Mathematics - 2012-06-26 (page 5 of 5)

experimentX

7:00 PM

Hmm ... has it something to do with domain??

anon

@StevenLi you needn't ask to ask; just ask

Peter Tamaroff

$$\eqalign{
& 2\int {\frac{{dx}}{{{x^2} - 2C}}} = y\left( x \right) + K \cr
& \frac{2}{{\sqrt {2C} }}\tanh \left( {\frac{x}{{\sqrt {2C} }}} \right) = y\left( x \right) + K \cr} $$

experimentX

Oh .. thanks

anon

@experimentX it "has something to do" with the fact that hyperbolic functions are just rotations of normal trig functions (rotations of the complex plane that is)

experimentX

I didn't know that integral ..

Peter Tamaroff

7:02 PM

@anon 100 for mod powers! hhahha

anon

seeing deleted posts is sometimes fun

Steven Li

@anon thks! i was just making sure someone is actually listening lol. in the definition for inner regular measure, is it necessary for there to be compact sets getting closer to the set u are measuring?

experimentX

oh ... i'll keep that i mind and search and study again. So what shall i say (to my friend) about $y = c$

he says that $ y = c $ is also solution ... if it is then how it is ... if it is not then how it isn't?

anon

@StevenLi What do you mean by "getting closer"? It is necessary that compact subsets get arbitrarily close to a set, in terms of measure..

Peter Tamaroff

@experimentX It is one. You just showed it.

Steven Li

7:04 PM

@anon thats what i mean. so there are infinite compact sets underneath?

experimentX

Hmmm ... can i say that every second order differential equation has two independent solutions??

Steven Li

@anon underneath, and getting arbitrarily closer

experimentX

and linear combination of two solutions is also the solution?

Peter Tamaroff

@experimentX I don't think you can be that general.

For linear odes you can be sure.

experimentX

can i say for this particular case??

anon

7:06 PM

@StevenLi "infinite" compact sets? What if the topology is finite?

Eugene

@dylan no I had no feelings about it one way or the other. I hadn't looked at it much today so I was wondering about why you thought so.

Steven Li

@anon if the topology is finite, then there is no compact sets getting arbitrarily closer to the set in terms of measure, right?

anon

@StevenLi ah duh, WP has a dumb typo

I can't say whether or not there are infinite / infinitely many (still not clear to me which you mean) compact subsets, I'm not that familiar with the idea.

Wait, no: isn't every set compact in a finite topology?

Mark Dominus

Yes.

Steven Li

@anon Sorry. I'll rephrase my question.

Peter Tamaroff

7:12 PM

This will prove useful later.

anon

Then it is vacuously true that there exist subsets arbitrarily close to a set in measure: take the set itself.

Steven Li

But isn't that circular?

anon

@PeterTamaroff Have you heard of Chebyshev polynomials?

@StevenLi How so?

Peter Tamaroff

@anon Yeah.

anon

Given a set $K$, for all $\epsilon>0$ there exists a compact $A\subseteq K$ such that $|\mu(A)-\mu(K)|<\epsilon$. Just pick $A=K$. This doesn't work generally, but it does when every set $K$ is compact.

Steven Li

7:16 PM

$\mu(A) = \sup \{\mu(K): K\subset A \} = \sup \{ \mu(A)\} = \mu(A)$

ablmf

If we have a random variable X such that $E(X) < \infty$, then do we have $P(X < \infty) = 1$ ?

Thx. I was in a rush.

anon

@StevenLi Indeed; I'm not trying to exhibit a measure, I'm saying every measure on a finite topology is inner regular (because of that very equality!), hence addressing your comment about "infinite" compact subsets. (Also, it's supposed to be $\subseteq$ right?)

Steven Li

I agree that every measure on a finite topology is inner regular (every compact set has the same measure)

anon

How does one define E(X) if X can take on the value infinity? (Curious.)

Steven Li

Wait, not every compact set has the same measure.

anon

7:21 PM

so?

Peter Tamaroff

@ablmf Ask did

Steven Li

I thought the definition only makes sense if there are finitely many compact sets

I mean infinitely

Eugene

@DylanMoreland do you know how to find good papers to read? i've been hunting around but don't really know how to find some.

anon

@StevenLi Why would you think that?

