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/sci/ - Science & Math

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Previously >>11784387

>what is /sqt/ for
Questions regarding math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc. >books?
libgen.is (warn me if the link breaks)
https://stitz-zeager.com/
>articles?
>book recs?
https://4chan-science.fandom.com/wiki//sci/_Wiki
>how do I post math symbols?
https://i.imgur.com/vPAp2YD.png (embed)
>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 here?
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
>look up the Tex guide beforehand
>if you've made a mistake that doesn't actually affect the question, don't reply to yourself correcting it. Anons looking for people to help usually assume that questions with replies have already been answered, more so if it has two or three replies
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Resources:
Good charts: https://imgur.com/a/kAiPAJx
Shitty charts: https://imgur.com/a/1Q1LIMk (Post any that I've missed.)
Verbitsky: https://imgur.com/a/QgEw4XN
Graphing: https://www.desmos.com/
Calc solver: https://www.wolframalpha.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

OP Question: $n^2+1$ objects are permuted into $n$ sets of $n$ objects and one object left over. What is the formula for the number of permutations for a given $n$?
>>
(N^2+1) choices for the one left over
then n^2 choose n * (n-1)n choose n * ... 2 choose n * 1 for the n lots of n-sets
but we must consider where the n sets are given in different orders, so divide by n!
havent done any probability/combinatorics for 4 years so someone correct me if its wrong
>>
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What is the name of this circuit?
>>
>>11810858
>cemicircles
>>
>>11810922
Mixer. The transfer function is Vout=V1+V2.
>>
>>11811006
1/9(V1+V2)
>>
I have a combinatorics question too: How many ways are there to make a sequence of length m of the numbers 1,2,3, if 1 cannot follow 2 and 2 cannot follow 1? I feel like this should be easy but I'm drawing a blank.
>>
>forget how to do a problem
>struggle for 30 minutes
>exit the exam room
>remember how to do it
>have the correct solution in my head in a minute
how do I stop doing this?
>>
>>11811191
Diversion. Get a piece of scrap paper and work on a completely unrelated task, like writing a limerick or rebuilding the periodic table from memory. After five, ten, maybe fifteen minutes of recess, go back to the last completed question and resume from there. Discard your previous scribbled attempts at solving the problem, as mulling over them might nudge your brain into getting stuck again.
>>
>>11810922
what does the triangle mean?
>>
>>11811290
>>
>>11811391
It's simple enough to remember the 2-8-8-18-18-32-32 (or 2+6+10+14) rule for building the electron orbitals that the table follows, and then you fill in the places in the table from memory.
If you do enough chemistry, it's easy enough to remember a few of the columns because everything in a particular column has similar properties. The classic example is Group VII - the halogens. They all have all but one place in their outermost electron shell filled and have a high electronegativity as a result. This high electronegativity means that they like to violently rip electrons away from other molecules that they bump into, and you probably recognise a few of the names as dangerous chemicals: Fluorine, Chlorine, Bromine, Iodine, Astatine.
>>
>>11811083
No, V1+V2. The voltage on the non-inverting input is (V1+V2)/3. The voltage on the inverting input is Vout/3. For the op-amp to be non-saturated, these must be equal: Vout/3=(V1+V2)/3 => Vout=V1+V2.
>>11811388
Operational amplifier aka op-amp.
>>
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>>11811391
What can I say? The periodic table itself is an elaborate mnemonic device for chemists, and you can find "submnemonics" to help you remember how it's laid out. For instance, the sequence of elements on the second line (Li Be B C N O F Ne) can easily be expanded into a meaningful sentence where each word starts with the symbol of the corresponding element (say, Little Benjamin Better Come Now Or Fucking Never). It gets trickier as you move down the table, but you can also consider columns or other meaningful subgroups.

I only mentioned that as a science-related memory task though.
>>
>>11811420
thank you for the answer, i am lacking even basic chemistry and always wish to catch up

do you chemists live by the periodic table?
i find it a unique tool in the sciences, i think its the most "methodical" and shit table in all of the sciences
is it strong like the maxwell eq in magneto electric?
i guess some time people used log tables, less today. not very much tables in science i can think of.
>>
>>11811107
First guess: recurrence relations. It's the number of ways to make a length m-1 sequence preceded by a 1 plus the number of ways to make a length m-1 sequence preceded by a 2 plus the number of ways to make a length m-1 sequence preceded by a 3.

