/sci/ - Science & Math

I want to ask the stupidest question of all. Why haven't the hot dogs asked him the what have you been to doing with Gauss and Laplace to orgasm within most sandwiches and have you to be already gone to the Red Bull product placement and then you have no barbecue?

Quoth the e-mag text:

>Do not confuse curl for a cross product.

Fukken why not.

>>10196021
did ANITA / IceCube really discover a new particle? they say it's a stop (SUSY partner of a top quark). is this bullshit or is it really fucking big?

>>10196031
Curl is rotation
Cross Product of 2 vectors gives a normal vector

>>10196036
So why is the curl for a vector field expressed as del cross said vector field?

I mean, was Maxwell just being a dick?

>>10196044
You’re not crossing another vector

>>10196031
Because the cross product is the wedge and curl is the exterior derivative. The only thing they have in common is their graded-ness.

Why do chemistry students get such bad grades on average?

I procrastinate to the extent I get zeros on some of my assignments just because I didn't submit anything (too late). How to fight with this? I keep watching old Jerma videos like a retard.

>>10196474
Make it as hard as possible to procastinate. Keep watching videos? Block YouTube using a browser addon or the hosts file. Maybe go do your assignments in the library and bring only your textbooks and a pencil.

>>10196031
You can abuse notation to express curl as a cross product. This has some mnemonic value, but it isn't an actual cross product. (∂/∂x,∂/∂y,∂/∂z) isn't actually a vector and application isn't actually multiplication.

>>10196495
>complaining about abuse of notation in differential geometry, the abuse of of notation field

For the physicists / radio enthusiasts / science fiction readers here:

If we could naturally transmit and receive electromagnetic radiation, and could control its properties enough to converse with one another, what natural conditions (or the radiation's properties) would allow for our conversations to remain relatively private?

By "private" I mean, that me saying "well I DID fuck his girl last night shit was CASH!" would not:
A) travel past my friend and into the street for all to hear until eventually out into space for millennia for distant cultures to learn
B) Fry his internal organs and give him cancer by molesting his DNA

I was trying to think of the density of the atmosphere, the wavelength being sufficiently swallowed by natural materials, the natural noise in the environment and so on. I mean, airwaves are much better for this purpose than like gamma radiation, but I was curious nonetheless. The bonus is that one could in theory kill someone by yelling at them loud enough.

I know of a few Youtube channels that teach physics, but they're not calculus heavy, actually, there's barely any calculus going on at all.

So, I'm looking for a channel that doesn't go nuts on integrals and derivatives and uses them as the only way to solve exercises, but a channel with possibly a mix of both solving with calculus and without. That actually teaches you the applications of it and how to use it effectively, but isn't some autistic nerd covering himself in cum because he can do calculus, so it's the only thing he does.

My request is simple.

>>10196530
>
>My request is simple.
lol fuck off

>>10196477
>Maybe go do your assignments in the library and bring only your textbooks and a pencil.
That's a bit extreme as I utilise internet a lot while doing my coursework (to look up formulas and whatnot).
May try an addon, because when I realise I'm wasting time I usually stop watching videos or browsing the chan or whatever. And obviously getting blocked from a website is the ultimate warning for "You were about to waste your time".
Thanks for the suggestion anon.

>>10196031
I bet you think that derivative df/dx is a ratio

Which is the most solid foundation for undergrad-tier linear algebra?

>>10196533
no u

It's not like I'm looking to meet the fucking Pope or something.

>>10196565
>please find a youtube channel for me that meets these incredibly specific criteria
Just read a fucking textbook, my dude. If you want to watch videos only, then watch Walter Lewin's lectures.

>>10196553
Hoffman and Kunze

Is economy a science? Why economists don't rely very often to economic statistic? Could machine learning help us to guide economy through pattern recognition?

>>10196612
In the 1970s, Robert Lucas made the Lucas critique. It basically goes like this:
Imagine you're a producer. Obviously, you want to maximize your profits, and to do that, you pay some general attention to how the government's acting on the economy, and the general theoretic basis of that, even if you don't read too much economics.
So imagine that the government notices that, if they bring down the interest rate they can trick you into investing, and then they let it go up again. So the government keeps doing this, but because you aren't an idiot, you notice. So, when the interest rate goes down, you let a couple of months pass before even thinking about investing.
In other words, even if there existed a correlation between the interest rate and investment, or more famously, between inflation and product, the moment the government's action on these things changes, the people start acting in different ways, because the game rules changed.
What this means is that using statistics in economics is something really important, but also strangely sensitive. If the government finds a correlation in the data, and tries to exploit it, it ends up shooting itself in the foot after people learn how to exploit that.
If you're using, say, the stock market, then you have a similar problem: the stock market efficiency hypothesis. Even if you want to try to use data to maximize profits, everyone else is already doing that.
You need to remember that people think. They might not be super rational geniuses, but they aren't retarded.

Anyone know what that textbook was called where the word problems are "funny"? Or pictures of the problems?
I forget what the problems were about, but there were threads about the problems in that book.

How am I supposed to sketch the solutions if I can't find x(t) analytically (This means I can't do integrals, right?)

>>10197134
Approximate it by a bunch of small line segments, aka numerical integration.

>>10197134
Literally just draw the function

>>10197149
as in the graph of x' vs. x?

>>10197146
There is a part c and d of this question that ask us to do exactly that. I've already used RK4 and Euler to approximate the solution.

>>10197183
Graph of x.
Use x(0)=0 or something.

>>10196021
>questions
how much longer?

>>10197189
Is that a question?

>>10197134
You should probably draw the direction field along the x axis, noting that the ODE is autonomous, then sketch a curve starting at (0,0) that fits that direction field. Here's a picture.

Is this correct?
Since this is a conservative vector field and start and end at the same spot, work should be 0?

Also, if we weren’t in a conservative vector field, should I just use Green’s theorem?

>>10197345
>Since this is a conservative vector field and start and end at the same spot, work should be 0?
Yes.
>Also, if we weren’t in a conservative vector field, should I just use Green’s theorem?
I don't understand why you would want to do that; why don't you want to parametrize the curve and integrate along it?

lol

>>10197345
if you think about it, when you use the fact that a vector field is conservative to deduce that the integral around a loop is zero, you're implicitly using Green's Theorem.

>>10196521
Still bumping this 'cause I'm curious.

>>10197345
Do it properly.
F(x, y)=F(-x, -y). Because the curve is symmetric, it zeroes.

>>10196918
My textbook has tongue-in-cheek jokes in problems here and there. It'll often refer to your cousin Throckmorton as the subject in some of them, and one had to do with Santa and said "standard reference texts note that he is a 'right jolly elf' and as such his height can be taken as 170cm" or something along those lines. Are you talking about something like that or one where every question has an element of comedy?

>>10197784
I dont know if it was every question or not, but the questions were definitely “meme worthy” and not like the ones you said.

>>10196495
>(∂/∂x,∂/∂y,∂/∂z) isn't actually a vector
It's a vector field in the tangent space.

>>10197134
Draw the phase diagram and do linearization around hyperbolic fixed points using Hartman-Grobman theorem.
>>10197345
What you have done is essentially showed the Cauchy-Riemann equation for the complex function [math]F(z) = u(z) + iv(z)[/math] under the complexification [math]\mathbb{R}^2 \rightarrow \mathbb{C}, ~(x,y) \mapsto x+iz = z[/math]. This means that [math]F[/math] is holomorphic and hence Cauchy integral formula gives [eqn]\int_C dz F(z) = \frac{1}{2\pi i}\sum_{\operatorname{Res}z_i}F(z_i).[/eqn] Since [math]F[/math] has no poles the integral is 0. Alternatively you have also showed that the 1-form [math]\omega = {\bf F} \cdot d{\bf x} = d\sigma[/math] is exact. Stokes's theorem in [math]\mathbb{R}^2[/math] then says [eqn]\int_C d\omega = \int_{\partial C}\sigma = 0[/eqn] since [math]\partial C = \emptyset[/math].
>>10197659
The vector field being even means that the path integral takes the same value on the two semicircles [math]C_+[/math] so [math]\int_C d{\bf r}\cdot{\bf F} = 2\int_{C_+}d{\bf r}\cdot {\bf F} \neq 0[/math]. What you're thinking is when [math]{\bf F}[/math] is odd, which the vector field in question isn't.

