second draft, April 15, 1975, with a note of late March 1975 detecting errors in the first draft
Typescript of fourth draft with corrections leading to the fifth and final draft, late spring, 1975
Later draft, not yet final
Correction of two errors in the kinetic theory, which have been used to cast unfounded doubt upon the principles of material frame-indifference, publication number 214, 1977, various
related drafts of 1975-1976:
On a shortcoming of the Chapman-Enskog Process and on its misinterpretation as being evidence against the principle of material frame-indifference, undated fragment, typescript, fourteen
pages, perhaps written before the following drafts, perhaps afterward
On some misinterpretations of formulae from the kinetic theory of gases which have been used to cast unfounded doubt upon the principle of material frame-indifference, and on the effects
of rotation according to the kinetic theory, holograph, about sixty pages, begun on August 31, 1975, finished September 1 at midnight
Second draft, September 15, 1975, On errors in the kinetic theory of gases which have been used to cast unfounded doubt upon the principle of material frame-indifference, and on the
effects of rotation according to the kinetic theory, altered to make the third draft, September 15, 1975
Correction of two errors in the kinetic theory of gases which have been used to cast unfounded doubt upon the principle of material frame-indifference, typescript with many corrections,
seventeen pages, written in Fall, 1975, corrected in June 1976 [note: this paper was at first intended as an abstract of part of the foregoing, but in the end the work on rotation in those
was left incomplete and abandoned]
Comments on rational continuum mechanics, lecture as delivered in Rio de Janeiro, August 1, 2, 4, 1977 (#530, 531, 532), published in somewhat revised form as Some challenges offered to
analysis by rational thermomechanics, publication number 219 (1978) and circulated later privately in a version with printer's errors corrected
History of constitutive relations:
Lecture number 589, September 1, 1980, publication number 226, 1980
Shortened for delivery, with closure written in Naples, and with Xerox copies of transparencies
The nature and use of constitutive relations, lecture number 559A, abstracted in publication number 227A
86-31/12 The computer, ruin of science and threat to mankind, outline, January 1980, holograph, two pages and typescript of lecture number 577 as delivered at Milano, February 7, 1980 with
handwritten corrections and notes made during the meeting, [note: this text is the first draft of publication number 234, and Italian translation. It served also as part of the first draft
of the essay of the same title in An idiot's fugitive essays, 1984]
Rapport sure le pli cachété No. 126 (de Cauchy), first draft, typescript of publication number 230 (1980), eleven pages, February 1980
The kinetic theory of gases, a challenge to analysts, typescript as read of lecture number 585, April 25, 1980, leading to publication number 235, 1982
Speech for commemoration of Daniel Bernoulli, lecture number 616, on September 5, 1982:
First draft, holograph, fifty-four pages, written with my great-aunt Yetta's gold pen, finished ("laus deo") on August 1, 1982
Fair copy, holograph, of the same date, August 1, 1982
The influence of elasticity upon analysis: The classic heritage, [note: the text of the lecture, shortened from this manuscript for delivery on August 25, 1982, is preserved in my notes of
miscellaneous lectures, number 615]:
Holograph abstract, three pages and typescript, June 8, 1982
Typescript of text for publication with handwritten alterations, March/April 1983, finished May 20, 1983, thirty-two pages
Nearly final text with holograph additions, thirty-six pages, June 1983
Final text of publication number 240
Correction of some errors published in this journal, ( The Journal of Non-Newtonian Fluid Mechanics):
Note by Truesdell:
The postscript on the fifth draft, deleted here, was later restored. At my request the second draft was refereed and checked for correctness by someone unconnected with Noll or me. When I
discovered that Rivlin and his sycophants made a different error in each of their papers, I recalled the accepted manuscript for revision. The final draft was also, at my request, checked
and refereed.
Second draft corrected to make the third, typescript with handwritten alterations, three pages, November 1983
Fourth draft corrected to make the fifth, five pages, November 16, 1983
Revised manuscript, December 1983
Preface to the re-issue of Volume Via of The Encyclopedia of Physics, holograph, eleven pages, September 15, 1983
Absolute temperature as a consequence of Carnot's general axiom, publication number 220, 1979:
First draft
Corrections, October 11, 1978
Text after five revisions, November 6, 1978
Text after six revisions, December 1, 1978
Texts of lectures in German and Italian, which served as first drafts of publications number 95, 88, 72L, and 96, 1956-1957
Texts of lectures on thermodynamics, which are first drafts of publications number 154L2. 163, chapter one of 169, and 206, 1966-1973
Texts of lectures in German and Italian, which served as first drafts of publications number 95, 88, 72L, and 96, 1956-1957:
Lecture 101, Neuere Anschauugen über die Geschichte der allgemeinen, Mechanik, Basler Mathematische Gesellschaft, December 2, 1956, first draft for lecture 101, published as publication
number 95
Lecture 102, Sulle equazioni fondamentali della termodinamica irreversibile, Seminario Mathematico dell'Universitàdi Bologna, March 1, 1957. Also Lecture 103. First draft for publication
number 88
Lecture 104, L'ipoelasticità, Seminario Matematico dell'Università, Napoli, March 23, 1957. Also Lectures 104-107. Published after mangling by Manarino as publication number 72L
Neuere Entwicklungen in der klassischen statistischen Mechanik und in der kinetischen Gastheorie, Gastvorlesung an dem Institut für Struktur der Materie der Universität Marburg a.d. Lahn,
May 28-June 5, 1957. First draft of publication number 96, before the improvements and Procrustean abridgments by D. Morgenstern
Lecture 110, Darlegung einiger Grund probleme der statistischen Mechanik und der kitetischen Gastheorie
Lecture 111, Zurückführung des asymptotischen Problems auf Begriffe der Wahrscheinlichskeitstheorie
Lecture 112, Khinchin's Beweis des Boltzmannschen
Lecture 113, Khinchin's Lösung des Erogdenproblems der statistischen Mechanik
Lecture 113, Khinchin's Lösung des Erogdenproblems der statistischen Mechanik
Lecture 114, Ein iteratives Lösungsverfahren für die kinetische Gastheorie
Lecture 115, Ein mathematisches Modell für das Momentengleichungs-systems der kinetischen Gastheorie
Lecture 116, Exakte Lösung für Scherbewegung
Lecture 117, Statistische Herleitung der Feldgleichungen der Thermomechanik der Kontinua durch Irving-Kirkwood and Noll
Texts of lectures on thermodynamics that are first drafts of publications number 154L2, 163, chapter one of 169, and 206:
Lecture 267, Thermodynamics of deformation, to the Solvay Congress on Non-equilibrium Thermodynamics, University of Chicago, May 17, 1965. First draft of publication number 154L2
Lecture 322, Termodinamica per principianti, to the Convegno dei Meccanici Italiani, Accademia Nazionale, Modena, May 29, 1966. Also lectures 321 and 323. Abridged from an unpublished
draft of publication number 163 and published in revised for as publication number 163L2
Lecture 324, Thermodynamics for beginners, to the IUTAM Symposium on Irreversible Thermodynamics in Continuous Media, Vienna, June 22, 1966. First draft of publication number 163, which
formed the basics of chapter one of publication number 169
Lecture 379, Termodinamica fondamentale, Seminario Matematico dell'Universitàdi Torino, january 10, 1968. Used also for lecture 380. Second draft of chapter one of publication number 169;
published, with some revision, as publication number 163L2
Lectures of 1973 at the Istituto Interdisciplinare per le Applicazioni della Matematica, Accademia Nazionale dei Lincei, Rome, January 19, 23, 25, and 27, 1973. First draft of publication
number 206:
Lecture 461, La dottrina dei calori latenti e calori specifici, e la velocitàdel suono secondo Laplace (1816)
Lecture 462, La termodinamica di Sadi Carnot (1824)
Lecture 463, La termodinamica di Clausius (1850, 1854)
Lecture 464, Il rendimento delle macchine termiche secondo la termodinamica razionale di oggi
Return to the Table of Contents
Series 3 - Manuscripts of publications and lectures
86-31/13 The bound copy of The Mechanical Foundations (publication number 43, 1952) with the published corrections and additions incorporated and with some further alterations, the whole forming the
basis for the reprint titled Continuum Mechanics I (publication number 43R, 1956)
Editor's introduction to volume 13 of series 2 of L. Euleri Opera omnia (publication number 77, 1956), manuscript sent to press
The rational mechanics of flexible or elastic bodies, 1638-1788, (publication number 111, 1960), first 210 pages of the manuscript typewritten in Madison, summer 1958, and sent to press
Essays in the history of mechanics, (publication number 165, 1968), manuscript of the front matter and pages 171-387 (roughtly 173-366 of the printed volume)
86-31/14 The mechanics of Leonardo da Vinci:
Lecture 83, public lecture at Indiana University, Bloomington, October 14, 1954
Lecture 123, Washington Philosophical Society, March 7, 1958
Lecture 257, University of Washington, November 5, 1964. Also lectures number 266 and 268. Publication number 165P, an abridgment, was based on this text or a revision of it.
Typescript as sent tot he printer for essay one of Essays in the history of mechanics, publication number 165, 168
Manuscripts of some other new essays for publication number 165, Essays in the history of mechanics, 1968:
Essay four, The creation and unfolding of the concept of stress, holograph, 1968, seventy-five numbered pages with some intermediary sheets, and with notes directing that parts of
publication number 117 (1961) be incorporated
Essay six, Early kinetic theories of gases, holograph 1967, about sixty-vive pages, with some typewritten sheets and some pages pasted up from extracts from my course notes on statistical
mechanics and the kinetic theory as given at Johns Hopkins
Appendix one, selected reviews and a preface, withheld and the publishers request [note: all but one of these were published, some of them somewhat revised in An Idiot's Fugitive Essays,
Six lectures on modern natural philosophy, lectures at the Johns Hopkins University, February 9-25, 1965, based on lectures at the University of Washington, November 2-12, 1964, and serving
as the first draft of publication number 153:
86-31/15 Twelve Centennial Lectures at the Drexel Institute of Technology, 1966-1967, in two binders. The manuscripts of the first nine served as the first drafts of the book:
Volume I: Lectures 359, 361, 362, 364, 365, 366
Volume II: Lectures 367, 368, 370, 371, 372, 374
Manuscript, typed by Charlotte Truesdell in Pisa, February 1968, and sent to press from Amsterdam on April 1, 1968
Part of a rejected draft, alterations made in March 1969 white the manuscript was in the hands of the press, and six galley proofs marked with important alterations.
86-31/16 Manuscript of lecture 631 on Leonardo da Vinci read at the Hammer Symposium, Walters Art Gallery, Baltimore, May 14, 1983:
Preliminary abstract, Renaissance Science, holograph, five pages, December 31, 1982
Outline, "The Codex Hammer in context: Renaissance science," holograph, thirteen pages, printed in the leaflets distributed at the symposium
First draft of the lecture, The mechanics of fluids in the Codex Hammer, holograph
The Codex Hammer in context: Renaissance science, typescript of the second draft, corrected to make the second, May 1983
Fundamental hydromechanics in Codex Hammer, typescript of the first draft, corrected to form the third, May 20, 1983
Return to the Table of Contents
Series 4 - Lectures on foundations of kinetic theory and statistical mechanics
Note by Truesdell
Notes on the course first given in 1950/1951 and more or less biennially for more than twenty years thereafter; after the first time these notes were simultaneously drafts of a book of the
same title, never completed as such.
This course was my first course at Indiana University. The topic had been requested by Gilbarg. Among the students in 1950-1951 were Serrin and Ericksen. The final examination is bound in
at the end of the notes. On that examination Serrin did original research on the methods of Hilbert and Enskog and got the grade A+. Noll and Morgenstern studied these notes, especially in
my seminar in the summer of 1954, and Morgenstern followed the course itself in 1954-1955, during which Morgenstern improved Khichin's proof of Boltzmann's law. Noll's paper "Die
Herleitung der Grundgleichungen der Thermomechanik der Kontinua aus der statistischen Mechanik," 1955, grew from a report he gave in the seminar of 1954; so did the two papers by
Morgenstern, and so did several papers by Ikenberry. This course and related seminars gave rise to all of my papers in its field, including:
• Number 45, "On the viscosity of fluids according to the kinetic theory," 1952
• Number 78 (co-author E. Ikenberry) and 79, "On the pressures and the flux of energy in a gas according to Maxwell's kinetic theory," 1956
• Number 96, "Neuere Entwicklungen in der klassischen statistischen Mechanik und der kinetischen Gastheorie, ausgearbeitet von D. Morgenstern," 1958
• Number 121, "Ergodic theory in classical statistical mechanics," 1961
• Lecture five of number 153, Six Lectures on Modern Natural Philosophy, 1966
• Essay six in number 165, Essays in the History of Mechanics, 1968
• Lectures 8-10 of number 169, Rational thermodynamics, 1969
• Number 170, "A precise upper limit for the correctness of the Navier-Stokes theory with respect to the kinetic theory," 1969
• Number 186, Mathematical aspects of the kinetic theory of gases, 1973
• Number 198, "Early kinetic theories of gases," 1975
• Number 214, "Correction of two errors in the kinetic theory of gases which have been used to cast unfounded doubt upon the principle of material frame-indifference," 1977
• Number 224, co-author R. G. Muncaster, Fundamentals of Maxwell's kinetic theory of a simple monotomic gas, treated as a branch of rational mechanics, 1980
Still in my hands are the notes of the last version of the course itself, which I had hoped to write up some day as an elementary introduction to the material in publications number 121
and 224 along with an exposition of some of the more recent researches on equilibrium statistics.
86-31/16 Notes of 1950/1951, Bloomington, holograph, approximately 250 pages, followed by some holograph notes for additions and the final examination
Notes of 1952/1953, Bloomington, typescript, with equations filled in by various students, and a table of contents made by one of them. These notes were intended as the first draft of a
86-31/17 Notes of 1954/1955, Bloomington, second draft of the book, new typescript, again with equations filled in by various students, followed by a holograph manuscript of the start of part
Notes of 1961/1962, Baltimore, hectographed, 460 pages. These notes included the improved treatment of ergodic theory at Varenna, presented in publication number 120
Return to the Table of Contents
Series 5 - Notes for Truesdell's courses that did not become the basis of books
86-31/18 His own notes:
At the University of Maryland:
Mathematics for engineers, 1946-1947
Electricity and magnetism, Math 239, 1948-1949
Functions of a complex variable, 1949-1950
Algebra, Math 103, 1950
At Indiana University:
Elasticity, 1951
Hydrodynamics, 1951-1952
Analytical dynamics, 1952
86-31/19 Elementary differential equations, 1953
Elasticity, spring 1958
Fluid mechanics, 1959-1960
Theory of functionals, 1959-1960
At Johns Hopkins University:
Classical continuum theories, 1964-1965
Navier-Stokes equations, 1967
Classical hydrodynamics, 1969
Charlotte Truesdell's notes on Clifford Truesdell's elementary courses at Johns
Linear algebra, late 1960s
Fluid mechanics, 1969
Return to the Table of Contents
Series 6 - Materials connected with the textbook on continuum mechanics (Publications number 183, 196, 211)
86-31/20 First draft of the preface for number 183 (French translation), typescript, two pages, February 22, 1971
Draft of the preface to number 211, typescript, six pages, October 1976
Corrected galley proofs of number 211
Corrected page proofs of number 211
Return to the Table of Contents
Series 7 - Early drafts leading to the book by Truesdell and Bharatha, Concepts and Logic of Classical Thermodynamics as a Theory of Heat Enginees, Developed upon the Foundation Laid by S. Carnot
and F. Reech (publication number 213, 1977)
86-31/20 The logical structure of classical thermodynamics according to Reech, holograph manuscript, October 1, 1973
The logical structure of the classical thermodynamics of reversible processes, developed upon the foundation laid by F. Reech (1851/3)
Third draft, October 21, 1973
Corrected to make the fourth draft, November 5, 1973
Fifth draft, November 12, 1973, corrected to make the sixth draft, November 25, 1973
Draft after the sixth, used to make one before the ninth, undated
Some pages of the ninth draft, April 30, 1974, altered for the tenth, May 1974
The logical structure of classical thermodynamics developed upon the foundation laid by F. Reech (1851/3), tenth draft, June 4, 1974, corrected to make the eleventh draft, July 15, 1974
86-31/21 The concepts and logic of classical thermodynamics developed upon the foundation laid by F. Reech (1851/3), twelfth draft, August 15, 1974, altered to make the thirteenth draft,
September 5, 1974
The concepts and logic of classical thermodynamics as a theory of heat engines, rigorously constructed upon the foundation laid by F. Reech
Fourteenth draft corrected to make the fifteenth, January 19, 1975
Fifteenth draft corrected to make the sixteenth and seventeenth, October 15, 1975, with the final title and with Bharatha's name added as co-author
Seventeenth draft, October 30, 1975, corrected to form the eighteenth, January 1976, followed by some pages with notes by Bharatha
86-31/22 Eighteenth draft, corrected to make the nineteenth, January 1976
Sheets from the nineteenth draft on which corrections were made to obtain the twentieth, summer 1976
Twentieth draft, June 3, 1976, revised August 4, 1976 and set to press:
Part one
Part two
Corrected galley proofs
Manuscript material used to make alterations on the galley proofs, August 17, 1977
Return to the Table of Contents
Series 8 - Materials connected with The Tragicomical History of Thermodynamics, 1822-1854, (Publication 225)
Note by Truesdell
While writing the fifth draft, here preserved, I came to think that Reech's ideas could form the basis of a modern axiomatic treatment. That idea led eventually to the book by Bharath and me,
Concepts and Logic, publication number 213, drafts of which are included in another part of this collection. From 1973 onward I developed both books alternatingly. Between 1973 and 1979 the
manuscript The Tragicomical History went through many drafts, at least four. Each of those was made by altering the sheets of the preceding draft. Numbers eight, nine and ten, preserved by
accident, provide specimens.
86-31/23 The Tragicomedy of Classical Thermodynamics:
Holograph manuscript of part one, eighty pages, late July 1970
Part two, seventy-six pages [note: this text, after revision for a year, was published without Truesdell's authorization as publication number 225P, 1973]
Apparently the text of publication 225P, shortened for delivery as a lecture in 1970 or 1971
Second draft, September 15, 1970, with corrections converting it to the third draft, mainly holograph, pages numbered and renumbered in batches as given to the typist, about eighty-eight
pages numbered in Arabic numerals, about thirty-four in roman capitals, about thirty-five in larger Arabic numerals
Third draft, corrected to become the fourth draft, manuscript as given to the typist but only through Rankine's work, September 1971
Sixth draft, formed by correcting and supplementing the first, August 1973
Pages for an early draft, probably of 1976, discarded in the early summer of 1978
86-31/24 The Tragicomical History:
Tenth draft converted to the eleventh, summer 1978
October 1978
November 1978
December 1978
86-31/25 Manuscript as sent to press (probably), 1979
86-31/26 Corrected galley proofs
Corrected page proofs
Second draft of the letter to Muttonhead Lervig regarding his lies about The Tragicomical History in his review, 1983
Return to the Table of Contents
Series 9 - Materials connected with Fundamentals of Maxwell's Kinetic Theory, publication number 224, 1980
Note by Truesdell
The text of this book is of three origins: 1. Truesdell's ideas deriving from the notes for his lectures for his biennial course, beginning in the august of 1950, from his publications
number 45 (1952), 78 and 79 (1956), 170 (1960) and 124 (1977) and his multiplied lectures at Rio de Janeiro (see below). 2. Mucaster's Ph.D. thesis at Johns Hopkins (see below) 3. Work
done by Truesdell and Mucaster in collaboration starting in 1973 or 1974 and continuing through the page proofs of the book. Much of the material went through ten to twenty drafts, or even
more. Each draft was made by correcting the sheets of the preceding draft, and at each stage the old manuscript was destroyed.
86-31/26 The kinetic theory of gases as a branch of rational mechanics, lectures number 439-445, 451, 452, 455-457, delivered at Rio de Janeiro in May-June 1972:
First draft of lectures one-seven
The notes of all the lectures as issued by the Instituto de Matemática, Univeridade Federal do Rio de Janeiro
Muncaster's Ph.D. thesis, Constitutive relations in the kinetic theory of gases, Johns Hopkins, 1975
Draft of chapter one, Mathematical aspects of the kinetic theory of gases, publication number 186, May 1, 1973, extensively corrected in February and October 1974 "with the assistance of
R. G. Muncaster," revised and amplified in the summer of 1975 with the title changed to Fundamentals of the kinetic theory of a simple monotomic gas with Muncaster listed as co-author
First draft by Muncaster, revisions by Truesdell, September-October 1978
Second draft with further corrections by both authors, November 16, 1978
86-31/27 Manuscript as sent to press
86-31/28 Corrected galley proofs
Corrected page proofs
Return to the Table of Contents
Series 10 - Introduction to rational elasticity, by C. C. Wang and C. Truesdell, publication number 182, 1973
86-31/29 First draft for §II.7, holograph, thirty-three pages
Finished typescript (not the final text, which was made by repeated alterations of copies reproduced from this original), chapters one through seven:
Chapters one and two
Chapter three
Chapter four
Chapter five
86-31/30 Chapter six
Chapter seven
Return to the Table of Contents
Series 11 - Unpublished papers and original manuscripts of papers translated or mangled by editors, 1942-1966
86-31/30 "Some exercises in elementary calculus," Brown, followed by a note on a lost manuscript developing Problem III, summer 1942
"A set of algebraic functions," probably Brown, summer 1942
"Some transformations of power series," probably in Ann Arbor, 1943-1944
"Certain infinite integrals involving sinh x and cosh x," either in Ann Arbor or Boston, 1943-1944
"A transformation of the equation of hydrodynamics," written for Monroe Martin in Washington, 1947-1948
"Is classical mechanics a dead language?," abandoned exordium of a general lecture, 1950
"On the vorticity theorem of Ertel and Rossby," beginning of a paper, abandoned, ca. 1951
Review of "Higher transcendental functions" by the Bateman Manuscript Project, written for the American Mathematical Monthly but censored by Allendoerfer. The censored version is
publication number 71
"A reversal theorem for finite elastic strain," set aside and forgotten for ten years after its results had been rediscovered and generalized by Shield, summer 1959
"Potentials," correct text of publication number 112, before editorial mangling
"Unified field theories," correct text of publication number 113, before editorial mangling
"Besprechung mit dem Basler Erziehungsdepartement," morning, February 17, 1961
"Inequalities in finite elastic strain," introduction to the lecture at Brown on December 6, 1962
After-dinner speech for the Society for Natural Philosophy, New York, March 22, 1962
Introduction to the lecture at the Pinebrook Conference, summer 1965
Comment on the paper by Hans Ziegler and Donald McVean, "Zum begriff des elastischen Körpers," Z. Angew, Mathematical Physics [?], vol. 17, 1919-194 (1966), one of two versions offered to
that journal, the one printed, much shorter, is publication number 158
Works abandoned or published only in translations not made by Truesdell himself:
The fundamental principles of analytic fluid dynamics, first draft of what was to be half of a book written by Neményi and Truesdell, multiplied manuscript of 1947/1948 issued as a
Technical Note of the Mechanics Division of the U. S. Naval Ordnance Laboratory, bound in black cloth, eight chapters, bibliography, and appendix on vectorial and dyadic formulas. The
handwriting is partly Truesdell's, party Charlotte Brudno's.
86-31/31 The motion of fluids, Part two: The foundations of analytical fluid dynamics, second and enlarged draft of part of the foregoing, chapters four, five and six, holograph, partly
transparencies, preceded by a prospectus of the whole work and followed by transparencies of the bibliography of the foregoing, written at the U. S. Naval Research Laboratory, bound in
black cloth, 1949-1950 [Note: these chapters may be regarded as a crude and immature first draft of chapters b-d of The classical field theories, publication number 107], 1960
A general introduction to fluid dynamics, holograph transparencies of chapters four and six, preceded by a table of contents of the part Neményi intended to write and followed by the
transparencies of the appendix to number one, above, [Note: these two chapters, based in part of publications number 13P, 13, 17, 17L, 18, 18L, 23, 23P, 29, 29P, 30, 30A1, 30A2, and 64P,
all written at the Naval Laboratories, may be regarded as a first draft of much of The kinematics of vorticity, publication number 64], 1954
86-31/32 Kinematics of fluid motion, 1966-1967, intended as a second edition of The kinematics of vorticity, typescript of chapters two-four, followed by some fugitive notes, the whole sent to
Wan-Lee Yin in 1982 for him to use or not in the volume he had agreed to write
Introduction to rational thermomechanics, typescript of chapters fourteen-sixteen of my textbook on continuum mechanics, sent to Masson & Cie in 1973 for translation into French,
according to contract, which Masson broke. Essentially this text was sent later to Russia, was translated into Russian, and appeared in publication number 196
Rational thermomechanics, typescript of the English original, 1974, for the Italian translation appearing as publication number 223 in 1979, marred by numerous and serious misprints
Textbook of classical thermodynamics, 1979, based in part on notes for the course given in 1974 at the Georgia Institute of Technology as written up and augmented by S. Passman
Short manuscripts:
Beginning of Conservation principles for classical continuum mechanics in any affine space, written probably in 1961-1963
The mechanics of Galileo, holograph draft, 1969, perhaps typewritten for lectures 396A/396D, before Truesdell decided to use Salusbury's translation instead of making his own
Rational thermodynamics, mixtures, and structured continua, report on two Italian-American meetings in Italy, June 1974, rejected by Science
Truesdell's translation of Fichera's ridiculous obituary of Tricomi, late 1970s, probably published by Fichera, Truesdell did not permit his name to be used
Comments on David Speiser's papers on impact of unsymmetric bodies and on a corresponding Maxwell-Boltzmann equation, Louvain-La-Neuve, May 1979, not intended for publication
Informal comments on history of mathematical sciences by and for active scientists, typescript of rough draft, nineteen pages, followed by a copy with alternations, abandoned,
Should history of science be written only by licensed professionals?, holograph manuscript, twenty-one pages, abandoned, 1983
Return to the Table of Contents
Series 12 - Notes taken by Truesdell in courses at the California Institute of Technology (1939-1942), Princeton University (1942-1943) and Indiana University (1950-1953)
86-31/33 Mathematical physics, Ph 5 abc, W. V. Houston, 1939-1940
Elementary number theory, Ma 119, Morgan Ward, 1940-1941
Functions of a real variable, Ma 106, A. D. Michal, 1940-1941
Geometry, Ma 113, L. E. Wear, 1940-1941
Modern differential geometry, Ma 256, A. D. Michal, 1941-1942
Applications of tensor analysis, Ma 1116, A. D. Michal, 1942
Analysis, Ma 114, Morgan Ward, 1941-1942
Statistical mechanics, Ch 224, S. Epstein, 1941
Partial differential equations, Ma 258 bc, H. Bateman, 1941
Methods of mathematical physics, Ma 255, H. Bateman, 1941-1942
86-31/34 Compressible fluids, AE 268, H. Bateman, 1942
Potential theory, Ph 221, H. Bateman, 1942
Functions of a real variable, 1942-1943:
Abstract from Bohnenblust's notes
Course by Bochner
Topology, Lefschetz and Tucker, 1942-1943
Algebra, Wedderburn, 1943
Functional analysis, E. Hopf, 1950-1951
Differential equations, Gilbarg, 1950-1951
Relativity, Hlavaty´, 1953
Return to the Table of Contents
Series 13 - Notes on miscellaneous lectures
86-31/34 Volume one:
Lecture A, Fréchet's 1906 thesis, Princeton University, Princeton, New Jersey, for Tucker's course in topology, winter 1942
Lecture B, Finite complexes, Princeton University, Princeton, New Jersey, at Lefschetz's request to help the weak graduate students, spring 1943
Lecture C, Elements of groups, Princeton University, Princeton, New Jersey, at Lefschetz's request to help the weak graduate students, spring 1943
Lecture D, Tensor analysis, Naval Ordnance Laboratory, White Oak, Maryland, summer 1948
Lecture E, Vorticity (non-technical), Naval Ordnance Laboratory, White Oak, Maryland, summer 1948
Lecture 17, A unified theory of special functions, Mathematics Colloquium, University of Tennessee, August 28, 1948, also lectures number 20, 21, 31, 45, 58, 59
Lecture 22, A new definition of fluid, Joint Meeting of the Graduate Mathematics Club and the Fluid Dynamics Panel, University of Illinois, Urbana, Illinois, December 16, 1948, also
lecture number 27
Lecture F, Foundations of fluid dynamics, Naval Research Laboratory, Washington D. C., December 1948 and January 1949
Lecture G, Tensor analysis, Naval Research Laboratory, Washington D. C., December 1948 and January 1949
Lecture 24, Recent continuum theories of fluid dynamics, Annual Meeting of the American Physical Society, New York, N. Y., January 27-29, 1949
Lecture 26, The kinematics of vorticity, University of Toronto, Department of Mathematics, February 3, 1949
Lecture 28, The membrane theory of shells of revolution, Applied Mechanics Colloquium, Johns Hopkins University, Baltimore, Maryland, February 9, 1949
Lecture 29, Vorticity theorems of fluid dynamics, Mathematics Colloquium, University of Maryland, February 17, 1949, also lecture number 30
Lecture 38, The aerodynamics of rarefied gases, Colloquium of the Low Pressures Research Group, University of California, Berkeley, California, December 12, 1949, also lectures number 39
and 42
Lecture 40, A new vorticity theorem of gas dynamics, Colloquium of the Meteorology Department, University of California, Los Angeles, California, December 16, 1949
Lecture 41, Vorticity Averages, Colloquium of the Meteorology Department, University of California, Los Angeles, California, December 16, 1949
Lecture 44, On the form of the heat flux vector in moderately rarefied gases, Meeting of the American Physical Society, Charlottesville, Virginia, December 19, 1949
Lecture 47, On Poincaré's analogy between vorticity and mass density, Mathematics Colloquium, University of Maryland, College Park, Maryland, March 2, 1950, also lecture number 49
Lecture 51, Two measures of vorticity, Colloquium of the Institute for Fluid Dynamics/Applied Mathematics, University of Maryland, College Park, Maryland, May 9, 1950, also lecture number
Lecture 53, Why are non-linear theories of solids necessary?, Strength of Solids Seminar, Naval Research Laboratories, Washington D. C., August 18, 1950
Lecture 56, A measure of vorticity, Mathematics Colloquium, Indiana University, Bloomington, October 1950, also lecture number 66
Lecture H, Invariant measures in kinematics, Naval Research Laboratories, Washington D. C., November 1950
Lecture I, The ergodic problem in statistical mechanics, Naval Research Laboratory, Washington D. C., November 1950
Lecture J, Strain measures, Naval Research Laboratory, Washington D. C., November 1950
Lecture K, Stress-strain relations in elasticity, prepared for the Naval Research Laboratory, Washington D. C., but never delivered, November 1950
Lecture 60, Large elastic strain, Applied Mathematics Colloquium, Naval Research Laboratory, Washington D. C., April 24, 1951
Lecture L, Three pages from Euler's works, in Whaples' course in the history of mathematics, Indiana University, Bloomington, Indiana, May 1951
Lecture 63, Rational mechanics from 1687-1788, Meeting of the Indiana University Chapter of Sigma Xi, Bloomington, Indiana, January 10, 1952
Lecture 64, Large elastic strain, Strength of Solids Seminar, Naval Research Laboratory, Washington D. C., March 20, 1952
Lecture 65, Finite elastic strain, Conference on Elasticity, Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, Maryland, March 22, 1952, also
lecture number 74
Lecture 68, Hydrodynamical theory of absorption and dispersion of forced plane infinitesimal waves in pure fluids, Symposium on Ultrasonic Absorption in Fluids, Brown University,
Providence, Rhode Island, October 16, 1952
Lecture 70, Non-linear continuum mechanics, Mathematics Colloquium, Indiana University, Bloomington, Indiana, October 27, 1952
Lecture 71, Analysis of Euler's first paper on fluid dynamics, Mathematics Colloquium, Indiana University, Bloomington, Indiana, November 1952
Lecture 74, Finite elastic strain, Colloquium on Applied Mathematics and Mechanics, Applied Physics Laboratory, Silver Spring, Maryland, June 26, 1953
Lecture 75, Precise theory of absorption and dispersion of infinitesimal ultrasonic waves according to the Navier-Stokes equations, Rarefied Gases Symposium of the American Physical
Society, Pennsylvania State College, July 2, 1953
Lecture 76, The hydraulic pendulum, Meeting of the Indiana Academy of Sciences, Richmond, Indiana, November 6, 1953
Lecture 77, Figures of equilibrium of rotating fluid masses, Mathematics Colloquium, Indiana University, Bloomington, March 15, 1954
Lecture 78, The development of the concept of stress, Institute for Mathematical Sciences, New York University, New York, February 8, 1954, also lecture number 79
Lecture 80, The simplest rate theory of pure elasticity, Symposium of the Office of Ordnance, and the American Society of Mathematics, University of Chicago, April 30, 1954
Lecture 81, Some problems in partial differential equations arising in the newer fields of mechanics, Mathematics Colloquium, Indiana University, Bloomington, May 2, 1954
Lecture 82, Solids and fluids, National Meeting of the American Society for Engineering Education, University of Illinois, Urbana, June 11, 1954
Lecture 84, Hypo-elasticity, Mathematics Colloquium, Indiana University, Bloomington, November 8, 1954
Lecture 86, Enlightenment of the kinetic theory of gases, Lecture one: Classical developments and Maxwellian iteration, Mathematics Colloquium, Indiana University, Bloomington, April 18,
25, and May 2, 1955
Lecture 87, Enlightenment of the kinetic theory of gases, Lecture two: A model for the equations of moments, Mathematics Colloquium, Indiana University, Bloomington, April 18, 25, and May
2, 1955
Lecture 88, Enlightenment of the kinetic theory of gases, Lecture three: Exact solution for shearing flow, Mathematics Colloquium, Indiana University, Bloomington, April 18, 25, and May
2, 1955
Lecture 97, A private contract in 1694, State University of Iowa, Iowa City, March 7, 1956, for Engineering Luncheon
Lecture 98, Bernoullian theorems, Hydraulics Seminar, State University of Iowa, Iowa City, March 7, 1956
86-31/35 Volume two:
Lecture 118, The integration problem in the kinetic theory of gases, Joint Colloquium of the ETH and the University, Zürich, November 5, 1957
Lecture 119, Euler Hauptversuch zur Lösung der Hydrodynamischen Gleichungen, Joint Colloquium of the Deutsche Versuchsanstale für Luftfahrtforschung, the mathematisches Institüt für
Angewandte mathematik, Universität, Freibrug i. Br., November 16, 1957
Lecture 120, Mathematische probleme aus der kinetischen gastheorie, Mathematisches Seminar der Universität Heidelberg, November 23, 1957
Lecture 122, Recent non-linear theories of materials, Rheology Colloquium, National Bureau of Standards, Washington D. C., March 6, 1958
Lecture 124, Exact theory of strain of a rod, U. S. Army Mathematics Research Center, and Mathematics Department Colloquium, University of Wisconsin, Madison, April 15, 1958
Lecture 125, General principles of motion, energy, and thermodynamics for reacting mixtures, Engineering Sciences seminar, Purdue University, October 6, 1958, Colloquium on the
Foundations of Rational Mechanics, Indiana University, November 18, 1958
Lecture 127, Current areas of research in rational mechanics, Lecture one: Non-linear continuum mechanics, Mathematics Department, Indiana University, March-April 1959
Lecture 128, Current areas of research in rational mechanics, Lecture two: A typical new concept: The oriented body, Mathematics Department, Indiana University, March-April 1959
Lecture 129, Current areas of research in rational mechanics, Lecture three: A typical underdetermined problem: General solution of the equations of motion, Mathematics Department,
Indiana University, March-April 1959
Lecture 130, Current areas of research in rational mechanics: Lecture four: A typical new theory: Hypo-elasticity, Mathematics Department, Indiana University, March-April 1959
Lecture 131, Current areas of research in rational mechanics, Lecture five: A typical overdetermined problem: Rods, beams, slabs, plates, and shells on the classical linear theory of
elasticity, Mathematics Department, Indiana University, March-April 1959
Lecture 135, A general theory of diffusion, Mellon Institute, Pittsburgh, August 4, 1959
Lecture 136, The monatomic gas as a visco-elastic substance, Mellon Institute, Pittsburgh, August 11, 1959
Lecture 137, Shear flow according to the kinetic theory, Mellon Institute, Pittsburgh, August 12, 1959
Lecture 138, Relaxation phenomena in the kinetic theory of gases, Mellon Institute, Pittsburgh, August 14, 1959
Lecture 139, The principles of continuum mechanics, Socony-Mobil Research Laboratory, Dallas, February 1960
Lecture 140, Some features of Cauchy's laws, Socony-Mobil Research Laboratory, Dallas, February 1960
Lecture 141, The classical theory of finite elastic deformation I: Principles, Socony-Mobil Research Laboratory, Dallas, February 1960
Lecture 142, The classical theory of finite elastic deformation II: Solutions, Socony-Mobil Research Laboratory, Dallas, February 1960
Lecture 143, The basic phenomena of non-linear viscosity, Socony-Mobil Research Laboratory, Dallas, February 1960
Volume three:
Lecture 144, The general theory of material constitutive equations, Socony-Mobil Research Laboratory, Dallas, February 1960
Lecture 145, Exact solutions for the viscometer flows of incompressible simple fluids, Socony-Mobil Research Laboratory, Dallas, February 1960
Lecture 146, Thermostatics of continuous media, Socony-Mobil Research Laboratory, Dallas, February 1960
Lecture 147, Oriented materials, Socony-Mobil Research Laboratory, Dallas, February 1960
Lecture 148, Mixtures, Socony-Mobil Research Laboratory, Dallas, February 1960
Lecture 160, Probleme aus dem gebiete der thermodynamik irreversibler prozesse, Kolloquium der physikalisch-chemischen Anstalt der Universität Basel, February 13, 1961
Lecture 161, Proprietàsostanziali secondo il punto di vista invariantivo, Seminario Matematico dell'Universitàdi Padova, March 20, 1961
Lecture 162, Termostatica dei corpi elastici a deformazioni finite, Seminario Matematico dell'Universitàdi Padova, March 21, 1961, also lecture number 169
Lecture 163, Teoria generale della viscosimetria, Seminario Matematico dell'Universitàdi Padova, March 20-23, 1961, also lecture number 170
Lecture 164, Materiali Orientati (Verghe, Lastre Curve, Fluidi Anisotropi, ecc.), Seminario Matematico dell'UniversitÊ di Padova, March 22, 1961, also lecture number 171
Lecture 173, Waves in elastic solids, Applied Mathematics Colloquium, Massachusetts Institute of Technology, February 26, 1962
Lecture 181, History of beam theory, Mechanics Department, Semi-annual Meeting, The Johns Hopkins University, May 22, 1962
Lecture 185, History and modern developments in continuum mechanics, Princeton University Summer Conference on Non-ideal Mechanical Behavior, August 13, 1962
Lecture 187, Modern theories of flow in tubes, Symposium on Hemodynamics and Hydrodynamics, The Johns Hopkins University, October 29, 1962
Lecture 188, The rational mechanics of materials, Technological Institute Colloquium, Northwestern University, November 2, 1962
Lecture 192, Dynamic problems in finite elastic strain, Department of Aeronautics and Engineering Mechanics, University of Minnesota, [November 13, 1962]
Lecture 194, The natural time of a visco-elastic fluid, Departments of Engineering Mechanics and Mathematics, University of Michigan, Ann Arbor, [November 13, 1962]
Lecture 195, Inequalities and analytical problems in elasticity, Depts of Mechanics and Mathematics, University of Michigan, Ann Arbor, November 13, 1962
Lecture 202, Whence the law of moment of momentum? Colloquium in Engineering Science, Mechanical Engineering Department, Columbia University, January 8, 1963
Lecture 204, Inequalities in finite elastic strain, Spring public lecture. Institute of Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, March 6, 1963
Lecture 216, Early concepts of a fluid, Meeting of the Society for Natural Philosophy, Pittsburgh, PA, November 11, 1963
Lecture 217, Non-linear material response, Short course, Extension Division, University of California, Los Angeles, December 2-6, 1963
Lecture 229A, A history of flexible or elastic bodies I, The Solid Mechanics Seminar, Johns Hopkins University, Baltimore, February 18, 1964
Lecture 229B, A history of flexible or elastic bodies II, The Solid Mechanics Seminar, Johns Hopkins University, Baltimore, February 25, 1964
Lectures 259-264, Original drawings for slides for the Lectures on Natural Philosophy at Johns Hopkins, 1965
Lecture 297, Elastic stability, as Distinguished Visiting Lecturer, Institute for Theoretical and Applied Mechanics, University of Kentucky, Louisville, December 3, 1965
Lecture 317, Substantially stagnant motions, Institutions of Pure and Applied Mathematics, Australian National University, Canberra, February 14, 1966
Lecture 318, The uselessness of rate theories of viscometry, Department of Mechanical engineering, The University of Sydney, February 16, 1966
Volume four:
Lecture 353, Continuum mechanics in the last two decades, Sandia Corporation, Albuquerque, New Mexico, September 12-16 and 19-23, 1966
Lecture 363, Angular momentum, History of Science Colloquium, Princeton University, December 9, 1966
Lecture 369, Wave propagation in materials with internal state parameters, Mechanical Engineering Colloquium, Yale University, New Haven, March 16, 1967
Lecture 378, Recent advances in rational mechanics, Department of Engineering Mechanics, Colloquium, North Carolina State University, Raleigh, October 26, 1967, also lecture number 392
Lecture 381, Termodinamica dei corpi continui, Istituto di Scienza della Costruzioni, Universitàdi Genova, February 28, 1968
Lecture 383, The structure of thermodynamics, Nordita, Copenhagen, March 13, 1968, also lectures number 389, 393, and 394
Lecture 388, Thermodynamics of chemical reactions, Institute for Theoretical Physics, University of Uppsala, March 25, 1968
Lecture 395, The development of mechanics in the eighteenth century and today -- some parallels, Science Faculty Colloquium, Rensselaer Polytechnic Institute, Troy, N.Y., October 3, 1938
Lecture 397, Punishment for original thinking in the kinetic theory of gases, Sigma Xi Initiation, (Monie A Ferst Memorial Lecture) Georgia Institute of Technology, Atlanta, [opening and
closing pages only], June 3, 1969
Lecture 398, Discovery of rigid-body motion, Seminar in Solid and Fluid Mechanics, Georgia Institute of Technology, Atlanta, June 4, 1969
Lecture 403, Rational mechanics -- An old and new part of pure mathematics, Simon Fraxer University, Canaada, September 24, 1969
Lecture 405, Che cos'è la teoria cinetica?, Istituto Linceo di Ricerche, Roma, April 2, 1970
Lecture 406, Che cos'è una soluzione nella teoria cinetica? Istituto Linceo di Ricerche, Roma, April 9, 1970
Lecture 407, Le soluzioni normali di Hilbert e Chapman-Enskog, Istituto Linceo di Ricerche, Roma, April 16, 1970
Lecture 409, Il metodo di iterazione differenziale, Istituto Linceo di Ricerche, Roma, April 23, 1970
Lecture 412, original drawings of slides for The tragicomedy of thermodynamics, 1822-1854, Rochester, October 1, 4, 1970
Lecture 413, Modern thermodynamics, University of Rochester, October 13, 1970, also lecture number 422
Lecture 415, A priori inequalities and uniqueness in elasticity, Johns Hopkins University, October 29, 1970, also for lecture number 423
Lecture 421, Rational mechanics, Past and Present, Southwest Graduate Research Conference, University of Houston, March 22, 1971
Lecture 431, The meaning of viscometry in fluid mechanics, American Physical Society, San Diego, November 23, 1971, forming the basis for publication number 192 in 1974, includes original
drawings for the transparencies
Lecture 434, Mathematical problems in the kinetic theory of gases, Oxford University Mathematics Colloquium, February 4, 1972
Lecture 438, Euler's relations with other scientists, Engineering Mechanics Colloquium, University of Michigan, Ann Arbor, March 22, 1972
Lecture 450, Continuum mechanics today, Coloquio da Engenharia da Universidade Federal do Belo Horizonte, May 26, 1972
Volume five:
Lecture 473, The logical structure of the classical thermodynamics of reversible processes, developed upon the foundation laid by F. Reech (1851/1853), Joint seminar in mathematics of the
University of Pittsburgh and the Carnegie-Mellon University, November 16, 1973
Lecture 479, La termodinamica dedotta in base agli assiomi di Reech (1851/1852), Seminario dell'Istituto di Scienze Fisiche dell'Universita, Genova, January 31 and February 1, 1974
Lecture 480, La termodinamica dedotta in base agli assiomi di Reech (1851/1853), Seminario dell'Istituto Matematica S. Pincherle, Bologna, February 8, 1974
Lecture 483, Interpretation of adscititious inequalities through the effects of pure shear stress produced upon an isotropic elastic solid, Seminar in Natural Philosophy, Johns Hopkins
University, April 10, 1974
Lecture 484, Classical thermodynamics based on the axioms of Reech, meeting of the Society for Natural Philosophy, Pisa, June 14, 1974
Lecture 492, Limitazioni più precise per il rendimento di una macchina termica, at the Istituto Matematics "Salvatore Pincherle," Universitàdi Bologna, November 7, 1975
Lecture 493, Macchine termiche irreversibili e la seconda legge della termodinamica, at the Convegno Modesto Panetti, Accademia delle Scienze, Torino, November 12, 1975
Lecture 494, Una assiomatica per la termodinamica elementare, at the Istituto di Fisica Matematica, Universitàdi Torino, November 14, 1975
Lectures 495-497, Fondamenti della termodinamica classica in base all'Assioma di Carnot, at the Istituto Matematica Università, the Scuola Normale Superiore, and the Istituto di Scienze
delle Costruzioni, Facoltàdi Ingegneria, Pisa, November 18 and 20, 1975
Lecture 498, Nuovi sviluppi dlla teoria cinetica dei gas, at the Accademia Nazionale dei Lincei, Cenro Linceo Interdisciplinare di Scienze Matematiche e loro Applicazioni, November 25,
Lectures 499-501, Problemi matematici della teoria cinetica dei gas, at the Istituto Matematica "Renato Cacciapoli," Universita di Napoli, December 2-4, 1975
Lectures 502-503, Sviluppo chiaro e rigoroso della termodinamica classica in base alle proprietàdelle macchine termiche
Lectures 504-510, Conceptual foundations of classical thermodynamics, and recent developments in the theory of irreversible processes, as Bicentennial Scholar in Residence, College of
Engineering, university of Delaware, Newark, January 5-16, 1976
Lecture 523, Concepts and logic of classical thermodynamics as a theory of heat engines, based on the concepts of Carnot and Reech, special lecture to the Engineering School, Tulane
University, New Orleans, May 14, 1976
86-31/36 Volume six:
Lectures 539 and 540, Entropy and its flux according to the kinetic theory of gases, at a joint colloquium of the Departments of Mathematics, Aerospace and Mechanical Engineering, and
Chemical Engineering, University of Minnesota, Minneapolis, November 17 and 18, 1977
Lecture 544, The scientific work of James Frederick Bell, at the meeting of the Society for Natural Philosophy, Domus Galilaeana, Pisa, May 18, 1978
Lecture 545, Don't be fooled by what they tell you about the kinetic theory, at the Italo-American Symposium on Non-Linear Continuum Mechanics, Fondazione Cini, Monselice, May 26, 1978
Lecture 550, Organizer's address at the Special Symposium, Conceptual analysis in rational thermomechanics, at the summer meeting of the American Mathematical Society, Providence, RI,
August 10, 1978
Lecture 551, Absolute temperature as a consequence of Carnot's general axiom, at the seminar in Natural Philosophy, Johns Hopkins University, Baltimore, MD, October 4, 1978
Lecture 552, Some challenges offered to analysis by elasticity, at the Mathematics Colloquium, State University of New York at Buffalo, November 14, 1978
Lecture 553, Conference: Why study mechanics? Why do research in mechanics?, to the students in the Engineering Science Program, State University of New York at Buffalo, November 15, 1978
Lecture 554, Conceptual structure of classical thermodynamics, to the Joint Mathematics and Applied Mathematics Colloquium, State University of New York at Buffalo, November 15, 1978
Lectures 555-569, The tragicomical history of thermodynamics, 1822-1854, to the seminar in Natural Philosophy, Johns Hopkins University:
Lecture 555, (Lecture one), The doctrine of latent and specific heats. Laplace's theory of heat and sound (1822/1825), January 24, 1979
Lecture 556, (Lecture two), Workless dissipation: Fourier's concepts of heat and its flux (1822), January 31, 1979
Lecture 558, (Lecture three), Dissipationless work: Carnot's ideas of heat and its capacity to do work (1824), February 14, 1979
Lecture 559, (Lecture four), Carnot's numerical calculations, his theory of specific heats, and his dilemma (1824), February 21, 1979
Lecture 560, (Lecture five), Equivalence, conservation, interconvertibility: When and of what? The assertions of Mayer (1842), Holtzmann (1845), and Helmholtz (1847);
Joule's early experiments (1845/1850); Kelvin's first "absolute temperature" and his fatal tables (1848/1949), March 7, 1979
Lecture 561, (Lecture six), Internal energy: The first paper of Clausius (1850), March 21, 1979
Lecture 562, (Lecture seven), Entropy: The first paper of Rankine (1850), April 4, 1979
Lecture 563, (Lecture eight), Kelvin's analysis of the "anomalous" behavior of water (1854). The disastrous effects of experiment upon the development of thermodynamics,
April 11, 1979
Lecture 564, (Lecture nine), Reech's return to first principles (1851); his discovery and burial of a too general theory, and his thermodynamic potentials (1853), April
18, 1979
Lecture 569, (Lecture ten), Kelvin's ideas on dissipations absolute temperature (1854); Clausius' absolute temperature and his surrender before irreversibility (1854),
May 9, 1979
Lectures 565-568, Conceptual analysis: Rational mechanics and infinitesimal calculus in the enlightenment (1690-1780), at the University of Chicago, under the auspices of the College, the
Department of Mathematics, and the Morris Fishbein Center for Study of History of Science and Medicine:
Lecture 565, Differential equations of motion: Generic principles and constitutive equations, April 30, 1979
Lecture 566, The wave equation: Trigonometric series, the concept of function, May 2, 1979
Lecture 567, Virtuosity: Convection of spin in fluids, proper numbers and bifurcation for elastic bands, May 3, 1979
Lecture 568, Leonard Euler, Supreme geometer (1707-1783), to the Department of Mathematics, University of Chicago, May 4, 1979
Lecture 570, Reflections of the history of thermodynamics upon teaching and research, Louvain-la-Neuve, June 5, 1979, Uppsala, June 7, 1979
Lecture 571A, Tradition and history in thermodynamics, to Society of Engineering Science, Evanston, IL, September 7, 1979
Return to the Table of Contents
Series 14 - Biographical and autobiographical material
86-31/36 Recollections of Truesdell written by his mother, Helen Truesdell Heath, in June 1968, and by Lucy Adams, his high-school teacher of mathematics in 1966, 1966-1968
Truesdell's recollections of his grandmother, Alice Feldman Walker
Miscellaneous autobiographical papers
3W111 Miscellaneous photographs [1921-1983]
86-31/36 Description of the products of his work at the Radiation Laboratory, M.I.T., 1944-1946, dated January 24, 1946
Main drawings produced under his direction at the Radiation Laboratory and his identification badge
86-31/37 Contents and abstracts of volumes of Truesdell's manuscript correspondence with Toupin, Ericksen, and Noll, the volumes themselves being still in his possession
Correspondence with the Bohr library, 1964-1984
Draft of the prospectus for books written and edited by Truesdell for Springer-Verlag, August 26, 1983
First and second proofs of books written and edited by Truesdell for Springer-Verlag, 1984
Hydro-mechanics, unpublished article by Paul Neményi which served as Truesdell's main introduction to continuum mechanics
86-31/38 Papers, memoranda, and notes, (excluding those by Truesdell) of the Theoretical Mechanics Subdivision, U. S. Naval Ordnance Laboratory, White Oak, Maryland, [Truesdell directed this
group], 1946-1948
Formal data, including vita, bibliography, and list of public lectures, 1984 and undated
Unrecorded lectures for which notes have been preserved, 1942-1951, and lectures, 1942-1984
List of Clifford Ambrose Truesdell III Papers prepared by Truesdell, used as basis for Archives of American Mathematics inventory
Return to the Table of Contents
Series 15 - Published works
[For publication numbers see list of published works in Box 39, folder 1]
86-31/39 List of published works
Abstracts, problems and queries
Three Lectures on Mathematics and Mechanics
Scientific papers, 1943-1950 (Bound volume)
Scientific papers, 1951-1953 (Bound volume).
