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Board
/sci/ - Science & Math

Testing if I'm still rangebanned edition.

Previously >>12502293

>what is /sqt/ for
Questions regarding math and science, plus related advice requests.
>where do I go for other SFW questions and (advice) requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc.
https://sciencecareergeneral.neocities.org/
>books?
https://spoon.wiki/Books
https://stitz-zeager.com/
>articles?
sci-hub.st
>book recs?
https://4chan-science.fandom.com/wiki//sci/_Wiki
>help with calculus?
https://spoon.wiki/WolframAlpha
>how do I post math symbols?
https://imgur.com/MDiglsS.png
>a google search didn't return anything, is there anything else I should try before asking the question here?
>where do I look up if the question has already been asked on /sci/?
https://warosu.org/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

>attach an image
>if a question has two or three replies, people usually assume it's already been answered
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Stuff:
Meme charts: https://imgur.com/a/JY6NNeL
Serious charts: https://imgur.com/a/0qDEgYt (Post any that I've missed.)
Verbitsky: https://pastebin.com/SmBc26uh
Graphing: https://www.desmos.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/
>>
>they actually lifted it
Nice.

Maths questions:
>>12509690
>>12512344 [I like Loring's book.]
>>12517172
>>12520720
>>12522166
>>12524202
>>12530124

Physics questions:
>>12511370
>>12512228
>>12520078
>>12530898

Biology questions:
>>12508864
>>12526373
>>12528937

/g/ questions:
>>12505606
>>12510710
>>12519239 [Possibly misclassified.]
>>12523092

Engineering questions:
>>12515863
>>12522358
>>12533021

Stupid questions:
>>12504634
>>12505192
>>12505402
>>12506731
>>12508647
>>12514555
>>12514684
>>12519748
>>12521364
>>12523491
>>12527914
>>12529278
>>
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>>12536145
Are there limits to what we can do with chemistry?
For example, could you start with hydrogen and assuming you had the right circumstances, eventually turn it into something like californium?
>>
>>12536171
>>12520720
Binomial distribution is the answer. This type of math is called probability theory.

$p \ \ \textrm{(prob. winning in a single trial)}$
$n \ \ \textrm{(number of trials)}$

Assume independent trials. The probability of winning $k$ times out of $n$ is

$P(k,n)=\frac{n!}{k!(n-k)!}p^k(1-p)^{n-k}$

In particular, the probability of winning respectively zero or all times out of all trials are

$P(0,n)=\frac{n!}{0!(n-0)!}p^0(1-p)^{n-0}=(1-p)^n$

$P(n,n)=\frac{n!}{n!(n-n)!}p^n(1-p)^{n-n}=p^n$
>>
Why would weed decrease heart rate?
>>
>>12536264
bump?
>>
>>12536504
i dont think we can change the individual atoms with chemistry. chemistry is all about playing with the valence shells of atoms. adding or changing the number of protons in a nucleus is a general physics thing. we can definitely turn lead into gold though. its just very slow and not worth it.
>>
>>12536513
Perfect!
Thanks that's exactly what I wanted to know
>>
Could i be so sensitive to CBD that the CBD effects are overriding the THC effects even in a standard strain(which has been bred to get rid of as much CBD as they can)?
>>
>>12536556
stop smoking weed. Weed was cool in the 00s and early 10s. Now it's not even cool deadbeat tier like Lebowski, it's cringe tier fag bs.
>>
Is there some notation like factorial, but for addition?
n! = 1*2*3*...*(n-2)*(n-1)*n
but is there
something(n) = 1+2+3+...+(n-2)+(n-1)+n
without the sigma sum notation?
>>
>>12536600
n(n+1)/2
>>
>>12536602
Thanks
>>
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Can I use BatchNormalization in tensorflow to rescale every batch element so they always start with 0 or 1? seeing as I'm only interested in training changes, not the starting value
for example
>[1 2 3 4] -> [0 1 2 3]
>[2 4 6 8] -> [0 2 4 6]
or is there some better way
>>
I need to find two real 2x2 invertible matrices $A,B$, both of finite order ($X$ is of finite order if $\exists n$ such that $X^n = I$), such that $AB$ has infinite order.

After screwing around with rotation matrices for a good 30 minutes, I believe now that this approach is useless: I suspect that a rotation matrix has finite order iff its rotation angle is a rational multiple of $2\pi$, and so the product of two such matrices would also be of finite order.

Does anyone have any better ideas? I'd be especially grateful if you could explain the geometric intuition behind any example you might give
>>
>>12536712
https://math.stackexchange.com/questions/2277783/group-generated-by-matrices-of-finite-order
>>
Are there any good algorithms that solve Travelling Salesman when negative weights are allowed, the "distances" are not symmetric, and triangle inequlity doesn't hold?

i.e we can have
edge(u,v) < 0
edge(u,v) != edge(v,u)
edge(u,v) + edge(v,w) < edge(u, w)

edge(v,v) = 0 holds
>>
why does 4chanX keep crashing in the middle of the page? Hide buttons disappear, filters stop working, and LaTEX doesn't render
It only happens periodically on /sci/, and I think one other board
>>
>>12536712
>geometric intuition
The stackexchange example anon posted works, and it's very nice, considering it's all integers, but it doesn't really have any clear geometric intuition to it, so I'll post a different one.
Recall that the matrix $R = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ rotates coordinates by ninety degrees.
The matrices $A' = \begin{pmatrix} 2 & 0 \\ 0 & 1/2 \end{pmatrix}$ and $B' = \begin{pmatrix} 3 & 0 \\ 0 & 1/3 \end{pmatrix}$ both expand the first coordinate and flatten the second by inverse factors.
These don't have finite order, but $A = A'R = \begin{pmatrix} 0 & 2 \\ -1/2 & 0 \end{pmatrix}$ and $B = B'R = \begin{pmatrix} 0 & 3 \\ -1/3 & 0 \end{pmatrix}$ do, because they rotate and then expand/flatten.
When you compute $AB$, what happens is that you rotate and expand/flatten, but these expansions have different factors, so you get $AB = \begin{pmatrix} -2/3 & 0 \\ 0 & -3/2 \end{pmatrix}$, because the expansions and flattenings don't cancel out since the factors are different.
>>
>>12537461
Typo, $R = \begin{pmatrix} 0 & 1 \\ -1 & 0\end{pmatrix}$
>>
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how hard do you think that a CS/Neurology Double major would be?
>>
>>12537477
No no, thats an extremely stupid idea. You're doong 2x the work for no reason. Just sign up for CS OR do neurology (really pre medical) and learn some coding and algos on the side.
>>
>>12537489
Which one would be "safer" to do research and look for a job if that flunks? I want to do research but I'm afraid of the possibility of going broke because I couldn't find a job.
>>
>>12536761
Thanks, and,

>>12537461
This is a fantastic explanation! Thank you so much, really appreciate it
>>
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Is there a term for what skin, exoskeleton and scales are? I mean there all different coatings of an organism, but what is the catch all term for them?
>>
>>12537989
cuticle maybe?
>>
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I've only recently started learning calculus for a problem I've been working on and I'm having a lot of trouble understanding pic related.

1. Is this integratable in it's current form without knowing fine details about the two function factors?
2. If working knowledge of the functions is necessary, I believe this would need to use integration by parts. For that, I would need to know how to get the derivative of the functions, right?
3. If this is super simple somehow and I'm really out of my depth on this all, can anyone suggest some resources so I can learn this all better? I feel like this is something I should know how to do, but I'm self-taught, so I'm not sure.

Sorry if this makes no sense. I'm just really trying to wrap my head around this.
>>
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I'm a dumbass that knows a little bit about real differentiable manifolds and complex analysis, but I came across pic related and I wanna try to decipher what the fuck it means.

