The h Bar

0celo7

13:04

I think you don't know what you're talking about.

yuggib

why?

I think you know much less what you're talking about since we're talking about analysis, well-known to be not one of your strong areas

Slereah

PhD level analysis

0celo7

@yuggib Savage

:,(

yuggib

don't cry

you will know it one day...

0celo7

@yuggib why are you on Skype

yuggib

13:12

I'm often on skype, so my parents/relatives can contact me in case of need

0celo7

@yuggib I will never know it, engineers do not need it

yuggib

but you will be double major

and mathematicians do need it

0celo7

I dunno

@yuggib what should I write my thesis on???

yuggib

anyways, I suppose you would already be able to define a continuous and infinitely differentiable function from $\mathbb{R}$ to $\mathbb{R}$?

0celo7

I must decide now, three years in advance

yuggib

13:19

o.O

it's early

0celo7

@yuggib hell no

We just did the algebraic limit theorem, have you not been paying attention

I gave you a report on what we did yesterday...

yuggib

yeah, but you know what a continuous function is

0celo7

Yeah, but not from that class

yuggib

you are making limit of functions

Slereah

Isn't it just a function that maps open sets to open sets or something

0celo7

13:21

What

Slereah

Connected open sets

or we

0celo7

@Slereah no

yuggib

@Slereah don't confuse @0celo7

0celo7

Preimage of open set is open

@yuggib I'm not going to be confused by him

Slereah

"a function f is continuous at a point c of its domain if, for any neighborhood N_1(f(c)) there is a neighborhood N_2(c) such that f(x)\in N_1(f(c)) whenever x\in N_2(c)."

That's the one

0celo7

13:22

That's totally equivalent.

But it does not mean "open sets go to open sets"

Slereah

w/e

Liam Lynch: United States of Whatever

►

^me

0celo7

@yuggib I know it's early

yuggib

will it be on maths or engineering?

that seems a question you can answer now as a starter

or will you need to make two theses, one for each major?

0celo7

I need to write two. Senior year will be hell.

(Fourth year)

yuggib

well, indeed

0celo7

13:29

I'll probably turn the work I do at my research position into my engineering thesis

So it'll be a pure physics engineering thesis

And my math thesis will probably have a strong math.ph flavor.

yuggib

That seems reasonable

either you try to link the two

0celo7

Eh, that's not likely

yuggib

i.e. investigate the math aspects of your physics-engineering thesis

0celo7

Unless I get in with some plasma folks later

Then I could do wave equations, Maxwell's equation

And that would almost work for both...

Slereah

Ew plasma

Fluid mechanics is awful you fool

0celo7

13:31

Hush GDP hater

Slereah

More like MHD hater

yuggib

if plasma physics is modelled by some non-linear wave/maxwell-type equations there is some interesting related maths

0celo7

@yuggib yup it is

And it's used for fusion so there is GDP potential.

yuggib

and could you do courses up to functional analysis or at least function spaces (Lebesgue, Sobolev, Besov, etc) before your last year?

if the answer is yes, then you could be able to do a thesis on non-linear PDEs of wave type

lot of fun stuff there...and a pretty good american school

0celo7

@yuggib Not before my senior year, no

yuggib

13:35

well, even in your senior year; in time to be using the stuff to write your thesis

0celo7

I'm doing more analysis text year + stupid courses needed for graduation. Then measure theory, complex analysis the next year

After that I'll take FA

yuggib

probably you could be capable of doing that

but it is hard to tell now

0celo7

What does that mean

yuggib

you could, at least in theory, have the instruments to do a thesis in non-linear dispersive PDEs by the time you need to do it

but it's difficult to tell right now

so it's a pretty shitty policy they have of making you choose the topic now

0celo7

It's not a policy

It's me being nuts

yuggib

13:39

ah, it's when you overreact and overplan :-D

0celo7

I still think twistors would be cool

But they're pretty irrelevant

yuggib

no idea of what a twistor is

and I'm not sure I want to know...

0celo7

It's a small Roger Penrose.

Slereah

Roger Twist

0celo7

@yuggib also considering "wtf is a spinor", Cartan geometry, positive mass theorem

GR Cauchy problem

Maybe gauge theory?

That's at the bottom of the list

Slereah

13:55

"What the fuck is a spinor" was a book title I had in mind

8

0celo7

Topological aspects of GR

Slereah

For a book on spin

Oh wait it was "What the fuck is spin"

0celo7

I wonder if I write my thing on GR, how much GR do I have to do. Also how much Riemannian geometry

Slereah

Depends

0celo7

Must I prove that the LC connection is unique and such

Slereah

13:56

If it's topological aspects, mb a bunch

0celo7

Do I have to go over all of the basic math?

