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14:02
Is the integral of a sum equivalent to a sum of integrals? For instance, does $\int \Sigma_i f_i(x) dx = \Sigma_i \int f_i(x) dx$
Anonymous
@Phase $\int (f_1(x)+f_2(x)) dx = \int f_1(x)dx + \int f_2(x)dx$
If you have infinite sums you have work to do
Sid
Sid
Um... guys. I need some help in English...
Anonymous
74
Q: When can a sum and integral be interchanged?

user192837Let's say I have $\int_{0}^{\infty}\sum_{n = 0}^{\infty} f_{n}(x)\, dx$ with $f_{n}(x)$ being continuous functions. When can interchange the integral and summation? Is $f_{n}(x) \geq 0$ for all $x$ and for all $n$ sufficient? How about when $\sum f_{n}(x)$ converges absolutely? If so why?

Anonymous
Too much for me ^
Anonymous
14:08
:P
Anonymous
@Sid ?
@Blue Great, now I have managed to confuse myself - it appears that I can derive the M-B distribution in the canonical ensemble under the assumption the classical particles are distinguishable, or in the grand canonical ensemble under the assumption the classical particles are indistinguishable. Which makes no sense.
Sid
Sid
What is the term coined to describe the unsightly proliferation of Plastic bags in streets?
It appears instead of answering your question I will have to ask another one myself.
@Sid There's a term for that?
Sid
Sid
Apparently there is. (Maybe a phrase and not a single word.)
Anonymous
14:11
@ACuriousMind I actually haven't learnt about ensembles yet. So I can't comment on that. I think the derivation of M-B distribution should be given in standard textbooks. I'm checking...
What does this mean with reference to Einstein - "I must seem like an ostrich who buries its head in the relativistic sand in order not to face the evil quanta. "
@Blue I don't need the derivation, I've got plenty of them already. The problem is that they seem inconsistent with each other
I thought I could make it very clear in the grand canonical ensemble how M-B assumes distinguishability, but it appears it actually assumes indistinguishability there!
Anonymous
9
Q: What is the relationship between Maxwell–Boltzmann statistics and the grand canonical ensemble?

Nikolaj-KIn the grand canonical ensemble one derives the expectation value $\langle \hat n_r\rangle^{\pm}$ for fermions and bosons of sort $r$: $$ \langle \hat n_r\rangle^{\pm} \ \propto \ \frac{1}{\mathrm{exp}[(\varepsilon_r-\mu)/k_B T] \mp 1} . $$ For $(\varepsilon_r-\mu) / k_B T\gg 0$, we find $$ \...

Anonymous
@ACuriousMind I see...hmm
Hey @0ßelö7
Do you see any major error in the section on bounded acceleration
14:26
@BAYMAX duffield?
@Slereah "switching back to canonical coordinates"
proof?
Proof of what
$t = v+u/2$
$x = v-u/2$
That's the definition
Anonymous
@ACuriousMind While deriving the MB statistics from grand canonical ensemble did you consider the system to be a single particle state rather than a particle(like an atom) ?
Also $e^x + e^{-x} / 2 = \sinh(x)$
That's basically it
Anonymous
"As a result, when multiple particles are placed into the same orbital, the overall collection of the particles (in the system phase space) does not count as one whole microstate but rather only a fraction of a microstate, because identical states (formed by permutation of identical particles) should not be overcounted. The overcounting correction factor is the factorial of the number of particles."
Anonymous
In statistical mechanics, a grand canonical ensemble is the statistical ensemble that is used to represent the possible states of a mechanical system of particles that is being maintained in thermodynamic equilibrium (thermal and chemical) with a reservoir. The system is said to be open in the sense that the system can exchange energy and particles with a reservoir, so that various possible states of the system can differ in both their total energy and total number of particles. The system's volume, shape, and other external coordinates are kept the same in all possible states of the system. The...
14:31
Although I didn't write in yet why I drop $A$
(I just set them to 1 because who cares)
@Slereah ln(cos)?
Seems like a bad idea
$$\int \tan(x) dx = -\ln(\cos(x))$$
Anonymous
@Slereah There will be a modulus there :P |cos(x)|
@Blue You can trust that I've read all relevant Wiki articles thoroughly before deciding I am confused by the situation :P
@Blue this
Anonymous
14:34
@ACuriousMind Okay, I trust you. :P
@Blue not wrong
Anonymous
I should read up the ensemble stuff soon
@ACuriousMind what is the issue?