Steven Li

I think the sup threw me off

anon

7:27 PM

@Eugene put random combinations of number-theoretic keywords (possibly with other subject-area keywords) into google search results. :)

Eugene

@anon i tried that. =)

anon

@StevenLi sup and max are not necessarily equal with infinite sets; however they are both well-defined either way, and in the finite case they are equal

Steven Li

Yeah. When I see sup, I think of something like sup of [0, 1)

anon

Well, scratch that, max is not necessarily defined, but sup always is

Steven Li

I know what you mean

anon

7:29 PM

yeah

Steven Li

Ok. I think my problem is that I haven't practiced enough with inner/outer measures

Eugene

@anon i think maybe i should dig around in the bibliographies of the papers i've read

anon

I don't do that as often because I rarely have access :/

Mark Dominus

That's one thing I do. Another is that if I like a paper by writer X, I go and read other papers by X even if I don't know yet that I'm interested in the topic.

2

And then often I find out that I am interested in the topic when X is writing about it.

Not always, of course.

Eugene

@anon well there are quite a few free papers online

@MarkDominus that is a good idea actually

Steven Li

7:33 PM

Thanks anon

Eugene

@MarkDominus thanks for that

Mark Dominus

Sure.

Eugene

hahaha. taking a look at the front page it does look like the questions are a little boring today

so much analysis!

anon

wat

Old John

Hi folks

anon

7:42 PM

yo

Mark Dominus

@OldJohn I really enjoyed your solution to that problem about $2002^{2002}$. That was great.

Old John

Thanks Mark - I enjoyed that one

Mark Dominus

I tried to revoke my upvote so that I could give it to you tomorrow instead but it was too late.

I could have edited your post, but there's a limit to how much work I'll do to game the system. :)

Old John

No problem - I really don't care about reputation :-)

Reputation is not why I come here - I just enjoy seeing solutions, and sometimes finding them

Eugene

@OldJohn did you find milne's notes useful?

Mark Dominus

7:44 PM

@Eugene If you're at university, have you tried browsing the current journals in the university math library? Supposing that you have a university math library?

Old John

@Eugene Yes indeed - they are really well written - and FREE

Eugene

@MarkDominus yes i've done that. it's a bit of a wide network to canvas though. i also picked through the arXiv.

@OldJohn they are indeed. and very voluminous too. on very good topics what's more

@DylanMoreland any good ideas for how to look for good papers?

Mark Dominus

I sometimes pick up the stuff people have left behind on tables just to see what it is. But my interests are pretty broad so I have a hig probability of finding something I consider interesting.

Eugene

oh that reminds me i should read bhargava's new paper

@MarkDominus my interests are pretty narrow so it's a problem

Old John

@Eugene Absolutely - almost wants me want to learn stuff like algebraic geometry - but I am a bit too old to start something totally new

Eugene

7:47 PM

@OldJohn you need it to learn elliptic curves so it wouldn't be a total waste.

Dylan Moreland

@Eugene Have you read everything interesting in the Antwerp papers? Old stuff by Mazur?

Eugene

@OldJohn besides all you really need is some ring, group, field theory to pick up enough to learn it

@DylanMoreland actually i wanted to ask you. i always hear stuff about the bourbaki seminars but i can't find the stuff by mazur in those seminars

Old John

@Eugene - I also dug out a copy of Ireland and Rosen that I bought years ago - started reading some of that yesterday, and found it really interesting

Eugene

@DylanMoreland i recently stumbled upon his deformation paper but that may be a bit over my head

Dylan Moreland

The deformation stuff isn't all that hard, it's just kinda dry.

Eugene

7:49 PM

@OldJohn ireland and rosen is the best survey on number theory that i've ever read

Dylan Moreland

Important, though. It's at the bottom of everything now.

Old John

@Eugene Really enjoying seeing the stuff that Gauss did all those years ago - and how some of it seems like it almost predicted what was going to be important 100 years after he died

Eugene

@DylanMoreland yeah. i need to learn a tad more though to understand it completely. i started reading his eisenstein ideal paper though

Dylan Moreland

@Eugene I haven't seen any reports on Mazur's work, but searching for bourbaki d'apres mazur should turn up whatever exists.

