The h Bar

John Rennie

18:00

Ah, he's going to use the BIG RED SWITCH then :-)

lılostafa

Yeah :)

Problem is solved :)

Thanks @JohnRennie

John Rennie

Well, you're welcome even though I didn't do anything :-)

Servers have a hardware reset module that can be used remotely. You can in effect reset or even power off and on the server remotely independently of the OS.

Very useful when Windows is irrecoverably hung!

Dell DRAC

The Dell Remote Access Controller or DRAC is an out-of-band management platform on certain Dell servers. The platform may be provided on a separate expansion card, or integrated into the main board; when integrated, the platform is referred to as iDRAC. It uses mostly separate resources to the main server resources, and provides a browser-based or command-line interface (or both) for managing and monitoring the server hardware. == Features == The controller has its own processor, memory, network connection, and access to the system bus. Key features include power management, virtual media access...

lılostafa

@JohnRennie What if the hardware reset module is hung?!

John Rennie

@lılostafa the hardware module is simple enough that it never hangs

skullpatrol

There's a math prof helping two people in the math room at the same time, in two different languages!

Anonymous

18:15

@skullpatrol I didn't know that Ted knows French

skullpatrol

Yup

Anonymous

Pretty impressive :)

Balarka Sen

Virus is a language from outer space

ACuriousMind

@EmilioPisanty Actually, Wegener is a variant of Wagner and has nothing to do with paths, but is the job title of someone who makes wheels.

@Slereah Yes. Yes, it is :)

0celo7

@BalarkaSen not sure I want to do CW

Your answer is already really long

skullpatrol

18:17

Wagon wheels? @ACuriousMind

ACuriousMind

@skullpatrol Sure

Balarka Sen

@0celo7 Totally fine

skullpatrol

:)

Anonymous

"wheels" ----> "movement" ----> "plate movement"....still related

skullpatrol

mnemonically, yes

Emilio Pisanty

18:18

@ACuriousMind yeah, well, the resonances are still there

0celo7

@BalarkaSen help me with my thesis pls. It’s too much work

skullpatrol

Stop asking a high schooler to do your work :P

Emilio Pisanty

@0celo7 I can help with some perspective.

All your other theses will be harder.

skullpatrol

^

much harder

Slereah

Such complaints

I'd love to be writing a thesis

Instead of doing some boring websites for ugly people

Hey @ACuriousMind, does that seem like an alright proof

0

A: Discontinuity of metric derivatives in the Israel junction formalism

I am you from the future. Here's a probably fine argument for this. Take the normal bundle of the hypersurface $N = (-1, 1) \times \Sigma$, with the adapted coordinates $(r, y)$ such that $\partial_r$ is a vector normal to the hypersurface. We can decompose the metric tensor as $$g = g(\partia...

ACuriousMind

18:26

That seems like a question for the ocelot

Slereah

the ocelot

ditto

0celo7

Are you talking about me

Slereah

Are you the ocelot

Balarka Sen

have you killed someone called desdemona yet

0celo7

@BalarkaSen I’ve killed her in every run I’ve done.

Fuck the railroad

Slereah

18:33

Replaying Fallout 4?

0celo7

No, playing Hitman and PUBG right now

And trying to bound subcritical Yamabe energies

Slereah

the most dangerous game

Emilio Pisanty

21

Q: Is Starman in the Tesla Roadster a real human?

I first need to know if starman is a real human or a robot. If he is a real human, how does he live? How many years can he live in that car?

oh, man, that's magical

hey @ACuriousMind can you migrate this one physics.stackexchange.com/questions/386275/…?

ACuriousMind

@EmilioPisanty I'm not confident enough it's on-topic there to do so immediately, but I've asked the academia mods whether or not they want it.

Emilio Pisanty

@ACuriousMind relevant

@PeterTaylor although it is a little bit of an XY problem, I think this would fall under university-level pedagogy because it is about teaching/learning/education. — StrongBad 2 hours ago

by an Academia mod

ACuriousMind

18:45

Alright, good enough for me

skullpatrol

rip

ACuriousMind

@skullpatrol ?

skullpatrol

The question can now "rip."

loocsieulb

lol.....

Emilio Pisanty

ooooohhh, is today an HNQ-fueled rep-cap day?

haven't had one of those in a while

skullpatrol

19:09

+ Valentino's day

Slereah

A thought for Saint Valentine plz

Balarka Sen

the old hag

skullpatrol

How long were you banned for? @BalarkaSen

Balarka Sen

5seconds

0celo7

@BalarkaSen do you want to help me with alg.top?

skullpatrol

19:16

What a joke.