26 mins ago, by ACuriousMind
@Blue Great, now I have managed to confuse myself - it appears that I can derive the M-B distribution in the canonical ensemble under the assumption the classical particles are distinguishable, or in the grand canonical ensemble under the assumption the classical particles are indistinguishable. Which makes no sense.
sounds like a main site question
Anonymous
14:36
@0ßelö7 I didn't mention the constant..lol
Anonymous
+C
26 mins ago, by ACuriousMind
It appears instead of answering your question I will have to ask another one myself.
@Blue if you say that one more time we will be done
there is never a constant
Anonymous
@0ßelö7 What?
there is no what
Anonymous
14:37
...
Indefinite integral is a big nonsense
It's just a differential equation
with unspecified initial conditions
indefinite integral is not real math
do you prefer the name ANTIDERIVATIVE
you big baby
no
that's not real math either
why not
14:38
real MAFF
Anonymous
REAL MATH is addition, subtraction, multiplication and division. Everything else is non-sense and doesn't increase GDP.
if you don't call it a primitive then you're trash at analysis
it's actually just writing a given 1-form as an exact form locally
everything else is a big abuse of notation
is that the case for all indefinite integrals, though
yeh bruh
14:41
What about the indefinite integral of the delta function
delta function is not a function you hipster ass
sigh
it's a flipping distribution
@BalarkaSen why do you have to bring topology into everything
an approximation to the identity if you prefer
14:41
Anybody here would like to help me on this - " The divergence of Eelectric field of a point charge is 0 everywhere except at the origin where it is rho/epsilon. What can we say about the divergence of Electric field due to an extended continuous distribution of charge like a cylinder or anything " Will the divergence be rho /epsilon...
>he doesn't know about the embedding of distributions into a function space
@BalarkaSen what?
...who prefers that?
weirdo
you prove weierstrass approximation theorem with that convolution shit
14:42
since when?
also that periodic functions are approximated by fourier series with enough regularity
What's a fourier series without enough regularity
@BalarkaSen I gave you that proof
$1_{\mathbb Q}$?
Anonymous
@Shashaank Look up Gauss law...divergence form...
14:44
what is the fourier series of $1_{\mathbb Q}$
@BalarkaSen Stone-Weierstrass has nothing to do with convolutions
read that paper
In fact, that's a god-awful way to prove it because it holds in much greater generality via a much easier proof
no u suck
14:46
@BalarkaSen Just look at the Preliminaries chapter of Yosida's FA book
10 ways to start a good debate: 1) Start personally attacking the opponent when you're feeling insecure
@Blue yes I know that the divergence of E = rho/epsilon . We use Gauss's law to get E for Cylinders , spheres , etc. But if after calculating the E of these bodies , I calculate the divergence of E I will get 0 (eg :for sphere ). Is the fact again that the divergence comes due to the fact that it will not be 0 at the charge itself ?
@BalarkaSen I am trying to help you. When you learn spectral theory you will need Stone-Weierstrass for subsets of $\Bbb C$
i am trying to troll you
What does that mean?
Anonymous
14:51
@Shashaank You are confusing yourself. If electric field lines entering a region (or point) is equal to the electric field lines leaving that region, then only divergence is $0$. At the positive charge itself there are electric field lines leaving but not entering, so the divergence there will not be $0$.
Anonymous
You can consider electric field to be a vector field.
15:10
@Blue So you mean that the divergence of E due to any charge distribution will be rho/epsilon irrespective of whether it is a point charge or an extended charge distribution (arbitrary in shape)
@0ßelö7 is that a place?
I have a couple of quotations and I am trying to understand them and thinking of writing about them
It's a person
Anonymous
@Shashaank Well, Gauss law says $\nabla.\mathbf{E}=\frac{\rho}{\epsilon_0}$ where $\nabla.\mathbf{E}$ is the divergence of the electric field.
One of the great minds of the site, actually. He was banned for unknown reasons.
oh
sorry for that
Anonymous
15:14
@Shashaank I advise going through the derivation from Maxwell's eqns...
@BAYMAX Einstein thought quantum mechanics was at best an incomplete theory, and he thought he could come up with a deeper theory that explained quantum mechanics. So he ignored all the developments in QM while he worked away at his own theory.
Anonymous
Also, learn the physical significance of the divergence operator
@Blue which is?
Are you talking about the old Russian definition using oarallelopiieds
In his quote the I must seem like an ostrich who buries its head in the relativistic sand referred to the fact he was ignoring contemporary developments in QM and concentrating on his own theory.
