« first day (2717 days earlier)      last day (2212 days later) » 

12:01 AM
Later, there is a black screen with some periodic but complicated waveform. Two white lines then started to appear and then squeeze towards the middle as it slows down its movement. It is some recursive algorithm such that whenever it stops, it subtract that frequency of sine waves with that amplitude away. The waveform also obey the property where the higher the frequency component, the smaller it's amplitude
 
12:21 AM
6
Q: Showing that derivative of conjugate is conjugate of derivative, using chain rule

bf905I'm trying to show that the derivative of the conjugate is the conjugate of the derivative, i.e. $\dfrac{d[f(x)^*]}{dx} = [\dfrac{df(x)}{dx}]^*$, using the chain rule. Calling the conjugate * function 'conj', we have by chain rule $\dfrac{d\ conj(f(x))}{dx} = \dfrac{d\ conj(f(x))}{d[f(x)]} * \d...

Whether you can define some notion of curl on the complex number by treating it as a vector field of its real part and imaginary part I have no idea
 
12:48 AM
The complex number part of this dream might be inspired from this conversation
in Mathematics, 11 hours ago, by Balarka Sen
@ShaVuklia I mean you did, you wrote $f = u + iv$, that's the same as writing $(u, v)$, which is the real function. The multiplication is the same old $(a, b)(c, d) = (ac - bd, ad + bc)$. There's no "real" interpretation of this multiplication.
8
Q: How much can we "cheat" and use vector knowledge in complex analysis?

DavidI'm an engineering-physics student taking a course in complex analysis, and it's a little frustrating, because I see all these connections to vector calculus over the reals (especially as applied to electromagnetics). For example, if we treat complex numbers like vectors, then the Cauchy-Riemann ...

I have no idea how useful or useless an expression xdz-ydz* will be
Where x and y are real and imaginary parts of z respectively
 
 
2 hours later…
2:36 AM
@vzn I think it is pretty interesting but not yet mature. There are still a lot of vagueness floating around...
Grrrrr! Sometimes QFT makes me want to eat my hat!
(not that I wear one...)
 
3:00 AM
Apropos of nothing...
Follow this link to watch a beautiful live feed of a nesting couple of white-tailed eagles in Estonia. (Only available during Estonian daytime.)
I've learned this species of eagle ^^ builds so-called "ancestral nests," to which they return clutch after clutch, generation after generation. So it's cost-effective for naturalists to install such high-quality cameras near them.
 
Anonymous
A bit too high quality :P
 
Anonymous
What's those blue lines in the sky?
 
Well, that was enjoyable
Just got back from an evening lecture/conversation
 
accurate representation of the next two months of my life i.gyazo.com/ef23596d4b3f58084eb9223613af4ae1.png
 
One of the people talking/being interviewed was Louisa Gilder of “The Age of Entanglement “
The other was Chad Rigetti of Riggeti Computing
 
3:10 AM
@0celo7 PDE's on As Fuck manifolds, eh?
 
look, I'm going to flag if you don't remove that
this is a Christian chat
 
vzn
3:21 AM
@G.Bergeron he has certainly captured the imagination of popsci writers, maybe why hardcore physicists have some aversion... o_O quantamagazine.org/… quantamagazine.org/… quantamagazine.org/…
 
@0celo7 Please stop using "flag" carelessly. If you're bothered by what Sen said say so, say why, and make an actionable request of them. (If you're not actually bothered by it then you're adding noise to a system--flagging--whose functioning you have complained about.)
 
I suspect it was tongue in cheek. or at least i hope so
 
vzn
lol on SE chat "f---" is a 4 letter word, found that out myself the hard way o_O :(
 
@vzn oh hey, I've been in that mine they mention
 
3:24 AM
@Semiclassical me too. I just think it's a bad idea. It contributes (IMO) to some of theproblems that very person complains about.
 
...and that's about the limit of my interest in that article, tbh
dark matter is another thing I don't know about and really am not interested in
 
vzn
@Semiclassical way cool sounds like a nice item (amongst many others) for AMA :)
 
it was fun. unfortunately the detector they mention has been decommissioned in the last few years
 
vzn
@Semiclassical GB is right, think it is deep & might have to do with unification. unification is of intense interest to a wide swathe of physicists, but then again, not everyone... its sort of the ultimate Big Picture™ :|
 
Ooh, dawn light hitting the eagle's back.
 
