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

11:00 PM

@DanielFischer But don't the two parameters, the second and the third correspond to the interval of the positions of the array that shall be partitioned? Or am I wrong?

Ted Shifrin

What are you doing with Fourier gadgetry, @Alex?

Jasper Loy

@TedShifrin I see you have also put on a silly hat!

Ted Shifrin

IT was assigned to me, @Jasper.

Jasper Loy

I think @Alizter looks a bit like @PedroTamaroff, lol.

Alizter

@JasperLoy Not really

Daniel Fischer

11:03 PM

@evinda There are two ranges. a) the range we are interested in at the end, where the elements we want to select will be sorted to. And b), the range of the array that shall currently be partially sorted. The range a) remains fixed during the complete recursion, range b) changes in every call.

Ted Shifrin

hi @Alizter

Alizter

hi @TedShifrin

I got my report card today

Ted Shifrin

@Jasper: Do you find that all white guys look alike?

evinda

@DanielFischer I see... but why does the range we are interested in at the end have to be a parameter?

Hippalectryon

@MikeMiller Are you still here ?

Ted Shifrin

11:05 PM

Is that good or bad, @Alizter?

Mike Miller

yeah @Hippa

Jasper Loy

@TedShifrin Not really. OK, my last approximation was a bad one.

Alizter

Maths: A
Further Maths: A
Computing: A
Chemistry: B
Physics: C

Hippalectryon

@MikeMiller What is $x$ in your answer ?

Alizter

it alright

Ted Shifrin

11:05 PM

Where are literature and history, @Alizter?

Mike Miller

@Hippalectryon Point in $K$ of minimal norm, @Hippalectryon

Hippalectryon

@MikeMiller I thought it was a coordinate of the closest point, but then you take its norm

Jasper Loy

@Alizter Why did you get B and C?

Mike Miller

Oh

Alizter

@TedShifrin I am very specialised at 16 years of age

Mike Miller

11:06 PM

I messed up

Ted Shifrin

I always thought math people should be interested in physics, @Alizter.

Mike Miller

Sorry

Let me edit that

@DanielRust I don't understand why solenoids aren't a counterexample to this question. It seems to me I can write the multiplication-by-$p$ complex with simplicial maps.

Alizter

@TedShifrin me too but I need to study it more

Ted Shifrin

I'm opposed to early specialization :(

Alizter

we don't even have a text

Mike Miller

11:06 PM

nevermind - just saw your comment that they all have to be subgraphs of a finite graph

Ted Shifrin

I can recommend an excellent text on mechanics for you, @Alizter.

Jasper Loy

@Alizter Wanna drop one subject?

Alexander Gruber

@TedShifrin trying to figure out necessary conditions for a function to converge to the Fourier series of another function

Jasper Loy

@TedShifrin But you would not know their syllabus.

Alizter

@JasperLoy I know that my chemistry grade will improve because I have literally only been studying chemstry

Alexander Gruber

11:07 PM

Transform, I mean

Ted Shifrin

Not my problem @Jasper

Daniel Fischer

@evinda It doesn't have to be a parameter, you can also make that global variables. But the partial sorting function needs to know that range, since that decides whether a recursive call to the front or back part of the currently partitioned slice is necessary after partitioning.

Mike Miller

@Hippalectryon Fixed

Alizter

I need to study some physics as well

I guess I got bored of the linear equations already

Hippalectryon

@MikeMiller Nope not yet "Because x had minimal distance to the origin"

Jasper Loy

11:08 PM

@Alizter If you are going to study math in Cambridge, it will have a lot of physics.

Ted Shifrin

I'm confused, @Alex: There's a sequence of functions? Converging in what norm?

Alizter

@JasperLoy I have no problems with the mathematics.

Ted Shifrin

@Alizter: Kleppner-Kolenkow is a fun and excellent text on mechanics, which fully uses multivariable calculus.