Not gonna try to fix that spelling
@0ßelö7 how much stuff goes out infinitisimally
So just what I said
Old Russian math is trash
@BAYMAX: sadly history shows that Einstein completely failed to come up with his improved theory while quantum mechanics went from strength to strength.
old comrades discovered pretty much literally every math
Oh I see
@JohnRennie
15:18
Ah the latest person to fall foul of random flaggings. At least it wasn't you this time @0ßelö7 :-)
@BalarkaSen: I did try to delete your post as soon as I saw a flag against it but I wasn't fast enough. Sorry :-(
@0ßelö7 okay so
I think everybody in that class hadn't slept in at least 36 hours
Y'all need Jesus
Or just know GR before taking the class
Another quote! @JohnRennie ?
@BAYMAX Yes?
today we talked about manifolds
and charts and atluses which sound like subcovers
15:20
You need to tell me who is teaching this
"There was a lady called bright, who could travel faster than light. She went out one day in a relative way came back the previous night".
That's a limerick I learned as an undergrad nearly 40 years ago :-)
I knew it!
literally 80 years?
Get a colonoscopy @JohnRennie, please
Anonymous
15:23
@JohnRennie Congrats. You'll be 100 soon. :D
:-) Oops
Freudian slip there :-)
Anonymous
@0ßelö7 Don't get chat-banned man...:P
|O|
Why would I get chat banned
Anonymous
Flags are flying around today
I think how bright can travel faster than light?
I was going to have a colonoscopy, but then I thought it would be a pain in the arse.
@Blue balarka was flagged. Were there more?
does anyone know about a paper which supports this video
a study on how smelling works
Anonymous
@JohnRennie I underwent colonoscopy once. It was TERRIBLE. I'd rather die of colon cancer.
Anonymous
15:26
I shouldn't say such things though
Anonymous
:P
Wow India is hardcore
I could make some jokes but I would get flagged
Anonymous
I had a stomach infection that time. Was 9 years old.
@BAYMAX according to special relativity it is possible to go back in time if you can travel faster than light. Though it's quite a complicated business. It isn't as simple as traveling faster than light means you automatically go back in time.
Probably from eating with your fingers...
15:27
INCOMING! :-)
Anonymous
Lol
@JohnRennie what?
@Blue That's a tough thing to happen to a nine year old.
As you get older you get hardened and less upset by that sort of thing, but for a child it must be pretty awful.
@0ßelö7 it's okay he drew us nice pictures
Anonymous
Yeah, I remember that day clearly even after 10 years. :/ It was traumatic.
Anonymous
15:29
Anyhow...
@GPhys that's completely standard
I saw a similar thing in interstellar like coop was hidden somewhere in 5th dimension and was seeing his past @JohnRennie
@BAYMAX I wouldn't take the film Interstellar too seriously :-)
haa,I watch it everyday for 10 minutes at least! @JohnRennie
Sid
Sid
@Blue WHat did they do?
Anonymous
15:33
@Sid Scroll up a bit...
ok,let's see the next quote - "If my theory of relativity is proven successful, Germany will claim ma as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and German will declare that I am a Jew."
Sid
Sid
Yeah. What do they do in Colonoscopy? Surgery?
It's normally checking for polyps isn't it?
Sid
Sid
Oh, got it.
Yeah. Those types of things can be bad.
The Matrix > Interstellar
15:37
@0ßelö7: yes you'd probably have got flagged for that, but for the record I literally laughed out loud :-)
@BAYMAX it just means everyone loves a success and everyone hates a failure
Anonymous
@Sid It's not really surgery. It's described here
As it turned out relativity was a success but Einstein was driven out of Nazi Germany anyway.
@JohnRennie would I? It's only bad in context
@Blue before I click that link, it hasn't got graphic pictures has it?
Sid
Sid
Ah, so they inserted some pipe into your anus?
15:39
Then lit a match
@JohnRennie why do you care?
@0ßelö7 I'm eating my lunch
Ugh. Europeans are so sensitive.
@JohnRennie Those often go together.
;<(::)>;
15:40
Let's put the whole thing behind us
Uh oh, two mods in the room :-)
Yeah, anyway we do have a chat session coming up.
@JohnRennie you interested in Chaos theory?
Anonymous
@JohnRennie Not as such. It's wikipedia. :P
Interesting chat topic
@BAYMAX no
Anonymous
15:42
@Sid Ya. In short. (In fact I underwent endoscopy the same day...it was a bad day for me)
I'm going to see if I can head into work for the session, and ping me if there's anything to put on the agenda.
Chaos is one of those pop sci things that I find absolutely boring
Actually most things that are popular in pop sci are really damn boring
Ok
Okk
three paradoxes of Photoelectric effect
Boring
15:46
1) emission of photoelectrons as soon as light of certain frequency is incident on the metal surface.
Lyrics (official; azlyrics.com)

Ayy ayy
Ayy ayy ayy ayy (lmao)
yeah-yeah

Cancer!