Is nutrition science all a meme? How do you even isolate intakes in a human to even prove anything? Why are people okay with the food pyramid?

Can somebody explain me how exactly the microcanonical, macrocanonical and grand ensemble describe the same physics? I initially thought the first was to describe enclosed systems, the second systems that exchange energy with their environment and the last one for systems that can exchange particles. Thanks in advance.

>>10198469
it's not

>>10199451
Yes it is. The tangent space [math]T_pM[/math] of a manifold [math]M[/math] at [math]p\in M[/math] with an associated chart [math](U,\alpha)[/math] such that [math]\alpha(p) = x[/math] is spanned by [math]\{\partial_i\}_i[/math]. The gradient is literally just [math]X(\alpha^{-1}(x)) = a_i\partial_i[/math] where all of the coefficients [math]a_i = 1[/math].
Might want to read up on elementary differential topology before making a post honey

>>10199457
it's not.
if something, (∂/∂x,∂/∂y,∂/∂z) is a basis on TpM. not a vector nor a vector field.
>Might want to read up on elementary differential topology before making a post honey
:-*

Can anyone give me their opinion on the latex template in picrelated? I'm planning on using it.

>>10199556
The technical skills overview part with the balls and the font color switching mid-word are embarassing to look at, but otherwise it works. I'd suggest asking in /wsr/, some people there actually know design.

>>10199561
>The technical skills overview part with the balls and the font color switching mid-word are embarassing to look at
Oof, that's harsh

>>10199556
Dates usually go on right as they are less important and out of the way. Also helps the bolded title stand out and separate sections more easily. I would suggest changing the colored text to just one letter instead of 3,that's what I did but partly because I had a section with a short name so it looked weird having half the word colored. On the left with the skills and bars, I don't know how you're quantifying the length and relative strength. If I was interviewing you for a quantitative position, I'd ask how you determined that as a way to see how well you apply what you know. Overall, look is professional and my comments are minor technical ones that may or may not matter. It is one of the better templates, but you can probably find a better one if you don't want to go in and make those corrections yourself to the sty file

>>10199556
What are you trying to use it for? It'd be pretty awful as a resume. The layout is too unconventional.

That chart for your "technical skills" looks like a joke. The programming section too, especially with Latex listed as a programming language. Don't put a number of lines of code, it's confusing and looks bad.

Designing a clip that in theory should be easy to remove, so it hooks in on the left

and does the action I've designed allow it to more easily hook out? As in pulls it out?

Basically just have one triangle pressing against the other once it starts to move, may need to make some things thinner to get more flex

It's a 3D printed part, there's holes because a bar connects them

the hook piece doesn't fill up the inside, so it's somewhat flexible.

Don't know if I need some kind of tab added to make pulling easier, I assume I could just squeeze the bars, though the bars themselves are flexible so a tab is probably better.

>>10199561
>The technical skills overview part with the balls and the font color switching mid-word are embarassing to look at
Yeah, I thought those were a bit extra. I mainly like the idea of the sidebar.

>>10199579
>What are you trying to use it for?
As a resume. It is listed as a latex template for "entry level resumes".

>The programming section too, especially with Latex listed as a programming language. Don't put a number of lines of code, it's confusing and looks bad.
Yeah, I may take out most of the diagrams and just leave lists. But wanted to know what other people thought. Also Latex is a programming language.

>>10199610
>Latex is a programming language
Are you actually using it as one? Saying "I wrote 3000 LoC of LaTeX" is nonsensical either way, though I guess LoC counts are pretty meaningless for every language.

>>10199639
I'm not the guy in the resume. That's probably the guy who came up with it and then put it online for others. He has written 3000 LoC of Latex, not me.

>>10199570
>tfw no one gets your pun

I'm still confused about Divergence Theorem and Green's theorem. What exactly are we measuring here?
Also, do surface integrals measure area?

>>10200092
>do surface integrals measure area
Not necessarily but if you set them up in the right way, they correspond to surface area.

>I'm still confused about Divergence Theorem and Green's theorem. What exactly are we measuring here?
Not anything in particular. You may, for example, set up a double integral in such a way that measures area. Then through a theorem like Green's theorem, you can transform that into another type of integral. What this other integral measures really means nothing as the point of Green's theorem is that now this line integral is equal to the original double integral, which you set up so that it corresponds to area. The same with Div theorem but now with triple integrals.

>>10200092
>I'm still confused about Divergence Theorem and Green's theorem. What exactly are we measuring here?
The divergence theorem measures the total amount of divergence of your vector field, more intuitively, the total amount that every "source" and "sink" contribute in a certain volume.

Green's theorem is a special case of Stoke's theorem which measures how your field is changing on a certain surface, and tells you that you can look on the sum of the values of your field on the boundary of that surface instead.

>Also, do surface integrals measure area?

Yes, they do. The measure of integration can be chosen to be an infinitesimal volume on the surface, which if you integrate (like integrating the identity scalar field over the surface) gives you the area.

>>10199376
bump

>>10199376
You can think of the term [math]\mu N[/math] in the grand canonical ensemble as a Lagrange multiplier for the canonical ensemble with the constraint of [math]N[/math] particles.

>>10200092
"the amount of stuff that's leaving the walls of a factory is equal to the amount they're producing inside the factory"
"the amount of water a cell uses and consumes is equal to the amount entering through its membrane"

a surface integral measures how much the vector field is exiting the surface. so if it's tangent to the surface, for example spinning around the surface, the surface integral is 0. if it's pointing out of the surface, the surface integral tells you how much is "leaving" the interior. if it points into the surface, the integral is negative and tells you how much the vectors are entering. if it's mixed, the sign of the surface integral will tell you whether more leaves or enters. this is called the "flux" through the surface.
the divergence theorem says that the amount leaving a surface is equal to the amount produced in the interior (or the amount entering is equal to the amount consumed). this is pretty obvious, since if stuff is leaving then you know it had to come from somewhere inside. but the divergence theorem is a way of stating that properly.
don't think about it too hard.

stoke's theorem is similar, it tells us that the amount that the vector field spins around a surface is equal to the amount of spinning going on inside the surface. very similar to divergence theorem but with a surface integral which measures how "tangent" vectors are and with the curl in the interior.

green's theorem is the 2 dimensional case of stoke's theorem, or of divergence theorem, depending on which form you're looking at. but really, they're all the same thing.

>>10200157
Yes, because they induce the bonds (I.e [math] \mathcalH (\vec{\mu})=E[/math] , [math] N= N_S[/math] , and so on) but I still don’t understand how I can derive the same partition function for a system, from three descriptions that are different.

>>10200186
Well no, you can't. But you can show that the grand canon ensemble is equivalent to the canon ensemble in case where your system has conserved particle number. The former is really a generalization of the latter

>>10200186
[math] \mathcal{H} \left( \vec{ \mu } \right) [/math] *

>>10200190
So when I’ve got a certain system (say an ideal gas in a box, or a set of oscillators, or a magnetic system of spins) I must choose what description fits for it? Or it doesn’t matter what I pick, cause these constrains are all happening at equilibrium? Thanks for your answer

>>10200205
>I must choose what description fits for it?
You need to know the conservation laws, and hence the symmetries, in equilibrium. Once you have that then the breaking energy/particle conservation tells you to use the micro/grand canon ensemble.
On the other hand it you're out of equilibrium then you can't even use the grand canon since Boltzmann factor doesn't work.

This is 33% correct?

>>10200224
It depends on how you read the problem and what assumptions you make. The 1/2 answer requires an additional assumption that know a particular attack was a crit. From a general statistics perspective, it's 1/3

>>10200221
thanks, I thing I’ve got it. It’s just that when we started doing quantum statphys, our professor told us that we have to use the grand canonical ensemble

as far as i can see, a quadratic function with a discriminant of 0 should logically only have 1 root, since you can't have positive or negative zero. But It is said that ever quadratic has TWO roots if you include imaginary roots. what is the second root for quadratics with a discriminant of 0?