3:27 AM
details on the Soudan mine experiments here: soudan.umn.edu
including a virtual tour
 
why can't I be offended by Karl
 
vzn
@Semiclassical am more and more surprised about UMN all the time, some really world class physics going on there, but it seems very low profile. think it would be interesting to look into its history, wonder how it happened...
 
well, part of it is location
 
vzn
@nitsua60 ?
 
when you think of California universities you get Berkeley, Santa Barbara, etc.
and when you think of the East coast there's a bunch as well
MN is sort of off on its own
 
3:29 AM
Trump U
 
I'm only counting universities that still exist
(and coincidentally only ones were that were ever worth talking about)
 
vzn
@Semiclassical did gilder do a lecture today? or some other day? whatd you think
 
@vzn it wasn't so much a lecture as an informal interview in front of an audience
half hour with her, half hour with Carl Rigetti, half hour for questions, half hour for book signing and informal conversation
(roughly)
They were recording it, so I'm curious if they'll post it online at some point
 
vzn
@Semiclassical am gonna watch that one if it gets online, encourage them to do so :)
 
3:32 AM
well, it wasn't being held on campus but at a book place nearby
so I dunno
But I'll ask about it
 
vzn
@nitsua60 wont play in my ipad what is it?
 
33 mins ago, by nitsua60
Follow this link to watch a beautiful live feed of a nesting couple of white-tailed eagles in Estonia. (Only available during Estonian daytime.)
 
vzn
11 hours ago, by John Rennie
@Semiclassical vzn specialises in making portentous statements, but when challenged is unable to point to any concrete evidence to back up those claims.
 
Anonymous
@nitsua60 The view looks better now
 
@Blue the light levels may have been low earlier?
 
Anonymous
3:37 AM
Yeah, a bit. And the yellow lighting in the bottom right end looks nice
 
vzn
re that: building new theories is very hard work, not for the fainthearted, impatient, or mere dabblers/ dilettantes. looking for any earnest volunteers, always welcome. there are copious details/ authoritative sci refs in my blog over ½ decade now, many cited here etc.
 
Anonymous
I guess those blue lines are the leaves? @nitsua60
 
The vague portentous idea I have is whether dBB could have any bearing on the mathematics of resurgence theory (aka asymptotic series gone wild). I have at least one reason to wonder about that but I don't plan on thinking about it any time soon
 
Anonymous
It looks a bit strange
 
Anonymous
And it started twisting it's neck after long
 
Anonymous
3:38 AM
lol
 
Anonymous
I see the face now
 
@Blue oh I see what you mean now. Pine needles just in front of the lens.
 
Anonymous
Ah, makes sense
 
vzn = JD is a plausible claim
I have never contemplated that actually
 
Anonymous
The eagle is lazy af though
 
Anonymous
3:40 AM
:P
 
vzn
@Semiclassical looked at one of your refs on that it looked interesting, but more mathematical. yes singularities are a big/ crosscutting mystery pondered by the greats (eg feynman) and ongoing. a premiere zen question™ one might say :P
 
@nitsua60 reporting: three counts of "heck" and one count of "hell" in seminars this week
 
I guess I have two reasons, come to think of it
though one of them has a big likelihood of just being coincidence
and the other might not really gain anything from thinking about trajectories.
 
egg turning!
 
vzn
@Semiclassical seems like a good choice of area to make a contribution. emerging, significant, deep etc.
 
3:43 AM
maybe.
the pitfall is that the main place people seem to want to apply resurgence theory is stuff like QCD
and uh
above my paygrade
 
Anonymous
@nitsua60 Ah
 
Anonymous
nice
 
Anonymous
finally
 
vzn
@Semiclassical "pitfall"? are you saying QCD is "above your paygrade"? btw phd sometimes called science work visa/ employment card by some.
 
QCD is, yes. though I guess it's not so much 'above' as 'outside'
 
3:45 AM
in RPG General Chat, 34 mins ago, by Rubiksmoose
Man eagle parenting is boring. You'd think they could get Netflix (Nestflix?) at least
 
@nitsua60 nestflix and roost
 
Anonymous
Heh
 
@Semiclassical that's hot
 
by and large, though, QFT stuff is not my thing
just not something I ever had a particular talent or inclination for
 
night, all
 
3:47 AM
night
 
Anonymous
Cya!
 