N(x,0)=1
N(1,m)=N(1,m-1)+N(3,m-1)
N(2,m)=N(2,m-1)+N(3,m-1)
N(3,m)=N(1,m-1)+N(2,m-1)+N(3,m-1)

So, it's
[eqn]
\begin{pmatrix} 1 && 1 && 1 \end{pmatrix} {\begin{pmatrix} 1 && 0 && 1 \\ 0 && 1 && 1 \\ 1 && 1 && 1 \end{pmatrix}}^{m-1} \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}
[/eqn]
>>
>>11811475
As the matrix is symmetric, A^m=U.Σ^m.U^T where U is orthogonal and Σ is diagonal. so the expression can be re-written as
[eqn]
\begin{pmatrix} 1 && 1 && 1 \end{pmatrix}
\begin{pmatrix} \frac 1 2 && \frac 1 2 && \frac 1 {\sqrt 2} \\ \frac 1 2 && \frac 1 2 && -\frac 1 {\sqrt 2} \\ -\frac 1 {\sqrt 2} && \frac 1 {\sqrt 2} && 0 \end{pmatrix}
{\begin{pmatrix} 1 - \sqrt 2 && 0 && 0 \\ 0 && 1 + \sqrt 2 && 0 \\ 0 && 0 && 1 \end{pmatrix}}^{m-1}
\begin{pmatrix} \frac 1 2 && \frac 1 2 && -\frac 1 {\sqrt 2} \\ \frac 1 2 && \frac 1 2 && \frac 1 {\sqrt 2} \\ \frac 1 {\sqrt 2} && -\frac 1 {\sqrt 2} && 0 \end{pmatrix}
\begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}
\\
= \begin{pmatrix} 1-\frac 1 {\sqrt 2} && 1+\frac 1 {\sqrt 2} && 0 \end{pmatrix}
{\begin{pmatrix} 1 - \sqrt 2 && 0 && 0 \\ 0 && 1 + \sqrt 2 && 0 \\ 0 && 0 && 1 \end{pmatrix}}^{m-1}
\begin{pmatrix} 1-\frac 1 {\sqrt 2} \\ 1+\frac 1 {\sqrt 2} \\ 0 \end{pmatrix}
\\
= \begin{pmatrix} 1-\frac 1 {\sqrt 2} && 1+\frac 1 {\sqrt 2} && 0 \end{pmatrix}
\begin{pmatrix} (1-\sqrt 2)^{m-1} && 0 && 0 \\ 0 && (1+\sqrt 2)^{m-1} && 0 \\ 0 && 0 && 1 \end{pmatrix}
\begin{pmatrix} 1-\frac 1 {\sqrt 2} \\ 1+\frac 1 {\sqrt 2} \\ 0 \end{pmatrix}
\\
= \frac {{(1-\sqrt 2)}^{m+1}+{(1+\sqrt 2)}^{m+1}} 2
[/eqn]
>>
Given an N*N grid, what is the number of possible ways to place 3 marks on different cells of the grid so that they are aligned?
>>
i have a trouble remembering names, i can remember facts and actions just fine but i can't remember names, they just fly off my head.
i also have difficult time to focus on a subject, i always think about multiple things and sometimes the previous thing i was thinking about flies off my head and i can't remember it till much later.

should i see a doctor?! am i schizo?
>>
>>11811731
no, you should stop browsing 4chan and read a book or something instead
>>
>>11810878
The logic looks correct.
Stirling numbers of the second kind, tho.
>>
>>11811731
>the previous thing i was thinking about flies off my head and i can't remember it till much later
That's how the brain works FWIK, and how clever thoughts are trampled by a flock of unimportant ones. To-do lists, turning off notifications, some form of meditation are all attempts to reduce the number of the latter.

