Mathematics - 2015-06-03 (page 3 of 4)

Agawa001

15:00

@Masacroso ur equation is perfectly right :/

Robert Cardona

Algebra question I'm hoping to avoid asking on main site: Given that $f : R \to S$ is a ring homomorphism between ID's, define $\varphi : \text{Frac}(R) \to \text{Frac}(S)$ by $\varphi(r/1) = f(r)/1$. I'm trying to figure out what $\varphi(r/u)$ is, and my guess is $\varphi(r/u) = f(r)/f(u)$, but I can't get that to follow from just what I'm given.

Soham Chowdhury

@anon didn't go to bed?

Robert Cardona

My goal is to show that $\varphi$ is in fact a ring homomorphism, but to do that, I need to know that it does to an arbitrary element of $\text{Frac}(R)$.

Agawa001

as long as this equation is solvable $y(2x+y)=w(2z-w)$

Masacroso

who is the guy of your avatar @RobertCardona??

Robert Cardona

15:03

It's robert cardona :P

it's me

Masacroso

lol, ok

Agawa001

its castro :/

Robert Cardona

That's what my parent's told me back when I had the long beard. :P

I've gotten rid of both the beard and the hair since

Agawa001

look even*even = even*even and odd*odd=odd*odd

Masacroso

sometimes I get long beard too @RobertCardona, but is so annoying xD

Robert Cardona

15:04

Yeah, I sleep on my stomach too, so my beard always gets squished to my face

Masacroso

haha... eating is a pain with a long beard, or just drinking anything... very very annoying

Soham Chowdhury

Is anyone here familiar with free abelian groups?

Agawa001

i fear when i lose my hair , some brilliant mathematical thoughts disappear with it

Robert Cardona

@Agawa001, don't dispair, Grothendieck was bald most of hist life (although by choice; he shaved it)

Masacroso

lol

Soham Chowdhury

15:06

@RobertC, can you help me?

Robert Cardona

@SohamChowdhury, on what? I can try.

Soham Chowdhury

it's about free abelian groups.

Agawa001

he grows hair sometimes

he s kinda like me

Robert Cardona

I can try, but it's not my strong suit

what's the question?

Agawa001

let his hair grow few decameters then shave it all off

Masacroso

15:08

@RobertCardona it seems like a multiplicative function or so

Soham Chowdhury

I need help understanding the motivation for this definition:
$H^{\oplus A} = \{\alpha : A \to H | \alpha(a) \neq 1_H$ for only finitely many elements $a \in A\}$.

apparently this is the free abelian group on A.

the "finitely many elements" bit.

(paging @Balarka for when he comes online)

Mary Star

Is someone of you familiar with fluid mechanics and especially with streamlines and pathlines?

Semiclassical

maybe try it out for a specific pair $H,A$ which seems simple?

Soham Chowdhury

all my simple pairs will be finite groups, in which case $H^{\oplus A} \cong H^A$ and the hairy bit of the definition isn't even needed

Semiclassical

fair enough.

Mary Star

15:14

Hello @robjohn ! Are you familiar with streamlines and pathlines?

Agawa001

@Masacroso look ur equation is right, $a²+b²=c²+d²$ if $d$ is smaller than $b$ then $c$ must be bigger than $a$

$a²+b²=(a+x)²+(b-y)²$

$x(2a+x)=y(2b-y)$ this means $x(A)=y(B)$ with $B>y$ and $A>x$ and if $x$ is odd than $A$ is odd and same if even , same with $y$ and $B$

i tried with $x=2$ $A=16$ $y=4$ $B=8$ it gives me $7²+6²=9²+2²$

Masacroso

oh, ty @Agawa001, I did something similar but failed in some point

Agawa001

well u were on right path

it happens to me often :D

suspect the track in middle road

xD

evinda

Hey @Semiclassical

Could I ask you something?