@Semiclassical Ugh, I have to generalize 5 pages of potential theoretic calculations to n dimensions
 
Good luck.
 
could use an em expert
 
vzn
@Semiclassical so whatd you think of riggetti/ gilder anyway?
 
3:49 AM
it was fun.
 
vzn
@Semiclassical so did you gain any )( new affinity for QC...?
 
didn't learn a lot about QM from the gilder part, but the history I was pretty well aware of already so I wasn't expecting to
the QC side was more informative in that regard. it seemed like a sober, realistic assessment of the field
 
vzn
@Semiclassical sober eh? seems like sometimes nobody working in it is sober :P gotta go look up gilders bkg, was amazed at depth of her book, seemed like she came out of nowhere & wrote the definitive history...
 
well, she spent a lot of time on it :)
it originated from a term paper and grew from there
 
vzn
@Semiclassical she has serious talent, a real writer/ storyteller/ raconteur, impressive, wonder what shell tackle next
 
3:53 AM
I think once she was put in touch with a publisher she spent another four years turning the manuscript into a publishable work
heh, one of the presenters was not-subtly urging her to write an update to her book that covers the last decade in QC
she didn't let on about her current projects, though
 
vzn
kind of a cipher who came from nowhere, she seems not even to have website penguinrandomhouse.com/authors/60477/louisa-gilder
 
Hi, can anyone please help me understand how U=v in the nobel lecture by de Broglie ? nobelprize.org/nobel_prizes/physics/laureates/1929/…
^ Page no: 5
There seems to be a interchanging use of variable v for frequency and velocity.
 
Anonymous
@Hritik I don't think that's derived in the paper. Rather looks like an assumption
 
Anonymous
Anyhow, I didn't go through it thoroughly
 
Anonymous
"the group velocity of the waves in the system
xyxt is equal to the velocity of the corpuscle in this system"
 
4:07 AM
@Blue I think that came from the equation above from Rayleigh but when I tried solving it I got something different. Can you try as well, please ?
 
Anonymous
Sorry, I need to leave now. Ask on the main site maybe.
 
OK, thanks anyway
 
ok so I will be looking at page p. 43 scattering Amp
hmm so I get $\theta (t' - t) \psi(x') = i \int d^3 x G(x';x)\psi(x)$
Let me just try to confirm that I can be ok with the integral representation of $\theta$
$\theta(\tau) $
$\theta(\tau) = lim - \frac{1}{2 \pi i} \int \lim d \omega \frac{e^{- i \omega \tau}}{\omega + i \epsilon}$
what the duce
. . .
ok let me think
. . .
why and how
. . .let me think
 
4:28 AM
thonk
 
I mean I know what a theta function (step function is) let me look at the integral representations in this context
let me think
hehe
so one can check, but this does not tell me why this form is used
hmm
The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a discontinuous function named after Oliver Heaviside (1850–1925), whose value is zero for negative argument and one for positive argument. It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one. The function was originally developed in operational calculus for the solution of differential equations, where it represents a signal that switches on at a specified time and stays switched on indefinitely....
close with small cigar
 
6:23 AM
yeeehaaa good playlist
This stuff is epic. Would listen to this while coding tomorrow!!
 
Guys, what are kets and bras in QM. I tried looking around, but I still can't get it.
 
@vzn Yeah, on that part he is rather prone to premature public declarations. And it comes back once in a while as if new.
@NovaliumCompany state vectors and their duals
 
I'm a beginner in QM, and what is a state vector?
 
Or elements of the Hilbert space (ket) and elements of the dual of the space, aka functionnal linear (bra).
 
... never mind.
 
6:27 AM
You should learn some abstract linear algebra
before learning QM
 
Then QM is just seeing physical states as vectors of a special vector space (Hilbert space) with linear operators (= matrices) representing time evolution and measurements. So infinite dimensional vector spaces and the associated theory of linear operators on them is kind of a necessary prerequisite
 
@NovaliumCompany it's simpler than G. Bergeron is making it sound because he is using technical language, but it will take a little while to explain ...
 
@JohnRennie LOL, but you'd agree linear algebra is kind of an obligatory prequisite?
especially when one is considering the bras and the kets...
 
@G.Bergeron bear in mind Novalium is 15 years old
I think you can get the basic idea without having to do a LA course.
 
6:33 AM
hmm, ok
 
But yes I absolutely agree that understanding LA is the best way, by far, to understand QM
 
hence the ''... never mind.''
 
