Mathematics - 2014-12-15 (page 7 of 10)

Huy

8:00 PM

Nominations close momentarily.

Primary closes in 4 days.

Hakim

3

Hippalectryon

KABOOM

STARTED

Balarka Sen

OK

G.T.R

voted !

Venus

Who should I vote for the other 2? Any idea??

G.T.R

8:01 PM

@DanielFischer you already have the lead !

Balarka Sen

voted

Hippalectryon

Can we downvote too ?

G.T.R

yes

Venus

Hey!? I can downvote!

Balarka Sen

Daniel is 21! Yee

Venus

8:02 PM

Why it never crosses to mind

Balarka Sen

Pedro = Thomas

Hippalectryon

@Chris'ssis=@PedroTamaroff

lol

Balarka Sen

Thomas is ahead oh noes

Venus

How many vote do we have?

Can I upvote or downvote every candidates?

Balarka Sen

Pedro is ahead yes

Chris's sis

8:05 PM

@Hippalectryon What is the meaning of "="?

Hippalectryon

@Venus yes

@Chris'ssis Like Cleo=T-F :D Just a joke though

Chris's sis

@Hippalectryon ;)

Jasper Loy

I downvoted most of the candidates. I upvoted only 3.

Balarka Sen

Daniel is on the lead and Pedro is ahead of Thomas. Way ahead.

Venus

@Hippalectryon What do you mean by YES? I suppose we only have 3 votes

Hakim

8:06 PM

@Chris'ssis What about this series, have you ever seen it? $$\sum_{k=0}^\infty\dfrac{(-1)^k\left(k+\dfrac{1}{2}\right)\sin\sqrt{\left(k+\df‌rac12\right)^2\pi^2+a^2}}{\left(k+\dfrac12\right)^2-b^2\sqrt{\left(k+\dfrac12\rig‌ht)^2\pi^2+a^2}}=\dfrac\pi2\sec(b\pi)\dfrac{\sin\sqrt{a^2+b^2\pi^2}}{\sqrt{a^2+b^‌2\pi^2}}$$ (the LaTeX code is fine but it doesn't work)

Huy

@Venus: This is just the primary phase.

Hippalectryon

@Venus You can vote for as many people as you like, I think

Huy

DanielFischer already surpassed 60 votes. :D

r9m

@Huy :D

Huy

70!

Balarka Sen

8:07 PM

OMG.

Mike Miller

There are lots of other things you can do if you like to watch numbers get bigger. Clocks do that most of the time, for instance.

Hippalectryon

@MikeMiller What's an example for $A,B$ closed where $A+B$ isn't ?

Huy

@MikeMiller: I got bored watching my clock.

Mike Miller

@Hippalectryon Define A+B.

Mathy Person

Can someone help me with this? $For any positive integer n, let G(n) be the number of pairs of adjacent bits in the binary representation of n which are different. For example, G(10)=3 because the bits of 1010_2 change at all three places and G(12)=1 because the bits of 1100_2 change only from the fours to the twos place.

For how many positive integers n<2^{10} is it true that G(n)=2?$

Daniel Fischer

8:08 PM

@BalarkaSen Thomas is a good man.

Hippalectryon

@MathyPerson $\{a+b\mid a\in A,b\in B\}$

Mathy Person

@Hippalectryon What does A and B stand for? Or did you mean to tag someone else?

Balarka Sen

@Hippalectryon What is "+"? in this context?

Daniel Fischer

@Hippalectryon $A = \mathbb{Z}$, and $B = \{ n + 2^{-n-1} : n\in\mathbb{N}\}$

Jasper Loy

I think Daniel, Jyrki and Pedro will win, just like what I am voting.

Venus

8:10 PM

@Huy @Hippalectryon I just did. I feel bad to those who get minus score :'(

evinda

@DanielFischer A ok... If the array has $2r$ elements, the two elements determining the median sit at positions $r-1$ and $r$ after sorting.
Why do we need the part of the array from positions $r-(p-1)$ to $(r-1)+(p-1)$?
Why to we take once r and the other time r-1?

Hippalectryon

@BalarkaSen @MikeMiller Oh sorry. $A,B$ are vector spaces

Huy

@Venus: Then don't downvote them, since it is already very clear they won't be elected.

Venus

@MathyPerson Hey! Can you fix your chat, please?

Jasper Loy

@Venus Well, I don't think it will ruin their life.

Hippalectryon

8:11 PM

@DanielFischer How do you show this one isn't closed ?

Mathy Person

@Venus not sure what you mean by that...

@Venus Do you mean fix the LaTeX?

