12:21 AM
@BalarkaSen Ok, so I have to integrate by parts for this to work. Recall Green's theorem $$\int_M (h\Delta f+\langle\nabla h,\nabla f\rangle)\, dv=\int_{\partial M} h \, \nu f\,d\sigma,$$ which holds for $h\in C^1(\bar M)$ and $f\in C^2(\bar M)$.
So if $\nu f=0$, like I am hoping, then $$B_f(h)=\int_M(h\Delta f+\langle \nabla h,\nabla f\rangle)\,dv=0$$ for any $h\in C^1(\bar M)$. Assuming $M$ to be compact, we find that $B_f$ is bounded. But $C^1(\bar M)$ is dense in $H^1(M)$, so $B_f$ extends to all of $H^1$. Also, its $H^1$ operator norm is zero...so it is the zero operator. This means I can integrate by parts even with Sobolev functions!
I think my program can work, but there are still more details!
@BalarkaSen The proof I had in mind was actually ridiculously complicated. Hint for a better one: Let $\mathfrak{iso}(M,g)$ denote the space of Killing vector fields on $(M,g)$. (i) Show that $\mathfrak{iso}$ is a Lie algebra. (ii) Show that for any $p\in M$, the map $\mathfrak{iso}\ni X\mapsto (X_p,\nabla X_p)$ is linear and injective.

12:48 AM
the thesis I'm reading says "We focus on
integrated systems [...]". What is an integrated system/how is it different from a non-integrated system.

@heather part of a larger system

ah, okay.
thank you.

It might make more sense for me to use the pressure from an analytic perspective

1:45 AM
@0celo7 Will you smite me if I give it to you in cgs units?
Try something on the order of $\sim10^{24}\text{ dynes cm}^{-2}$.
That figure I gave you for density was towards the upper end of the spectrum; so too is this.

1:55 AM
@0celo7 I should use Mathematica more often.

@HDE226868 Not me. I'm open minded.

@dmckee Good to know.
It took me two years to start thinking in SI units, as opposed to imperial.
Not sure how long it'll be 'til cgs becomes a bit more normal.

2:12 AM
@HDE226868 what the hell is a dyne
@HDE226868 Ideally I would have it in $G=c=\hbar=1$ units

@0celo7 I've said too much already.
$10^{-5}\text{ N}$, though.
@0celo7 Not doing that conversion for you.

@0celo7 I need to know if the cosmic event horizon's distance changes in a universe with $w = 2/3$
Or alternatively if the scale factor increases exponentially

@HDE226868 it would probably be easier to just put in the cs and Gs into my code

@0celo7 So are you doing a full relativistic treatment?

2:35 AM
@HDE226868 of course
@JohnRennie After several hours I got a crash on the same map in the same spot (ish)!

3:02 AM
@HDE226868 any idea for $K$ in $P=K\rho^\gamma$?

3:17 AM
@HDE226868 Oh, guess i should just plug in the pressure and density you gave me.

4:10 AM
@JohnRennie quick, what is the radius of a star in meters
on average
also good morning

$10^8$

@JohnRennie wow, I was several orders of magnitude off :)

Well it depends on what type of star. The Sun is about $7 \times 10^8$m.

@JohnRennie Right now I'm just playing around with the stellar structure equations
I seem to be getting 3,000 but this plot is for ants

4:13 AM
the $y$ axis here is...uh
not sure what's going on there
@JohnRennie I just told it to do the numerical integration out to $r=3,000,000$
I think I broke MMA
It's only using 9% of my CPU...cmon son
@JohnRennie Is the MMA software just not that good at high performance computing?

I don't have that much experience of using Mathematica. I really only use it for tensor algebra.

@JohnRennie If you know of another program that's relatively easy to use and can do massive nonlinear ODE systems, I'm all ears.

Maybe the more engineering orientated apps. Matlab possibly?

@JohnRennie I might try that. Never did a system in Matlab.
@JohnRennie How long should I let this disaster of a Mathematica script run?

I can't comment. Is there a way to run it with a coarser granularity or some other way to speed it up at the expense of lower accuracy? If so I'd start with a quick low accuracy run and gradually increase the accuracy.