>>10200312
The roots are degenerate. Notice that the statement is that every polynomial of order n acquires n zeros, NOT that it acquires n UNIQUE zeros. In the degenerate case you have a zero of order 2, or 2 zeros on top of one another.

>>10200317
>degenerate
>>>/pol/

>>10200312
Single root of multiplicity two. Like [math] (x - 2)^{2} [/math].

>>10200312
As other anons said, the roots are said to have multiplicity 2. But that's kinda cheating if you just heard about it - you're just fixing the statement of every quadratic having two roots by arbitrarily fixing it when it's one but "twice".

But there's a very real geometric interpretation of multiplicity, that applies to curves of any degree. The idea is that multiplicity measures how the roots change under small perturbations of the graph. What happens if you nudge the graph of x^2 a bit? It has only "one" root at 0, but if you move it a bit, you either suddenly get two new roots or no roots at all, no in between.

Now similarly for a cubic, say y=x^3, you have a triple root at 0. Now this nudge can be written mathematically as adding a very small term to each x. For example, draw the graph of y=x^3 and y=(x-0.5)x(x+0.5), and you will see what I mean

How much does grad school ranking matter for getting a job in industry or government lab? Ive heard it is important for maybe becoming a professor, but I just want to go to industry or government and not academia. Looking at top 10-55 programs

My differential equations professor hasn't graded my classes last 2 exams. The only thing he graded was our first exam and the mean was 57/100. He said that we're the lowest scoring class he has ever had and that it's very hard to grade bad exams.
Is this code for: "I'm with holding finalizing grades so I can do an insane curve just in case you all end up failing"?

>>10200414
he’s bad at his job and is fucking with you, if you all end up with failing grades i would complain to the math dept and the various admins at your school. they have to give back exams before they give out the next one or you have no idea what you’re weak on.

Working through a textbook (because I’m going to be taking Representation Theory next semester) and found this problem. I’ve been staring at it for two hours and don’t know what to do.

>Suppose V is a complex representation of a finite group G. Suppose K is a normal subgroup of G with index 2. Let V be irreducible with respect to G, and reducible with respect to K. Prove that V is the direct sum of two K-invariant subspaces of equal dimension.

I can prove that G acts on the set of K-invariant subspaces of V. I can show that the action factors through G/K. I know that there are two cosets of K: K itself and G / K. I know that if U is a K-invariant subspace of V, the so is gU for all g in G. I know that either gU = U, or the intersection of gU and U is trivial. I just don’t know how all these facts fit together to finish the proof.

>>10200429
You're almost there.
Define projectors. The fact that [math]G[/math] acts "properly discontinuously" (for a lack of a better term) on [math]V[/math] means that you can mod out the action of [math]G[/math] on [math]V[/math] to get two orbits, one is [math]K(0)[/math] and the other is [math]G/K(0)[/math]. Then it suffices to show that this projection [math]\pi: V\rightarrow V/G[/math] is orthogonal.

>>10200575
I think I might understand what you’re doing, but how does that imply the subspaces have the same dimension?

>>10200617
If the action of [math]G[/math] is transitive, then each element [math]v \in K(0)[/math] is obtained from [math]0[/math] by some [math]k \in K[/math], hence [math]|K(0)| = |K|[/math] (and also similarly for [math]G/K[/math]). Since [math]K[/math] has index 2 we have [math]|K(0)| = |G/K(0)|[/math].

>>10200643
|K(0)| = |K|, and |G / K| = |G / K (0)| I understand. But why does K being index 2 imply that these things are equal? What am I missing?

>>10200709
K being index 2 means |K| = |G/K|.

Does anyone know what type of question this is? Is this variation of parameters?

Does anyone know what I should look up to learn this? Is it variation of parameters?

>>10200725
Looks like a question from an introductory differential equations class.

>>10200717
Wow, I’m dumb. Thank you for your help.

>>10200736

My professor is an asshole and doesn't give us the correct terminology for mathematical concepts. Can someone help me figure what this actually is?

>>10201157
Given any neighborhood around [math]p[/math] the sequences at some point gets [math]\epsilon[/math]-close to [math]p[/math] and then eventually gets further. Though I would've called such a sequence a "grindr hookup sequence" instead of a flirting sequence.

>>10201165
Thanks, Anon.

Can someone explain 7a? Why is the answer not simply {(x, y) is an element of R^2}? Since an element in R can be 0 or lower, resulting in y being 0 or lower

>>10196021
>have random stream.yuv file lying around that I have no idea what is from
>try a bunch of encoding options with ffmpeg but nothing really makes sense
what do

>>10201280
idk but that's an interesting problem
Is there a way to like analyse it to figure out encoding might make sense?

>>10201280
the head of hexdump says

00000000 49 34 32 30 20 57 31 39 32 30 20 48 31 30 38 30 |I420 W1920 H1080|
00000010 20 46 31 30 30 30 30 30 30 3a 31 36 39 34 39 20 | F1000000:16949 |
00000020 49 70 20 41 31 3a 31 0a 46 52 41 4d 45 0a 10 10 |Ip A1:1.FRAME...|


so I guess yuv420p 1920x1080 which results in
>this

but the file is extremely repetitive and with xz it compresses from 140MB to 9MB

>>10201274
An element in R can be 0 or lower, but R is the set forming the first coordinate...
y comes from one of the [i, i+1] intervals, which begin at [1, 2] and get bigger from there. so y must be >= 1.

>>10201286
did hiro break

codetags


>>10201286
>>10201290
ohright this is /sci/ I thought I was posting on /g/
well that explains it
sorry

>>10201290
Doesn't work on sci. >>>/g/

>>10201287
Fuck you're right. I'm such a brainlet

Wtf does this mean?
Isn't pressure higher at the bottom?
Is he not assuming the effectss of gravity?
But then why does he say weight?
What's that energy variation? It can't be a gravitational potential?

>>10201576
>Isn't pressure higher at the bottom?
If it was, what would happen to Newton's law about equal and opposite forces (per unit area)?

>>10201581
That would mean the boundary would have to apply an equal and opposite reaction to the fluid, higher than at the top?
Inside the fluid pressure surely increases with depth?

>>10196329
chemistry is used for weeding out pre-med students

>>10201157
That doesn't have a proper definition because nobody would care about such a sequence (other than perhaps a counterexample). The idea of the exercise is to make you think what the condition means, and the name flirting is probably the most elucidating one for such a sequence.

Also the problem is obvious, just take in R the sequence 1/n where n is even and 0 otherwise

>>10201616
>>10201157
I meant 1+1/n

>>10201576
It's a gas inside, density is less. Delta pressure = rho * g * h.
About weight above, apply free body diagram on the Piston area. Weight equals pressure from inside * area

>>10201576
Pressure is higher at bottom but it doesn't matter that much because density of gas inside is rather small.

>>10201623
>>10201631
thanks, for some reason I was thinking of a liquid

Suppose you have a graph. Any graph. Let's say it's not a linear one, let's say it's a mixture of a linear, parabolic, etc. For example, something like pic related. Is it possible to find its equation? This just struck me, we've always been taught in school to graph from an equation. How do you do it the other way around?

>>10201727
Not every graph has an equation, but if it's continuous there is a sequence of polynomials that approximates it.

NEET who hasn't used his brain for over 5 years.

Is it realistic for me to get back to like a high level understanding of maths and chemistry without my taking courses or anything? I have mental health issues that stop me from working or interacting socially but I want to work on my intelligence again so I don't feel bad for squandering my mental potential.

Has my math teacher fucking lost his mind

ok, maybe here. could you please guys help me?
>>>/wsr/601085

>>10201876
Do you know what a geometric series is?

>>10201876
>what is a geometric sum

>>10200575
What is [math]K(0)[\math]? I've never seen that notation before.

>>10200575
What is [math]K(0)[/math]? I've never seen that notation before

>>10201876
[math] (1-x) \sum _{i=1}^{n} x^i = 1-x^{n+1}[/math], by induction. Pass the 1-x to the other side, and if x<1, x^{n+1} converges to 0, so that the sum of powers equals 1/(1-x).

