Mathematics - 2014-10-08 (page 1 of 3)

Samuel Handwich

00:00

@Studentmath now i'm looking for a counterexample.

Studentmath

Counterexample of what you tried to prove?

Samuel Handwich

i'm convinced it should be $(1-tz)^2$. it just works too well for that not to be it.

yeah. I think it's got to be a misprint.

Studentmath

$(1-t)^2z^2$ should be sharp for certain X's that could satisfy all your needs too, I think.

Alizter

eh I hate having to work till 1 am

now I am full of caffine and cannot sleep

Studentmath

Say now if we take $X$ that is almost surely 1

Would it work?

Nah, it won't.

@Samuel I have a rather easy discrete counter-example.

I think so at least.

Samuel Handwich

00:13

@Studentmath what's that?

Studentmath

Ah, wops. Scratch that.

Ice Boy

@Alizter how many cups of coffee did you have?

Samuel Handwich

Hmm: the crucial step in the $(1-t)^2$ proof is $(1-t)^2z^2<=(1-t)^2E(|X|)^2$ which has to be true. we want $(1-t)z^2<=(1-t)^2E(|X|)^2$ to fail, so we need $z^2>=(1-t)E(|X|)^2$. we already know $E(|X|)>z>0$ though, so $z^2<E(|X|)^2$, so we'd need for $1-t<0$. But we assumed $0<t<1$. Maybe this is it. i may be making a mistake.

Alizter

@IceBoy redbull

Ice Boy

@Alizter that stuff will get you wired, it has ginseng & caffine

Samuel Handwich

00:28

ah that is the mistake, im being dumb we don't need $1-t<0$. ok

so we need $\frac{z^2}{E(|X|)^2}\geq 1-t$. we should pick $t$ to be near $1$ and $z$ to be close to $E(|X|)$.

Studentmath

Shouldn't be too hard...

Shouldn't it be $t$ close to 0?

Ah no, being stupid here

Kasper

math.stackexchange.com/questions/652005/… 300 points bounty

for an easy analysis question

I actually meant to give it 50 bounty points, don't know what happened :P

Kaj Hansen

haha

Ice Boy

00:44

you'll get a lot of attention now

Jasper Loy

I never look at bounty questions lol

Ice Boy

so, you're not a bounty hunter?

Jasper Loy

Nope. I am a will hunter lol

Ice Boy

:D

hunting for good will or hunting for will power?

Jasper Loy

@Alizter You misspelled caffeine.

Studentmath

00:48

It seems it's not that easy at all to find a counterexample.

Jasper Loy

@IceBoy You misspelled caffeine.

Ice Boy

~~caffine~~ caffeine

sorry

please forgive me

Kaj Hansen

LOL

Jasper Loy

@KajHansen Hi Matt Damon.

Kaj Hansen

Hey there

Jasper Loy

00:54

Time for some coffee before seeing my psychologist.

Kaj Hansen

$\text{caffeine} \subseteq \text{coffee}$

Jasper Loy

If only rep can buy coffee lol

Ice Boy

Kaj Hansen

Ha

Ice Boy

Kaj Hansen

01:00

LOL

Ice Boy

:D

michaelb958

01:28

Just by the way, limits-without-lhospital makes me sad. L'Hospital (with an S) seems to be far too common a joke/typo these days.

Mike Miller

01:56

@michaelb958 It is neither a typo nor a joke; the correct spellings are L'Hospital and L'Hôpital. If one omits the circumflex over the o, the s should be included. (This is why the s is included in the tag - you can't use special characters in tags.)

michaelb958

02:23

@MikeMiller I stand corrected. Thanks!

nabla blah

Sit down corrected

JessicaK

02:50

If an alternating series diverges, does that tell us anything about the series absolute convergence?

Ted Shifrin

03:17

Yes @JessicaK: it must diverge absolutely. Why?

Kaj Hansen

@TedShifrin, I've started my real early enough to TeX it this time ;)

Ted Shifrin

With age comes less procrastination? @Kaj

did you figure out that connectedness ?

Kaj Hansen

Not yet. I've spent all my free time today either tutoring or doing my Quodes homework.

I'll probably get some food and think about it some before I go to bed.

Ted Shifrin

Very late for food!