4:28 AM
@JohnRennie I think I know what's happening.
The star radius is around 825,000 meters and I'm extrapolating to 3,000,000.

@0celo7 FFS, I practically gave you $K$ earlier

The ODE probably becomes horribly singular at the actual radius

@JohnRennie Know of any way for me to trace the value of the graph along the tail there?
the vertical axis is still messed up

Change the scale on the $y$ axis?

4:32 AM
@JohnRennie Yeah, or log it or something
Hmm, no, it's still 10E14 there.
this is a compact mofo star

Sounds like you've modelled a white dwarf ...

@JohnRennie computing mass now...
@JohnRennie are masses reported including binding energy or w/o?

I think the binding energy of even white dwarves is quite a small fraction of their total mass.

@JohnRennie what's your ballpark for the mass?

I've no idea. If it's a white dwarf then around 1% to 10% of the mass of the Sun I guess. Say $10^28$ kg.

4:47 AM
I can't get it to do the damn integral
this might have to wait for another day

@0celo7 Neutron stars can be on the order of 10km
It should be clear why stellar astronomy is cool :P
Hell, neutron stars are often 2-3 times the mass of the Sun

rubs eyes
this is future me's problem

You study nuclear science
You got a crazy teacher, he wears dark glasses
Things are going great, and they're only getting better…

@TheRaidersofLasVegas Uhhhh
@JohnRennie mathematica has this amazing ability to break itself even though the same shit worked a minute ago

5:20 AM
Welcome back @Cows

@Kaumudi.H I cheated. I ate some ice cream to keep me alive until the meal. Well, it was National Ice Cream Day after all :-)

What flavour?

Rhubarb

I've never tried that flavour.

Does rhubarb grow in India? I guess there will be areas cool enough for it.

5:25 AM
Yup.

It's a very traditional English dessert because it's well suited to the English climate. Go back a few decades and everyone used to grow rhubarb in their gardens. Even I had a rhubarb plant in my garden.

Don't like the flavour of it though.
Too sour.

It was ... OK. I probably won't buy it again.
@TheRaidersofLasVegas rhubarb contains a lot of oxalic acid, which makes it sharp. In fact the leaves contain so much oxalic acid that they are toxic. However you can put in lots of sugar to counteract the sourness.

I like maple walnut ice cream.

Mint choc chip is my favourite. And by quite a long way. But the rhubarb icecream was on offer at a reduced price and I was curious to try it.

5:32 AM
Praise Jesus
The error can be corrected now

user228700
5:51 AM
Hi, everyone :-)

user228700
@JohnRennie Rhubarb is a vegetable, no?!

@Kaumudi.H yes.

We all know John eats strange things.

Though it's normally served sweetened as a dessert.
Rhubarb crumble is very popular as a dessert in the UK.

user228700
Oh, wow, I see.

user228700
5:53 AM

Sandwiches for breakfast sounds good to me. Although I'm still feeling rather full from last night's meal so I'm not that entusiastic about food at the moment.

typical German breakfast

user228700
@JohnRennie Ah :-) I forgot to ask! What did u have?

"Diced lamb with ginger, garlic, coriander, peppercorn & whole red chilli, finished with

user228700
Didn't u have the same thing last time?

user228700
5:58 AM
@JohnRennie Was it good?

@0celo7 what?

@TheRaidersofLasVegas what?

It was very good. They cook lamb very well. Tender, but not overcooked.

user228700
Hmm, OK...

I have had the Hyderabadi gosht before, though I think I didn't have it last time.

user228700
5:59 AM
Wokay.

If you ask the chef nicely they will allow you to choose the lamb and slaughter it at your table :-)

user228700
Are u being serious?

No :-)
It was an attempt at humour - probably a poor one.

user228700
See, I didn't know because some restaurants may actually do that!

Dang, I would go to that restaurant
@BalarkaSen
we should find a place like that
perfect edge level

6:01 AM
@Kaumudi.H in the UK meat processing is heavily regulated because of scares like BSE. There's no way any restaurant would be allowed to do their own slaughtering.

user228700
@TheRaidersofLasVegas STOP.