Semiclassical

sure, can't guarantee i can answer

evinda

15:18

If $\int_{0}^{x}e^{at}|b(t)|dt$ diverges as $x \to +\infty$, we cannot deduce that $\int_0^x e^{at} b(t) dt$ diverges, or can we? @Semiclassical

Masacroso

lol

Semiclassical

i'm probably not going to be able to answer that, unfortunately. i haven't done analysis in a whie

evinda

@Semiclassical A ok... :)

Does anyone have an idea?

Semiclassical

though i think you're right, since if I take $b(t)=e^{i t}$ then I could imagine I get something convergent

Agawa001

@Masacroso im struggling hard with trigonometric pascal triangle lol its a pain

Masacroso

15:21

trigonometric Pascal triangle? there is something related to binomial coefficients?

Agawa001

yes

exactly

Masacroso

what relation with trigonometry?

Agawa001

$cos(nx)=f(cos(x))$

there pascal triangle for it

ok i ll link you

Semiclassical

hmm. $b(t)=e^{i t}$ doesn't work, but something which presents decaying oscillations around zero as $x\to +\infty$ should work

Robert Cardona

@SohamChowdhury, have you taken topology?

Agawa001

15:25

2000clicks.com/mathhelp/geometrytrigequivcos3xetc.aspx

Soham Chowdhury

well, i'm not in college yet, so, no

Robert Cardona

@Masacroso, yes it is, as it's a ring homomorphism, that's what I'm trying to show though.

Agawa001

proved by moivre theorem

Robert Cardona

In topology, we define the product and box topologies

look them up, that might help with the motivation to your question

Soham Chowdhury

@RobertCardona I am reading a topology book (Bredon) at the moment, and the product and box topologies are a few pages away.

Robert Cardona

15:28

Then keep a close eye for how the product topology is defined, as well as box, and then look at the examples of each.

The examples should help you realize why there was a need for both.

Soham Chowdhury

will do, thanks.

Robert Cardona

ping me if you get a more direct answer to your question, as I don't have one.

It just reminds me of the topo defn.

Soham Chowdhury

sure.

Robert Cardona

k, I'm out for now. see you all.

evinda

0

Q: Prove that Euler's equation can be written in a specific form

According to my notes, the following theorem holds: If $y$ is a local extremum for the functional $J(y)= \int_a^b L(x,y,y') dx$ with $y \in C^2([a,b]), \ y(a)=y_0, \ y(b)=y_1$ then the extremum $y$ satisfies the ordinary differential equation of second order $L_y(x,y,y')- \frac{d}{dx}L_{y'}(x,y,...

Could you take a look at the edit part?

Alec Teal

15:40

@SohamChowdhury what do you need?

Soham Chowdhury

I need help understanding the motivation for this definition:
$H^{\oplus A} = \{\alpha : A \to H | \alpha(a) \neq 1_H$ for only finitely many elements $a \in A\}$.

Alec Teal

maths.kisogo.com/index.php?title=Group

Okay, in what context?

maths.kisogo.com/index.php?title=Addition_of_vector_spaces Looks very much like "external direct sum" (see that page, scroll down, top of the indexed set section)

Masacroso

I dont know about your topic @SohamChowdhury but I think the words "finitely many" are the key of this definition

Alec Teal

Yeah, finite support.

It is some sort of projection

Masacroso

what mean $1_H$? It is the neutral for the operation?

Soham Chowdhury

15:45

identity, yes

Alec Teal

Yeah identity, $1_X:X\rightarrow X$ with $1_X:x\mapsto x$

Soham Chowdhury

oh, wait.

everything clicked.

Alec Teal

Not to be confused with $i_X:X\rightarrow Y$ with $i_X:x\mapsto x$ WITH $X\subseteq Y$

Masacroso

indirectly the definition says that it doesnt hold for infinite quantities

Soham Chowdhury

not really.

Masacroso

15:46

or at least it seems

Alec Teal

No not really

Masacroso

ok

Alec Teal

Well he's part right. Hilbert spaces sort of come into it. But not really enough to say more than "they're a bit similar"

Soham Chowdhury

it's just that if no element maps to the identity, then an element can't be part of that basis-like thing that $\Bbb Z^{\oplus A}$ has.