86-31/40 Scientific papers, 1954-1956 (Bound volume)
Publication nos. 6, 7A, 9, 13P, 14P, 15, 16P, 19P, 22P, 23P, 24, 26L1, 29P, 32P, 35P
Publication nos. 43R, 44R, 48P, 64P, 72L, 72R, 73R
Publication nos. 76, 79L1, 79L1T, 79L3, 80T1, 80T2, 86, 87, 88, 89, 90, 91, 92, 93, 94
Publication nos. 95, 96, 97, 98, 98P, 98R, 99.
86-31/41 Publication no. 100
Publication nos. 101, 102, 104, 104P, 105, 106, 107P, 108, 109
Publication nos. 109TE, 110, 111A, 112, 113, 114, 115, 117, 117T, 118
Publication no. 119
Publication nos. 120, 120L, 120R1, 120R2, 121, 122, 123
Publication nos. 124, 125, 126, 126L, 127, 127T, 128, 128 addendum, 128 2nd addendum, 129, 130, 131, 131 corrections
86-31/42 Publication nos. 132, 133, 134, 135, 137, 138, 139, 140, 140TE, 141, 142, 143, 144, 144P1, 144P2, 144P2T, 144RE part 1, 146, 147
Publication nos. 148, 149, 150, 151, 152, 153T1, 153TE
Publication nos. 154L1, 154L2, 154L3, 154L4, 154L5, 154L6
Publication nos. 155, 156, 157, 158, 159, 160 & 161, 160C, 161, 162, 163, 163L1, 163L2, 163T
Publication nos. 164, 164T, 165P, 165TE, 166, 167, 168, 169
Publication nos. 170, 170T, 171, 172, 172A, 173, 174, 175, 176, 177, 178, 179, 180, 181, 181C, 184, 184T, 185, 185 corrections, 185A, 185T
Publication no. 186
86-31/43 Publication nos. 187, 188, 189, 190, 191, 192, 193, 194, 195
Publication no. 196
Publication nos. 197, 198, 199, 200, 201, 202, 202T, 203, 203A, 203PT, 203R, 204, 205, 207, 207L, 208, 209, 210
Publication nos. 212, 213A, 214, 215, 216, 217, 218, 219, 220, 221, 222
Publication nos. 223, 225P, 225RE, 226, 227A, 228 & 229, 230, 230A
Publication nos. 231, 232, 233, 234, 235, 236, 236T, 237, 238, 238T, 239, 240, 241, 242
Return to the Table of Contents
Series 16 - Additions
86-31/44 Materials connected with An idiot's fugitive essays on science, publication number 243, 1984:
Drafts of texts published only or finally in An idiot's fugitive essays, 1978-1981
Manuscript as sent to press, 1981 or 1982
Index of names mentioned in manuscript sent to press, 1981-1982
Artwork for manuscript, 1982-1983
86-31/OS1 Galley proofs and some revised galleys
First page proofs, autumn 1983
Second page proofs, early 1984
Third page proofs, partial, spring 1984
Fourth page proofs, partial, June 1984
86-31/44 Materials connected with the second printing, revised and augmented, 1987
"Great scientists of old as heretics in "The Scientific Method," the Page-Barbour Lectures at the University of Virginia, lectures number 657-659 and the book of the same title,
publication number 250
"What did Gibbs and Carathéodory leave us about thermodynamics?," lecture number 633, June 6, 1983, and publication number 247
"A third line of argument in thermodynamics," publication number 246, manuscript, revised manuscript, and four proofs, June 10, 1983
Miscellaneous originals and short manuscripts, 1983-1989
Materials connected with Rational thermodynamics second edition, publication number 244, 1984:
Historical introit:
Parts of lecture number 597, Atlanta, December 15, 1980, revised to make the first draft of the Historical introit
Second draft, (first complete manuscript), November 1982
Third draft, February 12, 1983
86-31/45 Third draft with corrections converting it to the fourth, summer 1983, and some later corrections of the fourth
Final manuscript for the printer (corrections made on the manuscript sent in March 1983), July 1983
Thermodynamics for beginners, second, third and fourth drafts, 1982
Preface and appendices to lecture eight, 1982-1983
Final entire typescript of Truesdell's own additions, (including above), 1983
Manuscript sent to press, 1983
86-31/OS2 Proofs:
Galley proofs
First page proofs
Second page proofs
Third page proofs
Plaque from the Society for Natural Philosophy, 1985
86-31/45 Debating letters won at Los Angeles High School, 1935-1936, freshman football numerals from Cal Tech, 1938, and high school pins, 1933-1936
Unpublished papers, rejected papers, original manuscripts of papers translated or mangled by editors, 1942-1967
Notes on research never completed from the period 1946-1970
Cancelled pages from the lectures on statistical mechanics, before 1958
Work on the design of piston rings done for Perfect Circle Corp., 1952-1955 on which is based publication number 118, 1961
Work on diffusion preparatory for Mechanical basic of diffusion, publication number 126, 1962
De pressionibus negativis in sinu et in pariete regionis fluido viscoso moventi impletae schedula, quam conscripsit C. Truesdell apud Universitatem Johns Hopkins Baltimorae et amico
mechanicoque illustrissimo B. Finzi ob diem natalem sepuagesimum dedicavit
86-31/46 Is there a philosophy of science?, [lecture?] numbers 417, 425, 459, 522, 1971-1972, 1976
Elementary thermodynamics, Georgia Institute of Technology, fall 1974
Draft of a projected joint book with S. Passman based on notes for Truesdell's course on elementary thermodynamics, Georgia Institute of Technology, fall 1974
Unfinished manuscript on frame indifference in the kinetic theory of gases
Manuscripts on Leonardo da Vinci
Leonardo da Vinci's studies of deformable bodies
Leonardo da Vinci's studies of deformable bodies,typescript of the first draft, December 1984 with corrections making the second, 1 985
Classical thermodynamics cleansed and cured, 1985, publication number 248 and the corrected and revised text of 1987, circulated in 1988-1989
Corrections for the reprinting of Elements of continuum mechanics, 1985
Review of The higher calculus: A history of complex analysis from Euler to Weierstrass by Umberto Bottazzini
On the vorticity numbers of monotonous motions, publication number 253, 1988
Maria Gaetana Agnesi (1718-1799)
Sophie Germain:
Drafts of the review of Bucciarelli and Dworsky's book "Sophie Germain," end of December 1981-spring 1982
Drafts of the review of Bucciarelli and Dworsky's book "Sophie Germain," late spring 1982
86-31/47 Drafts of the review of Bucciarelli and Dworsky's book, "Sophie Germain," summer 1983
Draft, June 1, 1984
Major revision begun December 21, 1984 and completed December 31 of that year, followed by revision of January 1985 for §5
Draft of March 1985 converted to that of April 1985 followed by revision of §6, 1987, and a further revision as a progress report on an NSF grant, March 1, 1989
Of what use is the history of the mechanical sciences? (A che serve la storia delle scienze matematiche?) Lecture for the 900th [?] anniversary of the University of Bologna, 1987
Editorial for the 100th volume of Archives for Rational Mechanics and Analysis, publication number 252
Notes and texts of lectures of 1986-1989 made the basis of papers still incomplete in 1989
List of reviews
Reviews, A-G, 1949-1971
Reviews, H-O, 1949-1971
86-31/48 Reviews, P-Z, 1949-1971
Black binder containing master copy of first edition, with corrections through May 1986
86-31/49 Loose sheets, in roughly chronological order, most recent on top, for sheets providing corrections and additions for "A First Course in Rational Continuum Mechanics," volume one,
second edition, and volume two, 1984-1989
Return to the Table of Contents
Series 17. Archive for History of Exact Sciences
2010-045/49 Letters to Oscar. B. Sheynin, 1971-1973
Return to the Table of Contents
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Airfoil Analysis
3D Wing Analysis
Follow Us
Science Graphs
Science Graphs is useful for algebra, trigonometry, calculus, physics, differential equations and engineering. It can also be used to graph up to 1,000 x-y data points from an ASCII file. Perpetual
In addition, the software allows you to solve differential equations, graph color contour curves of 2-dimensional data generated by equations and contour structured data saved as text License
files. It has a number of features for displaying the contour graph and the data grid. $49.
The following are standard features of Dr. Hanley's Science Graphs software.
• Graph Contour and Surface: Z = F(x,y)
• Graph Contour and Surface: Z = F(R, Th)
• Graph Contour and Surface from Disk File
• Graph Contour Plot of Pressure, Density, Velocity Data Defined on a Conforming (x,y) Grid.
• Display Contours and Grid Together
• Display Contours and Grid Independently.
• Display Wireframe Surface
• Display Smoothly Shaded Surface
• Numerically Solve and Graph: y' = f(x,y)
• Numerically Solve and Graph: y'' = f(x,y,y' )
• Numerically Solve and Graph: x' = f(x,y,t); y' = g(x,y,t)
• Numerically Solve and Graph: x'' = f(x,x',y,y',t); y'' = g(x,x',y,y',t)
• Enter and Graph Data Points with Built-in Editor
• Graph Data Points From Disk (up to 1000)
• Graph Data Points from Clipboard (up to 1000)
• Graph Equation: y = f(x)
• Graph Equation: x = f(t); y=g(t)
• Fit Data to a Straight Line
• Fit Data to a Polynomial (up to 20th Order)
• Compute Mean and Variance of X and Y Data
• Graph up to 100 Curves
• Delete Unwanted Curves
• Change Curve Colors and Symbols
• Change Background and Border Colors
• Change Label and Text Colors
• Add Text, Ovals, Rectangles and Arrows to your Graph
• Create Linear-Linear, Linear-Log, Log-Linear and Log-Log X-Y Axes
• Proportional Scaling; Circles are Circular & Squares are Square
• Automatic or Manual Scaling
• Zooming
• Export Data to a Disk File
• Copy Data to the Clip Board
• Export Graph to a .BMP File
• Copy Graph to the Clipboard so you can Import to Reports and Presentations
• Save Your Work for Later
Graphs of: x^3-x^2-3x-2 and Sin(6*x)
• Use the equation editor to create and graph polynomials and other nonlinear functions.
• Use the calculator tool to estimate the roots of functions.
• Use the calculator tool to estimate the (x) value of a graph for a given (y) value.
Graph of: x=Cos(th)*Sin(2*th); y=Sin(th)*Sin
• Use the equation editor to enter and graph sin, cos, tan and other trigonometric functions x. (2*th)
• Enter and graph parametric equations for x and y. For example, enter x=cos(th); y=sin(th) to graph the unit circle.
• Use the proportional scaling function to display circular circles and not oval circles.
Graphs of: Sin(x) and d(Sin(x))/dx
• Use the equation editor to enter and plot the derivative of an arbitrary function of x.
• Use the equation editor to enter and plot the integral of an arbitrary function of x.
• Use the calculator tools to integrate and differentiate graphed data points.
• Use the calculator tools to find the definite integral of a curve between two limits.
Ordinary Differential Equations
Solutions of: y''= y, y''=-.4y'-y
• Use the equation editor to enter and plot numerical solutions of first order non-linear ordinary differential equations of the form y'=G(x,y). and y''=-.8y'-y
• Use the equation editor to enter and plot numerical solutions of second order non-linear ordinary differential equations of the form y''=G
The following figures show the use of Science Graphs for graphing contours from arbitrary 2-Dimensional functions. Here, the application is aerodynamics, but the software can be used to plot contours
for equations for any discipline.
Doublet Flow: 1/R*Sin(Th) Circular Cylinder:-10*R*Sin(Th) + 1/R*Sin(Th)
Corner Flow: X*Y Vortex Near Wall: Ln((X^2+(Y-.502)^2/(X^2+(Y+.502)^2)))
3-Dimensional Surfaces
Science Graphs Plus can generate plots of 3-Dimensional surfaces entered as equations or data. The following are graphs of the equation Z=Cos(4*R).
Computational Fluid Dynamics (CFD)
Computation Fluid Dynamics
• Import and plot contour data on a conforming structured grid.
• Display various combinations of the grid and data.
• Use the equation editor to plot contours or 2-D functions in (x,y) or polar coordinates.
Pseudospectral solution of viscous flow past a circular cylinder.
Sale! Single Perpetual License: Price $49. Buy CD Online
ScienceGraphs Plus is also available as a component of the Aerodynamics Toolkit CD.
System Requirements
Dr. Hanley's Science Graphs requires a PC running under Windows XP, Vista, or Windows 7.
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PLEASE Help!!!
April 29th 2008, 04:54 PM #1
Apr 2008
PLEASE Help!!!
Calculate monthly mortgage payment
A=monthly mortgage payment
P=amount borrowed
r=annual interest rate(decimal)
n=the total number of monthly payments
5.5% interest
30 year mortgage
$100,000 amount borrowed
P(1+r/12)n x r/12
----------------- =A
(1+r/12)n -1
If you are not coming up with the right answer it's because r must be in decimal form. As a percent, numbers are automatically multiplied by 100 to obtain the percentage. Example: 3/4=.75=75%.
Therefore, 5.5% is actually equal to .055.
April 29th 2008, 05:31 PM #2
Mar 2008
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Verify Solution of Differential equation
August 29th 2011, 05:19 PM #1
Sep 2010
Verify Solution of Differential equation
Hello, i didn't know whether to post this in the calculus section but since its in my differential equations book I'll start here.
The problem asks to verify the indicated function is a answer of the differential equation.
My memory on the natural e is rusty. Any guidance? I feel like this should be easier than it looks.
Re: Verify Solution of Differential equation
$y = e^{-x^2}\left[\int_0^x e^{t^2} \, dt + c_1\right]$
product rule to find $\frac{dy}{dx}$ ...
$\frac{dy}{dx} = e^{-x^2} \cdot e^{x^2} - 2xe^{-x^2}\left[\int_0^x e^{t^2} \, dt + c_1\right]$
$\frac{dy}{dx} = 1 - 2xy$
$(1 - 2xy) + 2xy = 1$
Re: Verify Solution of Differential equation
Do you have to solve the integral? i used mathway for guidance and it gave me zero. Heres a link
Mathway: Evaluate the Integral
Re: Verify Solution of Differential equation
Since it's first order linear, you could solve the DE using the Integrating Factor.
$\displaystyle \frac{dy}{dx} + 2x\,y = 1$, the integrating factor is $\displaystyle e^{\int{2x\,dx}} = e^{x^2}$, so multiplying both sides of the DE by the integrating factor gives
\displaystyle \begin{align*}e^{x^2}\frac{dy}{dx} + 2x\,e^{x^2}y &= e^{x^2} \\ \frac{d}{dx}\left(e^{x^2}y\right) &= e^{x^2} \\ e^{x^2}y &= \int{e^{x^2}\,dx} + C_1 \\ y &= e^{-x^2}\int{e^{x^2}\,dx}
+ C_1e^{-x^2} \end{align*}
August 29th 2011, 05:45 PM #2
August 29th 2011, 07:51 PM #3
Sep 2010
August 29th 2011, 08:49 PM #4
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Pre-Algebra Homework Help
Many students of every level and every background have problems with their math. But you need to master this subject if you want to be able to pass your courses and leave with good grades. If you
have been set pre-algebra questions as an assignment and you are having problems with finding the right way to answer the questions what do you do? Where can you find pre-algebra homework help to
cover everything from creating pie charts, prime numbers, roman numerals and even pre-algebra formulas? Well the simple answer is you can come to us for all of your pre-algebra homework help and we
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Our tutors are not just going to furnish you with your pre-algebra homework answers; they are going to show you exactly how they have come to those answers so that the next time you are presented
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Every math question should always be answered showing your working if you want to be awarded the full marks. Our service will provide you with the clearest of working out enabling you to see step by
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Lift-off of a single particle in Newtonian and viscoelastic fluids by
Lift-off of a single particle in Newtonian and viscoelastic fluids by direct numerical simulation
N. A. Patankar, P. Y. Huang, T. Ko and D. D. Joseph
In this paper we study the lift-off to equilibrium of a single circular particle in Newtonian and viscoelastic fluids by direct numerical simulation. A particle heavier than the fluid is driven
forward on the bottom of a channel by a plane Poiseuille flow. After a certain critical Reynolds number the particle rises from the wall to an equilibrium height at which the buoyant weight just
balances the upward thrust from the hydrodynamic force. The aim of the calculation is the determination of the critical lift-off condition and the evolution of the height, velocity and angular
velocity of the particle as a function of the pressure gradient and material and geometric parameters. The critical Reynolds number for lift-off is found to be larger for a heavier particle whereas
it is lower for a particle in a viscoelastic fluid. The equilibrium height increases with the Reynolds number, the fluid elasticity and the slip angular velocity of the particle. Simulations of
single particle lift-off at higher Reynolds numbers in a Newtonian fluid show multiple steady states and hysteresis loops. This is shown to be due to the presence of two turning points of the
equilibrium height as a function of the Reynolds number. A general data structure for the interrogation of direct numerical simulations for information necessary for the evaluation of models of lift
is proposed.
Download files in:
Postscript, part 1 Postscript, part 2
Acrobat PDF
February 2000. Contact N.A. Patankar for questions about this article.
| AEM Home | Institute of Technology |
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NA Digest Sunday, August 9, 1993 Volume 93 : Issue 29
NA Digest Sunday, August 9, 1993 Volume 93 : Issue 29
Today's Editor:
Cleve Moler
The MathWorks, Inc.
Submissions for NA Digest:
Mail to na.digest@na-net.ornl.gov.
Information about NA-NET:
Mail to na.help@na-net.ornl.gov.
From: Daniel Okunbor <okunbor@sal.cs.uiuc.edu>
Date: Mon, 9 Aug 1993 14:53:36 -0500
Subject: Change of Address for Daniel Okunbor
I have taken up a teaching position at the Univesity of Missouri-Rolla
effective August 3rd. My current address is
Daniel Okunbor
University of Missouri-Rolla
Rolla, MO 65401
e-maill address: okunborkmcs213k.cs.umr.edu
From: Stephen Vavasis <vavasis@cs.cornell.edu>
Date: Fri, 6 Aug 93 11:31:54 -0400
Subject: Numerical Analysis Ideas in Science Magazine
This week's Science magazine (30 July 1993, pp 578-584) contains an
article about pseudospectra in fluid flows. "Science" and its British
counterpart "Nature" rarely publish articles about applied mathematics,
so this event may be of interest to NA digest readers.
The article, "Hydrodynamic Stability Without Eigenvalues", by L. N.
Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, proposes
a new way to analyze the transition from stable steady-state laminar
flow to unstable flow. Both Trefethens, as well as Driscoll, are at
Cornell, and Reddy just recently moved from NYU to Oregon State.
A key point of the article is that the Navier-Stokes equations, when
linearized around the steady-state flow, have highly nonorthogonal
eigenvectors. This means that the eigenvalues -- which are crucial to
traditional stability analyses -- are ill-conditioned and perhaps tell
the wrong story about local perturbations.
The connection between nonorthogonal eigenvectors and ill-conditioned
eigenvalues is well-known to numerical analysts but perhaps not to the
larger scientific community. This article is a great example of
spreading knowledge from within our community to the world at large.
From: L. M. Delves <delves@liverpool.ac.uk>
Date: Tue, 3 Aug 93 9:31:34 BST
Subject: Formation of Institute of Advanced Scientific Computation
Liverpool University has recently set up the Institute of Advanced
Scientific Computation. This represents a merger of two previous
Research Centres: Center for Mathematical Software Research; and
North West Transputer Support Centre.
The Institute (IASC) has interests in all areas of technical computing, but
especial expertise and interest in MIMD parallelism. Current projects include:
1) Development of Distributed Data Library
2) Algorithms and software for oil reservoir simulation
3) Parallel database software for diagram retrieval
4) Temperature sensing for induction heating strip mill
5) Development of Fortran90 compiler
6) Development of HPF Fortran source-source translator
7) Parallelisation of codes for SAR processing, and Forging
All of these projects are collaborative with external sites/organisations.
The Institute has an active Visitor, and Postgraduate Teaching, program.
Here are some requests:
1) If you would like any info, mail me at
or the institute at
2) If your activities overlap ours, please put us on your email list for
circulation of whatever: iasc@liverpool.ac.uk
We are especially interested in collaboration with European and US sites.
3) Drop in and see us some time.
From: Robert I McLachlan <rxm@vortex.Colorado.EDU>
Date: Tue, 3 Aug 93 14:08:38 -0600
Subject: Two Preprints on the Numerical Integration of ODE's
Keywords: Lie-Poisson systems, Hamiltonian systems, symplectic integrators,
composition methods, operator splitting.
Postscript versions of the following papers are available by anonymous
ftp from newton.colorado.edu (128.138.249.1), directory pub/numerics/papers,
files sine.ps.Z and composition.ps.Z.
Please direct comments to the author at rxm@boulder.colorado.edu.
"Explicit Lie-Poisson integration and the Euler equations"
We give a wide class of Lie-Poisson systems for which explicit, Lie-Poisson
integrators, preserving all Casimirs, can be constructed. The methods are
extremely simple. Examples are the rigid body, a moment truncation,
and a new, fast algorithm for the sine-bracket truncation of the 2D Euler
"On the numerical integration of ordinary differential equations
by symmetric composition methods"
Differential equations of the form $\dot x=X=A+B$ are considered, where
the vector fields $A$ and $B$ can be integrated exactly, enabling
numerical integration of $X$ by composition of the flows of $A$ and
$B$. The relationships between various symmetric compositions
currently in use are investigated with regard to order, complexity, and
reversibility. Simple formulae are given for the number of determining
equations which must be solved for a method to have a particular order.
A new, more accurate way of applying the methods thus obtained to
compositions of an arbitrary first-order integrator is described and
tested. The determining equations are thoroughly explored, and new
methods up to 100 times more accurate (at constant work) than those
previously known are given.
Robert McLachlan
From: Alfred Gautschy <puls@cvxastro.MPA-Garching.MPG.DE>
Date: Thu, 5 Aug 93 19:09:49 +0200
Subject: A Difficult BEVP in Astrophysics
Numerical Methods for a Difficult BEVP in Astrophysics
In the following I describe shortly a problem in stellar astrophysics
I am working with for years now. I wonder if there is anything better
we can do for its solution than what we are applying presently.
I am sure the na-community would know best.
In stellar stability theory we usually have to solve a system
of four or six first-order linear differential equations, that,
together with suitable boundary conditions, constitutes the
boundary-eigenvalue problem. The domain of the independent
variable extends from 0 to 1, with the system having a regular
singularity at 0. Formally we can bring the system of
equations into the form:
d Y
x --- = A * Y (1)
d x
where Y is a complex vector with 4 or 6 components and A is a
4X4 or 6X6 matrix with complex coefficients. The eigenvalues
(normal modes of the system) enter the matrix A in two components
nonlinearly. The components of the matrix A are strongly varying between
x = 0 and x = 1 and the values of the components are known only
at a few hundred discrete points between 0 and 1. Furthermore, matrix A
has no patricular symmetry properties.
We are typically interested in the lowest few dozen eigen-solutions.
For particular stellar problems we have to extract high overtones,
but again only a few dozen of them.
For some time the BEVP was solved with finite difference methods
which, however, are pretty cumbersome due to the approximate solutions
which have to be guessed. Often the eigenfunctions are rapidly oscillating
in space, and that is something one cannot know ahead.
Another method we try for a few years now is the transformation of the
BEVP into an initial-value problem of Riccati type, which is then
solved by means of a shooting method and fitting the solutions by
adapting the eigenvalue. Due to the singularities of the Riccati equation
on the path of integration one has to transform to the inverse Riccati
form rather frequently which makes the calculations rather expensive.
My question is now, are there methods around that allow for the calculation
of eigenfrequencies and eigenvectors of a BEVP of the type (1) that
do not need any a priori guesses of the approximate solution and
do (hopefully) not need supercomputers for their application.
Is there anything like a generalized matrix eigenvalue method that
works for systems?
For any informtation concerning improvements a e-mail note would be
highly appreciated.
Kind regards
Alfred Gautschy
Max-Planck-Institut fuer Astrophysik
85748 Garching/Germany
From: Gustavo Montero Garcia <gustavo@titan.ulpgc.es>
Date: Fri, 6 Aug 93 11:54:06 +0100
Subject: Pollution & preconditioners
I'll be so grateful if you send me some information about the
following subjets:
Modelling the pollution phenomena by finite element method in:
- Atmosphera
- Groundwater
- Seawater
Fast preconditioners for solving linear and non linear systems
of equations.
Thank you.
Gustavo Montero Garcia
Prof. Tit. U.
Centro de Aplicaciones Numericas en Ingenieria CEANI
Universidad de Las Palmas de Gran Canaria
Campus de Tafira Baja
35017 Tafira ( Las Palmas de Gran Canaria)
Islas Canarias -Espa~na-
Tf.: + 34 28 451 917
FAX.: + 34 28 451 921
E-mail: gustavo@titan.ulpgc.es
From: Nick Higham <higham@vtx.ma.man.ac.uk>
Date: Fri, 6 Aug 93 14:44:16 +0100 (BST)
Subject: New Book ``How To Teach Mathematics''
The American Mathematical Society has just published a book called
``How To Teach Mathematics: A Personal Perspective'' by
Steven G. Krantz. While the book is not directly concerned with teaching
numerical mathematics, I think it will be of interest to many NA-Digest
readers. In 76 pages Krantz gives much valuable advice based on his
twenty years experience of teaching. Among the topics he covers are
- preparation of lectures
- blackboard technique
- how to deal with student questions
- how to deal with student complaints
- handling large classes
- setting homework and exams, and grading
- use of computers in teaching (he prefers traditional pen and paper
As Krantz says, ``this is a book about the obvious'', but the obvious
can be suprisingly easy to overlook and much of the advice proffered
here is often learned the hard way, by making mistakes.
The book contains many informative examples and entertaining
anecdotes, a quote from Bereseford Parlett, and advice from Paul
Halmos on how to teach the Fundamental Theorem of Algebra.
Every beginning mathematics lecturer will benefit from reading this
book. I recommend it to anyone who wants to improve their teaching
author = "Steven G. Krantz",
title = "How To Teach Mathematics: {A} Personal Perspective",
publisher = "American Mathematical Society",
address = "Providence, RI",
year = 1993,
isbn = "0-8218-0197-X"
Nick Higham
Department of Mathematics
University of Manchester
From: I. G. Graham <I.G.Graham@maths.bath.ac.uk>
Date: Fri, 6 Aug 93 20:07:40 +0100 (BST)
Subject: Finite Element Error Analysis
Dear Colleagues,
Can anyone help me with the following technical question about finite element
error analysis?
Let Omega be a bounded convex polygonal domain in the plane.
Triangulate Omega with a sequence of meshes which are regular in the sense of
Ciarlet's book (1978), and which are parametrised by the mesh diameter h.
For each h, let a_h be a continuous function on Omega which is
smooth in the interior of each triangle of the mesh.
Moreover assume that a_h is bounded above and below on Omega by
positive constants which are independent of h.
Consider (in weak form) the linear elliptic problem
- div [(a_h) grad u] = f,
which is to be solved for the scalar function u subject to mixed Dirichlet-
Neumann boundary conditions, with the Dirichlet part of the boundary having
non-trivial measure . The given function f and the given Dirichlet and
Neumann data are smooth and independent of h. Let u_h be the solution of
this problem by the standard finite element method.
Standard arguments then show that u_h is bounded independently of h in
the W^1_p norm when p = 2.
I am interested in proving the same property for some p > 2 (*)
(I wouldn't mind if p had to be arbitrarily close to 2.)
This property of finite element approximation was proved for the Dirichlet
problem for Laplace's equation by Rannacher and Scott (Math Comp 38, 1982).
By the Sobolev Embedding theorem the result (*) implies the slightly weaker
result that the uniform norm of the finite element solution is bounded
independently of h. There are many results around along these lines
e.g. Schatz and Wahlbin (Math Comp 38, 1982) or Suzuki and Fujita
(Numer Math 49, 1986). Again Schatz and Wahlbin (and many other authors)
considered only Laplace's equation, but Suzuki and Fujita proved their
result for quite general coefficients a which could be discontinuous but
which were independent of h. Both Schatz and Wahlbin and Suzuki and Fujita
considered only the Dirichlet problem.
These are the closest results I have found to (*). I have looked through
all issues of Math Comp, Numer Math and SIAM JNA since 1985 but have not
found anything else. I may of course have missed it. Can anyone help with
a reference or an opinion please?
Note that I do not care about convergence of finite element solutions, only
boundedness independent of h. I am also interested in the analogous result
but with a_h discontinuous across triangle boundaries.
Many thanks in advance,
Ivan Graham
School of Mathematical Sciences
University of Bath
Bath BA2 7AY
United Kingdom
email: igg@maths.bath.ac.uk
fax: (+44 225) 826492
From: Jorge More <more@mcs.anl.gov>
Date: Mon, 2 Aug 93 17:18:22 CDT
Subject: Postdoctoral Research at Argonne National Laboratory
Postdoctoral Research
Mathematics and Computer Science Division
Argonne National Laboratory
The Mathematics and Computer Science Division of Argonne National
Laboratory invites applications for a postdoctoral research position.
The successful candidate will help develop a parallel environment for
solving large-scale numerical optimization problems.
A strong background in numerical optimization and
tool development for scientific computing applications is desirable.
Nominal requirements include a Ph.D. in applied mathematics,
computer science, applied science, or engineering.
This project is interdisciplinary in nature, interfacing with efforts
in linear algebra, computational differentiation, parallel computing
tools, and large-scale simulation of physical processes.
Project members have access to state-of-the art computing facilities,
including the IBM SP1 and the Intel Touchstone DELTA.
Argonne is located in the southwestern Chicago suburbs, offering the
advantages of affordable housing and good schools, as well as easy
access to the cultural attractions of the city.
Applicants must have received their Ph.D. not more than three
years prior to the beginning of the appointment.
Applications must be addressed to
Walter McFall, Box mcs-postdoc, Employment and Placement,
Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439,
and must include a resume' and the names and addresses of three
references. For further information, contact
Jorge More' (708-252-7238; more@mcs.anl.gov).
Argonne is an affirmative action/equal opportunity employer.
From: Tony Skjellum <tony@Aurora.CS.MsState.Edu>
Date: Mon, 2 Aug 93 22:09:09 CDT
Subject: Scalable Parallel Libraries Conference
*** SECOND ANNOUNCEMENT + CALL FOR POSTERS ***
Scalable Parallel Libraries Conference
(including Multicomputer Toolbox Developers' & Users' Meeting)
October 6-8, 1993
National Science Foundation Engineering Research Center
for Computational Field Simulation,
Mississippi State, Mississippi
More information: Request from scl-conf@cs.msstate.edu OR
anonymous ftp announcement: aurora.cs.msstate.edu
directory: pub/SCL, files: SCL.2, Registration_Form
Deadline for posters extended to August 15 (please see files on anonymous ftp).
* Charles L. Seitz, Caltech, [KEYNOTE ADDRESS]
Title: High-Performance Workstations + High-Speed LANs >= Multicomputers
* Milo R. Dorr, LLNL
Title: "A Concurrent, Multigroup, Discrete Ordinates Model of Neutron
* David Walker, ORNL
Title: "The design of scalable linear algebra libraries for concurrent
* David Womble, Sandia ALBQ
Title: "Out of core, out of mind: making parallel I/O practical".
* Dan Quinlan, LANL
Title: "Run-time Recognition of Task Parallelism Within the P++
Parallel Array Class Library
* Steven Smith, LLNL
Title: "High-Level Message-Passing Constructs for Zipcode 1.0:
Design and Implementation"
* Robert Falgout, LLNL
Title: "Modeling Groundwater Flow on Massively Parallel Computers"
* Anthony Skjellum, MSU/NSF ERC
Title: "The Multicomputer Toolbox: Current and Future Directions,"
* William Gropp, Argonne National Laboratory
Title: TBD
* Ewing Lusk, Argonne National Laboratory
Title: "The MPI Communication Library: Its Design and a Portable
* Charles H. Still, LLNL
Title: "The Multicomputer Toolbox: Experiences with the Meiko CS-2".
* S. Lennart Johnsson, Harvard University and Thinking Machines Corp.
Title: "Scientific Libraries on Scalable Architectures"
* Linda Petzold, AHPCRC & UMN
Title: Solving Large-Scale Differential-Algebraic Systems via DASPK
on the CM5
* Dan Reed, UIUC
Title: TBD
* Dan Meiron, Caltech
Title: "Using Archetypes to Develop Scientific Parallel Applications"
* Eric F. Van de Velde, Caltech
Title: Stepwise Program Refinement in Concurrent Scientific Computing
* Padma Raghavan, UIUC/NCSA
Title: Parallel Solution of Linear Systems using Cholesky Factorization
* Anna Tsao, SRC
Title: "Performance of a Parallel Eigensolver Based on the Invariant
Subspace Decomposition for Dense Symmetric Matrices."
* Steve Lederman, SRC
Title: "Comparison of Scalable Parallel Matrix Multiply Libraries"
* Chuck Baldwin, UIUC
Title: "Dense and Iterative Concurrent Linear Algebra in the
Multicomputer Toolbox"
* Nikos Chrisochoides, NPAC Syracuse
Title: "An alternative to data-mapping for scalable iterative PDE
solvers : Parallel Grid Generation"
* Sanjay Ranka, NPAC Syracuse
Title: "Scalable Libraries for High Performance Fortran"
* Anthony Skjellum, MSU/NSF ERC
Title: "Building Parallel Libraries using MPI"
From: John Gregory <jwg@db.cray.com>
Date: Tue, 3 Aug 93 09:05:08 CDT
Subject: Call For Votes: sci.op-research
Perhaps most na-net readers have seen this announcement, but for
those few who have not, I send this copy of what appeared recently
on the Usenet group sci.math.num-analysis.
regarding the proposed creation of the unmoderated newsgroup sci.op-research
Votes must be received by 2359 GMT on Sunday 22nd August 1993.