@TheRaidersofLasVegas why were you at a restaurant with a monkey?

gotta sleep. PDE will have to wait for tomorrow
cheers, all

Goodnight

@Kaumudi.H sorry

user228700
6:02 AM
:38821722 You didn't need to delete it or anything.

I did.

user228700
It was quite gruesome even to imagine; I've lived my whole life in close proximity to monkeys.

Cya @0celo7

user228700
@0celo7 Goodnight!

user228700
@JohnRennie Ah, I see.

6:04 AM
It was a Chinese restaurant.

user228700
Man, am I excited about those sandwiches! I can't make 'em just yet because I'm waiting to take a shower because water supply around these parts is erratic.

user228700
@TheRaidersofLasVegas I guessed.

You're in Chennai? The water supply is erratic in Chennai?

user228700
Yes, of course.

user228700
I live in one of the better parts of Chennai, actually; the situation isn't supposed to be so bad around here.

6:06 AM
You hinted the family might move back to Kerala. Is that just some vague long term possibility?

user228700
I'm afraid so; it would depend on whether or not my sisters get admission in a good school at Kochi.

@JohnRennie Sounds interesting. I have seen Chicken getting slaughtered. Never seen lamb slaughtering.

"Afraid so" - you're not in favour of the idea?

user228700
If they do, they will move next year.

Is that closer to your school?

user228700
6:09 AM
@JohnRennie No, no, I am. Well, I dunno, actually; on the one hand, I'd be a lot less homesick and my sisters would have a chance at better education but on the other, I don't really want them to leave Chennai altogether; this place will always be home and I don't want to be able to stop coming back here.

user228700
@TheRaidersofLasVegas Huh?

Chicken slaughtering is gruesome, though.

@Kaumudi.H sorry miscommunication

user228700
Wokay.

Will your father be retiring, or getting a job in Kerala?

user228700
6:12 AM
No, he'll continue working with the same company; they have a branch at Kochi.

user228700
Sounds ideal, doesn't it?

user228700
I am, after all, hoping that my sisters do get admission at a much better school at Kochi so yes, I'd have to say that I am in favor of the idea.

@Kaumudi.H Quality of schools is overrated.

user228700
Sure, but you really dunno what my sisters' present school is like so.

Quality of students is the important thing, no?

user228700
6:17 AM
In primary school, I'd say quality of teachers is more important.

True dat.

@Kaumudi.H is that the same school you went to?

user228700
@JohnRennie No, no. I went to KVIIT. High school sucked for reasons other than raging hormones (our teachers didn't know very much) but primary school was the absolute best.

Duh... Students should study only from high School IMO. Let them enjoy their early childhood. Else, they would miss it.

user228700
They go to another school near my house. It's extremely difficult to get into KVs these days. Back when I was about to join, it was easier.

user228700
6:21 AM
@Sid I seriously disagree with you; primary school was important to me because it was the time when I developed a curiosity towards most things in this world. My great teachers may have had a huge role in that.

::makes popcorn::

I believe curiosity can be generated on its own. I don't believe teachers have a huge role to play there.

user228700
What do u mean by one its own?

Say, someone looks at the stars and wonders what it is all about. You don't need a teacher to tell you to look at the stars. I say that curiosity can be generated by everyday activities. You just need someone to patiently answer your questions.
which could be your parents, or teachers or elders, etc.

user228700
Had it not been for my sisters, I may have agreed with you; they don't ask any questions.

user228700
6:27 AM
And I don't believe that this is due to an inherent lack of curiosity/intelligence in them; I believe that this is because their teachers have made learning seem like the worst chore.

How old are they?

user228700
They're 11 (twins).

Hmm, this is actually the time they should be asking more questions

user228700
Yes.

user228700
Anyway, so that's why I think that primary school is important.

user228700
6:32 AM
OK, I think we have water again so I'm gonna go see about those sandwiches.

7:02 AM
mornin

hi pal

7:19 AM
@0celo7 i'd just burn my copy of Das Kapital to have a place like that
I noted your set of hints for that exercise.
@Sid Students should only study for high school International Math Olympiad? Damn, you have have some effed up syllabus in mind for us.

@BalarkaSen .... Damn. IMO=In my Opinion
Though, I would encourage anyone interested in Maths to go for Olympiads. They are loads of fun, if people are to be believed.