Balarka Sen

i liked the joke

skullpatrol

in Mathematics, 11 mins ago, by Mike Miller

Apparently "i should minimize my use of curse words" was flagged

Balarka Sen

@0celo7 sure

Loong

actually 37 s

0celo7

@BalarkaSen there's something called the Rosenberg index that's linked to positive scalar curvature

the problem is the paper on it is completely ridiculous

Semiclassical

19:17

@EmilioPisanty it's been moved now. which, as an unintended consequence, means that the formulas don't render by default. (mathjax is enabled by default on PSE, MSE, MO, etc but evidently not on Academia SE.)

0celo7

I'll learn the K theory this summer but don't have the time now

Emilio Pisanty

@Semiclassical ah.

interesting

0celo7

S. Stolz, Simply connected manifolds of positive scalar curvature. \emph{Ann. of Math.} \textbf{136}, 511-540. 1992.

Semiclassical

@0celo7 Ridiculous as "I don't believe it" or "I can't understand a word of it"?

0celo7

the second

Semiclassical

19:19

right

0celo7

it's like bordism and BSpin and KO theory

Semiclassical

yikes

0celo7

stuff I don't know at all

Balarka Sen

i have le paper

0celo7

@BalarkaSen so if you can tell me what the rosenberg index is, I would be mucho happy

Balarka Sen

19:20

Ah this does look bad

What is $\alpha$ in this paper

0celo7

an index of Fredholm operators related to the Dirac operator

I need to read Michelson and Lawson

blargh

Balarka Sen

This looks totally foreign to me. Sorry

0celo7

@BalarkaSen My best bet is probably to read all of Michselson and Lawson, eh?

and then see if makes sense

Balarka Sen

Shrug

0celo7

$T:\mathrm{MSpin}\wedge \Sigma^8\mathrm{B}G_+\to\mathrm{MSpin}$

ugh

what?

Balarka Sen

19:24

I can probably unwrap that bit for you

0celo7

@BalarkaSen maybe later, I still have to finish the rest of this chapter

Balarka Sen

Okay.

0celo7

I still have Kazdan-Warner which will probably take a week to write out

Balarka Sen

I love their theorem

0celo7

you only say that beacuse Mike does

the proof is not nice

Balarka Sen

19:26

naw its cute

I can believe that

Geometry is never nice

Slereah

@0celo7 wot

0celo7

@BalarkaSen You should read this thesis when it's done. It's quite self-contained if you believe my references to the elliptic PDE literature

Balarka Sen

I'd love to

skullpatrol

me too

0celo7

in particular I actually write out in detail how one solves elliptic PDEs

@Slereah I have no idea

Slereah

19:30

Is $MSpin$ the spin bundle or something?

0celo7

I have no idea

Balarka Sen

It's the Thom spectra whatever that means

Slereah

Also $\Sigma^8$ is a weird thing

You don't see a number as high as $8$ often in math

Balarka Sen

8 fold suspension

Slereah

what is an 8-fold suspension

Is it when you were very naughty at school

Balarka Sen

19:33

suspend 8 times yes

Slereah

though I guess that would only be a 2-fold suspension

0celo7

why should one suspend 8 times

Slereah

I kinda wonder if you can generate CTCs just from expanding a wormhole

The induced metric component for $g_{tt}$ does depend on $\dot r$

Also what's a good way to generate arbitrary shapes for the mouth, I wonder

For $S^1$ I can just use a Fourier series

Does that process generalize to $S^n$?

0celo7

ah shit

I tried to simply something and now it's coming back to bite me

Slereah

Can I generate all manifolds $\cong S^n$ via some Fourier legerdemain

0celo7

19:38

I have to add an epsilon, what a pain!

Slereah

Oh wait

Can I just use spherical harmonics for that

To define arbitrary spherical shapes

apparently so, yes

0celo7

I need three monitors

Slereah

20:00

is there a simple embedding for cubes in $\Bbb R^n$

One that I can do with only one chart

In spherical coordinates maybe

0celo7

20:14

@Slereah can I become french

I think that french people get analysis superpowers

Slereah

Apparently not

i am bad at analysis

0celo7

proof?