Daniel Rust

@MikeMiller each space in the limit needs to be a subcomplex of a single graph $G$ so in you example you'd have to have the number of edges you use to model the circle bounded by some $p^n$, but then the $n+1$st circle can't map simplicially onto the $n$th.

Alizter

It is clear explanations that I suck at

Mike Miller

11:09 PM

@Hippalectryon superfixed

Jasper Loy

@Alizter I just don't understand why you did so badly for physics when it is highly mathematical. Your teacher must be really bad.

Mike Miller

@DanielRust Yeah, I noticed that.

Hippalectryon

@MikeMiller Thanks :)

Ted Shifrin

There is intuition to be had for physics that is not just mathematics, @Jasper.

Alizter

@JasperLoy I strongly dislike one of my physics teachers

Mike Miller

11:09 PM

@AlexanderGruber how'd you get that box.

tell me.

Ted Shifrin

You can hate me, too, @Alizter, but that doesn't mean you should do badly in my class :P

Alizter

But I got an A in is class

Daniel Rust

@MikeMiller Actually I have a proof of the statement now. It's essentially an application of the same statement but in the category of finite sets. I should probably write it as an answer.

Alizter

I got a terrible grade in the class that I enjoy

Mike Miller

@DanielRust Prolly. I was just hunting for an unanswered question belonging to someone I know that I could actually attack.

Alexander Gruber

11:10 PM

@TedShifrin the context is from probability, I've got sequence of characteristic functions (specially Poisson) and I'm trying to figure out under which conditions it converges

Ted Shifrin

That sucks, @Alizter.

Alizter

@TedShifrin I just have to work harder. Nothing else can be done

Ted Shifrin

In $L^1$, in $L^2$, how?

Jasper Loy

@Alizter There are so many A level physics and chemistry books, just pick them up!

Daniel Rust

@MikeMiller haha, that's fair enough.

evinda

11:11 PM

@DanielFischer So don't we write the commands:
low=m/2-(p-1)
high=(m-1)/2+(p-1)
inside the function but we define them as global variables or give them as parameters to the function partialQuicksort?

Alexander Gruber

The problem doesn't say but I'm guessing almost sure convergence would be fine

Ted Shifrin

I dunno, @Alex ... This is beyond my current probability knowledge :P And my final is on Wednesday.

Mike Miller

ah, found one. and the friend will even be available after office hours.

Alexander Gruber

Wait that may have just answered my question

Ted Shifrin

leaves @Mike to his scavenging

Mike Miller

11:13 PM

Enjoy dinner, @TedShifrin

Ted Shifrin

Bubye ...

Daniel Fischer

@evinda Yes, these are computed outside the partial sort, and that computation is done only once. Then they are either passed a arguments, or stored in global variables.

Alizter

@JasperLoy My school chose OCR physics B that doesn't have a textbook

mmmm first meal of the day

at 11pm

Jasper Loy

@Alizter Hmm OK. I thought you were using Edexcel all the way.

Alizter

Not for physics

i am doing AQA for chem

just edexcel for math

evinda

11:17 PM

@DanielFischer Outside the first partial sort? If so, then we have to define them as global variables, right?

Alizter

At least I am not failing discrete math again

Jasper Loy

@Alizter I did CIE, of course.

Hippalectryon

@MikeMiller In the second part, where is the hypothesis $K$ bounded used ?

Alizter

I wish we could choose

But then there would be too little for teachers to do

Jasper Loy

@Alizter I wish we could choose the country and family to be born into.

Daniel Fischer

11:18 PM

@evinda No, don't forget that the partial sort is called from the function that at the end selects the $p$ elements closest to the median.

Mike Miller

@Hippa I didn't look at it closely, but I gotta leave something to you!

Alizter

@TedShifrin I imagine that you are not the kind of teacher that teaches from powerpoint?

Hippalectryon

@MikeMiller :/

Jasper Loy

@Alizter I think powerpoint for math and science really sucks.