>>10201876
>>10201884
>>10201885
>>10201894

OH FUCK I JUST REALIZED THAT THE FRACTION IS ACTUALLY THE SUM, I THOUGHT AT FIRST IT WAS MY TEACHER REWRITING THE SERIES IN A DIFFERENT FORM HAHAHAHH SORRY GUYS I AM RETARDED HAHAHAH

>>10201900
its ok, we all have those moments

>>10201773
Yes. It is entirely possible, if not easier than actually taking courses. Just find someone else who wants to study as well, so you have someone to check answers with. Find good textbooks with resources available. Or, if you really want lectures, use YouTube. I know Harvey Mudd had some upper-level mathematics stuff, and I'm sure other colleges do as well.

>>10201880
Could you elaborate a bit on exactly what part you don't understand?

>>10201935
thanks. I can't get Rs values shown on the paper. I can't solve the sigma function and I don't know how to properly interpret this definition: "and p _s, _m is the probability that signal variant s and meaning value
m co-occur."

Can someone help me understand these two concepts?
I just cant wrap my head around us looking into the past when we look deeper into space.
Also, how speed of light will always travel the speed of light faster than you no matter how fast your going. Something about reference frames?

The reason why e, a seemingly random number, is so special is because e^x is equal to its derivative, right? And no other number is like this, so e is unique and special in this regard?

>>10201961
I don't think you need to solve sigma for anything.If i understand correctly p_sm is the probability that a certain phrase has a certain meaning. For instance, the probability that ki means red is 8/9 and that it means blue is 1/9. You sum over all the possible meanings to get Rs. In this case Nm=3

For my Calc 1 class, I need to think of a problem and figure out a solution to it using calculus. I was trying to figure out a computer science application but I couldn't figure out anything that would be modeled as an equation instead of just data plotted on a graph. I know this isn't homework help general but I would appreciate any advice.

>>10201979
Thanks mate. That's what I did, but I can't get values given there.

>>10201973
Essentially, when light hits an object, a part of it is reflected. When you see things, this light hits your eyes. Because light takes time to travel, when you look at something that's a light year away, you're seeing what it kicked off of a year ago.
>>10201974
Yeah. More specifically, f'(x)=f(x) if and only if f(x)=ae^x, where a is a real number.
>>10201985
Think of something that has "speed" and use calculus to solve for the time it takes.

I'd like to confirm my understanding of something.

Maschke's Theorem gives us a set of circumstances in which a complex representation [math]\rho: G \to GL(V)[/math] can be written as a direct sum of irreducible representations [math]V = \oplus_{i \in I}V_i[/math]. So, if [math]\rho[\math] is K-reducible, there are representation [math]V_i[\math] fulfilling that condition. My confusion is thus: Are those representation [math]\rho_{i}: K \to GL(V_i)[/math]? Or are they something else?

>>10201986
You know that log is the natural log right? Sometimes its denoted as ln on a calculator

I'd like to confirm my understanding of something.

Maschke's Theorem gives us a set of circumstances in which a complex representation [math]\rho: G \to GL(V)[/math] can be written as a direct sum of irreducible representations [math] V = \oplus_{i \in I}V_i[/math]. So if [math] K \subset G[/math], and [math]\rho[/math] is K-reducible, there are representations [math]V_i[/math] fulfilling that condition. My confusion is thus: Are those representations [math]\rho_i: K \to V_i[/math]? Or are they something else?

>>10202012
Sorry, I meant [math]\rho_i: K \to GL(V_i)[/math]

Complete brainlet here.
Pardon ignorance but is this correct?

>>10202006
I didn't know that. I'll go to eat now and then I'll solve it again. Thanks mate.

how do I show [math]\displaystyle f_{n}(x) = \begin{cases} \frac{1}{\sqrt{x}} & , \frac{1}{n+1}\leq x \leq 1 \\ 0 & , \text{ otherwise } \end{cases}[/math] is Cauchy in [math]L^{1}[0,1][/math] using the definition?
Is [math]||f_{m}-f_{n}||_{1} =0 [/math]? I have no idea how to do this.

If an integral is an infinite sum of infinitely small areas, how does it possibly work with sums that are divergent?
It obviously works, but what is the concept here that I'm missing? How can we make a sum of areas that are ever increasing, for a simple equation like y = 2x?

>>10202093
Google: improper integrals.

>>10202039
>>10202006
thanks for the effort. I'm too retarded, couldn't do it. I still don't get the values of the paper.

>>10202175
Not that guy but did you include p_{ki, yellow} = 0 in your calculation too? You shouldn't because log(0) = -infinity

If I have a list of flame temperatures for fuel/oxidizer combinations, is there any reliable way to estimate the temperature of combinations of the tabulated mixtures? Namely I want to see if it is at all realistic to bump the temperature of a propylene/air (~2000 C) combination up to just under that of a propane/oxygen (~2500 C) flame by mixing oxygen/hydrogen (~3200 C) from a water electrolysis cell into the fuel/air mixture. This is for a torch, not an engine or rocket.

(Electromagnetism)

When i want to define the polarization density in some volume [math]V[/math] i write:

[eqn] \vec{P} (\vec{r} ) = N(\vec{r} ) \vec{p} (\vec{r} )[/eqn]

where [math] \vec{p} (\vec{r} )[/math] is the dipole moment. Now [math]N(\vec{r})[/math] is supposed to be the number of dipoles but it takes only one point as an argument. How it this possible? I get that a neighbourhood of [math]\vec{r}[/math] can have manny small dipoles, but how can one reduce this to a point? Thanks.

>>10202216
cont.

Because when i write the infinitesimal scalar potential i get:

[eqn]dV(\vec{r} )= \frac{1}{4\pi \epsilon _0} \frac{P(\vec{r} ') \cdot \vec{r}_i }{r_i ^3} d^3 \vec{r} ' [/eqn]

[eqn] = \frac{P(\vec{r} ) \cdot (\vec{r} - \vec{r} ' )}{\lVert \vec{r} - \vec{r} '\rVert ^3} \frac{dV'}{P4 \pi \epsilon_0}[/eqn]

where [math]\vec{r} '[/math] is the relative distance of a fixed point outside of [math]V[/math] from a point [math]\vec{r} \in V[/math] .

>>10201891
The space [math]\{k\cdot 0\mid k\in K\}[/math]

>wave function has complex numbers
>want to find expectation value of operator
>operate on wave function, still has complex numbers
>multiply result by complex conjugate of original wave function
>still fucking has complex numbers

>>10202412
>>operate on wave function, still has complex numbers
no it hasn't, the eigenvalues of a hermitian operator are always real. when multiplying with the complex conjugate you get [math] \omega_i \delta_{ij} [/math] which is the diagonalised matrix of your operator.

>>10202415
(of course assuming your state is an eigenstate of the operator)

>>10202412
>the virgin anon
>finds that his problem has complex numbers
>tries and fails to take them away
>the chad Riemann
>notices that his problem doesn't have any complex numbers
>adds them to masterfully solve it

I think it's over bros.
The last day for final exams my professor opened the class by saying "So, I've graded most of exam 2 and 3. I was watching LotR and.. all I can say is I'm Gandalf here. You(most of the class) shall not paaassssss."

>>10202175
>>10202187
why can't I solve it?

>>10202750
Are you still there?

>>10202796
yes...

>>10202808
Do you want help understanding your mistake, or are you looking for the solution spelled out?
If #1, tell me what you think [math]N_m[/math] is for the table you highlighted.

>>10202580
I can relate. I just failed my Alg II class because the final was 70% rep theory and Lie algebras, which we covered for two weeks early in the semester and I forgot to study them.

>>10202813
it is 3, that's what the paper says, so log (3), as natural log like some guy said, should be 1.09861228867

>>10202820
Then I don't know what your problem is. Here's the calculation for [math]R_s[/math] for 'ki':
[eqn]1+{\frac{1}{9}\cdot\ln\left(\frac{1}{9}\right)+\frac{8}{9}\cdot\ln\left(8\over9\right) \over \ln 3}[/eqn]

>>10202839
dude, thank you very much. I was writing sigma wrongly, a stupid mistake. I have been reading my old calculus books and I couldn't see the mistake. Thanks again.

here is a question for (You):

you start with a wall at your back.
you repeat this instruction forever:
you flip a coin. If it's a head, you make a step forward, if it's tails, you make a step backwards.

