@ACuriousMind I swear to god what I'm proposing here is what Yau did :(

I must be missing something

@ACuriousMind Ah, Fredholm alternative. Do you know it?

Yes, it would say that for $\mu$ not an eigenvalue, $L$ is a bijection.

Basically, we know that since $Lu=0$ is a Dirichlet problem and $D$ has nonempty interior that $L$ has no kernel on the appropriate Sobolev spaces. So we can solve the problem $Lv=-\mu$, $v=0$ on $\partial D$ uniquely.

Then letting $f=v+1$ gives the result.

@ACuriousMind Yep

Yeah, I agree, that works

There's a hypothesis that the first nontrivial Dirichlet eigenvalue of $L$ is positive

(I need to check that one too)

@ACuriousMind So Yau gives a hint to look in chapter 6 of Gilbarg & Trudinger, but Li says nothing -.-

Would it have killed him to say something?

@ACuriousMind Of course, I haven't checked the Fredholm alternative on manifold sobolev spaces...

@0celouvskyopoulos Do you need to? I don't know much about its proof, but it's just a statement about compact operators on Banach spaces, isn't it?

@ACuriousMind It is, but I don't really trust any of the "proofs" out there for Rellich's theorem on manifolds with boundary.

It's morally true :D

@ACuriousMind This is a mess. Aubin defines "elliptic" to mean $a$ in $L=a_{ij}D_{ij}+\cdots$ is positive, but then defines $\Delta=-\nabla^2$ so that $-\Delta$ is elliptic -.-

@0celouvskyopoulos :P Spacelike intervals are the silly things!!! Might as well give them the minus signs!

Your name...it has...mutated

yes

Hmm. So Yau uses the maximum principle but he has a zero order term

Whoops

Into the trash I guess

Maybe that's why Li uses this strange argument

@ACuriousMind Ok, so assume $f\ge 0$ in $D$. Claim: $f>0$ in $D$. We have $\Delta f+\mu f=0$. Since $f$ is smooth, $\Delta f$ and $f$ are continuous and attain extrema. So for $a$ very negative we have $\Delta f+af\le 0$. Let $u=-f$, then $\Delta u+a u\ge 0$. Apply the maximum principle: the maximum occurs on the boundary. But there it's nonzero.

Studies showed the CMB cold spot is unlikely to be a supervoid of any size or shape. They suggest other possible explanations including 1:50 chance occurence, inhomogeneities or defects in the early universe topology, or possibly Remanent of collision with other universes

Howdy

@0celouvskyopoulos Jesus

@SirCumference Yes, my son

This is getting out of hand

Flee, you sinners, before this entity assumes the $10^25$ names of God

Can I ask a question?

I mean is anyone active now?

depends on the question

A pulley system question (mechanics)

Can I?

$$\def\avint{\mathop{\,\rlap{-}\!\!\int}\nolimits} \avint_A f(x)\,dx = 1$$

^neat

@MadhuchhandaMandal I don't promise I'll answer.

Ok Still I am giving it

In this question, why conservation of energy is not working?

(I can do it using impulse)

how are you doing it with conservation of energy?

Initial energy of body A+ body B= Final energy of body A+ body B

and what are each of the terms?

So , (1/2) m * 0 + (1/2) m (2g) = (1/2) m v^2 + (1/2) m v^2 [Since by constraint, velocity of both the body must be same]

Solving for v, I get different answer than that when I apply impulse

what is 1/2 m (2g)?

what's wrong with mg

The energy acquired by body B just before the string is taught

(I represented like that for clearity)

Trying to find a GR solution which has oscillating wavelike time dilation effects

It is known that the vacuum solution does not admit that direction of oscillation

But are there more nontrivial wavelike solutions that admit oscillation in the time coordinate?

$$⚭=⟳\mathcal{T}(\frac{⚭}{⥁}\int^࿇ ◌^☉ d\mu)$$

@JohnRennie are there any wavelike solutions in GR that describe something that is similar to oscillation in the amount of time dilation in a region of spacetime. I only knew that there does not exist one for the vacuum solution, but I am not sure about more nontrivial cases?

@Secret any gravitational wave does that

If I had gravitational wave described by the metric $\eta_{\alpha\beta}+h_{\alpha\beta}$ where $h_{\alpha\beta}=diag(0,1,-1,0)$, it can be found to be propagating in the z direction and oscillating in the x and y direction (where x and y are antiphase to each other), but since the time component is also 0, does it mean it is propagating in the t direction as well?

In the weak field case the time dilation is related to the Newtonian gravitational potential by $$\frac{dt_1}{dt_2} = \sqrt{1 - \frac{2\Delta\Phi}{c^2}} $$ where $\Delta\Phi$ is the difference in the potential.

Anything that changes $\Delta\Phi$, like a GW, will change the relative time dilation, though in the case of a GW the change will be vanishingly small.

ok so in that case we can have gravitational time dilation that varies in magnitude as the wave pass through the region since GW changes the $\Delta \Phi$?