As for remembering names, there are tricks explained in details all over the web.
>>
I'm asked to sketch all complex numbers z that fulfils

abs(z+i)+(abs(z-i)=3

It's easy to find z=+-sqrt(5)/2 but is this really the only solutions?
>>
>>11811801
>it's an "anon forgets how ellipses work" episode
>>
Hey sci

What do you say is the difference between Persistence, Perseverance and Tenacity?
>>
>>11811541
> ((1-√2)^(m+1)+(1+√2)^(m+1))/2
The binomial expansion of (1+√2)^n is
[eqn]\sum_{k=0}^n {n \choose k} {\sqrt 2}^k[/eqn]
(1-√2)^n is similar but odd powers of √2 are negative. So their mean is just the even powers of √2. IOW, the expression can be written
[eqn]\sum_{k=0}^{\lfloor {\frac {m+1} 2} \rfloor} {m+1 \choose 2k} 2^k[/eqn]
>>
Arithmetic question : Prove that 5n+1 is divisible by n2+1

Honestly I would have done it by now it if were n+1, but n2+1 I got no idea.
>>
>>11812281
That's false
>>
>>11812415
It is true for n = 5

5^2+1 = 26
5x5+1 = 26

5 being a prime number it works for 0 and 1 too, I just can't find the solution.
>>
>>11812427
5n+1 + (n^2+1) = n^2+5n+1

The roots being 0 and 5 and 5 being a prime number, I can prove that it works with {0,1,5} or nah ?
>>
>>11812438
oh shit no I mean 5n+1 - (n^2+1) = -n^2-5n
>>
>>11812427
>find the solution
What are you even trying to do? Finding for which n the divisibility thing works? Also

>it works for 1
Then, did you mean n^2+1 is the one that has to be divisible by 5n+1?
>>
>>11812593
Prove that n^2 + 5n + 2 is divisible by n^2+1

but first they ask you to prove that 5n+1 is divisible by n^2+1
THEN finding for which n this thing works.
>>
I'm taking an honors abstract algebra class in the fall and wanted to do a bit of pre-studying. The textbook they're using is Dummit and Foote so since I wanted to learn the material from a different perspective I'd rather not use D&F. What book should I use to get a good grounding on the material?

>Herstein
>Artin
>Maclane

I tried Herstein, but I didn't like his presentation of the material, although the exercises were excellent. Artin seems too obsessed with matrix representations and it puts me off, but I like it. I'd also like recommendations for a good and rigorous number theory book.
>>
how nuclearfgas are going to achieve this meme "uranium from water"?
>>
>>11812631
Hungerford is intended to be a very concise summary for graduate students who've already taken at least one course. You're not going to make much headway if you've never really seen algebra before.
Artin is a very good book, deliberately targeted as a first course, and he has good reasons to be obsessed with representations; representations are really pretty, they give a geometric viewpoint to otherwise dry formal algebra, and they're massively important to modern math (including number theory, which you seem to be interested in).
Maclane is a nice book (it's what I learned from in undergrad) but you should try fast to kill the habit of constantly book-hopping trying to find a perfect textbook. Just stick with Artin if you've started it, it's a good book.
This can get very insidious because perfect textbooks don't exist and you can easily end up wasting months rereading introductory chapters over and over and not really learning much of anything.
>>
>>11812728
Ok, thank you. You are right. I am wasting too much time on this nonsense instead of actually doing the material. Can I skip the sections on Linear Algebra that I already know (vector spaces, modules, etc) from Hoffman and Kunze?
>>
>>11812763
That's up to you, really. Take 10 minutes to skim through the chapter and see how much of it is obvious, then you can decide for yourself which parts if any are worth reading.
>>
What're some good science related RSS feeds or podcasts?
>>
>>11812792
Thanks. Ireland and Rosen or Apostol for number theory after I am done with Artin?
>>
Does anyone have that image of a probability problem involving gold and silver balls that always gets infinite (you)s out of retards here?
>>
Can anybody debunk this:
https://youtu.be/5WPB2u8EzL8
It's called "How to enjoy the end of the world" and it talks about entropy
>>
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I need to find the initial speed $v_0$ of the particle P with charge q such that its speed at Q is 0. The rod on the left side has a linear charge distribution $\lambda = \frac{Q}{L}$.
How do I solve it? The electric field (and the acceleration) is non-uniform, so I guess an energy approach is the least retarded way to solve it but I'm not sure how to do it.
>>
>>11813205
conservation of momentum, work-energy, use the expression for force in terms of the field and the charge and reverse engineer the variables you need. you can figure it out if you can come up with a tractable expression for the force
>>
Bros how can I show that T is a linear transformation from R3 -> R2?

