Mathematics - 2012-06-06 (page 3 of 3)

Eugene

5:02 PM

zhen lin's bookmarklet is working

Gigili

@tb Ah yes. Thank you very much.

t.b.

@MarkDominus They explicitly do not want such tag implications. See also this blog post on "meta tags".

robjohn

the cloudfront url is down. I will change the URL in my bookmarks, because I know that the cdn.mathjax.org url works.

bbl

Gigili

Your bookmarklet works fine for me @robjohn.

Mark Dominus

Thanks. danbooru explicitly bans subjective and meta-tags with very few exceptions. Tags are required to describe exactly what is visible in the tagged picture. I think that's another reason they have been successful.

Otherwise you get a lot of pictures with the useless tag "gross" or "sexy" or whatever.

t.b.

5:06 PM

I see.

Mark Dominus

They also make better use of the tag wiki than we do. If you're not sure if some tag applies, there is sure to be a fairly clear description of it, with examples.

Oh well, it doesn't matter because our tags are not going to go in that direction.

Jeff Atwood sure can be doctrinaire about some curious things.

t.b.

There's not that many users that actively worry about tagging. You should probably talk to J.M. or Martin Sleziak if they happen to be here.

Willie Wong is the moderator who is most involved with tagging, as far as I can tell.

Mark Dominus

I'm mostly just thinking aloud.

Matt N.

Going to cook awesome delicious dinner. bbl

Martin Sleziak

If you have a look at tagging, most of those questions don't have high view counts.

I.e. not too many people look at them, only a few of them vote - no consensus is reached...

Mark Dominus

5:17 PM

right, thanks.

It also bugs me that I can't even suggest a tag synonym until I have some number of points scored in that tag.

Martin Sleziak

I did not know that.

But as I've learned here, mods can make synonyms, so in case of emergency, it is possible to create a synonym even without people having some rep in the particular tag.

Mark Dominus

"Users with more than 2500 reputation and a total answer score of 5 or more on the tag, can suggest tag synonyms."

So if there is some obscure tag X that is used occasionally but which should be a synonym for Y, then most users who notice it are effectively prevented from pointing this out.

Because you can't get 5 points on tag X without answering a question in it, and X is not used often enough for that to happen.

Yatin K

0

Q: DuckWord Lewis Method

I know when a rain hits an International match in world Cricket The match if unplayable then its been decided by a method called Duckword Lewis method i wanted to know as to how this method was derived and how it works ?

Hi , Everyone

Please look into my question

skullpatrol

Yo

Yatin K

ohh no

@skullpatrol: is here

Mark Dominus

5:22 PM

It's Duck*worth* Lewis. Have you tried WIkipedia?

Yatin K

ok

anon

also, not number theory

Yatin K

i will edit it

so

hmm

robjohn

Okay, I've updated all copies of my bookmark to use the unbroken url.

Yatin K

sorry

skullpatrol

5:24 PM

@YatinK You got that right, skullpatrol is in the house.

Yatin K

:P

robjohn

If you are using my bookmark for MathJax, please go here or here or here and reinstall it.

16

Mark Dominus

@robjohn What if I think I might be using your bookmark for MathJax but I'm not sure?

robjohn

@MarkDominus the old one seems not to work because the URL embedded in it is broken. If you see the LaTeX rendered in chat, then you're okay.

Mark Dominus

I see $\LaTeX$ rendered in chat, but new equations aren't rendered. I have to execute the script explicitly to render new $\LaTeX$. Is that expected behavior?

Or sometimes it gets rendered, and then unrendered immediately.

robjohn

5:32 PM

@MarkDominus If that is the case, then you're okay

You can try Zhen's bookmark which re-renders the LaTeX periodically

Paul Slevin

yo

robjohn

@ZhenLin: I think the ajaxComplete event is getting posted, but then the MathJax is reset soon thereafter. It may be that the ajaxComplete trigger was moved or something was added after it.

Zhen Lin

No, the ajaxComplete event is not getting triggered for received messages.

Only sent messages.

Paul Slevin

still problems with MathJax?

Zhen Lin

The mystery is really more about how the chat works than how MathJax works.

