Mathematics - 2012-03-26 (page 3 of 4)

Jonas Teuwen

5:02 PM

@KannappanSampath Yes.

Kannappan Sampath

@JonasTeuwen I am trying to review the criterion for Darboux's integrability criterion.

Jonas Teuwen

That's equivalent with the Riemann integral?

What is the criterion?

Kannappan Sampath

So, We say that $f$ is Darboux integrable if to each $\varepsilon >0$, there exists a partition $P$ such that $|U(P,f)-L(P,f)| \lt \varepsilon$.

Jonas Teuwen

Yes.

Kannappan Sampath

@JonasTeuwen Yes, they are equivalent. And, I am doing this with $\alpha(x)=x$

Jonas Teuwen

5:06 PM

Fine. So you want to take a particular function? That thing is certainly integrable on say $[0, 1]$ because it is continuous there.

So it suffices to compute the upper sum and compute the infimum over all partitions.

Kannappan Sampath

Now, say the mesh (norm) of the partition $P$ is $\delta$. (i.e.) $\|P\|=\delta$.

@JonasTeuwen No, I meant to say, I am not doing integral in full generality, like $\int f \rm d \alpha$.

Jonas Teuwen

So, you have $U(f, P) = \sum_{i = 1}^n (x_{i + 1} - x_i) x_{i + 1}$.

Oh.

I thought you wanted to compute it 8-).

Kannappan Sampath

: (

Sorry, I should have written it clearly.

Jonas Teuwen

Oh... you take the measure to be that.

Okay, good.

Kannappan Sampath

Now, the actual question, will the inequality with $\varepsilon$ hold for any partition $\hat{P}$ such that $\|\hat{P}\| \lt \delta_1$ where $\delta_1 \lt \delta$?

Am I clear? @Jonas

Jonas Teuwen

5:10 PM

Hmm, but the partition is not finer than the other?

See, if you just add points to your partition it will surely hold.

But I think you can mess them up a bit to get it larger...

Kannappan Sampath

Hmm. I don't understand what your last line means?

@JonasTeuwen I am not assuming anything, only norm is reduced.

Jonas Teuwen

I don't think that works.

But I can't give you an example off-hand.

Kannappan Sampath

OK. I'll try it out and let you know in this case.

@JonasTeuwen What do you mean here?

Jonas Teuwen

I'd take some ugly function and then try to mess things up.

Good :-).

Well, if your partition is finer, then it will be okay.

Matt N.

Cheers : )

Jonas Teuwen

5:13 PM

But if one is not a subset of the other or the other way around I think it fails, but that's just my intuition.

@MattN Cheers.

Matt N.

: )

Kannappan Sampath

I'll surely check it out. Since I have a quiz, it is good to know some plain implications of the definition.

@MattN Cheers. : )

Jonas Teuwen

@KannappanSampath My first attempt would be to find a counter example. If that fails, you might get some ideas how to prove that it works.

Kannappan Sampath

@JonasTeuwen I agree. I'll come back later. : )

Thank you for the help. : )

Jonas Teuwen

Good luck. I'll find some dinner :-).

fabianhjr

5:16 PM

Is it just me or is MathJAX not working on the chatroom?

anon

just you

@fabianhjr: math.ucla.edu/~robjohn/math/mathjax.html

Matt N.

I think they forgot to put the alcohol in my cider.

*)into

Ok, maybe they didn't : )

Hello again : )

Srivatsan

@Kannappan: Sorry, I had to leave because my internet connection started acting up; it first became painfully slow and then dropped dead altogether.

Thanks for the link anon

I wonder if there is a closed-form answer.

Daniil

5:31 PM

Hi everybody

Matt N.

Hi Daniil : )

Srivatsan

@Kannappan: The exercise from Artin is this (minus a few hints): Compute the class equation of $SL_2(F_p)$.

Daniil

Damn, I think I've failed my statistics exam. Well, not failed completely, but definitely could have done better.

Srivatsan

hi tb.

t.b.

Hi Srivatsan!

Hi everyone

Matt N.