Really, the only thing I actually need to understand is how they found the differential of the map they mention (which is the line that's marked near the bottom) so an explanation for that would be good enough. But additionally I'd like to know what I'd need to study to be able to understand the rest of the theory here. Is it just complex differentiable manifolds and some quaternion theory? Also, any book recommendations to get started on this?
>>
>>12538500
>Is this integratable in it's current form without knowing fine details about the two function factors?
No.
> If working knowledge of the functions is necessary, I believe this would need to use integration by parts. For that, I would need to know how to get the derivative of the functions, right?
Not necessarily.
>If this is super simple somehow and I'm really out of my depth on this all, can anyone suggest some resources so I can learn this all better? I feel like this is something I should know how to do, but I'm self-taught, so I'm not sure.
Just an undergrad calc book is sufficient, check the syllabi of some unis.
>>
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>>12538609
Thank you for the input
>>
Ok so I read somewhere that the hottest part of a Bunsen burner flame is a bit after the hot bit as opposed to in the middle of it. Can someone explain this to me, is it really the hottest or is it where the transfer of heat is the greatest? Doesn't a laminar flow make for lower rates of heat transfer, does the middle of the blue flame have more laminar flow?
>>
>>12539129
I don't know, but pulling capillaries out of glass pasteur pipettes is pretty hard if you don't hit the hottest bit just perfect, so try doing that
>>
Okay this is probably going to sound confusing but i'm autistic and can't see it, so give it yer best shot, i wont be surprised if it comes out as gibberish to you.

I figure that the reason why there isn't a better and more reliable response to many psychiatric conditions like depression and anxiety is because we don't have good enough diagnostics yet to fit people's individual flavor of dysfunction to a proper treatment yet. Is that right?

Can you explain how bad it is, or if maybe there are some hopes on the horizon in that regard? Like do we have any reason to believe we're gonna get better at matching people's particular dysfunction to their proper treatments in the near future? Or are we still stuck in trial and error, most commonly working to least commonly working one after another for the foreseeable future?
>>
what made you dislike Sheldon from the Big Bang Theory show?
for me it was favoring Newton over Leibniz.
shameful.
>>
>>12539695

I saw the word "bazinga" written out, not even said aloud, and i knew, we would never be close.
>>
>>12539703
I like bazinga, though.
>>
>>12539695
" the original series to The Next Generation, but Picard over Kirk"
>>
>>12539774
I'm not a fan of sci fi.
>>
>>12539795

but in actuality i liked the show for a while, once it became about funny reaction faces and penny somehow becoming a pharmacist the show became pretty shit
>>
>>12539672
The dsm-v rearranged a lot of conditioned and has a more spectral approach. Certainly though a diagnosis of mixed features/ anxious distress isnt super helpful on its own, but my understanding is the dsm6 will elaborate even further on this. Additionally more modern "e" related disorders are being addressed.
As for the guide the WHO uses, I'm not versed enough to comment on it.

The limit to this of course, is a better diagnosis doesnt instantly mean better treatment.
Psychology treatments - more mindful approach has resulted in better outcomes
Psychiatric treatments - I dont think theres been a huge change over the past few years, correct me if im wrong. The side effects are the real drawback to most treatments however, and especially in the case of depression, drugs are often the worst treatment (and, or should be the last resort).
Depression in particular has a lot of sub types and is reasonably categorised. The issue is less about treatement but more about prevention. It has to happen at a societal level (unless of course were talking about things like seasonal depression, postnatal depression, etc) and means the overturn of systems that cause depression, or in a sinister outcome the subversion of a class (no more on this).

Id like to know your thoughts on the current diagnosis and treatment system. To me at least, it seems the major hurdle in helping people to get treatment (for my country at least, where socialised healthcare exists) is actually getting them past the preconceptual stage.
>>
>>12538602
Considering the chart $\mathbb{H} \rightarrow \mathbb{HP}^1: q_1 \rightarrow [q_1, 1]$ on $\mathbb{HP}^1$ and $\mathbb{C}^3 \rightarrow \mathbb{CP}^3: (z_1, z_2, z_3) \rightarrow [z_1, z_2, z_3, z_4]$, your map becomes $(z_1, z_2, z_3) \rightarrow (z_1 + z_2 j, z_3 + j) \equiv ([z_3 + j]^{-1}[z_1 + z_2 j], 1)$.
You can then differentiate this map to obtain a $d \pi _S: T \mathbb{C}^3 \rightarrow T \mathbb{H}$ by the usual procedures (which I'm not doing, fuck off).
Notice however that the map in your image actually maps to quaternions. This is because of the $T_p \mathbb{H} \equiv \mathbb{H}$ identification.
>>
>>12540106
*and $\mathbb{C}^3 \rightarrow \mathbb{CP}^3: (z_1, z_2, z_3) \rightarrow [z_1, z_2, z_3, 1]$
>>
>>12539660
epic video, do you know where I can get glass I can use for doing things like this?
>>
>>12540138
I literally said glass pipettes. Although 6mm OD (outer diameter) is common for home chemist/jam jar setups
>>
>>12540239
I meant generally, what glass would be good and what are some good places to get them.
>>
suppose G is a subgroup of $\mathbf{Z}^r$ that's generated by strictly less than r elements. how can I show it has infinite index in $\mathbf{Z}^r$? I'd prefer hints rather than direct answers if y'all don't mind
>>
>>12540535
You can't. Take any finite r > 1 and the subgroup generated by (2, 2, ..., 2).
>>
>>12540535
$\mathbb{Q}$ is a field and you can do linear algebra over it.
Additionally, a a non-empty subspace of $\mathbb{Q}^n$ contains at least one element of $\mathbb{Z}^n$ (and hence infinitely many).
>>
If time is stopped for an external observer, shouldn't Black holes stay on their absolute position in space? So for an external observer it would look like all black holes are moving in the same direction.
So why are galaxies, as they have super massive black holes in the middle, move away from each other?
>>
>>12541101
to an external observer it isnt stopped. like, from our perspective, if the sun turned into a black hole, it would gravitationally act like the same amount of mass, and we'd fly around it interacting with it in that way normally. its only when you get so close to it that you're about to fall into its event horizon that time and space start getting fucky.
>>
if another black hole hit the sun black hole, they'd hit just like two bodies in space do, even if from the perspective of somebody at the event horizon the entire span of the universe would blaze by before they finally coalesced.
>>
>>12541118
No, a quick Google search gave me
>From the viewpoint of an observer outside the black hole, time stops. For example, an object falling into the hole would appear frozen in time at the edge of the hole.
https://www.cfa.harvard.edu/seuforum/bh_whatare.htm
It rather sounds, as time slows extremely down there, so it shouldn't be able to move.
>>
How is one equivalent to the other? I get they're related but equivalence doesn't make sense to me because y and x are from different sets. $y\in f(A)\iff x\in A$
>>
>>12541384
>>
>>12541384
I meant y in f(A) equivalent to x in A
I don't logically understand how it's "legal" to use when proving something like $f(\bigcup_{i=1} A_i) = \bigcup_{i=1} f(A_i)$
>>
>>12541384
>>12541438
Oh, I see, $f(x) \in f(a) \iff x \in A$.
That's only true if $f$ is injective. Otherwise it's just $x \in A \rightarrow f(x) \in f(A)$.
>>
>>12541384
I find the statement confusing. Does that mean that $\forall y \in f(A) \ \exists! x \in A:f(x)=y$ and viceversa?
>>
Let’s say you wake up from being unconscious (you have no idea how you got KO’d) and find yourself on a train. You’re a 6 foot tall, 180 lb, fit, 28 year old male.
(Roughly) what is the top speed the train could be moving at that would allow you to safely jump off the train to the side. Assume there are no dangerous rocks or anything next to the tracks. Just grassy meadow
>>
How do i find the maximum of this function between 0<x<15000?

y=((15000-x+x*1.5)/15000-1)*0.8-(15000/(15000-x)-1)*(1-0.8)
>>
Is simply writing the minus sign equal to 0? Or is this nonsense?
>>
Is there a simple formula for calculating how far the horizon would be on different planets? A quick google search can only find how far away it would be at different heights on earth, now how far it would be on planets that are larger or smaller than earth.
>>
>>12541903
Just do the usual business of setting the derivative equal to 0 and isolating x. Check that the second derivative is negative in that range to make sure you've got a maximum.
>>
>>12542549
https://en.wikibooks.org/wiki/Trigonometry/The_distance_and_dip_of_the_horizon
Just change the values for the size of the sphere you want.
>>
>>12542790
Thank you, that's exactly what I was looking for. I'm a bit of a brainlet, but even that's enough for me to work with.
>>
>>12540106
Nice, thanks a lot anon. I'll try differentiating it myself
>>
Is there any way to forget information, how to MK Ultra myself into forgetting if I have to? Been looking into pills and some could do it but I don't know what to do
>>
How do i find the x values that make x_1 = x_2, y_1 = y_2 from: y_1 = -x_1, y_2 = x_2 without drawing
>>
What function do I need to use to make a positive number smaller the closer to 0 it is and bigger the further away it is? I know log makes the number increase less the bigger it is.
>>
>>12543604
That's true for any monotonic increasing function, including f(x)=x, f(x)=log(x), f(x)=sqrt(x), f(x)=x^n, etc. What are you trying to achieve?

