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2 hours later…
03:12
Enter Bernardo.
@DanielSank HAI
So
Here's my problem, there's this humongous question
and at one point I gotta find $g'(t)$
@PhysicsMeta are you bot?
$$g(t) = \int_2^t (2-t)f(x)dx$$
03:14
ok
@Ramanujan Yes, he is
What is question?
@DanielSank How do I do this? I just did $(2-t)\int_2^t f(x)dx$ but then I got stuck
Should I just apply the fundamental theorem of calc on that integral?
Oh no
I gotta do the product rule for the derivative too
Sigh
Yep.
:D
Ged demmit
Gimme a sec
user228700
03:22
Hello, everyone :-)
Hello.
Tiramisu, eh?
I have been following your food journal.
user228700
:-) Yep. It was delicious.
user228700
I have a quick question about the rate law for a given reaction. My textbook says:
user228700
> "Generally rate law expressions aren't simple and these may differ for the same reaction depending on conditions under which the reaction is being carried out"
user228700
Is this really true? Can the same reaction have different expressions of the rate law depending upon the conditions?
03:25
I have no idea what your book means by "same reaction" under "different conditions".
That sounds like a contradiction in terms.
user228700
I think they mean the same reactants reacting to give the same set of products except, maybe the they add a catalyst or the temperature is increased, etc.
@DanielSank That derivative will be wrt $t$ and not $x$ right?
@DanielSank different conditions means different temperature,pressure…
@BernardoMeurer What do you think?
so, for example $(2-t)' = -1$
03:28
@Ramanujan Ah.
@DanielSank yes
The $'$ notation is ambiguous, but yes.
I think it will be a derivative on $t$ sine $g$ is a function of $t$ and not of $x$
Right, $x$ is meaningless. It's just a way to tell you what's being integrated. It's a for-loop dummy index.
This prof loves dumb code
03:32
prof?
user228700
Never mind, thanks!
@DanielSank Applying L'Hopital 8 times in a row?
@DanielSank I'm a little stuck, this is what I got
$$-\int_2^t f(x)dx + (2-t)f(t)f'(x)-f(2)f'(x)$$
I dunno maybe. I don't have paper in front of me.
.-.
It's not right
ok just a sec
$$\frac{d}{dt} \int_2^t (2-t) f(x) dx $$
03:40
$$g'(t)=-\int_2^t f(x)dx + (2-t)f(t)$$ is the right one
$$\frac{d}{dt} \left( (2-t) \int_2^t f(x) dx \right)$$
$$(2-t) \frac{d}{dt} \int_2^t f(x) dx - \int_2^t f(x) dx$$
$$(2-t) f(t) - \int_2^t f(x) dx$$
So yeah, you got it.
Should that last one be $f(t)$?
So I got it right?
@BernardoMeurer I don't know what "the last one" means. Use math, not English.
@BernardoMeurer Pretty sure, yes.
@DanielSank How is mine right? It looks different
$$-\int_2^t f(x)dx + (2-t)f(t)f'(x)-f(2)f'(x)$$
@BernardoMeurer That one is right.
03:50
Hm
Well then
Where did you get $f(2)f'(x)$?
@ACuriousMind d00d, use a password manager.
@DanielSank I just applied the fundamental thm
@BernardoMeurer Can you please use math instead of english?
$$F(x) = \int_{a(x)}^{b(x)} \\F'(x) = f(b(x))b'(x)-f(a(x))a'(x)$$
03:54
@BernardoMeurer That's because you have $x$ in both limits.
NOW THAT's REALLY STRANGE:
Looped trajectories in 3 slit experiments
@DanielSank How would I apply that here then?
Full paper here (is open access): nature.com/articles/ncomms13987
@BernardoMeurer $a'=0$ here, d00d.
AH
and t is constant wrt x
so it's just $f(t)$
03:58
0
Q: A visual perception of time

AlexexySo I'm creating a character that is an extradimensional being exists outside of time. If we experience time as a linear event, how would time be perceived if this being has the ability to see time in a way that we look at how people move through three dimensions. I was initially going to base it...

=>Refer to canonical answer
@BernardoMeurer I don't know what "it" means. Listen, please, use math to talk about math.