5:34 PM

@Daniil Oh noes : (

Srivatsan

tb: You and Matt look alike now. What's up with this attire? :)

Hello Teddy : )

hi Daniil

@Srivatsan ?

Hi, Matt

@Srivatsan what Matt said: ?

Srivatsan

5:35 PM

@MattN I meant the gravatar.

Matt N.

Srivatsan, you might want to see an optrician.

t.b.

Guess that must be your internet connection.

Matt N.

Can I see a screenshot?

Srivatsan

@MattN What tb said. The page just loaded completely, it seems :)

Matt N.

: )

Srivatsan

5:36 PM

Hm, that was rather embarrassing. :/

Matt N.

Not at all.

Holy cows. I spent hours and hours on my additive combinatorics presentation and I've just about managed to write half of it. Now I have 6 days left to finish it.

If there is such a thing as idiosyncratic notation then Tao does it right.

Srivatsan

@MattN Ah, seems interesting. What are you presenting in addi(c)tive-combinatorics?

Matt N.

@Srivatsan Fourier analytic methods : )

I'm so grateful he let me do this.

t.b.

addictive futile attempts. Hm. :)

Srivatsan

@MattN he?

Matt N.

5:39 PM

A PhD of Tao's. Probably hence the choice of book.

Srivatsan

Can you give an example of his idiosyncratic notation?

Matt N.

Use $Z$ to denote a group and $\textbf{Z}$ to denote the integers. Almost looks the same.

David K.

Can someone help me understand a bit of notation?

We are just starting to study Galois Theory, and in Dummit & Foote, they denote $\text{Aut}(K)$ as the collection of automorphisms of a field $K$. But they also denote the collection of automorphisms of $K$ which $\textit{fix}$ $F$ as $\text{Aut}(K/F)$ where $K/F$ is an extension of fields. This seems like the same notation $\text{Aut}$ for two different things...

Matt N.

Then to denote $ \hat{f} $, the fourier transform he uses $\textbf{E} f e(x \cdot \xi)$.

I guess one could argue that it makes perfect sense and is not idiosyncratic at all but I hate it.

Probably because I'm too undergrad and not clever enough for his book.

Srivatsan

What is wrong with the formula for the fourier transform?

Matt N.

5:44 PM

Why replace $\sum$ with $\textbf{E}$?

But the worst thing about the book is that he uses things he doesn't properly define.

</rant>

It's not that bad : )

anon

@DavidK: You seem to understand the notation well. Where's your issue?

David K.

@anon Well, $\text{Aut}(K)$ denotes the collection of all automorphisms, whereas $\text{Aut}(K/F)$ denotes a particular kind of automorphism. Does this mean that we're not concerned with the collection of all automorphisms of $K/F$? Or are all the automorphisms of $K/F$, in fact automorphisms of $K$ that $\textit{fix}$ $F$?

t.b.

Oh, wow. A new high profile guy contributing :)

@DavidK well, what does $K/F$ even mean?

Srivatsan

@MattN Well, it's quite "usual" to define it this way.

Matt N.

"Aged mathematician" : )

@tb Some fields such that $F \subset K$ probably.

David K.

5:51 PM

@tb That just refers to an arbitrary field extension.

Daniil

@anon, you have mentioned that you did not receive formal mathematical education IIRC. How did you manage to gain the information you currently posses?

anon

internet + brain

Matt N.

@tb I have a new film pick ready for you, btw : ) It won't run away. Just so you know.

t.b.

@DavidK sure, but what would "all automorphisms of $K/F$" be?

(as opposed to those of $K$ that fix $F$?)

@MattN great! Thanks! :)

Matt N.

Did you watch Aviator and road to perdition?

t.b.

5:56 PM

Yes, but not recently.

So, probably no :)

Matt N.

?

Srivatsan

Perhaps tb is concerned that you will quiz him on those movies... =)

t.b.

Well, if you were referring to my mentioning recently that I was going to watch them then the answer would be no. But I saw them some time ago.

Matt N.

I see : ) Didn't know you had already seen them and were planning to watch them again.