Slereah

LC being unique isn't too hard

0celo7

Yeah but you have to write it out

There's that one equation

Koszul formula or something

Slereah

$\nabla g = 0$ and torsion being 0 leads pretty fast to a unique connection

0celo7

It's tedious

There's no slick argument.

Slereah

13:59

It's not that long either

0celo7

@yuggib Hamiltonian mechanics/symplectic geometry

There's lots of interesting things.

yuggib

yeah, there are

this for example

link.springer.com/article/10.1007%2Fs11511-011-0060-4

Slereah

Can black holes actually form

What happens during a stellar collapse

Wouldn't a singularity forming violate topological change theorems

Slereah

14:26

Or is the whole singularity as a point removed from spacetime just a pious wish and in actual applications it would just be a divergent curvature

ACuriousMind

@Slereah What's the difference between removing the point and having stuff diverge there?

Slereah

Well definedness, I suppose

Although you can use distributions in GR but it is not fun

ACuriousMind

Definedness of what?

Slereah

I dunno, GR people seem uncomfortable with the notion of having a quantity diverge on the manifold?

ACuriousMind

Of course, because "having a quantity diverge" is not different from it being not defined there

Slereah

14:37

Well then what is the thrust of your question

ACuriousMind

You need to have the metric, curvature, etc. to be defined on the entire manifold for the usual geometric techniques to work

Slereah

But then what happens in, say, some $R^3$ slice with a collapsing spherical distribution

Does it just diverge and all goes to hell and we can throw GR out

ACuriousMind

What do you mean by a collapsing spherical distribution?

Slereah

Well imagine some spherical distribution of like

Dust

it will collapse eventually into a black hole

With a divergent curvature

GR people tend to prefer describing singularities as points removed from the manifold

But the topology of the spacetime cannot change

Well I guess it can, technically

Not sure in those circumstances that would be permitted, though

Obviously there's no time orientation or CTC shenanigans

Might be a singular point in the metric, maybe

I dunno

Just musing

ACuriousMind

Well...I guess a singularity is like a magnetic monopole: You have to remove the point where it is from the spacetime for the purposes of your theory, but, well, there is not an actual hole in the spacetime

Slereah

14:48

I guess then you actually have to use distributions

It is odd that it is not done more

ACuriousMind

Or like in the A-B effect, where you remove the line where the solenoid is

Nobody believes spacetime actually loses that line

Slereah

But then again distributions in GR are some awful shit

ACuriousMind

But in the theory, you have to pretend the line is removed to use the usual theory

GBeau

15:02

@FenderLesPaul ucb, northwestern

0celo7

@Slereah Topological change theorems?

Care to be more specific?

@Slereah The Holy Book proves that a black hole can be obtained by collapse. Chapter 9.

Slereah

There's a theorem stating that any topology change in the spacelike hypersurface will result in either singular points of the metric, closed timelike curves or failure to be time oriented

0celo7

Proof?

Slereah

Iunno

Look up Lorentz cobordism for details

0celo7

Do you understand the proof?

Slereah

15:08

I have not checked it

0celo7

Singular points in the metric is fine, no?

Slereah

Yes.

As in the signature gets 0 eigenvalues at points

0celo7

Brb algebra lecture

FenderLesPaul

15:32

@GBeau no uchicago or ucsb?

David Z

15:59

0

Q: Hilbert Schmidt inner product

I am desperately trying to solve the following problem, and would really appreciate help! Suppose $R$ and $Q$ are two quantum systems with the same Hilbert space $\mathcal{H}$ with $\dim(\mathcal{H})=N$. Let $|i_R\rangle$ and $|i_Q\rangle$ be orthonormal basis sets for $R$ and $Q$. Let $A$ be an...

Thoughts: should that be off-topic?

Under the current policy (as homework-like), and/or under whatever new policy we might come up with?

yuggib

I think so, yes...it seems not so useful for future users

0celo7

16:32

Bernard Meurer

Hahahahahaha

0celo7

@BernardMeurer so where are my pickup lines

good general musical ones

GOOD ones

Bernard Meurer

Oh they have to be good?

That I can't help you with, I keep mine cheesy

don't want to risk a relationship

0celo7

Yes they have to be good.

Cheese is fine, but it must be good.

I'm not sure there are pickup lines that aren't cheesy.

@BernardMeurer Do you have any German ones?

Bernard Meurer

As in in German or about germans?

0celo7

16:45

Auf Deutsch.

What's the German word for that, anyway? Aufheb Linie sounds completely wrong.

yuggib

alcohol has historically been one of the most effective pickup lines, and it needs no words

0celo7

@BernardMeurer You are a German speaker, right?

Bernard Meurer

I speak enough to make people angry, why?