Kaj Hansen

But dining hall is right next to Boyd and on my way back to my room :P

Ted Shifrin

03:22

Things are open now?

JessicaK

@TedShifrin I just wasn't 100% sure because I was trying to take the contrapositive of the alternating series test. I convinced myself it diverges just as I looked up to see your reply.

Ted Shifrin

Oh yeah, I remember you guys pigged out at 2 am last spring.

Kaj Hansen

@TedShifrin, one of the dining halls is open 24 hours during the week!

LOL

Ted Shifrin

No contrapositive. Direct inequalities with partial sums, @JessicaK

JessicaK

@TedShifrin Thanks you

Ted Shifrin

03:25

Sure :)

JessicaK

opps, I meant thank you

Hee Kwon Lee

Hi

I have a question. Is there upper limit of points that we obtain in a say ?

My answer has two votes but point is not counted.

anorton

03:54

@HeeKwonLee Yes. The upper limit is 200 reputation points per day, with some restriction. Specifically:

"You can earn a maximum of +200 reputation from upvotes and suggested edits in any given day. Accepted answers and bounties are counted separately... Reputation "lost" from the reputation cap is not awarded on following days." Source

(Note that reputation from accepted answers does not count towards the limit. That's how you have 275 points from today.)

usukidoll

helloooo!!!!

Hee Kwon Lee

04:21

@anorton Thank you for your explanation.

usukidoll

anyone here?

Balarka Sen

04:38

Hey @r9m

r9m

@BalarkaSen Hi :)

Balarka Sen

What's up?

usukidoll

why isn't anyone answering my pde questions? T_T

r9m

@BalarkaSen nothing interesting :|

Balarka Sen

That's sad.

r9m

04:41

\ (-o-) / Yaaawnn ..

usukidoll

-.-

shakes everyone talk to me!!!D:

Balarka Sen

@Kaj!

Ah, this one is excellent :

r9m

hehe :P

usukidoll

-.-

r9m

is TheGame new name of Hippa ?

Balarka Sen

04:50

yeah

r9m

ah thanks !

@TheGame Have you seen this book .. Exercices corrigés de théorie analytique et probabiliste des nombres - De Gérald Tenenbaum, Contributions de Jie Wu ( Société Mathématique De France) ? .. please let me know if your school/college library has a copy of it ;)

Balarka Sen

Someone just referred that to me recently.

An english version.

Kaj Hansen

Hey there

Balarka Sen

@KajHansen Are you still sticking to ODEs and PDEs.

or anything fun (e.g., algebra) lately?

Kaj Hansen

Not PDEs. I'm studying ODEs and real right now.

Balarka Sen

04:54

Never liked them. Blech.

Kaj Hansen

ODEs is kind of boring I agree.

Real can be boring, but I really enjoyed the topology section in Rudin. The problems are fun.

leo

05:15

@isukidoll hello

usukidoll

05:29

wahhhhh

this site needs more pde tutors

Tharindu

06:03

0

Q: $-1.4\sin 3x - 0.2 \cos 3x$ in the form $R \sin (3x+\alpha)$ such that $R>0$ and $0<\alpha<2\pi$

Write $-1.4 \sin 3x - 0.2 \cos 3x$ in the form $R \sin (3x+\alpha)$ such that $R>0$ and $0<\alpha<2\pi$ I found $R= \sqrt{(-1.4)^2+(-0.2)^2}= \sqrt{2}$ And $\alpha= \arctan \frac{0.2}{1.4}= \arctan \frac {1}{7}$ Now the problem is I could write this as $-\sqrt{2}\sin(3x+\arctan \frac{1...

trigonometry

Can someone help me in this problem? :)

robjohn

@r9m: hey there... haven't seen you in a while (probably my fault)

Joao

Hello Robjohn, I'm looking for a book to learn number theory with, what book did introduce you to number theory, or is there any book you could recommend as an inttroduction to number thoery.

usukidoll

06:22

@Joao try number theory by george andrews.... my class is using that book and it's easy to follow...well most of the time... the author kind of is eh when it comes to the proofs

r9m

@robjohn hello :D .. I was afc for a few days :-)

robjohn

@r9m that would explain it, too :-)

r9m

:)

robjohn

@Joao If you use @robjohn, it will ping me and I will see your comments sooner. My number theory studies came from many books. There are different ones that are better for different topics. I now that Borevich and Shafarevich and Hardy and Wright are highly regarded beginning general books.