Mike Miller

@Hippalectryon Oh, I thought they were just closed sets.

Hippalectryon

@MikeMiller GRR not what I meant to type

@MikeMiller They're sets in a vector space if finite dim

teadawg1337

DanielFischer is almost past 100

Mike Miller

subsets of vector spaces? Or subspaces?

Hippalectryon

8:12 PM

@MikeMiller subsets. I was looking for that word

Mike Miller

Daniel's example looks good then.

Balarka Sen

well R is also a vector space and look at the example of Daniel

ah Mike beat me to it

Jasper Loy

I just put on a new hat.

Hakim

@Chris'ssis
$$
\sum_{k=0}^\infty
\dfrac{(-1)^k\left(k+\dfrac12\right)\sin\sqrt{\left(k+\dfrac12\right)^2\pi^2+a^2}}{\left\{\left(k+\dfrac12\right)^2-b^2\right\}\sqrt{\left(k+\dfrac12\right)^2\pi^2+a^2}}
=\dfrac\pi2\sec(b\pi)\dfrac{\sin\sqrt{a^2+b^2\pi^2}}{\sqrt{a^2+b^2\pi^2}}.
$$

Huy

My students want to go ice-skating but I suck at ice-skating. What do?

Daniel Fischer

8:13 PM

@evinda Because we can, usually must, take both middle elements in the selection then. So the earliest possible choice is the $p-1$ elements before the larger of the middle elements and the larger of the middle elements, which gives indices $r-(p-1)$ to $r$, and the latest possible choice is the smaller of the middle elements and the $p-1$ elements following, indices $r-1$ to $(r-1)+(p-1)$.

Huy

@DanielFischer surpassed 100!

Mathy Person

@Venus Assuming that this is what you mean by fix, here it is: For any positive integer n, let G(n) be the number of pairs of adjacent bits in the binary representation of n which are different. For example, G(10)=3 because the bits of $1010_2$ change at all three places and G(12)=1 because the bits of $1100_2$ change only from the fours to the twos place.

For how many positive integers $n<2^{10}$ is it true that G(n)=2?

Daniel Fischer

@Hippalectryon $$(-k) + (k+2^{-k-1}) \to 0$$

Hippalectryon

@DanielFischer But that isn't enough, is it ?

Mike Miller

@Hippalectryon what's enough?

Hippalectryon

8:16 PM

@MikeMiller $\mathbb{Z}+A$ where the elements of $A$ are dense around $0$

Mike Miller

That's enough for what?

Michael Greinecker

@Hippalectryon Every integer is in the closure but not in the sum.

Chris's sis

@Hakim OK

Hippalectryon

@MichaelGreinecker :O of course, thanks

Venus

@JasperLoy I worry that the kids will

Mike Miller

8:18 PM

@Venus It doesn't show to any candidate a score below 0. If you are highly downvoted, your nomination score just looks like a 0, not a -157.

evinda

@DanielFischer Don't we have the latest possible choice when we look at the numbers till the position r+(p-1)? :/ Or am I wrong?

Jasper Loy

@Venus Hmm, OK. It's not as bad as a job or school application though.

Huy

@JasperLoy: Have you applied for many jobs?

Hippalectryon

@MikeMiller That's where the up/downvote displayer comes in handy :D

Mike Miller

My profile views have gone up by a few hundred since Bash started.

Jasper Loy

8:20 PM

@Huy No. I have been mostly jobless my life, sad to say.

@MikeMiller Why is that so?

Mike Miller

@JasperLoy I'm on the hat rankings.

N3buchadnezzar

why are le wuts (votes) public?

@MikeMiller w(hat)?

Jasper Loy

@MikeMiller Have you decided what your thesis will be on?

Huy

@JasperLoy: A lot of people have to apply many many times before they actually even get invited to an interview. So, I think, a lot of people will get used to being rejected for job applications, so it won't be too disappointing.

Hakim

@Chris'ssis Yes, but do you know how we can evaluate it? I have no idea though.

Mike Miller

8:22 PM

No, @JasperLoy. I think I've talked to you this before. One does not decide this in their first year of an american PhD program.

Jasper Loy

@MikeMiller Sorry, I tend to repeat the same things over and over again. Still, you might have a rough idea.

Chris's sis

@Hakim I have to think of it.

Venus

Daniel-sensei takes the lead

Mike Miller

Nope.

Huy

Daniel Fischer

8:23 PM

@evinda No, or, not necessarily. Usually one must take both middle elements in the selection (for $p > 1$ of course), and one can always include both. Deciding to always include the two middle elements makes the range a little smaller - not that it makes much of a difference, if you prefer, let the target range go from $(r-1)-(p-1)$ to $r+(p-1)$.