0celo7

@yuggib I'm convinced that my drinking habits in high school and first semester of college have damaged my brain.

It'll be a while before I drink again.

yuggib

@0celo7 each drop of alcohol damages your brain in some way

0celo7

16:48

@yuggib Exactly.

yuggib

and anyways, the point is that it's not you the one that has to drink

0celo7

I can't even solve quadratic equations anymore.

Bernard Meurer

@0celo7 I'm going to the store to make a Tux themed mug

brb

0celo7

@BernardMeurer What?

Ok

@yuggib Are there any continuous functions $\mathbb{R}\to\mathbb{R}$ which are not homeomorphisms and where both copies of $\mathbb{R}$ have the metric topology?

yuggib

If the $f$ is not surjective or injective it is not an homeomorphism

0celo7

16:55

Can it be continuous if it's not surjective?

yuggib

of course

0celo7

o.o

How

Please give an example

yuggib

the cosine is not surjective

0celo7

Oh, wait, I confused myself,

I meant "which are not open"

Drop the bijection part from homeomorphism.

i.e. image and preimage of open sets are open

@yuggib does that make more sense

yuggib

I see...let me think about it

I think there are continuous but not open functions

by the way

0celo7

17:00

I know if we allow for different topologies it's trivial.

@yuggib that's exactly what I'm asking...

I can't find one.

yuggib

hah

trivial

0celo7

?

yuggib

any function such that the range is the half line

like $f(x)=x^2$

because the half line is closed

0celo7

Right.

Thanks.

yuggib

no problem

open and continuous are always distinct

0celo7

17:05

@yuggib Just so you know I get it, $x^2$ maps the open interval $(-\epsilon,\epsilon)$ to $[0,\epsilon^2)$.

yuggib

well, or more simply maps $\mathbb{R}$ (open) into $[0,+\infty)$ (complementary of $(-\infty,0)$ so closed)

0celo7

Or that.

yuggib

I am not completely sure that $[0,\varepsilon^2)$ is closed...

0celo7

@yuggib It's not open.

That's all I need.

yuggib

yeah, true

0celo7

17:08

And I know that $[0,\infty)$ is closed :/

yuggib

:-D

0celo7

How about this: are there open discontinuous maps?

yuggib

that should be easier

maybe...

0celo7

@yuggib Just imagine this is an analysis problem for your kids

How would you solve it

yuggib

it turns out that is not so trivial

jstor.org/stable/10.4169/…

so I will not think about it and let you read :-D

(also I don't have access)

0celo7

17:17

why don't you have access

@yuggib you want the PDF?

yuggib

yeah

0celo7

Skype.

yuggib

thx

0celo7

uh send me a message I can't find you in my contacts

why don't you have access?

is it only for Murricans?

yuggib

probably I don't know

0celo7

17:21

huh

yuggib

not so nice-looking those open discontinuous maps...

0celo7

Is it nicer for $n=1$?

yuggib

no does not seems so

the old examples involve cantor sets and the alike

0celo7

Ugh...

yuggib

anyways, they exist

FenderLesPaul

17:26

@GBeau any more michigan admits btw?

0celo7

@FenderLesPaul what's the lowest ranked school you applied to

FenderLesPaul

@0celo7 probably UC Davis

all my friends are getting into places

:(

Physics Meta

17:56

0

Q: Reworded my question, is it on-topic now?

My question about hyperbolic orbits was put on hold recently, linked here. I did some significant rewording of the question, does it fit the rules of site now?

support

0celo7

18:10

@FenderLesPaul what if you get in nowhere

FenderLesPaul

18:28

@0celo7 go fuck yourself

0celo7

@FenderLesPaul myself? I'd rather you help me

FenderLesPaul

@0celo7 Ok :3

Balarka Sen

Re: Jorg Acker's answer. This is how a physical chemist solves chemistry problem.

@0celo7 Yes. Consider $f : \Bbb R \to \Bbb R$ given by $f(x) = 0$.

However, it is true that continuous bijections $\Bbb R \to \Bbb R$ are homeomorphisms.

0celo7

Oh?

@BalarkaSen What was the wrong question.

Balarka Sen

@0celo7 It follows from the fact that injective cont. maps $\Bbb R \to \Bbb R$ must be strictly increasing or decreasing.

0celo7

18:39

I know that's a fact but I can't prove it.

Balarka Sen

Go contradictions. Assume it's not strictly increasing/decreasing. See what happens.

0celo7

I can't do analysis.

Balarka Sen

It's not really analysis. Just calculus.

OK, I'm off.

0celo7

Calculus is analysis without doing any proofs.

So that's cheating.

@FenderLesPaul Is it fair to classify HE as one of those books everyone has heard of but very few have read cover to cover?