Alec Teal

Anyway @SohamChowdhury what does it call it, and what does it try to do?

Soham Chowdhury

15:47

@AlecTeal wouldn't know anything about Hilbert spaces yet :)

Alec Teal

Basis?

Soham Chowdhury

@AlecTeal so, with that construction, set $H = \Bbb Z$.

Alec Teal

You're in Linear Algebra?

Soham Chowdhury

Nope.

But free abelian groups have a basis-ish thing.

Alec Teal

Topology??!

Masacroso

15:48

when I encounter some definition that I cant understand deeply or in the deep that I want then I see it in many different books

Soham Chowdhury

This is an algebra book.

Chris's sis the artist

@robjohn @r9m did you ever try this one elementarily? $$\sum_{n=1}^{\infty} \frac{H_n}{(2n+1)^2}$$

Alec Teal

@SohamChowdhury take a picture of the page, OR shush about it

Context is needed.

Masacroso

sometimes you only see something clear from ONE book and not the others

Soham Chowdhury

Anyway. Set $H = \Bbb Z$. Then $H^{\oplus A}$ is the free abelian group on $A$.

Pic coming up.

@AlecTeal, there you go.

Also, about "basis" in this context: "In abstract algebra, a free abelian group or free Z-module is an abelian group with a basis." (if you didn't know, that is. I think you do, forgive me)

Alec Teal

15:52

@SohamChowdhury rather than talk you through it, I want you to talk me through it.

Balarka Sen

@SohamChowdhury yes, although I have never read it.

@anon has studied it, I guess, so you could ask him about it.

Soham Chowdhury

okay.

what did you do all day?

more big words? :P

Agawa001

16:08

elementary algerbra is torturing sort of death in long term :D

Hippalectryon

@evinda You called for me a few days ago, do you still need me ?

evinda

@Hippalectryon Yes, I have some questions.. :)

Hippalectryon

Assuming that my connection doesn't die I'll try to help :-)

evinda

A ok.. I am looking now at an exercise. I will ask you in a few. :) @Hippalectryon

Hippalectryon

Ok.

Agawa001

16:13

@SohamChowdhury speakin about super sonic :D

and here it apears

Soham Chowdhury

what?

Hippalectryon

<

Agawa001

xD

he was faster than u

Hippalectryon

Sanic is always fastur :3

Agawa001

lol

Semiclassical

16:16

Panic is always Hastur?

Soham Chowdhury

WTF is going on here?

Semiclassical

i dunno, i'm just rolling with it

Agawa001

just roll nver look back

Hippalectryon

@Semiclassical Panic is always Hatcher ! We did it !

Semiclassical

heh

Agawa001

16:18

@SohamChowdhury lol super sonic researcher , who dyes his hair blue

Soham Chowdhury

oh

Agawa001

i ll have signal procesing exam next saturday , its irrelevant of maths , but i really enjoy this place more :)

well not completely , but somehow

Mary Star

Hello @Hippalectryon !! Are you familiar with streamlines?

Agawa001

im readin about this amazing guy during my break , poor man he dies cuz of misery and indifference , and all his achievements were been stolen

Hippalectryon

@MaryStar Sorry for last time, my connection was so bad I couldn't reconnect btw

Mary Star

16:26

No problem... @Hippalectryon

Hippalectryon

@MaryStar I know a bit about those.

Mary Star

Could you take a look at my question: physics.stackexchange.com/questions/187494/… ?

@Hippalectryon

Andrew Thompson

Jet bundle

In differential geometry, the jet bundle is a certain construction that makes a new smooth fiber bundle out of a given smooth fiber bundle. It makes it possible to write differential equations on sections of a fiber bundle in an invariant form. Jets may also be seen as the coordinate free versions of Taylor expansions. Historically, jet bundles are attributed to Ehresmann, and were an advance on the method (prolongation) of Élie Cartan, of dealing geometrically with higher derivatives, by imposing differential form conditions on newly introduced formal variables. Jet bundles are sometimes called...