This Call for Votes will also be sent to the following mailing lists:
ORCS-L (ORCS-L@OSUVM1) and msys@bass.bu.edu
The main purpose of this group is to act as the umbrella group from
which different operations research interest groups will branch off in
the future, as envisioned by the technology committee of the ORMS
In the interim, the newsgroup will support the RESEARCH, APPLICATION
and TEACHING of operations research through the exchange of information
through various activities including:
-- Posting information about accepted papers
-- Asking questions and posting summaries of replies
-- Posting Frequently Asked Questions (FAQ) and other lists such as
-Ajay Shah's list of Free C/C++ programs for numerical methods
-Arthur Geoffrion's list of mail reflectors relevant to O.R.
-John Gregory's FAQ on LP
Those interested in a particular area could bring out regular FAQs
answering questions or likely questions from those new to their
-- Posting information about ARCHIVES (e.g. those at Rutgers,
-- Sharing teaching approaches
-- Announcement of new textbooks; Discussion on existing textbooks
-- New product announcements
-- Users' impressions of commercial software (No advertisements.)
-- JOB announcements in universities and industry
The group will be UNMODERATED.
Newsgroups line:
sci.op-research Operational Research
Cut this out this ballot form, fill in your name and delete the
choices that aren't applicable. Send it to iwj-vote@cam-orl.co.uk.
If your software honours Reply-To lines you can just reply to this
message (please trim the message down, though, if you do it by
quoting; I don't need a copy of the whole CFV!).
My name is:
My vote on sci.op-research: yes/no/abstain
End of ballot
The line with your name is mandatory. Do not insert any blank lines.
Votes posted to newsgroups or mailed to anyone except the vote taker
will not be counted. Votes for a group with a different name to that
shown above will likewise not be counted.
You will receive an acknowledgement of your vote by email; A mass
acknowledgement will be posted during the voting period; at the end of
the voting period a complete list of votes will be published.
You may only vote once and only from one address, if you have several.
The end of the voting period is specified at the top of this CFV.
This vote is being conducted by Ian Jackson <iwj@cam-orl.co.uk>, a
neutral third party, with possible assistance from Ron Dippold
Please contact iwj@cam-orl.co.uk if you have any questions about the
voting procedure or about particular votes.
Please contact the proposer, Mohan Sodhi <msodhi@agsm.ucla.edu>, if
you have questions about the proposed group.
Mohan Sodhi is grateful to the following, and to others, too numerous
to mention, for their constructive comments and encouragement: (In
alphabetical order by 1st name):
Arthur Geoffrion, Chris Bullen, Craig Willits, David Lawrence, James
Bean, Lester Ingber, Mark Moraes, Matthew Saltzmann, Ramesh Sharda,
Ron Dippold, Scott Huddleston, Taner Bilgic.
Ian Jackson iwj@cam-orl.co.uk ...!uknet!cam-orl!iwj
acting as vote taker for sci.op-research under the auspices of UVV.
These opinions are not necessarily those of Olivetti Research Ltd.
From: Bob Geller <bob@global.geoph.s.u-tokyo.ac.jp>
Date: Wed, 4 Aug 93 22:14:23 JST
Subject: Postdoc Opportunity in Japan and Preprint Offer
Greetings from Japan!
The main purpose of this email is to inform you about the opportunities
available to be a post-doc in Japan, and to ask you to call this to
the attention of anyone who's interested. Naturally, I'd especially
like to have inquiries from people interested in working with our
group at Tokyo University.
The following papers give an idea of what we're now working on. If
you'd like a preprint let me know, and I'll be happy to mail one
to you. The following are our recent papers that are now in the
(1) Hara, T., S. Tsuboi and R. J. Geller (1993). Inversion for laterally
heterogeneous upper mantle S-wave velocity structure using iterative waveform
inversion, Geophys. J. Int., in press.
(2) Geller, R. J. and T. Hara (1993). Two efficient algorithms for iterative
linearized inversion of seismic waveform data,
Geophys. J. Int., in press.
(3) Geller, R. J. and T. Ohminato (1993). Computation of
synthetic seismograms and their partial derivatives for heterogeneous media
with arbitrary natural boundary conditions using the Direct Solution
Method, Geophys. J. Int., in press.
(4) Hara, T. and R. J. Geller (1993). Anamolously large near-field
Rayleigh waves excited by the 1992 Landers, California, earthquake,
Bull. Seism. Soc. Am., submitted.
Obviously I'd be most interested in hearing from people who'd like
to work on the above topics, or topics closely related thereto.
But this is by no means an absolute requirement.
The Japan Society for the Promotion of Science (JSPS) Postdocs pay Y270,000
per month (tax free) with an extra housing stipend of up to Y100,000 per
month. One round trip air ticket is also provided. There is a one-time
settling-in allowance of Y200,000, as well as other gooodies (family allowance,
health insurance, Japanese language training, research funds, etc.).
The current exchange rate is Y104= $1 US (approx).
Tenure of appointment is 12 months, with a possibility of renewal for up to
12 additional months.
Citizens of almost any country are eligible. In many cases you can apply
through your country's own agency (e.g., NSF in the case of the US)
rather than through me to the JSPS. But in any case you need to have
an agreement with the host researcher in Japan before proceeding further.
For additional information contact:
Bob Geller (bob@global.geoph.s.u-tokyo.ac.jp). FAX +81-3-3818-3247
TEL +81-3-5800-6973
Address: Dept. of Earth&Planetary Physics, Faculty of Science,
Tokyo University, Bunkyo-ku, Tokyo 113 JAPAN
Please send publication list, c.v., names of three references (letters
are not necessary at this point), and reprints or preprints of three
recent papers.
Please hurry if you're interested. The deadline may be coming up soon.
(It varies from country to country).
Phil Cummins was a JSPS fellow in our lab from Feb. '92 to April '93. He's
kindly agreed to describe his experiences, and answer questions, for anyone
who's interested. He's now at ANU in Canberra. You can contact him at:
From: Karen Hahn <khahn@cs.rutgers.edu>
Date: Mon, 9 Aug 93 15:16:38 EDT
Subject: IMACS Workshop on Turbulence
First Announcement/ Call for Participation
IMACS WORKSHOP ON (theoretical and computational aspects of) TURBULENCE
Rutgers University, New Brunswick, NJ, USA / February 10-11, 1994
(organized by the IMACS Technical Committee
on Computational Fluid Dynamics and Rutgers University)
In order for CFD to get to new levels of usefulness to industry, there
is a need for better turbulence models for high Re flows. An honest
appraisal by industry on needs, and a similar word by academia and
researchers at national labs on what can be done now is probably
necessary. The workshop will deal with the numerical analysis and CFD
algorithms that could bridge the gap, and will include those aspects
of turbulence theory that have relevance to modeling used in
simulation. Topics to include: Modeling, Non-equilibrium
Turbulence, Sprectral and High Order Methods, Adaptive Grids,
Lagrangian Methods, Ocean Dynamics. It is currently planned to have
proceedings published after the workshop; preparing a written paper
for these proceedings is, however, optional.
Organizing Committee: Prof. R. Pelz (Rutgers University)
Dr. R. Agarwal (McDonnell Douglas Aerospace)
CALL FOR PAPERS/CALL FOR SESSIONS: Those wishing to contribute a paper,
or to organize a session are invited to make themselves known to the
Workshop Committee as soon as possible.
Mail to: IMACS Turbulence Workshop
c/o IMACS Secretariat
Department of Computer Science
Rutgers University e-mail: imacs@cs.rutgers.edu
New Brunswick, NJ 08903, USA fax: 908-932-0537
From: Richard Brualdi <brualdi@math.wisc.edu>
Date: Wed, 4 Aug 1993 14:52:13 -0500 (CDT)
Subject: Contents, Linear Algebra and its Applications
Contents Volume 191
Song Xu (Beijing, People's Republic of China)
Notes on Sufficient Matrices 1
Irving S. Reed (Los Angeles, California)
Generalized de Moivre's Theorem, Quaternions, and Lorentz
Transformations on a Minkowski Space 15
David E. Stewart (St. Lucia, Queensland, Australia)
An Index Formula for Degenerate LCPs 41
Robert E. Hartwig (Raleigh, North Carolina)
The Pyramid Decomposition and Rank Minimization 53
Ali H. Sayed, Hanoch Lev-Ari, and Thomas Kailath
(Stanford, California)
Fast Triangular Factorization of the Sum of Quasi-Toeplitz
and Quasi-Hankel Matrices 77
Bernd Fritzsche, Stefan Fuchs, and Bernd Kirstein
(Leipzig, Bundesrepublik Deutschland)
Schur-Sequence Parametrizations of Potapov-Normalized
Full-Rank jpq-Elementary Factors 107
Han H. Cho (Seoul, Korea)
Regular Matrices in the Semigroup of Hall Matrices 151
Miroslav Fiedler (Prague, Czech Republic) and Thomas L. Markham
(Columbia, South Carolina)
Quasidirect Addition of Matrices and Generalized Inverses 165
B. Najman (Zagreb, Bijenicka, Croatia) and Q. Ye (Winnipeg,
Manitoba, Canada)
A Minimax Characterization for Eigenvalues of Hermitian Pencils. II 183
Jiu Ding (Hattiesburg, Mississippi)
Perturbation Analysis for the Projection of a Point to an Affine Set 199
M. T. Alcalde, C. Burgueno (Casilla, Temuco, Chile) and
C. Mallol (Montpellier, France)
Les Pol(n, m)-Algebres: Indentites Polynomiales Symetriques
dans des Algebres 213
S. Gonzalez and C. Martinez (Zaragoza, Spain)
Bernstein Algebras With Zero Derivation Algebra 235
Eugene Seneta (Sydney, Australia)
Explicit Forms for Ergodicity Coefficients of Stochastic Matrices 245
Author Index 253
End of NA Digest
|
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|
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Find a Needham Heights Math Tutor
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|
Moment Generating Functions
May 9th 2012, 07:51 AM
Moment Generating Functions
So, the moment generating function of a random variable is a quick way to derive moments of the random variable through taking multiple derivatives and evaluating at t = 0.
Is there ever an instance where you would evaluate it at some t other than 0? What is the significance of doing so?
EDIT: I guess the I have the same question for joint distributions as well... I'm guessing they have similar significance but clearly the joint probabilities are a litttttle bit more complicated.
May 9th 2012, 11:40 PM
Re: Moment Generating Functions
Think of the mgf as a sum, like here : Moment-generating function - Wikipedia, the free encyclopedia (the formula with 1+tm1+tēm2/2...). If you differentiate with respect to t, you'll get
m1+tm2+... and so on. So if you don't set t=0, you'll have a residue that won't make you get the moments.
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|
A Moment of Zen
Note: This is a repost from an old weblog.
Like Binary Insertion Sort, Merge Sort is a recursive algorithm, but Merge Sort is O(n lg n) whereas Binary Insertion Sort had been O(n^2). It works by splitting up the set into halves until each set
is down to 1 item. It then merges them back together again in sorted order. It's a very simple concept although a bit hard to explain in words. Allow me to illustrate instead:
Given: [6 8 1 3 7 2 5 4]
The first thing we do is split this set in half:
[6 8 1 3] [7 2 5 4]
We keep splitting in half until we can't split anymore:
[6 8] [1 3] [7 2] [5 4]
[6] [8] [1] [3] [7] [2] [5] [4]
We now merge the items back into their previous sets in sorted order:
[6 8] [1 3] [2 7] [4 5]
And again:
[1 3 6 8] [2 4 5 7]
And again:
[1 2 3 4 5 6 7 8]
Not so bad, right? So how do we implement this? Well, breaking the sets into halves is fairly straight forward so I won't bother explaining that. The “hard” part is the merging, and even that's not
so hard. Let me illustrate step by step how we merged 2 sets back into a single set:
set #1: [2 7]
set #2: [4 5]
We start by comparing the first item in each set. Is 2 less than 4? Yes, so we put 2 into our “merged” set:
set #1: [7]
set #2: [4 5]
merged: [2]
Now compare 7 and 4. Since 4 is less than 7, we append 4 into our merged set:
set #1: [7]
set #2: [5]
merged: [2 4]
Now compare 7 and 5. Since 5 is less than 7, we append 5 into our merged set:
set #1: [7]
set #2: []
merged: [2 4 5]
Since set #2 is out of items, we just append the remainder of set #1 into our merged set:
merged: [2 4 5 7]
As you can probably see, it looks like we'll need a temporary array to hold our merged set as we merge the 2 subsets back together. If we want to keep to the same API we've been using for the
previous sorting routines, we'll need a second function that will do most of the work. Since we know we'll never need our temporary array to be larger than the original input array, we might as well
create it in our main function and pass it off to our recursive worker function:
MergeSort (int a[], int n)
int *b;
if (!n || !(b = malloc (sizeof (int) * n)))
msort (a, b, 0, n - 1);
free (b);
As you can see here, I called my worker function msort(), which takes as input the original array, the temporary array (b[]), the offset of the first item, and the offset of the last item. Now let's
take a look at msort()'s implementation:
static void
msort (int a[], int b[], int lo, int hi)
register int h, i, l;
int mid;
if (lo >= hi)
mid = lo + ((hi - lo) / 2);
msort (a, b, lo, mid);
msort (a, b, mid + 1, hi);
for (i = 0, l = lo, h = mid + 1; l <= mid && h <= hi; i++) {
if (a[l] <= a[h])
b[i] = a[l++];
b[i] = a[h++];
while (l <= mid)
b[i++] = a[l++];
while (h <= hi)
b[i++] = a[h++];
memcpy (a + lo, b, sizeof (int) * i);
You'll notice that the first thing we do is find the midpoint of our set starting with lo and ending with hi. We then call msort() on each of the 2 resulting subsets (lo to mid, and mid + 1 to hi).
After msort() is finished with each of those subsets, the 2 subsets will be in sorted order and will be stored back in array a[] at positions lo through mid and mid + 1 through hi.
We then need to merge the 2 subsets back together again into a sorted set starting at position lo and ending with position hi. We'll use i to represent the next position to add an item into our
temporary array, b[]. We'll use l and h to represent the cursor for each of the subsets (l for low and h for high). Notice that I check a[l] <= a[h] rather than a[l] > a[h], this is so that items
with the same value in the array are in the same order they were in originally. For integer arrays, this is no big deal – but it is often a preferred feature when sorting arrays of custom data.
Sorting algorithms that have this property are called “stable sorts”.
The for-loop merges 1 item from one of the 2 subsets into the temporary array until one of the subsets becomes empty. At this point, one of the 2 while-loops will be executed, appending the remainder
of the non-empty set to the merged set.
Now that we've merged the 2 subsets back together into our temporary array, b[], we need to copy the result back into a[] at the subrange we started with.
And there you have it.
Since I'm sure you're as anxious to find out how fast this is compared to our previous sorts for sorting 100,000 items as I am, let's give it a whirl and find out. Wow, that was fast – it averaged
0.044s for sorting that 100,000 item array of random integers. That's the fastest time yet! Now that we have such a fast algorithm for sorting, we'll need to bump up our array size in order to
compare further sorting algorithms. Let's go for 10,000,000. This time I get 6.344s which is still faster than most of our previous sort algorithms at 100,000 items!
The first optimization I see is that we could replace those while-loops with memcpy()'s. Turns out, that doesn't really change the results for our particular input (it might make a difference if the
majority of values of one set or the other was larger than those in the other, but this wouldn't be the case for our input).
To learn more about sorting, I would recommend reading Art of Computer Programming, Volume 3: Sorting and Searching (2nd Edition)
Update: I've written a follow-up article on Optimizing Merge Sort that may be of interest as well. This follow-up article deals with optimizing a general-purpose Merge Sort implementation to be on
par with the libc qsort() function.
Note: This is a repost from an old weblog.
The Shell Sort algorithm is designed to move items over large distances each iteration. The idea behind this is that it will get each item closer to its final destination quicker saving a lot of
shuffling by comparing items farther apart.
The way it works is it subdivides the dataset into smaller groups where each item in the group is a set distance apart. For example, if we use h to represent our distance and R to represent an item,
we might have groups: { R[1], R[h+1], R[2h+1], ... }, { R[2], R[h+2], R[2h+2], ... }, ...
We then sort each subgroup individually.
Keep repeating the above process, continually reducing h, until h becomes 1. After one last run-through where h is a value of 1, we stop.
At this point, I'm sure you are wondering where h comes from and what values to reduce it by each time though. If and when you ever figure it out, let me know - you might also want to publish a paper
and submit it to ACM so that your name might go down in the history (and algorithm) books. That's right, as far as I'm aware, no one knows the answer to this question, except, perhaps, God Himself
If you are interested, you might take a look at Donald Knuth's book, Art of Computer Programming, Volume 3: Sorting and Searching (starting on page 83), for some mathematical discussion on the
As far as I understand from Sorting and Searching, it is theoretically possible to get the Shell Sort algorithm to approach O(n^1.5) given an ideal increment table which is quite impressive.
Knuth gives us a couple of tables to start with: [8 4 2 1] and [7 5 3 1] which seem to work okay, but are far from being ideal for our 100,000 item array that we are trying to sort in this exercise,
however, for the sake of keeping our first implementation simple, we'll use the [7 5 3 1] table since it has the charming property where each increment size is 2 smaller than the previous. Yay for
ShellSort (int a[], int n)
int h, i, j;
int tmp;
for (h = 7; h >= 1; h -= 2) {
for (i = h; i < n; i++) {
tmp = a[i];
for (j = i; j >= h && a[j - h] > tmp; j -= h)
a[j] = a[j - h];
a[j] = tmp;
The nice thing about Shell Sort is that, while the increment table is a complete mystery, the algorithm itself is quite simple and well within our grasp.
Let's plug this into our sort program and see how well it does.
I seem to get a pretty consistent 6.3 seconds for 100,000 items on my AMD Athlon XP 2500 system which is almost as good as the results we were getting from our Binary Insertion Sort implementation.
Now for some optimizations. We know that an ideal set of increment sizes will get us down to close to O(n^1.5) and that it is unlikely that the [7 5 3 1] set is ideal, so I suggest we start there.
On a hunch, I just started adding more and more primes to our [7 5 3 1] table and noticed that with each new prime added, it seemed to get a little faster. At some point I decided to experiment a bit
and tried using a set of primes farther apart and noticed that with a much smaller set of increments, I was able to get about the same performance as my much larger set of primes. This spurred me on
some more and I eventually came up with the following set:
{ 14057, 9371, 6247, 4177, 2777, 1861, 1237, 823, 557, 367, 251, 163, 109, 73, 37, 19, 11, 7, 5, 3, 1 }
In order to use this set, however, we need a slightly more complicated method for determining the next value for h than just h -= 2, so I used a lookup table instead:
static int htab[] = { 14057, 9371, 6247, 4177, 2777, 1861, 1237, 823, 557, 367, 251, 163, 109, 73, 37, 19, 11, 7, 5, 3, 1, 0 };
ShellSort (int a[], int n)
int *h, i, j;
int tmp;
for (h = htab; *h; h++) {
for (i = *h; i < n; i++) {
tmp = a[i];
for (j = i; j >= *h && a[j - *h] > tmp; j -= *h)
a[j] = a[j - *h];
a[j] = tmp;
With this new table of increments, I was able to achieve an average sort time of about 0.09 seconds. In fact, ShellSort() in combination with the above increment table will sort an array of 2 million
items in about the same amount of time as our optimized BinaryInsertionSort() took to sort 100 thousand items. That's quite an improvement, wouldn't you say!?
To learn more about sorting, I would recommend reading Art of Computer Programming, Volume 3: Sorting and Searching (2nd Edition)
Note: this is a repost from an old weblog.
The Binary variant of Insertion Sort uses a binary search to find the appropriate location to insert the new item into the output. Before we can implement this variant of the insertion sort, we first
need to know and understand how the binary search algorithm works:
Binary Search
Binary searching, for those who don't know (no need to raise your hand in shame), is a method of searching (duh) in which you attempt to compare as few items in the dataset to the item you are
looking for as possible by halving your dataset with each comparison you make. Hence the word binary (meaning two). Allow me to illustrate:
Given the following dataset of 9 items in sorted order, find the value 8:
[1 2 3 4 5 6 7 8 9]
The first step is to check the midpoint (there are 9 elements, so the midpoint would be (9+1)/2 which is the 5th element):
[1 2 3 4 5 6 7 8 9]
Well, 5 is not 8 so we're not done yet. Is 8 less than 5? No. Is 8 greater than 5? Yes. So we know that the value we seek is in the second half of the array (if it's there). We are now left with:
[6 7 8 9]
Oops. 4 does not have a midpoint, so we round off any way we want to (it really doesn't matter). (4+1)/2 = 2.5, so for the sake of argument lets just drop the decimal and check the 2nd element (this
is how integer math works anyway, so it's simpler):
[6 7 8 9]
Well, 7 is not 8 so we're not done yet. Is 8 less than 7? No. Is 8 greater than 7? Yes. So we know that the value we seek is in the second half of the array (if it's there). We are now left with:
[8 9]
Again we find the midpoint, which in this case is 1.
[8 9]
Does 8 equal 8? Yes! We're done!
How many tries did that take us? Three. Three tries and we found what we were looking for. And, in the worst possible case for this particular array (searching for the 9), we would have been able to
do it in 4 tries.
Not bad, huh?
To implement our BinarySearch() function, the easiest way will be to write it using recursion. Recursion is a technique that allows us to break the problem into smaller and smaller pieces (or, the
array in this case - as illustrated above) until we arrive at the solution (or, in this case, the item we are looking for). Recursion is implemented by having a function call itself to process a
subset of the data, which, may again call itself (repeatedly until the problem is solved).
Notice in my above explanation of how to search the 9-item array using the binary search algorithm, how I continually break the array into smaller and smaller subsets? That's why binary search is
often described as a recursive algorithm - you keep repeating the the process on smaller and smaller subsets until your subset cannot get any smaller or until you find what you are looking for.
Hopefully I've explained that well enough, if not - perhaps taking a look at the following implementation will help?
BinarySearch (int a[], int low, int high, int key)
int mid;
mid = low + ((high - low) / 2);
if (key > a[mid])
return BinarySearch (a, mid + 1, high, key);
else if (key < a[mid])
return BinarySearch (a, low, mid, key);
return mid;
Note: To get the midpoint, we use the formula low + ((high - low) / 2) instead of (high + low) / 2 because we want to avoid the possibility of an integer overflow.
In my above implementation, a[] is our integer array, low is the low-point of the subset in which we are looking, high is the high-point of the subset in which we are looking, and key is the item
that we are looking for. It returns the integer index of the value we are looking for in the array. Here's how we would call this function from our program: BinarySearch (a, 0, 9, 8);
Remember that in C, array indexes start at 0. We pass 9 as the high-point because there are 9 elements in our array. I don't think I need to explain why we pass 8 as the key.
If we then plug this into our Insertion Sort algorithm from yesterday (instead of doing a linear search), we get a Binary Insertion Sort... almost. There's one minor change we have to make to our
BinarySearch() function first - since we are not necessarily trying to find an already-existing item in our output, we need to adjust BinarySearch() to return the ideal location for our key even in
the event that it doesn't yet exist. Don't worry, this is a very simple adjustment:
BinarySearch (int a[], int low, int high, int key)
int mid;
if (low == high)
return low;
mid = low + ((high - low) / 2);
if (key > a[mid])
return BinarySearch (a, mid + 1, high, key);
else if (key < a[mid])
return BinarySearch (a, low, mid, key);
return mid;
Okay, now we're ready to plug it in. Here's the result:
BinaryInsertionSort (int a[], int n)
int ins, i, j;
int tmp;
for (i = 1; i < n; i++) {
ins = BinarySearch (a, 0, i, a[i]);
tmp = a[i];
for (j = i - 1; j >= ins; j--)
a[j + 1] = a[j];
a[ins] = tmp;
There's a couple of optimizations we can make here. If ins is equal to i, then we don't need to shift any items nor do we need to set a[ins] to the value in a[i], so we can wrap those last 4 lines in
an if-statement block:
BinaryInsertionSort (int a[], int n)
int ins, i, j;
int tmp;
for (i = 1; i < n; i++) {
ins = BinarySearch (a, 0, i, a[i]);
if (ins < i) {
tmp = a[i];
for (j = i - 1; j >= ins; j--)
a[j + 1] = a[j];
a[ins] = tmp;
If you remember from our Insertion Sort optimizations, the memmove() function really helped speed up shifting a lot of items all at once. But before we do that, lets see what kind of times our
current implementation takes to sort 100,000 items (just so we have something to compare against after we make that memmove() optimization).
On my AMD Athlon XP 2500, it takes roughly 25 seconds to sort 100,000 random items (using the main() function from our Bubble Sort analysis a few days ago). That's already on par with yesterday's
optimized insertion sort implementation and we haven't even plugged in memmove() yet!
I'm pretty excited and can't wait to plug in memmove() to see what kind of results we get, so here we go:
BinaryInsertionSort (int a[], int n)
int ins, i, j;
int tmp;
for (i = 1; i < n; i++) {
ins = BinarySearch (a, 0, i, a[i]);
if (ins < i) {
tmp = a[i];
memmove (a + ins + 1, a + ins, sizeof (int) * (i - ins));
a[ins] = tmp;
After plugging in memmove(), our BinaryInsertionSort() sorts 100,000 items in about 5.5 seconds! Whoo!
Lets recap: We started off with the goal of sorting 100,000 items using Bubble Sort which took over over 103 seconds to accomplish. We then scratched our heads and optimized the Bubble Sort algorithm
the best we could and obtained a result that was twice as fast. Then we traded our BubbleSort() implementation in for another O(n^2) algorithm (generally not something I would suggest wasting time
on, but for the sake of learning about a bunch of sorting algorithms, why not?). Using InsertionSort(), we got that down to 26.5 seconds which is 4 times faster than our original sort! But wait, then
we took our InsertionSort() one step farther and used a binary search algorithm to help us find the ideal location in which to insert our item and we got it down to a whopping 5.5 seconds - 20 times
faster than what we started with!
That's pretty awesome if you ask me...
There's still one more optimization we can try on our BinaryInsertionSort() implementation to attempt to get faster speeds, but it may be over your head if you're a beginner so feel free to ignore my
following code dump:
BinaryInsertionSort (int a[], int n)
register int i, m;
int hi, lo, tmp;
for (i = 1; i < n; i++) {
lo = 0, hi = i;
m = i / 2;
do {
if (a[i] > a[m]) {
lo = m + 1;
} else if (a[i] < a[m]) {
hi = m;
} else
m = lo + ((hi - lo) / 2);
} while (lo < hi);
if (m < i) {
tmp = a[i];
memmove (a + m + 1, a + m, sizeof (int) * (i - m));
a[m] = tmp;
The basic idea here was that I wanted to get rid of recursion because, unfortunately, as nice as recursion is for visualizing (and implementing) our binary search, there is a cost penalty for every
time we recurse - there is both function call overhead (which slows us down) and a memory overhead (we need to grow the stack). If we're clever enough, we can sometimes bypass the need for recursion
like I did above which can often lead to significant performance gains.
In this case, however, we didn't improve the performance all that much (down from 5.5 to 5.2 seconds) but on other architectures (such as SPARC), it may be a lot more noticeable. It may also be a lot
more noticeable for larger datasets. In fact, lets try sorting 200,000 items and see what sort of times we get.
Ah, much more noticeable now. With recursion, it takes 46 seconds and without, it takes 37 seconds - so there is definitely an advantage to cleverly working around the need for recursion.
Okay, that's all I've got for Binary Insertion Sort, but there are still plenty more sorting algorithms to try before we call it a day - we've just barely scratched the surface - and so far we've
only looked into the O(n^2) algorithms - there are others that promise O(n lg n) performance!
To learn more about sorting, I would recommend reading Art of Computer Programming, Volume 3: Sorting and Searching (2nd Edition)
Note: this is a repost from an old weblog.
Insertion Sort is another O(n^2) sorting algorithm (just like Bubble Sort was) but is a little bit faster. Now, ideally, when trying to optimize by picking a new algorithm - you don't want to go from
one slow algorithm to another, but I figure while I'm explaining sorting techniques - I might as well explain a bunch of them. Anyways... it turns out that insertion sort works out to be faster than
Bubble Sort in the general case.
The way Insertion Sort works, is you move one item from your input dataset into an output dataset one item at a time. Take an item from the input and place it in the output at the proper position
such that the output dataset is always in sorted order. Allow me to demonstrate:
Given: [5 8 2 9 6 3 7 1 0 4]
That's our input dataset. Our output dataset is so far empty. The first thing we do, is to take the first item of our input dataset (or any item, really, but we might as well grab them out of the
input dataset in order, right?) and place it in the output dataset. Since the output dataset will only have 1 item this first round, there's nothing to sort. The result is:
Input: [8 2 9 6 3 7 1 0 4] Output: [5]
Now take the next input item and place it in the output, but in the proper sorted order:
Input: [2 9 6 3 7 1 0 4] Output: [5 8]
Lather. Rinse. Repeat.
Input: [9 6 3 7 1 0 4] Output: [2 5 8]
Input: [6 3 7 1 0 4] Output: [2 5 8 9]
Input: [3 7 1 0 4] Output: [2 5 6 8 9]
Input: [7 1 0 4] Output: [2 3 5 6 8 9]
Input: [1 0 4] Output: [2 3 5 6 7 8 9]
Input: [0 4] Output: [1 2 3 5 6 7 8 9]
Input: [4] Output: [0 1 2 3 5 6 7 8 9]
Input: [] Output: [0 1 2 3 4 5 6 7 8 9]
Tada! We have a sorted dataset. This is the basis of all insertion sort variants, the difference between the various insertion sorts (I only know of 2, but wouldn't be surprised if there were more)
is the way in which we find the ideal place to insert the new item from the input into the output.
Before I get into the different variants, however, let me address one of the concerns you likely have thus far: if we're sorting a large-ish array (note: if we are sorting a linked list, then this
isn't an issue), we don't want to have two arrays because that doubles the amount of memory we're using!
Indeed, but if you'll notice: as the output size increases, the input size decreases - together, both the input and output sizes total the same number of elements and if we iterate through the input
elements in order, then we can share the same array as both the input and output arrays. Let me re-illustrate:
Output | Input
[][5 8 2 9 6 3 7 1 0 4]
[5 ][8 2 9 6 3 7 1 0 4]
[5 8 ][2 9 6 3 7 1 0 4]
[2 5 8 ][9 6 3 7 1 0 4]
See how we can cheat now? Visualization is the key to solving so many problems. Don't be afraid to take a pencil and paper and "draw" the problem - many times the solution will present itself.
Linear Insertion Sort
Generally when someone refers to Insertion Sort, this is the variant that they are talking about. As I was saying above, the difference between the variants is how they find the proper position in
which to insert the new item into the output. As the name suggests, Linear insertion sort uses a linear search in order to find this position. Basically, this comes down to scanning through the
output array starting at the first position and comparing the values: if the new item is larger than the first output value, move to the next output item and so on until the new item's value is less
than the item we are comparing against in the output - once we find that, we have found the position to insert the new item.
Note: we could actually get away with using <= to minimize the number of comparisons we have to do, but then if we have multiple items with the same values, they won't remain in the same order they
were in in the input, but if that doesn't bother you, then definitely use <=. Sorts that guarantee that items in the output with the same comparison values are in the same order as they were in the
input are called "stable sorts". This is usually a pretty desirable trait (unless performance is more important). The lucky thing for us, though, is that in this particular case, keeping duplicate
items in the same order we found them in the input, would force us to work backwards starting at the end of the output array rather than working forwards starting at the beginning of the output array
which just so happens to allows us a more promising optimization. Pretty crafty, eh? I thought so...
One thing I should remind you about is that when you insert an item into the output, you'll need to shift all the items after that position one place to the right.
Okay, on to the implementation...
The first optimization you should notice is that after the first "loop", the first item of the input is always the first item of the output, so we might as well start with the second item of the
input array. So with that, go ahead and implement this algorithm - you should get something similar to this:
InsertionSort (int a[], int n)
int i, j = 0;
int key;
for (i = 1; i < n; j = i, i++) {
key = a[i];
while (j >= 0 && a[j] > key) {
a[j + 1] = a[j];
a[j + 1] = key;
You'll notice that I took the "work backwards starting at the end of the output array" approach that I noted above. As I started to mention, this approach has the added benefit of allowing us to
shift the output items as we go which means we get to shift fewer items per loop on average than if we had worked in the forward direction, resulting in a performance gain (shifting a bunch of items
is more expensive than an integer comparison).
If we feed this into our sort program and have main() call this new function rather than the BubbleSort() implementation we wrote yesterday, we find that we have a sort that is significantly faster -
down to 36 seconds from the optimized BubbleSort()'s 51 seconds. Not bad...
See any obvious improvements we can make that might result in a significantly faster implementation of our InsertionSort() implementation? I don't see anything I would consider major, but we might
try using memmove() instead of manually moving items one space to the right. We'll get the most bang for the buck if we wait until we find our optimal insertion point before moving anything around,
InsertionSort (int a[], int n)
int i, j = 0;
int key;
for (i = 1; i < n; j = i, i++) {
key = a[i];
while (j >= 0 && a[j] > key)
memmove (a + (j + 2), a + (j + 1), sizeof (int) * ((i - 1) - j));
a[j + 1] = key;
Okay, so with that very simple adjustment, we got our total sort time from 36 seconds down to 26.5 seconds. Nothing to scoff at, surely, but at the same time not as drastic an improvement as changing
algorithms had been (see why algorithms are so important for optimizations?).
Now just imagine if we used an algorithm that promised better than O(n^2) performance!
Before we jump to something better than O(n^2) though, I still have one more trick up my sleeve to improve our insertion sort algorithm (not implementation this time, but rather: algorithm). I dub
thee: Binary Insertion Sort.
To learn more about sorting, I would recommend reading Art of Computer Programming, Volume 3: Sorting and Searching (2nd Edition)
Note: This is a repost from an old weblog.
Bubble Sort works by iterating through the dataset, comparing two neighboring items at a time, and swapping them if the first item is larger than the second item. In order to sort a dataset of N
items, this operation must be done N-1 times. Let me illustrate:
We start by comparing the first two items, 5 and 8:
Since 5 is smaller than 8, we don't need to swap them.
Next, we compare the second set of items, 8 and 2:
8 is larger than 2, so we have to swap them, resulting in:
We keep doing this until we reach the end of the dataset and then we'll start all over again - repeating the process N-1 times (in this example, 9 times since we have 10 items).
At the end of our first loop, we end up with:
Now we start the whole process over again (we have 8 more loops to go!).
Notice anything interesting at the very end? You guessed it! That last comparison is pretty worthless - the last item in the dataset is always going to be the largest value after the first loop,
right? Right, but that's not all - each loop through the items, we can ignore more and more items from the end of the dataset (after the second loop, we can ignore the last 2 items; after the third
loop, we can ignore the last 3 items and so on). That little trick is our first optimization for this algorithm!
Let's see what the code would look like:
BubbleSort (int a[], int n)
int i, j, tmp;
for (i = n - 1; i >= 0; i--) {
for (j = 0; j < i; j++) {
if (a[j] > a[j + 1]) {
tmp = a[j];
a[j] = a[j + 1];
a[j + 1] = tmp;
Now that we have some code to test, lets see how long it takes to sort a random array of 100,000 integers. To do that, we'll need to write a little program to use our BubbleSort() routine:
#include <stdlib.h>
#include <time.h>
int main (int argc, char **argv)
int array[100000], i;
srand (time (NULL));
for (i = 0; i < 100000; i++)
array[i] = rand ();
BubbleSort (array, 100000);
return 0;
We'll just use our system's time command to get an estimate of how long it takes to sort.
Go ahead and run our little program a few times. For me, it seems to average about 103 seconds on my AMD Athlon XP 2500.
I don't know about you, but I saw a pretty obvious optimization that we could make to our BubbleSort() implementation that might make it a bit faster. Remember how we noticed that each time through
the inner loop, the net result was that the largest item was moved all the way to the right (discounting the largest items from previous loops)? What if, instead of swapping each time through the
inner loop, we waited until the inner loop finished and then swapped? Let's try it:
BubbleSort (int a[], int n)
int i, j, max, tmp;
for (i = n - 1; i >= 0; i--) {
for (max = 0, j = 1; j < i + 1; j++) {
if (a[j] > a[max])
max = j;
if (max < i) {
tmp = a[max];
a[max] = a[i];
a[i] = tmp;
In the above code, we use max to hold the index of the largest item we find. We initialize it to the index of the first item (0 in languages like C) and then start our inner for-loop. You'll notice a
change here: instead of starting j at 0, we start it at 1 because we've already "looked" at the first item. Also, we need to loop the same number of times - so we continue to iterate as long as j is
less than i + 1 (rather than j < i of the previous implementation).
If I now compile our benchmarking program to use this new BubbleSort() implementation, we notice a huge performance increase - or at least I did on my machine. The average execution time for this new
implementation seems to be about 51 seconds. That sure beats the pants off 103 seconds, doesn't it?
Even so, 51 seconds to sort 100,000 items is a long wait, especially since they are just simple integers. There's only one more optimization that I can think of. If you think about how bubble sort
works, each time through the outer loop, you notice that if we ever go through one of those N-1 iterations without having to swap any items that it is safe to conclude that we're done and so can skip
performing the remainder of the N-1 iterations. I'll leave this optimization as an exercise for my readers rather than posting a new implementation here.
Since I don't see any other real obvious optimizations that we can make which would drastically improve performance, I think it's time we consider another sorting algorithm.
To learn more about sorting, I would recommend reading Art of Computer Programming, Volume 3: Sorting and Searching (2nd Edition)
Things are not always as bad as they first appear.
There once was a farmer living in the country with his wife and son. One day, one of their horses escaped from the stable.
Bad luck, their neighbors said.
The father took his son to go look for the horse. In so doing, they came across a dozen wild horses which they rounded up and brought back with them.
Good luck, they thought.
A few days later, while trying to tame one of these wild horses, the son broke his arm.
Bad luck?
The very next day, the army marched through town gathering all the abled young men into their ranks. The son was wounded and so wasn't drafted.
Good luck.
A few months ago, I lost my job. Bad luck, you ask? Not at all. When I was laid off, I had been feeling burnt out and really needed a good break from programming. The two and a half months of
unemployment gave me the necessary time to regain my passion. As it turns out, I was hired by one of my best friends and mentors, Miguel de Icaza, to join him on his Mono team (which just so happens
to be the "dream job" I had wanted before getting laid off).
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Cancelling in Equations
Category: Shortcuts
Written by fisikastudycenter
physics.fisikastudycenter.com - Learning cancelling in an equation. What is a cancelling in here meant? You simplify and remove a pair of numbers or symbols in an equation that is called cancelling.
That's a significant difference when using a cancelling instead the ordinary way without cancelling. You could finish an equation quicker and easier but make sure that you don't make un-proper
cancelling and then your answer get wrong.
Here are some common examples of cancelling in physics, you might explore the others and make a lot of practices during handling your equations.
The Mechanichal Energy Conservation
Sometimes you don't see the mass of a body in alot of mechanichal energy conservation questions. That's no problem completely,you still have posibilities to solve the problems with unknown mass. Take
a look the mechanical energy equation below for instance
Read more...
Center of Mass a Calculation Simplicity
Category: Shortcuts
Written by fisikastudycenter
physics.fisikastudycenter.com - Learning the center of mass, How to simplify the center of mass calculations. Sometimes it's usefull enough applying this method but if you do not feel confidence
enough to use it, don't use! Some students got wrong answer when using this method but they got the correct one when using the ordinary way.
From above figure, try to find the location of center of mass of that shape, calculate only the x axis location, because we know that y[o] must be at 45 cm!
Read more...
Sinus Method in Equilibrium
Category: Shortcuts
Written by fisikastudycenter
Shortcut to physics equilibrium, finding forces using sinus rule. Given angles between three forces that are in equilibrium condition as below figure. You are asked to determine T[1] and T[2] rope
Read more...
An Elastic Collision Shortcut
Category: Shortcuts
Written by fisikastudycenter
physics.fisikastudycenter.com - A physics shortcut to collision problem wih conditions the collision should be elastic and the masses of the two bodies involved are the same.
Given two bodies in an elastic collision above.
What are the velocities of the two bodies after collision?
Read more...
Strings Tension on Blocks
Category: Shortcuts
Written by fisikastudycenter
physics.fisikastudycenter.com - How to find the ratio of strings tensions on a couple of blocks travel at frictionless surface. Given 5 blocks being pulled by a force F = 30 N along x direction. The
masses are m[1] = 1 kg, m[2] = 2 kg, m[3] = 3 kg, m[4] = 4 kg, m[5] = 5 kg. You have to find the ratio of T[1] and T[2] . See the figure below and the following steps both normally and the short-cut.
Read more...
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Possible Answer
How many feet is 72 inches? 6 feet, one foot = 12 inches. How many feet are in 72 inches? ... How tall is Melissa Mack? Answer it! How tall id the second tallest pyramid? Answer it! What did celeb
How tall is 72 inches in feet? ChaCha Answer: 72 inches is equal to 6 feet. - read more
Share your answer: 72 inches is how many feet tall?
Question Analizer
72 inches is how many feet tall resources
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User JBL
bio website math.mit.edu/~jblewis
location Massachusetts
age 29
visits member for 4 years, 1 month
seen Jun 18 '12 at 19:10
stats profile views 2,109
I am a graduate student at MIT. See my webpage for more information.
15 awarded Yearling
25 awarded Excavator
15 awarded Yearling
8 awarded Popular Question
15 awarded Yearling
Apr probability that a random element of Z/NZ can be written as a subset sum of others
5 comment It seems to me like the question in the postscript asks for the probability that every element of $\mathbb{Z}/ N \mathbb{Z}$ can be written as a sum of some elements of $A$, whereas the
original question asks for the probability that a particular element in $\mathbb{Z}/ N \mathbb{Z}$ can be written as a sum of some elements of $A$; which question are you really
interested in?
Apr Finding cycle with constraints
4 comment It might be helpful if you described your algorithm for cycles of even length. Also, what is the motivation?
Apr Finding cycle with constraints
4 comment Please edit for typos and LaTeX. Such a cycle obviously need not exist -- what is the actual question you intend? Is this a homework assignment?
Mar volume of the projected body
24 comment What sort of answer are you looking for?
Mar Fun question in additive combinatorics
24 comment Yes, my mistake.
Mar Fun question in additive combinatorics
24 comment Is this a question to which you already know the answer?
Mar Maximal number of directed edges in suitable simple graphs on $n$ vertices without directed triangles.
24 comment gordon-royle, this is ruled out for $k \geq 2$ by the condition that there be no 2-cycles.
Mar Assigning positive edge weights to a graph so that the weight incident to each vertex is 1.
22 comment @Didier Piau, good question!
Mar A density on the natural numbers invariant with respect to the multiplication
22 comment Which is consistent with what I wrote: Gerald Edgar's density is the limit of a subsequence of the sequence whose limit is the usual density.
Mar Assigning positive edge weights to a graph so that the weight incident to each vertex is 1.
22 revised added 88 characters in body
Mar Assigning positive edge weights to a graph so that the weight incident to each vertex is 1.
22 revised added 222 characters in body
Mar Assigning positive edge weights to a graph so that the weight incident to each vertex is 1.
22 comment Yes, that's correct. I'll edit to make it clearer.
Mar A density on the natural numbers invariant with respect to the multiplication
22 comment (In fact, your proposed definition must agree with the usual one whenever the usual one exists.)
Mar A density on the natural numbers invariant with respect to the multiplication
22 comment Then all the positive integers have density 1, but the even integers still have density 1/2. Right?
Mar comment Assigning positive edge weights to a graph so that the weight incident to each vertex is 1.