Jonas Teuwen

Why are there assholes on MSE that downvote answers that got a bounty? 8-).

Watman?

Matt N.

6:00 PM

Deep Purple.

t.b.

I like Sam Mendes, and I found out that Leo has more to offer than Romeo and Juliet and Titanic...

Matt N.

I have not come across a film with Leo in it that I enjoyed. (At least not as far as I remember : ))

David K.

@tb Well "all automorphisms of $K/F$" would just be a subcollection of $\text{Aut}(K)$. But I intuitively think of the collection of automorphisms of $K$ which fix $F$, as a subcollection of all automorphisms of $K/F$.

Asaf Karagila

Yes. That was a nap.

t.b.

@AsafKaragila I gather your Braveheart pin refers to your having handed in your Whitehead thing?

Asaf Karagila

6:03 PM

Indeed.

t.b.

Great!

Asaf Karagila

Yes.

Daniil

@anon did you follow any specific program? How did you know what to study?

Asaf Karagila

Heh, I made Iyengar delete his question.

anon

@Daniil: When you read something that involves mathematical background you don't have, you need to make a judgment call: ignore it and move on (this can be done oftentimes), or pause there and learn about other math first, then come back when you have the necessary background. Do this enough and you make headway. My 'program' was and is just exploring whatever interests me.

Daniil

6:08 PM

Hm, do you just browse wikipedia or you follow specific textbooks?

anon

(After awhile, though, making headway in the depth you want for a particular subject requires you to obtain a sufficient appreciation of everything from category theory to general topology.)

At first I just read Wikipedia and Mathworld and filled in the blanks on my own. Now I have a good collection of books to read on my laptop and flash drives.

Srivatsan

@tb any example of a better-than-Titanic DiCaprio?

@Srivatsan Inception

The Departed.

I see, thanks anon

6:13 PM

Oh. Haven't seen the departed. But inception I thought was only marginally better than Titanic...

hhh

@anon Translated now here.

t.b.

@Srivatsan anyone that isn't Titanic :) More seriously I found him amazing in Revolutionary Road but that's probably because I was just discovering Richard Yates around the time that movie came out.

Gigili

From my limited knowledge of biochemistry, DNA sequences are made of four intervals. How is the number of possibilities infinity?

'Ello, BTW.

anon

@hhh: Does "nears the surface" mean tangent to it?

Srivatsan

@anon Hm. I did not like Inception that very much (I found the plot convoluted), but Departed is better. In fact, I liked the Japanese version as much (or more).

Asaf Karagila

6:15 PM

@Gigili The actual definition of infinity is "more than three".

hhh

@anon It means that the surface and plane meets only in one point. Unfortunately, the language is not one of the clearest here. Also, the akselilla is a misleading...I thought it meant initially just $z\gt 0$ but that was corrected by Petersen and I think he is more correct here.

anon

@Gigili: Where are you getting "the number of possibilities is infinite" from?

@hhh: Locally, anyway. Yes, that's what the word tangent means. :-)

Asaf Karagila

@Srivatsan So when are you coming back from the dead (read: India)?

Matt N.

@Gigili You can count it. Iirc, proteins are encoded in 4 bases.

Now all you need to know is the possibilities they can dock into each other.

Iirc, not all four can map to all four.

Asaf Karagila

@tb You know what that means, right?

robjohn

6:18 PM

@JonasTeuwen Yeah, us mean people are like that. :-)

Asaf Karagila

I can take a day or two to write out the details of the Bananach spaces.

Gigili

DNA profiling

DNA profiling (also called DNA testing, DNA typing, or genetic fingerprinting) is a technique employed by forensic scientists to assist in the identification of individuals by their respective DNA profiles. DNA profiles are encrypted sets of numbers that reflect a person's DNA makeup, which can also be used as the person's identifier. DNA profiling should not be confused with full genome sequencing. It is used in, for example, parental testing and criminal investigation. Although 99.9% of human DNA sequences are the same in every person, enough of the DNA is different to distinguish o...