Whats the probability that after 'k' flips, you are at the distance 'm' steps from the wall?

>>10203123
0.4

how to expand this?
a / b(c+d)

is it
a / (bc + bd)?

>>10203129
Yes.

>>10203129
first you expand dong

>>10203131
so 6 / 2(1+2) = 1

>>10203165
yeah
6 / 2(1+2) = 6 / 2*3 = 6 / 6 = 1
[math] \frac{6}{2(1+2)} = \frac{6}{2*3} = \frac{6}{6} = 1 [/math]

Can somebody explain to me the difference between the Hamming metric and the Lee metric?

From what I have managed to understand they are used for different channels, but what channels are those?

Is the Lee metric used for linear q-ary channels and the Hamming metric used for symmetric q-ary channels?

My friend showed this to me, how to debunk this? I don't think I understand why it's wrong.

>>10203233
https://youtu.be/IJhgZBn-LHg

>>10203233
>it will face the same direction at 12:00pm no matter where it is in it's revolution around the sun
this is false, noon is defined to be when the sun is on your meridian as Micheal explains

>>10203246
So how does a tiny fraction like .0000006 longer days and .2421891 more days in a year correct for the fact that we don't swap day for night every 6 months? Now I'm really lost.
>>10203276
That doesn't seem to explain the claim that there's no transition for day to night provided earth is rotating at a practically constant rate while revolving for the year.

>>10203214
https://en.wikipedia.org/wiki/Lee_distance
Imagine that the alphabet cycles, so that instead of going 1 2 3 and finishing, it goes 1 2 3 1 2, and if you need to take the distance between 1 and 3 you take the smallest distance, 1.

>>10203233
Very simple: 24 hours is the amount of time it takes for the earth to rotate so that the same position is facing the sun, it's not the amount of time it takes for the Earth to make a full rotation with respect to the stars. The graphic is showing Earth making a sidereal rotation which is 4 minutes shorter than a solar day. So the times it's showing at each position are not correct.

Where is the soul located in our anatomy?
The brain? The heart? The spine?

>>10203288
But if there were 4 less effective minutes, in 365 solar days of 24 hours, we would experience 366 sunrises, correct? But we don't observe this. How does sidereal math even add up? ...Confusing.

>>10203355
No, we experience 366 full rotations and 365 sunrises.

>>10203295
In your aura.

>>10203286
Can you tell me about the channels?

>>10203233
>>10203246
>>10203276
>>10203285
>>10203288
>>10203355
>>10203364
https://www.youtube.com/watch?v=hNcwXUZN5aw

Do we just assume J is a proper subset of I here?

>>10203487
>m-muh 360 degrees in 24 hours is inaccurate
>even though we were told this
>but look they make an awkward 360+0.xxx degree adjustment per day and it works
>globelets amIright?
is this seriously the arguments of flatearthers, that just because the world does not fit arbitrary, perfect round numbers then the theory is wrong?

>>10203889
I understand how the sidereal theory could explain the lack of inverted day and night every half year months, as inelegant as it seems.
Good thing the heliocentric model has an explanation for everything.

>>10203943
You mean the curvature that's obscuring most of the mountains? Yeah, it's pretty neat.

>>10203951
Most? If you actually crunch the numbers, none of those mountains should be visible. Unless it's one of those strangely persistent mirages?

>>10203958
>he doesn't know about refraction

Oh my.

>>10203962
Oops, I forgot refraction could account for the bending of light over a 5Km bulge at <500Km, also that light only 'allegedly' travels in a straight path.

>>10203971
The change of density, and index of refraction, of air with elevation is well established.

>>10196021
How do I find infinitely many self-complementary graphs?
I only know that graph wil have n mod 4 = 0 or 1 vertexes. And that there will be no vertex of degree of n-1 or zero.

>>10203943
Not sure what they're doing with the maths, but that's grossly incorrect. If Earth had no atmosphere, the horizon for the Pyrenees would be 190 km, the horizon for the Alps would be 229, for a total of 419 km. This is still shy of the 440 km, but the Earth has an atmosphere whose refractory properties. So multiplying by (about) 7/6ths, the possible theoretical distance (assuming no extinction) would be 488 km. So there is no problem with 440 km, aside from being an astoundingly exceptional shot.

So the bigger question is, why did you take that meme at face value, and not do the math yourself? Are you a sheeple? If you simply lack the capacity to do the math, why would you assume you could trust something so silly as the claim made in the meme? What is wrong with you?

>>10196021
How do I motivate myself to do my homework /sci/? I do great on the tests but I can never get myself to do the homework. I'm skating by on C's at this point.

>>10203975
>>10204056
In what reality does on a clear day, a mountain that should be nearly 5km below the height of curvature is in nearly full view 'due to atmospheric refraction'? You are aware that factoring in the estimated arcing of light over such a relatively small distance does not explain this picture given any weather condition?

>>10204084

>>10203233
Sidereal days
How do they work?

>>10203129
What kind if brainlet 3rd grade math is this

>>10203943
>>10203962
>>10204056
>Youre talking about +15km that refraction is accountable for…. Mareta asked a legit question and you answer it bluntly with a belief based reason, nothing exact nor scientific. Shes asking why does -2x-3= 6 and you explain it by “math”. What a joke. At least say the reason is a superior mirage. Then prove it because the picture clearly doesnt depict such a thing.
Regardless of this insulting answer I’ll try to explain why you can see so far, curved or flat earth.

Mareta, I dont think you can calculate what the drop in height at that distance is simply because we dont have any info about what height the photo has been taken from. if we accept the height as being 2820m the drop at 443km would be 5km with visible horizon at 190km. so even at this height the highest peak would still be hidden by 900m at least.
Now Mark Bret said “atmospheric refraction” is the reason you can see the peaks. So just do the math to see what variables you need for more than 1km of mirage. Its probably even more since you dont see just the upmost part of the peak,

>In the image there was no superior mirage. The refraction was high but there was no inversion of temperature that made the curve of light of one part bend more than the other and produce a mirror.
To be able to observe hundreds of meters more of mountain than what would be logical in a rectilinear vision has no mystery above all for long distances. The sun itself, for example, due to refraction, most of it is always displayed higher than what is on the horizon when sunrises or sets. If we think about the measurements of the sun …How many? Thousands of tens of thousands of kilometers of the sun are the ones that are higher than their position on the horizon, much more than a few meters from the Alps.. It’s a matter of angular degrees, not vertical kilometers.

https://beyondhorizons.eu/2016/08/03/pic-de-finestrelles-pic-gaspard-ecrins-443-km/

So a black hole warps spacetime into a singularity, but what if it's not just a funnel stretching towards infinity away from spacetime? What if the funnel bends and warps as a structure of its own, eventually curving back towards spacetime again? Maybe more than one funnel could form as well?

Does the math allow for this? And if not, is perhaps the math too rigid or ideal to capture exactly how spacetime is warped by a black hole?

How to prove equivalence of the sets [math] [2,4) [/math] and [math] (3, \infty) [/math] a) using Cantor-Bernstein theorem, b) constructing a bijection between these two sets?

>>10196024
Improve comedy skills by surprising your audience with le randum stoopididy, not by preemptively informing them you will say something retarded and then saying something retarded.

>>10196521
Flux = Luminosity/(4pi*d^2)

If you emit energy is all directions, you can decrease the luminosity (energy per second) in order to decrease the flux, (luminosity per area), thereby requiring a sufficiently high d (distance) to receive a strong enough signal/amount of energy.

Theoretically, that signal will travel on forever, but in reality it will almost inevitably combine with other signals making it indiscernible by the time someone very far away can pick it up. It's the same concept for radio signals. A satellite can't track a radio signal on the ground unless the signal is beamed to the satellite, unless the radio signal is extremely strong.