Eugene

@OldJohn that is nuts isn't it.

@DylanMoreland oh my. it's all in french...

Dylan Moreland

7:51 PM

You'd better get used to French.

Eugene

@DylanMoreland lol. maybe that should be something i put on my priority list then.

it's not hard to pick up right?

Dylan Moreland

Right. You're not trying to speak it, or anything.

Eugene

@OldJohn you should try and find riemann's paper on the zeta function.

Dylan Moreland

If you don't know what a word means it's probably "let".

Eugene

i tried putting a document into google translate and it spat out garbage

Dylan Moreland

7:53 PM

I wouldn't recommend that, no. It gets confused.

Old John

@Eugene Yep - and amazing guy. I recently read about Gauss understanding that elliptic integrals were really inverse functions of doubly periodic functions - so I set about trying to investigate (for fun) the idea of pretending I knew nothing of trig functions, and trying to prove that the $sin^{-1}$ integral was inverse of a singly periodic function - it was hard work!

Eugene

@DylanMoreland hm... how did you learn?

Dylan Moreland

Bhargava's papers are probably pretty down to earth. Saw a talk by him a few days ago it was so seductive, in the sense that it's all just quadratic forms and pretty down to earth geometry of numbers arguments and so on.

Old John

@Eugene I think I have a copy of it somewhere - just need to find time to read it

Dylan Moreland

@Eugene Define "learn" :) Google Translate for a long time (still, even) and you eventually pick up what the common words mean.

Eugene

7:55 PM

@DylanMoreland yes i was thinking that. ok thanks for the information. i'll get to work on bhargava's stuff then

@DylanMoreland i know courbes means curves and that's about it =)

@OldJohn it's an 8 page paper mostly on complex analysis (which is right up your ally!)

Old John

@Eugene Absolutely!

Eugene

also going to check out the antwerp papers

Old John

@Eugene I retired recently so I now have time to do stuff that I want, rather than stuff I have to do - it is wonderful

Eugene

@OldJohn here you go

Dylan Moreland

@Eugene You know what this means, right? Modular Functions of One Variable I ... IV.

Eugene

7:58 PM

@DylanMoreland i thought antwerp was a place

Dylan Moreland

That's where the conference was held, right. And that seems to be what everyone calls these volumes. I just wanted to make sure.

Eugene

@DylanMoreland ah. the springer website doesn't have it online so i need to find physical copies

Old John

@Eugene Thanks - got it :-)

Dylan Moreland

@Eugene They don't? That's odd. I could have sworn that they did.

Eugene

@DylanMoreland oh so 5-6 aren't things i should be looking at?

Dylan Moreland

7:59 PM

In any event, they're on libgen.info for sure.

Eugene

@DylanMoreland oh ok.

Dylan Moreland

@Eugene No, those are probably good too. They just seem less instructional and I haven't needed anything in them.

Certainly good people have good papers in them. Just didn't want to overload you.

Springer's search is so bad. Gah.

Eugene

@DylanMoreland yes that is a good idea. with french now in the mix it'll be a stretch. thanks dylan!

@DylanMoreland oh my!!! i never heard of libgen before but it's a godsend!!!

Dylan Moreland

For example, Serre's paper is on SpringerLink. And from there you can probably get to the rest.

Eugene

@DylanMoreland ugh. learning french was the last thing i expected i had to do...

@DylanMoreland thanks again man. you're super experienced at this stuff man.

Old John

8:03 PM

@Eugene Must go - thanks for all the advice

Eugene

@OldJohn good luck with your learning!

Old John

@Eugene Thanks! - you too!

Dylan Moreland

@Eugene I wish. Happy to help, though.

Eugene

@DylanMoreland you really seem so to me though. even the guys around me don't dispense as much good advice as you do. thanks again man.

robjohn

9:03 PM

32 more days and I will have been here a year (it is a leap year) :-)

Jonas Teuwen

9:35 PM

@robjohn ... only a year? Seems like forever! 8-) (in a good way).

So, I have actually only started learning mathematics like 330 days ago.