Please.
It's right, don't worry about it
04:09
ладно
No more slavic languages today
Sorry
Nika already cursed me in like all the different Yougoslav languages while playing darts
4
04:54
@DanielSank
$$\int_0^{2\ln(x+1)} e^{\cos t}dt = e^{\cos(2\ln(x+1))}(2\ln(x+1))' - e^{\cos(0)}(0)'$$
05:06
9
Q: Does anyone know what that blue thing is?

NadsIt looks like the bulb of the lamp beside it but how why what

On topic? I'm a little skeptical
@DavidZ Do you know integrals?
Or rather, do you still remember how to integrate stuff?
user228700
05:25
Hi again. I have a "quick" question. I've been given that $rate=K1C/(1+K2C)$ and I've been asked to find the order of the reaction when $C$ s very very low. Since $C$ is very very low, I estimated that $1+K2C=1$
user228700
Is this an okay approximation to make? What my textbook has done is that they assumed $1+K2C=K′$. Hence, we get $rate=K1C/K′$. Either way, I find that the reaction is a first order reaction for very very small values of $C$. Which way is correct tho? Why does it make sense to assume that $1+K2C$ is just some constant?
05:41
@Kaumudi.H @0celo7 Wants to know why you are always talking about food
4
user228700
@BernardoMeurer x'D Firstly, tell him I say "Hi" and secondly, well, food is an excellent "simple pleasure" and I enjoy speaking about it to other enthusiasts, much like physics/math. However, I promise that there will be no more food-talk from my side from now till June.
0
Q: Are particles really in a superposition before you observe the particle

Don DixSo if I understood correctly, Schrodinger's Cat is a thought experiment that puts a cat inside a box, and there's a mechanism that kills the cat with 50% probability based on a quantum process. The argument is that the cat now must be in a superposition of dead and alive. But, is the cat really i...

It is, otherwise entanglement will not work
But what about isolated paritcles?
06:00
Update: Ok, looped trajectories are not strange, but still kinda interesting. I wonder when we will want more looped trajectories?
@BernardoMeurer Hi. Do you know how to integrate that function ? (Just curious as I could not figure out a direct way) What you did there seems more of differentiation using Leibniz rule...
@anonymous I do, yeah
Just follow from what I wrote
the right part will vanish
then it's handwaving
@JohnRennie I need help integrating :P
@BernardoMeurer Well, this term $$e^{\cos(2\ln(x+1))}(2\ln(x+1))'$$ remains
So I use substitution ?
Umm nice
Yeah, so, solve the derivative for $2ln(x+1)$
and you'll be done
@BernardoMeurer These days I generally leave integrals to Mathematica I'm afraid. I'm badly out of practice with integrals.
06:07
you should get $$\frac{2}{x+1}e^{\cos(2\ln(x+1)}$$
Ah great! But unfortunately it works only for this particular limit :P ...if we changed the bounds of integration then it won't be so simple :) BTW do you know of any direct method when we suppose solve the integral from 0 to $\pi$ ? @BernardoMeurer
IIRC, it's buried in my notes already
@anonymous Meh, I guess just use the fundamental theorem of analysis and handwave
@JohnRennie Have you seen that question yet?
@BernardoMeurer $\int_0^{\pi}e^{\cos(x)}dx$. Nah, I don't think fundamental theorem helps here.
@anonymous Then just solve it normally, i.e. $\int_0^\pi e^{\cos(x)} = e^{\cos(\pi)} - e^{\cos(0)}$, no?
$=e^{-1} - e$
@BernardoMeurer What??? You didn't even integrate the function... You just put in the bounds without integration
If you don't believe see Wolfram Alpha gives a totally different answer
06:15
it's 5am
I'm stupid
LOL XD
Anyway, yeah, it seems like you can't solve for that one
Seems so...I have to ask on Math SE
Not with Riemann integrals at least
Hmmm
Contour Integration will work I guess
06:16
@BernardoMeurer That's waaaaaaaaaaay over my head!