>>10196329
Very few chemistry majors actually have any intention on working in a lab immediately after their undergrad.

>>10204315
>Cantor Bernstein
[2, 4) maps to [0, 2) by subtraction. [0, 2) to (0, 2] is trivial. (0, 2] bijects with [1/2, infinity). Since this contains (3, infinity), we invert and restrict to get an injective function.
For backwards, subtract 2 from (3, infinity) to get (1, infinity), invert and restrict.

Bijection is a huge hassle.

>>10196553
Linear algebra can be learned in a couple of hours, you don't need an entire book.

>>10202216
I haven't taken electromagnetism in a couple years, but I think there is an approximation using the dirac delta function if I remember correctly. The answer should be pretty clean.

>>10204336
>Bernstein

D R O P P E D
R
O
P
P
E
D

>>10204365
I get the math behind it. I just can’t wrap my head around the idea of point dipoles. Delta functions usually represent point charges, but that’s like saying you have the [math] \vec{E}[/math] field of a dipole from a point change.

>>10204375
Maybe imagine that one of the charges is in another dimension located right on top of our own, but the voltage penetrates through to our dimension?

I'm just making stuff up.

>>10204374

>>10204337
Lol retard. I bet you think linear algebra is just knowing how to write a matrix

>>10204385
I was under the impression we where to disguise science in this board

Psych fag here

Should I skip my final? I have a 102% right now (from extra credit), and the final is worth 25%, meaning that I will still get a good grade as long as the professor curves (an 80% is an A-).

The reason I'm thinking about skipping is because the final isn't cumulative and I stopped going to class after the second exam so I literally know nothing.

>>10204422
No, I know about determinants, you fucking dumb redditor

>>10204427
I feel you. Last semester I had a class with three exams, and one gets dropped, so I just slept through the entire semester until it was time to take the final, and I learned everything I needed to a couple hours before and I ended up with an A because I got all the extra credit points on the final and the professor curved the class so that an 80% was an A.

>>10204428
So you think linear algebra is knowing how to calculate a determinant wow

>>10204433
It is, and the fact that you can't name what other things "linear algebra" constitutes of(none), just shows how much of a redditor you are

>>10204434
Are you really this stupid lmao
Tensors, canonical forms, etc. are all taught in undergrad linear algebra

>>10204433
It's funny because both of you are just joking, but in reality all you need to know from linear algebra is how to solve for an eigenvalue from a matrix, which is literally just one fucking formula. I took the linear algebra crash course in two physics classes (electro and quantum) and diff eq and this was literally the only takeaway.

>>10204437
Anyone can make up words, anon
Rackatacks, sumperflies and restigians are also taught, aren't they?

>>10204438
You probably went to a shit school

>>10204442
Nah I go to a public university in New England.

>>10204441
Literally just google jordan canonical forms

>>10204445
Literally just google rackatacks

>>10204446
Ok you got me. Nice bait

>>10204444
You were scammed anon

>>10204444
at least you're not an amerimutt

>>10204452
I'm scammed because I only have to pay 25k/year in tuition (before grants) to get a good education with a large research department that gets lots of funding?

Unless your argument is that I should have been a kid genius who got a full ride to Yale or Harvard then I think I did okay.

>>10204460
If determinants and eigenvalues were the only things taught in a linear algebra course for physics, that's pretty unfortunate

>>10204469
Well no, we did tensors too, but not in the linear algebra format.

>>10204472
Ok that's better I guess. Physics uses a lot of linear algebra afaik

Is it possible for {( , )} to be a subset of AxB?
Let's say A = {1.2}; B = {3,4}.

More generally, is it possible to have an ordered pair of nothing and nothing? I know it is a subset but is the empty set an element of A or B?

>>10205044
Sure is.
https://en.wikipedia.org/wiki/Peano_axioms#Set-theoretic_models

>>10204135
Was it correct?

>>10204336
>Bijection is a huge hassle.

Any ideas how I should approach solving this?

>>10205179
Yes or no, it depends on the parser (human or otherwise).
A left-associative parsing, arguably the more canonical one, of a/b(c+d) would be (a/b)(c+d) = (ac+ad)/b.

For another example, you would express [math]{a \over b}{1 \over c}[/math] as a/b/c -- try typing 10/2/5 into google or a CAS.

If things fall down when nobody is holding them then why don't the sun and the moon fall to the ground? Who is holding them up in the sky?

>>10205314
You can easily biject one with (0, 1) and the other with [0, 1). Building a bijection between these two is a pain, but it's doable.
Tip: use a function that maps irrationals to irrationals, and exploit the countability of rationals.

>>10205329
The jews

>>10205336
Meant to reply to >>10205308

so I'm looking for both industrial chemists and pharmacy associates (big dick engineers and pharmacists pls refrain from answering unless you've done/you do grunt work)
umm... what kind of work do you actually do? is the pay nice? do industrial chemists operate machinery or you're doing lab work most of the time?

>>10205400
(btw sorry for asking about career advice, but I've already asked for help in adv twice and everyone ignores me (´･ω･｀) )

This feels extremely wrong. What did I do wrong and how should I fix it?

Shouldn't recycling just make all plastic pollution nonexistent?

Hypothetically if we could produce as much antimatter as we wanted ( with perfected tech) could we use anhiliation as a means of clean energy? Is there an equation to find out how much energies produced through said process? Thanks everyone !

>>10206141
E=mc^2

>>10196021
When will aging be cured?

>>10196530
https://www.youtube.com/user/EugeneKhutoryansky/videos
not sure if this meets your vague description, but this channel is alright
r8

for this problem, I need to find an An such that Bn has no convergent subsequence. Would taking [math] An = \frac{1}{n} - 2 [/math] work?

>>10206013
Not all plastics are broken down by the same processes (but they all can be broken down). Especially if it. But beyond that I don't really know what kind of answer you're looking for.

>Why don't humans do x which would solve y?
No real fiscal incentive (unless you're homeless).

If you were to impose an artificially large electrochemical gradient across the mitochondrial inner membrane, would you expect electrons to flow up the respiratory chain, in reverse to their normal direction? Why or why not?

>>10206184
Never.
>Can't have kids anymore since it would increase the population too much.
>Either we have to introduce eugenics (we won't) or we're stuck with retards for the rest of eternity.
>"I have been wiping your ass for the last 500 years"

>>10196021
Is there an relatively quick way to check whether a rather large number is a Carmichael number?

>>10203295
it's not an anatomical thing located somewhere, it's more like a phenomenon.

>>10206903
There is, to the best of my knowledge, no polynomial time algorithm to determine whether a number is Carmichael

>>10206297
[math]\frac{a_n ^2+3a_n +4}{(a_n+2)^2}[/math].
You should be able to finish on your own.

>>10202021
Looks ok to me

>>10203295
It doesn't exist.

why isn't
d^2u/dy^2 = (1/u)(dP/dx)?

Would any be be kind of enough to help me with part c? Am I supposed to integrate the differential equation, use the initial condition to get the integration constant, and then just look at the function as it goes to +- infinity?

>>10207056
Those are different [math]\mu[/math]s. It just says „both expressions are constant multiples of each other“.

>>10207127
The phase portrait and stability tell you the limit, depending on the initial condition. You don‘t need to solve explicitly.

>>10207145
I don't see how. Are we supposed to just look at the phase portrait and see where the graph goes? In that case, they both go to positive infinity right? I don't see how the fixed points and their stability will help. I know fixed points are either attractors or repeller, but doesn't that only help if you start from a point?

>>10207159
Look, the ODE is autonomous, and x==0 and x==1 are solutions, right? if x(0) is between those points, how do you figure the solution through that point goes to infinity? Maybe post a picture of your solution to (a) and (b) for more comments.

>>10207191
>x=0 and x=1 are solutions
Solutions is a strong word.
Anyhow, it just goes to 1 at infinity and 0 at -infinity.

>>10207204
>Solutions is a strong word
What do you mean? I said x==0, meaning [math]x(t) = 0[/math]

>>10207191
>>10207204
I think I get it now. My main problem was that my definition of a differential equation is poor. I thought of the initial condition and the limits as two separate things, but they aren't. We need the i.c. to draw a trajectory and thus look at the limit, right? So like that's why as time goes on, the solution will go to 1 (the stable fixed point/attractor/whatever) and to negative infinity as time goes in reverse.