@JohnRennie I know it will be hard, but I am not giving up.
 
@NovaliumCompany I have to work for about half an hour but I'll be available after that if you want to pursue this
 
@NovaliumCompany Is your goal to get a feel or an intuition for the ideas or get to ''use it everyday''?
 
6:36 AM
I would like to get to the main ideas in quantum mechanics and computing, since I see a big future potential in it.
 
what's your current background in math?
and physics?
 
@JohnRennie I will be going to school soon, so I'll be here Saturday and Sunday.
@G.Bergeron I am 15. I think that explains enough :D
 
@NovaliumCompany I don't know your past nor what is typical in your country
 
Bulgaria
and I've learned Classical Physics through watching Khan Academy vids, and so on...
 
What are your learning in math?
Like functions, trigonometry, algebra?
 
6:38 AM
That's my main problem. My math is for a 15 year old.
But I am ready to learn it, together with QM.
 
which is?
 
Which is what?
 
Understand it's a bit beyond me and I don't remember what I knew at that time
 
Oh, well, I can't tell you what I know, because our 'titles' in our student books are in Bulgarian.
 
Have you done calculus?
 
6:40 AM
Yes... I guess :D
 
like derivative / integrals?
dx/dt and the like
 
I'm learning Integrals
 
ok
and polynomials and the like is fine? Like finding zeroes.
 
I like to do it this way: I'm reading a Quantum Mechanics book, and whenever I don't understand so math concept... etc, I google it or ask for help here.
I don't know the titles in English, but I think I know polynomials.
 
like 4 x^2 + 3x -3
 
6:42 AM
Yes...
I know these guyz :D
So yeah, any more questions? Cause I have to go to school.
 
Oh
THe next one was about real numbers
like 3.454634534621.....
 
I know them.
 
@NovaliumCompany Cool
Well good day if you have to leave, if I'm around I'll help, now that I know what to start from
@vzn Also what's a hardcore physicist?
 
Thanks. The community here is very good, and everyone is so kind and ready to help. Here is the book that I am following: ffmgu.ru/images/2/24/… I am at 'Creating Your Own Vectors in Hilbert Space' and I'll finish it soon.
So see you later @G.Bergeron and @JohnRennie
 
7:38 AM
@NovaliumCompany Griffiths is a very good book for QM. He introduces all the mathematical ideas and techniques in the book too.
If you’re interested to learn linear algebra separately, you can look into Sheldon axled, it’s a pretty awesome book
 
Anonymous
8:28 AM
@PrathyushPoduval For some reasons I don't like Griffiths at all. Firstly, it starts too early with the Schrodinger's equation. Secondly it does give a good introductory background in the Hamiltonian and Lagrangian formulations unlike Shankar.
 
Damn the torpedos, I'm going to have another coffee!
 
8:46 AM
@Cows still confused?
 
too board?
0
Q: What's a good book on experimental methods for physics?

Aidan RockeI have read many books which can guide one in becoming a better theoretician but I haven't come across many books that help one become a better experimental physicist. For some reason the history of science favours the theoreticians and while I admire Lev Landau, Henri Poincaré and Albert Einstei...

 
@Shing looks fine to me
 
@Shing There's no board at all
 
@Slereah sigh :-)
I suppose these jokes have to be made
 
8:51 AM
lol
 
@JohnRennie yes, they do
 
9:35 AM
How would we define the expectation value for the modulus of the velocity i.e. $\langle |v| \rangle$ ?
Could this be evaluated for the hydrogen atom?
 
9:51 AM
How do you define $|\hat v|$
Is it like $|\hat v | \psi = | \partial_x \psi|$?
 
I guess so ...
 
How do you define it on a complex wavefunction, though
$|\langle \hat v \rangle |$ I can see, but $\langle |\hat v|\rangle$ I'm not sure
Or I guess it could be that on an eigenvector you get $|\hat v| |p\rangle = \frac{|p|}{m} |p\rangle$?
 