You're a tiny dancer cancer

We didn't start the cancer
It continues growing with the posts you're flagging
2)Energy independent of intensity
Available on Spotify.
"I am Po and I'm gonna need a hat"
Anonymous
@BalarkaSen Welcome back...:P
15:52
@BalarkaSen hi
What math have the Russians done that is useful
nothing has changed between us
Anonymous
"An event is starting in 7 minutes in The h Bar - "Physics chat session"....are we topic-less as usual?
Yeah
Chat sessions have been pretty empty lately
@0ßelö7 dude the Russian school of topology and algebraic geometry is a thing
15:53
@BalarkaSen please delete this
as you wish
omg that was flagged
what is this, 9gag?
Not me
I promise
No, that was a pre-emptive deletion.
15:55
ah
i really enjoy the 30 minutes of epsilon more productiveness though
@BalarkaSen Must I remind you that you shouldn't insult others here, even in jest? I get that it's supposed to be harmless banter but it is simply not the kind of conversation SE chatrooms are supposed to host.
Flaggings aren't good for the reputation of the chat room
@ACuriousMind Ok lol I'll desist.
@Balarka have you heard Agalloch?
@BalarkaSen: and as for the We Didn't Start The Cancer meme that plumbs the depths of bad taste even by the standards of this chat room :-)
15:58
hahah sorry i couldn't resist not posting that meme
Are you saying this chat has bad taste?
after all there has been tons of pointless flags going around both this and the math chat for the few weeks
We can't even call each other cigarette butts without people getting upset
@Avantgarde Not yet
Cigarette butt? :-)
15:59
@BalarkaSen topology in the 20s and 30s
I don't know/care about topology after that. I doubt they had any good Differential topologists
rokhlin
i dunno what a differential topologist means
nobody does differential topology
In the 60s they did
anyway whatever you understand as a topologist, Rokhlin is one of them
Russian math is dead today. I'm talking about old school 20th century stuff
@BalarkaSen Should listen, sometime. Putting the link of the gem here: youtu.be/wnk2-Jctg6A
16:00
Arnold style math
Pretty awful stuff
Arnold is Rokhlin's student lol
@BalarkaSen I don't know about math but the flags in this room are not all facetious - y'all (=some of you) like to skirt the line here, intentionally or not :P
In any case, the chat session has officially started, and I guess we haven't got an agenda unless @DavidZ has something I don't know about
@ACuriousMind I'm pretty sure responding to someone's "X is trash" comment with "no u" is not offensive.
But yeah, I guess I do often troll the system.
16:02
@ACuriousMind nah nothing from me
@BalarkaSen have you read Arnold's mechanics book?
Nope but I am reading his ODE book
has 0% proof, but seems good for a reading course
No one does ODEs
Anyway, yes. The session is officially started, but if we don't have anything in particular to talk about, how about just dispensing with the standard boilerplate today?
If anyone is new to chat, new to chat sessions, or new to the site, please feel free to pipe up and say hello and/or ask questions, but other than that, if nobody minds, let's just have open discussion as usual.
@BalarkaSen I only vaguely remember what Rokhlin's theorem says because it's completely out of my area, but is the proof really sketchy?
16:06
It's a seminal result in the theory of 4-manifolds, and no, the proof is the very opposite of sketchy.
It's really nontrivial to prove.
So then it's not done in the Russian style?
Depends on how broken your idea of Russian style means!
Is inertial frame possible?
Arnold has a proof of an incorrect version of Huygens principle without ever talking about the wave equation
@BalarkaSen for the record, while that might not quite rise to the level of "offensive", I'd advise against it. Both the original comment and the response would be a little out of line in that case.
16:08
That's what Russian means to me
Like yes Earth is considered as an inertial frame
His proofs are almost more like thought experiments than actual proofs
Arnol'd has 0 proofs in his ODE book
"I am truly a lone traveller and never belong to my country,my home,my friend or even my family with whole heart"@JohnRennie
he's not the best representative of Russian mathematics
but still pedagogically pretty good
16:12
Besides Arnold I have two Russian books. One on Differential topology/surgery with a view towards Ricci flow and one on semigroups and heat kernels
They are very rigorous
@BAYMAX no idea
Although the topology one does the usual topological shenanigans
@DavidZ Sigh. Alright, fair enough.
hmm
I am new to chat sessions. Can someone summarise in one sentence what it is?
Anonymous
16:16
@Jasper In chat sessions we discuss recent discoveries, ask new users to introduce themselves, talk about site moderation/management, etc..