I wonder if more people have read MTW or HE cover to cover.

@ACuriousMind Do you contract "I" and "have" every time? If not, what's your rule for it?

@FenderLesPaul Have you ever seen this before:

FenderLesPaul

@0celo7 yeah that's fair

it's just not a useful book

and I would say MTW has definitely been read more in depth by people than HE

Bernard Meurer

18:49

I'm back

0celo7

$$f(z)=\frac{1}{2\pi\mathrm{i}}\int_{|\zeta|=r}\frac{f(\zeta)}{\zeta-z}\mathrm{d‌}\zeta+\frac{1}{2\pi\mathrm{i}}\int_{|\zeta|\le r}\frac{\partial_\zeta f(\zeta)}{\zeta-z}\mathrm{d}\zeta\wedge\mathrm{d}\bar\zeta$$

wow that took a long time to type

it looks like the standard Cauchy formula

but modified

@FenderLesPaul it's the only book that contains proofs of the singularity theorems and the Cauchy problem solvability

that's not entirely true -- there's maybe two or three others

but certainly none as ubiquitous as HE

FenderLesPaul

I haven't seen that modified form, no

Right but those proofs aren't useful to most physicists

just to mathematical GR people

0celo7

sadly HE lacks actual GR

I think Straumann should write a third edition of his book and include all of HE

+ some more 3+1 split, Ashtekar variables, etc.

@ACuriousMind Have you seen the above formula before?

Cauchy's integral formula

In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk, and it provides integral formulas for all derivatives of a holomorphic function. Cauchy's formula shows that, in complex analysis, "differentiation is equivalent to integration": complex differentiation, like integration, behaves well under uniform limits – a result denied in real analysis. == TheoremEdit == We begin with a theorem that is less...

@FenderLesPaul ^

Apparently it's a real thing.

Ohhhhhh

that's a bar on that zeta in the partial derivative

FenderLesPaul

ah

cool beans

0celo7

19:06

@FenderLesPaul do you know how to prove it

FenderLesPaul

No

0celo7

Hormander...

I must get you...

FenderLesPaul

What

0celo7

it's the reference for that formula

wat

0celo7

19:31

TIL...

DanielSank

19:44

@FenderLesPaul That's how I felt when I graduated from college. Something like five of my classmates got into and went to Harvard physics, including my girlfriend. Others were going to Stanford etc. I was rejected everywhere except CU Boulder and UCSB.

privetDruzia

Hi guys!

:)

DanielSank

@privetDruzia, moi dryg.

privetDruzia

hahahah :)

DanielSank

heheheheh

privetDruzia

I have another very short question!

$\beta = \frac{-1}{V}\frac{\Delta V}{\Delta p}$

DanielSank

19:48

...turning on mathjax...

privetDruzia

How should I express this formula using words?

DanielSank

Is that some thermo thing?

privetDruzia

yup

compressibility

DanielSank

Where did it come from?

Ah.

Oh I see, $\beta$ is not $1/\text{temperature}$ here, is it?

privetDruzia

the compressibility is inversibely proportional with the volume over pressure

?

No it's not

0celo7

19:49

what is inverse temperature anyway

I haven't seen it in the night sky

DanielSank

@0celo7 $\partial S / \partial E$.

Slereah

You know who I feel sorry for?

Pasch.

0celo7

why

DanielSank

@0celo7 You should know that. I recently wrote an answer about it.

5

Q: Is the Boltzmann constant really that important?

I read a book in which one chapter gave a speech about the fundamental constants of the Universe, and I remember it stated this: If the mass of an electron, the Planck constant, the speed of light, or the mass of a proton were even just slightly different (smaller or bigger) than what they ac...

thermodynamics physical-constants

0celo7

@DanielSank lol like entropy is even real

DanielSank

19:50

Anyway, @privetDruzia, I would say:

Slereah

For thousands of years proving that Euclidian geometry was complete or not complete or whatever was like the hardest thing ever

Mathematical tour de force

0celo7

@DanielSank I don't read all of your answers...

Slereah

He does it and nobody remembers him

DanielSank

"compressibility is the fractional change in volume divided by change in pressure."

@0celo7 Well there's your problem right there.

0celo7

wtf is a star-shaped neighborhood anyway

privetDruzia

19:53

@DanielSank, yes I completely agree on that one, seems better. It's actually the $\Delta V$ that disturbs me... this is the change (not rate of change) in volume right? So would this statement be correct: the more the volume increases the more the compressibility decreases

?

0celo7

(removed)

TanMath

lol

0celo7

are you here to bug Daniel

have you two made up?

TanMath

yes...

I just came here to see what was happening...

I saw it on the active list...

it seems DanielSank is already busy to currently help me... I will wait... I have other things to do as well...

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