usukidoll

@robjohn do you know pdes?

robjohn

06:37

@usukidoll a little, but I am not really an expert.

usukidoll

:/ it's about a theorem... the one after the max principle after my attempt wait let me get the link... I already figured out the other one with the heat equation Duhamels

@robjohn continuous dependence
http://math.stackexchange.com/questions/958928/proving-the-maximum-principle-and-the-continuous-dependence-on-initial-condition

Jasper Loy

07:27

I just returned from some psychotherapy.

@Joao Look at Alan Baker's Comprehensive Course in Number Theory.

usukidoll

yay for the rep points but still no answer T_T

Eric Gregor

@JasperLoy what's wrong with you?

Jasper Loy

@EricGregor Suffering from OCD for past 15 years, among other things. Not worked for past 7 years. That is just a summary of my shit life.

Eric Gregor

do you have a special diet?

Jasper Loy

No.

Eric Gregor

07:36

i was once interested in the idea of Jungian psychotherapy

but it's a little far out there, and Jung was basically a cult leader. but there was something fascinating about it. though i imagine in practice it's usually quite banal

Jasper Loy

08:12

Hi @jay

Jayesh Badwaik

@JasperLoy Hello, how are you?

Jasper Loy

@JayeshBadwaik When do you graduate?

Jayesh Badwaik

@JasperLoy in coming June.

Jasper Loy

@JayeshBadwaik Good good. My current plan is to enter grad school in 2017

Jayesh Badwaik

@JasperLoy Nice, not bad. Good luck. :-)

Will you start math again before it?

Jasper Loy

08:18

Yes, I am going to study math next year, take the GRE in 2016

Jayesh Badwaik

Good, good.

Jasper Loy

I will try to finish my 12 holy math books either by end 2015 or end 2016

Depends on how long each book takes

Jayesh Badwaik

12 books in one years seems ambitious unless you have studied quite a few before?

Okay, I have a class in 10 minutes now. Gotta go, bye. See ya around.

Jasper Loy

Bye

Chris's sis

Greetings

Jasper Loy

08:21

Hi @Chris'ssis you vanished last night after I asked you your age lol

Chris's sis

@JasperLoy I had some things to do like now

@r9m $$\sum_{k=1}^{\infty} \frac{(k+1)^s}{k^{2s} (k^s+(k+1)^s)}>\frac{1}{2}\zeta(2s)+\frac{1}{8}, \space s>1$$ As far as I know, you love these questions. :-)

Balarka Sen

09:10

@Studentmath!

Chris's sis

09:51

@robjohn I went further and I developed a new integral

$$\int_0^1\log^2\left(\frac{x}{2}+\sqrt{\frac{x^2}{4}+1}\right)\frac{\ dx}{x}=\frac{\zeta(3)}{10}$$

Chris's sis

10:15

My intuition tells me that $$\int_0^1\log^n\left(\frac{x}{2}+\sqrt{\frac{x^2}{4}+1}\right)\frac{\ dx}{x}=C \zeta(n+1),\space C \in \mathcal{Q}$$

Balarka Sen

What is $\mathcal{Q}$, @Chris'ssis?

Chris's sis

@BalarkaSen Q

Balarka Sen

Oh you mean rationals?

Chris's sis

@BalarkaSen Yeah

Balarka Sen

@Chris'ssis Standard notation is $\Bbb Q$

But the context is clear nevertheless.

Chris's sis

10:19

@BalarkaSen Well, I don't always use the standard notations. Actually I don't care too much the standard notations.

Balarka Sen

@Chris'ssis That'd only make stuff hard to read.

Chris's sis

@BalarkaSen Not in this case.

Balarka Sen

Fair enough.

But $\mathcal{Q}$ sure looks ugly :P

Chris's sis

@BalarkaSen lol. I like it that way pretty much. :-)

Balarka Sen

How about $\mathfrak{Q}$

Eugh

Chris's sis

10:22

@BalarkaSen not bad ...