22 Whoops, fair enough. All those pesky adjectives like "positive" and "connected" .... My apologies.
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Topic: Solving an unusual system of ODES
Replies: 7 Last Post: Apr 10, 2013 3:24 AM
Messages: [ Previous | Next ]
Torsten Re: Solving an unusual system of ODES
Posted: Apr 9, 2013 9:15 AM
Posts: 1,439
Registered: 11 D R G <grimesd2@gmail.com> wrote in message <5c502161-10e9-4863-9e76-57617f33fb35@googlegroups.com>...
/8/10 > Yes, that is what I want to solve; however, the case you're referring to is I believe the trivial case; we have already solved for when k = 0, and got a non-trivial solution. As K is
small, this will be close to it and there will be non zero solutions.
> Regards
> DRG
No, y=0 is the only solution that satisfies your differential equation together with the two boundary conditions - also for the case K and/or J not equal to 0.
You will have to change the boundary conditions to get a solution different from y=0.
Best wishes
Date Subject Author
4/9/13 Solving an unusual system of ODES DRG
4/9/13 Re: Solving an unusual system of ODES Torsten
4/9/13 Re: Solving an unusual system of ODES DRG
4/9/13 Re: Solving an unusual system of ODES Torsten
4/9/13 Re: Solving an unusual system of ODES DRG
4/10/13 Re: Solving an unusual system of ODES Torsten
4/10/13 Re: Solving an unusual system of ODES Torsten
4/10/13 Re: Solving an unusual system of ODES Torsten
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Vector Spaces
Date: 06/11/99 at 00:04:19
From: Brian Reid
Subject: Vector spaces
Is V = {(x,y) in R^2 | y = 3x+1} a vector space if addition and
multiplication by a scalar are defined by:
(x,y) + (x',y') = (x+x',y+y'-1)
k(x,y) = (kx,k(y-1)+1)
Part (b): give reasons for your answer in (a).
My son is taking math in summer session at the university and had
trouble with this question on his last assignment. I tried to help him
with it but couldn't. Can you show me how to do this one so I can help
him out when he comes home next weekend?
Thank you very much,
Date: 06/11/99 at 05:40:22
From: Doctor Mitteldorf
Subject: Re: Vector spaces
Dear Brian,
I remember when I was a freshman (1966) and heard the term "vector
space" for the first time, I couldn't help but carry with me all the
ideas about vectors that I had acquired in physics problems, and that
kept me confused for a few weeks. I broke out of that when I realized
that the mathematician's idea of a vector space is exactly what it's
defined to be: a set of objects in which you can guarantee that if you
perform the operations of addition or scalar multiplication on them,
you end up with another such object.
Actually, there's one more thing you need to assure: that scalar
multiplication is distributive over addition.
The conventional wisdom is that a line or a plane passing through the
origin is a natural vector space, but one that is skewed from the
origin, as we have here, is not. For example, using the natural
definition of addition, if you took two points that satisfied (y =
3x+1) and added them up, you wouldn't get another point that satisfies
(y = 3x+1). But the definitions of multiplication and addition
provided here are intended to fudge around this problem, by relating
back to the parallel line (y = 3x), adding, then shifting back over by
1. Do they work as advertised? That's what the problem is intended to
Why don't you try working it out yourself? Here are the three things
you are to verify:
1) If (x1,y1) and (x2,y2) both satisfy (y = 3x+1) and they are added
according to the prescription given, then the result also satisfies
(y = 3x+1).
2) If (x1,y1) satisfies (y = 3x+1) and it is multiplied by a scalar
according to the given definition of multiplication, then the
result also satisfies (y = 3x+1).
3) Finally, verify that, with the given definitions for addition and
scalar multiplication, k(A+B) = kA + kB, where k is a scalar and A
and B are vectors.
Will you write and let me know what you find?
- Doctor Mitteldorf, The Math Forum
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Explorations in Monte Carlo Methods
The Monte Carlo approach is a radically new approach to problem solving first developed in the 1940’s. Someone has said that the Monte Carlo method may be the most commonly used mathematical
technique which wasn’t familiar to Gauss. When faced with a problem that is too difficult to solve exactly, the Monte Carlo approach says to create a random process that is likely to give a good
approximation to the desired result. This approach has become so widely adopted that it is difficult to appreciate how groundbreaking it was a few decades ago.
Monte Carlo methods are often either omitted from the undergraduate curriculum or are presented in a misleading way. Perhaps the application most likely presented to undergraduates would be numerical
integration. Imagine the graph of a function of many variables sitting inside a high dimensional box. The integral of the function is the volume under the graph, and so one can approximate the
integral by generating random points and counting what proportion of points fall below the surface. There is some truth to this. Monte Carlo methods are the only practical way to estimate many high
dimensional integrals, and in principle the dart-throwing technique would work. However, numerical integration is almost never done in such a crude way. Such examples may do more harm than good
because they imply that Monte Carlo methods are trivial. Monte Carlo methods are conceptually simple, but they do require some sophistication to use effectively.
To see why the “just throw darts at it” approach might not work, imagine estimating the volume of a 40-dimensional sphere. Place the sphere in a cube of the same diameter and count the proportion of
random points that land inside the sphere. This proportion will converge to the volume of the sphere. However, this method is completely impractical without some refinement. The probability of a
single point landing inside the sphere is 3.44 × 10^-15. (The volume of a unit sphere of dimension 2n is π^n/Γ(n) and so the proportion of the unit cube taken up by the sphere decreases rapidly as n
increases.) To estimate the volume to three decimal places, you would need about 10^6 to land inside the sphere, which means you would have to throw on the order of 10^21 darts. Throwing a billion
simulated darts a second, this would take over 30,000 years. High dimensional volumes are often estimated using Monte Carlo techniques, but not by naively throwing darts at a box. In practice, darts
have to be thrown according to some non-uniform distribution that assures that a sizeable proportion of the darts land inside the target.
Monte Carlo methods are very commonly used in applications. Mathematics students should have a practical introduction to such methods, but introductions at an undergraduate level are hard to find.
Explorations in Monte Carlo Methods by Ronald Shonkwiler and Franklin Mendivil is an undergraduate text that is both practical and accessible. The book has minimal prerequisites. It assumes the
reader is comfortable with calculus and matrices, but it does not assume much background in probability or statistics. And although the book assumes little background, it covers advanced topics such
as Markov chain Monte Carlo (MCMC) and simulated annealing.
Explorations would make a good text book and would also be suitable for independent study. It makes ideas accessible at a sophomore level that are normally covered in graduate or advanced
undergraduate texts. The book leads up to big ideas by a sequence of simple motivating examples. For example, before introducing acceptance-rejection methods for generating random numbers, it first
explains how to generate random samples with probability of success 1/3 by tossing a fair coin. It gives numerous applications of Monte Carlo methods including applications in electrical engineering,
finance, optimization, and statistical mechanics. Each chapter has numerous exercises and the book concludes with an appendix listing several ideas for student projects applying Monte Carlo methods.
John D. Cook is a research statistician at M. D. Anderson Cancer Center and blogs daily at The Endeavour.
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Number of results: 771
Algebra 1A
How many solution sets do systems of linear inequalities have? Do solutions to systems of linear inequalities need to satisfy both inequalities? If so what are some examples?
Wednesday, June 26, 2013 at 4:00pm by Kim
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How many solution sets do systems of linear inequalities have? Do solutions to systems of linear inequalities need to satisfy both inequalities? In what case might they not?
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How many solution sets do systems of linear inequalities have? Do solutions to systems of linear inequalities need to satisfy both inequalities? In what case might they not?
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Systems of Inequalities-8th Grade Algebra
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Thursday, March 12, 2009 at 10:14pm by Marta
Gender Inequalities
Are there any inequalities between men and women in the armed forces?
Tuesday, May 27, 2008 at 9:30pm by Katherine
No inequalities were presented. You cannot copy from homework and and paste it here; you have to retype the inequalities.
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Wednesday, April 11, 2012 at 2:14am by Anonymous
math inequalities please check
your inequalities are right. :)
Monday, October 25, 2010 at 10:51pm by jai
Or would it having to be negative only for polynomial inequalities and for rational inequalities they have t be positive?
Monday, September 27, 2010 at 5:40pm by Amy~
i'm dealing with inequalities with one variable and i'm just curious as to why i am doing this? i would like to know the theories behind this.... please help or maybe give me a site?
Wednesday, March 25, 2009 at 9:54pm by cynthia
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Saturday, December 14, 2013 at 9:30pm by Maggie
graph the system of inequalities: ( x-3)^2/9 + (y+2)^2/4<=1 and (x-3)^2+(y+2)^2>=4 I do not know how to simplify this down enough to graph it
Saturday, April 21, 2012 at 3:26pm by Some1 Help Me Plz
algerbra 2
so how do I explain inequalities and why x<8 and y<40 are also inequalities for this system? Do I add or multiply by 4?
Friday, November 22, 2013 at 5:46pm by malik
Go on: wolframalpha dot com When page be open in rectangle type: ( x-3)^2/9 + (y+2)^2/4<=1 , (x-3)^2+(y+2)^2>=4 and click option = After few seconds you will see everything about your
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Saturday, April 21, 2012 at 3:26pm by Bosnian
education inequalities
What are some inequalities in education between men and women?
Friday, May 23, 2008 at 10:51am by Katherine
Re: Math
The only inequalities where I have to check the values between the points are polynomial and rational inequalities, right? And not any other type of inequalites By Checking I mean to know which way
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Tuesday, September 28, 2010 at 7:53pm by Amy~
algebra 1
I can't graph this for you here. Put "solving systems of inequalities" in google and click on the second link (the one with 'purplemath' in the address). This website gives an example of how to graph
and solve inequalities.
Tuesday, February 8, 2011 at 4:54pm by helper
Solve the compound inequalities. Write the solutions in interval notation. Graph your solution on a number line. 1. 2(3x + 1)< -10 or 3(2x - 4) ¡Ý 0 The or means union of these inequalities. 2. 5(p +
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Thursday, August 30, 2012 at 6:20pm by Neil
algerbra 2
. Explain your inequalities and explain why and are also inequalities for this system
Tuesday, November 5, 2013 at 3:26pm by nicki
Suppose you need $2.40 in postage to mail a package to a friend. You have 9 stamps, some $0.20 and some $0.34. How many of each do you need to mail the package? So to solve this problem, I came up
with two inequalities: 1. a + b is less than or equal to 9 2. 20a + 34b is ...
Friday, April 10, 2009 at 5:16pm by Angie
But we are doing systems of linear inequalities, so I'd want at least two different inequalities. Also, I don't understand how you put x,y, and -1 into the parentheses. Also, would this work? 30x +
15y >= 150 x + y - 10 <= 200
Monday, January 13, 2014 at 7:54pm by Anonymous
1. Marissa is a photographer. She sells framed photographs for $100 each and greeting cards for $5 each. The materials for each framed photograph cost $30, and the materials for each greeting card
cost $2. Marissa can sell up to 8 framed photographs and 40 greeting cards each ...
Monday, January 20, 2014 at 10:56am by Jessica
Math Check
The only inequalities where I have to check the values between the points are polynomial and rational inequalities, right? And not any other type of inequalites By Checking I mean to know which way
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Tuesday, September 28, 2010 at 4:55pm by Amy~
alg2 check?
Graph the system of inequalities then substitute the (x,y)order pair into both inequalities. y>3x+1 y<-2/3x+4 (second one has a line under the arrow) I don't get what they are asking for? if they
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Thursday, July 18, 2013 at 1:49pm by tyneisha
Math Ms. Sue Please help!
Can you find me a website how to do inequalities on line graphs on the less than and greater than inequalities. Ex: 2r-2<4 (A line goes under the sign "<")
Wednesday, February 13, 2013 at 7:05pm by Angelina
inequalities graph
You might want to try some of the following tutorials: http://search.yahoo.com/search?fr=mcafee&p=inequalities+graph+tutorial Sra
Sunday, November 21, 2010 at 8:04pm by SraJMcGin
Consider the two inequalities 2x - 4 < y and y < -2/3x + 2. (b) Graph the region of the plane that satisifies either inequality, or both inequalities. (c) Graph the region of the plane that
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Wednesday, February 4, 2009 at 5:23pm by Lilianne
Algebra 1 Concept Explaination
Tuesday, January 14, 2014 at 9:13pm by bobpursley
algebra 1
Material cost equation : 30x + 2y = 200 Profit equation : 100x + 5y = 400 B. Explain your inequalities and explain why x<8 and y<40 are also inequalities for this system
Friday, November 22, 2013 at 6:11pm by malik
Let our two variables be: p # of pharmacy hours b # of babysitting hours Then we should have two statements from the given facts: and We can graph these inequalities by solving for either p or b in
both inequality. Once the inequalities are graphed then any point that is ...
Monday, May 6, 2013 at 5:37pm by Taylor
You have to try to solve the inequality and then conclude at some point that there are no solutions. Sometimes you can use some inequalities that always hold, like: |a| >= 0 |a+b| <= |a| + |b| etc.
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Friday, January 16, 2009 at 7:25pm by Count Iblis
A home-based company produces both hand-knitted scarves and sweaters. please help please The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited
to 40 hours per week, and the total production capacity is 5 items per week. ...
Thursday, January 31, 2008 at 3:30pm by Brenda
Solving inequalities
I have to solve the following inequalities: x^2 + y^2 is less than or equal to 49 y is less than or equal to 3-x^2 I know that these are the equations of a circle and a parable. There should be 3
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Monday, March 30, 2009 at 7:11pm by Joanie
Math: Polynomial inequalities
Inequalities involving parabolas can get interesting. Solve as an equation: 2t^2 - t -3 = 0 (t+1)(2t-3) = 0 t = -1 or 3/2 Think now of the graphs of 2t^2 - 3 and t You want the region where the
parabola is below the line. That is, -1 <= x <= 3/2 Of course, you can do ...
Tuesday, October 18, 2011 at 3:34pm by Steve
Quadratic Equations
The solution to inequalities is a region, not just a point. In this case, think of the graphs. y < -x^2 is the whole inside of the downward-opening parabola with vertex at (0,0). x^2 + y^2 < 16 is
the inside of the circle of radius 4 centered at (0,0). So, is 9+4<16? ...
Tuesday, June 12, 2012 at 3:50pm by Steve
Write -14 <= 3x-7 <= -2 or -14 ≤ 3x-7 ≤ -2 (≤ is written as "& l e ;" without the double quotes and without spaces). There are two inequalities. We need to solve each one separately and find the
solution interval that satisfies both inequalities. -14 ≤ 3x-7...
Sunday, January 23, 2011 at 2:02am by MathMate
Write a system of inequalities to express the exterior of the triangle ABD if A=(-2,7), B=(4,0), and C=(1,-3). Please help! gracias<3 Derive equations for the three lines connecting the three points.
Then change the equations to inequalities to represent the region on the ...
Wednesday, December 20, 2006 at 7:10pm by Lily
Something that helped me determine whether to set up a double inequality versus separate inequalities... |expression|< k less thAN (and)= double inequalities -k<|expression|< k |expression|> k
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Saturday, October 2, 2010 at 1:10pm by TutorCat
I'm assuming this is one problem with 2 inequalities. 7 + m >= 2. m + 1 < 2. 7 + m >= 2, Subtract 7 from each side: m >= -5, m + 1 < 2, Subtract 1 from each side: m < 1. Compound the 2 simplified
inequalities: -5 <= m < 1. The inequality states that m ...
Tuesday, September 7, 2010 at 7:38pm by Henry
Pre-calculus-check answers
Describe the linear programming situation for this system of inequalities where you are asked to find the maximum value of f(x,y)=x+y. Answer: an optimal solution 2)Describe the linear programming
situation for this system of inequalities: Answer: an optomal solution
Saturday, August 23, 2008 at 2:06pm by Lucy
Pre-Calculus-check answers
Describe the linear programming situation for this system of inequalities where you are asked to find the maximum value of f(x,y)=x+y. Answer: an optimal solution 2)Describe the linear programming
situation for this system of inequalities: Answer: an optomal solution
Saturday, August 30, 2008 at 11:17am by Lucy
Pre-Calculus check answers
Describe the linear programming situation for this system of inequalities where you are asked to find the maximum value of f(x,y)=x+y. Answer: an optimal solution 2)Describe the linear programming
situation for this system of inequalities: Answer: an optomal solution
Sunday, August 31, 2008 at 11:46am by Lucy
Try to solve these inequalities first. Compound inequalities with 'Or', are solved separately and the solutions have 'or' between them. Example. If the solution to the first was x < 2 and the
solution for the second was x > 4, then the solution would be, x < 2 OR x &...
Saturday, January 29, 2011 at 10:32pm by helper
set the inequalities to 3 and pretend its an equal sign when you solve it. 1/2(6-2x)+2_>3 3-x+2_>3 5-x_>3 -x_>-2 x<_2 this means that for any x values that are less than or equal to 2, then the y
values would be greater than or equal to 3. *note that there are ...
Monday, October 22, 2007 at 10:21pm by jennifer
graph the system of inequalities, and classify the figure created bu the solution region. y¡Ü4x+4 y¡Ü-0.25x+4 y¡Ý4x-1 y¡Ý-0.25x-1 a)the shaded region is a plane minus a rectangle b)there is no region
common to all four inequalities c)the shaded region is a rectangle d)the ...
Thursday, May 17, 2012 at 6:46pm by jenika
graph the system of inequalities, and classify the figure created bu the solution region. y¡Ü4x+4 y¡Ü-0.25x+4 y¡Ý4x-1 y¡Ý-0.25x-1 a)the shaded region is a plane minus a rectangle b)there is no region
common to all four inequalities c)the shaded region is a rectangle d)the ...
Thursday, May 17, 2012 at 7:57pm by jenika
algebra 1
Marissa is a photographer. She sells framed photographs for $100 each and greeting cards for $5 each. The materials for each framed photograph cost $30, and the materials for each greeting card cost
$2. Marissa can sell up to 8 framed photographs and 40 greeting cards each ...
Friday, November 22, 2013 at 5:39pm by malik
Math (Absolute Value Inequality)
You probably would like to find the value of a. We established that to satisfy the quadratic inequality x^2−11x−210 < 0 -10<x<21 Now substitute this interval into each of the two linear inequalities:
x-8<a and 8-x <a (-10)-8<a => a>-18 8-(-...
Sunday, May 26, 2013 at 3:31am by MathMate
algebra 1
. Marissa is a photographer. She sells framed photographs for $100 each and greeting cards for $5 each. The materials for each framed photograph cost $30, and the materials for each greeting card
cost $2. Marissa can sell up to 8 framed photographs and 40 greeting cards each ...
Friday, November 22, 2013 at 5:21pm by nicki
Hi, I am having some problems with inequalities. It is asking us to solve and graph on a number line and then write it in interval notation and set notation. X>2 and X>4 I graphed them in a number
line already and i have the following: Interval notation (2,infinity) and ...
Monday, February 14, 2011 at 12:33pm by phobia
MATH 116
Look down about a third of the page http://www.sosmath.com/algebra/inequalities/ineq02/ineq02.html
Saturday, November 14, 2009 at 10:30pm by Reiny
Quanitive Methods
A car rental company has $540,000 to purchase up to 25 new cars of two different models. One model costs $18,000 each and the other model costs $24,000 each. Write a system of linear inequalities to
describe the situation. Let x represent the first model and y represent the ...
Monday, October 1, 2007 at 12:33am by Tam
Sunday, June 26, 2011 at 5:55am by drwls
College Algebra-Study Material
I am going to take the CLEP (College Level Examination Program) College Algebra examine. I am trying to decide on what books I should use to prepare for this examine. The following is what is going
to be covered in this examine: 25% Algebraic operations Factoring and expanding...
Friday, November 28, 2008 at 10:15am by G
Solve the following linear inequality graphically. x+2y<4 x-y<5 Each inequality is satisfied in a particular region of an x,y plot. The first inequality is satisfied below the line y = -x/2 + 2, for
example. The second inequality is satisfied above the line y = x + 5. ...
Sunday, June 3, 2007 at 10:54pm by Graphing Help!
math inequalities please check
A landscape designer has to design a rectangular pad of concrete at the centre of a rock garden. The lenght must be less than or equal to twice the width; the perimeter must be less than or equal to
40 m; and the area must be greater than or equal to 60 m². 1.)Write as system ...
Monday, October 25, 2010 at 8:23pm by Sandi
1) Why should we clear fractions when solving linear equations and inequalities? Demonstrate how this is done with an example. Why should we clear decimals when solving linear equations and
inequalities? Demonstrate how this is done with an example.
Wednesday, March 21, 2012 at 10:37am by jess
math (graphing)
Thank you VERY much! You're my savior :) just one more question.. I NOW understood how to graph equations.. but I still have to graph inequalities, which seems much more complicated from my point of
view. I've got two inequalities that I have to graph. 1. y > 2/3x-4 2. y &...
Sunday, May 3, 2009 at 5:45am by xxx
Algebra 1 (Reiny)
Will you please explain the steps I must take in order to graph these linear inequalities? Graph each system of linear inequalities. Give two ordered pairs that are solutions and two that are not
solutions. 1. y < 2x - 1 y > 2 2. x < 3 y > x -2 3. y => 3x 3x + y...
Thursday, January 9, 2014 at 9:55pm by Victoria
I can't quite make out your diagram, but your graph should look like the diagram #2 on the first page of this ... http://www.gradeamathhelp.com/support-files/compound-inequalities-b.pdf Your open
circles should be around the -3 and +5
Thursday, April 8, 2010 at 10:22am by Reiny
math inequalities please check
A landscape designer has to design a rectangular pad of concrete at the centre of a rock garden. The length must be less than or equal to twice the width; the perimeter must be less than or equal to
40 m; and the area must be greater than or equal to 60 m^2. 1.)Write as system...
Monday, October 25, 2010 at 10:51pm by Sandi
math link to instructions
Monday, December 10, 2012 at 6:02pm by Damon
algebra 1
Marissa is a photographer. She sells framed photographs for $100 each and greeting cards for $5 each. The materials for each framed photograph cost $30, and the materials for each greeting card cost
$2. Marissa can sell up to 8 framed photographs and 40 greeting cards each ...
Friday, November 22, 2013 at 10:27pm by malik
Math/ Algebra
Post your responses to the following. Answer each question in a separate paragraph: Techniques that can simplify solving equations and inequalities are to clear fractions and decimals when solving
linear equations and inequalities. 1. Demonstrate how fractions are cleared with...
Monday, June 14, 2010 at 5:26pm by Amanda
Algebra 1 (Reiny)
I desperately need guidance. Not only do I not know how to graph these systems of linear inequalities, but I also do not understand the concept whatsoever. I have watched several videos regarding the
subject, but I didn't retain anything from them. Please, I desperately need ...
Tuesday, January 14, 2014 at 10:21pm by Anonymous
An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function
at each corner of the graphed region. Use these values to determine the maximum...
Monday, February 22, 2010 at 4:29pm by ReRe
relations and fucntions
Seeds of type A and type B are sold in a packet each must contain a)both type a and type b seeds b)at least twice the number of type b c)as there are type a seeds no more thanm 12 seeds 1)state the
minimum number in each packet of type a and type b seeds. 2)if there are x type...
Tuesday, February 26, 2008 at 8:23pm by Keisha
math (urgent help needed)
Seeds of type A and type B are sold in a packet each must contain a)both type a and type b seeds b)at least twice the number of type b c)as there are type a seeds no more thanm 12 seeds 1)state the
minimum number in each packet of type a and type b seeds. 2)if there are x type...
Friday, February 29, 2008 at 3:16pm by Keisha
math(relation & functions) need help urgently
Seeds of type A and type B are sold in a packet each must contain a)both type a and type b seeds b)at least twice the number of type b c)as there are type a seeds no more thanm 12 seeds 1)state the
minimum number in each packet of type a and type b seeds. 2)if there are x type...
Thursday, February 28, 2008 at 8:09pm by Keisha
algebra - inequalities
Wednesday, November 20, 2013 at 10:58pm by orpheus
algebra 1
Marissa is a photographer. She sells framed photographs for $100 each and greeting cards for $5 each. The materials for each framed photograph cost $30, and the materials for each greeting card cost
$2. Marissa can sell up to 8 framed photographs and 40 greeting cards each ...
Saturday, November 23, 2013 at 7:57am by malik
what or the signs of inequalities ?
Monday, September 29, 2008 at 8:56pm by mikale
pressure inequalities
Sunday, October 2, 2011 at 5:47pm by Shaq
Inequalities (Math)
You're welcome. :-)
Thursday, October 10, 2013 at 7:36pm by Ms. Sue
Math- Inequalities
Monday, October 14, 2013 at 12:06am by Steve
Algebra 1--Three Word Problems (Reiny or Kuai)
to graph inequalities, draw the lines that represent the equations (as if not inequalities). Then shade the area above or below the line, depending on whether y is greater or less than the values on
the line. For example, on #1, if Linda works p hours at the pharmacy and b ...
Friday, January 17, 2014 at 11:57am by Steve
Math Inequalities
thank you bob I appreciated the help
Thursday, November 5, 2009 at 3:20pm by Anna
Math: Inequalities
I understand this now
Tuesday, September 21, 2010 at 3:54pm by Amy~
Algebra 1
-p/-7>-9 What is p? For solving inequalities.
Thursday, December 16, 2010 at 9:45pm by Lauren
Equations and Inequalities
Tuesday, February 22, 2011 at 3:35pm by RNRH
Thank you both so much.
Saturday, April 21, 2012 at 3:26pm by Some1 Help Me Plz
Linear equations and inequalities
Tuesday, June 5, 2012 at 5:24pm by Jewel
Math inequalities
good job
Tuesday, January 1, 2013 at 3:39pm by Reiny
inequalities x-5<15
Wednesday, April 17, 2013 at 10:24pm by tyson
algebra 1
i need help in linear inequalities
Tuesday, July 30, 2013 at 9:04pm by Anonymous
Inequalities (Math)
THANK YOU!!! You are A LIFE SAVER!
Thursday, October 10, 2013 at 7:36pm by Gabby
Math- Inequalities
Corrected it so fast? :)
Monday, October 14, 2013 at 12:06am by Anonymous
Math- Inequalities
you are correct, with the update.
Monday, October 14, 2013 at 10:35am by Steve
algebra - inequalities
You're right.
Wednesday, November 20, 2013 at 10:58pm by Ms. Sue
Directions:Write inequalities for the numbers 2 - 4 below. Do not solve them! Problems: 2.Your quiz grades are 19, 17, 20, and 15. What is the lowest grade you can receive on the next quiz and
maintain at least an 18 average? 3.Stacey and Luis volunteer at the local hospital. ...
Thursday, June 21, 2007 at 7:42pm by Erica
Pre Calc
1. Describe the linear programming situation for this system of inequalities. x<(or equal too)1 y>(or equal too)0 3x + y<(or equal too)5 2. Describe the linear programming situation for this system
of inequalities where you are asked to find the maximum value of f(x, ...
Monday, December 10, 2012 at 6:40pm by Carl
math please help
Take the real-life situation and create an equation or inequality that could be used for analysis, prediction, or decision making. Then, draw a graph to depict the variables in your situation (refer
to problem 40 on p. 649). Use your graph and what you know about linear ...
Tuesday, January 15, 2008 at 7:26pm by Anonymous
solving rational inequalities
1/(1+x^2) < 1/2 TIA
Wednesday, February 7, 2007 at 3:58pm by Jen
Wednesday, February 28, 2007 at 5:41pm by chelsea
hello, can you help me to solve this question? x^2+9>0 thank you''
Wednesday, February 20, 2008 at 2:56am by bat
correct on all counts
Thursday, April 17, 2008 at 9:44pm by bobpursley
With equations or inequalities that define the restriction.
Wednesday, November 5, 2008 at 8:19pm by drwls
2r + 5 < -1 solve for inequalities
Tuesday, June 16, 2009 at 11:44am by Anonymous
i need help with graphing inequalities ex: y < 4 + x
Thursday, January 28, 2010 at 2:19am by Rachel
Pages: 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Next>>
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Example 9.4: New stuff in SAS 9.3– MI FCS
September 6, 2011
By Ken Kleinman
We begin the new academic year with a series of entries exploring new capabilities of SAS 9.3, and some functionality we haven't previously written about.
We'll begin with multiple imputation. Here, SAS has previously been limited to multivariate normal data or to monotonic missing data patterns.
SAS 9.3 adds the
statement to
proc mi
. This implements a fully conditional specification imputation method (e.g., van Buuren, S. (2007), "Multiple Imputation of Discrete and Continuous Data by Fully Conditional Specification,"
Statistical Methods in Medical Research, 16, 219–242.) Briefly, we begin by imputing all the missing data with a simple method. Then missing values for each variable are imputed using a model created
with the real and current imputed values for the other variables, iterating across the variables several times.
We replicate the multiple imputation example from the book, section 6.5. In that example, we used the
statement for imputation: at the time, this was the only method available in SAS when a non-monotonic missingness pattern was present. We noted at the time that this was not "strictly appropriate"
method assumes multivariate normality, and two of our missing variables were dichotomous.
filename myhm url "http://www.math.smith.edu/sasr/datasets/helpmiss.csv" lrecl=704;
proc import replace datafile=myhm out=help dbms=dlm;
proc mi data = help nimpute=20 out=helpmi20fcs;
class homeless female;
var i1 homeless female sexrisk indtot mcs pcs;
logistic (female)
logistic (homeless);
In the
statement, you list the method (
logistic, discrim, reg, regpmm
) to be used, naming the variable for which the method is to be used in parentheses following the method. (You can also specify a subset of covariates to be used in the method, using the usual SAS
model-building syntax.) Omitted covariates are imputed using the default
ods output parameterestimates=helpmipefcs
covb = helpmicovbfcs;
proc logistic data=helpmi20fcs descending;
by _imputation_;
model homeless=female i1 sexrisk indtot /covb;
proc mianalyze parms=helpmipefcs covb=helpmicovbfcs;
modeleffects intercept female i1 sexrisk indtot;
with the following primary result:
Parameter Estimate Std Error 95% Conf. Limits
intercept -2.492733 0.591241 -3.65157 -1.33390
female -0.245103 0.244029 -0.72339 0.23319
i1 0.023207 0.005610 0.01221 0.03420
sexrisk 0.058642 0.035803 -0.01153 0.12882
indtot 0.047971 0.015745 0.01711 0.07883
which is quite similar to our previous results. Given the small proportion of missing values, this isn't very surprising.
Several R packages allow imputation for a general pattern of missingness and missing outcome distribution. A brief summary of missing data tools in R can be found in the
CRAN Task view on Multivariate Statistics
. We'll return to this topic from the R perspective in a future entry.
for the author, please follow the link and comment on his blog:
SAS and R
daily e-mail updates
news and
on topics such as: visualization (
), programming (
Web Scraping
) statistics (
time series
) and more...
If you got this far, why not
subscribe for updates
from the site? Choose your flavor:
, or
|
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|
Number of results: 771
Algebra 1A
How many solution sets do systems of linear inequalities have? Do solutions to systems of linear inequalities need to satisfy both inequalities? If so what are some examples?
Wednesday, June 26, 2013 at 4:00pm by Kim
Algebra 1
How many solution sets do systems of linear inequalities have? Do solutions to systems of linear inequalities need to satisfy both inequalities? In what case might they not?
Tuesday, September 4, 2012 at 12:00pm by Austin
How many solution sets do systems of linear inequalities have? Do solutions to systems of linear inequalities need to satisfy both inequalities? In what case might they not?
Sunday, January 27, 2013 at 9:52pm by monet
Systems of Inequalities-8th Grade Algebra
Graph the equation. The graph will divide the coordinate plane into four reqions. Write a system of inequalities that describe each region. Labe the region with these inequalities. 1) y = x - 3 y = 9
- x I already graphed it, I only need help on writing the systems of ...
Thursday, March 12, 2009 at 10:14pm by Marta
Gender Inequalities
Are there any inequalities between men and women in the armed forces?
Tuesday, May 27, 2008 at 9:30pm by Katherine
No inequalities were presented. You cannot copy from homework and and paste it here; you have to retype the inequalities.
Sunday, December 16, 2007 at 2:54pm by drwls
graph solution set of system of inequalities x+y< 4 x-2y>6
Wednesday, April 11, 2012 at 2:14am by Anonymous
math inequalities please check
your inequalities are right. :)
Monday, October 25, 2010 at 10:51pm by jai
Or would it having to be negative only for polynomial inequalities and for rational inequalities they have t be positive?
Monday, September 27, 2010 at 5:40pm by Amy~
i'm dealing with inequalities with one variable and i'm just curious as to why i am doing this? i would like to know the theories behind this.... please help or maybe give me a site?
Wednesday, March 25, 2009 at 9:54pm by cynthia
algabra II
does anyone have the answers to exam 00703600 inequalities, permutations, and probabilities i just need the part on graphing the inequalities
Wednesday, September 29, 2010 at 7:38pm by kay
math - inequalities
How many integers are common to the solution sets of both inequalities? x+7 ≥ 3x 3x+4 ≤ 5x
Saturday, December 14, 2013 at 9:30pm by Maggie
graph the system of inequalities: ( x-3)^2/9 + (y+2)^2/4<=1 and (x-3)^2+(y+2)^2>=4 I do not know how to simplify this down enough to graph it
Saturday, April 21, 2012 at 3:26pm by Some1 Help Me Plz
algerbra 2
so how do I explain inequalities and why x<8 and y<40 are also inequalities for this system? Do I add or multiply by 4?
Friday, November 22, 2013 at 5:46pm by malik
Go on: wolframalpha dot com When page be open in rectangle type: ( x-3)^2/9 + (y+2)^2/4<=1 , (x-3)^2+(y+2)^2>=4 and click option = After few seconds you will see everything about your
inequalities,including graph.
Saturday, April 21, 2012 at 3:26pm by Bosnian
education inequalities
What are some inequalities in education between men and women?
Friday, May 23, 2008 at 10:51am by Katherine
Re: Math
The only inequalities where I have to check the values between the points are polynomial and rational inequalities, right? And not any other type of inequalites By Checking I mean to know which way
to shade on a graph Just making sure
Tuesday, September 28, 2010 at 7:53pm by Amy~
algebra 1
I can't graph this for you here. Put "solving systems of inequalities" in google and click on the second link (the one with 'purplemath' in the address). This website gives an example of how to graph
and solve inequalities.
Tuesday, February 8, 2011 at 4:54pm by helper
Solve the compound inequalities. Write the solutions in interval notation. Graph your solution on a number line. 1. 2(3x + 1)< -10 or 3(2x - 4) ¡Ý 0 The or means union of these inequalities. 2. 5(p +
3) + 4 > p - 1 or 4(p - 1) + 2 > p + 8
Thursday, August 30, 2012 at 6:20pm by Neil
algerbra 2
. Explain your inequalities and explain why and are also inequalities for this system
Tuesday, November 5, 2013 at 3:26pm by nicki
Suppose you need $2.40 in postage to mail a package to a friend. You have 9 stamps, some $0.20 and some $0.34. How many of each do you need to mail the package? So to solve this problem, I came up
with two inequalities: 1. a + b is less than or equal to 9 2. 20a + 34b is ...
Friday, April 10, 2009 at 5:16pm by Angie
But we are doing systems of linear inequalities, so I'd want at least two different inequalities. Also, I don't understand how you put x,y, and -1 into the parentheses. Also, would this work? 30x +
15y >= 150 x + y - 10 <= 200
Monday, January 13, 2014 at 7:54pm by Anonymous
1. Marissa is a photographer. She sells framed photographs for $100 each and greeting cards for $5 each. The materials for each framed photograph cost $30, and the materials for each greeting card
cost $2. Marissa can sell up to 8 framed photographs and 40 greeting cards each ...
Monday, January 20, 2014 at 10:56am by Jessica
Math Check
The only inequalities where I have to check the values between the points are polynomial and rational inequalities, right? And not any other type of inequalites By Checking I mean to know which way
to shade on a graph Just making sure
Tuesday, September 28, 2010 at 4:55pm by Amy~
alg2 check?
Graph the system of inequalities then substitute the (x,y)order pair into both inequalities. y>3x+1 y<-2/3x+4 (second one has a line under the arrow) I don't get what they are asking for? if they
want me to solve it how am I suppose to set it up?
Thursday, July 18, 2013 at 1:49pm by tyneisha
Math Ms. Sue Please help!
Can you find me a website how to do inequalities on line graphs on the less than and greater than inequalities. Ex: 2r-2<4 (A line goes under the sign "<")
Wednesday, February 13, 2013 at 7:05pm by Angelina
inequalities graph
You might want to try some of the following tutorials: http://search.yahoo.com/search?fr=mcafee&p=inequalities+graph+tutorial Sra
Sunday, November 21, 2010 at 8:04pm by SraJMcGin
Consider the two inequalities 2x - 4 < y and y < -2/3x + 2. (b) Graph the region of the plane that satisifies either inequality, or both inequalities. (c) Graph the region of the plane that
satisifies either inequality, but NOT both. What I don't get is that in another ...
Wednesday, February 4, 2009 at 5:23pm by Lilianne
Algebra 1 Concept Explaination
Tuesday, January 14, 2014 at 9:13pm by bobpursley
algebra 1
Material cost equation : 30x + 2y = 200 Profit equation : 100x + 5y = 400 B. Explain your inequalities and explain why x<8 and y<40 are also inequalities for this system
Friday, November 22, 2013 at 6:11pm by malik
Let our two variables be: p # of pharmacy hours b # of babysitting hours Then we should have two statements from the given facts: and We can graph these inequalities by solving for either p or b in
both inequality. Once the inequalities are graphed then any point that is ...
Monday, May 6, 2013 at 5:37pm by Taylor
You have to try to solve the inequality and then conclude at some point that there are no solutions. Sometimes you can use some inequalities that always hold, like: |a| >= 0 |a+b| <= |a| + |b| etc.
If you can rearrange an inequality so that it contradicts these standard ...
Friday, January 16, 2009 at 7:25pm by Count Iblis
A home-based company produces both hand-knitted scarves and sweaters. please help please The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited
to 40 hours per week, and the total production capacity is 5 items per week. ...
Thursday, January 31, 2008 at 3:30pm by Brenda
Solving inequalities
I have to solve the following inequalities: x^2 + y^2 is less than or equal to 49 y is less than or equal to 3-x^2 I know that these are the equations of a circle and a parable. There should be 3
solutions. However, I am not sure how to solve these equations. CAn you help? ...
Monday, March 30, 2009 at 7:11pm by Joanie
Math: Polynomial inequalities
Inequalities involving parabolas can get interesting. Solve as an equation: 2t^2 - t -3 = 0 (t+1)(2t-3) = 0 t = -1 or 3/2 Think now of the graphs of 2t^2 - 3 and t You want the region where the
parabola is below the line. That is, -1 <= x <= 3/2 Of course, you can do ...
Tuesday, October 18, 2011 at 3:34pm by Steve
Quadratic Equations
The solution to inequalities is a region, not just a point. In this case, think of the graphs. y < -x^2 is the whole inside of the downward-opening parabola with vertex at (0,0). x^2 + y^2 < 16 is
the inside of the circle of radius 4 centered at (0,0). So, is 9+4<16? ...
Tuesday, June 12, 2012 at 3:50pm by Steve
Write -14 <= 3x-7 <= -2 or -14 ≤ 3x-7 ≤ -2 (≤ is written as "& l e ;" without the double quotes and without spaces). There are two inequalities. We need to solve each one separately and find the
solution interval that satisfies both inequalities. -14 ≤ 3x-7...
Sunday, January 23, 2011 at 2:02am by MathMate
Write a system of inequalities to express the exterior of the triangle ABD if A=(-2,7), B=(4,0), and C=(1,-3). Please help! gracias<3 Derive equations for the three lines connecting the three points.
Then change the equations to inequalities to represent the region on the ...
Wednesday, December 20, 2006 at 7:10pm by Lily
Something that helped me determine whether to set up a double inequality versus separate inequalities... |expression|< k less thAN (and)= double inequalities -k<|expression|< k |expression|> k
greatOR (or) = separate inequalities |expression|< -k or |expression...
Saturday, October 2, 2010 at 1:10pm by TutorCat
I'm assuming this is one problem with 2 inequalities. 7 + m >= 2. m + 1 < 2. 7 + m >= 2, Subtract 7 from each side: m >= -5, m + 1 < 2, Subtract 1 from each side: m < 1. Compound the 2 simplified
inequalities: -5 <= m < 1. The inequality states that m ...
Tuesday, September 7, 2010 at 7:38pm by Henry
Pre-calculus-check answers
Describe the linear programming situation for this system of inequalities where you are asked to find the maximum value of f(x,y)=x+y. Answer: an optimal solution 2)Describe the linear programming
situation for this system of inequalities: Answer: an optomal solution
Saturday, August 23, 2008 at 2:06pm by Lucy
Pre-Calculus-check answers
Describe the linear programming situation for this system of inequalities where you are asked to find the maximum value of f(x,y)=x+y. Answer: an optimal solution 2)Describe the linear programming
situation for this system of inequalities: Answer: an optomal solution
Saturday, August 30, 2008 at 11:17am by Lucy
Pre-Calculus check answers
Describe the linear programming situation for this system of inequalities where you are asked to find the maximum value of f(x,y)=x+y. Answer: an optimal solution 2)Describe the linear programming
situation for this system of inequalities: Answer: an optomal solution
Sunday, August 31, 2008 at 11:46am by Lucy
Try to solve these inequalities first. Compound inequalities with 'Or', are solved separately and the solutions have 'or' between them. Example. If the solution to the first was x < 2 and the
solution for the second was x > 4, then the solution would be, x < 2 OR x &...
Saturday, January 29, 2011 at 10:32pm by helper
set the inequalities to 3 and pretend its an equal sign when you solve it. 1/2(6-2x)+2_>3 3-x+2_>3 5-x_>3 -x_>-2 x<_2 this means that for any x values that are less than or equal to 2, then the y
values would be greater than or equal to 3. *note that there are ...
Monday, October 22, 2007 at 10:21pm by jennifer
graph the system of inequalities, and classify the figure created bu the solution region. y¡Ü4x+4 y¡Ü-0.25x+4 y¡Ý4x-1 y¡Ý-0.25x-1 a)the shaded region is a plane minus a rectangle b)there is no region
common to all four inequalities c)the shaded region is a rectangle d)the ...
Thursday, May 17, 2012 at 6:46pm by jenika
graph the system of inequalities, and classify the figure created bu the solution region. y¡Ü4x+4 y¡Ü-0.25x+4 y¡Ý4x-1 y¡Ý-0.25x-1 a)the shaded region is a plane minus a rectangle b)there is no region
common to all four inequalities c)the shaded region is a rectangle d)the ...
Thursday, May 17, 2012 at 7:57pm by jenika
algebra 1
Marissa is a photographer. She sells framed photographs for $100 each and greeting cards for $5 each. The materials for each framed photograph cost $30, and the materials for each greeting card cost
$2. Marissa can sell up to 8 framed photographs and 40 greeting cards each ...
Friday, November 22, 2013 at 5:39pm by malik
Math (Absolute Value Inequality)
You probably would like to find the value of a. We established that to satisfy the quadratic inequality x^2−11x−210 < 0 -10<x<21 Now substitute this interval into each of the two linear inequalities:
x-8<a and 8-x <a (-10)-8<a => a>-18 8-(-...