What is the dimension of the manifold described here? In particular, how does it depend on $r$?

Hippalectryon

@MaryStar It's div of a vector, so $div(\vec{u})$, not $div(u)$

Mike Miller

@AndrewThompson: You're asking what the dimension of the jet bundle itself is?

Andrew Thompson

16:32

No, that'll be clear once I know the dimension of $J^r(\pi)$ (as a manifold.)

I'm not used to the notation they are using; to me it seems as if its dimension should either be $\dim E$ or $\dim E + \dim M$, both of which are independent of $r$ and proves impractical as soon as we start looking at the bundles.

Mary Star

@Hippalectryon Yes, you are right!!

Mike Miller

Yeah, it's going to be much bigger.

Masacroso

the arrow over a vector is something prehistoric, lol

Hippalectryon

@Masacroso not in physics

Andrew Thompson

Agreed, although I don't see that given the definition given in the text.

Masacroso

16:36

Im joking... it is the standard cause we need to write in by hand

Mike Miller

I haven't internalized this stuff yet, @AndrewThompson, but I know that you should be able to find a discussion of the dimension in Eliashberg's h-principle book.

Andrew Thompson

Thank you, @Mike.

Mike Miller

I think the dimension of $J^1(\pi)$ should probably be something like $(\dim E)(\dim M) + \dim E$.

Maybe $+ \dim E - \dim M$ at the end.

Masacroso

I read some books claiming about the old style that is write vectors with arrow instead of bold... but the point is that you cant make bold letters easily by hand

Mike Miller

I would be hard pressed to justify that, though :)

Andrew Thompson

16:38

I'll have a look :)

Mike Miller

Let me know if you can't find the book, @AndrewThompson. My copy is at home and I can take a look tonight.

Hippalectryon

@MaryStar Seems correct to me, assuming that by $x^2t=C$ you meant $x^2y=C$

Mary Star

@Hippalectryon Great!! Thank you!! :-)

Andrew Thompson

Already found it. My Russian professor gave me the website. "I am Russian. While that is not an adequate justification for stealing books, I find it to be an adequate explanation."

5

Mike Miller

hahaha

Masacroso

16:40

lol @AndrewThompson xDD

Mary Star

@Hippalectryon Oh yes... It is a typo...

The cutoff points are the points of the $y$-axis, aren't they? @Hippalectryon

Hippalectryon

@MaryStar Yes

Ramanewbie

@hippa I thought you had die

Hippalectryon

@Ramanewbie I had

Mary Star

Could you also take a look at my other question: math.stackexchange.com/questions/1310701/… ? @Hippalectryon

Ramanewbie

16:45

@hippa And then you came back to life ? Wouahou !

Andrew Thompson

Hm, no immediate luck in that book, @Mike. I'll take a proper look later.

Mike Miller

@AndrewThompson: I'm confident there's a discussion early on where the dimension ends up looking something like $\binom{n+r}{r}$.

Hippalectryon

@MaryStar $div \overrightarrow{u}=0 \Rightarrow (u, v, w)=(0, 0, 0)$ where does that come from ? did you forget a $div$ ?

Mike Miller

This is for a special case (maybe it's for the fibration $M \times \Bbb R \to M$) but it should at the very least be a little helpful. Just a bit past the intrigue chapter.

Andrew Thompson

Hm, reading it now.

Mary Star

16:51

@Hippalectryon $div \overrightarrow{u}=0$ means that the flow is incompressible, right? It should be $(\partial_xu, \partial_yv, \partial_zw)$, right?

Hippalectryon

@MaryStar $div \neq \vec{grad}$. $div$ yields a number, not a vector

Andrew Thompson

Hm, ok, so the question is local, so assuming in the Wiki we have $M = R^m$ and $E = R^e$ I might be able to work something out in terms out dimensions.