N3buchadnezzar

10:52

@BalarkaSen cute hat

@BalarkaSen I like to write $\mathcal{C}$ for my constants in integration, and C and B for my continouos and bounded spaces functions eg $f \in C^1$

Jasper Loy

Just answered a lhf.

I have yet to learn proper LaTeX.

N3buchadnezzar

@JasperLoy low five

Jasper Loy

@N3buchadnezzar No meat, no pudding.

N3buchadnezzar

@JasperLoy Start with a whip, and then slowly add a gag ball. And then the suit when you are up for it.

Jasper Loy

11:49

The user X likes to make stupid edits on other people's posts...

However, it is good that the silly comments have stopped.

If I read a paper written by X, I will throw it into the dustbin because of its poor formatting and punctuation.

N3buchadnezzar

@JasperLoy Someone who enjoys blue colors?

Jasper Loy

@N3buchadnezzar Well, shh...

N3buchadnezzar

@JasperLoy He tried to pull that on one of my posts. I really pulled his nut, and kicked his dog.

Jasper Loy

Anyway, many people like blue here.

@N3buchadnezzar Are we thinking of the same person? The username has 5 letters.

N3buchadnezzar

@JasperLoy A single name, not a double name?

Jasper Loy

11:56

@N3buchadnezzar Yes, single word with 5 letters.

N3buchadnezzar

Mmm, not the same.

nabla blah

12:12

Hi @JasperLoy

Jasper Loy

@nablablah Hi Bart.

Just answered a lhf.

robjohn

@Chris'ssis That looks an awful lot like an inverse hyperbolic function

Chris's sis

@robjohn Yeah, sure. :-)

robjohn

@Chris'ssis I think looking at it that way, we might get your generalization

Chris's sis

@robjohn I think getting the generalization is a very hard thing to do.

robjohn

12:24

@Chris'ssis okay. I would have to look closer.

Jasper Loy

@robjohn You are up very early

nabla blah

@JasperLoy You are up very late

Balarka Sen

@N3buchadnezzar LOL

N3buchadnezzar

@BalarkaSen It does look like a hat, fit for a cat.

Balarka Sen

Rather crumpled.

Hat for hats : $$\widehat{\mathcal{Q}}$$

r9m

12:43

@Chris'ssis Nice !! :-)

Balarka Sen

typo $\widehat{\mathfrak{Q}}$

Chris's sis

@r9m Yeah, it's awesome. BTW, how are you doing?

r9m

@Chris'ssis trying to survive somehow :-)

N3buchadnezzar

@BalarkaSen thats hatception, a hat on a hat. The second one looks more like a sloopy triangle than a hat though

Balarka Sen

LOL @N3buchadnezzar

Chris's sis

12:46

@r9m I understand your point. :-)

Balarka Sen

@r9m How's analytic number theory going?

r9m

'survive somehow' .. thats how its going ..

Balarka Sen

Grumph.

You need to have fun with the subjects, @r9m, seriously.

r9m

_ /\ _ _ /\ _

N3buchadnezzar

@r9m Weird boobies, or cat hats? Can not quite decide

r9m

12:48

neither

N3buchadnezzar

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Well that failed misserably, poor attempt at hat.

r9m

if that's a poor attempt .. hats off =P

N3buchadnezzar

@r9m The topp part is fine though!

r9m

ya .. and I just took it off !

N3buchadnezzar

             _
           /`_>
          / /
          |/
      ____|    __
     |    \.-``  )
     |---``\  _.'
  .-`'---``_.'
 (__...--``

┌─┐
┴─┴
ಠ_ರೃ

Ice Boy

12:55

-2

Q: Welcome back Brian M. Scott!!!

