Mathematics - 2012-10-24 (page 2 of 2)

Old John

9:00 PM

@spernerslemma maybe because it is quite likely that there are none

user19161

@PeterTamaroff I told them to do that, Pedro. Just for you.

user19161

@spernerslemma Because a number cannot be funny and free of mistakes at the same time.

user19161

@JonasTeuwen He does not have your huge glasses to look closely.

Jonas Teuwen

8-).

@Nimza Mm, robjohn knows quite a bit about PsDOs, I'd have o think.

user19161

@N3buchadnezzar Just talk to your pillow. I do that all the time.

Argon

9:03 PM

@JasperLoy Interesting avatar.

user19161

@Argon Haha. Not as interesting as yours.

Nimza

@JonasTeuwen good

anon

who invites people to a costume party only one day in advance. that's just lame.

user19161

I have gotten almost no downvotes on TeX and some downvotes on math and many downvotes on Eng. TeX is too friendly, Eng is too unfriendly, and math is in between.

user19161

@anon Well, I never go to costume parties as I have none.

anon

9:08 PM

that's the thing. how do they expect people to arrange for costumes in only a day or two?

user19161

I would not go to the trouble of getting any special costume either. It's just not my type of thing. And I only have a few clothes in my closet.

Nimza

maybe they are girls who always have plenty of costumes for any possible party?

user19161

Maybe anon is a girl, I am not sure yet.

Nimza

he-he :)

user19161

Welcome to chat @robjohn!

Nimza

9:13 PM

Anon is a common Thai footballer's name, says wiki

user19161

@Nimza According to anon, anon stands for anonymous.

user19161

@old I saw you posted your pic in chat that day, the one with the camera!

Old John

@JasperLoy The one where I was crouching by a moss-covered wall?

user19161

@OldJohn I think I only saw one, other than the distorted one, so must be it.

Old John

@JasperLoy It was a really cold and wet day in the lake district - my wife took the pic

robjohn

9:16 PM

@JasperLoy Thanks! what goes on here?

Nimza

Hi @robjohn, JonasTeuwen says that you are familiar with PsDOs. Do you know some series by powers of $(a+bt)^{\alpha}$ invariant under action of some PsDO? Like Mittag-Leffler series by powers of $t^{\alpha}$ is invariant under fractional differentiation of order $\alpha$

robjohn

@Nimza when $\alpha\in\mathbb{Z}$, the FT of $(a+bt)^\alpha$ is supported at the origin

Nimza

@robjohn, the main problem is that $\alpha$ is noninteger positive real

and even nonrational, I can't use Puiseux theory

robjohn

@Nimza yes, I figured that by your amended comment

Old John

@JasperLoy I think it is time I moved on - I feel my time on MSE is coming to and end

robjohn

9:22 PM

@Nimza Sorry, I am not familiar with any off-hand

Nimza

:(

user19161

@OldJohn OK. I think I will hang around on SE until the end of 2012.

Argon

:(

user19161

After 2012, I will return to SE if and only if I overcome my tragedies, in which case I will announce my victory.

Old John

@JasperLoy In the unlikely event that anyone wants to contact me, my email/fb address is with one or two people here

user19161

9:27 PM

@OldJohn So secretive!

Old John

@JasperLoy I hope you overcome your difficulties

user19161

@OldJohn I hope you enjoy the rest of your life. We might meet in our next life! =)

Old John

I am sure we might :)

Jayesh Badwaik

@OldJohn you are leaving?

Old John

@JayeshBadwaik taking a break

user19161

9:28 PM

@JayeshBadwaik He is leaving the computer to pee.

Old John

good bye for now - and thanks for all the fish :)

3

Jayesh Badwaik

@OldJohn I hope you have a good time :-) and we will always be comrades in glory glory... :-)

you know the rest ;-)

Old John

@JayeshBadwaik yep :)

Jayesh Badwaik

@OldJohn :-)

Charlie

@oldjohn Oh, OldJohn...

Thanks for the words of wisdom!

user19161

9:32 PM

Oh, Marilia!