T([x,y,z]) = [x-y, z]

I know that I am supposed to prove it by showing that it is closed under addition, and closed under scalar multiplication but I really don't know how to set up the problem
>>
>>11813219
literally just do what you said
does T([x+w,y,z])=[x-y,z]+[w-y,z] ?
does T([ax,ay,az])=a[x-y,z] ?
plug in the conditions for linearity and check whether they're true
>>
>>11813219
to show that it's closed under addition, give yourself two vectors U and V and prove that T(U)+T(V)=T(U+V)
to show that it's closed until scalar multiplication, prove that a*T(U)=T(a*U) where a is a scalar
>>
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Hi /sci/,
I just wanted to say that I went back to school last year, after a long time off and switching to stem, and I made the president's list with a 4.0 this year
It's gay, but this is the first time I've ever been academically recognized for anything, so thank you fags for helping me
We're all gonna make it
>>
>>11813219
Show that for each $\alpha, beta \in R^3$ and scalars $c \in R$ that

[eqn]T(c \alpha + \beta) = c T(\alpha) + T(\beta)[/eqn]

You just take 2 arbitrary vectors alpha and beta and a scalar c and show that this is true.
>>
I am a super brainlet. If you have an expression such as x+y-z, is that equivalent to x-z+y?
>>
>>11813412
Depends, is your structure commutative under addition? If so, yes, otherwise no.
>>
>>11813380
congrats anon you did well
>>
>>11813388
Are there conditions on T? This seems to be impossible to prove without some sort of conditions on T but my linear algebra background is that the richest. If it's linear, then you can split it up and then take out the scalar.
>>
>>11813727
what he wrote is a definition of linearity
to show your transformation T is linear you have to show these conditions hold. which means you have to know what your T is
>>
Is the coset of the group itself equal to the group? i.e. $gG = G$ for any $g \in G$?
>>
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how the heck can the total current through an ac circuit be less than the individual currents in different branches?
>>
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>>11810858
the result should be -0.5... but how also dont know what integral of a lone dirac-delta is I guess 1 but still I get 0.5
>>
>>11813754
x = gg^-1x
>>
>>11813219
u = (x1, y1 z1)
v = (x2, y2, z2)
a, b real numbers

compute T(au + bv)

compute aT(u) + bT(v)

compare
>>
>>11814526
Error is on the last line. cos(-pi) = -1
>>
>>11810858
DC=1/(sqrt(2)-1)
>>
Is there way to download all papers in sci-hub and all books in libgen? How large would these collections be?
World seems to be going to shit and I want to save papers and books for warm days when world is burning and there is no internet anymore.
>>
does 10^2n +1 ever have a factor multiplicity >1?
>>
how do i get into modern probability theory?
>>
>>11814885
learn measure theory
>>
>>11814398
Phase. If the currents in the two branches are out of phase (180° apart), the amplitude of their sum will be the *difference* in their amplitudes.
E.g. an ideal parallel L-C circuit has current circulating between L and C but nothing goes in or out.
>>
Alright. Question regarding Talebs claims regarding economists.

One obnoxious faggot I know keeps quoting "Skin in the game" to discredit economics (not an econcel myself but it comes up in conversations a lot) and keeps applying it to other issues "X group has no skin in the game" and derives his argument from that.

From what I've seen many such popular books especially ones that make tall claims like this have holes in them or at least smart enough to only fool midwits(like that sapiens book or plethora of self-help books).

So did Taleb BTFO economists in his book or is it overrated?
>>
>>11815133
But the central idea is true, isn't it?
People act differently if their choices do not impact them.
>>
>>11814812
Just look at the "download" section on libgen, it has all sorts of information regarding this.
>>
>>11815189
I mean, anyone working to help politicians manage the economy would be in a similar a position wouldn't they? Not like some other math or finance guy could provide more "certainty" or face consequences more than economists do if you're in that position of managing a country.