Jordan

I started learning math about 800 days ago

I hate geogebra!

yes

<3 Tikz!

@N3buchadnezzar Wut?

9:50 PM

@JonasTeuwen I draw things using tikz

ctan.uib.no/graphics/pgf/base/doc/generic/pgf/pgfmanual.pdf

Jonas Teuwen

@N3buchadnezzar I figured that. But why does that make you hate geogebra?

@N3buchadnezzar Thanks for the manual. Do you think I do not know TikZ?

Or actually: why do you think I don't know TikZ?

N3buchadnezzar

@JonasTeuwen Because I have to recreate some of the figures using geogebra, and it is a nightmare.

The program crashes, it wont save my files, it barely accepts javascript..

Jonas Teuwen

So instead of blaming it on yourself you blame it on geogebra? Works as well I suppose.

Hmm, never had that.

N3buchadnezzar

@JonasTeuwen Well the saving thing and the crashing thing is not a part of my controll.

Liek I finally managed to make the file, and then geogebra refuses to save the file.

You know tikz? I knew you were into mathematics, but I did not know you had use for tikz in your work =)

Jonas Teuwen

@N3buchadnezzar So a program trolled you succesfully?

N3buchadnezzar

9:53 PM

@JonasTeuwen SEVERAL TIMES

Jonas Teuwen

@N3buchadnezzar I do! 8-). I made a cone. And a tent.

N3buchadnezzar

A icecream and a tent? awesme

Jonas Teuwen

@N3buchadnezzar Thought so too.

@N3buchadnezzar Oh yeah and they are very much related... You project the atoms from your tent back to your space eh... and then! You integrate them over your icecreams.

N3buchadnezzar

Heh, I did not know it worked uploading pdf files here. Well this is an example of stuff I use tikz for...

Jonas Teuwen

Hmm. I don't have pdf autoload.

Ah, it is a verrrry small image.

N3buchadnezzar

9:58 PM

Horrible quality

Le high quality tikz drool

Also

in tikz :p

Jonas Teuwen

That is like too 2D.

N3buchadnezzar

It is a pound.

They are supposed to be 2d when viewed from above.

user19161

Check out my new Bieber pic!

user19161

@N3buchadnezzar One look at it and we know it is tikz!

N3buchadnezzar

It could be pstricks, but it is much better than things drawn in word..

user19161

10:03 PM

Well, I still prefer pstricks to tikz! Just look at pst-solides3d and you know that nothing like it will be implemented in tikz for the next 9000 years.

N3buchadnezzar

@JasperLoy Indeed,but I need the pdf support...

user19161

@N3buchadnezzar Hmm, you can use latex+dvips+ps2pdf.

Eugene

@JasperLoy i didn't know you were a girl

user19161

OK it's three steps but if you use latexmk it's one click too.

user19161

@Eugene In case there is confusion, I am male and heterosexual.

N3buchadnezzar

10:06 PM

@JasperLoy Did i mention I am using W7 too =(!

Eugene

@JasperLoy i was making a joke about your justin bieber gravatar

user19161

@N3buchadnezzar Windows 7? I am not using that!

user19161

@Eugene I guessed so, but I just wanted to add the info for everyone's benefit.

Eugene

@JasperLoy i'm sure no one cares

user19161

@Eugene Well, now you are being a wet blanket!

N3buchadnezzar

10:08 PM

@Eugene Jasper does, and the gays.

robjohn

@JasperLoy is that like a soggy sheet?

user19161

Now I wonder who starred that!

robjohn

@JasperLoy I'd worry about any flags.

user19161

It's OK, you can star it.

user19161

I just like to guess who stars something.

Eugene

10:12 PM

@robjohn if you look to your right at this time you'll see ragib zaman's post

user19161

And I love my messages being starred too!

3

robjohn

@Eugene I know... I saw that. I wondered if it had been flagged.

user19161

Oh, the ELU room is full of stars with F***.

Eugene

@robjohn apparently not

N3buchadnezzar

@JasperLoy No ?

user19161

10:14 PM

@N3buchadnezzar Er, yes. Not now but yes if you check the entire star record.

user19161

Where's Ben? I wonder if he got my email!