Alizter

Never seen a powerpoint in maths

but all my physics lessons are slide show readings

Mike Miller

11:20 PM

@Alizter I don't know any math professors that use PowerPoint for their lectures.

Daniel Rust

You'll see plenty of powerpoint /beamer presentations at seminars/conferences

Jasper Loy

I wonder who my secret upvoter is.

@MikeMiller Don't they use beamer?

Alizter

I hate learning from powerpoint.

Jasper Loy

@DanielRust I think I will use powerdot and not beamer.

Alizter

They are ideal for conferences/talks but silly for teaching

Also being forced to copy from them is silly

Hippalectryon

11:22 PM

@MikeMiller Harald's answer/hint seems logical "graphically" but I can't make it into a proof

Alizter

I do have the advantage that I type pretty fast so I can dictate the teacher sometimes

Jasper Loy

Most people use pgf, pgfplots and beamer. I prefer pstricks, pst-plot and powerdot, lol.

Daniel Rust

I still don't understand how some people type their notes up on a laptop instead of hand-writing

Jasper Loy

@DanielRust They must type really fast. Maybe all latex experts.

Mike Miller

@JasperLoy I don't know anyone who doesn't teach from the board.

Daniel Rust

11:23 PM

@JasperLoy Yeah I don't know

Alizter

horray 80wpm

Daniel Rust

I had one lecturer at undergrad who would just talk through his beamer slides, but not upload them for the class. So you ad to basically just copy the slides verbatim.

Alizter

@DanielRust I can't do it in maths. If I use latex I might get away with it but I prefer to write in maths

evinda

@DanielFischer We have this:
partialQuicksort(A,p,r){
if p<r{
k=medianofMedians(A,p,r)
q=hoare(A,p,r,k)
low=m/2-(p-1)
high=(m-1)/2
if (q>low) partialQuicksort(A,p,q-1)
if (q<high) partialQuicksort(A,q+1,r)

When we pass low and high at partialQuicksort after having calculated them, we have to pass them also at the initial fuction.

Or didn't you mean this?

Alizter

Blackboards have information cycle through however powerpoints clear everything so it is hard to keep up.

Jasper Loy

11:25 PM

@DanielRust That is so silly.

Alizter

I'm not a big fan of projectors but they are like a lazy white board.

Alexander Gruber

Startin to look like I should change my name to Alexander Fischer.

9

Alizter

They are not that bad

Mike Miller

@AlexanderGruber heh.

by the by, tell me how you got the box.

Alizter

Who knows. @DanielFischer might have a sudden storm of downvotes

Mike Miller

11:28 PM

my guess's been editing or answering old questions, but either mine haven't been old enough, or i haven't done enough

Alizter

Damn it @Daniel! Why did you help me!

I would of loved to run for mod

but I have no time

N3buchadnezzar

@AlexanderGruber Are yer fishin fur sumethin?

Hippalectryon

@MikeMiller At least give me a hint on the hint :/

N3buchadnezzar

Also it is a rule that the winners are the top X users with the highest rating. Here X is the number of moderators required.

Alizter

Today is day 94 consec

Daniel Fischer

11:30 PM

@evinda The low and high should be parameters.

Daniel Rust

Apparently the primaries are very coarse in terms of it's predictive accuracy

Daniel Fischer

@N3buchadnezzar That's only an informal rule.

Behaviour

@MikeMiller Editing is correct. Pick a cluttered / misused tag, and clean up some old posts from it. I'm not sure that tag-only edits count, but there's usually an opportunity to fix something in the post itself along the way.