What function do I need to use to make a positive number smaller the closer to 0 it is and bigger the further away it is? I know log makes the number increase less the bigger it is.
>>
>>12543653
Basically I’m trying to take into account diminishing returns on a risk metric. I have a ratio x/y. If I do log(x/y), it gets me closer to my goal of the next peak of the normalized ratio being 1. Right now my problem is that each time the price peaks the risk metric gets lower instead of being 1 each peak.
>>
>>12543694
I think you have no idea what you're doing.
>>
Bros, is it true that

$\left(\cup^{\infty}_{n=1}O_n\right)\cup\left(\cup^{\infty}_{n=1}P_n\right)=\cup^{\infty}_{n=1}(O_n\cup P_n )$

where O_n and P_n are countable collections of open intervals of $\mathbb{R}$?
I think it's true for finite unions, but for countably infinite ones? It's assumed that both terms on the left hand side exist.
>>
>>12544018
It's true without any of those assumptions.
>>
How to stop being demotivated after a demoralizing experience with an Introductory math book? I was doing the exercises about multisets from the book of proof and I had to look up solutions for half of the exercises in the solutions in the back.
>>
Is it really necessary to drudge through all of the classical anticonstructive haze before I can get to the good stuff that's being used in current (this century) papers on computable results?
>>
>>12544323
How? Is there a proof that transposes

$(A_1\cup A_2)\cup(B_1 \cup B_2)=(A_1 \cup B_1)\cup (A_2 \cup B_2)$

to the case $n \to \infty$?
>>
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Going to be starting my Advanced Inorganic Chemistry course in a few weeks.
Pretty daunting as I skipped the previous inorganic course.
Any good resources to learn group theory/crystal field theory?
>>
>>12544403
Let $\beta, \gamma , \delta$ be arbitrary sets, and $f: \beta \rightarrow \gamma$, $g: \beta \rightarrow \delta$.
Then $(\bigcup _{\alpha \in \beta} f(\alpha) ) \cup (\bigcup _{\alpha \in \beta} g(\alpha)) = \bigcup _{\alpha \in \beta} (f(\alpha) \cup g(\alpha))$ and both sides are well-defined in ZF.
>>
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>>12544802
This is the secret book
>>
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>>12544802
>>12544923
It's the sequel to this book, in case you forget the basics
>>
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Broskis I feel sick, I have a lot of nausea and my back hurts a lot.
I don't want to study today but my moral thinks that I have to.
Should I rest for today or what could I do to get rid of the symptoms.
>>
>>12544923
>>12544927
Thanks, anon. Wish me luck.
>>
>>12544941
Good luck!
>>
>>12543085
What do you want to forget?
>>
>>12544908
Thanks man
>>
>>12544936
>>
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>>12536145
>>
If you were trapped in a concrete cell with a gag in your mouth and your hands cuffed behind you, could you reasonably guarantee a method of suicide? Like is there a specific way to bang your own head against the wall to kill you as opposed to knocking you out or causing brain damage? What if you were tied down as well, could you induce vomiting via thought and choke to death on your own puke? Could you give yourself an aneurysm by clenching really hard repeatedly? Could you hyperventilate yourself to weaken your lungs or give yourself a heart attack or something?

what would be the most reliable or the fastest method?
>>
>>12545250
>not carrying a cyanide pill in a false tooth
ngmi
>>
>>12545137
C desu.
>>
>>12545410
thanks
percentage, brainlet moment
>>
>>12545137
C. You only need to know that their speeds are in a 5:4 ratio to know that they first "sync" after Viktor has swam 10 lengths (250 m) and Tomas 8 lengths. Their absolute speeds don't matter .
>>
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If the facet joints of the cervical vertebrae are practically flat wtf is stopping the vertebrae from completely rotating? The facet capsulary ligaments? Seems kinda weak no?
>>
>>12545785
tons of vertebral ligaments
and also the disc and annulus pulposus and the the forces on the spine
>>
>>12537989
Integument
>>
what's it called when you can compose two functions in one way but not the other way?
>>
>>12544936
drink water, eat, sleep

and begin to lift weights. use starting strength book.
>>
>>12536145
Does /sci/ think that a flexible ferrite product like this, made into a sleeve for an NFC-enabled credit card, would prevent it from being read surreptitiously?
https://www.fair-rite.com/flexible-ferrite/
>>
if I have a strategy that wins 70percent of the time what percentage would I lose 10 times in a row?

Thank you.
>>
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>>12546531
30 percent
>>
>>12546549
How did you come up with that? What about 20 times in a row?
>>
>>12546531
0.3^10
https://www.mathsisfun.com/data/probability-events-independent.html
>>
>>12546531
Use the binomial distribution. The probability of success is 0.7 and you want to know the probability of having no successes in 10 trials. The probability of having no success after 10 trials is 0.0000059049.
>>
>>12546566
Thank you, I used the article
>>12546562
Sent me and I got the same answer as you. It seems to be an abbreviated version of the binomial distribution formula.
>>
It's known that $u \cdot v = \sum_i u_i v_i$ constitutes an inner product on $\mathbb{R}^n$.

Let's work in $\mathbb{R}^2$ for simplicity. If $u$ lies on the x-axis and $v$ on the y-axis, it makes perfect sense to me that the sum $u_1 v_1 + u_2 v_2$ vanishes - each one of the summands is zero on its own. BUT, suppose the angle formed between $u,v$ is still 90 degrees, only they're no longer parallel to the axes. WHY, on a purely geometric level, do the products of their matching coordinates cancel each other?

Please don't give the $u \cdot v = \lVert u \rVert \lVert v \rVert \cos(\theta)$ formula as an explanation, because $\theta$ is actually defined in terms of the dot product and the norms, so it feels circular IMO (but maybe I'm just a retard). Besides, I expect the case I'm interested in - namely $\theta = \pi/2$ - to be explainable from first principles. (Perhaps even in terms of high-school level cartesian geometry)
>>
>>12546766
Keeping the vectors fixed you can rotate the axes until they are parallel to u and v. Then your previous statements all still hold.
>>
>>12546766
Rotation preserves distances, so if your points do not lie on the axes you simply rotate them until they are on the axes and the result follows (again)
>>
>>12546766
do you know how to express rotation by a fixed angle in coordinates?
>>
>>12546766
Consider the vectors in polar coordinates:
u = [r1*cos(a1), r1*sin(a1)]
v = [r2*cos(a2), r2*sin(a2)]
Their dot product is
u.v = r1*r2*cos(a1)*cos(a2) + r1*r2*sin(a1)*sin(a2)
= r1*r2*(cos(a1)*cos(a2)+sin(a1)*sin(a2))
= r1*r2*cos(a1-a2) (by the difference identity).
= 0 when |a1-a2|=π/2
The thing is, if you want to do this without trig, you have to come up with some other way to express perpendicularity; and you can't use their dot product being zero as that's what you're trying to prove. For an inner product space in general, "perpendicular" (more precisely, "orthogonal") just means that their inner product is zero.

If you want to generalise beyond the 2D case, you just need to show that the dot product is invariant under rotation, as any pair of vectors can be oriented to lie in a 2D plane. For any rotation matrix A, you have
[eqn]A^{-1}=A^T \implies A^TA = I[/eqn]
So
[eqn]A u \cdot A v = (Au)^T(Av) = (u^TA^T)(Av) = u^T(A^TA)v = u^Tv = u \cdot v[/eqn]
>>
I've just remembered that there was a pseudoscience general once.
How do we bring it back?
>>

Prove that

$Y=\{f \in C[0,1]:\|f\|_\infty\leq 1\}$

is closed.