First of all thank you for coming back. We missed you Professor.

discussion celebration

Jasper Loy

@IceBoy More drama lol

Ice Boy

;-)

N3buchadnezzar

13:26

Someone told me they would integrate my face, I had no idea what they meant.

r9m

can someone help me with a problem involving Fourier transforms .. if $\omega$ and $\hat{\omega}$ are both ${\ell}^1(\mathbb{R})$, where, $\displaystyle \hat{\omega}(\tau) = \int_{-\infty}^{\infty} \omega(t)e^{-it\tau}\,dt$, then for $k > \sigma$ ($\sigma$ being the abscissa of convergence of the dirichlet series $\displaystyle F(s) = \sum\limits_{n=1}^{\infty} \frac{a_n}{n^s}$) ..

$$\sum\limits_{n=1}^{\infty} a_n (\frac{x}{n})^k \omega(\log \frac{x}{n}) = \int\limits_{k-i\infty}^{k+i\infty} F(s)\frac{x^s}{s}\hat{\omega}(\tau)\,ds$$

this is a problem from the second chapter exercise of Tenenbaum's book .. Intro to analytic and probabilistic NT

typo .. sorry $\displaystyle \sum\limits_{n=1}^{\infty} a_n (\frac{x}{n})^k \omega(\log \frac{x}{n}) = \frac{1}{2\pi i}\int\limits_{k-i\infty}^{k+i\infty} F(s)x^s \hat{\omega}(\tau)\,ds$

Ice Boy

@N3buchadnezzar you should have asked them with what?

r9m

13:41

my confusion is in $\displaystyle \frac{1}{2\pi i} \int\limits_{k-i\infty}^{k+i\infty} x^s \hat{\omega}(\tau)\,ds$ .. should it be $\hat{\omega}(s)$ inside there instead ?

N3buchadnezzar

@IceBoy with by fish!

Ice Boy

@N3buchadnezzar so he wanted to slap your face with a fish

N3buchadnezzar

@IceBoy I didnt say tthat (and fish souns more amusing)

Ice Boy

@N3buchadnezzar you are typing like you are drunk

N3buchadnezzar

@IceBoy hic

Ice Boy

13:48

@N3buchadnezzar :D

Chris's sis

@robjohn If I'm able to find that $\displaystyle \int_0^1\log^3\left(\frac{x}{2}+\sqrt{\frac{x^2}{4}+1}\right)\frac{\ dx}{x}=C \zeta(4)$ and then I manage to get that $C$, I think I'll be the first one that have ever managed to answer a certain mathematical problem (I cannot share it now).

N3buchadnezzar

dont drink and derive, kids

9

r9m

@Chris'ssis oho !! an open problem at your mercy ! Lord have mercy on its 'soul' :D

Ice Boy

@N3buchadnezzar MADD = Mathematicians Against Drunken Derivations

Chris's sis

@r9m What do you mean? :-)

@r9m Did you figure out the problem I was referring at?:-)

r9m

13:55

@Chris'ssis I prayed the to the Lord to have mercy on the 'soul' of the problem (assuming it has one) 'coz I think it won't have any form your part :D

Chris's sis

@r9m lol:-))))))))

r9m

@Chris'ssis homeworks at hand ! will try it later please ! ^_^

N3buchadnezzar

@IceBoy I 2 week old superstrong coffe, har mercy on my typing capabilities

Mats Granvik

@N3buchadnezzar I have been 2 weeks without drinking coffee.

N3buchadnezzar

@MatsGranvik I was too. Yesterday the last bits of cofeein ran out of me.

r9m

13:59

haha !! @N3 good one !! :)

Jasper Loy

@N3buchadnezzar Not funny, lol.

N3buchadnezzar

I am also a second hand drinker.

Chris's sis

I need to be careful as regards coffee, it affects your Calcium level in your body, not necessarily for bones, but also for other parts of the body.

Jasper Loy

@r9m Do not use the Lord's name in vain, lol.

Ice Boy

@r9m you need at least 3 characters after the @

r9m

14:01

@IceBoy o ! I see .. thanks !

Ice Boy

np pal :-)

r9m

@JasperLoy so you are a believer in 'The Book' ? :-)

Jasper Loy

@r9m No, I am a semi-Buddhist and an ex-Christian.

Chris's sis

"The calcium level in blood can be moderately low without causing any symptoms. If levels of calcium are low for long periods, people may develop dry scaly skin, brittle nails, and coarse hair. Muscle cramps involving the back and legs are common. Over time, hypocalcemia can affect the brain and cause neurologic or psychologic symptoms, such as confusion, memory loss, delirium, depression, and hallucinations. These symptoms disappear if the calcium level is restored."

Jasper Loy

@Chris'ssis Where does it say that coffee affects calcium levels?