Srivatsan

Not very subtle :).
Anyway, some more time.

robjohn

@AsafKaragila Banana-nach spaces. They have a certain ap-peel.

t.b.

@AsafKaragila free indulging in Garnir's dream spaces and other set-theoretic obscenities.

Gigili

6:19 PM

> Although 99.9% of human DNA sequences are the same in every person, enough of the DNA is different to distinguish one individual from another

Asaf Karagila

Yes.

Srivatsan

(Obviously, I will tell you guys when I am going back.)

Gigili

Um, that doesn't work.

robjohn

@Srivatsan would that be going back, or coming back? :-)

Matt N.

@Gigili I think that's at a higher level than the proteins I mentioned : )

hhh

6:20 PM

@AsafKaragila openbsd.org/images/tshirt-7b.jpg for which you need to fight for :P

Asaf Karagila

I am meeting with my advisor later this week before he goes to the USA for a couple of weeks for the holidays. Then we'll sketch out the details of the thesis and I'll start writing it.

robjohn

@Gigili Even Ilya and me?

anon

infinite/infinity/bound/limit is not anywhere in that dna article

Gigili

@robjohn Even that.

t.b.

@AsafKaragila that sounds great, have fun!

Asaf Karagila

6:20 PM

@hhh I never need to fight for my right to freedom. It is a given since I am so lazy, that I am free.

robjohn

@hhh for which you need to fight

Asaf Karagila

@tb I'll keep you posted.

Gigili

@MattN No two DNA profiles are the same, so they are as many as the world population.

Asaf Karagila

@robjohn ...for

t.b.

Oh, 'Ello Gigili, almost didn't recognize you.

Gigili

6:21 PM

How is that possible.

Matt N.

That's not possible since the thing is finite.

t.b.

@AsafKaragila yes, please :)

robjohn

@AsafKaragila No!!!

Matt N.

But it's probably close enough.

t.b.

@robjohn ...for :))

Gigili

6:22 PM

'Ello @tb. Umm, I thought I was recognizable. =|

Matt N.

Many more possibilites than humans. : )

Asaf Karagila

@robjohn You're just being mean... ;-)

Gigili

Right, it should be something like that.

hhh

@robjohn err yes right.

Matt N.

So does that answer your question? : )

Gigili

6:22 PM

I leave it to biochemists and biologists.

Srivatsan

"Proving Crazy Vector Space with addition and multiplication" =) .

Gigili

@MattN Not really. =\

robjohn

@AsafKaragila your point?

t.b.

@Srivatsan Challenging problem: Always an indicator for a good question.

Asaf Karagila

@robjohn What point?

Matt N.

6:23 PM

@Gigili A string of DNA looks like bits of gibberish mixed in with proper codes. One "code" thingy might for example be your hair colour.

Now if you made all the possible humans out of all the possible strings and one more then you'd get at least two same humans. : )

robjohn

@Srivatsan now is that "proving with addition and multiplication" or "vector space with addition and multiplication"?

Matt N.

But I'd double check this with a biologist.

robjohn

@AsafKaragila my bad. :-)

Matt N.

I don't actually know much about biology...

Asaf Karagila

@robjohn You should know better by now!

Srivatsan

6:24 PM

@tb Certainly. Which is why I singled out that question to read in the main page. I wasn't disappointed.

Asaf Karagila

Don't know much about history
Don't know much biology
Don't know much about a science book
Don't know much about the French I took

hhh

@AsafKaragila As you wish, I only trust my feet -- have to RuN -- then soon back to math :P

Matt N.

Yes, that's exactly what I was thinking when I wrote that : )

Asaf Karagila

@hhh Running? That's so unmathematical.

t.b.

@Srivatsan speaking of which (see revision history :))

hhh

6:27 PM

@AsafKaragila You should read the "Born to run" -book, running is natural -- gets more blood to my brains and can work harder -- and can think clearer :P

Gigili

@MattN Oh I see your point now, but it's true about the humans who are not born yet or something. But not infinite, yes.

It'd be great if you could ask them about it. Thank you.