Matt N.

5:39 PM

@robjohn Fixed. You are so awesome! Hail King Rob the Square!

3

Paul Slevin

so

@ZhenLin any comments on that exam?

Zhen Lin

Disastrous.

Paul Slevin

yup similar for me

Gigili

Umm, it doesn't work for me.

Paul Slevin

I thought it was horrendous. I think i answered 1 question

Gigili

5:43 PM

When I click on the bookmark in the toolbar, it goes to a page instead of rendering the page.

Zhen Lin

the worst part is that he put the twisted cubic on the exam

He gave the solution for that, so we have no excuse for not knowing it...

Paul Slevin

which question was that?

Zhen Lin

Q3b

Paul Slevin

I did 3 but I waffled a tiny bit

Im pretty sure I got the r=1 and r=3 bit

and I didn't now how to show every vector space was free, so I showed it in the finite dimensional case and said that because V is the direct limit of its submodules that might have something to do with it...

skullpatrol

@PaulSlevin & @ZhenLin : have you guys ever attended the same class together?

Paul Slevin

5:47 PM

we have some common exams

I couldn't even parse the language for a lot of it. I wish he would jst stick to commutative algebra

skullpatrol

Thanks, just wondering :D

Zhen Lin

every vector space is free by a Zorn's lemma argument

you should know that, being a set-theorist :p

Paul Slevin

I know but I've never looked at it

its just something people have talked about

I am more of a chapters 7,8,9 of Jech - theorist

Zhen Lin

I mean, you just do the standard thing

Paul Slevin

I invented my own extremely bizarre argument

Zhen Lin

5:49 PM

let $\Sigma$ be the set of linearly independent subsets of $V$ partially ordered by inclusion, etc.

Paul Slevin

ah shit i bloody did that first!!!!

Zhen Lin

I mean, it's not at all obvious to me that the direct limit of free modules is free

Paul Slevin

(its not I don't think )

I had to write something

Did you talk to anyone that found it easy / not hard?

Zhen Lin

not so far

everyone seems to think it was quite hard

Paul Slevin

yeah

that is of course good

it is depressing I am losing about 10-15% every time I sit an exam

skullpatrol

5:54 PM

Does your University have retests?

Paul Slevin

nope

I don't think so anyway

I'm nt sure what happens if you are ill

I mean I'm pretty sure I will pass thought, my expected average is about 53% across all the exams

including today

skullpatrol

All or nothing is so old school :(

Paul Slevin

as long as I don't truly balls up Operations Research

" Let R be a ring. A connected component of Spec(R) is of the form
V (I), where I is an ideal generated by idempotents such that every idempotent of
R either maps to 0 or 1 in R=I "

some columbia notes I found. Guess I got that question wrong wahh

skullpatrol

@PaulSlevin There are some liberal schools now that not only allow retests, but also have open book exams with the option of being able to leave and go to the library to find info, even take home exams are becoming popular.

Zhen Lin

6:14 PM

Yeah, I had a vague idea of what was needed to do Q1a, but Q1b put me off

Totaro has mastered the art of writing questions with an easy half and a hard half

skullpatrol

@robjohn I missed that :(

robjohn

@skullpatrol just testing something

$$\psi(x)+\gamma=\sum_{k=0}^\infty\left(\frac{1}{k+1}-\frac{1}{k+x}\right)$$

skullpatrol

@robjohn Oh, are you in favor of open book exams?

Zhen Lin

$$\Theta = \mathrm{d} \theta + \theta \wedge \theta$$

robjohn

@skullpatrol I have no objection against them

skullpatrol

6:26 PM

@robjohn How about take home exams?

Paul Slevin

hard half and a hard half to me

I think exams are good but they are only good if they actually reflect the work you've done

like if you have studied the course you should be able to answer something

But some exams I've seen it wouldn't matter if you studied for 4 million years before them

Zhen Lin

Funny thing in Cambridge is, there are people who say that exams should be, well, like that one. Problem-based tests of "understanding" rather than "knowledge".