I don't think it's some profound insight.
>>
>>11812415
It's not
>>11812602
>Prove that n^2 + 5n + 2 is divisible by n^2+1
I think you misread, they probably told you that n^2 + 5n + 2 is divisible by n^2+1, this way it's much easier to do the rest.

a divides b if there is at least one value of k for which ka = b is true

then it's pretty straightforward :

k(n^2+1) = n^2 + 5n + 2
k(n^2+1) - (n^2+1) = n^2 + 5n + 2 - (n^2+1)
k(n^2+1) - (n^2+1) = 5n+1

Bingo you just proved that n^2+1 divides 5n+1
>>
>>11815043
How can the total current (V_in/|Z_total|) be less than individual branch currents though?
>>
>>11815229
>>11812602

Now the answer is very easy to get.

You need to find for which n value n^2+1 = 5n+1
n^2+1 = 5n+1
n^2 = 5n
n = 5

n being a prime number, n^2 + 5n + 2 is divisible by n^2+1 if n € {0,1,5)

Done.
>>
>take undergrad class taught by research prof who doesn't normally teach
>" dont worry this class will be easy :) i'm not here to make your life difficult :) dont stress out over the exams :)"
>lectures are nothing but abstract/proof deriving devoid of practical examples
>exams are randomly selected textbook problems that are completely different than every lecture and homework problem
why
>>
>>11815463
Because the Professor is based.
>>
>>11815260
I*sin(x)+I*sin(x+pi)=I*sin(x)-I*sin(x)=0.
At any given time, all of the current in one branch is coming from (or going to) the other branch, with none of it coming from (or going to) the input or output.

For vectors, |A+B|<|A|+|B| if the angle between A and B is greater than 90°. If |A|=|B|, then |A+B|<|A| if the angle is greater than 120°.
>>
>>11813754
Only if it's cyclic.
>>
I have to hand in homework online for a course I'm taking.
The problems are mostly of the plug'n'chug type but I'm not sure how I want to do them.
Anyone has a $\LaTeX$ template that's useful for this kind of stuff?
>>
>>11815463
>practical examples

I wish math didn't have to suffer from midwits incapable of abstract though
>>
>>11815909
just look up a latex template and adapt it to your liking.
there's plenty of easy ones online, you'll find one before someone here links you one you like.
>>
>>11816213
it doesn't people like this don't get out of undergrad
>>
>>11816230
Thanks, but I wanted to be spoonfed
>>
is minoxidil a meme?
>>
>>11815463
I dunno.
I feel like, if I were a professor, the least effort possible way to teach would be copying and pasting the books onto the blackboard while adding minimal commentary and answering questions.
>>
>>11816213
>>11816238

is there anything more cringe than a grad student who actually gets to take classes that aren't a mile wide and an inch deep, nor are they required to do 40+ homework problems a week, so they actually have a chance to study material
>>
Hallo brothas, What resources do y'all recommend to get good at Equation Modeling?
I might be OK at it in my mother tongue, but In english I'm trash, also, Is reading the only solution to get better at reading comprehension? which genre is best for that.
>>
is the shape of the universe a sphere?
>>
>>11816286
No. It's not a wonder cure or anything, but it provides at least some help for a significant amount of people.
The only hair loss treatments that are not a meme are minoxidil, finasteride and related drugs, and transplants. Everything else (except maybe some illegal experimental drugs imported from China) is a scam.
>>
>>11816506
alright, and how permanent is it? as in if i use it for a year and it works i can stop using it after since the hairs back and healthy right?
>>
>>11816503
we have no idea
>>
>>11816494
don't read the solutions before doing the problem, ever. just keep doing problems and practicing and understanding what you got wrong
>>
>>11816679
Apparently I'm also shit at communicating.
I was asking if the only solution to poor reading comprehension is reading more, and if it is, which genre is the most useful for that.
>>
>>11816685
there's no "best" genre. I wouldn't recommend old novels because the language is dated. honestly just reading online, especially news articles, often is good. reading comprehension comes with practice mostly, but I'm sure there are ways to do it smarter.
practice problems will help too unless you really don't know what to do.
>>
>>11816692
I feel that the dude that answered me though that by " Is reading the only solution to get better..." I was referring to the solution of math problem.
>>
>>11810858
how does expression of an allele work if the mom chromosome and the dad chromosome are different? Are both somehow used, or is one selected?
>>
>>11815909
Making up your own template is highly instructive.
Otherwise just use koma script, raise the DIV and switch the title font to rmdefault.
>>
>>11815218
>I mean, anyone working to help politicians manage the economy would be in a similar a position wouldn't they?
Obviously.