I know, I was just joking

Though, If students prepare for IMO, they don't have to study High school Maths anymore

It's not entirely true that IMO is universally fun for mathematics enthusiasts.

It's certainly true for math fanatics :P

7:34 AM
Under what condition is a curve of the same "magnitude" as its range
That is, a finite interval is finite
So that $\gamma((0,1))$ doesn't fuck off to infinity

user228700
The sandwiches were delicious!

What kind?

user228700
Cheese and tomato.

No lettuce?

7:37 AM
@Slereah This is epic

user228700
@skullpatrol Nope.

Those are squares @Slereah

@skullpatrol Not in the $\ell_\infty$ norm

Are those lines parallel? @Slereah

7:43 AM
Depends on the metric

@Avantgarde There was a game today(yesterday) at 23:30 UTC.

Cricket?

user228700
@JohnR: I've decided to revise for C.S a bit by watching this series on YouTube.

@Kaumudi.H If you find it interesting then go for it, though I'm not sure how useful it will be. Your course may be very different to the videos.

user228700
7:49 AM
I know, I know but I think it would help at least a little and it is interesting, yeah :-)

Always good to get a different perspective.
Crash courses are very "quick & dirty."

It's alright
CS is a snooze anyway

8:12 AM
Not if you read Knuth's Art of Computer Programming.

Snooooooze

Have you read his Concrete Mathematics book?

I did not
I have read a fair bit of computation theory
It's alright but odds are good you're not gonna do that in a CS class

@Slereah if you do a reasonably theoretical course in CS, that sort of stuff should be covered, at least in a bit of detail. Or, I would certainly hope so anyway

8:31 AM
Knuth's textbook has unsolved research questions as exercises.

So does Visser
The last problem in Visser's book is "quanticize gravity"

I keep hearing ppl saying sth like "cosmology is black magic". Anyone can shed some light on this joke for me?

I do not know
Cosmology is fairly straightforward

anyway, I am thinking hard now for my future career paths.
I enjoy a lot building my understanding.
but doing research so far seems to me quite ...

You'd better enjoy building websites because there's a bigger job market for that

8:40 AM
not as much as doing one wants to do
I may start a business later

AI is fine, but you'd better be good at it
Oh and you'd better do AI for data analysis, because that's what people want
They want to know what brand of bananas people want

lol

@Slereah it seems a risky business...
I have uncles who are highly successful business men in China
not sure if I should ask them if they are willing to take me under their wings
probably a good starting point for doing business

Hello guys I would like to ask about something related to set theory . If I would say { (x=a1) or (x=a2) or (x=a3) } , this means its a set containing a1 and a2 and a3 (I guess) but what if I wanted to mean that it may contain a1 or a2 or a3 , here ("or" has the meaning it has in english and not in math; not summing up ) so if I cant put it this way , is there another logical connective for that?

9:01 AM
Have mercy on me Carter

9:18 AM
@0celo7 Yeah, it is (no telling if it will really come out next month though). I'm also not sure you'll like the game, but I guess since it's free it doesn't hurt to try.

@ZaKh The notation you're using is not one I've seen before. Typically $\{a_1, a_2, a_3\}$ would be used to designate a set containing those three items.
If I understand correctly, you're talking about a situation where you have a set whose contents are unknown to you, but the contents could be just $a_1$, or just $a_2$, or just $a_3$, right? Or could the set contain more than one of those elements? Or none?
Either way, you could designate the set itself with a variable, like $X$ (it's common to use capital letters for sets), and then you could even write $X \in \{\{a_1\}, \{a_2\}, \{a_3\}\}$ (yes, that is a set of sets) to show that $X$ is one of the three sets $\{a_1\}$, $\{a_2\}$, or $\{a_3\}$.

9:46 AM
@Sid I was asleep then

10:02 AM
Does anyone know what $\natural$ is for

@Slereah Muscially, it means that any prior $\flat$ or $\sharp$ is invalid for the note it precedes.