For example in a 1D SHO $\langle v \rangle = 0$ but $\langle v^2 \rangle \ne 0$
Since $v^2 = |v|^2$ I was wondering if there is any meaning to $\langle |v| \rangle$
 
You can use the spectral theorem thing
$f(A) \psi =\sum f(a_n) \psi_n$
Though of course many asterisks on that formula
 
10:07 AM
@BernardoMeurer tex.stackexchange.com/a/60855/13423 for the first one
though don't use quotes inside entries when {} will do
@BernardoMeurer the second one.... goodness
what even is that text?
one option, for simplicity, is to just cite the subsequent essay, which is apparently included in amazon.com/gp/product/B000FBFM9I/…
if you want to cite the excerpts you linked to, then (1) decide what you want the citation itself to look like, and then (2) use the bibtex @misc{} class to implement it.
 
10:24 AM
@Blue ah yeah you’re right about that.I had an idea about the intuitive reasoning behind schroedinger-equation before Griffith, which might’ve made it easier. But all the mathematical intricacies, like Hamiltonian and lagrangian approach can be learnt later (Like I did), though it’d be helpful to know it beforehand
 
10:42 AM
If a guy pulls a rope with force F from the right side and another guy pulls it with force G from left side , wouldn't the tension on the rope be F+G.?
 
@BalarkaSen The first song sounds like some soundtrack that is being ran backwards
 
@AlexKChen this is one of those situations that seems unintuitive.
The tension in the rope must be the same everywhere in the rope otherwise the rope would just stretch/contract until the tension was the same everywhere.
 
Tension is one reason why I suck at newton box problems
 
And the tension in the rope is just the force acting on F or indeed G.
 
only 7 stars?
I would have expected it to be pinned
 
10:51 AM
@0celo7 :-)
That would imply room owner approval of discussions about our dearly departed friend.
 
well the mods obvioussly didn't appreciate it
but you? I'm surprised
 
@0celo7 Really. I thought my views were fairly clear. I have never seen a post by Duffield, either here or on the main site, that I thought made any useful contribution.
@Secret Estonian eagles?
 
8 hours ago, by nitsua60
Follow this link to watch a beautiful live feed of a nesting couple of white-tailed eagles in Estonia. (Only available during Estonian daytime.)
They are so pretty
but I am biased, becase I like birds
 
10:55 AM
I watched for a few minutes, but it isn't enthralling viewing :-)
 
the american eagles are better
 
I guess it's more interesting if you see the chicks being fed.
(assuming there are chicks)
 
@JohnRennie I don't think he made a contribution either, but I can still mourn the execution of a friend
 
@Secret I like birds too, though I find eagles to be a bit chewy.
 
well, nitsua did said there's an egg being turned, and that the eagle sit so still in the nest, so it might be incubating an egg or something
 
10:56 AM
Sorry I don't understand. What do you mean by " F or indeed G.
" ¿
 
@AlexKChen it's simpler to understand if the two forces are the same because then the system is in equilibrium. If the two forces are different then the whole rope has to be accelerating.
So suppose you and I are pulling on opposite ends of the rope with the same force F. Then the question is whether the tension in the rope is F or 2F. Yes?
@0celo7 a friend? He called you a cheeky, obnoxious git. (git is English slang for bastard and is not a term of affection)
 
@JohnRennie boys will be boys
 
Unfortunately so will some middle aged men
 
@JohnRennie You ol' git
 
11:04 AM
@Slereah I'll have you know I was born nine months and one day after my parents got married!
They didn't waste any time :-)
 
busy wedding night
 
@JohnRennie Yes. And I guess the answer is 2F?
 
@JohnRennie gross
 
plus really can we trust what the english think of words
They think French is a swear word, too
 
"pardon my French"
 
11:08 AM
@AlexKChen by Newton's third law the force I exert on the rope is the same as the force the rope exerts on me. The force I exert on the rope is F, so the force the rope exerts on must also be F. But the force the rope exerts on me is just the tension in the rope, so the tension in the rope is F not 2F.
I know it does feel like the tension should be 2F, but it isn't.
 
@JohnRennie if two cars drive into each other at 60mph, is it like one car hitting a wall at 120
 
You know what was my least favorite leadt intuitive thing in classical mechanics?
 
@0celo7 I'm sure that's been asked on the main site ...
 
Wheels
 
im asking you, not the main site
 
11:09 AM
The bloody velocity distribution on wheels
That was my twin paradox of the galilean relativity
 
@0celo7 seriously? As in do you genuinely want to know the answer?
 
im testing you
 
Choose, but choose wisely
 
@JohnRennie OK. But can't it happen that the rope has different magnitude of force acting on the sides (eg Imagine two parallel walls A, B. Now attach a stiff spring to A and a loose spring to B, and attach a rope between the two springs. What would be the tension then?)? Also, what's then the answer for two distinct forces F, G?
 