Charlie

:D

@OldJohn really thanks , Mr.John!!!

user19161

And here begins a new chapter in the life of Old John, to be continued...

Charlie

@JasperLoy Hi Jasper

user19161

@Charlie Marilia!

Charlie

@JasperLoy stop saying my true name

user19161

9:37 PM

@Charlie Oh, is it a secret?

Charlie

@JasperLoy yes..shhh

user19161

@Charlie OK, OK.

Charlie

@JayeshBadwaik Good Night!Sleep Tight!

robjohn

@spernerslemma: I went for 1-1 rather than injective to be more accessible to a person beginning to study functions.

Jonas Teuwen

9:52 PM

@robjohn We never learnt "1-1"...

"A function is said to be injective if..."

robjohn

@JonasTeuwen here, the introductory term is 1-1. Injective was the fancy term we learned in college

@JonasTeuwen same with "onto" and "surjective"

kahen

1-1 appears to be an English thing. Injective is the usual term on continental Europe as far as I know

Probably French (Bourbaki?) influence.

sperners lemma

great answer robjohn

I was trying it but I got a complicated thing which had som emistakes

robjohn

@spernerslemma Thanks.

sperners lemma

but I can't upvote something that uses "one to one"

that's why I edited it

robjohn

9:57 PM

@spernerslemma really?

sperners lemma

it's my ideology

although I do conjecture that sin(a sin(x)) has period 2pi for all a > 0

what you said proves it for all 0 < a <= pi I think

mick

hello guys

I posted some new questions on mse

Charlie

@mick Hi mick, wassup??

mick

math.mse

@Charlie : LOL imitating me ? how are you ?

sperners lemma

wolframalpha.com/input/?i=y+%3D+sin%2830+sin%28x%29%29

Charlie

10:02 PM

@mick Fine

good

Argon

@spernerslemma Awesome!

robjohn

@spernerslemma $\pi/2$

mick

@ Argon : what ? did he plot sin(sin(x) ?

sperners lemma

oops yes

mick

sin(sin(x)) is hard to integrate ;)

Argon

10:03 PM

@mick $\sin(30\sin x)$

kahen

God, I hate links to Wolfram Alpha. NoScript always ends up filtering them for being potential cross-site scripting attempts

sperners lemma

it's quite interesting look at something like

y = sin(sin(x)/10000000)

mick

why is that intresting ? it seems to behave as expected not ?

Charlie

@spernerslemma Funny

sperners lemma

but sin(sin(x)/10000000) looks like just sin(x)/10000000 !

I suppose we know why, sin(t) roughly equals t for small t

mick

10:05 PM

I bet sin(sin(2^2^(x+1)/10000000) doesnt :)

of course lim sin(x)/x = 1

Charlie

@mick in the first year of college, in calculus I, i turned to a friend of mine, and said:"Hey, we are differentiable functions... in all domain..." he stared me thinking:"what a freak..."

mick

Im nowhere differentiable

Charlie

@mick how?

mick

Im a nondifferetiable fourrier series

Argon

@mick I can differentiate you from @Charlie

Charlie

10:08 PM

@Argon ahaha

sperners lemma

:( I can't get this representable functor stuff sorted out, I wrote out the entire theorem and it's not proving itself

Charlie

@Argon but serious we are differentiable

mick

thats just because he is differentiable Argon

You can differentiate him eitherhow

There are some tricks to avoid reciprocity laws in some proofs

just saying :)

sperners lemma

does nondifferetiable fourrier series exist?

mick

ofcourse

you know that

sperners lemma

10:10 PM

no I don't

mick

how much is your rep ?

I looked at your profile neverm

Hey guys , do me a favor and check out some of my questions i posted :)

Charlie

@mick url

sperners lemma

I didn't lik e your questions

mick

just look at my profile

Jonas Teuwen

@robjohn Would you know, that if $\mu$ is a distribution of order $0$ some results about its regularity if I have that for $C^\infty$ coefficients (on $\mathbf R^d$) $c_\alpha$ that $$\sum_\alpha \partial^\alpha (c_\alpha \mu) = 0?$$

Charlie

10:12 PM

@spernerslemma don't be do rude...

sperners lemma

sorry

Charlie

@spernerslemma good boy

mick

well , like really sperners ?