Asaf Karagila

@tb Hah, I guess he heard the proof that chess is determined (assuming that a tie is a victory to the white player).

hhh

@AsafKaragila ...but most people are unable to run (efficiently/naturally), there are quite many things to do wrong even in running like in Math -- the simplest/most-natural strategy wins :P

Jonas Teuwen

@AsafKaragila Sam?

Asaf Karagila

@hhh I can assure you, if you study descriptive set theory and in particular Games and Determinacy, you'll soon learn how wrong that statement is.

Srivatsan

6:30 PM

@tb Ah, that's a nice one.

"...there must a definite way for you to lose when you taken your first move as the first player since you lose every time." My question is" Is this just a sarcasm on my chess skill? I was torn between laughter and sympathy at this point.

Gigili

I read hhh as hehehe, quite funny.

hhh

@AsafKaragila High-brow does not help here, every masterpiece is always unfinished -- also our mathematical models :P ...I always like to do basic course the latest...then it is odd that I cannot understand the basic questions the way other do :P

t.b.

@Srivatsan he is way past the point of sympathy as far as I'm concerned.

Asaf Karagila

@hhh You're not making any sense!

t.b.

@AsafKaragila you're the one to complain :)

3

Asaf Karagila

6:33 PM

@tb Of course! Have I ever missed a chance to complain about things?

Jonas Teuwen

Yeah, you could have been Dutch...

Asaf Karagila

@JonasTeuwen If anything, you are doused in mayonnaise.

t.b.

@JonasTeuwen So, did Mr exclamation! mark! explain his downvote? He! Should!

Jonas Teuwen

Yes! He! Should!

t.b.

Hm. There is a Halmos measure theory influx over on MO... but nobody had the decency to explain that a less than sign confuses the engine over there :)

Jonas Teuwen

6:39 PM

@AsafKaragila What's wrong with mayonnaise? It eat it for breakfast (with a spoon).

@tb Do you have a particular example?

Matt N.

@Gigili Ok, will do. : )

Asaf Karagila

@JonasTeuwen Right. That's what that white gooey stuff you for breakfast.

t.b.

@JonasTeuwen this, this, this, this if you mean the Halmos thing. If you want to see exclamation marks, see here

Asaf Karagila

:3971993 No. I am a descendant of Iraqi Jews. :-)

t.b.

@JonasTeuwen to stir it into your espresso? :)

Jonas Teuwen

6:43 PM

Yes, that too... of course.

Should it be intuitively clear why LDC holds for Lebesgue integrals?

anon

I remember when @Kanna was first talking here, he was all exclamation marks. :)

Asaf Karagila

@JonasTeuwen Yes.

Jonas Teuwen

Okay, do explain what your intuition is about this.

Asaf Karagila

"Obviously."

What's LDC, by the way?

Kannappan Sampath

@anon Yes. I was. But I only hope I am better now.

Asaf Karagila

6:45 PM

Le Dominated Convergence I suppose...

Jonas Teuwen

Yes.

Gigili

Long Double Box

Asaf Karagila

@Gigili How is that LDC?

Jonas Teuwen

Maybe for dyslectics.

Gigili

The box is like a can, a candy can

Asaf Karagila

6:47 PM

"Mama always said that a box are like a box of chocolates... you open it up and see these are disgusting chocolates with orange peels."

Kannappan Sampath

I am dead.

Asaf Karagila

@KannappanSampath Congratulation!

Kannappan Sampath

As always, if I should have said so.

Asaf Karagila

@KannappanSampath Iyegnar deleted that question oh homologies.

Srivatsan

Gosh, if Kannappan goes to sleep, it must be late. :) See you guys.

t.b.

6:50 PM

Is Kannappan pulling a Will Hunting or what?

@Srivatsan Bye Srivatsan, see you!

Jonas Teuwen

See you!

anon

the user Will Hunting?

t.b.

Yes, he has this tendency to jump in and out of the chat room repeatedly.