Thanks!

Mary Star

@Hippalectryon So, it should be $\partial_xu + \partial_yv + \partial_zw=0$, right?

Hippalectryon

Indeed. Which immediately gives you $c$

That's why they asked you to do that first, it makes the following computations easier

Mary Star

@Hippalectryon Is it $div \overrightarrow{u}=0 \Rightarrow \partial_xu + \partial_yv + \partial_zw=0\\ \Rightarrow -cy=0 \Rightarrow c=0$ ?

Hippalectryon

16:55

@MaryStar That's what I get

Mary Star

Great!! Thanks a lot!! :-) @Hippalectryon

The streamlines are correct, aren't they?

How can we draw them? @Hippalectryon

Hippalectryon

@MaryStar I haven't checked the streamlines yet though

@MaryStar Back in ~20 mins

Mary Star

Ok... @Hippalectryon

Mike Miller

Glad to help, @AndrewThompson. What are you reading this for?

r9m

17:15

@Chris'ssistheartist nope ... but seems quite difficult .. $\sum\limits_{n=1}^{\infty} \frac{H_n^{-}}{(2n+1)^2}$ seems tricky business!!

Chris's sis the artist

@r9m By series manipulation only?

r9m

@Chris'ssistheartist I don't know if it can be managed by series manipulation alone

Chris's sis the artist

@r9m Maybe it's not that hard as I can see now.

r9m

@Chris'ssistheartist okay .. I'll try and see if I get sth later

Chris's sis the artist

@r9m I think I'm done with it.

r9m

17:19

@Chris'ssistheartist fine

Chris's sis the artist

@r9m $$\frac{49 \pi ^2}{1296}+\frac{\log(2)}{6}+\frac{\psi ^{(1)}\left(\frac{2}{3}\right)}{108}-\frac{\psi ^{(1)}\left(\frac{1}{6}\right)}{108}$$

r9m

@Chris'ssistheartist and you got that with series manipulation?

Chris's sis the artist

@r9m No

@r9m BTW, I'm working on a proposed problem for RSME. It's not that (in general) I like to do that but I need some stuff published for my book.

r9m

@Chris'ssistheartist oho!!! I see!!! I'm done as well !! :-) Nice problem ;)

Chris's sis the artist

@r9m Yeap. :-)

r9m

17:24

@Chris'ssistheartist I see!! that's good :)

@Chris'ssistheartist I'll complete the calculation and add it to my blog later (if you allow me to share the stuff that is) :-)

Hippalectryon

@MaryStar I'll be back later than planned (~40 more mins)

Chris's sis the artist

@r9m Which stuff? Not sure what your point is.

r9m

@Chris'ssistheartist the series you just showed me :)

Chris's sis the artist

@r9m Well, sure, no need to ask for that. I didn't create that series. :-)

@r9m You found an elementary way by series only? :-)

Mary Star

@Hippalectryon Ok...

r9m

17:30

@Chris'ssistheartist no way :P I'll have to think if there is an elementary way for that or not .. the integral is not too difficult to compute if I use a few reflection and summation formulae for digamma function .. I have computed a similar integral before too :)

Chris's sis the artist

@r9m OK :-)

r9m

@robjohn @Chris'ssis see this!! this hxthanx guy rocks!! :D

Chris's sis the artist

@r9m ooo, that's nice!

robjohn

@r9m That was the sort of proof I was looking for. I knew there was something that simple.

@r9m I looked at something similar, but I was looking at something else at the same time and never came back to it.

r9m

@robjohn ya! I remembered the periodicity of $S_n$ (I read about it in one of Andrescuu's books when I was preparing for olympiad)!! it's a nice proof

robjohn

17:40

@r9m I have that very $S_n$ in my notes, but never realized that it was periodic.

Anonymous

Where's Alex Clark?

r9m

@Ashwin ping him @AlexClark if you wanna reach him ..