Attempt:

$V_\epsilon(f)=\{g \in C[0,1]:\|f-g\|_\infty<\epsilon\}$

$||f(x)|-|g(x)||\leq|f(x)-g(x)|\leq\|f-g\|_\infty<\epsilon$

$|g(x)|\in(|f(x)|-\epsilon,|f(x)|+\epsilon)$

Choose the function g* in C[0,1] such that

$|g^*(x)|=|f(x)|-\epsilon/2 < \|f\|_{\infty} \ \textrm{hence} \ g^*(x) \in Y \ \textrm{and} \ g^* \subseteq V_\epsilon(f)$

Therefore all f are limit points of Y because every neighborhood of f intersects Y at some point other than f. All f belong to Y so Y is closed.
>>
>>12547743
If f is not in y, say |f(x)|>1+e, e>0, then
all functions g with ||f-g||<e/2 are also not in Y.
>>
>>12546985
>>12546993
>>12547018
>>12547418
Thanks, you've given me some food for thought
>>
>>12547743
I realize the last passage is shaky, I'd say just
$|f(x)|-\epsilon<|g(x)|<|f(x)|+\epsilon \leq 1+\epsilon$
So $|g(x)|\leq \|f\|_{\infty}$
>>
>>12547743
Do you know the definition of a metric space?
Because you should be proving that closed balls are closed for an arbitrary metric space.
>>
>>12547865
cut me some slack bro I'm a noob
>>
>>12547876
They're right though. Also, it looks like you made a couple of mistakes in your steps: like you said the last line in your first post is wrong, since you've explicitly picked g* to be in the open ball around |f|, not f. Also your correction must be wrong, since I can just choose g = f + epsilon/2 yielding ||g|| > ||f||. I'll leave it to you to figure out where you went wrong there. If you can't figure it out just post again. A useful tip when dealing with closedness (and compactness) is to start by trying a proof by contradiction.
>>
>>12548073
Ok, thanks, I'll try to ponder.
>>
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>>12548111
Any luck with the pondering?
If you get stuck, you can just google the exact statement in >>12547865
>>
>>12548152

https://math.stackexchange.com/questions/2700749/a-closed-ball-in-a-metric-space-is-closed

How can I git gud like this?
>>
Let $\mu$ be a finite measure on $X$, and suppose that for any $\epsilon > 0$ there's some measurable $A$ with $0<\mu(A)<\epsilon$. How might one construct a sequence of pairwise disjoint sets $(A_n)_n$ such that $0 < \mu(A_n) < 2^{-n}$? I'm really struggling with assuring disjointness
>>
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I just cant figure out what this theorem is supposed to mean, what do U1 and phi look like for a given function? I'm trying to come up with some concrete examples but it's only making me more confused, so examples would be appreciated
>>
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Me no understand. Me big Dumb Dumb.
>>
>>12548285
Give it a couple years.
>>12548361
Choose $A_n$ such that $0 < \mu (A_0) < 1$ and $0 < \mu (A_n) < 2^{-n} \mu (A_{n-1})$.
Set $B_n = A_n - \bigcup_{m>n} A_m$
$B_n$ can't have zero measure because of our beefy overexaggerated estimate.
They're also all trivially disjoint.
>>
>>12548770
As you can see I get that the pump requires 14,9kW when it should require 39,2kW
>>
which semester do you typically start thesis research in a masters degree?
>>
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why are cs/finitists tards like this?
>>
>>12536145
Is a study flawed if it's using a placebo control but not putting in the effort to maximize the effectiveness of the placebo?
>>
>>12549535
mechanistic thinking kills their capacity for the smallest abstraction, its why modern science is shit
having a single mechanism is just assumed to be the only important factor and proper statistical research is secondary
>>
>>12549535
autism
>>
>>12536454
It generally tends to increase it (through vagus nerve inhibition), one of the main risk factors with weed is the increased heart rate if the person already has heart problems. Perhaps it has a different effect when ones incredibly tolerant, but I highly doubt that's been researched.
>>
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Is there a Sakuyafag here? Like there is (was) a Yukarifag, a Remiliafag, etc.
>>
Suppose I have calculated the SVD of a symmetric matrix, A = U D U.T. How can I use the SVD I already calculated to find the SVD of the sum of A and a particular vector outer product v v.T without performing the entire SVD again?
>>
>>12536145
>Testing if I'm still rangebanned edition.
I'm rangebanned on many big boards /fit/, /pol/, /tv/, although I never did anything wrong there or never actually posted anything there except a couple of replies or maybe two or three harmless threads. I guess this is because I use a mobile internet provider that gets used for shit a lot by some real asshole idiots. I hope this gets lifted one day. I contacted the 4chan.org ban email address, no response.
>>
>roommate tells everyone that she sees dead people
>walks into a room and there's shadow people and corpses waiting in the room for her
>tells everyone she's a medium
what mental illness does she likely have?
>>
>>12550612
>>
In first order logic what's the correct way of laying out a contradictory argument? Is this acceptable? What do you even call this sort of argument?

$A \Leftrightarrow B \\ ¬B \\ ∴ ¬A \\ C \Rightarrow A \\ C \\ ∴ A \\$
>>
>>12550765
attention seeking cunt syndrome
>>
>>12549033
2 years msc: second year
1 year msc: either you begin the program with an already developed idea or you just rush up some bullshit in the summer term
>>
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Can anyone tell what they did in this passage? It's probably some trivial substitution but I don't see it.
E_1 is the energy of the idrogen atom in the fundamental state
>>
Is calculus still necessary
I am studying algebraic number theory with a few papers in some notable journals, but I have yet to learn calculus. I'm 25.
>>
>>12551263
Yes, absolutely, at least in my experience. I don't know if there's some niche field out there that somehow manages without it.
>>
>>12549886
Don't think so.
>>
>>12551263
Modern algebraic number theory definitely needs calculus.
>>
how do I look for something like
$x^3\ln(1-e^{-x})|_0^\inf$
and secundarily, is this 0 or inf?
>>
>>12551671
also wtf did I do wrong with the latex?
>>
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>emailed professors for recommendation letter
>all ignored, not even a "no"
there goes my my plans for grad school, I'm done
>>
brainlet here
how do I substitution on double integrals?

i manage to calculate the area of the region without subbing (gave me 2), but when subbing it gives me 4.

Region A is delimited by x+2y=2, x+y=1, y=-1 and the variable change is u=x+2y, v=x+y
>>
>>12551690
did you have good grades in their class(es) or do research with one or two? maybe send the email again or try to meet with them in person, dont know why they wouldnt do it unless they are just dicks or you asked for them to be done on short notice
>>
>>12551744
Change of variables means that the bounds are u=2, v=1 and u=v-1 <=> v=u+1.

The scale factor is the absolute value of the determinant of the Jacobian, which in this case is 1. The Jacobian is
[eqn]\begin{pmatrix}1 && 2 \\ 1 && 1 \end{pmatrix}[/eqn], its determinant is -1, its absolute value is 1.
>>
>>12551915
how did you get the bounds? I tried getting the points that defined the region and somehow plugging it in u and v and got a bogus region
>>
>>12551764
I did pretty well in all the classes yeah. The first time I asked was 3 weeks before the deadline, and I sent a follow up a week later. I was kind of an autist and didn't talk much, but I'm pretty sure they remember me because everyone else was borderline failing.
>>
>>12551690
Best wishes. This virus is shit for networking, getting jobs/internships, getting letters of recommendations, etc. As a grad I'm grateful I've dodged the bullet and feel for you undergrads.
>>
>>12550905
No, I'm not allowed to post in threads neither
>>
>>12550905
>>12536145
>Posting from your IP range has been blocked due to abuse
That's what I see one every time. I never did anything wrong. Can't post or reply, can't open threads.
>>
>>12552574
>>12552590
The only thing I actually did was open the feedback page and firmly tell Hiro that I wasn't going to buy a 4chan pass.
[spoiler]And occasionally whine about my rangeban here.
[/spoiler]

I imagine that it being lifted was completely unrelated to either and most likely caused by my IP range becoming less active, mostly because an IP range becoming less active is the only real reason Hiro should have to lift a range ban.
>>
can somebody explain the algebra behind this in retard-terms for me, please? my math is very rusty
>>
>>12551966
> how did you get the bounds?
>>12551744
> the variable change is u=x+2y, v=x+y
=> y=u-v
> Region A is delimited by x+2y=2,
=> u=2
> x+y=1,
=> v=1
> y=-1
=> u-v=-1 <=> u=v-1 <=> v=u+1
The intersection of this line with u=2 gives v=3, with v=1 gives u=0.