@JonasTeuwen Maybe it's a matter of getting used to it, but I think monotone convergence isn't too surprising and as soon as you have that, the dominated convergence theorem shouldn't be a surprise either: no mass can escape.

Jonas Teuwen

I use it all the time of course... I was just wondering if it was "obvious" that it holds given that it doesn't hold for Riemann integrals. Right, maybe I should think about the ingredients.

t.b.

But making that precise amounts to a proof of LDC from Beppo Levi or Fatou.

Jonas Teuwen

6:56 PM

I'm not so much interested in the proof now, but why one would come up with this integral :-).

Would it be luck or would he have been thinking: (in French) "Hmm, if I partition the range instead of the domain the integral might commute with limits!".

Okay, I do understand why you could come up with that idea if you think where it can go wrong.

So maybe it is just luck that those convergence theorems hold.

Matt N.

Well well. Time for round two. Cheers!

t.b.

Cheers!

Matt N.

"Centerlizer", huh? : )

Asaf Karagila

I am waiting for the third Batman movie.

Matt N.

I know. You've said it before.

t.b.

7:05 PM

Oh, babgen... he never has any idea how to deal with it...

Matt N.

Maybe he needs some sticks...

Jonas Teuwen

theoatmeal.com/comics/wwddd I like this.

t.b.

@JonasTeuwen well, he has his wonderful leçons: archive.org/details/leonssurlintgra00lebegoog

Jonas Teuwen

That's interesting. Are they any good?

t.b.

I think so, it's an elaboration on his thesis. Especially chapter VII is very nice.

Jonas Teuwen

7:12 PM

Great!

t.b.

Starting here: archive.org/stream/leonssurlintgra00lebegoog#page/n112/mode/2up

Jonas Teuwen

Hmm, I can check it in the library, but not take it home :(.

Joe Stavitsky

hey guys... what's (x+4)^3(sqrt(x+1)) and why? thanks

Jonas Teuwen

It is (x+4)^3(sqrt(x+1)).

Gigili

If a chat room is like a ghost room or something, and you're bored ... Just flag a random message or say Something inappropriate to get flagged.

Matt N.

7:18 PM

@Gigili You're bored quite often.

Beginning depression?

Joe Stavitsky

@JonasTeuwen: sorry, mistyped: ((x+4)^3)(sqrt(x+1))

Gigili

I'm not bored right now, I was just planning what to do at weekends.

Jonas Teuwen

Nothing. Just do nothing and have a drink.

That's great.

I just grab my stuff, go sit at a bench somewhere and bring drinks.

And do... nothing.

anon

@Joe: What do you want out of that expression?

Gigili

Nice idea, but it seems really boring.

Joe Stavitsky

7:20 PM

pporduct

*product

Gigili

I'd sit on a bench alone and drink something if they gave me points or if it was something to go to next level ..

Matt N.

Heh, you're a gamer?

anon

@Joe: It already is a product. Do you have a genuine question?

Gigili

I am addicted to them, let's say.

Matt N.

That's awesome! : )

Jonas Teuwen

7:22 PM

That's awesome?

Joe Stavitsky

anon: what is the multiplication? Can it be reduced any further than it is?

Jonas Teuwen

What do you mean with "reduce"?

Gigili

The product?

Joe Stavitsky

As in, can I do FOIL? If so how? If not why?

Gigili

Bah, I don't know if I'll be alive by that time - but yes, sure, of course and whatnot.

Matt N.

7:24 PM

Why wouldn't you? : )

Gigili

I would but I have no choice, it's like a raffle or something.

anon

@Joe: The multiplication is (x+4)^3 times sqrt(x+1). You will not get a simpler form, though you can expand it by multiplying out (x+4)^3 = x^3+3(4)x^2+3(4^2)x+(4^3).

Gigili

Maybe I am the next one, who knows .. burst into tears

Joe Stavitsky

anon: so if I want to take the derivative I should leave it as is or not?

Matt N.

@Gigili The next one for what?

But if you're a gamer you can just spend your weekend playing games, no?

Like WOW or any of the other online games : )

But I'd suggest that you refrain from that and use your time to do something more sensible.