Jonas Teuwen

I do not have that $c_\alpha(x) \neq 0$ for all $x$ for some $\alpha$ in general, but perhaps I do have more structure on $\mu$.

mick

or where you joking ?

sperners lemma

10:13 PM

the fractals one I don't know anything about that, this inequality is way too hard for me to even approach and statistics..

mick

Yeah , I sometimes am pretty rough and tough

chuck norris questions ;)

sperners lemma

:)

Charlie

@mick yup...

mick

To be honest , not rude ... I expected you to be a very good mathematician sperner

well maybe you are in some domains. Or maybe its just because of your name : sperners lemma

sperners lemma

sorry I'm not good at all

mick

10:16 PM

oh well , maybe your a good gamer ;)

sperners lemma

no I dont play games

Charlie

@mick hey mick, your last is not Jagger?or Mouse?or Rourke?or hucknall?

mick

you are popular with the girls then :)

sperners lemma

yeah. LOL

mick

@Charlie : dont be so rude x)

Charlie

10:17 PM

@mick I'm sorry...sometimes i have a "Joke moment"

mick

im chuck norris brother :)

Charlie

@mick no you're not

mick

did you look at my questions Charlie ?

Charlie

@mick yup

Jonas Teuwen

@robjohn Perhaps I should just assume analyticity of $c_\alpha$ and see how far I get 8-).

mick

10:18 PM

Good luck Jonas

@Charlie : and ?

Charlie

@mick interesting

mick

THanks

@Charlie : You can upvote :)

Charlie

@mick Sure,Micky

mick

Im so cheap :)

Jonas Teuwen

@mick How much? Tell me your price!

Charlie

10:20 PM

@mick I'm so expensive...

Jonas Teuwen

@Charlie Is that because you're a woman?

mick

infinitesimal :)

@JonasTeuwen : Dont be so rude :)

Jonas Teuwen

8-).

Charlie

@JonasTeuwen no, i don't think so..but i didn't understand...

mick

dont understand what ?

Charlie

10:22 PM

@mick I am expensive because i'm a woman..

3

sperners lemma

why are representations unique :(

mick

what kind of representation ?

sperners lemma

I tried to show it with yoneda lemma but it just twists things

representations of a functor

Charlie

@JonasTeuwen there are many cheap women, Jonas...

Jonas Teuwen

@Charlie But luckily you are not one of those!

mick

10:23 PM

chesp = chess ?

Charlie

@JonasTeuwen very expensive....

mick

im not into functors actually

sorry

sperners lemma

en.wikipedia.org/wiki/Representable_functor

mick

maybe post the problem here on mse as questioin

sperners lemma

ohI just finally understood it!

Charlie

10:24 PM

@mick functors reminds me a joke...

mick

plz tell charlie

Are your really a women btw ?

Charlie

@mick wait..let me check

yes

sperners lemma

lol

mick

...THat... was ....not... convincing...

Gustavo Bandeira

@mick Are you wanting something via webcam?

mick

10:27 PM

ueh

sperners lemma

I found that phi'^-1 o phi : C(A,-) -> C(A',-), but apparently there's some f : A -> A' such that C(f,-) is actually equal to that

but why should it be of the form C(f,-)?

Gustavo Bandeira

@spernerslemma LATEX!!!

Charlie

mick

do you want to see me kicked gustavo ? :)

robjohn

@JonasTeuwen taking the derivative of a distribution?

sperners lemma

10:28 PM

what is that? lol

mick

ITs MATHMAN !!

Jonas Teuwen

@robjohn Yes?

Gustavo Bandeira

@Charlie O->A->B-> Ordem dos Advogados do Brasil

mick

tadadadaddada

Peter Tamaroff

@Charlie That is $\bf Tor$

mick

10:29 PM

im off guys bye

Jonas Teuwen

@robjohn That is just taking derivatives of their test functions... right?