If you integrate wrt du dv, the outer bounds are 1<v<3 and the inner bounds are v-1<u<2. If you integrate wrt dv du, the outer bounds are 0<u<2 and the inner bounds are 1<v<u+1.
>>
>>12552738
The first step is just addition of fractions:
1/b^2-1/x^2 = (1/b^2)(x^2/x^2) - (1/x^2)/(b^2/b^2)
= x^2/(b^2 x^2) - b^2/(b^2 x^2)
= (x^2-b^2)/(b^2 x^2)
The second step is factoring the difference of squares:
(a+b)(a-b) = (a+b)a-(a+b)b
= (a^2+ab) - (ab+b^2)
= a^2-b^2
>>
Mathematically speaking, did biden steal the election?
>>
Given two ideals $I,J$ of a commutative ring, does $(IJ)^n=I^nJ^n$ in general?

I don't want to think anymore and just need a yes or a no. Thanks.
>>
What is histamine? Apparently I'm allergic to it but my doctor didn't explain what it is.
How do I avoid histamine?
>>
>>12553725
I highly doubt you're allergic to histamine since its naturally produced in the body by the immune system. They are what cause an allergic reaction. Being allergic to anti-histamines I could believe.
>>
>>12553425
Yes.
For future reference, ideals in a ring form a semiring.
>>
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how can (area of paraloligram) = (base) * (height)?
That's like saying (area of paraloligram) = (area of square or rectangle)
I can't seem to visualize how would they be equal, my brain doesn't accept it.
>>
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>>12554228
A shear transformation doesn't change the area. In pic related, the triangles on the left and right have the same area (they're the same triangle). The area of the parallelogram is that of the rectangle with triangle on the left removed and the triangle on the right added.
>>
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What is the best place to buy a domain and a webhotel? I just want to learn basic website/hosting shit.
>>
>>12554270
Install VirtualBox, install a Linux VM, install a LAMP stack, RTFM's
>>
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>>12554228
etc
>>
>>12554276
I just realized i'm not on /g/ either, this is going to be a hard journey my friend...
>>
>>12554296
Deboonked
>>
>>12554406
we're talking about area, not circumference
>>
>>12554418
Are you implying those two are not related?
Anon: 0
Deboonk: 2
>>
>>12554428
They are pretty much unrelated, correct.
>>
>>12554435
Then explain how I can see things
anon: -1
Deboonkening: 3 (critical level)
>>
>>12554406
If you repeat to infinity you aren't getting the limit. You get a fractal, not a line.
>>
>>12554450
>If you repeat to infinity you aren't getting the limit.
well, you aren't trying hard enough
>>
>>12554428
>Are you implying those two are not related?
no
>>
>>12554450
prove it
>>
This is a proof of the CS inequality from Arfken. Why should the function I be minimized and how do i check that the obtained value of lambda minimizes the function I, since the second derivative of I reduces to zero?
>>
>>12554501
You don't need to look at the second derivative. It achieves unboundedly large real values and is bounded below, hence the critical point needs to be a global minima.
Proof left to you.
>>
>>12552710
alright, I'll gonna wait some more time then
I'm too stupid to go to the IRC anyway
>>
this might be a really easy question, but lets say i have a two-dimensional plane with x between 0-1000 and y also between 0-1000. i also have some points arbitrarily scattered across the plane, my initial position is (0,0) and the objective is to reach every single point with least total distance traveled, but i cannot move diagonally. in this case, how do i minimize the total distance traveled? do i just order points by the manhattan distance from my current position, pick the minimum, move to it, pick a new minimum relative to my current position, and so on until done?
>>
>>12555317
How is that any different to the travelling salesman problem?
>>
>>12555400
>>
>>12536513
>>12536531
>>12536504
>>12536264
Transmuting elements is the field of nuclear physics. As the joke goes, if you are working with 1 atom, you are a physicist, if you are working with 2 you are a chemist.

You could theoretically, using gratuitous amounts of energy, shoot atoms down a particle accelerator to smash them into each other and create heavier elements, or you could use the accretion disc of a small artificial black hole to do the same thing.

tl;dr You need energy inputs measured as percentages of a star's total energy output to make californium from hydrogen.
>>
>>12555408
You don't in the salesman problem either. It is just about calculating the shortest path/travel time given some random locations.
>>
>>12555509
it's literally in the wikipedia definition: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?". i also cannot calculate the minimum hamiltonian path because i don't know which would be the last vertex.
>>
>>12555528
The algorithm to solve it doesn't change because of that last step.
>>
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If I met a giant beating heart and tried to hug it, will I feel the electrical impulses sent out by its sinoatrial node tingling me like constant static jolts or will I just feel it beating?
>>
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>>12536145
So I mixed together vitamin C and ethanol and boiled it for some time together using a water bath.
I poured that shit on a plate and burned all the remaining ethanol.
What I got is a dense inflammable clear liquid.
The problem is I inhaled it all the way it burned and now I feel a bit sick.
Am I about to die? It might be covid though, because someone from work had it.
>>
>>12556040
HELP I NEED YOU CHEMISTRY DUDES
>>
>>12556063
>>12556040
Never mind, I'll just drink some water and go to sleep. Esters are totally safe I guess.
>>
>>12555993
>will I feel the electrical impulses sent out by its sinoatrial node tingling me like constant static jolts or will I just feel it beating?
yes
>>
>>12556688
Which one is it
Can I also feel the tingling of its electrical impulse?
>>
$a^n=n$ is there such an a?
been looking, but couldn't find anything
>>
>>12557530
$a = \sqrt[n]{n}$
>>
>>12557544
thanks
>>
Assume undergrad-tier background. I was wondering if /sqt/ can explain, in a nutshell, what are the main approaches to axiomatizing probability theory, other than Kolmogorov's. Are there any shortcomings to the beautiful realization of p.t. via measure spaces that justify alternative approaches?

P.S. Much love to all the kind anons that always help out on /sqt/. You're all wonderful people.
>>
>>12558320
While my background is entirely in calculus-based and measure theory-based probability, I am aware that probability can also be defined as a special case of quasiprobability. Quasiprobability is used in quantum mechanics and it is particularly fascinating, and still can't be interpreted clearly.
>>
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Consider a convex optimization problem, named problem A. Now let f(x) be a convex function. We include f(x)=0 as a constraint in problem A, resulting in a new problem, named problem B. Is problem B also convex?
>>
>Prove that $\alpha$ and $\beta$ are homomorphisms
but they aren't are they? unless I'm misunderstanding the problem, $\mathscr{L}(\mathbb{R})$ is the set of real functions, $f : \mathbb{R} \to \mathbb{R}$ such that $f^{-1}$ exists and the binary operation is function composition.
Now [eqn]
\alpha(f\cdot{g}) = (f \cdot{g}) (1) = f(g(1)) \neq f(1) g(1) = \alpha(f) \alpha (g)
[/eqn]
>>
>>12558939
forgot image
>>
Is it there a definition for the rank of an arbitrary module over a commutative ring?