@Jasper Sure, it's a regularly scheduled time for people from the Physics SE community to get together and discuss... anything we want, really, although normally there are some standard things we go through as @Blue mentioned.
Anonymous
However, often we don't have topics to discuss :P
@0ßelö7 Is the one on differential topology written by Kosinski?
Well,hi all I am BAYMAX and I am not new here but new to chat session.
Welcome @BAYMAX
16:18
Thanks@DavidZ
Light is WAVICLE
@BalarkaSen I don't like Arnold's books because although he is famous, his proofs seems handwaving to me.
He has no proofs in his ODE book
Literally none
They are not really meant as formal textbooks, just staple foods that are good for you, like vegetables
Is it V.I.Arnold?
@Jasper yes
@BalarkaSen Really? I must have forgotten. I thought there are proofs but they are just not marked as such.
16:21
That's what Federer does.
is that the book on Mathematical Physics?
That book is interestingly written
I think there are a few in the appendices where he deals with uniqueness and existence of solutions to ODE's with various regularity
@BAYMAX FWIW this is a slightly atypical chat session. We often don't have much to discuss but most times we will go through a more structured introduction and we'll mention some recent developments in physics. Today it's very low-key though (because I didn't get here in time to do a proper intro :-P).
I see
16:24
Oh today is International Talk Like A Pirate Day, but let's not do that now, lol.
surrrrrrrre :-P
@Avantgarde I am pleasantly surprised that the guy who wrote and sang sappy songs like this turned out to be one of the artistically notable postmodern rock artists later :P
(Actually, I like that song, but I wanted to call it sappy to sound edgy)
On a totally new topic, did anyone follow the Cassini finale?
16:40
@DavidZ didn't we all?
Though I guess it was inconveniently early for people in the US
@DavidZ planned to but didn't
@JohnRennie Talk Like A Pirate Day is still running? I thought Mad Cap'n Tom had drifted out to sea
@JohnRennie Yeah, unfortunately I missed the actual end - it was something like 4 AM for me and I had to get up early
@DavidZ so you're back stateside?
I'm hoping the mission control feed is up on YouTube
@EmilioPisanty yeah, been back for a while now. I just started a new job in California though.
so I'm no longer an east-coaster
@DavidZ oh, you're at SoundHound? nice
I had noticed you left the academia rollercoaster bud that didn't register
16:43
ha, I see someone's been trawling my profile :-P Yeah, it took a while to get here after finishing my postdoc
@DavidZ It wasn't that interesting if I'm honest. Given there was no live video and the long time lag the actual impact passed almost unnoticed.
@JohnRennie hm really? I thought there was a live stream from the control center
@DavidZ no live video from Cassini I meant. I'm not that interested in live video of NASA engineers :-)
@JohnRennie Oh. Well I am interested in video of engineers.
Though not interested enough to stay up until 4 AM, I suppose
16:46
lol
@DavidZ "trawling" is a weird description
considering it took two clicks and it's the first thing under your name
yeah, kind of intentionally so
also the ":-P"
@DavidZ so.... are you in charge of the soundhoundy magic algorithm?
I'm a pretty assiduous user ;-)
oh sweet! Nah, I'm not in charge of anything yet, I've been here a week
I'm working on the Hound backend (the voice assistant)
@DavidZ how'dyou mean, voice assistant?
16:53
Have a look: soundhound.com/hound
It's like Siri or Alexa or so on
ah, gotcha
makes sense for soundhound to have a go at voice recognition
are you on the voice recognition, or on what happens with the text once it's been identified?
Yeah apparently they've been working on it for a long time - like ~10 years
@EmilioPisanty the latter. I believe I'm technically on the natural language understanding team
@DavidZ ah. nice.
although they're not big on titles here so it's a little fuzzy
It looks like really interesting work
well, kudos on a job well found
17:01
Thanks! I have high hopes for this one
It might actually come up again because the first thing they have me working on (just as a learning project) is enabling Hound to answer questions about particle physics
simple stuff like elementary particle properties
or whatever seems appropriate
Anyway, our scheduled chat session time is over. We'll have another one in two weeks; hope to see everyone back then!
Anonymous
17:17
@DavidZ That sounds really interesting. :)
17:27
Yeah, agreed. It'll be a little tricky figuring out how to accurately answer some questions without overloading users with detail
@BalarkaSen oh this is good! I often love sappy songs
@JohnRennie Yep! Nice album there. You've heard Agalloch before then?
Just discovered a day ago that the ex-guitarist (because Agalloch disbanded) is an English professor at a New York college!
17:59
@Avantgarde This is my Saturday morning jam.
It's kinda confusing how these two guys are the same persons lol

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