Daniel Rust

see this comment: chat.stackexchange.com/transcript/message/19085568#19085568

evinda

@DanielFischer So, should it be like that?
low=m/2-(p-1)
high=(m-1)/2
partialQuicksort(A,p,r,low,high){
if p<r{
k=medianofMedians(A,p,r)
q=hoare(A,p,r,k)
if (q>low) partialQuicksort(A,p,q-1,low,high)
if (q<high) partialQuicksort(A,q+1,r,low,high)

N3buchadnezzar

11:31 PM

@DanielFischer Tounge in cheek comment. That is the standard, but not a standard I am particuarly fond of. Cough gone cough

usukidoll

burps

Behaviour

Current challenge: figure out how to type a good question in Android app without killing myself.

Alexander Gruber

@Arkamis I voted for you, buddy.

Pedro Tamaroff

@Behaviour Don't do that.

It's masochism.

Behaviour

@PedroTamaroff I think I'll type it on the desktop, email to myself, then copy and paste.

Alexander Gruber

11:35 PM

@Behaviour Oh God I know, me too

Pedro Tamaroff

@Behaviour Hehe, that seems roundabout.

cxseven

@TedShifrin are you here?

evinda

@DanielFischer Also, here:
if (m%2==1) m=A[(m-1)/2];
else m=0.5*(A[m/2-1]+A[m/2])
left = (m-3)/2;
right = m/2+1;
if (m%2==1) count = 1
else count = 2;
while(count < p) {
++count;
if (left < 0){
++right;
continue;
}
if (right >= m){
--left;
continue;
}
if ((median-A[left]) < (A[right]-median)) {
--left;
} else ++right;
}

shouldn't we save at m the position of the median element?

Hippalectryon

WUT

evinda

Or am I wrong?

Hippalectryon

11:36 PM

^ WAAT ?

Alexander Gruber

"Question: What would compel anyone to type Mathjax on a phone?"

Alizter

@Hippalectryon I clicked. I hate hats

cxseven

is there an app for these chat rooms, or do you use a mobile browser?

Alexander Gruber

"Answer: Hat."

Hippalectryon

@Alizter :/

Alizter

11:37 PM

@Hippalectryon CBA

Hippalectryon

What's CBA

Alizter

Can't Be Asked

Alexander Gruber

@MikeMiller I edited an old post. Really can't believe there's a badge for that

Hat*

Hippalectryon

Those 25 hats in a row though

Alizter

@Hippalectryon Let $\varnothing$ denote how much I care :P

Ted Shifrin

11:38 PM

@Alizter: Not even from my grave.

Behaviour

@AlexanderGruber I can believe it. Anything to make people edit posts other than their own... at least once in a year or so.

Hippalectryon

@Alizter :)

Alizter

@TedShifrin Well yeah. Most of physics is taught like this.

Alexander Gruber

@Behaviour but that's the beautiful part, it was my own post

Alizter

But why blame the teacher? The student is obviously bad and should improve

Ted Shifrin

11:40 PM

Not by the good physics teachers here ... @Alizter

Pedro Tamaroff

@TedShifrin $F=ma$. HA!

Alexander Gruber

Maybe there should be a hat for spam upvoting an alternate account, too.

Jasper Loy

@PedroTamaroff F= (mv)'

Alizter

Force is the change in momentum

cxseven

@TedShifrin remember when I asked if an invertible continuous $f:S^n \rightarrow S^n$ must have degree 1 or -1? You suggested that there is an answer to math.stackexchange.com/questions/1064763/… , which I haven't found yet. However, there's a different approach that seems to work.

Pedro Tamaroff

11:41 PM

@JasperLoy From far away, you look like a floppy disk.

Alizter

momentum is the change in kinetic energy

Jasper Loy

@Alizter Wrong. The rate of change of momentum.

Alizter

@JasperLoy that is what i mean

Jasper Loy

@PedroTamaroff I used to be very handsome, but I have become old and ugly now.

@Alizter Now we know why you got C.

Pedro Tamaroff

@JasperLoy You're not even 40.

Alizter

11:42 PM

@JasperLoy Basically from stuff like that

Jasper Loy

@Alizter Exactly.