Sunday, May 26, 2013 at 3:31am by MathMate
algebra 1
. Marissa is a photographer. She sells framed photographs for $100 each and greeting cards for $5 each. The materials for each framed photograph cost $30, and the materials for each greeting card
cost $2. Marissa can sell up to 8 framed photographs and 40 greeting cards each ...
Friday, November 22, 2013 at 5:21pm by nicki
Hi, I am having some problems with inequalities. It is asking us to solve and graph on a number line and then write it in interval notation and set notation. X>2 and X>4 I graphed them in a number
line already and i have the following: Interval notation (2,infinity) and ...
Monday, February 14, 2011 at 12:33pm by phobia
MATH 116
Look down about a third of the page http://www.sosmath.com/algebra/inequalities/ineq02/ineq02.html
Saturday, November 14, 2009 at 10:30pm by Reiny
Quanitive Methods
A car rental company has $540,000 to purchase up to 25 new cars of two different models. One model costs $18,000 each and the other model costs $24,000 each. Write a system of linear inequalities to
describe the situation. Let x represent the first model and y represent the ...
Monday, October 1, 2007 at 12:33am by Tam
Sunday, June 26, 2011 at 5:55am by drwls
College Algebra-Study Material
I am going to take the CLEP (College Level Examination Program) College Algebra examine. I am trying to decide on what books I should use to prepare for this examine. The following is what is going
to be covered in this examine: 25% Algebraic operations Factoring and expanding...
Friday, November 28, 2008 at 10:15am by G
Solve the following linear inequality graphically. x+2y<4 x-y<5 Each inequality is satisfied in a particular region of an x,y plot. The first inequality is satisfied below the line y = -x/2 + 2, for
example. The second inequality is satisfied above the line y = x + 5. ...
Sunday, June 3, 2007 at 10:54pm by Graphing Help!
math inequalities please check
A landscape designer has to design a rectangular pad of concrete at the centre of a rock garden. The lenght must be less than or equal to twice the width; the perimeter must be less than or equal to
40 m; and the area must be greater than or equal to 60 m². 1.)Write as system ...
Monday, October 25, 2010 at 8:23pm by Sandi
1) Why should we clear fractions when solving linear equations and inequalities? Demonstrate how this is done with an example. Why should we clear decimals when solving linear equations and
inequalities? Demonstrate how this is done with an example.
Wednesday, March 21, 2012 at 10:37am by jess
math (graphing)
Thank you VERY much! You're my savior :) just one more question.. I NOW understood how to graph equations.. but I still have to graph inequalities, which seems much more complicated from my point of
view. I've got two inequalities that I have to graph. 1. y > 2/3x-4 2. y &...
Sunday, May 3, 2009 at 5:45am by xxx
Algebra 1 (Reiny)
Will you please explain the steps I must take in order to graph these linear inequalities? Graph each system of linear inequalities. Give two ordered pairs that are solutions and two that are not
solutions. 1. y < 2x - 1 y > 2 2. x < 3 y > x -2 3. y => 3x 3x + y...
Thursday, January 9, 2014 at 9:55pm by Victoria
I can't quite make out your diagram, but your graph should look like the diagram #2 on the first page of this ... http://www.gradeamathhelp.com/support-files/compound-inequalities-b.pdf Your open
circles should be around the -3 and +5
Thursday, April 8, 2010 at 10:22am by Reiny
math inequalities please check
A landscape designer has to design a rectangular pad of concrete at the centre of a rock garden. The length must be less than or equal to twice the width; the perimeter must be less than or equal to
40 m; and the area must be greater than or equal to 60 m^2. 1.)Write as system...
Monday, October 25, 2010 at 10:51pm by Sandi
math link to instructions
Monday, December 10, 2012 at 6:02pm by Damon
algebra 1
Marissa is a photographer. She sells framed photographs for $100 each and greeting cards for $5 each. The materials for each framed photograph cost $30, and the materials for each greeting card cost
$2. Marissa can sell up to 8 framed photographs and 40 greeting cards each ...
Friday, November 22, 2013 at 10:27pm by malik
Math/ Algebra
Post your responses to the following. Answer each question in a separate paragraph: Techniques that can simplify solving equations and inequalities are to clear fractions and decimals when solving
linear equations and inequalities. 1. Demonstrate how fractions are cleared with...
Monday, June 14, 2010 at 5:26pm by Amanda
Algebra 1 (Reiny)
I desperately need guidance. Not only do I not know how to graph these systems of linear inequalities, but I also do not understand the concept whatsoever. I have watched several videos regarding the
subject, but I didn't retain anything from them. Please, I desperately need ...
Tuesday, January 14, 2014 at 10:21pm by Anonymous
An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function
at each corner of the graphed region. Use these values to determine the maximum...
Monday, February 22, 2010 at 4:29pm by ReRe
relations and fucntions
Seeds of type A and type B are sold in a packet each must contain a)both type a and type b seeds b)at least twice the number of type b c)as there are type a seeds no more thanm 12 seeds 1)state the
minimum number in each packet of type a and type b seeds. 2)if there are x type...
Tuesday, February 26, 2008 at 8:23pm by Keisha
math (urgent help needed)
Seeds of type A and type B are sold in a packet each must contain a)both type a and type b seeds b)at least twice the number of type b c)as there are type a seeds no more thanm 12 seeds 1)state the
minimum number in each packet of type a and type b seeds. 2)if there are x type...
Friday, February 29, 2008 at 3:16pm by Keisha
math(relation & functions) need help urgently
Seeds of type A and type B are sold in a packet each must contain a)both type a and type b seeds b)at least twice the number of type b c)as there are type a seeds no more thanm 12 seeds 1)state the
minimum number in each packet of type a and type b seeds. 2)if there are x type...
Thursday, February 28, 2008 at 8:09pm by Keisha
algebra - inequalities
Wednesday, November 20, 2013 at 10:58pm by orpheus
algebra 1
Marissa is a photographer. She sells framed photographs for $100 each and greeting cards for $5 each. The materials for each framed photograph cost $30, and the materials for each greeting card cost
$2. Marissa can sell up to 8 framed photographs and 40 greeting cards each ...
Saturday, November 23, 2013 at 7:57am by malik
what or the signs of inequalities ?
Monday, September 29, 2008 at 8:56pm by mikale
pressure inequalities
Sunday, October 2, 2011 at 5:47pm by Shaq
Inequalities (Math)
You're welcome. :-)
Thursday, October 10, 2013 at 7:36pm by Ms. Sue
Math- Inequalities
Monday, October 14, 2013 at 12:06am by Steve
Algebra 1--Three Word Problems (Reiny or Kuai)
to graph inequalities, draw the lines that represent the equations (as if not inequalities). Then shade the area above or below the line, depending on whether y is greater or less than the values on
the line. For example, on #1, if Linda works p hours at the pharmacy and b ...
Friday, January 17, 2014 at 11:57am by Steve
Math Inequalities
thank you bob I appreciated the help
Thursday, November 5, 2009 at 3:20pm by Anna
Math: Inequalities
I understand this now
Tuesday, September 21, 2010 at 3:54pm by Amy~
Algebra 1
-p/-7>-9 What is p? For solving inequalities.
Thursday, December 16, 2010 at 9:45pm by Lauren
Equations and Inequalities
Tuesday, February 22, 2011 at 3:35pm by RNRH
Thank you both so much.
Saturday, April 21, 2012 at 3:26pm by Some1 Help Me Plz
Linear equations and inequalities
Tuesday, June 5, 2012 at 5:24pm by Jewel
Math inequalities
good job
Tuesday, January 1, 2013 at 3:39pm by Reiny
inequalities x-5<15
Wednesday, April 17, 2013 at 10:24pm by tyson
algebra 1
i need help in linear inequalities
Tuesday, July 30, 2013 at 9:04pm by Anonymous
Inequalities (Math)
THANK YOU!!! You are A LIFE SAVER!
Thursday, October 10, 2013 at 7:36pm by Gabby
Math- Inequalities
Corrected it so fast? :)
Monday, October 14, 2013 at 12:06am by Anonymous
Math- Inequalities
you are correct, with the update.
Monday, October 14, 2013 at 10:35am by Steve
algebra - inequalities
You're right.
Wednesday, November 20, 2013 at 10:58pm by Ms. Sue
Directions:Write inequalities for the numbers 2 - 4 below. Do not solve them! Problems: 2.Your quiz grades are 19, 17, 20, and 15. What is the lowest grade you can receive on the next quiz and
maintain at least an 18 average? 3.Stacey and Luis volunteer at the local hospital. ...
Thursday, June 21, 2007 at 7:42pm by Erica
Pre Calc
1. Describe the linear programming situation for this system of inequalities. x<(or equal too)1 y>(or equal too)0 3x + y<(or equal too)5 2. Describe the linear programming situation for this system
of inequalities where you are asked to find the maximum value of f(x, ...
Monday, December 10, 2012 at 6:40pm by Carl
math please help
Take the real-life situation and create an equation or inequality that could be used for analysis, prediction, or decision making. Then, draw a graph to depict the variables in your situation (refer
to problem 40 on p. 649). Use your graph and what you know about linear ...
Tuesday, January 15, 2008 at 7:26pm by Anonymous
solving rational inequalities
1/(1+x^2) < 1/2 TIA
Wednesday, February 7, 2007 at 3:58pm by Jen
Wednesday, February 28, 2007 at 5:41pm by chelsea
hello, can you help me to solve this question? x^2+9>0 thank you''
Wednesday, February 20, 2008 at 2:56am by bat
correct on all counts
Thursday, April 17, 2008 at 9:44pm by bobpursley
With equations or inequalities that define the restriction.
Wednesday, November 5, 2008 at 8:19pm by drwls
2r + 5 < -1 solve for inequalities
Tuesday, June 16, 2009 at 11:44am by Anonymous
i need help with graphing inequalities ex: y < 4 + x
Thursday, January 28, 2010 at 2:19am by Rachel
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Reverse Modulus Operator
Date: 10/09/2001 at 07:13:05
From: Charles
Subject: Reverse modulus operator
In mathematics, for each action we do, there is normally a reverse
action that allows us to get back to the original two numbers. This
can be seen in the relation between addition and subtraction,
multiplication and division, or even logarithmic and exponential
I am curious to find out if there is an operator that would return 2
when we we do 6 * 0, * being this new operator.
Date: 10/09/2001 at 11:57:20
From: Doctor Roy
Subject: Re: Reverse modulus operator
Thanks for writing to Dr. Math.
I assume that you mean the modulus operator as used in computer
science, i.e. 6 mod 2 = 0.
There cannot possibly be a well-defined inverse operation. This can be
seen easily following this example:
6 mod 2 = 0
6 mod 3 = 0
Let's call the inverse operation invmod
6 invmod 0 = ? 2 or 3 or 1 or 6 or ?
Since there cannot be a single value that satisfies this operation, it
is not well-defined.
It turns out that there are several operations that work in one
direction and have no inverse operation.
I hope this helps.
- Doctor Roy, The Math Forum
Date: 10/09/2001 at 12:15:03
From: Doctor Peterson
Subject: Re: Reverse modulus operator
Hi, Charles.
Interesting question! I don't think the final answer will be what you
want, but the thinking on the way there will be worth having gone
You have probably learned about inverse functions, and know that not
every function has an inverse. The same is true of inverse operations.
The existence of an inverse is not "normal," but a very special
situation. The reason you think of it as normal is that invertible
operations are particularly useful, so we tend to use them and give
them names. Among familiar operations, therefore, invertibility is
common, though not by any means universal.
Also, it's worth noting that not all operations are commutative, as
addition and multiplication are. When an operation is not commutative,
you have to be careful about order, and it turns out that there are
two different kinds of inverse you can talk about. For addition, the
inverse operation, subtraction, is defined by
(x + y) - y = x
(x - y) + y = x
We can call subtraction the "right inverse" of x, since doing it on
the right of an addition undoes that addition. (I'm not positive that
this is a standard term in this context, but I think it's right.) If
we try to make subtraction a "left inverse," we find that it doesn't
quite work:
x - (x + y) = -y
x + (x - y) = -y
That happens because subtraction is not commutative.
You are asking about the "mod" (remainder) operation. Recall that this
is defined by
x mod y = z if x = ny + z for some integer n, and 0 <= z < y
(I'll ignore questions that arise if x or y are negative.)
Apparently you want a left inverse of the mod operation, which we'll
call "*", that gives the divisor when you know the dividend and
remainder, so that if
x mod y = z e.g. 6 mod 2 = 0
x * z = y e.g. 6 * 0 = 2
This can be written as
x mod (x * z) = x e.g. 6 mod (6 * 0) = 0
x * (x mod y) = y e.g. 6 * (6 mod 2) = 2
The problem is that there is not just one divisor for a given dividend
and remainder:
6 mod 1 = 0
6 mod 2 = 0
6 mod 3 = 0
6 mod 6 = 0
Which of 1, 2, 3, and 6 should be the result of 6*0?
The same sort of problem occurs with the "right inverse," which gives
the dividend given the divisor and remainder:
(z ** y) mod y = z e.g. (0 ** 2) mod 2 = 0
(x mod y) ** y = x e.g. (6 mod 2) ** 2 = 6
This time, we see that
2 mod 2 = 0
4 mod 2 = 0
6 mod 2 = 0
and so on, so there are many solutions to the equation
x mod 2 = 0
and no one value to choose for 0 ** 2.
Just as with functions, the fact that the "mod" operation takes
multiple inputs to the same output makes an inverse operation
However, just as we have an inverse function "square root" that
inverts the square function _when we restrict the domain of the
latter_, we can do the same here. It's not very useful, however. Note
x mod y = x when 0 <= x < y
so if we restrict the function f(x) = x mod y to that domain, the mod
function becomes the identity function f(x) = x. Therefore, the
inverse operation is simple:
x ** y = x when 0 <= x < y
What this does is to find ONE of many possible dividends that give the
desired remainder, namely the remainder itself. Another approach would
be to have a multivalued "function" that gives ALL possible dividends;
this is
x ** y = x + ny, for any integer n
It's a little more complicated to do this for your "*" operation. Here
you would want to find either one, or all, divisors that leave the
given remainder. Given that
x mod y = z
we can express this as
x = ny + z for some integer n
To solve for y, we get
y = (x-z)/n, for any integer n that divides (x-z)
x * z = 1
x * z = x - z
x * z = smallest factor of x-z greater than 1
are possible partial inverse operations that give ONE possible
divisor; and
x * z = all divisors of x-z
gives all possible answers. But that doesn't really give you what you
wanted, does it? Defining the inverse doesn't help in actually doing
You may be interested in these answers related to the mod function:
What is Modulus?
Mod Function and Negative Numbers
This one, about inverse operations, is also worth reading:
Inventing an Operation to Solve x^x = y
- Doctor Peterson, The Math Forum
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Distance Between Two Points
People usually forget a formula to find a distance between two points. The thing is that, you don’t need to memorize the formula if you know where the formula comes from.
The key essence to find the distance between two point is Pythagorean Theorem. If you have a right triangle, the square of hypotenuse is equal to sum of squares of other two sides.
a^2 + b^2 = c^2
If you know this equation you don’t needs to worry about formula for the distance between two points.
For example, let’s find the distance between (2,4) and (5,8).
You should connect these two points, then the length of the line should equal to distance between two points.
Then you should make a right triangle with the line as a hypotenuse.
(5,8) |
(2,4)|__ (5,4)
Like this. Then you can easily get the other two sides. By subtracting.
One side is 5 – 2 = 3
The other side is 8 – 4 = 4
So now, you got a right triangle with two sides, so you can easily find the hypotenuse.
Hypotenuse = square root of (3^2 + 4^2) = square root of 25 = 5
Previously, I said the hypotenuse is the distance between two points, so the distance between two point (2,4) and (5,8) is 5.
The general formula for getting distance between (a,b) and (c,d) is
R = square root of ((c-a)^2 + (d-b)^2)
Where R is the distance between two points.
This article was written for you by Edmond, one of the tutors with SchoolTutoring Academy.
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A parallelogram is a quadrilateral with opposite sides parallel and equal. The opposite angles of a parallelogram are congruent. Any side of a parallelogram is called its base (in general, the bottom
horizontal line is considered to be base). The perpendicular distance from the base to the opposite side is called the altitude or height of a parallelogram.
Parallelogram results to few other quadrilaterals by adding restrictions.
• A parallelogram with all equal sides and equal angles of 90° is a square.
• A parallelogram with all right angles is a rectangle.
• A parallelogram with all sides equal is a rhombus.
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Re: st: Looking up values in a 2 dimensional table
[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]
Re: st: Looking up values in a 2 dimensional table
From David Kantor <kantor.d@att.net>
To statalist@hsphsun2.harvard.edu
Subject Re: st: Looking up values in a 2 dimensional table
Date Thu, 17 Apr 2008 20:58:19 -0400
At 06:26 PM 4/17/2008, Mike Lacy wrote:
A colleague of mine has a data file with family income and family size for a large sample, with real family income for each of a series of years, in the wide format, e.g., something like:
famid FamSize1985 FamSize1987 FamSize1991 ... Inc1985 inc1987 Inc1991 ...
with family sizes and family incomes recorded for about 20 different year, not at fixed intervals.
He needs to create a poverty status indicator corresponding to each year, based on a 2 dimensional table giving poverty thresholds for each value of year and family size. All the ways I can
imagine doing this seem relatively clumsy. (Among other things, I thought about ways of doing this with a matrix but they would require using the value of the family size variable as an index
into the matrix, which is beyond my ken.)
I also considered something involving reshape and merge, but that seemed awkward as well.
First, you probably mean Poverty Guideline.
Poverty Guideline is a simple, rough calculation based on family size, income, and year.
Poverty Threshold is a more complex calculation that considers number of children and number of elderly in addition to the other factors. It is the "officially correct" measure, but is more
complicated to compute.
Those are U.S. government standards. (USDA, I believe.)
I have ado files to calculate both of these. But for the threshold, it works for 1997 & 1998 only.
For the guideline, it does 1982-2007.
Either of them can be "filled in" to handled other years. (And BTW, the poverty guideline program uses a matrix.)
Write me privately if you want these. But note that there are no help files yet.
--David Kantor
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
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Need Help with Trig Modeling
March 19th 2009, 05:52 PM #1
Mar 2009
New York
Need Help with Trig Modeling
Could someone help me with trig modeling problem?
4)Assume that are aboard a submarine, submerged in the Pacific Ocean. At time t=0 you make contact with an enemy destroyer. Immediately, you start "porpoising" ( going deeper and shallower). At
time t= 4 minutes, you are at your deepest, y= -1000 meters. At time t= 9 minutes, you next reach your shallowest, y= -200 meters. Assume that y vries sinusoidally with t for t > 0.
a) Sketch the graph of y versus t.
b) Write the particular equation expressing y in terms of t.
c) Your submarine is "safe" when it is below y = -300 meters. At time t=0, was your submarine safee? Justify your answer.
Trig equation
Hello tictac
4)Assume that are aboard a submarine, submerged in the Pacific Ocean. At time t=0 you make contact with an enemy destroyer. Immediately, you start "porpoising" ( going deeper and shallower). At
time t= 4 minutes, you are at your deepest, y= -1000 meters. At time t= 9 minutes, you next reach your shallowest, y= -200 meters. Assume that y vries sinusoidally with t for t > 0.
a) Sketch the graph of y versus t.
b) Write the particular equation expressing y in terms of t.
c) Your submarine is "safe" when it is below y = -300 meters. At time t=0, was your submarine safee? Justify your answer.
The equation you need will be something like
$y = a\sin b(t+c) +d$
In this equation, the amplitude = $a$ = half the difference between the deepest and shallowest positions. (So you can work out the value of $a$, from the information given.)
The period $= \frac{2\pi}{b}=$ the time for one complete 'cycle' = twice the time between the deepest and shallowest positions. (So you can work out the value of $b$.)
$d$ represents the average depth; so it's mid-way between the deepest and shallowest. $y$ then varies from $d+a$ to $d-a$.
$c$ is the phase shift; you can work it out (once you've found $a, b$ and $d$) if you know a value of $y$ at a certain time t. So plug $t = 4, y = -1000$ into your equation, and you're there.
Thanks Grandad! I already solved it! The ans I got is:
y = -400 sin (.628t -.943) - 600.
Hello tictacThe equation you need will be something like
$y = a\sin b(t+c) +d$
Thanks Grandad! I already solved it! The ans I got is:
y = -400 sin (.628t -.943) - 600.
In this equation, the amplitude = $a$ = half the difference between the deepest and shallowest positions. (So you can work out the value of $a$, from the information given.)
The period $= \frac{2\pi}{b}=$ the time for one complete 'cycle' = twice the time between the deepest and shallowest positions. (So you can work out the value of $b$.)
$d$ represents the average depth; so it's mid-way between the deepest and shallowest. $y$ then varies from $d+a$ to $d-a$.
$c$ is the phase shift; you can work it out (once you've found $a, b$ and $d$) if you know a value of $y$ at a certain time t. So plug $t = 4, y = -1000$ into your equation, and you're there.
March 19th 2009, 11:20 PM #2
March 20th 2009, 06:28 AM #3
Mar 2009
New York
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zero point, AIP4WIN
Citizen Sky is now officially permanent part of the AAVSO. In the coming weeks we will be moving additional content to the AAVSO site and freezing this site as an archive of the 1st three years of
the project. Please visit
the new landing page
for future updates.
By c_hofferber on July 19, 2010 - 3:00pm
Hi Chris, To see the zeropoint Zp drop out - Write the photometric equations for V1 the variable and V2 the comparison: V1 = v1 + Tc*(B-V)1 - k'*X1 + Zp V2 = v2 + Tc*(B-V)2 - k'*X2 + Zp Subtract the
two i.e. we perform differential photometry: V1-V2 = v1-v2 + Tc*[(B-V)1 - (B-V)2] - k'*(X1-X2) Add V2 to both sides of the equation: V1 = V2 + v1-v2 + Tc*[(B-V)1 - (B-V)2] - k'*(X1-X2) Solve for
variable star V1 which is epsilon using say lambda as a comparison star V2. Note: AIP4WIN calles the first star to be measured Var and the second measured star C1. V2 = cat value of lambda =
4.705Vmag v1-v2 is measured by AIP4WIN seeMeasure, Photometry, Single Image window. Click first on epsilon Var, then on lambda C1, then click get magnitude and plug the differential magnitude
reported by AIP4WIN into v1-v2 above. Besure to average enough frames so that sintillation errors of short exposures are the equivalent of one long exposure of about 1 minute. Tc is the color
transformation coefficient determined elsewhere. My NikonD100 with a skylightfilter is -0.1204. I thinksomeCannonDSLR have about +0.15.Negative values means myNikon's greenfilter is too blue of
Johnson V filter. The CannonI believe are positive meaning they are too yellow ofthe Johnson V filter. (B-V)1 is epsilon pre-eclipse cat value = +0.54mag. Caution, eclipse may alter the color index.
Check with those who can measure UBV for changes. (B-V)2 is lambda cat value = +0.624mag k' is a positive number usually between 0.2 and 0.5 that must be measured from various field star pairs each
night while high air mass conditions exist. Pick field pair stars far apart in altitude such a Lambda and Eta so as to measure a greater airmass as possible. Later, say end of September, with epsilon
much higher from the horizion, you may choose to take a short cut and totally ignore differential extintion. For now try k'=+0.25 and see how close you get to other reports. You can use the above
differential equation to solve for k' each night using using two or more pairs of stars having know cat values, say lambda for V1 and eta for V2. X1-X2 is the difference in air mass between epsilon
and lambda in that order. Use AAVSO or other airmass calculator. I like www.mirametrics.com/airmass_planner.htm There you have itAND NOZERO POINT! Read the earlier disscussion in this interest area
for tips on how to import your raw camera images into AIP4WIN and how to debayer it properly. Dark frame subtraction is about the only pre calibration I would recommend. Nikon D100 does dark frame
subtraction inside the camera. Most skip flats as it is hard to obtain a wide field illumination source. Watch out for saturation! AIP4WIN analysis can help detect over exposure. Defocus to AIPWIN
default of about 6 pixel radii. etc. Tc, the color tranformation coefficient can be determined from others that have the same camera model (i.e. sensor). Or measure several non variable close star
pairs having greatly different color index and use the equation: Tc = [(V1-V2)cat - (v1-v2)AIP4WIN] divided by [(B-V)1 - (B-V)2]cat.Average at least half a dozen different pairs. You should be able
to derive this equation from the differential photometry equation above. When eps is near zenith this fall/winter you can use Brian Skiff's list of stars see http://www.hposoft.com/Campaign09.html
news letter #6 else use AAVSO's map generator and data base for something near zenith right now. Good luck, Charlie Hofferber
By bkloppenborg on July 22, 2010 - 12:19am
Charlie, You are correct that the zero point is not needed if you calibrate against one star (it drops out exactly like you stated above). We elected to calibrate against several stars in our
tutorials to remove the chance that the varability in the comparision stars (all stars are variables to some extent) would affect the resulting number. Plus by fitting multiple stars using a
least-squares method we can also determine errors in both the transformation coefficient and zero point offset. We also include several stars in our reduction to determine the extinction coefficient
for that exposure, hopefully yielding a more accurate estimate for the target star(s) brightness. I've worked up the spreadsheet for doing these calculations and we're testing it now. I'd be more
than happy to have your input as well (see this thread). Cheers, Brian
By c_hofferber on July 22, 2010 - 4:51am
Hi Brian, I also calibrate or average aginst up to 5 or 6 stars. I wrote the differential form of the photometric equations to show how Zero point drops out for determining Tc and k' as well epsilon
itself. So far I see no need to determine the Zero point. I understand Zero point and the traditional least - squares methode slope and intercept, but have neverused it. Using up to 5 pairs of non
variable field stars, I measure differentially to get 5 values of k' thentake a simple average of k'. I then measureepsilon differentially aginst 5 different comparison stars, apply green filter
color correction, extintion correction, then average the 5 epsilon Vmags and finnally compute the SD of the average. This methode only works well for very high air mass because epsilon and k' are all
measured from the same set of 10 exposure. Also any error in theX air massmodel is absorbed in k' measurement. Also it is easy to find pairs of stars in the wide field that have significant
differential air mass. As epsilon climbs higher, i.e. X become smaller, this method will fail because field star pairs do not have enough differential extinction to calculate k' accurately. I think
this will happen at about X = 2.0. I will then likely assume a seasonal average k' or if I have time, follow a star(s) 30 minutes either side of my main exposue sequence. In the winter it is 20 deg
below in Minnesota, but eps will be near the zenith and I will take 10 quick expsoures and ignore extinction all together! I am aware of a couple spread sheets out there, but have nottried them. They
would probably save time and reduce accounting errors. Charlie Hofferber
By Chris Allen on July 22, 2010 - 8:13am
Hi Charlie, Once again, many thanks for taking the time to help me with this- it really is much appreciated! I think I am now more on the right lines as I have clicked on the 'Get magnitude'. The
file I am using to practise with is the sample file from the citizen sky site and not one of my own files. These are the values I now derive for the 6 comp stars: C1- minus 1.037 plus/minus 0.018 C2-
minus 0.469 plus/minus 0.016 C3- plus 0.023 plus/minus 0.013 C4- plus 0.337 plus/minus 0.012 C5- plus 0.539 plus/minus 0.012 C6- plus 0.869 plus/minus 0.010 Looking at C1, I derive an instrumental
magnitude of 4.705 minus 1.037= 3.668 for eps which is roughly what might be expected (not sure when the images where taken). If you could just 'walk' me through the equations with these values I
would be most grateful. Am I correct in saying that it is not necessary to stack lots of images for a bright variable like Eps and that you could do an average for a number (say 10-20) of separate
images? I have taken some pictures of my own of beta Lyr and will see how far I get with this as eps is currently so low, even from Sweden where I live. All the best, Chris
By c_hofferber on July 24, 2010 - 12:33am
Hi Chris, I can see you are on the right track with measuring raw differential mags in AIP4WIN. I would caution beginners to not click on more than one comparison star. C2, C3, C4 C5 etc. form a
super composite comparison star that is hard to use and will not tell you epsilon differential mag directly. Always Click CLEAR before you make another measurement of a pair of stars. The first star
you click is my v1 which AIP4WIN labels yellow V. Inthis case it looks like you selected epsilon. The second star is my v2 which AIP4WIN labels green C1. Then as you have done, click GET MAGNITUDE
and record the differential mag as -1.037 which is my (v1 - v2). After clicking CLEAR, I suggest you also measure the pairs epsilon - eta, and epsilon- 62 Aur. If photometry isdone right, the three
comparsion stars should yeild appoximately the samemagnitude for epsilon. You can then average the three estimates for epsilon and determine a Standard Deviation. Let me now walkyou thru the
differentialform of the photometric equation for Vmag. Assume the online image was takenDec 20, 2009 at about 11pm localatan observatory about +47 deg north lat (just happens to be my location). I
pulled up The SKY planetarium and see that epsilon isonly 5 deg fromzeneth.The sky reports Epsilon Air Mass X1 = 1.00 and Lambda Air Mass X2= 1.01 The differentialphotometric equation: V1 = V2 + (v1
- v2) + Tc * [(B-V)1 - (B-V)2] - k' * (X1 -X2) Assume the test online image was taken with a Cannon DSLR camer having Tc = +0.15 V is epsilonhaving V=variable, (B-V) assumed cat value of +0.54(yes
the B-V of eps couldbe variable also, but most assume this eclipse isgray thus does not change much). C1 is lambda comparison star cat values of V=4.705, (B-V) = +0.624 AIP4WIN measured -1.037 for
the epsilon - lambda pair Thenightly k' was measuredor assumed to be a typical +0.24 value. V1 = 4.705 + (-1.037) + 0.15 * [(+.54) - (+.624)] - 0.24 * (1.00 - 1.01) V1 = 3.668 + (-0.0126) - (-0.0024)
= 3.657 reported mag for 20 Dec 2009! Thus V1 = 3.657 = epsilon reported Vmagtransformed to Johnson V filter and corrected for extinction. See V band composite light curve at http://www.hposoft.com/
Campaign09.html for other observer reports on orabout 20 Dec 2009. As you see the color correction of -0.0126mag is sizeable due to the camera green filter not being the same as Johnson's standard
Vband filter. As expected, the extinction correction of just -0.002mag is so low it can be ignored in differential photometry if the star to be measured is only a few degrees from the comparison
catalog star and both are say 30 degrees or less from the zenith. Finnaly, you need to stack about 10 exposures or measure 10 frames separtely and average them with a calculator due to sintillation,
i.e. star twinkle. The rull of thum is the number of short exposures should add up to about 1 minute or more total. There is some sintillation estimators on the web. The last time I checked for my
50mm f.l. lens at about f2.8 and 8 sec exposure, the error was about +/-0.02 mag. So by averaging 10exposures the sintillation error is reduce to about0.002 mag. I am kinda embarrassed here in that I
have not taken the time to get AIP4WIN stacking of images to work, soI waste a lot of time with the calculator averaging. One final note youdo not need to use the +/- error reported by AIP4WIN. It is
based upon some S/N statistics. You should report a standard deviation of epsilon measuredby three or more different comparison stars. Others, measure epsilon only aginst lambda. To report standard
deviationthen you need 3 sets of 10 exposures. Average the three estimates and report a SD. There are SD and Air Mass estimator tools on the web, do a google search. All the best Charlie
By Chris Allen on July 25, 2010 - 6:54am
Hi again Charlie, I have just a couple of last questions before trying to put this all into practice on Beta Lyr (as Eps is still so low). Firstly I wondered if you could again walk me through the
calculation of Tc using the AIP4WIN data for Eps Aur. Seeing how the values plug into the equation really is a very big help! Secondly, how do you determine k'? Is 0.25 a typical value? Hopefully I
will soon stop pestering you and start reporting data! I have been interested in variable stars for many years (I am a member of the AAVSO and BAA VSS) but this measurement of digital images is new
to me. All the best from a rainy Swedish island Chris
By c_hofferber on July 27, 2010 - 9:22am
Hi Chris, You are almost ready, but need to determine your camera/lense system Tc, and maybe k' if you can not observe within 60 degrees of the zenith. I think all the differential form of the
equaions I use have been presented by now in the thread that was startedto show zero point is not needed.Rather than extend the length of this thread to show how Tc and k' are extracted from real
images, let me work with you by direct email. If your email found on your web site is current I will contact you there. I amexamining somepreadsheets that others have developed in this form. The
beginner/tutorialversion should determine your Tc and Zero point as well as the Variable mag to report. It lacks extinction correction. An intermediate spreedsheet is under development to
includeextinction. Spreadsheets help automate the process.It is still important to understandthe basis and to be able to hand check your resultsusing the photometric equations. Clear Skies, Charlie
By Chris Allen on July 28, 2010 - 4:11am
Hi Charlie, Thanks for your reply. I am aware of the need to get spreadsheets to work in order to make this process manageable- I have a question about the spreadsheet found on the Citizen Sky
website which I wonder if you could help me with. In AIP4WIN, firstly I click on the variable, eps, which comes up yellow and then on the six comp stars in turn, which are then labelled C1- c6
respectively. The tutorial talks about check stars / calibration stars. Am I correct in thinking that the first comp star I click on, C1 or lambda will be the check star. The differential magnitudes
which AIP4WIN reports when I click 'get magnitude' will then be differential with respect to lambda. Thus if I get a value for C2 (rho) as -0.469, the instrumental magnitude I report in the yellow
space in the spreadsheet for rho will then be 4.705-0.469 = 5.174? I then repeat this for the remaining comp stars which the spreadsheet will then compare with the catalogue values for the
computation of Tc. Is this a correct understanding? If you have an old spreadsheet with your own values in, this would be useful to see. If you give me your email address I'll correspond with you
directly. My email address is chris.allen@telia.com All the best, Chris
By bkloppenborg on July 29, 2010 - 1:45am
Greetings Chris, I'll field this one for Charlie if he hasn't replied to you directly. We tried to make the spreadsheets as simple as possible and, in an effort to minimize errors, made it so you
need not compute anything by hand. So you'll just plug in the imags from your photometry software directly, i.e. the -0.469 you mentioned above. After you insert the calibrator's V-magnitude, and B-V
value (from the calibration standards page or from the 2MASS catalog we link to there), you'll see that the D Cat value (your 5.174) is automatically computed (the value will actually be -5.174 due
to the algebra involved in rearranging the equation, I think we explained that in the tutorial... please let me know if we didn't). At a minimum, you'll need to measure the imags for at least three
stars: your target and two calibrators. I'd suggest using six calibration stars: lam Aur, rho Aur, mu Aur, ome Aur, sig Aur, and 58 Per. You can use one of these stars or some other field star as a
check star. You'll use this star to verify that you are getting reasonable values out of the equations. The spreadsheet will automatically compute the transformation coefficient and zero point based
upon the best fit to the comp star data you provide. The transformation coefficient is the slope of the graph and the zero point is the intercept. Ideally all of your points should fit very closely
to the line and the R-squared term should be close to 1. If you notice that one star is far from the line, it is likely that something was mis-measured or incorrectly entered into the sheet. Lastly
you'll put in the check star imags and target star imags into the cells in the bottom table and the equations in the sheet will automatically compute the calibrated magnitudes. If the check star is
within a few 10s of milli-mags of the catalog value, you'll likely have a valid value for the target object. As Charlie mentioned above, the beginner spreadsheet doesn't account for air mass. The
intermediate spreadsheet has been through the ropes and is ready to be used in general. I'm in the process of writing the documentation for this spreadsheet and Ihope to have it up over the weekend.
Please let us know if you think anything needs to be clarified on the tutorials! Dark Skies, Brian
By c_hofferber on July 29, 2010 - 3:35pm
Hi Chris and Brian, Sorry to take so long getting back to you,I am busy and wanted to try out Brian's Intermediate form of the spreedsheet since the beginner version does not correct for extinction.
For observation of epsilon on 2010/07/25, RJD 5402.8666, 08:47:53 UTC I obtained: Calculator method: V3.644,SD.012,X=2.213, Tc=-.1204, k'=+0.2309 Brian's Spread Sheet: V3.657, ______, X=2.213, Tc=
-.1140, k'=-0.2910 The difference in the two results is only 0.013Vmag or about 1% The Tc differed about 5% k' differed by 20%, but Irejectederrant measures before averagingonly 3 star pairs to
determine k'. The spreed sheet performs a least squares fits of all 6 stars even if some appear morescattered. NOTE, do not be concerned with the sign of k'.The sign of k' isdetermined differently
but consistant within each methode. Classically, I think k' is a positive number. The "Calculator" method is based on the differential phometric equations I presented in this thread. I used 5
comparison stars's average measure of epsilon having the SD noted above. I think Brian's advanced version will have statistical estimate of error and other features perhaps k". Chris, for beta lyra,
you can try the beginner version if imaging is done 60 degrees or less of overhead. For epsilon Aur, theextinction corrections requires you to use theintermediate version at present X=2 or so. Brian,
as an aside, epsilon aur seem to have a dome shaped brightning curve heading for a peak of>= 3.6Vmag in 20 days. I know we are not suppose to extrapolate, but it is fun to speculate on the "donute
hole". Good luck with your visit to CHARA. Clear Skies, Charlie Hofferber
By Chris Allen on July 24, 2010 - 4:57am
Many thanks, Charlie This is now beginning to make some sense. I might have to pester you with a few more questions though! All the best, Chris
By Chris Allen on July 21, 2010 - 3:28pm
Hi Charlie, Many thanks for taking the time to answer my questions. I have a few more questions about the calculations:
Tc = [(V1-V2)cat - (v1-v2)AIP4WIN] divided by [(B-V)1 - (B-V)2]cat Towork out Tc, you need to know the catalogue value of V1 but surely this is the value of the variable you are trying to measure?
From AIP4WIN, I derive v1-v2 as -(minus) 5.7000plusminus 0.017. Am I correct: Tc= (V1-4.705) - (-5.700) / (0.54-+.624). What answer do you get? As I struggle with maths, I wondered whether you could
help me by plugging values into the equation below and again giving me the answer V1 = V2 + v1-v2 + Tc*[(B-V)1 - (B-V)2] - k'*(X1-X2) Many thanks for helping me, Chris Allen / Sweden
By c_hofferber on July 21, 2010 - 10:59pm
Hi Chris, Hang in there, it took me a while to figure some of this photometry out. I am worried if AIP4WIN is giving you -5.700 for (v1-v2) measurement. With lambda as the comparison star V2and
Ignoring color correction and extinction, corrections we have for V1 epsilon: V1 = V2 + (v1 - v2) where (v1- v2) is the differential magnitude reported by AIP4WIN epsilon Vmag = 4.705 + (-5.7000) =
-0.995 Vmag for epsilon! This would make epsilon the brightest star in the sky even under eclipse conditions! Right now (mid July 2010) most observers are reporting Epsilon Vmag = 3.7 or a little
brighter. In AIP4WIN, after reseting or clearing previous measurments, besure you click first on epsilon and it will label the star V, then click on say lambda and it will be labeled C1. Then click
GET MAGNITUDE to find the differential magnitude (v1 - v2). You should get something close to 3.7 - 4.705 = -1.005. Some things to check: Do not overexpose or you will saturate one ormore stars. I
use 8sec at f2.8 to f4.0 at ASA 400 for a 50mmfocal length lens. The raw DSLR image loadsinto AIP4WINso dark you can not see any stars until you click AUTO to scale the image for monitor display.
Under Preferences, DSLR, I only click DeBayer, White balance using camera settings, and BILIN (Bi-Linear Interpolation). On my camera I use white balance sun or daylight. Check on this blog page
about 6 months ago, for Richard Berry, the author of AIP4WIN,slightly different recommendations. I assume you split the color DSLR image by clicking color, split, RGB. Click X-off the other
separatedcolors so you only use the "Green" debayered image. Agin check with the discussion about 6 month ago with Richard Berry for recommendations if you stack images. I have not got the stacking
to work, so I measure 10 images and average using a calculator. You need about 10 images to reduce sintillation error of short exposures. Let me know when you can get AIP4WIN diff mag of about -1.0
for the eps - lambda pair and I can walk you through the rest of the equations. SHORT CUT: If you measure epsilon using the comparison star 62 Aur (05h 07m, +43deg 10') you can come within about
0.03mag of epsilon's true mag without ever correcting for color or extinction. This only works for 62 Aur because it is very close to eps and has almost the same color index (B-V). 62 Aur =
6.218Vmag, B-V = +0.451 and is about 1 degree away from eps. I found your web site but not sure what DSLR and lens you are using. Please get back to me with exposure info so I can try to understand
your data. Also you may have been resetting the AIP4WIN zero point, try to reset AIP4WIN to its defaults to be sure you do not have clipping going on. Good Luck, Charlie Hofferber
By c_hofferber on July 21, 2010 - 11:42pm
Hi Chris, Forgot to answer you question about determining Tc. We do not use epsilon or any other variable star for V1 or v1. Here V1 and v1are the 1st star which AIP4WIN always calls V. V2 and v2 are
the second star which AIP4WIN calls C1. We pick stars having well known catalog values. I use capital letters usually for cataloge values, while small letters represent measured i.e. AIP4WIN values.
It is important to keep the 1st star 2nd star order to avoid sign errors. Never click on lambda the comparison star 1st then on eps the variable second or a sign error will result. We wait untill
epsilon's field of starsare near the zenith so we do not have to worry about extinction. Then we find pairs of stars close to each other aginto minimize extinction corrections. The pairs of stars
should have widely different color indexes (B-V) i.e. a blue star nearby a yellow star. Avoid the realy red stars. Right now, the stars near epsilon will not be near the zenith till fall so we would
have to use another field. Fourtunately, we only have to measure Tc once provided we do not change camera, lens, or telescope. Jeff Hopkins's Epsilon Aurigae news letter #6 has a list of suitable
star near by eps. I can give you an example later if you wish to evaluate the Tc. For now let work on getting AIP4WIN to report the correct differential magnitudes. Charlie Hofferber
By bkloppenborg on July 16, 2010 - 1:33am
Greeting Chris, I think they were about 0.10 for the slope (transformation coefficient) and 2.17 for the intercept (zero point). Don't be worried if the zero point offsets between the two software
packages don't agree as they probably don't use the exact same method for determing insturmental magnitudes. They should, however, yield the same or similar calibrated magnitudes given the same input
data. Cheers, Brian
By Chris Allen on July 18, 2010 - 10:22am
Thanks, Brian. I think you are referring to the graph generated by the Excel data (see tutorial) but in order to determine the coefficient, surely I need to derive a realistic instrumental magnitude
from the stacked image first. I enclose a screen shot from AIP4WIN- would be grateful to know what values to feed in to generate a realistic instrumental magnitude. From the sample image files, I
have so far derived instrumental magnitudes of about 5.2 to 6.1 for the comp stars. Is this realistic? Grateful for any help you can provide. Best wishes, Chris Allen
By bkloppenborg on July 18, 2010 - 11:46am
Greetings Chris, One of the tricky parts about how we've implemented our spreadsheet is that the instrumental magnitudes you get don't necessarily need to match what other people are getting.