Paul Slevin

well they should all be like that. its absurd that some are easy and other are brutal

others*

What I mean is that

they should be similar

Zhen Lin

definitely

Paul Slevin

otherwise you can inadvertently completely screw yourself

by picking the wrong courses

robjohn

6:33 PM

$$\psi(x)+\gamma=\sum_{k=0}^\infty\left(\frac{1}{k+1}-\frac{1}{k+x}\right)$$

Zhen Lin

yes... but that's a well-understood principle, surely?

Paul Slevin

yes but

it's not very fair

I guess they tell us that. Part III is not fair, get over it

Zhen Lin

that's what normalisation is for...

Paul Slevin

yeah I guess

I hope it gets done

anyway I am spent. literally goign to bed now

robjohn

Would someone post some LaTeX please?

Paul Slevin

6:35 PM

$ \mathrm{Goodnight.}$

Zhen Lin

goodnight!

skullpatrol

LaTeX :D

Zhen Lin

$$\exp x = ({\textstyle 1 - \int})^{-1} 1$$

robjohn

Drat! I got my bookmark to work when I post LaTeX, but not others :-(

as soon as I type something, yours render.

Zhen Lin

Yeah, that's how it should work if you hook into ajaxComplete.

I haven't had the time to track down how the chat is loading new messages. If I could figure that out we could hook into that instead.

Américo Tavares

6:37 PM

Why is $$f\left( x\right) \equiv \sum_{k\geq
1}\frac{c_{k}}{\left( x+a_{1}\right) \left( x+a_{2}\right) \ldots
\left( x+a_{k}\right) }.\tag{A}$$ http://math.stackexchange.com/q/123632/752

robjohn

@ZhenLin The Ajax code is all compressed so it is hard to read.

Zhen Lin

Yeah... you can pass it to a prettifier, but all the function and variable names have been encrypted.

robjohn

@ZhenLin bleah!

Zhen Lin

Probably the easiest thing for us to do is post a question on the main StackExchange. As a hypothetical programming question. Hah.

skullpatrol

What Zhen said

robjohn

6:40 PM

obfuscation is good and obfuscation is bad

Zhen Lin

Well, it's not so much obfuscation as it is compression, to be fair.

robjohn

@ZhenLin the names are encrypted as part of the compression?

Zhen Lin

Sure. If you rename variables so that they're all one or two letters long, that counts as encryption, right? :p

robjohn

@ZhenLin that's what happens when you obfuscate Java code.

Zhen Lin

Surely not, because the function names have to stay the same...

robjohn

6:42 PM

@ZhenLin only the public ones

Zhen Lin

Right, but most are public, no...?

It seems difficult to write object-oriented software using mostly private methods.

robjohn

Not private, but protected or package-protected

Zhen Lin

ah

robjohn

and those can be obfuscated for some software protection

Zhen Lin

but in principle, protected functions should also have unobfuscated names, because they could be invoked by subclasses.

Isaac Solomon

6:47 PM

Let F = \overline{\mathbb{F}_{3}}(t). Are there any irreducible, separable cubics in F[x]?

robjohn

@ZhenLin If they are intended for use by classes outside the program, then yes, but those are mainly pubilic

Most obfuscation programs let you specify functions to be left unobfuscated and whether to obfuscate protected methods

Zhen Lin

But it seems like an exercise in futility, somewhat. The Java bytecode (and MSIL) is just too structured...

(irony!)

robjohn

@ZhenLin There are some obfuscators that try to rewrite the code to make it less structured.

skullpatrol

@ZhenLin Problem-based tests of "understanding" rather than "knowledge". Seem to me to favor the argument for open-book exams don't you think?

Zhen Lin

Yeah, I would expect any half-decent one to do that.

robjohn

6:51 PM

and without the names, the purpose of a section of a large program is hard to determine

Zhen Lin

But there's only so much you can do when everything has a type annotation!

The ultimate way to obfuscate Java should be to compile it down to native code, statically link, and strip out symbols.

robjohn

@ZhenLin that is hard to do in Java

the compiling is usually at runtime

I think most implementations use a JIT compiler

Zhen Lin

Sure, but by the same token it can be done ahead of time.

robjohn

@ZhenLin in Java?