@ACuriousMind for the next two years at least shipping laptops anywhere in the EU is trivial. Shipping laptops to India is a complete nightmare. I know India are just trying to protect their growing home industry, but their import rules are a complete nightmare. Even eBay won't ship to them.

India is the one of the few big economies excluded from the eBay shipping program because of the hassle involved.

@Secret yes.

I see. Next question: We knew that the wavevector of any wave gives its direction of propagation. Analogously we should be able to assign a wave-4-vector to show the propagation of gravitational waves in spacetime. Looking at the above metric, it is clear this wavevector will have a z component, but does it also have a t component as well since it is a propagating and not a stationary wave?

A gravity wave just follows a null geodesic in the same way that a light wave does.

just look up the G wave metric

Ah yes, forgot that it travels at the speed of light

Hi, I had a doubt.

Which bond does exist in TiO?

Ionic/ Ionic + covalent?

I don't think people will know it off the top of their head

Just look up a reference book

The handbook of physics and chemistry probably has it

Wikipedia said it is an ionic solid with vacancies

(Although TiO molecules does exists in interstellar space, the context of your question suggest you are dealing with the solid)

So Ionic?

Ic.

Ti is transition element right?

But covalent does exist?

Anything even negligible couldn't be ignored.

Ti is a d block metal thus transition metal

Ohk.

@Kaumudi.H anti-virus still behaving itself?

I like the first sentence of "Lost causes in physics"

"This subject has been thoroughly worked out and is now understood. A thesis on this topic, even a correct one, will not get you a job."

Short and to the point

Oh no

Jammer is now doing math on theories

"We assume that a theory $T$ contains three observational terms $a$, $b$ and $c$, denoting, for example, certain set-theoretical predicates, and three theoretical terms $x$, $y$ and $z$ which will soon be specified more closely. We also assume that the formalism $F$ of $T$ contains as (primitive) "logical" constants" equality, assumed to be reflexive, symmetrical, and transitive"

etc etc

@vzn, Bell's just seems to come up in casual conversation sometimes, I think when I'm chilling with Dan Bells equality has come up twice, and sometimes I get into interesting philosophical discussions that take a quantum route and people will all the time challenge me on the true random part

@Kaumudi.H Hi :-)

Everything OK laptopwise?

It's been a tiring few days then? :-)

See you in a bit then. I'm finally getting down to that programming job that I managed to procrastinate over yesterday, so my latency may be a bit high today.

@JoshuaLin Yes. $S^2\times \Bbb{RP}^3$ and $\Bbb{RP}^2 \times S^3$ - both are double covered by $S^2 \times S^3$.

So they have the same homotopy groups in all dimensions ($\pi_1 \cong \Bbb Z/2$) but they are definitely not homotopy equivalent.

@Kaumudi.H Cool (literally :-)

If you want we can uninstall AVG and go through th reinstallation, though whether it's worth it is debatable.

Do it now?

To uninstall just open Control Panel then Programs and Features and uninstall from there

OK. I'm going to run through the install on my test PC so we're looking at the same screens. Please don't leap ahead an click things during the installation until we've agreed what options we're going to choose.

How are we doing?

You've still got the AVG_Protection_806.exe installer from yesterday?

OK, run it.

Can do. Did you get TeamViewer installed?

OK run teamviewer and give me your ID. e-mail me the password so all the hackers here can't see it :-)

The ID is the 8 digit number

The password is the four digit number

Hmm, no mail yet ...

Mail can take a little while to work its way through the chain of SMTP servers ...

"Heisenberg's objections-for example, that Planck's basic radiation law could not be understood at all within the framework of Schrodinger's interpretation-were regarded as pedantic"

look at that nerd

@Kaumudi.H Still no mail. I've just mailed you. Have you received it?

gonna watch Lynch's Rabbits today

@Kaumudi.H or can you text me the details?

@BalarkaSen It's a good show

"If all this damned quantum jumping [verdammte Quantenspringerei] were really to stay, I should be sorry I ever got involved with quantum theory"

Aha! Got it. Right, I'm about to try and connect. You'll get a prompt to allow the connection.

It works! :-) Would you like to run the installer?

@Kaumudi.H Run the installer ... ?

OK I'm going to choose the custom install (once the download is complete)

@JoshuaLin See this MO thread, counterexamples include the closed topologist's sine and the product of Eilenberg-Mac Lane spaces for any given space.

I normally install only the top two option

Hacker attacks is a firewall, but Windows already has a firewall

Private data can do encryption, but Windows already has encryption built it

And payments shield attempts to spot phishing web sites but (a) it's a bit hit and miss and (b) you have a brain to do that :-)

OK to proceed?

Hello@yashas

@Maxwell hi

What's the question? :P

@Yashas, would you like to share your opinion on this question physics.stackexchange.com/questions/328686/…?

I have added my teachers logic as well

Wasn't it discussed before?