Does that make sense or does it sound like I'm pulling shit out of my ass after seeing the solution.

>sun is oblate
>sun has a clear and obvious surface
>exhibits transverse waves
>solar flares make impact flash when returning to surface
>emits continuous spectrum
but
>sun is supposedly a gas

>>10207231
I can't tell from what you've written whether you have understood it nor not.
>So like that's why as time goes on, the solution will go to 1 (the stable fixed point/attractor/whatever) and to negative infinity as time goes in reverse.

But that's not true. Have you looked at the solutions? When I said that x==1 and x==0 are solutions, it also means that a particular solution curve [math]\tilde{x}(t)[/math] that lives between 0 and 1 (for any t) can't ever cross those two lines.

Test.

>>10207304
No, I didn't get it. So, solutions are all trajectories on the phase plane. They make the DE true. Due to existence uniqueness these lines don't cross other nearby solutions. You're saying that x = 0, x = 1 as functions satisfy the differential equation. This is true because x' = 0 for both. That's my attempt at understanding so far. My calculus knowledge is really rusty, which is why this limit part is throwing me off. I don't understand what the limit of x(t) goes to +-infinity means in this context. I also don't understand how or if the initial condition is relevant at all. Are we supposed to be looking at the trajectory at the initial condition?

>>10205958
bump

>>10207368
>So, solutions are all trajectories on the phase plane.
Yes. Also, in this case the phase plane is really a phase line, because the ODE does not depend on t explicitly.
>I don't understand what the limit of x(t) goes to +-infinity means in this context.
It's t that goes to infinity. How do solutions behave in the limit, "to the far right and left" in the image.
> I also don't understand how or if the initial condition is relevant at all. Are we supposed to be looking at the trajectory at the initial condition?
Yes. In your initial condition x(t=0) = c, the t is irrelevant because of the autonomy of the equation -- if x_1(t) is a solution, so is x_1(t-something). So it all depends on the value c: If c is larger than 1, the solution curve will tend to infinity as t increases, for c between 0 and 1 they tend to 1, and for c below 0 the solution tends to negative infinity.

I'm actually confused by two different concepts, moment (torque) M=rF, and angular acceleration/rotation whatever. Does a moment cause this? Is there a moment in dynamics and doesn't it produce acceleration? I mean, if you apply a moment to something, won't that make it rotate? And doesn't that then mean that the rotating object has gained speed? I am mixing shit up here please help

why can't a D be passing

>>10207391
I get it now, thanks.

>>10207442
You don't deserve to pass. Why are you even in school?

>>10207395
> I'm actually confused by two different concepts, moment (torque) M=rF, and angular acceleration/rotation whatever. Does a moment cause this?
Yes. With linear motion, a net force applied to an object results in linear acceleration. With rotational motion, a net torque applied to an object results in angular acceleration.

The rotational analogue of mass is either the moment of inertia (in the 2D case, where either the rotational axis is fixed or the mass lies in a plane) or the inertia matrix (in the general 3D case).

> Is there a moment in dynamics and doesn't it produce acceleration? I mean, if you apply a moment to something, won't that make it rotate?
If the total moment is non-zero, there will be angular acceleration. Equal-but-opposite moments will cancel, resulting in zero angular acceleration. Applying a torque to an object which is held in place will result in an equal-but-opposite torque from whatever is holding the object.

> And doesn't that then mean that the rotating object has gained speed?
It will gain angular speed at a rate proportional to the total moment. In the same way that a linear force causes an object to gain linear speed at a rate proportional to the force.

>>10207486
Thanks man. You cleared it up really well. Appreciate it !

My professor said we will more than likely see something like this on the finals. This is type of problem is an awful lot to do in 120 mins for only 20/100. I'm not nuts right?

How and when can i apply Taylors' series and Landau symbols in limits/in the analysis of a function? I am never able to use them correctly and it's so frustrating.

>>10196021
>questions have sizes
wat

>>10207540
So you get roughly 5 questions and two hours to do them in? I wouldn't call it awful. Maybe you need more routine?

(a+c)/(b+d) can not be less than a/b and can not be more than c/d. Can someone explain why, simply? I have a kind of proof but it is dumb and convoluted.

Linear Algebra teacher showed us some applications for Quantum mechanics stuff, specifically momentum of a hydrogen atom, and wrote these down:
L+|n, l, m>=h sqrt(l(l+1)-m(m+1))|n, l, m+1>
L-|n, l, m>=h sqrt(l(l+1)-m(m-1))|n, l, m-1>
Teacher has kinda shitty handwriting, so wasn't quite sure whether I'd gotten them right or not.

OK, here is my question:

Larson vs Adams vs Thomas.

Which calc book is the best for beginner self-learning?

>>10207696
What? Take a=1, b=2, c=0, d=1.
a/b = 1/2 > (a+c)/(b+d) = 1/3
c/d = 0 < 1/3

>>10207696
Sounds annoying. I won't do it because I hate proofs, but I'd start by trying small cases and then probably do a proof by contradiction.

>>10207746
Sorry I wrote the question from memory. The question is that the (a+c)/(b+d) is between a/b and c/d, not that c/d is the max etc

Being asked to show that a factor group of a cyclic group is cyclic. But since all subgroups of cyclic groups are cyclic, couldn't I just show that a factor group must be a subgroup? and then reference the earlier theorem.

Or are "factor groups" and "subgroups" not equivalent concepts

>>10207696
>guys can you prove me something that's literally wrong
Tip: which ones are a, b, c and d are arbitrary.
>>10207786
They aren't, no.

>>10207771
assuming all variables are positive - otherwise you'd need to check a few more cases
Assuming
[math]
\frac{a+c}{b+d} \geq \frac{a}{b}
[/math]
then
[math] ab+cb \geq ab+ad [/math]
and finally
[math]
\frac{c}{d} \geq \frac{a}{b}
[/math]
now if we also had
[math]
\frac{a+c}{b+d} \geq \frac{c}{d}
[/math]
we could repeat the same process and get
[math]
\frac{a}{b} \geq \frac{c}{d}
[/math]
Thus
[math]
\frac{a}{b} = \frac{c}{d}
[/math]
which also means
[math]
\frac{a+c}{b+d} = \frac{a}{b} = \frac{c}{d}
[/math]
So [math] \frac{a+c}{b+d} [/math] can't be strictly bigger than both.
The same can be done with [math] \leq [/math] instead of [math] \geq [/math] to get the thing you want to prove

>>10207822
Thank you, this was essentially my train of thought but I just couldn't put it simply.

>>10196495
This has been bugging me for years, but I could never figure out why. So is the cross product like the vector field of the tangents to every neighborhood of each point in the parent field?

>>10207395
"Moments" actually refer to angular momentum, not torque.
Any motion a rigid body undergoes can be generated by the generators [math]\{p_i,L_i\}_{i=1}^n[/math] of the Lie algebra of the Euclidean group [math]\mathbb{E}(n)[/math]. This means that any external influence, be it forces or toques, must give rise to a change in these generators. These are the Euler equations.
In addition, the fact that the moments [math]L_i[/math] and momentum [math]p_i[/math] commute in the Lie algebra means that any external change in the inertia of the rigid body decomposes into a linear part and an angular part. These are the forces and torques on the body.
>>10207720
Looks alright. These ladder operators [math]L_\pm[/math] furnish a representation of the Lie algebra [math]\mathfrak{su}(2)[/math] on the sphere. By a fundamental result in conformal field theory, a singular vector (the cyclic vacuum) exists in the highest weight Verma module [math]V_\mu = \oplus_{\lambda \leq \mu}V_{\lambda^\dagger} \otimes V_\lambda [/math] (the Fock space of momentum eigenstates) only if the conformal blocks [math]V_\lambda[/math] (the span of the momentum eigenstates) satisfying the quantum Clebsch-Gordan conditions, i.e. the [math]\lambda[/math]'s satisfy a certain algebraic condition before the [math]V_\lambda[/math]'s can be combined into a Verma module. From this you can obtain the coefficients in front of your eigenstates.