Anonymous

@AlexClark How you doing?'

r9m

alrighty then!! back to watching one piece :)

Hippalectryon

17:56

@MaryStar I'm here

@MaryStar Well, Abel told you it was right so I guess it's ok :-) unless you have another question

Mary Star

Yes, it is ok... @Hippalectryon

Chris's sis the artist

@r9m You rarely saw such a beautiful series problem as the one I prepare now. :-)

@r9m referring to the proposed problem. :-)

felipa

18:12

hi

hi @Chris'ssistheartist

Chris's sis the artist

@felipa Hi

felipa

@robjohn I posted a question is quite similar to one you answer beautifully before. Do you think your method might work for it too? math.stackexchange.com/questions/1308085/…

@Chris'ssistheartist still doing really hard integrals?

Chris's sis the artist

@felipa Not really. Now I'm trying to finish a proposed problem to some magazine.

felipa

@Chris'ssistheartist aha... I saw a really nice and hard looking coin weighing puzzle recently. Do you like things like that?

Chris's sis the artist

@felipa Sure, when I have some time. :-)

felipa

18:16

@Chris'ssistheartist mathoverflow.net/questions/208015/…

Agawa001

@felipa i know these puzzles

felipa

@Chris'ssistheartist It would be nice if people added the optimal solutions for more small cases

Agawa001

i solved most of them

felipa

@Agawa001 the one I pasted just now?

@Agawa001 try that one

I think n = 10 is already interesting to do

and n = 20 is very interesting :)

Chris's sis the artist

@felipa btw, do you somehow know me from the real life? :-) Asking me such a question cannot be just a coincindence (or, well, it might be).

Agawa001

18:18

im big fan of logic puzzles , as far that i can leav my priorities for em :D so i will try

felipa

@Chris'ssistheartist no.. I just read your questions/puzzles online :)

@Agawa001 great! I look forward to see your contribution to that puzzle

Chris's sis the artist

@felipa My posts on MSE?

felipa

@Chris'ssistheartist and mathematica.se

Chris's sis the artist

@felipa OK :-)

robjohn

@felipa I remember doing something like that a while ago. Have you looked at that? I will have to find it.

felipa

18:20

@robjohn yes.. it is math.stackexchange.com/questions/1021933/… . I stole my notation from there :)

@robjohn but I feel I don't think I understand your trick well enough to extend it to my problem

@Chris'ssistheartist the mathematica.se answers to your questions are great

Chris's sis the artist

@felipa Yeah, but not all though. ;)

Agawa001

my goood , its generalisation of the classic N coins and a scale puzzle

robjohn

@felipa so the difference is that in your question, we have $(\frac14,\frac12,\frac14)$ instead of $(\frac12,0,\frac12)$ for the $w$

Agawa001

i claim for creating a group devoted for matlab

as there is for mathematica

Hippalectryon

A matlab sect ?

Agawa001

18:32

but i cant deny that mathematica is the best :D

yes a section

felipa

18:42

@robjohn yes.. I don't know what to do with the 0's basically

evinda

Is the radius of convergence also defined for a polynomial or only for infinite series?

@Hippalectryon http://math.stackexchange.com/questions/1182796/legendre-differential-equation-y-1-y-2-linearly-independent-solutions
If $p \in \mathbb{R} \setminus{\mathbb{Z}}$, is the radius of convergence defined?

Hippalectryon

@evinda Finite series are a special case of infinite series. Any finite power series (eg a polynomial) has an infinite radius of convergence

evinda

So the radius of convergence will be $+\infty$ if $p \in \mathbb{Z}$, right? @Hippalectryon

r9m

@robjohn OP here is asking a derivation using differentiating under integral sign! I'm not all that much used to the method .. could you take a look? :-)

Hippalectryon

@evinda What's $p$ ?

evinda

18:59

@Hippalectryon Did you take a look at this link I sent you?
The differential equation is $(1-x^2)y''-2xy'+p(p+1)y=0, p \in \mathbb{R} \text{ constant } \\ -1 < x<1$ and:

$$a_{2k}= \frac{\prod_{j=0}^{2k-1} (j+(-1)^{j+1} p)}{(2k)!}a_0$$

and

$$a_{2k+1}= \frac{\prod_{j=1}^{2k} (j+(-1)^j p)}{(2k+1)!}a_1$$

Hippalectryon

@evinda Why would it be ? The series is $\sum a_k$, which is not finite, right ?