Zhen Lin

GNU Compiler for Java

The GNU Compiler for Java (GCJ or gcj) is a free software compiler for the Java programming language and a part of the GNU Compiler Collection. GCJ can compile Java source code to either Java Virtual Machine bytecode, or directly to machine code for any of a number of CPU architectures. It can also compile class files containing bytecode or entire JARs containing such files into machine code. History Almost all of the runtime-libraries used by gcj come from the GNU Classpath project (but compare the libgcj library). As of gcj 4.3, gcj integrates with ecj, the Eclipse Compiler for Java....

t.b.

6:58 PM

How can one even know there exist such things as Fréchet spaces, weak$^\ast$-topologies, Radon measures and not be able to figure this out?

robjohn

The bytecode is not really compiled code as one normally thinks of it. However, the compiling to machine code is nice, but not portable, and definitely not Java

Zhen Lin

@robjohn I know what the bytecode is. I read the JVM spec many years ago back when I had thoughts of doing computer science. :p

robjohn

@tb The first comment is wrong. Lebesgue first proved that

Zhen Lin

@tb I've heard of all those things but I can't immediately figure it out either!

robjohn

@ZhenLin I wasn't trying to denigrate, I was just commenting on their use of "compiled"

skullpatrol

7:02 PM

@tb What do you think of open book and take home exams in Mathematics?

Matt N.

@tb Perhaps he decided to learn the more basic stuff first.

Zhen Lin

I dunno. I don't really think of Java as being a way of writing platform-independent apps anymore...

t.b.

@robjohn It was addressing the typo "Reimann". Actually it was Riemann who first proved that result. You don't need Lebesgue measure to define null sets.

robjohn

@tb I know that, but I read that it was Lebesgue who proved it. I will have to check my sources.

t.b.

@robjohn It's the content of §5 here.

robjohn

7:05 PM

here it is called "Lebesgue's criterion for Riemann integrability"

that is what must have confused me

Matt N.

Never mind.

skullpatrol

:D

t.b.

@robjohn I know that people call it that way, but it really was Riemann, I think. Maybe people thought that argument was a bit too "handwavy"

robjohn

@tb however, I had thought I'd heard it elsewhere, too. I am trying to read that section. It definitely talks about null sets, not countable?

skullpatrol

I'm still trying to figure out what MathJax has to do with the game of Jacks ;-)

robjohn

7:17 PM

@ZhenLin: I have changed .ajaxComplete(function(){MathJax.Hub.Queue(["Typeset",MathJax.Hub]);}); to .ajaxComplete(function(){setTimeout(function(){MathJax.Hub.Queue(["Typeset",Mat‌hJax.Hub]);},1000);}); in my bookmark and that makes it so that every time I type something, all the LaTeX renders.

and it keeps the LaTeX I type from immediately reverting (it stays renedered)

However, it seems that ajaxComplete is not called by others typing.

Nimza

Hello everybody!

skullpatrol

Hello.

Nimza

If I'm not mistaken, a unit ball in $L_{1}$ is not weakly compact?

t.b.

No the unit ball is weakly compact if and only if the space is reflexive.

Nimza

thanks

Matt N.

7:23 PM

Good night.

Nimza

@MattN hi

t.b.

@MattN Good night

Nimza

And is the space $C^{} = BV$ reflexive? (I think that $C^{*}$ is a space of finite-additive measures, but I don't know anything about it's conjugate)

David Wheeler

good-day mathaholics and reputation-chasers!

Nimza

@DavidWheeler good evening

skullpatrol

7:31 PM

Hey, I just won the award for the least talkative person in the English language and usage chat room :D

skullpatrol

7:48 PM

t.b.

@robjohn I looked in one of my old history books (by Walter, no online version available): there the situation is presented as follows. Riemann's student Hankel fleshed out the passage I linked you to. Unfortunately he made some mistakes, which subsequently led Smith to find the fat Cantor sets (found independently by Volterra in his construction of the function named after him). The situation was clarified only Lebesgue, Vitali and Young who independently proved the "Lebesgue criterion".

3

Jonas Teuwen

Hi guys!