Although you are using the sample data, most photometric packages let you apply a constant offset term to the data that, in turn, changes the zero-point offset which, in turn, modifies the
instrumental magnitudes. That's one of the reasons why we didn't include any goal-numbers in our tutorials! In the document you attached, you can safely set the zero point to anything you wish. I'd
suggest using zero, but it's completely arbitrary. The math behind the situation is thus: (V - v) = e * (B-V) - z The import term is the z on the end which is the zero point offset (see the beginner
calibration page for a complete explanation of the other terms). If you add a constant value of say 3.5 to every star (which is your current zero-point offset in your settings tab), we have the
following equations: Star 1: (V - v) = e * (B-V) - (z + 3.5) Star 2: (V - v) = e * (B-V) - (z + 3.5) ... Star 3: (V - v) = e * (B-V) - (z + 3.5) Then, when we do a least-squares fit to solve for the
transformation coefficient, 'e' and the zero-point offset, 'z' we find that z = something - 3.5 where the "something" is the true zero-point offset from your camera and the 3.5 mag is subtracted to
remove the boost of 3.5 given in the above equations. So, in that respect, the zero point values you obtained are completely reasonable. I am, however, interested in what you obtained for a
calibrated magnitudes for the stars in the data set. You should obtain a more-or-less constant comp-star reading (I had changes in the third decimal place for lam aur) and get a calibrated magnitude
for eps Aur around mag 3.7xx(ranging between 3.713 - 3.730) What I'm really trying to stress above is that the zero-point offset is (for our purposes) a completely arbitrary number that is removed
during the calibration process. Because of this, comparing your i-mags with other people's i-mags shouldn't be done. Also, because of atmospheric changes and camera drift, comparing i-mags over
different nights shouldn't be done unless you really, really understand what is happening with your instrument night to night. Hope that helps, Brian
By thomask on August 3, 2010 - 7:23am
I calibrate all my images by setting an offset in my photometry program so that I get Vi=4.705 for lambda. As pointed out what you set really don't matter, but I think it is nice to get roughly the
same values for Vi as for V. In my spreadsheet then I calculate Tc, k' and Zp. The zeropoint now become the valuewhere the sum of (V calculated - V catalog) for all compairsion stars is zero. This is
about the same as: -Tc * (B-V)[lambda] - k' * AM[lambda]. It is exactly this value if it happens that V=Vi=4.705 for lambda. But in general Vi for lambda, as the other compairsion stars, suffer of
random error of about +/-0.02 magnitudes, that can make the zeropoint to differ by that amount to get the best fit value.
By Bikeman on July 18, 2010 - 10:51am
Hi Chris Zero points are highly overrated :-) Now seriously, if you are doing differential photometry, you just don't care about the zero-point. Let me explain: By selecting a certain zero-point for
the instrumental magnitude calclulation, you effectively add a constant offset value to your instrumental magnitude values. So let's say you make two arbitrary choices for the zero point, one being
10.0 higher than the other. You might get these results for the instrumental mags: 1st choice: Var star: 4.3 Comparison star: 3.7 2nd choice: Var star: 14.3 Comaprison star: 13.7 Quite dramatic, but
then again, we are doing differential photometry. So we know that (say) the comparison star has catalog magnitude 3.2 In both cases the result from your measurement is that the var star is 0.6 mag
darker than the comp star (4.3 - 3.7 ) = (14.3 - 13.7) , so we add this to the catalog mag of the comp star and get 3.8 for the variable star, no matter what zero point we selected. That's the beauty
of differential photometry: sometimes it's so much easier to measure the difference of two values than their absolute values. Zero point would be interestinrg if you tried to make a measurement
without a comparison star, but that requires so much more calibration precision that it's not a good idea unless you are somehow forced to do that (e.g. absolutely no suitable comparison star in the
field). Hope that helps, HB
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A 225kW Direct Driven PM Generator Adapted to a Vertical Axis Wind Turbine
Advances in Power Electronics
Volume 2011 (2011), Article ID 239061, 7 pages
Research Article
A 225kW Direct Driven PM Generator Adapted to a Vertical Axis Wind Turbine
Swedish Centre for Renewable Electric Energy Conversion, Division for Electricity, Department of Engineering Sciences, Uppsala University, P.O. Box 534, 751 21 Uppsala, Sweden
Received 14 March 2011; Revised 24 August 2011; Accepted 24 August 2011
Academic Editor: Jose Pomilio
Copyright © 2011 S. Eriksson et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any
medium, provided the original work is properly cited.
A unique direct driven permanent magnet synchronous generator has been designed and constructed. Results from simulations as well as from the first experimental tests are presented. The generator has
been specifically designed to be directly driven by a vertical axis wind turbine and has an unusually low reactance. Generators for wind turbines with full variable speed should maintain a high
efficiency for the whole operational regime. Furthermore, for this application, requirements are placed on high generator torque capability for the whole operational regime. These issues are
elaborated in the paper and studied through simulations. It is shown that the generator fulfils the expectations. An electrical control can effectively substitute a mechanical pitch control.
Furthermore, results from measurements of magnetic flux density in the airgap and no load voltage coincide with simulations. The electromagnetic simulations of the generator are performed by using an
electromagnetic model solved in a finite element environment.
1. Introduction
The use of wind power is increasing all over the world, and there are several different types of electrical systems available for converting the wind power to electricity, but no single technology is
dominating the market [1]. In this paper a direct driven permanent magnet (PM) synchronous generator is presented [2–4]. The generator presented here has been specifically designed to be directly
driven by a vertical axis wind turbine (VAWT) [5] and to be placed on ground level. One of the advantages of using a VAWT is that it is omnidirectional; that is, it can accept wind from any direction
and does not need a yawing mechanism. The present vertical axis turbine is a straight-bladed Darrieus turbine [6]. A presentation of the design of the same type of wind turbine can be found in [7]. A
more extensive presentation of the generator type, generator experiments, and verification of simulations can be found in [8, 9].
A direct driven generator is spared from losses, maintenance, and costs associated with a gearbox. However, direct drive yields a larger generator than with a generator connected through a gearbox.
For a vertical axis wind turbine where the generator can be placed on ground level, the size and weight are of less concern. The generator can therefore be optimized considering efficiency and cost
instead of focusing on lowering the weight. Thus, the vertical orientation of the axis allows for a general study of generator design freed from weight and size constrains.
The presented generator is unique in several ways. It is a permanent magnet generator with many poles and a large diameter. It is cable wound, which means that the stator has circular cables. It has
a relatively high voltage. The generator is designed to have a low rotational speed, since it is directly coupled to a vertical axis wind turbine. The generator also has an unusually high overload
capacity in order to enable electrical control and braking of the turbine. Furthermore, it has a low reactance, in order to fulfil the design requirements. The electromagnetic simulations of the
generator are performed by using an electromagnetic model. The model is described by a combined field and circuit equation model and is solved in a finite element environment.
This paper presents the generator design objectives, results from generator simulations, and results from initial tests of the generator. Two important features of this type of generator is the high
efficiency over the whole operational regime and the desired overload capability. Therefore, these aspects have been investigated more thoroughly in simulations by taking wind turbine aerodynamic
behaviour into consideration. In addition, experiments have been performed to verify the simulations. Designing, building, and testing of the generator were done at Uppsala University during 2009.
The generator was installed in a 200kW VAWT in 2010, which has been built in Falkenberg, Sweden.
2. Theory
2.1. Electromagnetic Model
Electromagnetic simulations using the finite element method (FEM) are performed in order to simulate the generator’s behaviour at different loading conditions. In the simulations the electromagnetic
field inside the generator is assumed to be axisymmetrical and is therefore modelled in two dimensions. Three-dimensional effects such as end-region fields are taken into account by introducing coil
end impedances in the circuit equations of the windings. The permanent magnets are modelled by surface current sources.
The electromagnetic model is described by a combined field and circuit equation model. The field equation (1) originates from Maxwell’s equations, and is the conductivity, is the permeability, is the
axial magnetic potential, and is the applied potential. The right-hand term of (1) corresponds to the current density constituted by the current density in the armature and a current density
representing the permanent magnets. The magnetization curve of the stator steel is modelled as a nonlinear, single-valued curve, that is, in (1) is not constant for the stator steel, taking
saturation into account. The circuit equations are described by where are the conductor currents, and are the terminal line voltages, are the terminal phase voltages obtained from solving the field
equation, is the cable resistance, and represents the coil end inductance.
After a generator geometry is decided, the generator parts are assigned different material properties such as conductivity, permeability, density, and sheet thickness. The electromagnetic model is
solved in the finite element environment ACE [10]. The mesh is finer close to critical parts such as the airgap and coarser in areas like the yoke of the stator. Since the generator is symmetric,
only a few poles have to be modelled.
Simulations can be performed either in the stationary mode where the results are given for a fixed rotor position or in a dynamic mode including the time dependence and thereby giving more accurate
results. The simulations have been verified by comparison with experimental results for a generator similar to the one studied here [8, 9].
2.2. Electromagnetic Losses and Efficiency
The electrical efficiency, , of a generator is found from where is the electrical output power and are the total electromagnetic losses found from. where are the iron losses and are the copper
losses, see below. The iron losses per cubic meter stator steel can be found from the following equation [11, 12]: where is the stacking factor, is the hysteresis losses coefficient, is the eddy
current losses coefficient and is the excess losses coefficient, is the peak magnetic flux density, is the frequency, and denotes the rotational losses [13]. The eddy current losses coefficient can
be calculated according to where is the conductivity and is the steel thickness, so the eddy current losses are dependent on the steel thickness squared and can be decreased by choosing thinner steel
plates. The coefficients for hysteresis and excess losses and are found from the loss characteristics specified from the steel manufacturer [14].
The iron losses have to be multiplied with the total stator steel volume, , and a loss correction factor to find the total losses: In the simulations a loss correction factor of 1.5 is used for all
iron losses. The loss correction factor represents differences in the theoretical modelling of iron losses and experimental measurements, caused for instance by stray losses, and the value of 1.5 is
verified for a similar generator in [15].
The copper losses consist of resistive losses and a small amount of eddy current losses in the copper conductors and can be written as where is the cable resistance, is the current, and denotes the
eddy current losses in the conductors. The eddy current losses in the cables are included in the simulations but only constitute a small amount of the total copper losses.
Eddy current losses in the PMs and in the iron ring that the PMs are mounted on are expected to be small as they are subjected to mostly DC magnetic field and are therefore neglected.
The mechanical losses in a direct driven electric machine, consisting of friction in couplings and bearings and windage losses, are usually small. Here, mechanical losses are not considered.
3. Method
3.1. Wind Turbine Characteristics
The generator was designed to be used together with a VAWT with characteristics presented in Table 1. The vertical axis turbine is a three-bladed turbine with a cross-sectional area of 624m^2. The
VAWT does not have a pitch control. It is passively stall controlled by control of the rotational speed through the generator. Therefore, the generator needs to be robust and has a large maximum
torque. The required overload capability was chosen from aerodynamic simulations in order to ensure stall control capability.
The variable speed turbine will be controlled according to the control strategy presented in Table 2. At wind speeds between 4 and 6m/s the turbine will be run at a higher speed than optimum in
order to limit the operational speed window from 18 to 33rpm, that is, 0.55 to 1p.u. This is important for structural dynamic purposes. At wind speeds between 6 and 10.9m/s, the wind turbine is
controlled for optimum aerodynamic efficiency. The rotational speed is kept constant at 33rpm for wind speeds between 10.9 and 11.7m/s. At wind speeds above 11.7m/s, the rotational speed is
controlled to stall the turbine. Thereby an even power production of 200kW can be achieved from wind speeds of 11.7m/s up to the shut-down wind speed.
3.2. Generator Design Objectives
The most important generator design objectives were as follows: (i)a design adapted to the turbine, (ii)a design adapted for diode rectification, (iii)low speed (i.e., direct drive),(iv)high overload
capacity, (v)high efficiency,(vi)high reliability and low need for maintenance, (vii)low cost.
The directly driven turbine operates at variable speeds. Therefore, the generator should be designed to have a high efficiency for all operational speeds and loads. In a study, the average losses for
several variable speed generators, similar to this generator, were compared [16]. The result showed that the generator with highest average efficiency also had a rather high overload capability, low
load angle, and low reactance.
A generator designed with a low load angle can handle a higher power than it is rated for. Thus, low load angle enables electrical braking of the turbine and also the possibility to extract more
energy in high wind speeds. The turbine’s power absorption can thereby be controlled electrically. This electrical power control can replace an active mechanical power control of the wind turbine,
such as pitch control. Furthermore, the electrical control responds much faster than the mechanical control and is not subject to mechanical wear.
A variable speed generator needs a frequency converter before it is connected to the grid, allowing the voltage and current levels to be chosen freely. The converter consists of a rectifier and an
inverter. For this concept, diodes will be used for rectification, which is a cheap and reliable option with low losses. When using diodes instead of an active rectifier no reactive power can flow to
or from the generator. Therefore, the generator needs to have a low load angle throughout the operational regime.
The generator is designed with a low reactance which gives a machine that fulfils several of the requirements: (i)low reactance implies a low load angle, which enables the use of diodes for
rectification, (ii)high efficiency [16],(iii)high overload capability, which enables electrical control, (iv)low voltage drop even at high loads.
3.3. Simulations
The electromagnetic simulations of the generator using the finite element method (FEM) are performed by using the model described in Section 2.1. Stationary simulations are performed to dimension the
generator in order to save time during the iterative design process. Dynamic simulations are then performed to verify the chosen design and to simulate the generator in different modes of operation.
All presented results are from dynamic simulations. The generator model is connected to a resistive load, which gives a good estimate for modelling the braking torque since the generator is connected
to the dump load before the rectifier by a circuit breaker. For modelling the efficiency and armature reaction, this is a simplification but will give rather accurate results. However, the copper
losses could be expected to be slightly higher during diode rectification due to current peaks. The efficiency is modelled according to the theory described in Section 2.2. The generator has been
simulated with a varying rotational speed and a varying load sweeping through a wide range of values to cover the whole operational interval as well as extreme cases of braking at higher rotational
speeds than expected during normal operation.
The electrical efficiency at different wind speeds has been calculated by using the values found from FEM simulations of the generator for varying load and speed and combining these with the control
strategy presented in Table 2. A theoretical curve of the aerodynamic efficiency and its dependency on wind speed and rotational speed is used in the simulations. The aerodynamic efficiency is
calculated using complex aerodynamic models for vertical axis wind turbines [17]. An average value of the losses in the generator is calculated using the results from the calculations of the
electrical efficiency at different wind speeds and assuming a Rayleigh distributed wind speed with an average wind speed of 6.7m/s.
The turbine torque is derived from theoretical calculations based on complex aerodynamic models [17]. The unlikely load case called “extreme coherent gust with direction change” in IEC standard
61400-1, where the wind speed increases by 15m/s in 10 seconds, is considered [18]. This is an extreme operational case which is unlikely to occur.
3.4. Experiments
Experiments were performed after the generator was constructed. A Gauss/Teslameter (Sypris Model 7010) was used to measure the magnetic flux density in the airgap at high accuracy. The generator was
accelerated, and several measurements of the voltage were done at a rotational speed of 18.5rpm. An oscilloscope (Tektronix TDS2014) and high voltage probes (Tektronix P5120) were used to measure
the voltage.
4. Results and Discussion
4.1. Generator Characteristics
The generator characteristics were derived by dynamic simulations using the electromagnetic model described in Section 2.1. The mechanical design of the generator, developed in SolidWorks, has been
focused on finding a stiff design which can maintain the airgap and withstand large airgap forces during faulty conditions.
The stator winding consists of PVC insulated circular cables. The circular shape gives an evenly distributed electric field in the cables and hence makes better use of the insulation material [19].
In large machines, a cable wound generator is of great interest since it enables the use of higher operating voltage than for traditionally wound machines [19]. A generator with high rated voltage
and consequently a low rated load angle has a high maximum torque [20].
The low reactance is achieved by choosing a relatively high voltage for the given power rating, that is, a low rated load angle. The generator has 36 poles, and the armature is wound as a wave
winding with 5/2 slots per pole and phase and six cables per slot. The winding is divided into two parallel current paths.
The rotor of the generator is equipped with large, surface-mounted, arched, high-energy magnets made of Neodymium Iron Boron. The stator consists of steel laminations with a thickness chosen as a
compromise between losses in the stator steel and cost. The generator is rated at 225kW as the wind turbine system is designed to deliver 200kW to the grid at rated speed. The higher rating of the
generator accommodates for some losses in the electrical system as well as possible deviations between the simulation programs (aerodynamic and electrical) and reality. The generator power rating is
given in kW rather than the more conventional kVA, since the generator will be rectified through diodes. The generator characteristics are presented in Table 3, where L-L voltage means line-to-line
voltage. The voltage drop is only 3.3% at rated conditions. The ratio between the machine reactance, , and the rated load, , the -ratio, is 0.17p.u., where typical generator values for the -ratio
are in the range of 1.7 to 3.3p.u. [21]. The load angle is less than 10 degrees at rated operation.
The maximum torque of the generator is 218kNm, which is 3.3 times the rated torque. The generator overload capability is used in two different ways when the wind turbine is operated. First, it is
used to control the DC level voltage at high power. Second, the generator can be connected to a dump load that will brake the turbine in a few seconds from any operating regime. Thereby an electrical
control is established and the overload capability makes the operation at rated power level safe and reliable.
During manufacturing a few deviations occurred from the original design. All the simulations presented here are based on the actual generator geometry as opposed to the theoretical design. A picture
of the generator and the magnetic flux density in the designed generator from dynamic simulations is shown in Figure 1.
4.2. Results from Simulations
4.2.1. Efficiency
The generator has been simulated for all different rotational speeds and power levels appropriate to find the efficiency over the whole operational regime when the turbine is operated according to
the chosen control strategy; see Table 2. The result can be seen in Figure 2.
The strange shape of the curve is a result from the different control strategies. At wind speeds above 11.7m/s the rotational speed needs to be decreased in order to limit the power absorption to
225kW by stall regulation. The voltage will then decrease and the current will increase, resulting in increasing copper losses and lower efficiency. The efficiency is shown to be high, above 96% for
all wind speeds above 6.6m/s. The generator efficiency is kept high even when the turbine is operating in the aerodynamic stall regime. For wind speeds above 11.7m/s, the amount of losses remains
roughly constant. The average efficiency during operation becomes 96.0%, which is close to the rated value of 96.7%.
4.2.2. Brake Capacity
The dump load, rated at 1.1Ω, is designed to brake the turbine efficiently over the entire operational regime. A figure of the braking torque from the generator when connected to the dump load at
different rotational speeds can be seen in Figure 3 together with the turbine torque. The dump load can brake the turbine for all extreme loads at rotational speeds up to 37.1rpm. However, a
rotational speed well above 33rpm will not be reached since the dump load is triggered immediately if the rotational speed exceeds 33rpm.
The torque changes with different rotational speeds, which is an inherent characteristic of a fixed resistive load. The braking procedure will automatically be smooth, since the braking torque
decreases with decreasing rotational speed. If the rotational speed would increase uncontrollably both the turbine torque and the braking torque would increase. However, as long as the rotational
speed does not increase above 37.1rpm, the dump load will be able to brake the turbine even for an extreme gust.
The intrinsic passive stall control of the turbine works as a self-protection for the generator and the shaft as well as for the electrical system. The generator and the shaft are protected against
too high currents and torques as long as the generator is able to control the turbine speed. If the rotational speed is kept constant and the wind speed increases rapidly, the turbine will start to
stall and absorb less power; that is, no high currents will be reached. If the turbine speed, is not longer controlled and exceeds the rated speed the dump load will be triggered. However, high
currents and torques can still be reached during faults such as short circuits.
4.2.3. Armature Reaction
Results from simulations of the voltage drop at a fixed rpm and varying load is shown in Figure 4. The armature reaction is low, which is a result of the low reactance. The low voltage drop is an
important feature for a generator connected to diodes. If the voltage drop would have been large, the current would have been increased at high loading, resulting in increased resistive losses.
4.3. Experimental Verification of Simulations
The magnetic flux density has been measured along a tangential line in the middle of the generator airgap for two adjacent magnets; see Figure 5. The flat shape of the magnetic flux density is due to
the wide and flat magnets. The jagged shape of the magnetic flux density is caused by the stator teeth; see Figure 1. In both Figures 1 and 5 it can be seen that about five teeth are opposite to each
magnet. The experiments correspond very well with simulations. However, in the experiments the magnetic flux density is smaller for the magnet with the positive flux than for the magnet with the
negative flux. This is probably due to the rather large tolerances of remanence for the magnets.
The no-load phase voltage has been measured at 18.5rpm; see Figure 5. Results from experiments coincide with simulations. However, the amplitude of the measured voltage is slightly lower for the
negative voltage than for the positive voltage. This is due to the generator slowly decelerating while the measurements were made. The rms value of the no-load phase voltage at 18.5rpm was 271.3V
according to the simulations and 269.8V in the experiments. The experimental result corresponds to a line-to-line voltage at rated speed of 838 V, which was expected from simulations to be 839V.
5. Conclusions
A unique direct driven permanent magnet synchronous generator is presented, and the design objectives are motivated. Some important design features are analysed. It is concluded that the efficiency
remains high during the whole operational range. Furthermore, the braking torque, calculated for a resistive load of 1.1Ω, shows that the generator can brake the turbine during the whole operational
regime even in extreme loads, which makes operation safe and reliable. Thereby, electrically induced stall control has been demonstrated, made possible by the low load angle of the machine and the
resulting overload capacity. Furthermore, simulations confirm that the voltage drop in the generator is low due to its low reactance.
Results from experiments verify the simulations. The generator is now installed in a 200kW vertical axis wind turbine built in Falkenberg, Sweden.
Dr. Arne Wolfbrandt and Dr. Urban Lundin are acknowledged for assistance with electromagnetic FEM simulations. David Österberg is acknowledged for providing data for the aerodynamic efficiency and
turbine torque. Acknowledgments are given to Vertical Wind, E.ON, Falkenberg Energy, and the Swedish Energy Agency. The Swedish Energy Agency, Vinnova, and Statkraft are acknowledged for
contributions to Swedish Centre for Renewable Electric Energy Conversion. This research was carried out as part of the Statkraft Ocean Energy Research Program, sponsored by Statkraft (http://
www.statkraft.no/). This support is gratefully acknowledged.
1. A. D. Hansen, “Generators and power electronics for wind turbines,” in Wind Power in Power Systems, T. Ackermann, Ed., pp. 55–65, John Wiley & Sons, New York, NY, USA, 2005.
2. S. Eriksson, Direct Driven Generators for Vertical Axis Wind Turbines, Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, 2008.
3. P. Lampola, Directly driven, low-speed permanent-magnet generators for wind power applications, Ph.D. thesis, Department of Electrical Engineering, Helsinki University of Technology, 2000.
4. A. Grauers, Design of direct driven permanent magnet generators for wind turbines, Ph.D. thesis, Department of Electric Power Engineering, Chalmers University of Technology, 1996.
5. S. Eriksson, H. Bernhoff, and M. Leijon, “Evaluation of different turbine concepts for wind power,” Renewable and Sustainable Energy Reviews, vol. 12, no. 5, pp. 1419–1434, 2008. View at
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of Emerging Electric Power Systems, vol. 10, no. 1, article 3, 2009. View at Publisher · View at Google Scholar
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11. A. Broddefalk and M. Lindenmo, “Dependence of the power losses of a non-oriented 3% Si-steel on frequency and gauge,” Journal of Magnetism and Magnetic Materials, vol. 304, no. 2, pp. e586–e588,
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13. L. Ma, M. Sanada, S. Morimoto, and Y. Takeda, “Prediction of iron loss in rotating machines with rotational loss included,” IEEE Transactions on Magnetics, vol. 39, no. 4, pp. 2036–2041, 2003.
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15. F. Bülow, S. Eriksson, and H. Bernhoff, “No-load core loss prediction of PM generator at low electrical frequency,” Renewable Energy. In press.
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vol. 17, no. 3, pp. 10–15, 2001. View at Publisher · View at Google Scholar
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21. T. A. Loehlein, “Calculating generator reactances,” white paper, power topic #6008, Technical information from Cummins Power Generation, 2006.
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weighted arithmetic mean
The topic weighted arithmetic mean is discussed in the following articles:
• ...the arithmetic mean is commonly used as the single value typical of a set of data. For a system of particles having unequal masses, the centre of gravity is determined by a more general
average, the weighted arithmetic mean. If each number (x) is assigned a corresponding positive weight (w), the weighted arithmetic mean is defined as the sum of their products (wx)...
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In the xy-plane, the point (-2, -3) is the center of a circl
Author Message
In the xy-plane, the point (-2, -3) is the center of a circl [#permalink] 18 Nov 2010, 04:25
rite2deepti E
Intern Difficulty:
Joined: 02 Sep 2010 25% (low)
Posts: 48 Question Stats:
WE 1: Business 76%
Development Manger
(02:04) correct
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Manager-Carbon 23% (01:02)
WE 3: Manager-Carbon
Trading based on 137 sessions
Followers: 2 In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the
circle is an integer, then r =
Kudos [?]: 5 [0],
given: 16 A. 6
B. 5
C. 4
D. 3
E. 2
Spoiler: OA
Re: Problem with question Coordinate Geometry [#permalink] 18 Nov 2010, 04:50
This post received
Expert's post
First of all:
Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/
Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/
No posting of PS/DS questions is allowed in the main Math forum.
rite2deepti wrote:
In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the
circle is an integer, then r =
A. 6
B. 5
C. 4
D. 3
E. 2
The easiest way to solve this question will be just to mark the points on the coordinate plane. You'll see that the distance between the center (
Bunuel -2
Math Expert , -3) and the point inside the circle (
Joined: 02 Sep 2009 -2
Posts: 17317 , 1) is 4 units (both points are on x=-2 line so the distance will simply be 1-(-3)=4) so the radius must be more than 4, and the distance between the center (-2,
Followers: 2874 -3
Kudos [?]: 18380 [2] ) and the point outside the circle (4,
, given: 2348
) is 6 units (both points are on y=-3 line so the distance will simply be 4-(-2)=6) so the radius must be less then 6 --> 4<r<6, thus as r is an integer then r=5.
Answer: B.
For more on this issues check Coordinate Geometry chapter of Math Book:
Hope it helps.
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Manager Re: Problem with question Coordinate Geometry [#permalink] 18 Nov 2010, 06:23
Joined: 16 Jul 2010 Nicely explained. Thanks!
Posts: 161
Followers: 3
Kudos [?]: 9 [0],
given: 0
Joined: 02 Sep 2010
Re: Problem with question Coordinate Geometry [#permalink] 18 Nov 2010, 08:24
Posts: 48
Thanks ...
WE 1: Business
Development Manger
WE 2: Assistant
WE 3: Manager-Carbon
Followers: 2
Kudos [?]: 5 [0],
given: 16
Re: Problem with question Coordinate Geometry [#permalink] 20 Nov 2010, 13:26
Bunuel wrote:
First of all:
Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/
Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/
No posting of PS/DS questions is allowed in the main Math forum.
rite2deepti wrote:
In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the
circle is an integer, then r =
A. 6
B. 5
C. 4
D. 3
E. 2
girisshhh84 OA=B
Intern The easiest way to solve this question will be just to mark the points on the coordinate plane. You'll see that the distance between the center (
Joined: 27 Aug 2010 -2
Posts: 30 , -3) and the point inside the circle (
Followers: 0 -2
Kudos [?]: 3 [0], , 1) is 4 units (both points are on x=-2 line so the distance will simply be 1-(-3)=4) so the radius must be more than 4, and the distance between the center (-2,
given: 4
) and the point outside the circle (4,
) is 6 units (both points are on y=-3 line so the distance will simply be 4-(-2)=6) so the radius must be less then 6 --> 4<r<6, thus as r is an integer then r=5.
Answer: B.
For more on this issues check Coordinate Geometry chapter of Math Book:
Hope it helps.
What would be more time saving is just to use the distance formula to get the dist between center and point inside the circle as 4 &
Distance between the center and outside point as 6 so 4<r<6 as above and Answer is B .
This time , its my time .
Re: Problem with question Coordinate Geometry [#permalink] 03 Jan 2013, 21:07
rite2deepti wrote:
Senior Manager
In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the
Joined: 13 Aug 2012 circle is an integer, then r =
Posts: 465 A. 6
B. 5
Concentration: C. 4
Marketing, Finance D. 3
E. 2
GMAT 1: Q V0
GPA: 3.23
Simply plot the coordinates and you will figure out that r is greater than 4 but less than 6: 4 < r < 6
Followers: 14
Answer: B
Kudos [?]: 152 [0],
given: 11 _________________
Impossible is nothing to God.
Manager Re: In the xy-plane, the point (-2, -3) is the center of a circl [#permalink] 12 Mar 2013, 02:02
Joined: 13 Aug 2012 Okay i used another method but i'm not getting the answer
so I used the equation (x-a)^2+(y-b)^2=r^2, and put in the values of the center (-2,-3), which then comes out to be
Posts: 69 (x+2)^2+(y+3)^2=r^2. Then i substitute the values of the inside point i.e (-2,1) for x and y and my radius comes out to be 4. I don't know what am i doing wrong here?
Followers: 0
Kudos [?]: 7 [0],
given: 63
Re: In the xy-plane, the point (-2, -3) is the center of a circl [#permalink] 12 Mar 2013, 03:47
mau5 This post received
Verbal Forum
Moderator Expert's post
Joined: 10 Oct 2012 mahendru1992 wrote:
Posts: 626 Okay i used another method but i'm not getting the answer
so I used the equation (x-a)^2+(y-b)^2=r^2, and put in the values of the center (-2,-3), which then comes out to be
Followers: 35 (x+2)^2+(y+3)^2=r^2. Then i substitute the values of the inside point i.e (-2,1) for x and y and my radius comes out to be 4. I don't know what am i doing wrong here?
Kudos [?]: 488 [1] , What you are doing wrong is that the point (-2,1) doesn't lie ON the circle. You can not substitute this value for the circle's equation.
given: 135
All that is equal and not-Deep Dive In-equality
Hit and Trial for Integral Solutions
Re: In the xy-plane, the point (-2, -3) is the center of a circl [#permalink] 15 Mar 2013, 14:14
This post received
See the attached drawing.
johnwesley We can easily see by drawing the problem that a Radius=4 is not enough, as the circle will have its frontier in (-2,1) - see the clear circle - and therefore the point will NOT
be inside the circle.
If we increase the radius to the next integer Radius=5, this is solved, as the point (-2,1) will fall inside the circle, while the point (4,-3) will fall outside the circle - see
Joined: 24 Jan 2013 the dark circle -. And this is the only feasible solution to the problem.
Posts: 82 Solution: Radius=5
Followers: 3 Solution B
Kudos [?]: 52 [1] ,
given: 6 Imagen2.jpg [ 10.79 KiB | Viewed 1251 times ]
Does this post deserve KUDOS?
Free Prep: Self-prepare GMAT for free and GMAT Math tips for free
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More: "All I wish someone had told me about GMAT beforehand"
There are many things you want to know before doing the GMAT exam (how is exam day, what to expect, how to think, to do's...), and you have them in this blog, in a simple way
Re: In the xy-plane, the point (-2, -3) is the center of a circl [#permalink] 01 Aug 2013, 06:36
Could someone help me how go about this?
Joined: 13 Aug 2012 Since (4,-3) lies outside the circle, it is clear that one of the point that lies on the circle is (x,-3). The other point (-2,1) lies inside the circle, so another point on the
circle would be (-2,y). We also know that the center is (-2,-3). Join the center to the point (x,-3) and (-2,y) to form the 2 radius. After equating the 2 lines I get (y+3)^2=
Posts: 69 (x+2)^2. What should I do ahead?
Followers: 0
Kudos [?]: 7 [0],
given: 63
gmatclubot Re: In the xy-plane, the point (-2, -3) is the center of a circl [#permalink] 01 Aug 2013, 06:36
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Larsen, Michael - Department of Mathematics, Indiana University
• Math M120 Exam 1 February 7, 2003 Name: Michael Larsen
• This appendix gives, for all n N, an affirmative answer to the question of whether there exists a symmetric matrix A in Mnn(Z2) with An
• Maximality of Galois Actions for Compatible Systems 0. Introduction
• Integration by Parts The Leibniz rule for differentiation says that if f(x) = g(x)h(x), then
• Math S212 Exam 3 Name: For each convergence problem, you should not only indicate whether the sum
• Math M120 Exam 3 April 4, 2003 1. (20 pts) Suppose the supply curve for a certain commodity is given by p = q2
• MJL 1. Prove that there is a positive integer n such that in the decimal expansion of , the four digit sequence after the decimal point is 1996.
• Rank of Elliptic Curves over Almost Separably Closed Fields
• Topological Hochschild homology of algebras in characteristic p
• On the Conjugacy of Element-Conjugate Homomorphisms II Michael Larsen*
• Filtrations, Mixed Complexes, and Cyclic Homology in Mixed Characteristic
• Homology of Maximal Orders in Central Simple Algebras Michael Larsen*
• On -independence of Algebraic Monodromy Groups in Compatible Systems of Representations
• Compatible Systems of -adic Representations of Dimension Two Let E be an elliptic curve defined over a number field K. For each prime , define
• Determining Representations from Invariant Dimensions
• Math Circle Topics Spring 2009 1. Difference calculus
• 1. What is the sum of all two digit numbers? What is the sum of all four digit numbers?
• Random generation in semisimple algebraic groups over local fields
• ON THE EULER CHARACTERISTIC OF AN EVEN PERIOD COMPLEX
• Products of Two Eigenforms of Level One Michael Larsen
• On the rational Chow ring of flag bundles Dan Edidin*
• Math S212 Exam 2 Name: 1. (12 pts) What estimate does Simpson's rule give for 1
• Math S212 Exam 2 Name: 1. (12 pts) What estimate does Simpson's rule give for 1
• Math S212 Exam 3 Name: Michael Larsen For each convergence problem, you should not only indicate whether the sum
• Math M120 Exam 1 February 7, 2003 1. (10 pts) What continuous growth rate would make the world population grow from 6
• Abelian varieties, l-adic representations, and l-independence M. Larsen* and R. Pink
• On the semisimplicity of low-dimensional representations of semisimple groups in characteristic p
• Math M120 Exam 2 March 5, 2003 Name: Michael Larsen
• On the Conjugacy of Element-Conjugate Homomorphisms Michael Larsen*
• NUMBER THEORY 1. Galois Representations
• Math M120 Exam 3 April 4, 2003 Name: Michael Larsen
• Putnam Competition Outtake Solutions 1. Let n = m2
• On a Lemma of Deligne-Serre Michael Larsen*
• Probability Problems 1. Randomly take three scrabble letters, one at a time, out of a sack
• Math S212 Exam 1 Name: Michael Larsen 1. (10 pts) If f(x) = ln x
• 1. Start with a stack of monopoly money: seven bills ranging from $500 to $1, with the smallest on top. On each turn, you may remove the top
• Singular Plane Curves and Mordell-Weil Groups of Jacobians Michael Larsen*
• On the rationality of zeta functions Let Fq denote a finite field of characteristic p and V/Fq a variety. For all n N, we
• A Combinatorial Lemma Proposition: Let
• Cyclic Homology of Dedekind Domains M. Larsen* and A. Lindenstrauss
• Math Circle Topics Fall 2009 1. Inequalities
• The Normal Distribution as a Limit of Generalized Sato-Tate Measures Michael Larsen*
• 1. A power means a perfect square (like 1, 4, 9, 16, . . .), a perfect cube (like 1, 8, 27, 64, . . .), a perfect fourth power, etc. How many powers
• Algebra Roadmap November 6, 2009
• A Non-abelian Free Pro-p Group Is Not Linear Over a Local Field
• Math M120 Exam 2 March 5, 2003 0. (10 pts) Write down your name!
• Appendix: Lifting Homomorphisms from Characteristic p to Characteristic 0 Lemma A.1: Let be a finite group. Let E be a field, of characteristic zero or characteristic
• Counting Problems 1. How many ways are there to write a three letter word (not necessarily
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On the automorphism groups of q-enveloping algebras of nilpotent Lie algebras
Launois, S. (2006) On the automorphism groups of q-enveloping algebras of nilpotent Lie algebras. In: From Lie Algebras to Quantum Groups, 28-30 June 2006, Dep. Mathematics, Univ. Coimbra. (Full text
We investigate the automorphism group of the quantised enveloping algebra U of the positive nilpotent part of certain simple complex Lie algebras g in the case where the deformation parameter q \in \
mathbb{C}^* is not a root of unity. Studying its action on the set of minimal primitive ideals of U we compute this group in the cases where g=sl_3 and g=so_5 confirming a Conjecture of
Andruskiewitsch and Dumas regarding the automorphism group of U. In the case where g=sl_3, we retrieve the description of the automorphism group of the quantum Heisenberg algebra that was obtained
independently by Alev and Dumas, and Caldero. In the case where g=so_5, the automorphism group of U was computed in [16] by using previous results of Andruskiewitsch and Dumas. In this paper, we give
a new (simpler) proof of the Conjecture of Andruskiewitsch and Dumas in the case where g=so_5 based both on the original proof and on graded arguments developed in [17] and [18].
• Depositors only (login required):
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Posts by
Total # Posts: 14
Geometry, help!
Circle O has a radius 28. Radii OM and ON form an angle of 60 degrees. Find MN. A) 28 radical 2 B) 28 C) 56 D) 56 radical 3 Is it A) ?
so if you do 3*2.5=7.5*6=45...you yae 45 from the three numbers you just multiplied and you got 45....now do 25 that is the part of the fridge and do 45-20=25 feet3=25 feet cubed!!!
so if you do 3*2.5=7.5*6=45...you yae 45 from the three numbers you just multiplied and you got 45....now do 25 that is the part of the fridge and do 45-20=25 feet3=25 feet cubed!!!
7.5 micrmeters will go into 7.5 millimeters how many times?
If the arc on a particular circle has an arc length of 14 inches, and the circumference of the circle is 84 inches, what is the angle measure of the arc?
how can the chemical energy of your lunch today become the energy you need to deliver the newspapers after school tomorrow?
An car was purchased for $47000 and its depreciation value is 22% each year. How long would it take the car to be worth nothing (zero dollars)? Explain.
Calculate the entropy change of the universe (in J/K) when 12.2 g of chlorine are melted in a laboratory at 24.8 oC. Report your answer in scientific notation to three significant figures. Melting
Point (°C) -101.0 Boiling Point (°C) -34.1 ÄHo(Fusion) (kJ/mol) 6.4...
College Calculus
Write a trial solution for the method of indetermined coefficients: y''+9y' = xe^(-x)cos(pi*x) ....I have no idea.
Logs-check my anwers
Evaluate or simplify the expression without using a calculator. ln e i got 1
Logs-check my anwers
log10 sqrt of 10 i got 1 log3 3^11 i got 11 log5^5 i got 1
Logs-check my anwers
Write the equation in its equivalent exponential form. log5 x = 2 I got 5x = 2 logb 256 = 4 i got b4 = 256 log10 sqrt of 10 i got
How do you graph the following logs? f(x)=log5 (x-2) f(x)=log5 x-2 f(x)= log5 x f(x)=log5 (x+2)
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Monmouth Junction Algebra 2 Tutor
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10 Subjects: including algebra 2, calculus, Chinese, algebra 1
...If you are looking for more basic levels of math or science tutoring, I can do that too! I love kids and would love to see them eager to learn about math and science. I have taken and done very
well on the quantitative (math) section of both the SAT and the GRE.
13 Subjects: including algebra 2, chemistry, calculus, biology
...I recently took the math SAT at a tutoring service and scored 790. I am one of the best math SAT tutors and consistently get great results. I teach the math that is on the math SAT, and make
sure the student knows it.
32 Subjects: including algebra 2, English, GRE, algebra 1
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Is this line noise?
⍉' *'[⍎'1+0<|z',(∊150⍴⊂'←c+m×m'),'←c←(¯2.1J¯1.3+(((2.6÷b-1)×(¯1+⍳b))∘.+(0J1×(2.6÷b-1)×(¯1+⍳b←51))))']
NOTE: if you are not seeing several Greek looking letters and arrows in the line above, some UTF8 stuff got wrong. Sorry, I'll try to fix it,
drop me a tweet
Nope. This is not line noise, but a complete APL program to display the Mandelbrot set in glorious ASCII, with asterisks and spaces just like Brooks and Matelski did a long time ago while studying
Kleinian groups (it's a short paper, read it someday). I'll explain in (a lot, I hope) detail this line in a few moments. So, what's APL first?
APL is literally
A P
anguage. Funny, isn't it? Its origins can be traced back to a way to formalise algorithms created by Kenneth Iverson while at Harvard. It is famed as a very cryptic language, for a reason. Its
fundamental functions are unicode chars, and at first it feels extremely weird.
I got interested in it after finding an iOS interpreter for
, a programming language developed as a successor to APL, also by K.I. It just got away without Unicode, leaving only cryptic dygraphs, like <.@o. (from a Wikipedia example of high precision
computing.) J is very cool, in that it offers a terse syntax to operate with matrices and vectors, very much like Matlab (Octave in my case) or R. But I felt I'd rather check the first idea, before
diving into the even weirder syntax of J. So, it was APL.
The first problem was finding a good APL interpreter. Most were paid (and extremely expensive) and I could only find 2 APL interpreters working in Mac OS. One is
an implementation focused on node.js Also usable on a browser, so it is cool. But I'd rather get a little closer to the system... And decided to use
Gnu APL
instead. Of course, using an emacs mode for
. Caveat: make sure to add
export LC_ALL=es_ES.UTF-8
export LANG=es_ES.UTF-8
to your .zshrc or similar, without it you'll need to add a hook to gnu-apl mode reading
(set-buffer-process-coding-system 'utf-8 'utf-8)
to make sure emacs and apl talk in utf-8. Without it, there are no commands to send to the interpreter!
Since I'm also a heavy
user, and acme is well-known in its unicode support, I used it instead to develop that line above. But emacs works correctly, I just like having things to tinker with acme.
Getting back to the line-noisiness of APL, first you need to know that precedence is right-to-left, so
in APL yields 12 instead of the expected 10. You can change this with parentheses. Now that I have taken this out, we can analyse the line above. Instead of explaining it from right to left, I'll
explain how I proceeded to develop it.
Iterating the quadratic polynomial
Put it succintly (I could explain a lot of the mathematics behind, but I just want to do a picture today) to draw the Mandelbrot set we need to find complex points c=x+iy (remember: you can think of
a complex point as a point in a plane, like a screen: it has an x coordinate and a y coordinate) such that computing
a lot of times with z=c is eventually a point outside a circle of radius 2. For instance, if c=1 this would be:
1. f(1)=1^2+1=2
2. f(f(1))=f(2)=2^2+1=5
3. f(f(f(1)))=f(5)=25+1=26
And so on. In this particular case, after the first iterate we could stop. Remember that to do so, the product c·c is the product of complex numbers.
So the first part I wanted to get out of my way was generating this iteration. There are several ways to do it in APL, but a very cool way I found was to first generate the required computation like
above. How?
computes exactly this, if m=c or if m is any other iterate, like m=f(f(f(c))). In APL speak, making m hold the same as c would be
and since right-to-left priority,
means "assign to m the value of c, multiply m by m (remember: it's the same as c) and add c." Likewise,
ends is computing the 2nd term in the list above, if c 1. So we have a pretty clear idea of how it should look like:
This is essentially "many times" the string " c+m×m" There's a very very easy way to repeat stuff in APL. For instance, 3 ⍴ 1 (read 3 reshape 1) creates a vector with three ones, 1 1 1. Reshape
essentially multiplies or trims vectors. But... 3 ⍴ 'tomato' is 'tom'. The reshaping also cuts, of course! What we need is to make APL treat the string ' c+m×m' as one element. This is done with the
next instruction in the Mandelbrot line, as you may guess: encapsulate.
ensures APL treats it as one element, so
generates a neat and long string of what the iterates should look like. To make sure the final string makes APL-sense, first we "enlist" with ∊. Turn the vector of repeated iterates into just one
iterated element, like a long string all together. This could actually be removed, but it allowed me to learn a new function and I think it's pretty interesting. To end in a proper way, we add to the
string a receiver variable 'z' and fuse the strings with comma.