Gato

@Hippalectryon hello

Hippalectryon

@Gato $\huge\text{:(}$ $\frac{5}2$

Gato

@Hippalectryon résultats ??

evinda

@Hippalectryon If $p \in \mathbb{Z}$, then one of $\sum_{n=0}^{\infty} a_{2n} x^{2n}$ or $\sum_{n=0}^{\infty} a_{2n+1} x^{2n+1}$ will be a polynomial.

@Hippalectryon Then will the radius of convergence of one of them be $+\infty$ ?

Gato

19:02

@Hippalectryon ENS et X ? Mines ? Centrale ?

evinda

and from the other 1? @Hippalectryon

Hippalectryon

@evinda How do you know that it will be a polynomial ?

@Gato Pas admissible à X/ENS. Seules les ENS m'intéressent, donc .... :(

Mary Star

Could someone take a look at my question:

0

Q: Find the forces

Air of pressure $p_0$ and velocity $|\overrightarrow{u}_{A}|=|\overrightarrow{u}_{B}|=c$ enters the space $D$ from the sections $A, B$ of surface $S$. If at the orifices the distribution of the pressure and the velocity is uniform and at the exit $\Gamma$ the pressure is equal to the atmospheric ...

physics classical-mechanics fluid-dynamics

?

evinda

@Hippalectryon If p=2*i, then $a_{2j}=0, \forall j>i$. Or not?

Gato

@Hippalectryon Dommage!! a peu de choses ou ?

Hippalectryon

19:05

@Gato A en croire le barème (barra vers 12.5/20), j'en suis loin... j'en suis assez étonné mais bon ....

@evinda But what about the $a_{2j+1}$ ?

Gato

@Hippalectryon Ah bah désolé pour toi, l'année prochaine tu l'auras. Tu vas quand même passer des oraux ?

evinda

$sum_{n=0}^{\infty} a_{2n+1} x^{2n+1}$ will be a series.
So won't it hold that the radius of convergence of $sum_{n=0}^{\infty} a_{2n+1} x^{2n+1}$ is $1$ and the radius of convergence of $sum_{n=0}^{\infty} a_{2n} x^{2n}$ is $\infty$ ? Or am I wrong?

Hippalectryon

@Gato j'ai passé les mines/centrales donc j'aurai probablement des oraux que je passerai comme entraînement (les résultats mines/centrale arrivent plus tard)

@evinda Your product only becomes $0$ for $2k=p$ (or something similar), so indeed the radius for the even terms is $\infty$ iff $p\in\mathbb{N}$

Gato

@Hippalectryon Ah d'accord, je connais pas trop le système. ET sinon à Llg des beaux résultats ? LegrandDoDom ?

Hippalectryon

@Gato Il est à llg ? :O Sinon oui aparemment au global cette année est très bonne

evinda

19:11

Oh yes, right... @Hippalectryon But the radius of convergence from the solution will be 1 , right?

Gato

Oui, tu discutais avec l'année passée non ? C'était un autre pseudo.

Hippalectryon

@Gato Il était à llg l'année dernière, je ne sais pas s'il a fait 5/2 où s'il a intégré (je n'étais pas à llg l'année dernière)

Gato

@Hippalectryon Bha vu ses questions sur le forum il était en 5/2, il a posté une question qui venait d'un sujet de ENS.

Hippalectryon

@Gato D'un autre côté, ça va être drôle d'exploser tous les exercices l'année prochaine :3

Agawa001

lol

Gato

19:15

@Hippalectryon Oui, tu pourras aller encore plus loin et très bien maitriser. Tu pourras m'aider comme ça ;p

Agawa001

room is frenchified ..... INVADERS

Gato

@Agawa001 :D

Hippalectryon

@Gato Toi tu passe en L3, non ?