Ah alright
(It is also used to denote the completion of a spacetime)

10:21 AM
Budic and Sachs define $\downarrow U = I^-(\{ x | \forall p \in U,\ x \ll p \})$
Isn't that just $I^-(I^-(U)) = I^-(U)$
Hm

folks, some tagging feedback requested
0

I'm making a NMR experiment using paraffin wax. I measured its $T_2$ values as function of its temperature. Now I have my results. However I couldn't find any reference in the internet for earlier measurements of $T_1$ and $T_2$ of wax. Is there any chance someone knows these values or at least c...

I just created the nmr and relaxation tags
I wanted but it's one character too long
should we make and redirect it to ?
or something like that?

@EmilioPisanty Hm, I don't think a "chopped off" tag is a very good idea
Maybe SE will increase the tag length network-wide soon, as they did on Literature

@ACuriousMind it would only be a synonym, so nothing would actually get tagged with it
but it would allow you to start typing nuclear-magn... and be redirected to the right place
@ACuriousMind if they do, we can make a full-named tag and redirect everything there

@EmilioPisanty Hm, maybe just put "nuclear magnetic resonance" in the first sentence of nmr's tag wiki excerpt? I think the tagging box also searches the excerpts

@ACuriousMind doesn't seem to
also, if you add spaces in the tag box it separates it as a single tag

10:36 AM
Hm, well, that's crap :P

@EmilioPisanty wow, we didn't already have a tag for it? That's weird. Anyway, we could also try which sort of gets the idea across

@DavidZ you want that as the main tag?

and then we really hope that SE gives us another character for tag names

or as a synonym redirecting to nmr?

@DavidZ Then people typing 'nuclear' quickly won't see it
If we're gonna cut-off a bit of that name, I guess Emilio's suggestion of chopping off the end is the best

10:40 AM

@EmilioPisanty I dunno... personally I tend to prefer the longer one being the main tag but I don't know if it matters

@DavidZ I agree with longer tags as main, so long as they don't have bits lopped off

@EmilioPisanty That works too. Actually we could have both. Pick one to be the main tag and make a bunch of synonyms for it to help searches.

but then having as many synonyms as possible redirecting to the main target does no harm

Now that I'm thinking about it, the one we'd want to be the main tag should be the one that will make the most sense to people reading the question or seeing it on the index page or the like, because the main tag is the one that will actually get displayed

10:45 AM
@DavidZ yeah
or maybe as main?
with the others redirecting in

If I see "magnetic resonance" I don't immediately make the association with NMR, but maybe that's just me

in Mathematics, Jul 12 at 18:19, by Secret
In the past, I have encountered/saw people like koolman in h bar and periodic table, ramajaran in maths chat and periodic table, Mary star in some occassions, and at least 2 other users who tend to just dump the problem and wait for the people to solve for them. Ramajaran is particularly worse (he is much better now) he used to mass ping people, Balarka knows what it is like
@Secret hope you still see Ramanujan ..

@DavidZ I don't much either, but there isn't a perfect choice absent an increase in the limit

Yeah, agreed. Well, initials do play a significant role in getting people to recognize words, so I'd go for a three-part main tag name with the proper initials of NMR - I think it's safer to leave letters off the end of one of the parts. Given that we can't get the full name in, I don't know that it makes much of a difference precisely which part we leave letters out of.

@DavidZ but if we're cutting stuff out, why not just go directly for the initials?
they're a bit diminished in lowercase but they still pack most of the associative punch

10:58 AM
For just you mean? Because if someone who doesn't know what NMR is looks at that tag, they're completely clueless about what the tag actually means. Looking at or the like gives some idea of what it means.

@Secret you said “Ramanujan is particularly worse (he is much better now)” You mad bro 😠

11:21 AM
is there any "real-life" homogeneous Lagrangian?
Maxwell perhaps?
hmmm
this looks like Euler's theorem

Ah, I finally got what the common past is
It's not just points that are to the past of every point, the points each have to individually be to the past of every single point
Hence $\downarrow I^+(p) = I^-(p)$, if the spacetime is causally continuous
Or $\downarrow I^+(p) \subset I^-(p)$ in general

11:44 AM
@Fawad Well, since around 2016, I have not seen much help vampires other than koolman, so you are fine

11:58 AM
I don't have the reputation to downvote you, but I would highly recommend physicsclassroom.com/classJohn Kennedy 6 mins ago
lol