I know this was long, but the iteration was the trickiest part!
Generating the grid of points
Since APL is cool with matrices (and complex numbers!) we can assign to the initial c a whole matrix of complex points (our screen pixels) and then we'll have all the stuff required for the picture.
This weird piece is just a compact way of generating a grid. To make it easier to understand, ⍳5 (that's iota 10) generates the sequence 1 2 3 4 5. To create a matrix we need two sequences (one for
the x coordinates and another for the y coordinates.) For the complex numbers we can do 0J1 ⍳× 5 which yields 0J1 0J2 0J3 0J4 0J5. As you may guess, 0J1 is just the complex number i. For some weird
reason APL uses the j letter instead of i. No big issue. Now we have the x's which go from 1 to 5 and the y's which go from i to 5i Now we need to find all the complex points in the plane. This means
adding one of each x to each y, to get a grid. Similar to a multiplication table, but with sums instead of products. APL magic to the rescue!
(⍳5) .+ (0J1×(⍳5))
1J1 1J2 1J3 1J4 1J5
2J1 2J2 2J3 2J4 2J5
3J1 3J2 3J3 3J4 3J5
4J1 4J2 4J3 4J4 4J5
5J1 5J2 5J3 5J4 5J5
which is pretty close to what we need. To plot the Mandelbrot set we are only interested (mostly, and in this particular instance) in points with real coordinate x between -2.1 and 0.5 and complex
coordinate between -1.3 and 1.3 (just to make it square which is easier.) This long blurb just adds a matrix similar to the one above to a complex point, generating the grid of points we want, and
assigns it to c. Almost done!
Computing and plotting
⍉' *'[⍎'1+0<|z',
After we have the set of points in c, we merge this string (with comma) to the iteration we developed above. At the far right of the iteration we find this piece
As you may guess, this adds to the string 1+0<|z which from right to left does:
1. Compute the norm (distance to the origin) of the final iterate, which was assigned to z at the end of the iteration with |
2. Check if this is larger than 4. This generates a matrix of 1s and 0s
3. Add 1 to all entries of this matrix (so we have a matrix full of 1s and 2s
The first version of this code had 0<|z, which works well for rough images of the Mandelbrot set, since most iterates are eventually INFNAN, which is a funny number in programming, since it is
positive, smaller than 0, different from itself... Almost anything :D
We have a neat string which can generate a matrix of 1s and 2s and represent the Mandelbrot set. How do we make this string compute something? Magic!
⍎ (known as execute) takes a string and computes it as an APL function. Magic! (just like eval in Lisp or Javascript, actually)
Represent it neatly
Since a matrix can be used to index a vector, we use this newly computed matrix as indexes (i.e. between square bracket) with the vector ' *' so we get almost a Mandelbrot set. But since I was
slightly lazy when generating the grid of points, it is transposed. ⍉ (transpose) fixes it and finishes the program.
Writing this line of code took me quite a long time, mostly because I was getting used to APL and I didn't know my way around the language. Now that I'm done I'm quite impressed, and I'm looking
forward to doing some more fun stuff with it. And if possible, some useful stuff.
A few months ago (woah, so long already!) I had an impulse buy: I purchased a circular slide rule from Etsy. It was cheap, and I had always wanted one, so... I just bought it (a neat addition to my
I guess if you are geeky enough to read mostlymaths.net, you know how a slide rule works. Although I knew how to use it, getting to grips with it took a little while. Just to make sure you follow
along here's a brief explanation.
In a normal rule (as pictured below) you can measure a distance, add the distance to another one and get a new distance. 4 and 4 are 8, see?
A slide rule works exactly the same, but the scale on the rule is logarithmic. This means that if you measure the distance between 1 and 3, and add it to the point 3, you get 9 (which is 3 times 3.)
This is because in a linear scale distance measures the difference (b-a) and in a logarithmic scale it measure ratios (b/a)
Usually you will do this using a piece labeled the same as the slide rule:
In a normal slide rule (the long wooden or aluminium thing) you have several scales, all placed together with an indicator to know where to measure. In the simplest setting a slide rule is basically
what is shown above: a way to fix a distance and displace it along. You could do it with your fingers, even!
In a basic model of circular slide rule (like the KL-1) you have something that works much like this. See the picture below:
If you look carefully you'll see a marker (which is place just below a knob, and fixed in the glass cover) and a red marking needle (it's hard to see, but it's red.) In this picture you'll also see
the logarithmic scale (below, from 1 to 9) and a square scale just on top (from 1 to 90.)
The black knob (on top of the fixed marker) displaces the scale, leaving the red marking needle wherever it is (it moves the paper where the scale is written!) and the red knob (the other one) moves
just the needle, hovering above the paper.
If you set the black marker on 1 by moving the black knob and then the red marker on (for example) sqrt(2) (which is the number just below 2 in the square scale!) you are fixing the ratio 1-sqrt(2)
(roughly 1-1.4)
If you now twist the black knob, you are moving the scale while the distance black-red remains perfectly fixed. So if you place the black marker above 2, you are "adding" the ratio of sqrt(2) and 2,
which means 2 times sqrt(2) (roughly 2.8):
So, no mysteries in how this works! In the back there are a few trigonometric scales (known in the slide rule lingo as the S and T scales, for sin and tan):
For the sin and tan scales, you place the cursor (the red marker) in the degrees scale (the one from 10 to 90) and you read the sin of it on top. For the tan, you need to check the degrees in the
spiraling scale in the center, and read the tan of the angle also on top.
What's it good for?
Such a small circular slide rule has a very low precision (2 digits more or less.) This essentially makes it pretty much useless for me, since I have more or less the same precision in mental
division or multiplication.
Anyway, I have used it several times when checking traffic numbers for websites, when estimating daily visits from monthly or bimonthly numbers. Once you set the number of days as ratio, it's pretty
An interesting use would be for quick currency conversions while abroad (you fix the ratio and can easily convert from currencies) but since I travel mostly in Europe, I can't use it for this
(Norway, Iceland, Great Britain and Denmark are good targets still.)
People still use slide rules though: nomographs (what the sin and tan scales are, actually) are a quick way to compute things, and are used in aviation, electric engineering and other fields where
speed is interesting and 5 digit precision is not as important.
A few days ago I found myself with a problem. I wanted a reddit button in one of our websites, and our technical guy wanted it to be asynchronous. After a little poking around and deciding that
reddit doesn't offer asynchronous buttons, I rolled my poor man's version: wrap it in a $(document).ready() It's not asynchronous, but at least it won't block page loading.
Both happy, we deployed and I tested. Worked well, no problem. Well, actually, yes. A problem shared by all reddit buttons, one that was very troublesome here in mostlymaths (back when I had a share
on reddit button just beside the post title.)
When setting up the button you select the target reddit you'd rather have your users send your content. In a page about Apple stuff, it would be r/apple. The problem is though that your users are
free and can do whatever they want. So they go and submit to r/technology. Fine, r/technology is cool enough, lots of readers. Trouble is, when a user arrives from r/technology to your blog, after
clicking on the link... He will see your widget with an ugly submit text, and no upvotes or downvotes:
even though your post has quite a few votes already in r/technology. The trouble comes from setting the target subreddit beforehand: if the url is not in this subreddit, reddit looks nowhere else. Of
course, you'd rather have:
with the real counter. After all, this means making the experience completely seamless:
1. Reddit user sees a cool link to your content in r/whatever. Clicks
2. Lands on your page
3. Upvotes (or downvotes)
instead of
1. Reddit user sees a cool link to your content in r/whatever. Clicks
2. Lands on the page
3. Tries to upvote, needs to submit instead
4. Is forced to submit to r/whatever, gives up (or not)
An easy way to solve this problem is to check the referring URL. If it matches a subreddit, we can set the target of our widget to that subreddit instead of the default one. All reddit readers happy!
There's another issue, though: users not arriving from reddit.
A random user landing in your awesome post, which has a bazillion points in r/whatever likes your content, and wants to upvote it. But, alas! He sees the dreaded submit button, because our default is
r/apple. Or worse, sees 0 (or even a negative number!) because it has been downvoted in our target subreddit.
This can also be solved. Reddit offers a clear-cut json API, allowing jsonp callbacks. This means that we can write a small piece of javascript that will check whether our post has been submitted to
another reddit AND change the target to that one! All reddit users happy!
Below you can find the code. Fork it, use it, whatever. Be happy. If something breaks or doesn't work as expected it's not my fault: use cases may vary.
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Symmetries of probability distributions
up vote 5 down vote favorite
When talking about a single random variable, knowing only its distribution, the construction of a probability space is quite easy. Namely, let $(X,\mathscr A)$ be a measurable space and let $\mathsf
Q$ be some probability measure over this space which we refer to as a distribution of some random variable. The usual definition states that there is some probability space $(\Omega,\mathscr F,\
mathsf P)$, the random variable is $$ \xi:(\Omega,\mathscr F)\to(X,\mathscr A) $$ i.e. it is a measurable map, and its distribution is a pushforward measure: $$ \mathsf Q:=\xi_*(\mathsf P) $$ i.e. $\
mathsf Q(A) = \mathsf P(\xi^{-1}(A))$ for any $A\in \mathscr A$.
Clearly, given $(X,\mathscr A,\mathsf Q)$ for a single random variable there is no reason to come up with a new sample space and we can take $(\Omega,\mathscr F,\mathsf P) = (X,\mathscr A,\mathsf Q)$
and $\xi:=\mathrm{id}_X$.
Let us stick to this latter case. It may happen, that there is a map $$ \eta:(X,\mathscr A)\to(X,\mathscr A) $$ such that $\eta\neq \rm id_X$ but still it holds that $\mathsf Q = \eta_*(\mathsf Q)$.
I wonder if the existence of this other maps is studied somewhere.
The brief statement of the problem is thus the following: given a probability space $(X,\mathscr A,\mathsf Q)$ if the identity map $\rm id_X$ is the unique solution of the equation $$ \mathsf Q = \
xi_*(\mathsf Q) \tag{1} $$ where the variable $\xi$ is any measurable map from $(X,\mathscr A)$ to itself. As far as I am not mistaken, the space of solutions of $(1)$ is a monoid as it is closed
under the composition of maps.
Also, if $\xi$ is a bijection which solves $(1)$ then $\xi^{-1}$ solves it as well: $$ \xi^{-1}_*(\mathsf Q)(A) = \mathsf Q(\xi(A)) = \mathsf Q(\xi^{-1}(\xi(A))) = \mathsf Q(A). $$
Hence, bijective solutions of $(1)$ form a group - which may seem to be thought of a group of "symmetries" of $\mathsf Q$. For example, the standard normal distribution over reals $\mathsf Q = \
mathscr N(0,1)$ admits at least two representations $\xi(\omega) = \omega$ and $\xi(\omega) = -\omega$. As well as any Haar measure over a group admits representation via $\xi(\omega) = \alpha \
omega$ where $\alpha$ is any element of the group.
I've asked this question on MSE, but I have not received any answers.
Edited: To clarify (as requested), my question is exactly as follows: are such groups of symmetries of measures studied somewhere in the literature - may be, providing some interesting results for
measures exhibiting such symmetries. I have studied the Lie groups of ODE/PDE symmetries, and I wonder if there is anything similar known for measures.
measure-theory pr.probability gr.group-theory reference-request
2 What exactly is the question here? Are you just asking whether such symmetries have been studied? – Mark Meckes Sep 4 '12 at 13:40
2 Incidentally, it's easy to give a lot more symmetries of the normal distribution. Start by representing a uniform random variable $U$ in $[0,1]$ as $\sum_{n=1}^\infty 2^{-n} \xi_n$, where the $\
xi_n$ are i.i.d. Bernoulli random variables. Then every permutation of $\mathbb{N}$ induces a symmetry of the distribution of $U$. If $F$ is the c.d.f. of the standard normal distribution, then $F
^{-1}(U)$ is a standard normal random variable, and those permutations yield symmetries of the standard normal distribution. – Mark Meckes Sep 4 '12 at 13:51
1 I haven't thought through the details, but at least any probability distribution on $\mathbb{R}$ with strictly positive density on a bounded or unbounded interval can be shown in this way to
possess infinitely many symmetries. – Mark Meckes Sep 4 '12 at 13:53
1 Of course Noah's answer, typed simultaneously with my comments, gives a probably simpler approach. – Mark Meckes Sep 4 '12 at 13:55
I don't know how much work has gone into describing the automorphism group of a probability space $(X,\mu)$, but it is likely to be fairly large for some natural examples. Any amenable group $G$
1 acting on a compact Hausdorff space will preserve some Radon probability measure. If that measure turns out to be isomorphic to the one you started with, then you have an embedding of $G$ into $\
mathrm{Aut}(X,\mu)$. – Colin Reid Sep 5 '12 at 3:05
show 5 more comments
4 Answers
active oldest votes
This is a fascinating topic. One impressive systematic study of symmetries is in the book by Olav Kallenberg (2005)
In there, though, the measurable space has to have some structure to get the most out of the results.
I don't know of any systematic applications of Lie groups to probability theory. However, there are here and there some interesting results. For instance, this book contains a
study of measures that are invariant under O(n).
There is also plenty of results and applications of discrete symmetries (among others) in here:
up vote 6 down vote
accepted Maybe one should ask a community wiki question where everyone tries to list the results they know. That would be a very interesting list!
Edit: I recently came across this book that is a quite relevant reference for studying symmetries of probability measures:
It has an extensive discussion on Lie groups ans Lie algebras.
Edit 2: Another book with an extensive discussion on Lie groups in Probability and Statistics!
add comment
Maps such as $\eta$ and $\xi$ are called measure-preserving and are studied in ergodic theory. In particular ergodic theory views these as dynamical systems, because the maps can be
iterated. One then studies properties of such maps, such as Poincaré Recurrence.
up vote 4 For, say, Lebesgue space there are many such transformations. Perhaps the simplest such maps defined on $[0,1)$ with Lebesgue measure are the maps $x\mapsto nx+\alpha\mod 1$ for fixed $\
down vote alpha\in\mathbb{R}$ and $n\in\mathbb{N}$ (invertible iff $n=1$). See e.g. Silva's textbook for a variety of more intricate examples.
Thanks a lot for the answer, though as far as I faced ergodic theory, there was considered some (fixed) measure-preserving map and nice results were indeed derived for the asymptotic
properties of the iterations of this map. I've added clarification for what I mean with my question: I am more interested in studies on the group of symmetries of a given measure (or,
perhaps, a family of measure). I cannot check out Silva's book at the moment, maybe it concerns the topic I've mentioned as well. – Ilya Sep 4 '12 at 14:14
@Ilya: one might fit ergodic theory into the framework of your question by saying it deals with cyclic subgroups (or cyclic subsemigroups) of the group of symmetries. – Mark Meckes Sep 4
'12 at 15:14
@MarK: indeed, but my hope was that there is something beyond it. – Ilya Sep 4 '12 at 15:16
add comment
Usually, such symmetries have been either studied in the context of Lebesgue spaces or studied in the context of homogenous measure algebras, where autmorphisms are easy to study. Every
automorphism of a probability space gives rise to an automorphism of the corresponding measure algebra.
The easiest case are Lebesgue spaces, or even simpler, studying the uniform distribution on $[0,1]$. This is of course essentially the case of a Haar measure. A nice property is that one can
take any automorphism of the measure algebra and find an automorphism of the probability space inducing it. Moreover, two automorphisms of the probability space giving rise to the same
automorphism of the measure algebra can differ only on a set of measure zero. Every, homogenous, atomless, separable measure algebra can be represented as a Lebesgue space.
If one starts with a homogenous measure algebra, one may look for probability spaces representing the measure algebra. The two most prominent representations are by the Stone space of the
measure algebra or in the form of a product of coinflips $\{0,1\}^\kappa$ with $\kappa$ infinite, which can represent every atomless (normed) homogenous measure algebra by Maharam's theorem.
In the case of the Stone space, the automorphisms of the measure algebra correspond essentially to the automorphisms of the representing probability space. In the coin-flipping
up vote representation, every automorphism of the measure algebra is induced by an automorphism of the probability space. But very different automorphisms may give rise to the same automorphism of
2 down the measure algebra. Actually, there exists an automorphism of $\{0,1\}^\mathfrak{c}$ that induces the identity on the measure algebra but has no fixed point.
The discussion so far is largely adapted from the introduction to Ergodic theory on homogeneous measure algebras. by Choksi and Prasad. The book this has appeared in is likely to be available
somewhere on the internet...
One can also study the case of rigid probability spaces, where there is essentially no automorphism but the identity. It is actually possible to find a countably generated and countably
separated measurable space in which all automorphisms differ from the identity only on a countable set. This is done in the booklet Borel Spaces by Rao and Rao in Proposition 4. There also is
an example of an atomless, countably generated probability space with no autmorphism but the identity (up to a countable set) in Section 48 of Values of non-atomic games by Aumann and
add comment
I don't know of any systematic study of such symmetries in any great generality. On the other hand, as in most (if not all) fields of mathematics, probability theory happily exploits
symmetries to help solve more concrete problems. For example, if $X$ is a random variable and $\xi$ is a bijective solution of your (1), then $X' = \xi(X)$ is a new random variable with the
same distribution as $X$, coupled to $X$ in a nontrivial way, which can be a helpful technical tool. In particular, if $\xi\circ \xi = \mathrm{id}$, then $(X,X')$ is an exchangeable pair,
up vote which can be used together with Stein's method to prove distributional approximation theorems for $X$.
1 down
vote In a similar vein, your example for Haar measure is essentially the definition of Haar measure, and as such can of course be used (frequently quite directly) to prove many things about Haar
add comment
Not the answer you're looking for? Browse other questions tagged measure-theory pr.probability gr.group-theory reference-request or ask your own question.
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Kids.Net.Au - Encyclopedia > Pythagoras
Pythagoras (582 BC - 496 BC) was a Greek mathematician and philosopher, known best for the Pythagorean Theorem.
Pythagoras, "the father of numbers," was born on the island of Samos off the Greek coast. At a very early age he travelled to Mesopotamia and Egypt where he undertook his basic studies and eventually
founded his first school. Political unrest subsequently necessitated a move to Croton in Southern Italy where he founded his second school. The doctrines of this cultural center were bound by very
strict rules of conduct. His school was open to men and women students alike, and discriminatory conduct was forbidden. His students included those of all races, colours, religions, and financial or
social standing.
History has documented that the doctrines of the Pythagorean school have had a profound effect on philosophy throughout the ages - even to the present day. Pythagoras believed that mathematics could
exist without music or astronomy but mathematical principles were universal and implicit in all things; thus nothing could exist without numbers. His teachings encompassed not only the investigation
into the self but into the whole of the known universe of his time. Pythagoras is widely regarded as the founder of modern mathematics, musical theory, philosophy and the science of health (hygiene).
There are no known surviving texts by Pythagoras, but he founded one of the most influential and devoutly followed schools in pre-Socratic Greek thought.
Pythagoras is sometimes considered to be the pupil of Anaximander and is reputed by very early sources to have visited Thales in his twenties, just before Thales died. There is no account of the
specifics of the meeting, other than the report that Thales recommended that Pythagoras travel to Egypt in order to further his philosophical and mathematical training. There is certainly evidence
that the Egyptians had advanced further than the Greeks of their time in mathematics and astronomy and it is now widely believed that Egyptians used the Pythagorean Theorem in some of their
architectural projects before the 6th century BC.
It is sometimes difficult to determine which ideas are original to Pythagoras and which are latter additions by his followers. However, there is general agreement that Pythagoras either developed the
Pythagorean Theorem himself or at the very least introduced it to Greek thought. In addition to the Pythagorean Theorem, it there is general agreement that the numerical ratios which determine the
musical scale trace back to a discovery by Pythagoras himself, since this plays a key role in many other areas of the Pythagorean tradition, and since there is no evidence of earlier Greek or
Egyptian musical theories.
The pentagram (five-pointed star) was an important religious symbol used by the Pythagoreans. It was called "health".
Diogenes Laertius (about 200 BC) quotes Alexanders (about 100 BC) book Successions of Philosophers[?] (and according to Diogenes Alexander has access to a book called The Pythagorean Memoir) in his
account of how the pythagorean cosmology was constructed (Diogenes Laertius, Vitae philosophorum VIII[?], 24):
The principle of all things is the monad or unit; arising from this monad the undefined dyad or two serves as material substratum to the monad, which is cause; from the monad and the undefined
dyad spring numbers; from numbers, points; from points, lines; from lines, plane figures; from plane figures, solid figures; from solid figures, sensible bodies, the elements of which are four,
fire, water, earth and air; these elements interchange and turn into one another completely, and combine to produce a universe animate, intelligent, spherical, with the earth at its centre, the
earth itself too being spherical and inhabited round about. There are also antipodes, and our ‘down' is their ‘up'.
This cosmology also inspired the arabic gnostic Monoimus to combine this system with monism and other things to form his own cosmology.
There are just a few relevant source texts to consult about Pythagoras and the pythagoreans:
Most are available in different translations. Other texts usually build solely on these three books.
All Wikipedia text is available under the terms of the GNU Free Documentation License
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Can anyone tell what this box is tuned to and how many cubes it is [Archive] - Car Audio Forum - CarAudio.com
View Full Version : Can anyone tell what this box is tuned to and how many cubes it is
11-08-2004, 08:55 PM
I bought some subs and this is the box they came in...http://img76.exs.cx/img76/4867/box4.jpg
11-08-2004, 08:56 PM
I dont need anything exact, as my measurements werent exact, just something approximate
Im sure great sounds on mcgalliard should be able to tell u if ur looking for a really quick answer. Well if they are in a good mood they might help u out!
Moe Lester
11-08-2004, 11:29 PM
13" tall, port is 11.25 tall? 7/8" MDF? im not sure how long the port is either, or whether all the measurements are internal or external.
11-08-2004, 11:36 PM
probably around 4 - 4-1/2 cubes, i didnt figure in the port or anything. the 35"x13"x18" box is 4.7125 ft^3
11-09-2004, 09:15 AM
those are all external, 3/4 MDF...and the people at GS are *****!
Yea thats why i wrote if they were in a really good mood the might help, might
11-09-2004, 11:11 AM
my calculations come up with 3.844, and that is not factoring the port, or basket displacment.
3.679 with 3/4 inch MDF. The first numbers were using 5/8 MDF
11-09-2004, 12:21 PM
where at in Muncie are you...we should hook up sometime...I am off Oakwood
11-09-2004, 02:02 PM
This is just a rough estimate and no where near accurate because, well your diagram *****.
2.98 after port displacement. Not factoring speaker displacement tuned to 32hz
11-09-2004, 03:16 PM
my diagram is the ****...it was made with OLD SCHOOL MS PAINT!
11-09-2004, 05:50 PM
my diagram is the ****...it was made with OLD SCHOOL MS PAINT!
It was pain tryin to read it.
Where did you get the box. Did the person who sold you the subs make it??? Or is it pre fab.
11-09-2004, 09:54 PM
those are all external, 3/4 MDF...and the people at GS are *****!that is an estimate for internal volume. correct me if i am wrong, but it is probably closer to 3.5 with the subs in it. the box empty
is close to 3.8 or 3.7
11-10-2004, 10:57 AM
Guys, can you explain to me how this is figured out.
Is it wxhxd then divide it by what number? 1728?
and how do you figure out displacement?
11-10-2004, 11:06 AM
Guys, can you explain to me how this is figured out.
Is it wxhxd then divide it by what number? 1728?
and how do you figure out displacement?
Box Internal L x W x H = ? then Divide by 1728 to get cubic feet.
Port L x (W+.75) x H = ?
Subtract the port area from the box area.
Then subtract your speakers displacement. Which can be found in the manual.
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Area of a segment of an ellipse
http://img253.imageshack.us/img253/8324/image002h.gif How to find the area of a segment of an ellipse (shaded portion) with respect to height?
The formula for the area of an entire elippse is a*b*pi where a and b are the lengths of the major and minor axes. If you can find what the fractional amount of the whole ellipse that shaded region
is...... That should be enough to get you going.
I'm afraid methods of calculus will be required to find the shaded area. http://img253.imageshack.us/img253/8324/image002h.gif
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Middle School Mathematics Endorsement
Illinois Institute of Technology's Department of Mathematics and Science Education has developed an endorsement program for elementary school and middle school teachers who want to teach middle
grades mathematics in the State of Illinois. Math endorsement can be achieved by completing 15 credit hours in mathematics, 3 credit hours in methods of teaching middle school mathematics, and 6
credit hours in adolescent psychology and middle school curriculum. The 24 hour program results in an endorsement in middle grades mathematics, it does not provide an academic degree.*
Course of Study
• Problem-Based Algebra (3 credits)
• Problem-Based Number Theory (3 credits)
• Problem-Based Probability and Statistics (3 credits)
• Problem-Based Geometry (3 credits)
• Problem-Based Foundations of Calculus (3 credits)
• Instructional Strategies for Middle School Mathematics (3 credits)
• Middle Level and Secondary Mathematics Curriculum (3 credits)
• Adolescent Psychology (3 credits)
Total Credits for Endorsement in Middle Grades Mathematics: 24
Teachers are encouraged to take the whole sequence of courses, but are allowed to take individual courses that fit their needs.
Suggested courses are consistent with ISBE requirements.
*All math endorsement courses count toward a Master's degree in Mathematics Education. Nine additional graduate credits are needed for the Master's degree, totaling thirty-three (33) graduate
MSED 509 - Instructional Strategies for Middle School Mathematics (3 credit hours)
Instructional Strategies for Middle School Mathematics specifically addresses concerns of teaching grades 5-8 mathematics by considering the social and psychological characteristics of students in
transition from elementary to high school mathematics. The course uses a focus on rational number and proportional reasoning (topics that span the middle school curriculum) to study students'
development of powerful representational systems and conceptual flexibility. Participants will learn about building mathematical community in which students construct mathematical evidence for claims
of perceived regularities and patterns on logical reasoning and mathematical thinking. Participants will select, adapt and design worthwhile mathematical tasks to serve various instructional
purposes. Finally, the participants will learn what it means to build an on-going assessment system that integrates self-, peer-, teacher-, formative and summative assessment into a system of best
practice that blurs the line between learning and assessment.
MSED 510 - Problem-Based Algebra (3 credit hours)
Algebra is taught via a problem solving approach with connections to other topic areas such as geometry, statistics and probability. Explorations with and conjecturing about number relationships and
functions provide experiences from which students develop algebraic habits of mind: Doing and undoing (algebraic thinking that involves reflective or reverse algebraic reasoning, doing problems/
procedures backwards); building rules to represent functions (recognizing patterns and organizing data to representation situations in which input is related to output by well-defined functional
rules); and abstracting from computation (developing the capacity to think about computations independently of particular numbers used).
MSED 511 - Problem-Based Number Theory (3 credit hours)
Number theory is taught via a problem solving approach with connections to geometry, logic, and probability. Explorations with and conjecturing about number patterns provide experiences from which
students study various topics including: factors, primes, and prime factorization; counting techniques; greatest common factor (GCF) and least common multiple (LCM); divisibility; number patterns
(e.g., Pascal's triangle, polygonal numbers, Pythagorean triples; Fibonacci numbers); Diophantine equations; remainder classes and modular arithmetic; iteration, recursion, and mathematical
MSED 512 - Problem-Based Statistics and Probability (3 credit hours)
This course emphasizes statistics and probability as practical subjects devoted to obtaining and processing data with a view toward making statements that often extend beyond the data. These
statements (i.e., inferences) take the form of estimates, confidence intervals, significance tests, etc. The content of this course is concerned with the production of good data, and involves
consideration of experimental designs and sample surveys. The activities have their origin in real data and are concerned with processing the data in the widest contexts and with a wide variety of
applications such as social, administrative, medical, the physical sciences and the biological sciences.
MSED 514 - Problem-Based Geometry (3 credit hours)
Geometry is taught via problem solving with connections to other topic areas such as algebra and number theory. Participants use Geometer's Sketchpad to investigate about fundamental concepts of
Euclidean geometry in two and three dimensions and their applications. Explorations of and conjecturing about these concepts provide experiences from which students study various topics including:
properties and relationships of geometric objects; geometric proof; area and volume; transformations, symmetry and tessellations; trigonometric ratios; and visual modeling of algebraic operations and
abstract algebraic concepts.
MSED 515 - Problem-Based Foundations of Calculus (3 credit hours)
The course is focused on the development of foundational ideas, concepts, and methods of introductory calculus and its basic applications with emphasis on various problem-solving strategies,
visualization, mathematical modeling, and connections to algebra, geometry, number theory, and logic relevant to the middle school mathematics curriculum. Explorations with the SimCalc software and
conjecturing about linking graphs, tables, and concrete to represent dynamic situations provide experiences from which students study various topics including: linear, quadratic, cubic, exponential,
logarithmic, and trigonometric functions and their graphs; limits and continuity; rate of change, slope, tangent, and derivative; area under a curve and integration; elements of infinite series.
MSED 555 - Middle Level and Secondary Mathematics Curriculum (3 credit hours)
This course is a lecture/discussion course focusing on the history/sociology of education, rationales and goals of current reform efforts, curriculum design, development, and curriculum analysis.
This course helps students develop a functional understanding of the various factors that influence the development and direction of secondary science curricula, and the ability to apply knowledge of
subject matter, curriculum development, and curriculum theory to construct a hypothetical curriculum that recognizes cultural and individual differences with special emphasis on the interdependence
of science, technology, and society. Particular emphasis is placed on the analysis and revision of existing curriculum relative to national and state reforms.
MSED 580 - Adolescent Psychology (3 credit hours)
This course is designed to develop the participants' understanding of adolescent psychology. The main foci throughout the course are the unique aspects of adolescents and how those aspects influence
behavior, learning, and social interactions, especially with regard to middle schools. Studies will include educational psychology theories and models, motivation and learning, developmental changes
during adolescence, cognitive abilities, human ecology, diversity, and cultures. Additionally, participants will examine historical and philosophical perspectives of adolescent psychology and
synthesize how these perspectives have influenced teaching, learning, and cultures in middle schools. The course will involve weekly readings and reflections, classroom experiences, short
assignments, tests/quizzes, research projects, and formal class presentations.
│ FALL │ SPRING │ SUMMER │ FALL │ SPRING │
│ MSED 555: │ MSED 580: │ MSED 509: │
│Middle Level and Secondary Mathematics Curriculum*│ Adolescent Psychology │ Instructional Strategies for Middle School Mathematics** │
│ MSED 510: │ MSED 514: │ MSED 513: │ MSED 511: │ MSED 515: │
│ Problem-Based Algebra │ Problem-Based Geometry │Problem-Based Probability and Statistics│Problem-Based Number Theory│Problem-Based Foundations of Calculus│
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[Numpy-discussion] Fastest distance matrix calc
Bill Baxter wbaxter@gmail....
Fri Apr 13 05:43:44 CDT 2007
I think someone posted some timings about this before but I don't recall.
The task is to compute the matrix D from two sets of vectors x (M,d)
and y (N,d).
The output should be D where D[i,j] is norm(x[i]-y[j])
The Matlab NetLab toolkit uses something like this to compute it:
d2 = (x*x).sum(1)[:,numpy.newaxis] + (y*y).sum(1) - 2*mult(x,y.T)
And then does
because roundoff in the above can sometimes create negative values. And finally
d = sqrt(d2)
But it just doesn't seem like the best way to do it. Whatever was
posted before I don't remember anything about a subtract.outer
solution. Seems like something along the lines of
might be faster, and also avoid the need to check for negatives.
I'll do some timings if no one's already done it. Just wanted to check first.
More information about the Numpy-discussion mailing list
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Integrated Mathematics Sequence
Integrated Mathematics Sequence for High School Mathematics
Download Integrated Mathematics Information Sheet here
Integrated Mathematics has been in the NC SCS for Mathematics since the 1998 revision. The integrated mathematics courses should be treated as a package. The courses are listed as a group in the high
school graduation requirements . A student who has had IM I and IM II should proceed to IM III. The three courses (as a package) are equivalent to the conventional courses (Algebra I, Geometry &
Algebra II as a package).
The Integrated Mathematics I and II curriculum should not be used as a substitute for an Algebra IA, Algebra IB sequence. Integrated Mathematics is in the Standard Course of Study and should be
taught with the objectives in the SCS.
End of Course Tests
Once the new assessment system is developed (expected in 2011-2012) the set of EOCs for the integrated mathematics sequence (IM I, II, III) will be similar to the set of EOCs for the conventional
sequence (Algebra I, Geometry, Algebra II).
Up until this school year (2008-2009) the students in the integrated sequence took all 3 of the math EOCs (Algebra I after IMII; Geometry during IM III; and Algebra II at the end of IM III). However,
the State Board of Education has granted a waiver for integrated mathematics students as we wait for a our new testing system to be developed (expected in 2011-2012), and integrated mathematics
students during 2008-2009; 2009-2010, and 2010-2011 will not be required to take the Geometry EOC. This is an interim measure to allow for the new assessment system to be developed (expected in
2011-2012). Once the new assessment system is developed, the EOCs expected for the integrated sequence will be comparable to the EOCs expected for the conventional sequence.
Currently IM students take the Algebra I EOC after IM II and Algebra II EOC at the end of IM III.
The Textbook commission did not choose a book for Integrated Math I, II, III during the last mathematics textbook adoption; so, there is not a book on the state list at this time. The new adoption
list for high school mathematics textbooks in NC is expected in October 2009. The next textbook list will have choices for Integrated Mathematics. The Integrated Mathematics I, II, III standards
include all objectives in Algebra I, Geometry, Algebra II plus some topics in discrete mathematics and statistics. There are Integrated Mathematics textbooks available for purchase.
Integrated Mathematics
Course Codes and Sample Descriptions
2051 Integrated Mathematics I (IM I)
Note: The Integrated Algebra/Geometry sequence of courses is an investigative mathematics sequence that includes four major strands: algebra, geometry, statistics, and discrete mathematics. The first
year the topics are dealt with on an introductory level and each successive year the topics are studied in more depth. IM I, II, and III include all of the objectives for Algebra I, Geometry, and
Algebra II in the NC Standard Course of Study.
Integrated Mathematics I (IMI) provides students the opportunity to study the introduction of algebra, geometry, statistics, and discrete mathematics using a problem centered approach that emphasizes
the connections between the four strands. Students who successfully complete IM I will take IM II the following year.
2052 Integrated Mathematics II (IM II)
Note: (See note for IM I.) All students in this class take the Algebra I End-of-Course Test.
This course provides students the opportunity to study matrices, systems of equations, coordinate and transformational geometry, least squares regression, linear models, power models, network
optimization, introductory trigonometry with triangles and circles, and probability. The instruction features a problem-centered approach that emphasizes connections between algebra, geometry,
statistics and discrete mathematics. Students who successfully complete IM II will take IM III the following year.
2053 Integrated Mathematics III (IM III)
Note: (See note for IM I.) All students in this class take Algebra II End-of-Course Test.
This course provides students the opportunity to study law of cosines and sines, linear programming, voting preferences and sampling techniques, advanced algebraic concepts (polynomial, exponential,
periodic and rational expressions to model relations among quantitative variables), congruence of triangles, properties of parallelograms, inductive and deductive reasoning, normal distribution as a
model of variation, statistical process control, and solving problems including recursive and sequential change. The instruction features a problem centered approach that emphasizes the connections
between algebra, geometry, statistics and discrete mathematics. Students who successfully complete IM III may choose to continue their study of mathematics by taking IM IV, Pre-Calculus, or Advanced
Functions and Modeling.
2054 Integrated Mathematics IV (IM IV)
This course provides the opportunity for students to study limits, rates of change, how area relates to integrals, permutations and combinations, mathematical induction, logarithmic functions,
composite and inverse functions, periodic functions, vectors, linearizing data, polynomial and rational functions, complex numbers, binomial distributions, space geometry, informatics (the
mathematics of databases and search engines, cryptography, error-correcting codes, data compression), problem solving, algorithms, and spreadsheets. The instruction features a problem centered
approach that emphasizes the connections between algebra, geometry, statistics and discrete mathematics. Students who successfully complete IM IV may choose to continue their study of mathematics by
taking AP Calculus AB or AP Calculus BC, and/ or AP Statistics. It is recommended that those students considering calculus should take Honors IM IV. The honors level of the course serves as a bridge
between Honors IM III and AP Calculus and is designed for college-bound students who plan to major in math or a math-related field.
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Whole Number Addition
1.1: Whole Number Addition
Created by: CK-12
Practice Whole Number Addition
Have you ever been to the zoo? Have you ever had to add whole numbers to solve a problem? Adding whole numbers is a skill that can help you to solve many real - world problems. Jonah is a student
volunteer at the city zoo. He is working with the seals. Jonah loves his job, especially because he gets to help feed the seals who live at the zoo. There are 25 female and 18 male seals. In order to
figure out how much to feed them, he will need to know the total number of seals. Use what you will learn in this Concept to help Jonah figure out the total number of seals.
Adding whole numbers is probably very familiar to you; you have been adding whole numbers almost as long as you have been in school. Here is a problem that will look familiar.
$4 + 5 = \underline{\;\;\;\;\;\;\;\;\;\;}$
In this problem, we are adding four and five. We have four whole things plus five whole things and we get an answer of nine. The numbers that we are adding are called addends. The answer to an
addition problem is the sum. This first problem was written horizontally or across.
In the past, you may have seen them written vertically or up and down. Now that you are in the sixth grade, you will need to write your problems vertically on your own.
How do we do this?
We can add whole numbers by writing them vertically according to place value. Do you remember place value? Place value is when you write each number according to the value that it has.
Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones
This number is 1,453,221. If we used words, we would say it is one million, four hundred and fifty-three thousand, two hundred and twenty-one.
What does this have to do with adding whole numbers?
Well, when you add whole numbers, it can be less confusing to write them vertically according to place value. Think about the example we had earlier.
If we wrote that vertically, we would line up the numbers. They both belong in the ones column.
$& \quad 4\\& \ \underline{+5}\\& \quad 9$
What happens when we have more digits?
$456 + 27 = \underline{\;\;\;\;\;\;\;\;}$
When you have more digits, you can write the problem vertically by lining up each digit according to place value.
$& \quad 456\\& \ \underline{+ \ 27}$
Now we can add the columns.
Now let's practice.
Example A
$3,456 + 87 =\underline{\;\;\;\;\;\;\;\;\;\;}$
Solution: 3,543
Example B
$56, 321 + 7, 600 =\underline{\;\;\;\;\;\;\;\;\;\;}$
Solution: 216,091
Example C
$203,890 + 12, 201 = \underline{\;\;\;\;\;\;\;\;\;\;}$
Solution: 63,921
Now let's go back to Jonah and the seals. Jonah knows how many male seals and how many female seals are in the seal area at the zoo. He wants to figure out how many seals there are altogether. To
accomplish this task, Jonah will simply need to add the two quantities together.
Here is what he knows:
25 females 18 males
Now we add those values together.
$25 + 18 = 43$
There are 43 seals at the zoo.
Here are the vocabulary words found in this Concept.
the numbers being added
the answer to an addition problem
up and down
Guided Practice
Now here is one for you to try on your own. Add the following pair of whole numbers. Then you can find the answer below.
$675 + 587 = \underline{\;\;\;\;\;\;\;\;}$
To solve this problem, we line up the columns vertically according to place value.
When you have more digits, you can write the problem vertically by lining up each digit according to place value.
$& \quad 675\\& \ \underline{+ 587}$
Now we can add the columns.
Our answer is 1,262.
Interactive Practice
Video Review
These videos will help you with adding whole numbers.
Directions: Use what you have learned to solve each problem.
1. $56 + 123 = \underline{\;\;\;\;\;\;\;\;\;}$
2. $341 + 12 = \underline{\;\;\;\;\;\;\;\;\;}$
3. $673 + 127 = \underline{\;\;\;\;\;\;\;\;\;}$
4. $549 + 27 =\underline{\;\;\;\;\;\;\;\;\;}$
5. $87 + 95 = \underline{\;\;\;\;\;\;\;\;\;}$
6. $124 + 967 = \underline{\;\;\;\;\;\;\;\;\;}$
7. $1256 + 987 =\underline{\;\;\;\;\;\;\;\;\;}$
8. $2345 + 1278 = \underline{\;\;\;\;\;\;\;\;\;}$
9. $3100 + 5472 = \underline{\;\;\;\;\;\;\;\;\;}$
10. $3027 + 5471 =\underline{\;\;\;\;\;\;\;\;\;\;}$
11. $13027 + 7471 =\underline{\;\;\;\;\;\;\;\;\;\;}$
12. $23147 + 5001 =\underline{\;\;\;\;\;\;\;\;\;\;}$
13. $23128 + 7771 =\underline{\;\;\;\;\;\;\;\;\;\;}$
14. $43237 + 5071 =\underline{\;\;\;\;\;\;\;\;\;\;}$
15. $22027 + 6001 =\underline{\;\;\;\;\;\;\;\;\;\;}$
16. $45627 + 2471 =\underline{\;\;\;\;\;\;\;\;\;\;}$
17. $83027 + 51471 =\underline{\;\;\;\;\;\;\;\;\;\;}$
18. $94127 + 5471 =\underline{\;\;\;\;\;\;\;\;\;\;}$
19. $83777 + 3321 =\underline{\;\;\;\;\;\;\;\;\;\;}$
20. $95527 + 12471 =\underline{\;\;\;\;\;\;\;\;\;\;}$
Files can only be attached to the latest version of Modality
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A ball is thrown vertically upward at 20 m/s from the roof of a bus travelling at constant velocity 30 m/s along a... - Homework Help - eNotes.com
A ball is thrown vertically upward at 20 m/s from the roof of a bus travelling at constant velocity 30 m/s along a straight road. After how many distance travelled by bus, the ball returns to the
thrower's hand?
In order to solve this question we must first solve for how long the ball is in the air:
`v_2-v_1 = at -gt t=(v_2-v_1)/a`
At 2.04s the ball has reached its maximum height
Next we must calculate its maximum height:
After 2.04s the ball has travelled 20.4m vertically.
Now we need to know how long it takes the ball to fall back to the throwers hand. Remember, that `v_1` is now 0 (starting from rest at max height):
As expected, the ball takes the same amount of time to fall as it does to raise. Therefore, the total time spent in the air is 2.04+2.04=4.08s.
The last step is to determine how far the bus has travelled in 4.08s:
Although, it is important to note that the ball would not return to the thrower's hand, but would fall to the ground 122.4m behind the thrower at the bus' position when the ball was thrown.
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Patent US4463377 - Arrangement for storing or transmitting and for recovering picture signals
1. Field of the Invention
The invention relates to an arrangement for coding and decoding picture element signals (pels), obtained by line by line scanning of the picture elements of a picture, said picture element signals
being transformed in a transformation arrangement for generating coefficient values. These coefficient values are quantized in a quantizing device and thereafter stored in a storage medium or
transmitted to an associated receiver. For the recovery of the original picture element signals the quantized coefficients are applied to a retransformation arrangement which, as is also the
transformation arrangement, is formed by a plurality of transformers T(i) of the order i, wherein i=1, 2, 3, . . . N and the transformer T(i) having i inputs and 2i outputs, the i inputs being
connected to the i outputs of the preceding transformer T(i-1). Each transformer T(i) is formed by i auxiliary transformers each having an input connected to the associated output of the preceding
transformer T(i-1); this auxiliary transformer also comprises an arithmetical unit having two inputs, one of which is connected directly and the other via a delay device to the input of the auxiliary
transformer, the arithmetical unit having two outputs which represent two of the outputs of the transformer T(i).