>I don't think it's some profound insight.
Which doesn't make it false or irrelevant. You usually do not need profound insights to describe basic social phenomena, but I think the observation that someone will or will not face consequences for his actions can be relevant.
>>
Why are lizards always doing push-ups?
>>
>>11817318
asserting dominance and showing that they arent a little bitch like you
>>
>>11815830
wrong
>>
>>11817287
Then why call them charlatans? It's the nature of the field which economists themselves recognize.
>>
Given a graph whose vertex set is $V$, determine whether it contains three (not necessarily disjoint!) cliques $V_1, V_2, V_3$ such that $V_1 \cup V_2 \cup V_3 = V$.

Is the problem NP-hard? I've been at it for more than an hour and made no real progress. I thought I might be able to poly-time reduce either $\mathrm 3$-$\mathrm {SAT}$ or $k$-$\mathrm {CLIQUE}$ to this problem, but so far I couldn't come up with anything.
>>
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I'm really having trouble wrapping my head around tensors, both the definition and intuition seem really opaque to me.
Did you have any "eureka" moments with regard to the subject and can you share them with me?
>>
If you join two magnets do you get a long magnet or will it stay in a NSNS configuration?
>>
>>>/g/76434844
posted in the wrong /sqt/
>>
>>11810858
Suppose I have n charged particles, each moving on a set path with their position as a function of time. Is there a general method using Maxwell's equations to calculate the electric and magnetic field as a function of position and time?
>>
>>11818248
Calculate the electric and magnetic fields generated by each particle (Coulomb's law and the the Biot–Savart law respectively) and sum them.
>>
>>11818279
Doesn't it get more complicated if some of the particles are on an accelerating path? I never specified that they were moving at constant velocity necessarily. Only that the path is fixed.
>>
>>11810858
why numerous times when i scratch things on paper and cannot think of a solution if i try to type it here in latex preview, suddenly i get an idea that happens to solve the issue? I only restrain to posting here if something takes me several days.
>>
>>11817328
But they run away as soon as the see me.
>>
It doesn't make sense to me that the observable universe is way larger than it is old. If the universe is 13.8bil years old, and what we can see is 46bil light years across, how can the universe be getting bigger faster than light can travel across it?
>>
>>11818431
That's because you think the universe gets bigger because of light scattering into an empty void.
>>
>>11818461
But that would mean that either FTL is possible or that space and time being created with the big bang is wrong.
>>
>>11818465
Why?
>>
>>11818291
How would that change it?
>>
>>11818470
Well, accelerating charges create electromagnetic waves, right? But I don't see any way in which just Coulomb and Biot-Savart could lead to oscillations in the electric or magnetic field.
>>
Has anyone made a meme infographic quantifying coronavirus deaths in relation to the holocaust/people Hitler killed/people Mao killed/etc?
>>
>>11817773
some tensors have a physical description that you can intuit, but more often than not they are abstract quantities with values at certain indices. I think when I stopped trying to think of them as matrices and instead realized they were just pure mathematical "organizers" of numbers, variables, etc.. then it helped me.
the intuition is hard though
>>
A photon is just the minimum size you can divide an em wave into?
>>
i feel like that recently i've started learning new things way faster than i used to
>>
>>11818814
no
>>
sea water smells like bleach which means that there is a redox reaction happening but how does it happen? there is no electricity in the ocean.
>>
>>11819243
there are a lot of ions in the ocean
>>
>>11810858
Lets say there are two concepts of centers of a convex polytope in R^n. There is the vertex center, which is just the average of the vertices of the polytope and there is the analytical center, which is found via a conic maximization on the log potential function. If we sample uniformly from the polytope P. does the average of sample points approach the vertex center or the analytical center or some other point as n-> inf?
>>
>>11819261
Pretty sure the average converges to the center of mass.
Unless you're selecting points along the polyhedron's surface, in which case I have no idea.
>>
>>11819366
even if the points are on the surface, it will still tend to the center of mass/ analytical center
>>
Posted this in the previous thread and didn't get an answer, so i'll give it another try:

I want to prove the following vertex function $V_{\mu\nu} (q)$ for a Feynman diagram:

[eqn] \left< p' \left| T_{\mu\nu} \right| p \right> = p _{\mu} p'_{\nu} + p' _{\mu} p_{\nu} + \frac12 q^2 \eta _{\mu\nu}[/eqn]

where T is the energy momentum tensor of a scalar quantum field:

[eqn]T_{\mu\nu} = \partial _{\mu} \Phi \partial _{\nu} \Phi - \frac12\eta_{\mu\nu} \left( \partial \Phi \cdot \partial \Phi - m^2 \Phi ^2 \right) [/eqn]

How exactly am i suppose to get this? I tried plugging in the expansion of the field in terms of creation and annihilation operators as:

[eqn] \Phi (x) = \int \frac{d^3 k}{(2\pi )^{3/2} \sqrt{2\omega _k }} \left( a^{\dagger} _k e^{ik\cdot x} + a_k e^{-ik\cdot x} \right) [/eqn]

but the integrals i have to solve are very complicated, having delta functions of the 4 three-momenta $p$, $p '$, $k$, $k'$ (the k and k' are from the expansions of phi). Any help appreciated.
>>
>>11819649
Nice, thanks.
Do you happen to have a source handy? I thought about that at first, but then I realized that I could replace a face of a cube by a squiggly fractal that doesn't actually change the volume much but adds in extremely large area, so it doesn't work for arbitrary bodies like the points along the interior thing. But I could see it working for polytopes.
>>
Why is R^5 -> R^8 NOT onto?
>>
>>11819676
finding the AC is equivalent to performing surface integrals. The original question was on convex polytopes, i THINK it still works in nonconvex sets
>>
>>11819678
You're gonna need to be more specific what you want. It can be onto as a set map.
It can't be onto as a vector space map or a map of topological spaces, but for different respective reasons.
>>
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>>11819701
For a vector space
I'm studying linear algebra
>>
>>11819718
Dimension of the domain is 5, so the dimension of the image can be at most 5. You can get that formally from the rank-nullity theorem.
>>
>>11819691
I'm looking at the definition of the AC I found (this one https://www.wolfram.com/language/12/convex-optimization/analytic-center.html?product=language )
and I'm pretty sure it doesn't work in the non-convex case.
In particular, if you have a thin enough "U", then the average of the positions on the surface converges to the average of the positions on the interior (by extreme thinness), so it gets thrown to the the middle of the U (outside of it), and the AC is always inside the object (at least, the definition doesn't make sense if you allow it to leave the body).

I'm honestly really not seeing it working for convex sets, either, if the wolfram definition is the one you're thinking of. Consider a triangle. We mark a point in the middle of side, and then we consider the two parts of the triangle's sides to be different sides when computing the AC. From what I can see in the definition, this should skew it off a bit (I haven't actually performed any computations, so please correct me if I'm wrong).
However, by choosing points outside of the triangle very near the point marked out on the side, you can construct convex quadrilaterals very, very close to the original triangle, and with very similar ACs and average-position-along-the-surface, but on the limit of the quadrilaterals approaching the triangle the average converges, and the AC jumps.
>>
>>11818225
bump
>>
How do you guys handwrite your Pi symbols?
>>
so I just had the stunning realization (or at least, it finally clicked for me) that the sine function (for one period) is linear in the phase domain (and that the entirety of the sine function can be defined via a linear function in the phase domain)

now I've got my noggin joggin
how do you convert/transform any given function into the phase domain? Does it even make sense to? Even if it doesn't make sense, how do you do it?
>>
>>11819893
three straight lines, quickest and still unambiguous. top horizontal line extending over the legs.
>>
>>11820003
also, is there a phase-form/definition of the sine function?
>>
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Which weighs the most out of the 3? A pound of copper, a pound of aluminum, or a pound of tin?
>>
>>11820143
yeah
>>
What's a good journal for civil engineering that decides quickly and a has a high acceptance rate

I am currently looking into elsevier journals and wondering if theres anything else