Nimza

Help me please: the unit ball in BV[0,1], is it a weak*-compact? (It isn't weak-compact since BV is not reflexive)

Hi @JonasTeuwen

skullpatrol

Yo

N3buchadnezzar

@skullpatrol Buuhuhhuuuuuuuu

skullpatrol

8:06 PM

@N3buchadnezzar I'm proud of it ;-)

N3buchadnezzar

Oh, I was just saying hi.

skullpatrol

OK :D

Mark Dominus

8:18 PM

What is weak*-compact? I keep seeing it, but I don't know how to look it up.

never mind, I think I found it.

here should anyone else care to look

t.b.

@MarkDominus it's the topology of pointwise convergence of linear functionals so $f_i: X \to \mathbb{R}$ converges to $f$ if $f_i(x) \to f(x)$ for all $x \in X$. The most important result is weak*-compactness of the norm unit ball in a dual Banach space (Banach-Alaoglu Theorem) -- all that's probably on the wikipedia page you found.

Jonas Teuwen

My second (unofficial) supervisor is... awesome.

t.b.

why? did you have some beer and coffee together?

Jonas Teuwen

Why?

Is that a rhetoric question?

Because the man has taste.

t.b.

presumably a rhetoric question :)

Jonas Teuwen

8:26 PM

8-).

Mark Dominus

@tb thank you.

t.b.

@MarkDominus M Turgeon recently wrote a really nice answer containing the proof of the Alaoglu theorem (under the heading "instructive proofs in functional analysis").

2

Mark Dominus

Thanks. I don't think I have enough background to understand the statement though.

I will put it on the list of thing I need to investigate.

I already needed to learn how the double-dual space is isomorphic to the original space.

Jonas Teuwen

Brr, would there be a way to compute $\partial_x e^{f(x) L} u(x)$ for some unbounded operator $L$?

Is there even a way to compute $e^{f(x) L} u(x)$. I have an integral kernel for $e^{tL}$ 8-).

Peter Tamaroff

8:48 PM

Has someone read Truesdell's Essay on the $F$ equation?

Namely $$\frac{\partial}{\partial z}F(z,\alpha)=F(z,\alpha+1)$$

t.b.

@MarkDominus The main use of this result is "existence via compactness". For example you can rephrase the solution of certain differential equations as a (unique) solution to a minimization problem for which you can find good approximants. Compactness coming ultimately from that abstract result then gives you the extistence of a minimizer with which you can then work further to understand the differential equation and its solution.

(Very roughly)

Adelaide Dokras

9:02 PM

Does anyone here know how math graduate schools view the general GRE and the math GRE subject test? Are they a big deal, like the LSAT is for law school?

Mark Dominus

My impression was that although a bad score on the GRE could count against you, a good score could not count in your favor.

Adelaide Dokras

So as long as you don't do poorly, it's more a formality?

Mark Dominus

I should probably not have said anything, since I really don't know and have not looked into this since about 1990.

Adelaide Dokras

Oh that's all right, I was just curious. Thanks.

robjohn

@tb Thanks for the research! above the call of duty

t.b.

9:14 PM

No problem -- I wanted to know the details myself :)

An accept less than two minutes after posting.

robjohn

@anon twas I :-) I was just poking to see if you had seen my comment on your answer.

@tb with no votes

t.b.

That, too. MathJax was still compiling when I saw the green checkmark appear :)

Eugene

so i have a curiousity. is
$$
\int \sqrt{\tan^5 x} dx
$$
integrable and if it is, is it hard to integrate?

robjohn

@tb that is amazing.

N3buchadnezzar

Soup?

t.b.

9:18 PM

@Eugene wolfram spits out a mess but it is elementarily integrable, it seems. At least if you trust SW.

SW = Stephen Wolfram.

Eugene

@tb yikes. it was a challenge given by my friend. very mean spirited one looking at this now.

@tb thanks!