I'm also looking for some bibliography where I can read about the properties of the rank.
>>
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e.g.
>0, 1, -1, 0
vs.
>0, 1, 0, -1

Considering the twisty way we solve matrices (ad - bc), isn't that a sign we're doing it all wrong?
>>
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Why would university students exercise the option to be graded with pass/fail mentions (as some universities are offering these times) when one can infer one's letter grade anyway? No one with a good grade will want to request this grading scheme after all, so aren't bad students just self-selecting and not doing themselves any good?
>>
Sean Carrol said in his podcast that we can't tell if we are perfectly still in space because something about reference frames? But if the speed of light is constant and not relative can we not use that to work out our speed relative to it or something?
>>
>>12559030
>Why is non-standardized procedure standardized in this way and not another why?
These are by far the worst shitposts on /sci/
>>
>>12559030
I can't tell if you're trolling or just retarded.
>>
>>12559063
A frame of reference in GR is just a choice of coordinates. So you could pick ones that made you stationary and the something else moving, or you could choice coordinates where the something is stationary and you are moving, or you could pick ones where you both are moving. No matter which ones you pick the physics is still the same. There is no universal "correct" reference frame to pick to measure yourself against.
>>
>>12558942
>>12558939
never mind, I worked it out. the binary operation on $\mathscr{F}(\mathbb{R})$ is supposed to be $f\cdot g = h \iff h(x) = f(x) + g(x)$, not function composition.
>>
Do humans have organs homologous to gill slits?
>>
>>12558952
https://en.wikipedia.org/wiki/Length_of_a_module
>I'm also looking for some bibliography where I can read about the properties of the rank.
It's covered in most commutative algebra texts.
>>
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Anons im fucking retarded. I want to go for an engineering degree, but I am having trouble with

>intermediate algebra
>in fucking college
>because i coasted in high school

I am having the fucking hardest time trying to translate word problems into equations.

Question:
>Six less than the product of seven and the difference of a number and three is four times the number. What is the number?

Here is what my small brain had attempted

>Six less than the product of seven
7x-6

>the difference of a number and three
x-3

>is
=

>four times the number
4x

7x-6+x-3 = 4x
>correct answer is suppose to be 9
>I can't get 9

im doing something wrong, and im too fucking stupid to see what I am doing wrong.
>>
>>12559505
7 times the difference less 6 ...

$7(x - 3) - 6 = 4x$
>>
>>12559505
How are you able to use a computer?
You know how to save images and find the folder when you click "Browse.."
But you can't simply look up the definition of a few words?
7(x-3) - 6 = 4x
the difference of a number and 3 -> (x-3)
the product of seven ... -> 7*(x-3)
six less than ... -> 7(x-3) - 6
is four time the number 7(x-3) - 6 = 4x
solving this equation gives
7x - 21 - 6 = 4x
3x = 27
x = 9
You are fucking retarded.
>>
>>12559505
The product of (seven) and (the difference of a number and three)
>>
>>12559544
Thanks anon, I initially had (x-3)-6 but I doubted my ability to think I understood it, so I told myself its not right, and just google it, and found similar examples for the phrase

>six less than the product of 7
and people wrote it like Nx - N and convinced I was wrong to begin with.

So I went with that.

>>12559550
Thanks anon, it help clear things up.

>>12559562
thanks anon, I appreciate the help
>>
>>12558672
The wikipedia definition is, and I quote:
"A convex optimization problem is an optimization problem in which the objective function is a convex function and the feasible set is a convex set."
Assume the function $f$ is defined by $f(x, y) = x^2 + y^2 - 2$. Then $f$ is a convex function but $f = 0$ isn't a convex set, hence problem B can't be a convex optimization problem.
>>
>>12560417
>Then f is a convex function but f=0 isn't a convex set
I'm a mathlet, how can I figure out whether a set is convex?
>>
>>12559177
I'm looking for patterns
>>
>>12560455
It's literally a fucking circle lad.
>>
>>12560455
https://en.wikipedia.org/wiki/Convex_set
In general, anything of the form f(x,y,...)=k isn't convex unless f is linear (i.e. the set is a plane).
>>
>>12560516
>In general, anything of the form f(x,y,...)=k isn't convex unless f is linear
Is there any exception or is it truly a general rule of thumb?
>>
>>12536670
seems like you could just subtract it directly like x=x-x[0]
>>
>>12541811
500mph unless you're a massive PUSSY
>>
>>12560574
well it's obviously wrong for a kind of trivial reason, for example consider f(x,y)=(x-y)^2, then f(x,y)=0 is a line, which is convex

what probably is true is that if the set f(x,y)=k is convex, then the set must be a line or line segment (but this does not mean that f itself is linear). that's because the set f(x,y)=k has dimension 1 (barring pathological examples), and the only way you could have a convex dimension 1 subset of R2 is if it's a line segment.
>>
>>12561146
>what probably is true is that if the set f(x,y)=k is convex, then the set must be a line or line segment (but this does not mean that f itself is linear).
Nah, but close.
Consider $f(r, \theta) = \max (1-r, 0)$ , where $r$ and $\theta$ are the usual polar coordinates. $f^{-1}(0)$ is a disk.
What is true is that, if $k \neq \inf f$, then $f^{-1}(k)$ is convex if and only if it's a line or a line segment.
Just notice how if it contains three non collinear points it needs to contain an entire simplex. Then you consider the symplex's barycenter and some point $x$ such that $f(x) < k$ and look at the convex combinations.
>>
>>12561373
*$f(r, \theta) = \max (r - 1, 0)$.
It's supposed to just be a cone that's flattened on the unit disk.
>>
What does it mean that "Universe is mostly nothing"?
>>
>>12561468
It means most of the universe it empty space. What else would mean??

macro scale - the distance between galaxies is measured in millions of light years and is mostly vacuum.
micro scale - volume of an atom is mostly empty, 99.99% of the mass is in in the nucleus.
>>
>>12551235
Anyone please? Physicists where are you?
>>
How do philosophical platonists look at mathematical objects that only exist by analogy, like the field with one element or noncommutative topological spaces?
>>
is there a site like wolframalpha or symbolab but with all steps being free?
>>
>>12551235
>>12561667
It does not look trivial. I would guess that if you substitute in the formula for $E_1$ and the Bohr radius $a$ in terms of $m_e, e, \epsilon_0, \mu_0, c$ etc then do some tedious rearranging and cancellation and then finally simplify you would get the RHS. If there are any identities to make those steps easier I'm not aware of them.
>>
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I've been sitting on this one for too long.
AB=AC
ADC triangle is an equilateral triangle.
How can i find the DBC angle?
>>
>>12561137
tensors and tensorflow datasets are immutable, so I had to make a really fucky solution by converting them back to numpy arrays, apply the operation you suggested, then convert back. Thanks!
>>
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Chemically-speaking, what makes an oil good or bad at drying?
>>
>>12536171
>>12530898
Feynman's Lectures

>>12504634
I would say that food tastes different depending on your nutritional needs. If you live in a humid environment or eat oily foods (especially with unhealthy oils). If you have a history of eating unhealthy oils, it could be an allergic reaction. Do you live in the American South?

>>12505192
Why not, but it would likely be a useless theory. If your universe is an empty set, everything would be nothing.
>>
>>12562715
https://en.wikipedia.org/wiki/Drying_oil
>Since oxidation is the key to curing in these oils, those that are susceptible to chemical drying are often unsuitable for cooking, and are also highly susceptible to becoming rancid through autoxidation, the process by which fatty foods develop off-flavors.
>>
>>12561938

If you make points B C and D fit on it's circumcircle, you'll find that A is the centre of said circle.
You'll also find that quadrilateral ABCDs angles must sum to 360. you know the angles in triangle ADC, they are 60.
Let y be the angle BAC. As ABC is isoceles, angles ABC and ACB must be 2y. You now know that angle ABC must be:
360 - (y + 60) - 60 - (2y+60) = 180 -3y
However angle ABC is also 2y
Therefore you have 180-3y = 2y, making y = 36.

Recall earlier we said that A could be treated as the centre of our circumcircle, and D was a point on the circle. You can employ the fact that an angle at the edge of a cicle will be half that at the centre of the circle.