Although
I guess the set of discontinuities is countable so it does suffice for Riemann integrability
Yeah, well, it is Riemann integrable I believe
Just hard af
@BernardoMeurer e^(cos x) isn't discontinuous...
@anonymous Which is exactly equivalent to what I said
@BernardoMeurer In a twisted fashion :P
anyway it was a nice problem
I used the stronger version of the statement :P
i.e. that the function doesn't have to be continuous, it just needs to have a countable set of discontinuities
06:22
@BernardoMeurer True :)
(Proof provided by Lebesgue's Theorem)
user228700
@JohnR: Hello :-) Did u see the message I left for u last night?
@JohnRennie I might just get rekd in my calc exam
@Kaumudi.H Hi :-)
@Kaumudi.H No-one can work all the time. We all have to have some time off, and chatting with friends is a great way to relax. If you want to procrastinate some of the time I think that's an excellent idea. Just not all the time :-)
I procrastinate a lot
06:28
@BernardoMeurer <insert morale boosting message here> :-)
user228700
@JohnRennie No, it's not about procrastination, per se. I don't procrastinate that much, truth be told. It's just that when I start talking about music/food, I generally miss deadlines that I may have set for myself. Dyou understand what I'm saying?
@JohnRennie I much prefer if you could mail me your knowledge in a pill :P
2
@Kaumudi.H Yes, absolutely, and I used to do that as well. (I say used to because I no longer have deadlines not because I got better at meeting them :-)
user228700
Ah :-) Anyway, alright then, I will control urges.
@BernardoMeurer You guys are much better than me at the hard core stuff. I can't even understand 0celo7's question about metric, let alone answer it :-)
06:31
You might find this article about procrastination interesting :) time.com/51883/procrastination-is-in-your-genes I don't want to believe it though :-P
@Kaumudi.H it's OK to miss some deadlines. If you don't miss some of your deadlines you're probably not setting them aggressively enough. The point is to get a balance.
Get ahead of your schedule some days and behind it on others.
@JohnRennie I doubt that Mr. PhD
user228700
@anonymous Me neither :-P Then again, it's not about procrastination itself.
user228700
@JohnRennie Hmm, I don't have that many days, you see.
There will be days when physics seems easy and other days when it just seems a faff. On the latter days talking about food and Coldplay is a good way to get your mojo back.
user228700
06:33
:-D
@Kaumudi.H That's why I think regular exams are important. My speed of studying increases 10 times on the eve before the exam day :D
(Fear of failure :P)
user228700
Yeah, I agree :-)
Speaking of music I have been rehearing some of Bowie's stuff and it strikes me similar to the works of one of India's earliest rock bands. Funny, huh.
Communication and influence of art is one of the strangest things I'd never get.
@Kaumudi.H Both methods look correct but your one is better. K' is nearly equal to 1 anyway as C tends to 0.
@Kaumudi.H I would use a binomial expansion for that ...
user228700
06:54
Hmm, it doesn't actually matter anyway, since they've only asked about the reaction order. Thank you :-)
Hello. Happy Galileo + Hawking's B'day!
@SwapnilDas Galileo' s bday is on 15 th Feb I guess
(If you meant Galileo Galilei)
user228700
07:18
I've a quick-ish question. This is what my textbook says:
@Kaumudi.H Whenever you see $(1 + x)^n$, where $x$ is small, always think about a binomial expansion. We use that all the time in physics.
user228700
@JohnRennie Riight. Isn't the Taylor series for this function $1+nx+...$(negligble terms for small $x$) ?
user228700
> "All functions (whose domain is symmetrical about the origin) can be expressed as the sum of an even and odd function as follows: $f(x)= \{f(x)+f(-x)\}/2 + \{f(x)-f(-x)\}/2$"
user228700
Oh, hang on.
@Kaumudi.H Yes. So in this case you'd get: $$(1+K_2C)^{-1} \approx 1 - K_2C $$
So: $$ \text{rate}=K_1C(1 - K_2C) \approx K_1C $$
user228700
07:24
Oh, yes of course! Thanks! :-D
user228700
And never mind that about the even/odd function thing. I figured it out.
I can't emphasise enough how important a tool the binomial expansion is. As you study physics you'll use it time and time again :-)
user228700
Boy, that chapter Gravitation uses a lot of this for all of its derivations.