He used F = ma :|

You get F = ma from the 2nd law

@yashas , but I didn't show you the teacher proof earlier

You get the concept of inertia from the first law

mass is the measure of inertia

@Kaumudi.H I doubt the TeamViewer link would be fast enough for that. As a general rule video won't play over this sort of link.

When you're streaming video it's heavily compressed to squeeze it through the restricted Internet bandwidth. But TV can't do that level of compression.

If you want to watch video now I will have to disconnect the TV session then reconnect it to complete the install. Let me take a quick look now before you do that ...

meh forrest gump is ok

@yashas, so d correct or b?

I dono

I don't like his explanation

I would mark D

I feel so weird now after looking at that proof.

@yashas, what's the defect/ where is the defect? So that I could say him about that.

The concept of inertia is defined from first law.

@Kaumudi.H restart now?

@yashas, yeah. Then

The first law says that a body has inertia: it tends to continue its motion unless acted upon by an external agent. This defines the concept of inertia and mass.

@yashas, is it over?

Momentum is defined as mv :/

I don't like this now lol

Newton's second law uses momentum

I don't know what the definition of momentum is

@yashas, please pinpoint his mistakes so that I can aware him.

@Kaumudi.H can you mail me the password again - the password changes each time

I don't know

@yashas, so what's the angle of dip and declination?

@Maxwell declination is the angle b/w magnetic meridian and the geographical meridian

I think I have got the spelling of meridian wrong

nvm it was correct

the angle of dip is the angle b/w the magnetic field and the horizontal component

@yashas, what is magnetic meridian and geographical meridian?

.

@Kaumudi.H providing further evidence that my taste in films are strange :)

@Maxwell Magnetic Meridian and Geographical Meridian

@yashas, Do you know Mr. Pradeep Khsetrapal?

Nope

I have heard of that name somewhere

@yashas, I guess so. He is a physics teacher as far I know

Is there a source for quantum interpretations that don't drag you through the entire history of quantum mechanics

It's a bit tedious to go through a hundred year of quantum theory for that

@Kaumudi.H everything should be fine now. Remember to do an initial scan some time soon.

@Kaumudi.H It's several days work. But I'm making good progress.

@Kaumudi.H You keep doing everything other than studying? lol

Walking is studying the road, for sure.

@Yashas Sometimes, studying life might be more worthwhile than studying books :P

@ACuriousMind How about this?

JEE Advanced is less than a month away.

if JEE Advanced is the only thing worth studying for to you, I feel sorry about that

:|

I did not mean that

@paracetamol it's fitting, I guess.

@BalarkaSen I liked the iff :P

Woo!! I'm off the hook! \o/

^ @rob :3

@ACuriousMind well I might have many reasons to feel sorry, the "only if" part wouldn't apply

Is there an orthocetamol?

No ._.

There is an orthocresol, however ;)

@BalarkaSen I know, but I liked the bizarre mindset the iff implied - you can only feel sorry for people to whom JEE Advanced is the only thing worth studying. I didn't actually approve of the message with "iff", I just liked it.

Apparently there is ...

...and a paracresol too ._.

@JohnRennie I thought you were talking about an SE user -_-

Anyway, I'm back to the coding grindstone. More chat later.

o/

Giving someone nothing but heavy water to drink is a great prank

@ACuriousMind Sounds 0celo-ish to me.

"I'm drinking all that water and still I'm dying of dehydration!"

Classic prank

@Slereah Brine does the trick ;)

Brine tastes fairly briny

I don't think heavy water tastes different

I did not mean to say study just because they would need to write JEE Advanced. It is an important exam which decides college so it is something which shouldn't be ignored?

@Slereah No...no it doesn't :(

sniffs

Gauld calls the manifold $\Bbb R \times \Bbb L^+$ the "long drink"

@Slereah $\mathbb{L}^+$ being the long line? Why call it the "long drink"?

@JohnR Oh wait, I forgot! I tried melting the cheese the other day! Quick, ask me how it went!

I guess because it looks like a very tall glass

@Slereah Hmm? Would that rather be something like $S^1\times\mathbb{L}^+$?

It's like a three miles island tea, except $\omega_1$

Oh right

I must be misunderstanding something, since $\mathbb{R}\times\mathbb{L}^+$ looks rather like a version of the plane to me where one direction is "more infinite" than the other

Actually the long drink is some manifold called $\Lambda_{0,1}$

Not exactly sure what it is

let's see

That was pretty damn scary for a sitcom.

It's great

plus it's adorable because everyone is a bunny

i liked the laugh tracks to the seemingly random dialogues

@Slereah Bunnies? WHERE?! ಠ_ಠ

Sighs

I like (real) bunnies :3

Try Watership Down, then

it also has bunnies

^ Real 'uns?

well, realistically drawn ones

This one has a sad ending too.

@Slereah I guess that's good enough for me! ^_^

I should watch more of Lynch but it's very scary. Lost Highway scared the hell out of me.

god knows what really goes on his mind when he does those transcendental meditations