(The angle formed at the centre of the circle by lines originating from two points on the circle's circumference is double the angle formed on the circumference of the circle by lines originating from the same points. )
Therefore we know that angle BDC must be half BAC which makes it 0.5 * 36 = 18

angle DBC = 180 - 18 - 60 - 72
angle DBC = 30
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Is there any way to learn super manifolds without a PhD?
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>>12561686
Any quantum effect makes your phase space
non-commutative; this is true in QFT/QG and QM/CM. There's no "analogy" here, they're real.
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>>12541811
define "safe." Bruised elbow? Twisted ankle? Broken toe? Or full chinese liveleak (where they somehow live)?
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>>12559287
some kids are born with gills IIRC
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>>12551235
you just gotta write out everything bro and do the cancellations
there's no secret trick, just be careful while doing the manipulations
P.S. this is why chads use either totally arbitrary units or natural units
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>>12562601
>tensorflow datasets are immutable
now i see why all the cool kids are using pytorch
>>
Let's say I have two discord users and I'm trying to determine if they are the same person.
Is there a tested way to use machine learning models for that?
I thought of training a neural network classifier and looking at its accuracy or probability differences, but I'm not sure if it's a good way to do it.
>>
i need to draw a slope field for this;
x'' = (1-x^2)x' - xsint, x = x(t)

how do
>>
Why am i so bad at word problems? how do i get better?
>>
>>12563466
I tried to study supergeometry once by reading Alice Rogers's book but dropped it ~70 pages in because I thought it was uninteresting.
Anyhow, I don't remember it requiring much. Flipping through it again now:
>abstract algebra
>smooth manifolds (read at least the entire Lee book)
>Clifford algebras and spinors
>enough functional analysis for QM
>probability theory
>basic knowledge of lie groups, lie algebras and algebraic topology
Should be good enough.

If you go into it without motivation from physics you'll probably also drop it, tho.
>>
How should I interpret the quadrupole tensor? The dipole vector is easy enough: it corresponds to two opposite charges Q and -Q at the origin, separated by a distance d. One then takes d to zero as the product Qd is kept constant (which is equivalent to looking at the object from very far away). But I do not understand the quadrupole tensor, in the sense that I could look at a picture and tell explain what the tensor should look like.

I've calculated the quadrupole tensor of the "typical" quadrupole configuration: Q at (+/- d/2, +/- d/2) and -Q at (-/+ d/2, -/+ d/2); the Wikipedia definition then yields Qxy = Qyx 3Qd^2, Qxx = Qyy = 0. I have two questions: First, wouldn't it be tidier if the factor 3 would disappear? The dipole definition is very neat in that it only has a component Qd, I expected the same here. Second, how do the degrees of freedom determine the geometry of the quadrupole? In 2D space A dipole has 2 degrees of freedom which basically just means the direction and magnitude of the dipole; a quadrupole also has 2 (since it is defined by the components of a vector), does this also correspond to the angle and size of the square? I hope what I say conveys a clear picture.
>>
Does LASSO regularization always force at least one coefficient to be zero? If, e.g., I have only two variables, is it guaranteed that just one will be selected?
>>
“The average lifespan of a computer is 5 years. What is the probability a computer is still working after 8 years”

What the fuck am I looking at here? Surely there isn’t enough information to give a numerical answer, or are some assumptions implicitly made in a context like this?
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>>12565726
Lifespan is defined as "the time after which only half of the computers still work." So after two lifespans, only 1/2 * 1/2 = 1/4 of the computers still work, and so on. Your question is a bit tricky since 8 years isn't a multiple of 5: the probability is less than 1/2 but more than 1/4.
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>>12565767
Ah that does clear it up, cheers fren
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>>12565767
>Your question is a bit tricky since 8 years isn't a multiple of 5: the probability is less than 1/2 but more than 1/4.
[spoiler]You're just pretending not to know how to solve this, right?[/spoiler]
>>
I finished Calculus I with a 99%(100.5% on exams) and I feel like I'm rusty on some of the subjects we covered after just a month-long break, with Calculus II and the spring semester starting tomorrow. Is that normal or is my memory fucked?
>>
>>12565891
Of course I can solve it, but I'm not doing that because Anon has to solve it himself. I just cleared up the the words and aim of the exercise.
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>>12565998
you're just like a lot of people who are successful in school: really good at short-term understanding and pseudo-memorization, but shit at long-term retention because you didn't actually internalize the material.

t. the exact same kind of person
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>>12566009
Ah, I see.
I was concerned for a second there because of the the phrasing. Specifically the bounds.
>>12565998
Sounds normal.
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>>12566173
>AdS went to the trash can.
Did something happen with AdS spaces that makes them no longer physically relevant?
>>
How do I get better at manipulating summations. I don’t understand the "removing k = n+1 term and adding k = 0 term" part, which is arguably the most significant step in the proof.
>>
>>12566205
The only way I got familiar with it was a ton of exposure.
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Can I run a Particle Swarm Optimization inside a Cellular Automaton?
>>
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>>12566198
It's technically "antigravity" since $\Lambda<0$ is hyperbolic, so geodesics accumulate at the spatial infinity/horizon boundary. However this makes the space compact, and the strong-coupling at the boundary gives rise to a quantum theory, which is a CFT if the boundary preserves the conformal $PSL$ subgroup from the maximally-symmetric bulk.
This is all a basic, however, and perhaps she was referring to phenomenological results that I'm not aware of.
>>
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For a beam with one end fixed and another end attached to a large body, with an off-center axial load, how would you calculate the stiffness of the beam and the resultant deformation?
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>>12566244
Thank you for the explanation.

>perhaps she was referring to phenomenological results
That's what I'm assuming.
Do let me know if you hear of anything, please.
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>>12559550
>insults someone for asking a stupid question
Dude fuck off
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>>12565998
Completely normal. Fortunately, if you’re in a position where you’ll need calculus, you’ll have to keep using these tools again and again in subsequent classes. Eventually it’ll become as natural as HS algebra

Really, with any class you take, the point isn’t to learn everything and have it stick forever. The point is to keep developing your ‘’maturity’ with the field and to learn enough so that if you ever need to use the subject again, you can relearn it quickly. The only way to really internalize a complicated subject is to use it again and again
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>>12565603
It shouldn’t: try drawing from a multivariate Gaussian where x1 is uncorrelated with x2, and both x1 and x2 are correlated with x3. Apply LASSO. If my intuition is right, you shouldn’t have either coefficient go to 0
>>
Are there any easy to visualize homeomorphisms from the sphere to itself with a single fixed point?
Consider $f: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ defined by $f(x, y) = (x+1, y)$. $f$ has no fixed points, obviously.
Since the Alexandroff one-point compactification is a functor $AOP$ (name invented right now, there's probably something else that's used more often)(see wikipedia for a source) we can get $AOP(f): S^2 \rightarrow S^2$, which is a homeomorphism and only fixes the point at infinity.

But this example is super fucking jarring, I want something cuter.
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>>12566576
I've just noticed I somehow misread wikipedia and it isn't really a functor.
The construction still works tho.
>>
what's a good, free software for plots?
I need one that marks the intersection points with at least 8 digit precision..., bonus if it can show all at the same time
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>>12566587
$f\in C(X)$ pushes forward to the compactification $\overline{X}$ only if $f\in C_0(X)$, i.e. vanishing outside a compact set (specifically $f\neq0$ around open neighborhoods around $\infty$). Translations obviously don't do this,
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>>12566659
just use python and matplotlib
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>>12566576
To answer your question, homotopies of maps from one sphere to the other can be interpreted as a (pinned; i.e. satisfying certain homotopy conditions) path into the wedge product $S^2\wedge S^2$. This path "drags" one sphere into another, so to speak.
>>12566684
Meant $f=0$ on open sets around $\infty$.
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>>12565726
I'm fairly sure that you should assume that the probability of failure in any given time interval is constant, so the probability that a specific computer works at any point in time follows an exponential decay.
>>
>>12566205
$\sum_{k=1}^{n+1}ar^k=(ar+ar^2+...+ar^n+ar^{n+1})+(a-a)=(ar^0+ar+ar^2+...+ar^n)+ar^{n+1}-a=\sum_{k=0}^{n}ar^k+ar^{n+1}-a$
>>
>>12565891
>>12566009
Yes I don't expect to be spoonfed the answer, anyway it should work out to 7/20 if the lifespan stuff scales "uniformly". Should I read a stats inference book to learn more about this stuff? So far I've just been doing regular probability problems
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>>12566870
what if computer lifespan is normally distributed? uniformly distributed? exponentially distributed? all of these options give different answers to your question, yet there's no way to know which one to use
>>
>>12566964
>>12566827
yea that's what I thought, the problem is from a shit tier source so they didn't specify but after doing some research and staring at the answers in this thread I agree it's probably assumed to be exponentially distributed so should just be 2^(-8/5). fuck it
>>
rolling for set.seed()
>>
>>12566846
>>12566222
Thank you. I understand the full proof now. I think what confused me was the change of index and setting k = j+1.