@Kaumudi.H Be a little careful about that, because it only works for $|x| < 1$. But yeah.
user228700
OK, what my textbook says. I have a really quick question.
user228700
07:31
@BalarkaSen Yes, of course. Thanks for the reminder :-)
@BalarkaSen tum yahaan kyon ho?
Tumi ēkhānē kēna?
I like physics
wow, they are quite different lol
the "tum" is the same though
@BalarkaSen Binomial theorem works for all $x$ I think. Why should $|x|<1$ ?
user228700
07:33
The 2nd one is in Bengali? 'Cause I don't understand that.
yes
user228700
@anonymous U can only neglect all of the other terms if $|x|<1$ in the Taylor series.
@anonymous Try nonintegral $n$, or negative.
@BalarkaSen Does the approximation nature of physics disgust you as a mathematician?
e.g. for 0<theta<pi/3, we take sin theta = theta
07:35
Not when it can be justified with some work.
When they claim 1 + 2 + 3 + 4 + ... = -1/12, yes
@BalarkaSen Yes, true. But in that case we can use the generalized binomial theorem after some manipulation. gradestack.com/JEE-Main-2015-Complete/Binomial-Theorem/… I understood what you meant though.
@BalarkaSen I forgot where this result is used in physics
Me too.
Could someone have a look at this question math.stackexchange.com/q/1963640/333392 . It's maths but it's about the Lagrangian
@JohnRennie could you please have look a t this question. It has been confusing me since weeks
@DHMO String theory :D
07:38
I see
I came across this xkcd:
How would I solve the question on the top-right hand corner?
@DHMO Easy. Put two current inputs and analyze separately.
By superposition theorem
Of electric circuits
It seems there's something interesting going on, the same kind of transposition phenomenon I have seen throughout my life: The Maths chat is becoming more like h bar with the addition of the non maths rule. The lack of activity in h bar recently seemed to shift to maths, and the activity in maths seemed to shift to here

I wonder when ocelo7 returns everything can go back to normal. This overall "lack of activity" is like being in a sound proof room
@anonymous what is that?
The superposition theorem for electrical circuits states that for a linear system the response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where all the other independent sources are replaced by their internal impedances. To ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by: Replacing all other independent voltage sources with a short circuit (thereby eliminating difference...
never mind
07:41
It is from IE Irodov
that problem
@Secret Our definition of "normal" seems to be very different - you're thinking of "0celo-normal".
You just need two grounded cells each of potential V.
But actually I'd like him to be unbanned. There was more math when he's around.
Well truth is, a lot of users like the 0celo normal in h bar as evidenced by the many stars about it. And ever since his absense, something is going out of balance in terms of user base, and the activity trend of this room. This room rarely get quiet in the afternoon period corresponding to sydney
I also like his GR discussion. Slereah sticks around more with his QFT stuff when ocelo is around ,so is MAFIA
Currently, the average activity in this room is mainly contributed by kaumudi and johnrennie. WIthout them two, this room is pretty much dead
@Secret that's not really true. Kaumudi and I tend to be very active for a few hours in the morning (UTC) when our time zones overlap. But the other 20 hours of the day there is lots of other activity.
user228700
07:52
@JohnRennie :-| I'm on here for around 8 hours everyday. Oftentimes, I ask random questions during that whole time.
hmm ok, I guess my bias might be due to my wake up periods are often when the room is having low activity
user228700
(Actually, I'm on here for more than just 8 hours but @JohnR: Our time zones overlap neatly only during those 8 hours)
08:07
@DHMO You can solve the problem using recursive methods too mathpages.com/home/kmath668/kmath668.htm
It is more of a maths problem :)
@Kaumudi.H Incidentally (and this is not an excuse to procrastinate :-) this is what I ended up eating for lunch yesterday:
It's bread cooked with cheese and chutney. Still warm from the oven!
And it was absolutely delicious :-)
@JohnRennie What is chutney ?