Gigili

7:29 PM

I can, that's what I do. But you cannot play all day and night because it'd be boring.

More sensible? Like what?

Asaf Karagila

Nolan is doing a Batman movie is fine, his work has a bit of a dark touch. I wonder how Superman will end up.

anon

@Joe: I don't know, would you rather do a single product rule on two terms, or at least three product rules with many more terms?

Matt N.

@Gigili What are your hobbies? What do you enjoy doing apart from playing games?

Gigili

It's still more sensible than most of things.

Joe Stavitsky

anon: true

Matt N.

7:30 PM

@Gigili That's true.

Gigili

@MattN The problem is, I'm not sure about that. That's why I play games.

Matt N.

@Gigili Nothing wrong with that. : )

@Gigili What's your favourite game?

Gigili

Spiral Knights for now.

Matt N.

@Gigili Looks good. So that's a browser game, as far as I can tell?

Nimza

Hi everybody!

Gigili

7:36 PM

@MattN No, it's online but not browser game, I believe.

Matt N.

Hi Nimza.

Gigili

'Ello.

Nimza

Is it possible to count explicitly the Fourier transform of 1/||x||^2 ?

Matt N.

@Gigili That's what I meant. I meant that you don't have to install anything to be able to play it. : ) Not an important detail.

@JonasTeuwen Did you hear "Fourier transform"? ^

Gigili

@MattN But you can install it so not to open your browser each time, blabla.

Jonas Teuwen

7:38 PM

Count a Fourier transform?

@Gigili I see.

Find)

Compute?

yes)

But $1 / || x ||^2$ is a constant, no?

Nimza

7:39 PM

f(x) = 1/||x||^2

Gigili

If you don't know the verb, just say evaluate. That's what I've learned from MSE.

anon

Nimza means as a function of $\mathbb{R}^n$.

Nimza

ok

Matt N.

Oh. I read it as $1 / || x ||_2$ : )

anon

how is that any more of a constant? scratches head

Jonas Teuwen

7:41 PM

So $f(x) = \frac1{x_1^2 + \dots + x_n^2}$?

Nimza

yes, f(x) = x_1^2 + ... + x_n^2

....

...?

you mean 1/ that?

Hum...

7:43 PM

1/

anon

indeed.

Jonas Teuwen

Maybe you should first figure out which function you want.

Can you compute the Fourier transform of $x^{-2}$?

Nimza

I said many times

Matt N.

@anon $|| f ||_2 = || x ||_2 = \sqrt{ \int_X |x|^2 dx}$... for $f(x) = x$. I'm not saying I'm making much sense.

Jonas Teuwen

You didn't mention which norm.

Nimza

7:44 PM

||x|| is a default notation for euclidean norm I think, ||x|| = ||x||_2 by default. And what ||x|| is for you?

Jonas Teuwen

No.

anon

@MattN: x as a dummy and a free variable? decidedly not. :)

anyway, showertime

Jonas Teuwen

Anyway $1/x^2 = - \frac{d^2}{dx^2} \log |x|$ or something like that.

Matt N.

@anon What? No, $x$ as a function in $L^2$.

Jonas Teuwen

Sense. It does not make.

Matt N.

7:46 PM

I've lost sleep so I'll blame it on that.

And on a growing headache.

Jonas Teuwen

Wow, read: "moustache".

Must be my Kopfschmerz 8-).

Matt N.

: D

Speaking of which: I dared Ilya to shave off his moustache. Can you verify if he did that?

Jonas Teuwen

Does he have a moustache?

Matt N.

That dare was my good deed for that day.

Gigili

Hugh.

Matt N.

7:49 PM

@JonasTeuwen He wrote that he'd grown one the other week.

Jonas Teuwen

I'd like to see that.

Matt N.

I don't.

Jonas Teuwen

Why not?

Matt N.

Because I don't want to see moustaches.

Jonas Teuwen

Why not?

I have shaven off one before I took this picture <

Matt N.

7:56 PM

I'm grateful : )

Transcript for

$Mathematics$ Mathematics