Jonas Teuwen

Does every limit in a category also occur as a limit in some topological space?

Peter Tamaroff

@JasperLoy HAHAHAHAHA maybe they are the ones who are flagging us

robjohn

@JonasTeuwen are you implying that topological spaces (which were created to study limits) are not the most general space in which to study limits? Oh, no!

Jonas Teuwen

@robjohn No, my question is if this would be the case! :D.

Jonas Teuwen

10:43 PM

Hmm, I am trying to prove that we have an operator $H$ such that $H^n x = H_{n + 1}(x) 2^{-n - 1}$. where $H_n$ is the $n$-th Hermite polynomial.

Jordan

polar coordinates are like getting kicked in the balls by math

Jonas Teuwen

They are supposed to make your problem easier, Jordan...

Jordan

oh

N3buchadnezzar

@Jordan You should try chinese coordinates then 的中文翻譯 | 英漢字典.

Jordan

No thanks

Jordan

10:57 PM

Newton sure did make up a lot of stuff

Peter Tamaroff

@Jordan What's your problem now?

Jordan

Just learning polar coordinates

Peter Tamaroff

@Jordan And what's the fuzz about?

Jordan

Learning

Peter Tamaroff

@Jordan Duh, but what's your concrete problem?

N3buchadnezzar

11:00 PM

@PeterTamaroff Mathematics in general by the looks of it ...

Jordan

I think I am learning it alright for now actually

Jonas Teuwen

I think the answer to my question is yes, you can Cauchy it on some ... space.

N3buchadnezzar

That was lame, outright lame.

Jonas Teuwen

@N3buchadnezzar What was?

N3buchadnezzar

Your joke

BenjaLim

11:15 PM

@JonasTeuwen hey

excited about coming to ANU?

Jonas Teuwen

@BenjaLim Heya.

A bit.

BenjaLim

How come Ragib did not get a suspension even though he used a profanity?

:D :D

Jordan

oh lawd polar coordinates is requiring some trig knowledge

Peter Tamaroff

@BenjaLim What the hell did he do?

BenjaLim

@JasperLoy I saw your email

@PeterTamaroff Look at the starred message

Peter Tamaroff

11:17 PM

@BenjaLim Hahahaha "profanity".

user19161

@BenjaLim Yeah, now you know some of my secrets!

BenjaLim

@PeterTamaroff Well the other day I was suspended for saying that maths is ****** deep and abstract

@JasperLoy no worries

@DylanMoreland I misread the question

user19161

@BenjaLim You told me one of yours too!

BenjaLim

@DylanMoreland Next semester Jarod Alper and Scott Morrison are coming to ANU. Next year: David Smyth

Dylan Moreland

@BenjaLim Those are good hires.

user19161

11:18 PM

@BenjaLim Is that the f word? Being suspended for that is too excessive.

Dylan Moreland

@BenjaLim It's a weird question. I'm not even sure whether it's true.

BenjaLim

@DylanMoreland I completely misread the question!!!!!

@DylanMoreland Hey

Do you think I should do something like Matsumura in the future before doing AG?

user19161

@BenjaLim Well, I thought it was a secret as you deleted it.

BenjaLim

Maybe his book commutative algebra

Dylan Moreland

I also think that Deborah is the same as Ashley.

BenjaLim

11:20 PM

I now have :D

@DylanMoreland Exactly the questions are almost the same....

user19161

@BenjaLim So it is a secret!

BenjaLim

@JasperLoy Not really :D

user19161

@DylanMoreland You mean one person with two accounts?

Dylan Moreland

The Gravatars are, as well.

user19161

@BenjaLim Alright, pseudosecret then!

BenjaLim

11:21 PM

@JasperLoy You don't get stoned in australia for being gay :D :D

what happened to ragib's starred message?

user19161

@DylanMoreland If they are the same then it is likely it is the same person.

user19161

The avatar is generated from the email address.

BenjaLim

Everyone please star Ragib's message to protest against unwarranted flagging here in the chatroom

user19161

@BenjaLim Well, only you would know what you would really want to do, seriously.