Slereah

I don't have a proof

which is proof

0celo7

@Slereah what are you stuck on

Balarka Sen

@0celo7 What is the Sobolev class $H^1 = W^{1, 2}$

pls enlighten me

Slereah

20:20

right now not much

but overall I am not v. good

0celo7

@BalarkaSen why are you subjecting yourself to this

what is the context?

@Slereah you haven't practiced

Balarka Sen

reading page 6 of arxiv.org/pdf/1406.3107.pdf

Slereah

yeah

alas it's harder these days

where I have to actually work

0celo7

@BalarkaSen ugh

Sobolev into a manifold?

Ok take what I'm about to tell you and use Nash embedding

@BalarkaSen Let's consider an interval $[0,1]$ and maps $u:[0,1]\to\Bbb R^n$, so curves

Balarka Sen

OK

0celo7

20:23

For a smooth $u$, we consider an energy $$\|u\|_{H^1}^2=\int_0^1[|u|^2+|u'|^2]$$

Balarka Sen

Mmkay

That expression is less foreign to me now

0celo7

now that if we just take $$\|u\|_{L^2}^2=\int |u|^2$$ that's just the L^2 norm

Balarka Sen

True

0celo7

and if we complete $C^\infty((0,1);\Bbb R^n)$ wrt. this, we just get L^2

Balarka Sen

I agree

0celo7

20:25

technically, you take the completion of those smooth functions for which that is finite

Balarka Sen

mhm

0celo7

after all, something like 1/x won't be in that class

so to get $H^1((0,1);\Bbb R^n)$, you take the completion of those smooth functions whose $H^1$-norm is finite

Balarka Sen

Makes a chunk of sense

So in my case I'm just using the Riemannian metric on $M$

for $|\bullet|$

0celo7

Now the key is that the derivative operator is clearly defined on the smooth functions, say $C^\infty\cap H^1$, and defines a bounded linear operator into $L^2$

so you can extend the notion of differentiation to all of $H^1$

Balarka Sen

Ahh

0celo7

20:27

and the "derivative" of a function in $H^1$ is a function in $L^2$

this is a stronger notion of derivative than the distributional derivative

it has all of the same properties, however

Balarka Sen

That's pretty dope

What kind of functions can appear as limits of smooth functions under the H^1 norm? How badly discontinuous?

0celo7

They turn out to be absolutely continuous in this baby case

Balarka Sen

huh

0celo7

that's because they are integrals of their derivatives

Balarka Sen

I see. L^2 fails there because I don't include the u' term

Maybe the right question is, how badly non-differentiable?

0celo7

20:30

Any AC function is in there, I think.

So differentiable a.e.

Balarka Sen

Ah

cute

0celo7

Actually, I think $H^1\subset AC$ is strict because of stuff near the boundary

Balarka Sen

Gotcha

0celo7

But you can have nasty stuff in the interior for sure

But if you have $H^2$ functions, they are $C^1$

This is called the Sobolev embedding theorem

exercise: prove it using what I've told you

(I think it can be done using what I've said)

Balarka Sen

shite. H^2 being $\int (|u|^2 + |u'|^2 + |u''|^2)$?

0celo7

20:32

yes

hint: where does the derivative of an $H^2$ function live?

(weak derivative)

Slereah

Florida?

Balarka Sen

$H^1$, doesn't it?

0celo7

yes

Balarka Sen

'Cuz I got $\int(|u'|^2 + |u''|^2)$ finite

which is the $H^1$ norm of $u'$

Slereah

Per Geroch-Traschen, I think an embedding that's not $C^1$ is gonna have Problems

wrt to the stress energy tensor

I'm not 100% sure why

Either the metric isn't gonna be locally bounded or the connection won't be square integrable

0celo7

20:37

@BalarkaSen so the derivative is AC...meaning?

Balarka Sen

It's $C^1$. Fun.

0celo7

That's the idea. I think there's a detail missing because that shows the weak derivative is AC.

But whatever, no one likes measure theory

Balarka Sen

hahah

thanks man this was a nice little intro

0celo7

np

if you only have to work on the line you're good

Emilio Pisanty

0

A: Does light actually travel through glass?