Balarka Sen

@Huy Mike looks hideous.

Huy

@BalarkaSen: Spoiler alert: He dies.

Daniel Fischer

@Hippalectryon Ah, but $0\notin A+B$.

Balarka Sen

Now wonder. He has Ebola.

Hippalectryon

@DanielFischer Ah true

Venus

8:24 PM

@DanielFischer Your ava looks weird using that hat. Please change it. You'll soon be a mod. You should care with your appearance

Mike Miller

@Huy lol

Jasper Loy

It seems I am the only person who downvoted those election guys...

Hippalectryon

@JasperLoy You're funny

evinda

@DanielFischer So, because of the fact that we take at the one case r-(p-1) we take at the other case (r-1)+(p-1) so that we consider both middle elements?

Hippalectryon

@JasperLoy Who did you downvote ?

Huy

8:25 PM

@Venus: Do you think teachers should care about their appearance?

Jasper Loy

@Hippalectryon I downvoted all the candidates with less than 20,000 rep.

Venus

@Huy Of course he must! Not only should

Jasper Loy

@Venus Still waiting for the picture, lol.

Hippalectryon

@JasperLoy That's what you call 'being the only one' ?

Huy

@Venus: Good. Some teachers don't - for some reason. But I think they should too.

Hippalectryon

8:26 PM

Daniel Fischer

@Venus Get me a new hat, and I'll put that on.

Hippalectryon

@DanielFischer Use mine

Balarka Sen

Looks like most people doesn't want to realize dreams

Hippalectryon

@DanielFischer The Russian hat :D

Alyosha

@MikeMiller I know the homology definition of the Euler characteristic. Do you know how to, using that, prove that $\chi(X \cup Y)= \chi(X) + \chi(Y) - \chi( X cap Y)$?

Daniel Fischer

8:27 PM

@Hippalectryon I have it not.

Balarka Sen

Your russian hat would slide off the edge of your superman symbol @Hippa

Hippalectryon

@DanielFischer Review a first post

@BalarkaSen Quantum hat

@BalarkaSen And more importantly

Daniel Fischer

@Hippalectryon Hah-Hah, the review queues are emptier than usual these days.

Mike Miller

@Alyosha Use Mayer-Vietoris.

Hippalectryon

@BalarkaSen Don't tell a russian hat what to do

Venus

8:28 PM

@JasperLoy If Jack is elected to be a mod, I'll change my ava using my real face. I promise

teadawg1337

I'm afraid to post any answers to questions because of the hat-gaming going on...

Jasper Loy

Again, Daniel, Jyrki and Pedro are leading.

@Venus You like Jack?

Balarka Sen

OK I am chatting nonsense

Hippalectryon

@DanielFischer Anyhow, if you manage to find two working subsets, please ping me :)

Balarka Sen

I should log out

Venus

8:28 PM

@Huy We must care with our appearance!

Balarka Sen

@DanielRust Hi

Daniel Rust

@BalarkaSen Hi

Venus

@JasperLoy He is mature enough. Look cool also. I've seen his real picture while drinking beer

Daniel Rust

I have a hat. I like hats.

Mike Miller

Novice mistake, @DanielRust. You wait 'til he logs out before you say hi.

Venus

8:29 PM

@DanielFischer OK, I'll do it for you sensei

Balarka Sen

throws table at @Mike

Jasper Loy

@Venus I see. Well, you already have a boyfriend, so forget about Jack, lol.

Daniel Fischer

@Hippalectryon I thought you wanted $A,B$ closed with $A+B$ not closed?

Venus

@JasperLoy Adoring someone doesn't mean we love him

Hippalectryon

@DanielFischer Indeed

evinda

8:31 PM

@DanielFischer Also why can we take low = (m/2)-(p-1) and high = (m-1)/2 + (p-1) at both cases? If the dimension of the array is odd, isn't it low=(m-1)/2-(p-1)? Or am I wrong? :/

Mike Miller

@Hippalectryon He gave you such a pair, though.

Daniel Fischer

@Hippalectryon I gave you an example.

Daniel Rust

It's a little worrying that so many votes have already been cast in the primary election when there are no answers in the Q&A thread yet.

Hippalectryon

@DanielFischer Didn't you say there was a problem with $$0 not being in $A+B$ ?

Oh wait that does not really matter

Daniel Fischer

@evinda Integer division. If m is odd, then m/2 == (m-1)/2.

Jasper Loy

8:32 PM

@DanielFischer Why did you drop below 100k again?

Daniel Fischer

@Hippalectryon That shows that $A+B$ is not closed.