BenjaLim

@JasperLoy I hope you can get into grad school

user19161

11:23 PM

@BenjaLim The more stars it has the more likely it will be flagged!

Peter Tamaroff

@BenjaLim Bah!

user19161

@BenjaLim I am trying to recover first. That may take a few more years, or it may never happen.

BenjaLim

@PeterTamaroff Star ragib's message in protest!!

Peter Tamaroff

@Jordan Tell me if this helps.

@JasperLoy I thought that was Danny Shai.

BenjaLim

@Jordan By a suitable substitution you can turn your calculation into just calculating the area of the unit circle

user19161

11:25 PM

Anyway I was expecting some kind of reply from you via email @ben.

user19161

But there is no need for one.

BenjaLim

@JasperLoy I just saw it this morning

Peter Tamaroff

@BenjaLim Can I send something to your mail? (A personal little finding I think is mildly cool)

BenjaLim

@PeterTamaroff Sure :D

@PeterTamaroff on my FB profile you will find my email

@JonasTeuwen

user19161

@ben So I guess you know my email now of course.

BenjaLim

11:26 PM

yes

Jonas Teuwen

@BenjaLim Yes, Sir?

BenjaLim

btw Loy is not a common surname in SG

@JonasTeuwen Got really high friday night

really high man

user19161

@BenjaLim Most people with it are dead.

@BenjaLim 8-).

11:27 PM

@JasperLoy en.wikipedia.org/wiki/Yap_Ah_Loy

Peter Tamaroff

@BenjaLim It will get your brainzzzzz

BenjaLim

@PeterTamaroff Have you tried it?

@JasperLoy This guy is hot: youtube.com/watch?v=cvkWVAj6ojo

Peter Tamaroff

@BenjaLim Yeah. But I don't think it is good to make it a habit.

BenjaLim

@PeterTamaroff I have only smoked it 4 times :D

Peter Tamaroff

Just the same with booze.

user19161

11:29 PM

@BenjaLim I saw that that day. I think JB is hot!

BenjaLim

@PeterTamaroff vodka!

Peter Tamaroff

@BenjaLim Yeah, I only drink beer and vodka.

BenjaLim

@JasperLoy No he looks IMHO disgusting in the new boyfriend clip

he has sunk to a nwe low

@PeterTamaroff It's in your blood to drink vodka

Peter Tamaroff

@BenjaLim It is.

user19161

@BenjaLim What do you think of Taylor Lautner?

BenjaLim

11:30 PM

horrible

Peter Tamaroff

@JasperLoy Llama face!

user19161

I think TL is hot. If I were a girl he is my no 1.

BenjaLim

@JasperLoy Look at RP

Peter Tamaroff

@JasperLoy Sad.

BenjaLim

@JasperLoy EDWARD CULLEN

Peter Tamaroff

11:32 PM

@BenjaLim Sadder.

I'll go play the blues for you guys.

user19161

@BenjaLim NOOOOOOOOOOOOO

Peter Tamaroff

@BenjaLim Should I send it to your fb mail?

BenjaLim

@PeterTamaroff No

my charlescalculus one

Peter Tamaroff

@BenjaLim Darn, I have to reopen fb again.

BenjaLim

@JonasTeuwen should be proud of tiesto :D

Jonas Teuwen

11:35 PM

@BenjaLim What is that?

BenjaLim

►

@JonasTeuwen Tiesto is a DJ

Mainly house music

robjohn

Hmm... after this answer and this answer, I almost feel like a number theorist :-)

Jonas Teuwen

I know nothing about pop music.

@robjohn Hmm, I want to compute some sums, would that make you feel less like a number theorist? 8-). There are only like three binomial coefficients.

BenjaLim

@JonasTeuwen It's not pop music. What do you listen to?

robjohn

@JonasTeuwen I'm sure you've hear "Pop Goes the Weasel"?

Peter Tamaroff

11:36 PM

@robjohn Good ones!

Jonas Teuwen

@BenjaLim Mainly (modern) classical music, but sometimes I feel like an idiots and listen to very old things. I often feel like an idiot, actually.

BenjaLim

@JonasTeuwen Rachmaninoff, shostakovich, people like that?\

Peter Tamaroff