Chris's sis

14:05

@JasperLoy from my doctor

Jasper Loy

@Chris'ssis Is it because of caffeine?

Chris's sis

@JasperLoy Perhaps.

Jasper Loy

@Chris'ssis I drink a lot of coffee these days. Oh no!

Chris's sis

@JasperLoy Be sure the great companies take care such information are not clearly put in some studies. They recognize there is a small loss of calcium, but just a small that has no importance.

@JasperLoy Now that might be true for some, but not for all. I felt these effects many times.

N3buchadnezzar

nestle-family.com/nutrition-for-all/english/…

Daniel Fischer

14:11

@JasperLoy Just also drink milk or eat cheese.

Sawarnik

@r9m

r9m

@Sawarnik yes

Sawarnik

@r9m after a looong time?

r9m

@Sawarnik not that long ,, I was only away for a few days

Sawarnik

@r9m where, why

Jasper Loy

14:17

Anyone here smokes?

I am just trying to see whether math people smoke.

N3buchadnezzar

i smoke the fools who try to smoke

r9m

@Sawarnik just away from the chat .. thats all

Sawarnik

@r9m good work .. it must have saved you alot of time

r9m

not really =P .. I waste a lot of time anyway :P

Daniel Fischer

:18054421 Well, it was off-topic, wasn't it?

Ice Boy

14:22

yes

Jasper Loy

Users here are too serious, they downvote congrat posts on meta.

Such seriousness is not conducive for the production of high quality mathematics lol.

2

I will try not to come to chat anymore after this year. This will be my last year in chat.

Ice Boy

Such seriousness is not conductive of a user-friendly place.

Jasper Loy

Kids like to remove things they say.

Ice Boy

Hey, I removed somethings

Daniel Fischer

@IceBoy Did you like it?

Ice Boy

14:27

@DanielFischer what?

Sawarnik

There are two barber shop in a small town – one located in the eastern market and the other on the northern market. The shop in the eastern market is quite untidy and the barber has a shabby haircut. While the shop in the northern market is quite neat and clean and the barber is sporting an excellent haircut himself.
Which of the two shops should you opt for?

Daniel Fischer

@IceBoy Did you like removing the somethings?

Ice Boy

no

Daniel Fischer

@Sawarnik The one of the guy who cut the hair of the northern barber.

Sawarnik

@DanielFischer :) You are intelligent we know.

Daniel Fischer

14:28

@IceBoy Then you're safe. Nobody will call you a kid.

Ice Boy

:D

Jasper Loy

In fact, although I will keep my account for life as promised, I think I won't visit the site or chat after this year.

I should devote all my time to mathematics alone.

Sawarnik

@JasperLoy You blabber a lot.

Kiddish behavior, I should add.

Ice Boy

and you don't?

Jasper Loy

Who says I am not a kid?

The purpose of this chat is for us to blabber lol

N3buchadnezzar

14:41

@JasperLoy chat log

Sawarnik

@IceBoy I do.

Ice Boy

@Sawarnik what is your problem?

Jasper Loy

@N3buchadnezzar There are many different definitions of kid lol

Sawarnik

@IceBoy None.

N3buchadnezzar

@JasperLoy IWTBTG

Sawarnik

14:42

@N3buchadnezzar :D

Ice Boy

@Sawarnik ok np pal :-)

Jasper Loy

I have not been following the Millennium Problems. Has any of them been solved other than Poincare?

Sawarnik

@JasperLoy Yeah, google gives two. 'a child or young person' and 'a young goat'.

N3buchadnezzar

@JasperLoy Two of them have been solved I think (quite sure)

Jasper Loy

@N3buchadnezzar Ah, which one?

Sawarnik

14:44

@JasperLoy Google.

Ice Boy

@Sawarnik he has a mental illness

don't be mean

N3buchadnezzar

@JasperLoy I was wrong

Jasper Loy

@Sawarnik He is not a kid.

I am going to take a nap.

Ice Boy

later pal

in Mathematics Educators, 3 hours ago, by Joel Reyes Noche

So what is a math warrior to do?
Many analysts answer this with a slogan: When all else fails use a computer. If that fails then use a bigger computer.

Transcript for

$Mathematics$ Mathematics