Ted Shifrin

I've been too busy to ponder it, @cxseven.

Alizter

Hurrdurr strong, stiff are the same thing

cxseven

@TedShifrin by invariance of domain and the compact hausdorffsness of the domain and range we can assume the function has an inverse

Alizter

today I learnt about Lagrangian multipliers

Ted Shifrin

11:44 PM

continuous inverse, yes. Then done.

teach @Pedro, @Alizter. He's stubborn.

cxseven

@TedShifrin if we then approximate $f$ and its inverse with smooth versions, the composition of the smooth versions is within an arbitrarily small distance of the identity map

Hippalectryon

Oho epic new avatar :3

Mike Miller

@AlexanderGruber There's definitely not - I would have gotten it within minutes, of course.

mick

Hi all

I asked a new question

0

Q: Why is this integral $\int_{-\infty}^{+\infty} F(f(x)) - F(x) dx = 0$?

Let $a_n > 0$ and $b_n$ real. Let $f(x)= x - \sum_{i=0}^{\infty} \dfrac {a_n}{x+b_n}$ Now apparantly for every function $F(x)$ : $$\int_{-\infty}^{+\infty} F(f(x)) - F(x) dx = 0$$ If the integral converges. Why is this true ? I considered contour integrals and substitution but found no pro...

Ted Shifrin

you don't need anything smooth, @cxseven.

cxseven

11:45 PM

@TedShifrin and since the degree of a composition is the product of degrees, and the identity has degree 1, the smooth version of $f$ must have degree 1 or -1

mick

maybe you can help with it

Ted Shifrin

Use homology, @cxseven.

Hippalectryon

@mick Can't vote anymore today sorry

r9m

shamelessly asks for a hat ;) .. just a (+1) here and I'll get a new hat ! :D

cxseven

@TedShifrin what exactly from homology?

Hippalectryon

11:46 PM

@mick ~~I would have loved to downvote your question though~~ kidding :)

Ted Shifrin

Defn of degree, @cxseven

Hippalectryon

Good night/... everyone

Don't get eaten by Ted

Ted Shifrin

Bonne nuit, @Hippa.

cxseven

@TedShifrin I haven't read much about homology

Ted Shifrin

Oh, then how did you define degree, @cxseven?

mick

11:49 PM

@Hippalectryon sonic !!!

:)

cxseven

either take a suitably close triangulation or smooth approximant and look at a ray that passes through a nice region

mick

goodnight all

Ted Shifrin

What with triangulations?

cxseven

with triangulations you look at the orientation of simplices

Ted Shifrin

You're doing PL transversality?

Daniel Rust

11:51 PM

Bah I feel stupid whenever i ask a question on MO.

cxseven

i don't know what that is

Ted Shifrin

And then?

I asked one, @DanielRust, and Robert Bryant, a very smart old friend, made me feel like you. ;)

Daniel Rust

@TedShifrin The answer is always with so much authority and seemingly effortless. Maybe one day I'll not be intimidated by it :P.

cxseven

and then what? you triangulate $S^n$ so that each simplex is within a small enough epsilon ball to keep the to-be-described calculation invariant, and look at the image of those simplices

specifically the image of the points of each simplex

Ted Shifrin

So if it's a homeo, you get $\pm 1$ immediately?

cxseven

11:56 PM

no, i'd argue something within a certain distance of the identity function has degree 1, and then that a composition of maps has a degree which is the product of the degrees of the individual maps

Ted Shifrin

It can be far from the identity ...

evinda

@DanielFischer I have to go to sleep now... Good night!!!

Good night to you all!!!

cxseven

an injective continuous $f:S^n \rightarrow S^n$ has a continuous inverse

Mike Miller

I feel stupid all the time, @DanielRust

cxseven

surjective due to invariance of domain, and continuous inverse since the domain is compact and range Hausdorff

Daniel Rust