The short answer to the core of your question, do the particles that make up the glass absorb the waves and re-emit them in the forward direction? Or do the light waves manage to travel through the glass, without being absorbed and then exit the glass? is that both processes are at play, th...

gah

Balarka Sen

20:41

They're upgrading to $H^1$ paths because they want $\Omega_{p, q} M$ to be Hilbert and not just Frechet

Emilio Pisanty

that took much longer than intended

0celo7

I saw that. It seems reasonable.

no one understands Frechet spaces

Balarka Sen

infinite dimensional stuff are too weird

0celo7

@BalarkaSen When I'm 70 I will write a 10-volume saga on this stuff

but that's far away

Balarka Sen

I'd read it and praise the 0celord

Slereah

20:45

0 dimensions is all you need

Emilio Pisanty

doi.org/10.1103/PhysRev.33.195

Slereah

What's the covering dimension of the discrete and coarse topology, anyway, is it $\operatorname{Card}$ and $0$?

Emilio Pisanty

> L Tonks and I Langmuir

lolz

Slereah

Wait, or are they both 0 dimensional

I'm not sure

Balarka Sen

@0celo7 If you have the time and energy, want to explain why $\nabla_{\gamma'} \gamma' = 0$ is an elliptic equation (what are those?) and why that implies $H^1$ solutions are smooth

Sounds like regularity theory - right up your toes

0celo7

20:50

Yes, this is in fact one of the most ridiculous things I've ever heard.

I blame the fucking French

Balarka Sen

lol why so

0celo7

Using elliptic regularity for ODEs -- completely ridiculous

Balarka Sen

lololol

0celo7

it's a French thing

Slereah

hon hon hon

0celo7

20:52

@BalarkaSen Consider an operator $L=a^{ij}\partial_i\partial_j+\text{LOT}$ on $\Bbb R^n$

Balarka Sen

Mhm, so got a second order PDE hanging in there in the linear part

skullpatrol

How early do they start teaching English in France?

0celo7

assume the matrix $A=(a^{ij})$ is smooth, so we can write this as $Lu=\partial_i(a^{ij}\partial_ju)+\text{LOT}$, aka "divergence form"

Slereah

@0celo7 if I have a geodesic equation of the form $$\ddot x^\sigma + \theta(x)({\Gamma^\sigma}_{\mu\nu})^+ \dot x^\mu \dot x^\nu + \theta(-x)({\Gamma^\sigma}_{\mu\nu})^- \dot x^\mu \dot x^\nu$$

0celo7

I'll just stop writing the LOT part, but imagine some $b^i\partial_i+c(x)$ hanging out there

Balarka Sen

20:53

Righty ho

Slereah

Is the result still unique

Balarka Sen

oh LOT means Lower Order Terms not Lots Of Terms

silly me

0celo7

lol

We say that $L$ is elliptic if its eigenvalues are all positive

Balarka Sen

Eigenvalues of $A$?

Sounds reasonable

0celo7

yeah eigenvalues of $A$

We usually impose uniform ellipticity, meaning $\langle \xi,A\xi\rangle\ge \theta|\xi|^2$, $\theta>0$ for every $\xi\in R^n$ and everywhere on the domain of $A$

So a uniform positive lower bound on the smallest eigenvalue

Balarka Sen

20:57

Mmm I see

0celo7

Ok so take some $f$ in the dual of $H^1$, or just $L^2$ if you like

Balarka Sen

Okie dokie

0celo7

We say that $-Lu=f$ in the "weak sense" or "$H^1$ sense" if $$\int\langle Dv,ADu\rangle =\int fv$$ for every $v\in C^\infty_c$

Slereah

Man all existence theorems for ODEs involve continuous functions

tough

0celo7

Now using this, and hard work, you can show that in fact $u\in H^2$ automatically

Balarka Sen

21:00

Strange notion but I have seen this before

@0celo7 woo

0celo7

@BalarkaSen it's just using weak derivatives

you can check that if things are smooth, this is completely equivalent to the classical notion of solution

Balarka Sen

True

0celo7

use the Gauss-Green theorem

Balarka Sen

That'd make sense

Sir Cumference

Humanity needs 8 day weeks, so we could have 3 day weekends...

0celo7

21:02

@BalarkaSen Now in the case of the geodesic equation, you just get $A=1$, which is clearly uniformly elliptic

but using this theory for ODEs is really a nuke

Balarka Sen

:P right, it's a 1x1 matrix with only entry 1

Wait but u \in H^2 means I get a C^1 solution. Is it trivial to see why we can extend that to C^infty?

0celo7

What I said is true for any dimension

And $H^2$ functions can be very bad in $\Bbb R^2$, for instance

Sobolev embedding depends on the dimension

Balarka Sen

Ahh right

skullpatrol

But 5:7 is not the same as 3:8 @SirCumference

0celo7

H^2 might be BMO in R^2, not sure...