Chutney (Devanagari- "चटनी" also transliterated chatney or chatni, Sindhi: چٽڻي‎) is a sauce in the cuisines of the Indian subcontinent that can vary from a tomato relish to a ground peanut garnish or a yoghurt, cucumber and mint dip. An offshoot that took root in Anglo-Indian cuisine is usually a tart fruit such as sharp apples, rhubarb or damson pickle made milder by an equal weight of sugar (usually demerara or brown sugar to replace jaggery in some Indian sweet chutneys) Vinegar was added to the recipe for English-style chutney that traditionally aims to give a long shelf life so that fall...
We Brits imported it from India during the days of the Raj.
Looks tasty (and spicy)! You know how to cook Indian food ? :) @JohnRennie (I guess you are from UK)
In this case I think it was basically pickle
08:16
Oh I see. That was readymade chutney
:)
@anonymous I like my food, but I'm not a very good cook. Indian food is very popular in the UK, so lots of us Brits are familiar with it.
in Mathematics, 1 hour ago, by user400188
Secret you probaly would find that it was one of them tht put all those ideas in your head
lol
user228700
08:43
@JohnRennie Awesome! :-)
user228700
@Shashaank: Do I know you (IRL)?
user228700
@anonymous :S Aren't u Indian?
[Is bored]
@Kaumudi.H after all he wants to be "Anonymous"
user228700
08:50
@Ramanujan I read the transcript at The JEE Launchpad and he/she said that he/she is preparing for JEE, which is very good reason to assume that he/she is Indian, in my opinion.
@Secret why 0x=x?
oops, that'sa typo
there, fixed
0x=x0=0
(next slide skipped cause not going to to bore people with more meadow stuff)
@Secret 1/0 ≈infinity I suppose :(
@Kaumudi.H My birthplace was India but I live in the Middle East. I visit India sometimes during vacations. I am preparing for the JEE though as I wish to join a college there as there are not many good tech institutes here.
08:57
@Ramanujan That's how we treat it in calculus, and indeed it will be valid in that context. But we are interested in algebraic structures where you can say there is an elemnt q such that q0=1 and not cause contradictions
And you want to say q=1?
user228700
@anonymous Oh, interesting!
@Kaumudi.H And where are you from ? Which state ?
09:15
@Ramanujan nope, q can be anything, I only want q0=1
@Kaumudi.H I don't know you in IRL so I guess you might not be knowing too.
@anonymous If you were referring to me then does Nationality holds such a significance for you
@anonymous Sorry! I read that wrong
user228700
09:44
@anonymous I'm from South India.
user228700
@Shashaank Oh, I'm sorry, then. I have a friend whose profile would match yours exactly.
user228700
I have a quick-ish question about the product of functions. This is what my textbook says:
user228700
> "If $f$ and $g$ are both even or odd, then the function $(f.g)(x)$ will be even but if any one of them is odd and the other even, then $(f.g)(x)$ will be odd"
user228700
Is anybody familiar with a proof of this, perhaps?
+×+=+ and -×-=+
user223506
09:50
@Kaumudi.H how was the tiramisu?
+×-=-×+=-
Idk just guessing by previous knowledge :D
@Kaumudi.H apply the definition of odd and even functions
user228700
@Ramanujan -__- Thanks, but hang on, while I'm trying to work on a more rigorous proof.
user228700
@Doc Oh, it was excellent! :-)
user228700
@DHMO ...doing.
user223506
09:53
@Kaumudi.H thi is good - it is one of my favourite desserts
user228700
@DHMO Because it's the product, I dunno how to prove it for all functions.
@Kaumudi.H I'll only prove one case as an example.
user228700
@DHMO Thanks but no, I don't need you to prove any single case--that I am able to do by myself.
user228700
I'm struggling to prove it for all cases.
@Kaumudi.H Ugh, prove all cases independently.
user223506
09:55
I got all chatty yesterday - 2 answers!
There is just 4 cases.
user228700
Oh, hang on.
Your statement basically includes 4 theorems, all of which are independent.
@DHMO just curious was my proof right?
user223506
I am conjuring up a question - but will take my time to make sure it is a good and well researched one
09:56
@Ramanujan yes, if you had elaborated it.
How I could elaborate it?