What helped me was to instead just look at the expanded form of the summation after we distributed r, and that made it easy to see that the necessary relation to S (it’s the same thing but with the r^0 term removed and an r^(n+1) term added). Everything after that is just normal algebra.
>>
How do I compute
[eqn]\int_C \frac{z^5}{(z-1)(z+1)^3} [/eqn]
where C is the circle of radius 3 centered at 0
>>
>>12566964
> yet there's no way to know which one to use
The fact that the mean lifespan is the only piece of information given regarding the distribution implies that it is the only piece of information required, which in turn implies that the hazard rate is constant.
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>>12567392
Partial fraction decomposition and residue theorem. I get 8πi.
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>>12567392

I got 3/8pi i.

I could've fucked up but you just have to evaluate this closed contour on the poles of your function, you have a.. oh i did the wrong question.

But anyways, here's the method anyways, you have a first order pole at z = 1 and a third order pole at z = -1, so when you evaluate the residues you will need to take the (order-1)^th derivative of the integrand and add up those residues. Then you multiply the result by 2pi * i.

If I recall correctly, this is cauchy's residue theorem.
>>
What chemistry is happening for a girl's hair to smell so good?
Is it the shampoo they wear? I don't think it is.
I believe there's body odor made in their hair and it smells nice. What chemicals and what chemistry is happening for a girl's hair to smell so good?
>>
>>12536556
You're just getting too high, smoke CBD flower instead to see the difference
>>
>>12561802
>>12564057
Thanks, at least I know I'm not missing something stupid
>>
Can someone tell me what is calculus used in physics called and why is it so fucking different from the math courses that I did? Why are there weird notations such as du/dy in fluid mechanics, like does this mean for every step dy I take the speed changes by du? And this is completely different from say dx/dt which actually makes sense.

I tried finding on the web how physicists use calculus because there isn't the slightest connection to the math calc. course I had. I managed to find some site mentioning there are "amount" and "change" differentials, and I think this is my problem. I've never been taught there even is a difference, I've been taught derivative is a slope of the tangent at a point of a curve. I want to be able to understand physics proofs that use calculus, but it's used in such an alien way, like a strip of infinitesimal width is dx, and its mass is dm, and it's represented as dm/dx. This surely cannot mean that at some point mass changes by dm i I move by dx. Because what is then the difference between m(x), where I plug an x and get the exact mass there, and dm/dx(x), where I plug in an x and get.... I don't even know what it represents.
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>>12568474
you nudge y an infinitesimally small amount and see how much u changes, that's all
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>>12568474
A straight line has a slope, right? For y = mx + b, this slope is m, and it's the same everywhere on the line. The m tells you how much y changes when x changes, so if you go 1 to the right you go up by m. Well, any curve has a slope, only their slope is different. For example, for y = x^2 the function is flat at x=0 so the slope is 0, and the higher x gets, the steeper the slope becomes.

To obtain the value of the slope at f(x) = x^2, we look at some interval h and see how much y changes so "slope at x" = (f(x + h) - f(x))/h = (x^2 + 2xh + h^2 - x^2)/h = 2x + h. Now all we have to do is to make h infinitely small since we want to get the approximation as accurate as possible, so we find that "slope of f(x) at x" = 2x. This x-dependent slope function is called the derivative of f, and it is often written f'(x) or dy/dx, where dx = h and dy = f(x+h) - f(x). This was a rigorious derivation, a seasoned student knows that in general the derivative of x^n is n x^(n-1). Other functions have derivatives that take different forms but it all comes down from this definition of looking at how the function changes for small change of x.

Calculus is the mathematical study of everything that involves derivatives. At this point you really shouldn't be doing fluid mechanics yet, just watch Khan Academy videos or find another elementary source. Master basic differentiation, integration (those factors of dm I'm sure appear in integrals), vector calculus, differential equations and then it's time for fluid mechanics.
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>>12568572
>rigorous
Well, not entirely rigorous of course, but it shows how the rule is derived. inb4 this statement gets mathematicians angry.
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Do stars with $M<0.5M_s$ become subgiants after exiting the main sequence?
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>>12568572
Ok, I've had Calc 1 and Calc 2, and then I've been thrown into Thermodynamics and Fluid Mechanics. Yeah, maybe I shouldn't be doing Fluids with insufficient knowledge on math, but guess what, does my uni care? No. So I could choose to just ignore mathematical proofs of physical concept like every other mech. eng. student and just go with the flow (no pun) and learn to solve exercises, but I'd much rather have an intuition of why stuff works. Guess I should've studies physics and not engineering.
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>>12568677
Okay, in that case I hope the course is being gentle with you. If you feel itchy looking at derivatives I would strongly urge you to look through tutorials and do exercises; if you're doing calculus without feeling confident in that notation you probably won't get far. I can still explain what they mean with the dm if you like, although like I said it involves writing down an integral.
>>
Are metals a solid plasma? Are solutions of electrolytes a liquid plasma?
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>>12568784
No. They still have their electrons. A true plasma is where all the electrons have been stripped from their nuclei and are free.
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>>12568666
Assuming they're not too light (at least 0,4 Ms) then yes.
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>>12566684
Yes, yes, that's the usual case.
But here we just map the point at infinity to itself, so it isn't an issue.
>>12566733
>homotopies of maps from one sphere to the other
I don't follow, what homotopies have to do with anything here?
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>>12566244
Bruh
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>>12568812
Thanks. And what happens to lighter stars? It was not very clear in my professor's lectures, don't they also expand to compensate the nucleus collapse?
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>>12567490
Polynomial division gives
[eqn]\frac{z^5}{(z-1)(z+1)^3} = z-2 + \frac {4z^3+2z^2-3z-2} {(z-1)(z+1)^3}[/eqn]
Partial fraction decomposition of the remainder gives
[eqn]\begin{align} \frac {4z^3+2z^2-3z-2} {(z-1)(z+1)^3} & = {A \over z-1} + {B \over (z+1)} + {C \over (z+1)^2} + {D \over (z+1)^3} \\ & = \frac {(A+B)z^3 + (3A+B+C)z^2 + (3A-B+D)z + (A-B-C-D)} {(z-1)(z+1)^3} \end{align} \\ \implies A+B=4,\,3A+B+C=2,\,3A-B+D=-3,\,A-B-C-D=-2 \\ \implies A=\frac 1 8,\,B=\frac {31} 8,\,C=-\frac 9 4,\,D=\frac 1 2[/eqn]
The poles with coefficients C,D have zero residue, leaving the total residue = 32/8=4, and the integral is 2πi times that.

At least, I think that's how it works.
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>>12536145
Do stupid questions exists?
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>>12568950
Most of them are red dwarfs, they burn up their entire hydrogen reserves until they're 100% helium, and never expand because they're fully convective. However they do it at a much slower pace than the Sun or other heavier stars, so right now the Universe is not old enough to see what happens at the end. The theory is that they become "blue dwarfs" and later on white dwarfs.
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What are some introductory applications of complex analysis to physics?
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>>12568983
quantum mechanics lmao
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>>12568982
Ok I see. Thank you very much anon, here's a cute Yukinoshita as a sign my gratitude.
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>>12567560
It's the shampoo.
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>>12569007
I like how she's got 2 right feet
>>
why do certain wavelengths cause ionizing radiation while others don't?
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>>12569269
the energy of light is what gives it its ability to ionize, not anything else. energy depends on the frequency (inverse wavelength) only.
if you're asking why ionization can occur in the first place, it is the energy required to remove an electron from something. this is equal to the energy that holds the electron in its stable position. once your light has energy greater than this, it can ionize the substance.
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>>12569236
Lol
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How do we slow /sci/ down?
>>
What's wrong with just simply wanting to win in life, having money/status? How come in every college application/job application, I have to have a selfless passion like wanting to feed starving African kids? In the US, pure high performance and grades is almost looked down upon.
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>>12570365
I like charitous people because they're more likely to help me if I need it, get me?
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>>12570365
What? I've never had to do that. T10 UG and grad schools. Americans are crazy individualists. Yeah you should be passionate about the subject. Passionate people work harder and smarter. But selflessness? Never had to do it

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