@BalarkaSen well you get $H^2$, which is fine

so now suppose $f\in H^1$

Sir Cumference

21:05

@skullpatrol Who says the ratio needs to be the same?

0celo7

then you can differentiate the equation in a sense and get another equation

and then get $u\in H^3$

Balarka Sen

I see

0celo7

eventually $u$ is in every Sobolev space, and so is $C^\infty$ if $f$ is

skullpatrol

Society says @SirCumference for the sake of the GDP :P

Balarka Sen

magical

where can I find a reference for learning this stuff as a mortal?

Warner?

0celo7

21:07

I've had a fight with Jack Lee about Warner

I don't think it's very good, especially not for an introduction

Balarka Sen

loool

0celo7

Read Evans like everyone else

Balarka Sen

Full name?

(of the book)

0celo7

PDE

Balarka Sen

no copyleft available in libgen

ok its elsewhere

0celo7

21:09

lies

I have it

get the second edition...

Balarka Sen

got it

0celo7

@BalarkaSen Also get Brezis, Functional Analysis, Sobolev Spaces, and PDE

Balarka Sen

i'll save it for future use

@0celo7 noted accordingly

Slereah

that is theft

i'm calling the police

Balarka Sen

don't use such vulgar unparliamentary words

say copyleft

0celo7

21:11

@BalarkaSen Wells, Differential Analysis on Complex Manifolds

it's a very algebraic approach to this stuff

Balarka Sen

thanks for all the refs

i shall head off to bed now

0celo7

@BalarkaSen oh that's just the L^2 theory

for scalars!

you need to know the L^p theory for nonlinear vector-valued minimizers

Balarka Sen

wai tho

thats my response

0celo7

suffering is good

Balarka Sen

analysts are basically sadomasochists

0celo7

21:17

@BalarkaSen there's also a very weak theory

where one interprets the equation completely in the distributional sense

Balarka Sen

i see

skullpatrol

cya

0celo7

this is important if you don't know the integrability of your weak solution

Balarka Sen

right good point

0celo7

but then you need the negative Sobolev spaces

dmckee

21:19

@EmilioPisanty That one got away from you, didn't it?

Those questions are very hard to answer well because of the tension between needing to keep it simple and actually trying describe the full implications of the theory.

I think there is a very real limit to this sort of thing for reasons I mentioned in a comment under a similar question

skullpatrol

Did you see the one they shipped off to Academia.SE?

Emilio Pisanty

@dmckee how'd you mean?

dmckee

@EmilioPisanty The complexity of the answer rose steeply after the opening lines. Mind you, I like it better than I like Ján's answer, which I think is mathematically defensible but not helpful in developing a useful picture of what is 'really' happening.

Emilio Pisanty

21:34

@dmckee hmmmmm. Maybe I should reread that answer.

@dmckee Yeah, I guess I see where that comes from

dmckee

@EmilioPisanty Depends. I read the original question as implying that the OP was not particular sophisticated. If that's a correct reading and they were your intended audience then it might be an issue. If you mean it as definitive treatment for better prepared reader then it's fine as it is.

Emilio Pisanty

@dmckee I probably did want to aim for OP's level but I don't know how to simplify further

dmckee

Yep. Hard problem, so there is a lower limit on how simple the answer can be. No help for that.

Emilio Pisanty

Hopefully even the technical parts will be useful, at least for flavour

@dmckee while you're here, can you take a look at my latest flag?

Pieter

@dmckee It would need figures. And even then the answer would probably become too long and too difficult to read for people that think in terms of bullet-photons.

Emilio Pisanty

21:40

There's a horrendously long chatroom conversation for background

But the short of it is that OP makes assertions about how they were treated that are plainly false (and for which OP repeatedly refused to provide textual support for under explicit prompting) but which don't really need moderator adjudication anyways because they don't belong on the question to begin with.

dmckee

@EmilioPisanty Oh. My.

Emilio Pisanty

I repeatedly prompted OP to implement suitable edits but eventually jumped in as it was CW. OP then rolled back the edits and I feel moderator action is required on the edits.

@dmckee yeah, it's that one that got away from me

dmckee

Okay. I've taken a crack at it, and will bring it to the attention of the rest of the mods as well.

Emilio Pisanty

thx

@dmckee your version looks good to me.

@dmckee You might want to shadow mod edit that 'a argument' though

=P

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