@Agawa001 Ssh you must now speak French or pay $10 :D

Agawa001

lmao

oh sorry , MDR

Gato

@Hippalectryon Non, je suis en L3, j'étais en L2 physique puis L3 maths, ils avaient acceptés... mais j'ai bien progressé, en plus le niveau des élèves n'est pas excellent à la fac.

Hippalectryon

19:17

@Gato Après c'est M1 ?

Gato

@Hippalectryon Oui, M1 maths pures.

Hippalectryon

:D

Gato

@Hippalectryon ça va être dur, j'ai encore beaucoup, de lacunes.

Agawa001

i wont pay ten bucks it costs too much in my currency

Hippalectryon

lacunes.... éléctroniques ? :D

@Agawa001 You live in Zimbabwe ? :)

Agawa001

19:18

lol its worse

nvm

Hippalectryon

1.00 EUR = 407.295 ZWD

Gato

@Hippalectryon :DD

Agawa001

je suis algerien :)

Gato

@Agawa001 Salam

Agawa001

oh les compatriotes

salam

Hippalectryon

19:20

Agawa001

i didnt mean it when i said its worse than zimbabwe :D , its just sarcasm

Philip Hoskins

Can someone help me evaluate the following limit: mathb.in/37120? I'm wondering if there is some sort of dominated convergence argument that could be made since the integrand has a pointwise limit of 0

Ramanewbie

@hippa For the second time, I have someone on irc asking straightly for my asl, any idea why they do that ?

Hippalectryon

'asl' ?

Agawa001

in zimabwe u must pay bag full of money for bread

Ramanewbie

19:25

age sex location @hippa

Hippalectryon

@Agawa001 That used to be the case... litterally

@Ramanewbie no idea

Ramanewbie

@hippa nvrmd then

Agawa001

@Ramanewbie lol its a bot

Ramanewbie

@Agawa001 I don't think so ! The way it / he talks is too natural...

Agawa001

i have been there , and once you log in , you get loads of requests

Hippalectryon

19:28

@Agawa001 reminds me of that I just received

Agawa001

yes they r subtly programmed bots

in way u dont touch any difference

Hippalectryon

@Ramanewbie on the 42 room or your private channel ? Are you a registered user ?

Ramanewbie

@hippa on another room. Yes I am

Hippalectryon

What room ? (continue on irc to avois flooding the chatroom)

Agawa001

i like freenode , no much trolls there

Ramanewbie

19:31

ok

Hippalectryon

I'm usually on freenode, sometimes #maths or #physics, or reddit /r/maths and /r/science. /r/science is a very good way to keep up to date with new findings

Antonio Vargas

@PhilipHoskins I can help you in about 30 mins if you still need it by then. Send me an email to remind me.

Agawa001

and moderators are more numerous than chatters :D

Antonio Vargas

maybe 45 mins

Agawa001

u would be banned for saying , shit , or crap , wtf etc

Hippalectryon

19:33

@Agawa001 freenode is a network, not a channel though

Agawa001

i know

Antonio Vargas

@PhilipHoskins the basic idea is to expand f in maclaurin series and integrate term by term

Philip Hoskins

Thanks @AntonioVargas.

That was an approach I tried and nothing immediately jumped out to me. Maybe I should go back and try it again

Gato

@Hippalectryon Corps quotient tu fais ?

Hippalectryon

@Gato Non. Avec les nouveaux programmes, ça a disparu en PC. J'ai juste un peu travaillé sur $\mathbb{Z}/n\mathbb{Z}$ par moi même.

Gato

19:45

@Hippalectryon Ah ok too bad.

Agawa001

i have new heuristic for this question codegolf.stackexchange.com/questions/50467/… , but its sophisticated for bein implemeted :/

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$Mathematics$ Mathematics