Charlie

@PeterTamaroff yup

it's a joke

@mick Bye Mick!

mick

i get it :)

thanks

bye

robjohn

@JonasTeuwen If the coefficients vanish on the support of $\mu$, not much.

Jonas Teuwen

I bet they only vanish on points.

It is a differential operator, what lousy coefficients would that be?

Perhaps I can figure out the support of $\mu$.

sperners lemma

10:31 PM

I wuold think f : A' -> A

robjohn

@JonasTeuwen It's the support of $c_\alpha$

Jonas Teuwen

@robjohn Yes, but I think the support of $\mu$ is never $0$, but the $c_\alpha$ might vanish on null sets.

I believe that $\phi u = 0$ means $u$ vanishes on the null set of $\phi$.

And vanishing on points puts a delta in there, so I am okay I guess.

Would be pretty weird ass for the associated model. A Brownian motion with friction would have a finite time where it stays stationary indefinitely! 8-).

robjohn

@JonasTeuwen I'd start by looking at things that are orthogonal to $\partial^\alpha$ of a Schwartz function

Jonas Teuwen

You mean, test against such a derivative?

robjohn

yes

Jonas Teuwen

10:36 PM

Putting in more derivatives... crazy, but I like it! I will see what that brings me.

sperners lemma

does a fully faithful functor map isomorphisms to isomorphisms?

robjohn

@JonasTeuwen not really more derivatives, just moved derivatives.

sperners lemma

I hope it does that would prove the theorem

Jonas Teuwen

But... that is where I've got them from! 8-))).

From $$\sum_\alpha \langle c_\alpha \mu, \partial^\alpha \phi \rangle = 0$$

I wanted to know something about what $c_\alpha$ can be.

sperners lemma

oh every functor preserves isomorphisms, I didn't get to use fully faithfulness :(

Luke Allen

10:41 PM

Hello smart people :)

sperners lemma

bye

Jonas Teuwen

Hmm, I wonder if it there is an easy classification of "cycling derivatives", if you take say a finite order derivative you obtain the thing you started with. Assuming that neither is $0$.

Oh what the heck! Let just make it at most second order, all else is esoteric anyway.

Pilot

Hello everyone

I am having hard time to prove that sequence $a_n$=$\sqrt[3]{n^3+n^2}$-$\sqrt[3]{n^3-n^2}$ is divergent

can anyone help me with that

Jonas Teuwen

Did you try multiplying with the same thing with a $+$? Additionally, did you ask on the main site (this is a chat, not only for Q&A, so might get more replies there).

Pilot

@ Jonas, the site is not accepting my question,plus I tried multiplying, but found it useless

Jonas Teuwen

10:53 PM

It is not accepting??

Then you have not tried well enough.

Also.

Pilot

i have been trying to submit for about half an hour..

kahen

math.stackexchange.com/questions/220410/… - man, I hope my counter-example is correct. Otherwise, I'd look rather silly.

Jonas Teuwen

Also $a_n = n^{2/3} (\sqrt[3]{n + 1} - \sqrt[3]{n - 1})$.

@kahen Looks okay, but it is late... 8-))).

Hence $a_n (n + 1)^{2/3} n^{-2/3} = (n + 1) - (n - 1)^{1/3}(n + 1)^{2/3}$.

Luke Allen

can anyone help me understand how to plot a Flame Detectors field of view, like a general equation for it, given any "cone of view" data? This is what they typically look like - en.wikipedia.org/wiki/File:Flame_detection_field_of_view.JPG but I can't figure out how to 'draw' that mathematically

Jonas Teuwen

Oh yes, that is really hard. Sorry man. Out of luck here.

Luke Allen

10:58 PM

here's a better picture patol-limited.com/rootgifs/hangar-1.jpg

and here patol-limited.com/rootgifs/hangar-2.jpg

basically, at the center point of any typical camera lens, it can see further than the sides

there must be some mathematical way to write that?

Jonas Teuwen

11:14 PM

@robjohn Oh, blimey! I've got a nice restriction which gave me the result from the thing above! 8-))).

robjohn