Guys I need a quick run down on how to do a change of basis in quantum mechanics, like what is the procedure? I'm pretty sure we actually never did this in class and Griffiths explanation is not really helping me.

>>10208684
Suppose we have a 1-body Bloch Hamiltonian given by [math]H(k) = \sum_{\alpha,\beta} c_\alpha(k)^\dagger A_{\alpha\beta}c_\beta(k) [/math], where [math]\alpha,\beta[/math] are multi-indices denoting internal degrees of freedom in the theory (spin, orbital, sublattice, valley, particle-hole, etc.) and [math]c^\dagger,c[/math] are electron creation and annihlation operators, respectively. In its current form the Hamiltonian is in the "electron" basis, whence you can see directly upon acting on the vacuum/Fermi sea what 1-electron states (a basis of the 1-particle Fock space) are created.
Now we can diagonalize [math]H(k)[/math] by a unitary transformation [math]U(k)[/math] for which [math]H(k) = \sum_\alpha \epsilon_\alpha(k)q_\alpha^\dagger(k)q_\alpha,[/math] where [math]\epsilon_\alpha(k)[/math] is the dispersion relation of branch [math]\alpha[/math] and [math]U_{\alpha\beta}(k)q_\beta(k) = c_\alpha(k)[/math] (similarly for the h.c.). This is called a Bogolyubov transformation, and the operators [math]q^\dagger,q[/math] are now [math]quasiparticle[/math] creation/annihilation operators. This means that the eigenstates of the Hamiltonian are actually the quasiparticles (another basis of the 1-particle Fock space), i.e. a linear combination of electron states of different [math]\alpha[/math]'s; in other words, the exicitations of [math]H[/math] are given by the quasiparticles, not the electrons.
This process is a basis change in our Fock space [math]\mathcal{F}[/math], defined as a (non-free, there are CAR relations) [math]\langle c,c^\dagger\rangle[/math]-module over [math]\mathbb{C}[/math].

>>10208718
Thx for the help buddy, if I could ask another question. I have it in my notes that if two Hermitian operators commute, we can choose them to be simultaneous eigenvalues, but what exactly does that mean?

>>10208835
For example [L^2,Lz]=0

>>10206892
>implying that brain augmentation technology will never be created
>implying that retards even want to live forever in the first place

>>10208840
>>implying that retards even want to live forever in the first place
Well, im fairly retarded and id quite like living as long as possible

>>10208846
Transhumanism in general is still extremely unpopular though. For instance, there are only around 3000 people worldwide who are signed up for cryonics, despite it existing for 50 years and being fairly well known.

https://alcor.org/AboutAlcor/membershipstats.html
https://www.cryonics.org/ci-landing/member-statistics/
http://kriorus.ru/en/cryopreserved%20people

Tell me what I'm doing wrong sci:

Let x = 1/y, then log(1+x) = -log(1/(1+x)) = -log(y/(y+1)). Let Y be near 0. The linear approximation for y/(y+1) is y. So,
log(y/(y+1)) [math]\approx[/math] log(y), i.e.
log(1+x) [math]\approx[/math] -log(y) = log(x).

But this should only work when x is small. x is big here since y is small.

>>10208835

commutating operators can be simultaneously diagonalized so that there exists basis states which are eigenvectors of both operators, so then general states may be eigenstates of both operators (i.e. having well defined values for both observables simultaneously.)

>>10208718
condensed matter detected, lol.

but honestly, I like what you do, even if most of your posts worthless as responses to questions, and I suspect you're just flexing(the avatar fagging gives the game away). Still, some of this stuff is interesting, but I cannot for a second believe that anyone thinks this formally about anything. I can follow maybe about 50-75% of what you post, but its certainly not how I think about physics, and my background is mathematics to boot.

>>10209002
> for large x, log(x+1) \approx log(x)
I mean, yeah.. that is true.

>>10201773
Hmm I took calc 1/2 in 2012 and just took calc 3 in 2018. I got an A. You'll be surprised how much knowledge stayed dormant over those five years, and how easily it comes back. I suggest khan academy if you don't have resources. I personally just used YouTube in addition to my textbook though. Same with Ochem, got an A, despite having took gen chem in 2012. All I used was my textbook and YouTube.

I have two questions:

can someone explain evolution to me? I'm not asking this as a passive aggressive assertion of my views btw, I just genuinely don't understand it so maybe someone can explain

how exactly is it possible for DNA to adapt to its environment in such complexity that a single celled organism managed to selectively mutate and breed itself from a cell to fish to dinosaurs to birds and dogs and humans and everything in between without any sort of consciousness or direction or design or programming, it just happened randomly for no reason out of thin air

how could the building blocks of life hold so much seemingly unlimited potential without intent? explain the sequence of events and the underlying mechanism that makes a single cell react to its environment in such a way that it mutates and over time becomes a radically different complex multi celled organism, what is the causation in this?

it always seems to lead back to "we dunno why, but we know how" which just leads me to think it makes far more sense to trace it back to creative design than just "THE BIG BANG AND NOTHING BEFORE THAT". religion has given it such a bad rep that it's precluded from even being considered, when it's basically a logical conclusion

which brings me to my second question -- isn't this whole latest trend of "dude we're in a simulation!" just gateway creationism for atheist? the idea that the laws of nature and physics and atoms and DNA etc are just the algorithms that comprise this universe and something must have programmed it that way, so how is that any different than any other form of creationism? it's just semantics, playing with words to make the same concept sound scientific

>>10207696
Suppose 0<a/b<c/d
then ad<bc
then 0<bc-ad
then (a+c)/(b+d) - a/b = ((ab+bc)-ab-ad)/(b(b+d))= (bc-ad)/(b(b+d)) > 0
so (a+c)/(b+d) > a/b

>>10207786
third isomorphism theorem:

[math]\frac{a\mathbb Z / c\mathbb Z}{b\mathbb Z / c\mathbb Z}\cong a\mathbb Z / b\mathbb Z[/math]

>>10203295
pineal gland

Can a differential equation be solved using both separation OR integrating factor? Is it always a binary choice?

why isnt the energy density of a laser focal point infinite?

>>10209801
The first example in
https://en.wikipedia.org/wiki/Integrating_factor#Use
does exactly that.

>>10209191
no. go plot that shit and you'll see that it's false

>>10209002
>approximation trickery
>thinking it'll work

>>10210064
close enough for me

engineer here
i want to start self-studying pure math, where do i begin?

>>10210239
relearn the concepts you have already been taught like analysis and linear algebra and go from there

I think I just passed my final exam in differential equations. The questions were literally baby tier. Now I can graduate and never have to remember calculus ever againnnnnnnnnnnnnnnnnnnnnnnnn.

>>10210305
Funny, I just failed mine. Kill me

Why do I feel the most clear headed after not eating for a while? It's like as soon as I put food in my body, it becomes difficult to concentrate, remember and think critically about things

>>10210392
Become an ascetic monk. Achieve enlightenment.

>>10210392
What's your BMI (are you well nourished)? It is often the opposite for me. I'm 12 pounds from the lower end of what is regarded normal weight.
Also what do you eat? Is it high in carbohydrate content?

Dear OP.
310 is the bump limit.
Feel free to make a new thread.
I like your sqt names.
Love, anon.

Question about expansion of spacetime, of which I have the barest layman's understanding: I've heard about models of our universe predicting a Big Rip, where the increasing rate of expansion will eventually overcome gravitational and even nuclear forces and smear out all matter into nothingness. But I've also read that expansion accelerates by creating negative pressure via dark energy, meaning that any volume of space contributes a fixed "amount" toward creation of more volume. Expansion is only inflationary because more space creates more space to create more space. Therefore, as long as local forces such as gravity can overcome the negative pressure exerted by dark energy at any point in time in a given space, they should be able to do so indefinitely and a Big Rip should never occur, because the local expansion of space is constant.

What did I get wrong?

>>10210745
New thread
>>10210745
New thread
>>10210745
New thread
>>10210745
New thread