2. Description of the Prior Art
For the storage or transmission of pictures it is advantageous to use the lowest possible number of information units and yet display the scanned picture as accurately as possible. Reducing the
number of information units is possible if in a picture the redundancy and, possibly, also the irrelevance are significantly suppressed. It is known, for example from the periodical "IEEE
Transactions on Computers", Vol. Com-19, No. 1, February 1971, pages 50 to 61 inclusive, or from the book by Pratt "Digital Image Processing", John Wiley and Sons, 1978, pages 232 to 278 inclusive,
to use transformation coding to reduce the number of information units and to quantize the resultant coefficients. A non-linear characteristic is usually used for the quantization.
After the arithmetical operations are performed in the arithmetical unit, this unit produces an output quantity the value of which is located in a value range which is wider than the range in which
the input quantity of the arithmetical unit (and consequently also of the auxiliary transformer) is located. This can be explained with reference to a Walsh-Hadamard-transformation of two picture
element signals A and B. The transformation of these two picture element signals produces the two coefficients
If now the two picture signals A and B had the maximum value, the coefficient F(1) would be of twice the value, that is to say a doubling of the value range has occurred. Depending on the polarity of
A and B this also relates to the coefficient F(2). As the transformation arrangement is formed by a cascade arrangement of a plurality of transformers, doubling of the value range occurring in each
transformer, the value range of the transformed signals is wider than the value range of the original picture signals.
The invention has for its object to provide an arrangement of the type described in the opening paragraph which does not require an increase of the value range of the output quantity produced by the
arithmetical units, an advantageous quantization being rendered possible at the same time. According to the invention, each auxiliary transformer includes at least one additional logic circuit to
which the carry bit of a first value out of the output values and the sign bit of the second output word of the arithmetical unit are applied to generate an auxiliary bit which is added as the most
significant bit to the first output value, the least significant bit and also the carry bit of the first output value and the sign bit of the second output value being suppressed.
The invention utilizes inter alia the fact that the summation and the difference formation result in two numbers which are always either both even or both odd, so that the least significant bit of
one of the two output values may be omitted, without information being lost.
An embodiment of an arrangement in accordance with the invention will now be further described by way of example with reference to the accompanying drawings.
FIG. 1 shows a general block circuit diagram of an arrangement for transforming and retransforming picture signals,
FIG. 2 shows a block circuit diagram of a transformation arrangement or a retransformation arrangement,
FIG. 3 shows schematically mapping of portions of the value range of the output values on a different value range,
FIG. 4a shows an auxiliary transformer provided with the measures in accordance with the invention for use in a transformation arrangement,
FIG. 4b shows an auxiliary transformer provided with the measures in accordance with the invention for use in a retransformation arrangement.
In the arrangement shown in FIG. 1, the picture element signals applied via the conductor 1 are transformed in the transformation arrangement 2 in accordance with the desired transformation algorithm
and under the control of the control unit 6; that is to say they are converted into coefficients which are applied by the conductor 3 to the quantizing device 4, which is also controlled by the
control unit 6. The quantized coefficients are applied to the transmission path 10. Instead of being applied to the transmission path they may alternatively be applied to a store.
The coefficients are applied to a decoder 14 and decoded therein. The decoded coefficients are applied to the retransformation arrangement 12 via the conductor 13, so that predominantly the original
picture element signals applied to the input 1 appear at the output 15.
The control of the decoder 14 and of the retransformation arrangement 12 is effected by the control unit 16.
The general construction of a transformation arrangement 2, a quantizing device 4, a decoder 14 and a retransformation arrangement 12 is known in principle.
For the further description, the mathematical background will first be described, more specifically on the basis of a Walsh-Hadamard-transformation. A 2-point-transformation of two picture elements A
and B are effected as the basic step: ##EQU1## wherein ##EQU2## The resultant coefficients are thus defined by the expressions
F(1)=A-B (3)
These coefficients can easily be determined by means of conventional arithmetical means.
A Wash-Hadamard-transformation for a complete picture or a sub-picture of 2n(n=2^N, N=1, 2, . . .) picture elements can be derived step-wise from the above-indicated basic step in the following
manner. ##EQU3## So two coefficients always formed from different basic transformation steps are further processed with such a basic transformation step until finally all picture elements of said
picture or sub-picture have been considered. Thus the transformation is effected in a plurality of steps.
An arrangement for performing such a Walsh-Hadamard-transformation is shown in FIG. 2. Of the signals applied to the input 21, every second signal is temporarily stored in the intermediate store 24,
so that two consecutive signal values are available at the output of the arithmetical unit 22. When the Walsh-Hadamard-transformation is used, the arithmetical unit 22 forms each time the sum and the
difference of these two values and applies the result to the correspondingly designated outputs 23 and 25. These output values correspond to the coefficients F(0) and F(1) of the formula (3) and
shown in FIG. 2.
Every first value of the output values at the output 23 is temporarily stored in the intermediate store 28 and thereafter applied to one input of the arithmetical unit 26, while the second output
value is directly applied from the output 23 to the other input of the arithmetical unit 26. The corresponding operation is also effected on the output values at the output 25, each first value of
which is temporarily stored in the store 32 and then applied together with the second value in parallel to the arithmetical unit 30. The arithmetical units 26 and 30 have absolutely the same
construction as the arithmetical unit 22, which also applies to the subsequent arithmetical units 34, 38, 42 and 46.
Output values which correspond to the coefficient of a sub-picture consisting of 2×2 picture elements are then produced at the outputs of the arithmetical units 26 and 30. Also these output values
are alternately applied, via the intermediate stores 36, 40, 44 or 48 and directly, to the calculating units 34, 38, 42 and 46. These arithmetical units produce at the outputs the coefficients F"(0),
F"(1) . . . of a sub-picture consisting of 4×2 picture elements.
This arrangement can be extended at option, so that correspondingly larger sub-pictures are transformed.
In order to prevent a doubling of the value range of the output values compared with the value range of the input values from occurring in each arithmetical unit or at each stage of the processing
operation, respectively, a different mapping of the output values is now effected, as will be further explained with reference to FIG. 3. The slanting coordinates A and B denote the possible input
values of an arithmetical unit. The Walsh-Hadamard coefficients F(0) and F(1) formed therefrom are shown in the systems of coordinates. From this it can be seen that the coefficients F(0) and F(1)
each have a value range of 2G if the value range of the applied signals A and B is equal to G. The value range is extended because of the fact that at the summation a carry bit and at the difference
formation a sign bit may occur. On the other hand FIG. 3 also shows that the value combinations, denoted by means of crosses, of the coefficients F(0) and F(1), do not encompass all the possible
value combinations of these coefficients within their full value range. This means that the coefficients have a redundancy produced by the transformation itself. This redundance can be further
determined as follows. From the formula (3) it follows that the coefficients F(0) and F(1) are both either even or odd. Upon binary notation of these values the least significant bits are equal to
each other, so that in this respect only one coefficient must be taken into account.
FIG. 3 further shows that the value combinations (denoted by crosses) of the coefficients F(0) and F(1) are defined by an uncertainty principle of the following shape:
[F(0)-G]+[F(1)]≦G (5).
This relation indicates that the actually occurring value combinations, denoted by crosses, of coefficients F(0) and F(1) occur in an area formed by a tilted square, so that the areas in the corners
are not occupied by the dashed-line outersquare which includes the total number of value combinations, so that the total number of value combinations cover an area which is twice as large as the area
of the actually occurring value combinations of the coefficients F(0) and F(1).
The restriction (both even or both odd) of the value combinations of the two coefficients cannot be used to form coefficients whose value range has not become larger compared with the value range of
the applied input values A and B. For that purpose at least a portion of the coefficients first formed is mapped in another area of the field shown in FIG. 3. Several mappings are possible. Each of
these mappings is based on a division of the original field, shown in FIG. 3, into four areas I, II, III and IV, which are determined by the carry bit of the sum coefficient F(0) and by the sign bit
of the difference coefficient F(1). This is based on the assumption that the representation of the difference A-B for the difference coefficient F(1) is performed in the two's complement, so that
F(1)=A-B+G (6)
wherein G represents the number of values of the variables A and B, respectively.
As a result thereof positive differences are represented by a bit having the value "1" in the position of the most significant bit, which is denoted as the sign bit VZ, and negative differences
include a bit having the value "0" in the position of the most significant bit. In the sum coefficient F(0) the most significant bit indicates the carry bit U. By combining the carry bit U and the
sign bit VZ of the coefficients F(0) and F(1) different mappings can be realized, so that the total value range to be represented of the two coefficients together is halved. By making additional use
of the property that the two coefficients are odd or even, modified coefficients can be obtained whose value range is equal to the value range of the applied signals A and B. With such a mapping no
loss of information occurs, so that by a corresponding retransformation the picture element can be accurately reconstructed.
FIG. 3 shows a mapping method in which the area I is moved to the right above (K') the area IV and the area III is moved to the right below (III') the area II. So, the modified coefficients F*(0) and
F*(1) thus obtained are formed in accordance with the following Table 1, the difference values being shown in two's complement.
TABLE 1______________________________________F (0) F (1) U + VZ F* (0) F* (1)______________________________________I U = 0 VZ = 0 1 A + B + 2^4 A - B + 2^4II U = 0 VZ = 1 0 A + B A - BIII U = 1 VZ = 0 0 A + B - 2^4 A - B + 2^4IV U = 1 VZ = 1 1 A + B A - B______________________________________
This is based on the assumption that G=2^4 =16. So the shift of the areas can be formed by an exclusive-NOR-gate to which the carry bit U and the sign bit VZ are applied.
A circuit arrangement, which realizes such a mapping of the coefficient and can be used for each arithmetical unit 22, 26, 30 etc. of FIG. 2, is shown in FIG. 4a. The two signals A and B occur in the
form of binary four-bit-words, which is shown by the block with four boxes in the signal path. These two signals are applied to both an adder unit 60 and a subtracting unit 62, a carry signal having
the value "1" being continuously applied in order to obtain the corresponding difference in two's complement. The output values of the two units 60 and 62 represent the coefficients F(0) and F(1),
which are represented by five-bit binary words. For the coefficient F(0) the bit U in the position of the most significant bit indicates the carry bit and for the coefficient F(1 ) the bit VZ in the
position of the most significant bit indicates the sign bit.
These two bits are now applied to the inputs of an exclusive-NOR-gate 64, and the output signal of this gate replaces the carry bit U of the coefficient F(0). In addition, the least significant bit
(denoted by means of a cross) of this coefficient is omitted, since the corresponding bit of the other coefficient F(1) has the same value. This results in the modified coefficient F*(0), which has a
length of only four bits, that is to say it contains the same number of information units as the applied signals A and B. The sign bit is not further used at the coefficient F(1) as it is already
indirectly present in the most significant bit of the modified coefficient F*(0). The last four bits of F(1) now represent the modified coefficient F*(1). As a result thereof, also this coefficient
has the same number of information-units as the applied signals A and B. All together this results in the coefficients F*(0) and F*(1) in accordance with Table 1, which comprise the same number of
information bits as the applied signals A and B. So when the arithmetical units 22, 26, 30 etc. of FIG. 2 are realized by an arrangement shown in FIG. 4a, it will be obvious that also in the event of
a longer cascade arrangement of arithmetical units for the transformation of a larger sub-picture the word length of the coefficients is not increased.
The re-transformation unit 12 in FIG. 1 is of approximately the same construction as the transformation unit 12, the two units even being identical when the Walsh-Hadamard transformation is employed.
So the step-wise processing of each time two coefficients restores the original picture data again. When the modified coefficients, which are produced by the arrangement shown in FIG. 4a are used, a
modified retransformation is, however, also necessary. First the mathematical background of the retransformation of the modified coefficients will be described. When the Walsh-Hadamard-transformation
is employed also now the sum and the difference of the two coefficients are formed. Taking account of the modified coefficients there is now obtained for the retransformed values A and B, which here
consequently do not directly represent the retransformed picture signals but resulting values, the calculation shown in the following Table 2.
TABLE 2______________________________________A B______________________________________Area I: 1/2 · (A + B + 2^4) 1/2(A + B + 2^4) + 1/2 · (A - B + 2^4) - 1/2(A - B + 2^4) + 2^4 A + 2^4 B + 2^4Area II + IV: 1/2(A + B) 1/2(A + B) + 1/2(A - B) - 1/2(A - B) + 2^4 A B + 2^4Area III: 1/2(A + B - 2^4) 1/2(A + B - 2^4) + 1/2(A - B + 2^4) - 1/2(A - B + 2^4) + 2^4 A B______________________________________
The values which may be combined in the individual areas can be obtained from Table 1. The factor 1/2 is obtained at the sum coefficient F*(0) because of the fact that the least significant bit has
been omitted. The factor 1/2 is also obtained at the difference coefficient F*(1) because of the fact that the least significant bit is processed separately and differently from the other bits, as
will be further described hereinafter with reference to an embodiment.
Table 2 shows that with this retransformation, the subtraction in the two's complement being again equal to the addition of the value 2^4 to the difference, the original values A and B are directly
recovered, only with coefficients of defined areas in accordance with FIG. 3 a carry in the form of the term 2^4 occurring, which can therefore be simply eliminated by limiting the output values to
the last four bits of the information words produced during the processing operation.
FIG. 4b shows such an arithmetical unit. Also this unit comprises an adder unit 68 and a sub-tracting unit 66, to which two decoded coefficients F*(0) and F**(1) are applied in parallel. The
coefficient F**(1) is obtained from the coefficient F*(1), because the latter is extended with one bit in the most significant position, this additional bit having the value "0". The four most
significant bits of the coefficient F**(1) are applied together with the four bits of the coefficient F*(0) to both the subtracting unit 66 and the adder unit 68, the coefficient F*(0) receiving the
last significant bit of the coefficient F**(1) by way of carry bit, while the subtracting unit 66 continuously receives a signal having the value "1" by way of carry-bit.
Of the output signals of the units 66 and 68 the most significant bit is not further processed, as the four lowest bits directly indicate the required value, as has already been described with
reference to the Table 2. So in this manner it is possible to avoid an increase of the word length also during the retransformation, it only being necessary for the two units 66 and 68 to process the
number of bits which also comprise the applied modified coefficient.
As a complete Walsh-Hadamard transform to a larger number of picture elements in accordance with the formula (4) can be derived step-by-step from the two point transformation, each output value may
be used for the retransformation as the modified coefficient of the subsequent stage and can further be processed in exactly the same way. Consequently, both during the transformation and the
retransformation exceeding the word length is avoided, so that each arithmetical unit need only to be constructed for the shortest possible word length.
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Continuity and Limits
Continuity can be defined conceptually in a few different ways. A function is continuous, for example, if its graph can be traced with a pen without lifting the pen from the page. A function is
continuous if its graph is an unbroken curve; that is, the graph has no holes, gaps, or breaks. But terms like "unbroken curve" and "gaps" aren't technical mathematical terms and at best, only
provide a reader with a description of continuity, not a definition.
The more formal definition of continuity is this: a function f (x) is continuous at a point x = a , if and only if the following three conditions are met. 1) f (a) is defined. 2) f (x) exists. 3) f (
x) = f (a) . Otherwise, the function is discontinuous.
A function can be continuous at a point, continuous over a given interval, or continuous everywhere. We have already defined continuity at a given point. For a function to be continuous over an
interval [a, b] , that function must be continuous at each point in the interval, as well as at both a and b . For a function to be continuous everywhere, it must be continuous for every real number.
Discontinuities in functions can be classified according to the reason that the function is discontinuous at a given point. If there exists a vertical asymptote at x = a for a function, that function
is said to have an infinite discontinuity at x = a .
Figure %: The function f (x) = has an infinite discontinuity at x = 1 .
f (x)≠f (x)
, then
f (x)
does not exist, which means that the second condition necessary for continuity is not met. Such a discontinuity is called a jump discontinuity, and looks like this:
Figure %: The function f (x) = - 1 for x < 0 , f (x) = 1 for x≥ 0 has a jump discontinuity at x = 0 .
f (x)≠f (a)
, the function has what is often called a point, removable, or gap discontinuity. The point
(a,f (x))
is often called a hole.
Figure %: The function f (x) = has a point discontinuity at x = 1 .
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Dynamic point location in general subdivision
Results 1 - 10 of 29
- ALGORITHMICA , 1996
"... We present a randomized strategy for maintaining balance in dynamically changing search trees that has optimal expected behavior. In particular, in the expected case a search or an update takes
logarithmic time, with the update requiring fewer than two rotations. Moreover, the update time remains ..."
Cited by 139 (1 self)
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We present a randomized strategy for maintaining balance in dynamically changing search trees that has optimal expected behavior. In particular, in the expected case a search or an update takes
logarithmic time, with the update requiring fewer than two rotations. Moreover, the update time remains logarithmic, even if the cost of a rotation is taken to be proportional to the size of the
rotated subtree. Finger searches and splits and joins can be performed in optimal expected time also. We show that these results continue to hold even if very little true randomness is available,
i.e. if only a logarithmic number of truely random bits are available. Our approach generalizes naturally to weighted trees, where the expected time bounds for accesses and updates again match the
worst case time bounds of the best deterministic methods. We also discuss ways of implementing our randomized strategy so that no explicit balance information is maintained. Our balancing strategy
and our alg...
, 2001
"... In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this
chapter we discuss recent advances in the development of provably worst-case efficient external memory dynami ..."
Cited by 81 (36 self)
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In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter
we discuss recent advances in the development of provably worst-case efficient external memory dynamic data structures. We also briefly discuss some of the most popular external data structures used
in practice.
, 2007
"... In the design of algorithms for large-scale applications it is essential to consider the problem of minimizing I/O communication. Geographical information systems (GIS) are good examples of such
large-scale applications as they frequently handle huge amounts of spatial data. In this paper we develop ..."
Cited by 76 (30 self)
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In the design of algorithms for large-scale applications it is essential to consider the problem of minimizing I/O communication. Geographical information systems (GIS) are good examples of such
large-scale applications as they frequently handle huge amounts of spatial data. In this paper we develop efficient external-memory algorithms for a number of important problems involving line
segments in the plane, including trapezoid decomposition, batched planar point location, triangulation, red–blue line segment intersection reporting, and general line segment intersection reporting.
In GIS systems the first three problems are useful for rendering and modeling, and the latter two are frequently used for overlaying maps and extracting information from them.
- In Proc. 23rd Annu. ACM Sympos. Theory Comput , 1991
"... This paper describes new methods for maintaining a point-location data structure for a dynamically-changing monotone subdivision S. The main approach is based on the maintenance of two
interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using ..."
Cited by 46 (11 self)
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This paper describes new methods for maintaining a point-location data structure for a dynamically-changing monotone subdivision S. The main approach is based on the maintenance of two interlaced
spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using a centroid decomposition of the dual tree to drive searches in the primal tree. These trees
are maintained via the link-cut trees structure of Sleator and Tarjan, leading to a scheme that achieves vertex insertion/deletion in O(log n) time, insertion/deletion of k-edge monotone chains in O
(log n + k) time, and answers queries in O(log 2 n) time, with O(n) space, where n is the current size of subdivision S. The techniques described also allow for the dual operations expand and
contract to be implemented in O(log n) time, leading to an improved method for spatial point-location in a 3-dimensional convex subdivision. In addition, the interlaced-tree approach is applied to
on-line point-lo...
, 1996
"... In this thesis we study the Input/Output (I/O) complexity of large-scale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer
graphics, and design I/O-efficient algorithms for them. A general theme in our work is to design I/O-effic ..."
Cited by 38 (12 self)
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In this thesis we study the Input/Output (I/O) complexity of large-scale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer
graphics, and design I/O-efficient algorithms for them. A general theme in our work is to design I/O-efficient algorithms through the design of I/O-efficient data structures. One of our philosophies
is to try to isolate all the I/O specific parts of an algorithm in the data structures, that is, to try to design I/O algorithms from internal memory algorithms by exchanging the data structures used
in internal memory with their external memory counterparts. The results in the thesis include a technique for transforming an internal memory tree data structure into an external data structure which
can be used in a batched dynamic setting, that is, a setting where we for example do not require that the result of a search operation is returned immediately. Using this technique we develop batched
dynamic external versions of the (one-dimensional) range-tree and the segment-tree and we develop an external priority queue. Following our general philosophy we show how these structures can be used
in standard internal memory sorting algorithms
- In Proc. 35th Annu. ACM Sympos. Theory Comput , 2003
"... Given a sequence of k polygons in the plane, a start point s, and a target point, t, we seek a shortest path that starts at s, visits in order each of the polygons, and ends at t. If the
polygons are disjoint and convex, we give an algorithm running in time O(kn log(n/k)), where n is the total numbe ..."
Cited by 31 (4 self)
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Given a sequence of k polygons in the plane, a start point s, and a target point, t, we seek a shortest path that starts at s, visits in order each of the polygons, and ends at t. If the polygons are
disjoint and convex, we give an algorithm running in time O(kn log(n/k)), where n is the total number of vertices specifying the polygons. We also extend our results to a case in which the convex
polygons are arbitrarily intersecting and the subpath between any two consecutive polygons is constrained to lie within a simply connected region; the algorithm uses O(nk log n) time. Our methods are
simple and allow shortest path queries from s to a query point t to be answered in time O(k log n + m), where m is the combinatorial path length. We show that for nonconvex polygons this "touring
polygons" problem is NP-hard.
"... We present the first provably I/O-efficient dynamic data structure for point location in a general planar subdivision. Our structure uses O(N/B) disk blocks to store a subdivision of size N ,
where B is the disk block size. Queries can be answered in ... I/Os in the worst-case, and insertions and de ..."
Cited by 29 (17 self)
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We present the first provably I/O-efficient dynamic data structure for point location in a general planar subdivision. Our structure uses O(N/B) disk blocks to store a subdivision of size N , where B
is the disk block size. Queries can be answered in ... I/Os in the worst-case, and insertions and deletions can be performed in ... and ... I/Os amortized, respectively. Previously, an I/O-efficient
dynamic point location structure was only known for monotone subdivisions. Part of our data structure...
- SIAM Journal on Computing , 1996
"... Abstract. We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map dX/ [ with n vertices and apply it to the development of a unified
dynamic data structure that supports pointlocation, ray-shooting, and shortest-path queries in A4. The space re ..."
Cited by 24 (8 self)
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Abstract. We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map dX/ [ with n vertices and apply it to the development of a unified dynamic
data structure that supports pointlocation, ray-shooting, and shortest-path queries in A4. The space requirement is O(n log n). Point-location queries take time O(log n). Ray-shooting and
shortest-path queries take time O(log n) (plus O(k) time if the k edges of the shortest path are reported in addition to its length). Updates consist of insertions and deletions of vertices and
edges, and take O(log n) time (amortized for vertex updates). This is the first polylog-time dynamic data structure for shortest-path and ray-shooting queries. It is also the first dynamic
point-location data structure for connected planar maps that achieves optimal query time. Key words, point location, ray shooting, shortest path, computational geometry, dynamic algorithm
, 1997
"... Given a collection S of n line segments in the plane, the planar point location problem is to construct a data structure that can efficiently determine for a given query point p the first
segment(s) in S intersected by vertical rays emanating out from p. It is well known that linear-space data struc ..."
Cited by 20 (1 self)
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Given a collection S of n line segments in the plane, the planar point location problem is to construct a data structure that can efficiently determine for a given query point p the first segment(s)
in S intersected by vertical rays emanating out from p. It is well known that linear-space data structures can be constructed so as to achieve O(log n) query times. But applications, such as those
common in geographic information systems, motivate a re-examination of this problem with the goal of improving query times further while also simplifying the methods needed to achieve such query
times. In this paper we perform such a re-examination, focusing on the issues that arise in three different classes of pointlocation query sequences: ffl sequences that are reasonably uniform
spatially and temporally (in which case the constant factors in the query times become critical), ffl sequences that are non-uniform spatially or temporally (in which case one desires data structures
that adapt to s...
"... We present an efficient external-memory dynamic data structure for point location in monotone planar subdivisions. Our data structure uses O(N=B) disk blocks to store a monotone subdivision of
size N, where B is the size of a disk block. It supports queries in O(log2B N) I/Os (worst-case) and upda ..."
Cited by 20 (15 self)
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We present an efficient external-memory dynamic data structure for point location in monotone planar subdivisions. Our data structure uses O(N=B) disk blocks to store a monotone subdivision of size
N, where B is the size of a disk block. It supports queries in O(log2B N) I/Os (worst-case) and updates in O(log2B N) I/Os (amortized). We also
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2009-10 Course Descriptions
Department Location
Science Center – Room 324
Special Requirements
1. All mathematics majors are required to take and pass Math 200 (Introductory Seminar in Mathematics) during their first year. Students who declare mathematics as a major after their first year are
required to take the course at the first available opportunity.
2. Mathematics majors are required to take a Major Field Exam in February of their senior year. Data from this exam is used for departmental awards, recommendations, and advising.
Placement Examinations
Upon entrance to the college all students must take the College Placement Exam. On the basis of performance on the placement exam, all students will be assigned to appropriate courses, such as MATH
107, 115, 116, 120, 193, 211, 212, 231, 232, 324, or they may be exempted from taking a mathematics course. Placement depends on the choice of major or minor in addition to performance on the
placement examination.
The primary goal of the Mathematics Department is to teach all students to think logically and critically. The curriculum supports the development of higher level mathematical skills and computing
expertise for students in fields such as the natural, computer, engineering, and social sciences.. Furthermore, the departmental programs and activities provide opportunities for academic excellence
and leadership development, which enhance a liberal arts education.
Upon completion of the prescribed program of study in mathematics, the students should be able to
1. recognize that mathematics is an art as well as a powerful foundational tool of science with limitless applications.
2. demonstrate an understanding of the theoretical concepts and axiomatic underpinnings of mathematics, and an ability to construct proofs at the appropriate level.
3. demonstrate competency in mathematical modeling of complex phenomena, problem solving and decision making.
4. demonstrate a level of proficiency in quantitative and computing skills sufficient to meet the demands of society upon modern educated women as global leaders.
General Core Requirements
MATH 107, 115, 193 or 120 or any higher level mathematics course may be used to satisfy the core curriculum requirement in mathematics. First-year students are placed in these courses on the basis of
their performance on the placement examination.
International/Women’s Studies Requirement
Teacher Certification
See Education Department.
Departmental Honors
The following criteria for Departmental Honors for Mathematics majors have been adopted by the Mathematics Department: (1) Overall GPA > 3.0, (2) GPA in major courses > 3.5, (3) No grade less than
“C” in a major course, (4)* Honors thesis. Students meeting these standards may petition to graduate with Departmental Honors whether or not they are in the College’s Honors Program.
*If the student is in the College’s Honors Program, the honors thesis will satisfy this requirement; otherwise, a student can complete the thesis through Independent Study and Research or can expand
the Senior Seminar project into a thesis.
Departmental Honor Societies
Students who qualify may be elected to membership in the Pi Mu Epsilon Mathematics Honorary Society, Georgia Delta Chapter. This chapter is composed of students from all Atlanta University Center
schools. In addition, high-achieving students may join the Beta Kappa Chi Scientific Honor Society.
Off-Campus Course Requirements
Mathematics majors and minors are expected to take all of their required and elective mathematics courses at Spelman College. In the case of a student having justifiable difficulties, the student’s
advisor(s) and the chair of the department will be willing to review a formal written request to receive approval to take a course at another institution. This course will be approved to count toward
the Math major only if all parties agree. Please note:
1. No math course can be taken off campus without prior written approval.
2. Requesting approval is not a guarantee of obtaining approval.
3. A separate approved application form is needed for each mathematics course.
4. Of the entire sequence of required math courses, two (at most) such courses can receive this type of approval.
5. At most, one of Math 371/472/463/464 (or equivalent) may be taken off campus.
6. Neither a required course nor an elective may be taken off campus in a semester in which it is offered at Spelman.
7. Courses can only be taken off campus if all pre-requisites have been met.
8. Courses taken in violation of the above stipulation must be successfully retaken at Spelman.
Major Requirements
A major in mathematics provides an excellent background for a variety of careers. Students have the option of selecting electives designed to prepare them for graduate study in pure mathematics,
mathematics education, operations research, computer science, statistics, business administration, actuarial science or other applied mathematics areas, secondary school teaching, medical or dental
school, or employment upon graduation in business, government, or industry. The Department will assist students in planning elective courses that will give maximum support to their career objectives.
The major in mathematics consists of 13 courses (at least 43 hours) in mathematics: MATH 200, MATH 231 and 232 (or 295 and 296), 214, 233, 324, 371, 463, 487, and either 464 or 472 are required along
with three approved electives above the 200 level. Elective courses at Spelman include MATH 314, 322, 355, 358, 361, 365, 366, 367, 368, 455, 456, 464, 472, 481, and PHY 305.
The Bachelor of Arts degree will be awarded in this major after the successful completion of 13 courses (at least 43 hours) as outlined above. The Bachelor of Science degree will be awarded with an
additional two courses (8 credits) beyond the core requirements, in one science (biology, chemistry, physics, computer science) or 2 additional mathematics electives (8 credits) above the 200 level.
Both degrees require successful completion of all courses with no grade lower than a “C” in those courses counted toward the 43 (54) hours for graduation. Students must make a grade of “C” or better
in order to progress to a subsequent course.
Major Cognate Courses
A two-semester sequence of a laboratory science course (biology, chemistry, or physics) at the level of majors in that discipline (6–8 hours) and one semester of a computer science course in a
high-level programming language (e.g., a C++ or Java course such as CIS 121). Cognate courses must be completed with grades of “C” or better.
Minor Requirements
The minor in mathematics consists of one computer programming course, such as CIS 121, and five mathematics courses (at least 19 hours): MATH 231 and 232 (or 295 and 296), 214, 233, and one approved
mathematics elective above the 200 level.
Course Descriptions
MATH 107 – CONTEMPORARY MATHEMATICS (3)
An introduction to mathematics in the real world, including elementary probability and statistics, financial and consumer mathematics, with emphasis on quantitative reasoning skills and problem
MATH 115 – PRECALCULUS MATHEMATICS I (3)
This course covers the basic concepts of algebra, the real number system, equations, inequalities, applications of algebra in problem solving, functions, graphs and transformations, polynomials and
rational functions, exponential and logarithmic functions and complex numbers. A one-hour weekly lab is required to help develop and reinforce algebra skills. Prerequisite: College placement exam.
MATH 116 – PRECALCULUS MATHEMATICS II (3)
A continuation of MATH 115. Topics covered include trigonometric functions, systems of equations, matrices and determinants, , sequences and series, the binomial theorem. Prerequisite: MATH 115 or
college placement exam.
MATH 120 – PRECALCULUS (ACCELERATED) (4)
A fast-paced course that reviews polynomial, exponential, logarithmic, and trigonometric functions, systems of equations, and mathematical induction. A student may not receive credit for both MATH
120 and the 115–116 sequence. Prerequisite: College placement exam.
MATH 193 – HONORS QUANTITATIVE REASONING AND METHODS (3)
A rigorous introduction to mathematical ideas. Varying topics selected from the following: Set theory, logic, polynomial and rational functions, exponential and logarithmic functions, matrices,
linear programming, trigonometric functions, mathematical induction, probability, and statistics. Required independent study papers or projects. Prerequisite: Honors Program enrollment or
departmental approval in conjunction with performance at appropriate level on the college placement exam.
MATH 200 – INTRODUCTORY SEMINAR IN MATHEMATICS (0)
This seminar provides a forum for new mathematics majors to interact and learn about the major. Course topics include an introduction to mathematical software, careers in mathematics, technical
writing and mathematical problem solving.
MATH 205 – GENERAL STATISTICS (4)
An introduction to statistics suitable for liberal arts students. Topics covered include descriptive statistics, graphs and charts, introduction to probability and probability distributions,
sampling, hypothesis testing, and an introduction to data analysis using the computer while stressing a wide variety of applications from real-world situations. Prerequisite: MATH 107 (or 115, 116,
120, or 193). Does not count as a math elective.
MATH 211 – APPLIED CALCULUS I (4)
An introduction to the basic ideas of calculus expressly designed for biology and economics majors. Topics include functions and graphs, tangent lines, derivatives, rate of change, maxima-minima
problems, exponential and logarithmic functions, integration, multivariable and calculus applications to biology and economics. Prerequisite: MATH 115 (or 120) or college placement exam.
MATH 212 – APPLIED CALCULUS II (4)
A continuation of MATH 211. Topics covered include partial derivatives, graphing techniques, integration techniques, trigonometric functions, double integrals, differential equations, functions of
several variables, series, and Taylor polynomials. Emphasis on applications and problem solving in economics, biology, and other life and social sciences. Prerequisite: MATH 116 (or 120) and MATH
211, or college placement exam.
MATH 214 – LINEAR ALGEBRA AND APPLICATIONS (4)
This course is a study of systems of linear equations, vectors and matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalization, orthogonality and the
Gram-Schmidt algorithm, and selected applications. Emphasis on introduction to proof techniques as well as computer implementation. Prerequisite: MATH 231 (or equivalent).
MATH 231 – CALCULUS I (4)
An introduction to single variable calculus, including limits and continuity, derivatives of algebraic and trigonometric functions, optimization, related rates of change, integration, and
applications. Prerequisite: MATH 115 and 116 (or MATH 120), or college placement exam.
MATH 232 – CALCULUS II (4)
A continuation of MATH 231.Topics covered include derivatives of exponential, logarithmic, and trigonometric functions, methods of integration, polar coordinates, improper integrals, de L’Hopital’s
rule, sequences, series, power series and Taylor polynomials. Prerequisite: MATH 231 (or 295), or college placement exam.
MATH 233 – FOUNDATIONS OF MATHEMATICS (4)
A transition to higher mathematics emphasizing logic, set theory, propositional calculus and proofs, partitions, relations and functions, and cardinality. Prerequisite: MATH 231 (or equivalent) or
permission of Department Chair.
MATH 234 – DISCRETE MATHEMATICS (4)
An examination of algorithms, counting methods, recurrence relations, algorithmic analysis, graph theory, paths, spanning trees, traversal, Boolean algebra, circuits, and elementary probability.
Prerequisite: CIS 121 (or equivalent). Offered spring semesters. Does not count as a math elective.
MATH 295 – HONORS CALCULUS I (4)
A rigorous treatment of introductory calculus that includes the study of limits and continuity, derivatives of algebraic and trigonometric functions, applications of the derivative, and integration.
Independent study projects will be required. Prerequisite: MATH 116 or 120, enrollment in the Honors Program or departmental approval.
MATH 296 – HONORS CALCULUS II (4)
A continuation of MATH 295. Topics covered include derivatives of exponential and logarithmic functions, methods and applications of integration, improper integration, and infinite series.
Independent study projects will be required. Prerequisite: MATH 231 or 295, enrollment in the Honors Program or departmental approval.
MATH 314 – LINEAR ALGEBRA II (4)
A continuation of Math 214. Topics include the theory of linear operators, canonical forms, unitary transformations, and the spectral theorem. Prerequisite: MATH 214 and 233. Offered fall of odd
MATH 322 – GEOMETRY (4)
Varying topics chosen from: finite geometries, axiomatic systems, foundations of geometry, congruences and isometries, metric problems, and non-Euclidean geometries (e.g., spherical and hyperbolic).
Prerequisite: MATH 233. Offered spring of odd years. Honors elective.
MATH 324 – CALCULUS III (4)
An introduction to multivariable calculus, covering parametric equations, vectors, functions of several variables, partial derivatives, multiple integrals, vector calculus. Prerequisite: MATH 232 (or
295), or college placement exam.
MATH 355 – BIOSTATISTICS (4)
A basic statistics course emphasizing applications of statistics in the biomedical and health sciences. Descriptive statistics in the health sciences, probability distributions, statistical
inference, analysis of health statistics. Stresses use of calculators and computers. Prerequisite: A calculus course or consent of the instructor. MATH 355 offered fall of even years.
MATH 358 – MATHEMATICAL MODELS (4)
Varying topics, including linear programming models, analytical queuing models, forecasting models, and computer simulation. Corequisite: MATH 232. Offered spring of even years.
MATH 361 – THEORY OF NUMBERS (4)
An introduction to number theory. Topics covered include Euclid’s algorithm, primes, unique factorization, linear diophantine equations, linear congruences, the Chinese Remainder Theorem, Fermat’s
theorem, arithmetic functions, Euler’s theorem, primitive roots, quadratic congruences and quadratic reciprocity, sums of squares, Fermat’s Last Theorem. Stresses modern primality testing, factoring
techniques and applications to public key cryptography. Prerequisite: MATH 233. Offered fall of odd years.
MATH 365 – DIFFERENTIAL EQUATIONS (4)
A first course in ordinary differential equations that includes separable and exact equations, integrating factors, linear first-order equations and applications, equations with homogeneous
coefficients, constant coefficient linear equations, methods of undetermined coefficients and variation of parameters, systems of equations, Laplace transforms, numerical solutions, and applications
of higher-order equations and systems. Prerequisite: MATH 212, 232, or 295.
MATH 366 – NUMERICAL ANALYSIS (4)
A study of the derivation and use of techniques for the numerical solution of problems involving zeroes of functions, linear systems, functional approximation, numerical integration/differentiation
and eigenvalues. Error analysis will also be included for each technique studied. Prerequisite: MATH 214 and MATH 212, 232, or 295. Requires computer programming skills in one language. Cross-listed
with Computer Science. Offered fall of even years.
MATH 367 – APPLIED MATHEMATICS (4)
A study of partial differential equations and boundary value problems with applications in physics and engineering. Special emphasis on the use of Fourier series, Bessel functions, Legendre
polynomials, and Laplace transforms in solving partial differential equations. Prerequisite: MATH 232 and 365. Offered spring of odd years.
MATH 368 – COMPLEX VARIABLES (3)
An introduction to the theory of complex variables. The major topics explored in this course are the complex plane, functions of a complex variable, differentiation, integration and the Cauchy
Integral formula, sequences, power series, the calculus of residues, conformal mappings, and applications. Prerequisite: MATH 324 and either MATH 214 or MATH 233. Offered spring of even years.
MATH 371 – ABSTRACT ALGEBRA I (4)
A study of algebraic structures, focusing on groups, rings, and fields, including normal subgroups, ideals, quotient groups, quotient rings, integral domains, and homomorphisms. Prerequisite: MATH
232, 214 and 233. Offered each semester.
MATH 394 – HONORS THESIS RESEARCH (4)
Departmentally supervised research that could lead to a thesis. Required: Oral presentation of research findings.
MATH 431 – INDEPENDENT STUDY AND RESEARCH (2-4)
An in-depth study of a significant topic in mathematics under the direction of a member of the mathematics faculty. The student will engage in independent study or research and meet weekly with her
advisor. Required: A written paper or public talk. Prerequisite: Junior standing and consent of the Department.
MATH 455 – PROBABILITY AND STATISTICS I (4)
An introduction to the theory of probability and statistics. Topics covered include combinatorial methods, sample space, probability, random variables, probability distributions and densities,
mathematical expectation, Chebyshev’s theorem, moment generating functions, descriptive statistics. Prerequisite: MATH 324 or departmental approval. Offered fall of odd years.
MATH 456 – PROBABILITY AND STATISTICS II (4)
A continuation of MATH 455. Topics covered include sampling theory, statistical inference, estimation, testing hypotheses, decision theory, correlation and regression, goodness of fit, nonparametric
statistics, analysis of variance. Prerequisite: MATH 455. Offered spring of even years.
MATH 463 – REAL VARIABLES I (4)
A theoretical treatment of the real number system, topological properties of the real line, sequences of real numbers, and properties of continuous functions. Prerequisite: MATH 324, 214 and 233.
Offered every semester.
MATH 464 – REAL VARIABLES II (4)
A continuation of MATH 463. Topics covered include differentiation of functions of one variable, Riemann-Stieltjes integration, infinite series, convergence tests, series of functions and Fourier
series. Prerequisite: MATH 463. Offered each spring.
MATH 470 – SPECIAL TOPICS (1-4)
Lectures in topic of current interest. The topic for a given semester selected by the instructor offering the course and in consideration of the needs and interests of the students. Prerequisite:
Consent of the instructor.
MATH 472 – ABSTRACT ALGEBRA II (4)
A continuation of MATH 371 covering additional topics in groups, rings, and fields, including the Sylow theorems and field extensions. Prerequisite: MATH 371. Offered each spring.
MATH 481 – TOPOLOGY (4)
A study of the structure imposed on point sets in order to give a meaningful notion of continuity of mappings, convergence of sequences, etc. Metric topology of the real line and of
finite-dimensional Euclidean spaces, connectedness, compactness, properties of topological spaces, and continuous mappings. Prerequisite: MATH 324 and 371. Offered fall of even years.
MATH 487 – SENIOR SEMINAR (2)
Readings and weekly student lectures or student-led discussions of a variety of mathematical topics determined by the interests of the students and the instructor. Emphasis on independent research
and clear exposition. A paper is required. Prerequisite: Successful completion of either 371 or 464, and senior standing or departmental approval.
MATH 491 – HONORS THESIS RESEARCH (4)
Departmentally supervised research. Required: A written paper and public talk. Prerequisite: Consent of the Department.
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1.4.1.2.1 Splicing in Modified BNF Syntax
The primary extension used is the following:
An expression of this form appears whenever a list of elements is to be spliced into a larger structure and the elements can appear in any order. The symbol O represents a description of the syntax
of some number of syntactic elements to be spliced; that description must be of the form
O1 | ... | Ol
where each Oi can be of the form S or of the form S* or of the form {S}1 . The expression [[O]] means that a list of the form
(Oi1...Oij) 1<=j
is spliced into the enclosing expression, such that if n /=m and 1<=n,m<=j, then either Oin/=Oim or Oin = Oim = Qk, where for some 1<=k <=n, Ok is of the form Qk*. Furthermore, for each Oin that is
of the form {Qk}1 , that element is required to appear somewhere in the list to be spliced.
For example, the expression
(x [[A | B* | C]] y)
means that at most one A, any number of B's, and at most one C can occur in any order. It is a description of any of these:
(x y)
(x B A C y)
(x A B B B B B C y)
(x C B A B B B y)
but not any of these:
(x B B A A C C y)
(x C B C y)
In the first case, both A and C appear too often, and in the second case C appears too often.
The notation [[O1 | O2 | ...]]+ adds the additional restriction that at least one item from among the possible choices must be used. For example:
(x [[A | B* | C]]+ y)
means that at most one A, any number of B's, and at most one C can occur in any order, but that in any case at least one of these options must be selected. It is a description of any of these:
(x B y)
(x B A C y)
(x A B B B B B C y)
(x C B A B B B y)
but not any of these:
(x y)
(x B B A A C C y)
(x C B C y)
In the first case, no item was used; in the second case, both A and C appear too often; and in the third case C appears too often.
Also, the expression:
(x [[{A}1 | {B}1 | C]] y)
can generate exactly these and no others:
(x A B C y)
(x A C B y)
(x A B y)
(x B A C y)
(x B C A y)
(x B A y)
(x C A B y)
(x C B A y)
The following X3J13 cleanup issue, not part of the specification, applies to this section:
Copyright 1996-2005, LispWorks Ltd. All rights reserved.
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