@JasperLoy Drop below 100k? goes to SO to check

Venus

Everyone, please vote this answer for @DanielFischer-sensei so that he can get a new cool hat. Thanks ^^

Hippalectryon

@DanielFischer Why ? I see how it would show it's not compact, but not that it's not closed

Balarka Sen

@DanielRust Is it true that if $G$ acts prop discountinously and freely on connected space $X$ then there is a SES of Cech fundamental groups $1 \to \check{\pi_1}(X) \to \check{\pi_1}(X/G) \to G \to 1$?

I have a proof but not sure if it's right.

Hippalectryon

@DanielFischer Oh nvm I see now, thanks

Michael Greinecker

8:33 PM

@Venus That is not the point of voting here.

Daniel Fischer

@JasperLoy No drop. You may have misread my score here, it was 98K+ here, not 99K+.

N3buchadnezzar

@MichaelGreinecker O hai. What brings you to chat? =)

Jasper Loy

@MichaelGreinecker Hi! Welcome to this chat.

Daniel Rust

You may need some additional hypotheses on the space $X$ as I think I've asked a question like this before @BalarkaSen

Mike Miller

@MichaelGreinecker In a question where the OP is self-defacing (sorry for asking such an elementary question, it's very hard, etc) is it standard practice to remove that?

Michael Greinecker

8:34 PM

Thanks.

Balarka Sen

Hmm @DanielRust. What do you suspect the hypothesis is? Hausdorff?

Daniel Rust

@BalarkaSen well I think manifold is certainly enough

Balarka Sen

eh

Michael Greinecker

@MikeMiller Sorry, I'm not sure I understand the question.

Balarka Sen

a solenoid is not a manifold, so that's not useful for me

Mike Miller

8:36 PM

@MichaelGreinecker In a question where the OP has remarks like "Sorry for asking such an elementary question", or "This is very hard for me", or similar things, is it standard practice to remove or leave that?

evinda

@DanielFischer A ok... And then do we have to find the p-closest elements to the median with a for loop?

Michael Greinecker

@MikeMiller I don't think there is an official policy, but I think it is worth editing out.

Jasper Loy

@MikeMiller Remove it if you feel it does not add important context to the question.

N3buchadnezzar

@DanielFischer When do you think you will have more points here than on overflow?

Balarka Sen

no, @DanielRust

Daniel Rust

8:37 PM

@BalarkaSen nvm I was wrong :P

$G=\pi_0(\mbox{fiber})$.

Balarka Sen

I think what we want is given a covering map of connected spaces, $p : X \to Y$, an existence of a covering map of abstract simplicial complexes $\mathcal{N}(U) \to \mathcal{N}(p(U))$ given an open cover $U$ of $X$.

Mike Miller

Thanks.

Mathy Person

Anybody? """"" For any positive integer n, let G(n) be the number of pairs of adjacent bits in the binary representation of n which are different. For example, G(10)=3 because the bits of $1010_2$ change at all three places and G(12)=1 because the bits of $1100_2$ change only from the fours to the twos place.

For how many positive integers $n<2^{10}$ is it true that G(n)=2?"""

Balarka Sen

wonder what are the sufficient conditions for that

Daniel Rust

@BalarkaSen I think it's probably a difficult question. You would need a covering space on the limit to somehow induce a covering space on the approximants, but that seems unlikely. In particular there are spaces which have no branch point (can be foliated by real lines), but for which all approximants are branched manifolds, so a covering map doesn't induce coverings of the approximants.

Venus

8:41 PM

@DanielFischer If you've voted, you can use Uncle Sam hat. Not very bad

Huy

@Venus: I've reviewed 10 posts. Where the hell is my football hat.

Daniel Rust

@BalarkaSen or at least, that would be my first method of attempt at a proof.

Venus

@Huy Just wait. it takes time 3-5 minutes

Huy

Patience, I don't have any.

Mathy Person

same ^^

Venus

8:42 PM

@Huy You should have it as a teacher

Balarka Sen

if it turns out that X has to be very smooth then I'm doomed :P

Jasper Loy

@Huy I think I have lots of it.

Daniel Rust

@BalarkaSen If I gave you a toy example to check, would that help?

Huy

@Venus: It is different. If I want something, I want it immediately. If they don't understand something in maths, that's not worrying me so I'm patient.

Balarka Sen

erm, sure @DanielRust.

Daniel Rust

8:44 PM

Actually it might take a while to explain the space involved.... Are you happy with the 'Thue-Morse' sequence?

the limit word of the substitution $a\mapsto ab,\:\: b\mapsto ba$.