I'd say no since a wall doesn't crumple like a car
Unless it's an idealized rigid car
 
@Slereah clearly not because the impulse experienced by the car is the same whether the car is colliding with another car or a wall. That means the force has to bethe same as well.
 
samuel is correct
 
Hurray
 
the crumpling decreases the impulse
 
@AlexKChen the tension in a rope is constant. That means the force the rope exerts on the things it's tied to is the same at both ends.
 
11:15 AM
I owe my wisdom to many wall collisions
 
@Slereah I stick to beating my head against walls.
 
Sid
I stick to just facepalms
 
Then what'll be the tension if there's a mass of M on one side and 2M on another side of a pulley? Would the thread snap? @JohnRennie
 
@Secret Yeah it does
It's so good tho
Boi in a box the fever 'sall tzey
 
Sid
@AlexKChen there will be acceleration of the masses
 
11:23 AM
Oh Ok
 
@AlexKChen that's a pretty standard problem that you'll be set if you continue studying physics. The answer is that the force on the masses is the tension in the rope plus $mg$.
The tension in the rope will be the same on both sides.
 
@BalarkaSen Joe Rogan should have ST Yau on his podcast
maybe tell him about some actual science for once
 
@JohnRennie OK thanks
 
11:45 AM
Who is String Theory Yau
 
Shing Tung
 
@Slereah maybe you'll like my thesis now that it has some GR in it i.gyazo.com/8e18760c6eb262a0464492a6b7c8cdf0.png
 
@0celo7 where are the observables
 
@0celo7 You should start passing out ads for your thesis throughout SE and MO
Get em hyped
 
@BalarkaSen who knows when it will be done
my advisor wants another chapter
 
11:47 AM
RIP
 
at this point he legit wants me to write a book
 
Find a question on the topic of your thesis and then answer "There is this great paper on the topic!"
@0celo7 If you're at 170 pages already, yeah, pretty much
 
172 now
 
He crossed 200 I'm sure
welp
 
this proof will probably take another 6?
and then I have a 40 page paper to cover
 
11:48 AM
such is the folly of doing analysis
 
so definitely 200 by the end
problem is, I can't publish a book by myself but no one deserves to be a coauthor
 
What about this great book
 
this thesis has some really nice things in it that haven't been done carefully before
 
the big book of spacetime
 
Kazdan-Warner doesn't exist in any book, at least not with a correct argument
 
11:51 AM
most math doesn't exist in any book rly
it's scattered in a bunch of papers nobody read
 
accurate
 
sometimes in languages nobody remembers
The ancient civilization of the Soviet Union
The forbidden texts of Успехи физических наук
So far I've been mostly lucky, the weirdest language I've had to deal with is Italian
I don't want to have to make sense of a russian paper
 
thankfully the Russians never did any interesting math so it's not an issue
 
phew
 
LU was translated to English
so it's all fine
 
11:54 AM
It is weird that there aren't more russian papers that were never translated
You'd think they wouldn't share all their papers with the US during the Cold War
oh wait, there was that one time I found a paper written in Uzbek
that was not translated at all
 
My sense is from the 70's on you'll get a lot more translations, the thaw was in the 50's and it probably took a while
@0celo7 Your God Sobolev was Russian
 
I think he wrote in English
 
Although it's possible that there are many, but they're just not referenced in american paper because of this
 
so it doesn't count
and one never has to read what he did, because it was barely rigorous and fixed later by Morrey
 
Sergei Lvovich Sobolev (Russian: Серге́й Льво́вич Со́болев; 6 October 1908 – 3 January 1989) was a Soviet mathematician working in mathematical analysis and partial differential equations. He was born in St. Petersburg, and died in Moscow. == Work == Sobolev introduced notions that are now fundamental for several areas of mathematics. Sobolev spaces can be defined by some growth conditions on the Fourier transform. They and their embedding theorems are an important subject in functional analysis. Generalized functions (later known as distributions) were first introduced by Sobolev in 1935 for weak...
He wrote in French apparently hah
 
11:58 AM
so does Gromov
 
it is the language of love
I kinda lucked out being able to read French and English for physics
 
pfeh
 

« first day (2717 days earlier)      last day (2212 days later) »