Do you think "+×+=+" is a valid proof of anything at all?
user228700
@DHMO: I'm sorry, I misunderstood what u meant by "case". One case is absolutely fine, thanks.
@Kaumudi.H Alright, so we'll prove this statement:
> If $f$ and $g$ are even, then $(f.g)(x)$ is even.
user228700
Okay.
09:57
Consider $h(x) := (f.g)(x)$.
$h(-x) = f(-x) g(-x)$.
user228700
Right.
By definition, $f(-x) = f(x)$ and $g(-x) = g(x)$.
Therefore, $h(-x) = f(x) g(x) = h(x)$.
Therefore, $h$ is even.
user228700
:-| That was ridiculously easy. Gosh, I'm an idiot.
user228700
Thanks.
You are welcome.
user223506
09:59
@Kaumudi.H you are not an idiot
Really, all of them are said by Kaumudi
Yeah,its a habit lol
user223506
dang!
user223506
anyone who likes tiramasu is a legend as far as I am concerned
10:08
I like mocha cakes and icecream
user223506
@Secret that is legendary also
user228700
@DHMO Well, he searched for "When said by Kaumudi" so of course, all of them were said by me.
@Kaumudi.H oh, lol
I'm an idiot.
Interestingly, I don't like the actual drink itself because coffee is too bitter with a watery taste
@Kaumudi.H Yes I thought that
user228700
10:10
@DHMO x'D It's a bit of a habit, but like I have said before, it doesn't affect my self-esteem or anything. Gosh, I hope Daniel Sank doesn't read all this. He once gave me a lecture about this very habit :-P
@Shashaank No, not at all. I was talking about how to choose inertial reference frames if you read my previous message aimed at you.
user228700
@Doc :-) U're kind.
user223506
@Kaumudi.H you have some great contributions
@Doc I see you are atmospheric radiation physicist. Do you still work in that field (like academia) or something else ? :) I never heard of atmospheric physics as a different subject. Just curious.
user223506
@anonymous I do research in that field when i can - ofteen making my own tools. For a wage, I work as an editor, programmer, teacher
10:24
@Doc Ah, so how do you research ? Are you a member of some university or institute ? Or you have your own labs ?
user223506
I mainly do research with solar UV
user223506
I am an Adjunct for one University, a researcher for a solar UV team and a Skin Cancer research fellow (part time)
user223506
My lab is often where I set down my 'lab-bag'
@Doc Fascinating :)
user223506
I have a backpack that I am developing - solar powered, with my equipment in it
10:27
@Doc What is the use of the "solar powered" bagpack ? :O
What is the power used for ?
user223506
my electronic devices - some IoT devices for measurements
@Doc I see. Wow!
user223506
it's partly a hobby and it's my somewhat vain attempt to get into fulltime research
@Doc I guess full-time research gets a bit boring after a certain length of time..(I might be wrong)
user223506
@anonymous perhaps, but it would be a dream for me
10:35
@Doc Then why don't you go for full time research ? I think the pay is quite low for full time researchers ( which is very sad )
user223506
@anonymous oh I am trying
user223506
but the compromise I have now is fine
@anonymous Yes I got that ! I read it wrong. That's why I said sorry ! I read it wrong.
@Shashaank Okay !
Example of a vague statement:
"I know nothing about <topic>except anything that I happened to seemed to understand when other people said it"
11:06
1
Q: Can an atom own a non zero total angular momentum $\bf{L}$ and a zero total magnetic moment $\bf{m}$ at the same time?

SørënIn the explanation of diamagnetism, the atoms do not have a total magnetic moment $\bf{m}$. This magnetic moment comes from the sum of all magnetic moments of electrons, that have an orbital $\bf{m_{o}}$ and a spin component $\bf{m_{s}}$. My question is: can the total angular momentum $\bf{L}$ ...

nuclear magnetic moment?
11:42
Am I the only one bothered by the starting assumption of physics.stackexchange.com/q/2328/8851 ? Just what kind of super high resolution CRT with building-sized vacuum tube screen does the OP have at home?
I'd like to have such a television.
Or the textbook author, really.
Is that just a case of bad textbooks?
12:11
Oi
12:33

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