Venus

Why the heck there -6 in Daniel's vote?

Huy

@Venus: Hater's gonna hate hate hate hate hate.

Venus

@Huy it seems the other candidates do that thing

N3buchadnezzar

@Huy Hatters gonna hat hat hat.

4

Venus

$$\Huge\text{We Have a Dream! Let's Realize it!}$$

Daniel Rust

8:46 PM

haha

Jasper Loy

@PedroTamaroff has 13 downvotes, lol.

Mike Miller

They're all from me.

Venus

Give me stars for the previous comment :D

Balarka Sen

for not choosing a hat, @Mike?

Mike Miller

Aye.

Balarka Sen

8:47 PM

@DanielRust OK, googled what Thue Morse is. But what's that got to do with such a space?

Jasper Loy

@MikeMiller Only the British say that.

Mike Miller

No, only pirates do.

Daniel Rust

I can't personally endorse a candidate that eschews the great tradition of wearing winter hats.

Jasper Loy

@MikeMiller It means love in Chinese.

Mike Miller

@DanielRust Me neither - which is why I have downvoted him 13 times so far.

Daniel Rust

8:48 PM

only 13?

Mike Miller

I'm spreading them out.

Daniel Rust

@BalarkaSen ok if you take the 'suspension' of the shift space on the Thue-Morse sequence, you get a space which is a bit like a solenoid, except it has two 'exceptional leaves' which are forward and backward asymptotic composants.

Balarka Sen

what is le shift space of the Thue Morse sequence?

Daniel Rust

@BalarkaSen And there is a $2-1$ covering map from the suspension of the shift on the Thue-Morse to the suspension of the shift on the 'Period-doubling' sequence

Jasper Loy

I wonder why so many people downvoted Pedro. Are they jealous of his good looks?

Daniel Rust

8:51 PM

@BalarkaSen ok, yeah you might need more background than I initially thought :P Sorry.

Jasper Loy

@DanielRust Have we spoken before? There are too many Daniels in chat for me to recall.

Daniel Rust

@JasperLoy possibly. I recognise your name from chat.

I haven't been too active recently... end of term is always hectic here.

Jasper Loy

@DanielRust OK. Anyway, I have deleted my account and changed my username many times over the last few years.

Venus

I've just seen my review flag & I got this message: "declined - It's actually not a question. IT'S SPAM!!! PLEASE FLAG IT AS SPAM!!!!!!!!!!!!!!! "

Balarka Sen

yeah what d'you expect from a beginner on algebraic geometry still stuck on covering spaces, @DanielRust :P

but if you can give me explicit conditions on X, I am interested.

Venus

8:53 PM

Does the mod who handle the flags?

Balarka Sen

I want to know if it works with the solenoid and Z_p acting on the solenoid

Daniel Rust

@BalarkaSen No it's fine. topological dynamical systems is a pretty niche subject anyway, so I shouldn't have expected you'd know the example.

Jasper Loy

@DanielRust Are you a professor?

Daniel Rust

the solenoid is about as nice of a 'pathological space' as you can get

@JasperLoy nah, postgrad student

Huy

@Venus: Look at my new picture!

Balarka Sen

8:55 PM

do you expect it to work for the solenoid, @DanielRust?

Daniel Rust

@BalarkaSen Maybe. so you're expecting to get a SES of the form $0\to \mathbf{Z}_p\to \mathbf{Z}_p \to \mathbf{Z}/p\mathbf{Z}\to 0$?

Venus

@Huy Is that you?

Huy

@Venus: Of course. I just took a selfie.

Balarka Sen

@DanielRust Err?

Venus

@robjohn You look cool with that hat. 2 thumbs up!

@Huy Yeah. Finally, you get that hat. Congrats! :D

Daniel Rust

8:57 PM

I imagined you were considering the $\times p$ covering map on the $p$-solenoid?

Huy

@Venus: Thank you. I was beginning to worry.

Balarka Sen

Not quite. I am thinking of ... --> R/p^2Z --> R/pZ --> R/Z where the maps are x \to x mod p^{n-1}

Venus

OK, gotta go. Bye everyone... ^^

robjohn

@Venus It finally showed up. I put it on, but it did not show up in chat for quite a while. The same thing happened with my last hat. I guess there is a significant delay.

Jasper Loy

@robjohn Did you try refreshing? Works immediately for me.

Daniel Rust

8:59 PM

@BalarkaSen R/Z is the circle group $\mathbf{R}/\mathbf{Z}$?

Venus

@robjohn I see it now. You look cool. Trust me ^^

Balarka Sen

yes

Huy

Good night, @Venus.

robjohn