N3buchadnezzar

@Eugene I am writing on a integral document, and yeah. That one is a mess =)

The cubic root is nicer, and the square root is even nicer. But still requires some trickery to be solved. The intital step is to use $u=\sqrt[a]{\tan x}$

Eugene

oh well at least i didn't spend too much time on it.

robjohn

@Eugene it is equal to $$\frac23\tan^{3/2}(x)-\int\sqrt{\tan(x)}\,\mathrm{d}x$$

N3buchadnezzar

For a more interesting question is $$\int_0^{\pi/2} \sqrt[\Large a]{\tan x} \, \mathrm{d}x$$ solvable for all a>2 ? ;)

@robjohn Parts?

Eugene

9:23 PM

@robjohn hm..

Nimza

I have a little problem: will a support function of open neighborhood of zero in $C[0,1]$ be positively defined?

robjohn

@N3buchadnezzar nope, just noting that $\tan^2(x)=\sec^2(x)-1$

N3buchadnezzar

I meant does the integral converge, not if it is solvable. but meh =)

Peter Tamaroff

@N3buchadnezzar The case $a=2$ converges.

robjohn

@N3buchadnezzar It converges for all $a>1$

N3buchadnezzar

9:25 PM

@PeterTamaroff for $a\in[2,3] \, \Rightarrow \, I=\pi/\sqrt{a}$

Eugene

i found pete clark's reply on this very insightful. i have a lot to think about now.

N3buchadnezzar

Gah, I hate my nett, obviously this only holds for a integer.

robjohn

@N3buchadnezzar what?

Peter Tamaroff

@N3buchadnezzar Have you tried Leibniz Rule?

Eugene

is math really a young man's game still these days?

t.b.

9:37 PM

Never was, never will be.

N3buchadnezzar

@PeterTamaroff You would rather integrate $$ \int_0^{\pi/2} \left( \tan x\right)^{1/a} \log\left( \tan x\right)\,\mathrm{d}x $$ ?

Eugene

@tb that makes me feel better.

Peter Tamaroff

One never knows what will work out better!

@tb I see that you disagree with GH Hardy then.

t.b.

@Eugene It's one of those overemphasized things from Hardy's apology, written by a sad old man who saw himself unable to rise up to his mathematical power from his earlier days.

Eugene

@tb yes i read hardy's math apology recently (a gift from my professor) and it made me a little freaked out.

Peter Tamaroff

9:41 PM

@tb I see his apology as a lament or something of the sort..

Eugene

he certainly was a very good mathematician though.

Peter Tamaroff

@Eugene Sure.

t.b.

@Eugene No doubt. I liked the book, but I don't like how some highlights are taken out of context.

Eugene

@tb i'm glad you liked the book. maybe someday i'll appreciate it more.

t.b.

I know quite a few mathematicians who did really good work after sixty.

Eugene

9:44 PM

@tb i had this is discussion with my professor and when i mentioned that he said sure but they did their best work in their youth

@tb oh well. maybe i'll just take his advice and just do math instead of talking about it.

@tb thank you for your replies.

t.b.

@Eugene I simply don't believe in the myth. Maybe it is true that younger people are more daring than older ones and that their early results were more surprising because they were unexpected (and coming from someone people didn't know already).

Eugene

@tb ellenberg wrote an article in slate magazine which also disagrees with hardy

@tb thanks for the pep talk = )

t.b.

@Eugene thanks for that! Funny that the picture on Ellenberg's homepage was taken by Kowalski who is my neighbor (he lives about 200m away from me)

Eugene

@tb emmanuel kowalski?? wow! i heard him speak in 2010 in madison as part of our distinguished lecture series.

it was on compressed sensing.

that guy is amazing

t.b.

Yes, he's really cool

I only saw two talks of his. But unfortunately both were disrupted by his brats.

Eugene

9:56 PM

@tb his brats?

@tb i'm guessing the both of you are colleagues?

t.b.

@Eugene Yes, he had his kids with him and told them to sit in the back of the room and be quiet. Obviously, his mathematical authority surpasses his parental authority by a huge amount :)

Eugene

@tb lol

t.b.

@Eugene Not really. He's a full prof while I'm still lingering along as a post doc.

Eugene

@tb well i think that qualifies as being colleagues

@tb anyway thanks again for the cool reply.

t.b.

Oh, it was quite funny the first time, the second time it was a bit annoying.

I would really have loved to see more of his work on hyperbolic threefolds.

Eugene

10:02 PM