I need to publish something ASAP to demonstrate my research skills so I can hopefully land a good phd scholarship
>>
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Does anyone have book recommendations for a complete beginner in Chemistry? I'd prefer being able to go with a foundational approach, i.e understanding the actual reasoning for things in basic Chemistry as opposed to the memorization bullshit they have you do in school, but if that's not possible or not preferred I understand.
>>
>>11820670
General Chemistry, Linus Pauling it is written to teach the conceptual aspects of highschool and freshman chemistry with very little in the way of emphasis on memorization or calculations. Pauling stresses intuition and will convey easy rules of thumb you can use for analyzing basic chemical reactions and understanding the logic of chemistry. I really enjoyed using it for my gen chem courses along side my trash required textbook.
>>
>>11820684
>it is written to teach the conceptual aspects of highschool and freshman chemistry with very little in the way of emphasis on memorization or calculations.
This won't sacrifice any understanding, right? i.e I'll be able to go directly into organic Chemistry without losing anything?
>>
>>11820711
>this won't sacrifice my understanding
IIRC no he covers most of what would be necessary to do the majority of basic lab experiments. The books i likely far more comprehensive than what the typical uni Gen Chem series will cover, but there are some explicit calculation tricks he just leaves for you to figure out when doing exercises. If you really just want to understand chemistry you would be good to jump right into P-Chem or O-Chem after finishing it. Just remember you do need to be able to calculate and so doing the exercises is a good use of your time
>>
>>11820725
Alright then, thanks.
>>
>>11819701
>or a map of topological spaces
are you sure about that ?
>>
>>11810858
Technically speaking, there isn’t enough information to solve the semicircle problem, but if we assume the diameters are parallel, then its pretty easy to show that the blue line segment is length $\sqrt{2} + 1$.
>>
How long should I take to learn algebra studying 4 hours a day?
>>
>>11821099
5 days
>>
>>11821104
If I still feel weakness after complete it, should I review with precalculus or study algebra again?
>>
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I forgot the rules for differential equations again
>>
I am a sand nigger and we had a solar eclipse today.
People were using pinhole projections to view the eclipse.
Now the thing that I don't understand is why would the light coming from sun, when goes through the pinhole, comes out as an eclipse?
>>
>>11821124
I forgot basic trig and now I'm messing up in calculus
>>
>>11821485
Yea that too.
What the heck is csc and cnn and bbc even supposed to mean?
>>
>>11820908
Nah, anon's wrongerino.
You can partition $R^8$ into a countable number of 8-dimensional cubes.
Then, by choosing a bijection between these and the natural numbers, you can exploit Hahn-Mazurkiewicz to obtain a sujective map from the [2n, 2n+1] interval to the cube, and then you can glue these space filling curves together with the (2n+1, 2n+2) intervals we left over.

And then you use a projection from $R^5$ to the real line.
>>
>>11821523
nice
>>
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>>11810858
Are we to assume O1-C and O2-C are the same distance?
>>
>>11821550
Sorry obviously meant O1-O2 and O2-C
>>
>>11821550
Yeah, obviously. Isn't it obvious that O2 and O1 are supposed to be the centers of their respective (semi)circles?
>>
>>11821560
Also, it's just pythagoras.
>>
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>>11821560
How about now?Could you solve this???
>>
>>11810858
taco
>>
>>11821485
having to memorize trig derivatives and trig power algorithms is big gay
>>
>>11821130
https://en.wikipedia.org/wiki/Camera_obscura
Basically, given a pinhole and any point on the projection plane, you have a straight line passing through those two. The pinhole means that the only light falling on a given point comes from a specific direction, essentially creating focus. Enlarging the hole means that light can reach a point from a wider range of directions, resulting in a blurred image.
>>
>>11821499
csc = cosecant = 1/sin (sec = secant = 1/cos, cot = cotangent = 1/tan).

sin=o/h, cos=a/h, tan=o/a
csc=h/o, sec=h/a, cot=a/o
(o = opposite, a = adjacent, h = hypotenuse).
>>
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Can some helpful anon check my work here?
Did I do this right?
>>
Would jumping in front of a train as it arrives in station at about 50km/h be enough to kill a feeble person such as myself? Asking for scientific purposes.
>>
>>11821977
The square root divided by H to find the geometric equivalent is not at its crux but the juxtaposition of the right angle √ by the by H to find the last interger is mot necessarily found through a tree structure but a rhombus matrix.
>>
>>11819748
well the center of mass can be outside a nonconvex geometry...

and yes if you mean to double up on the halfspace that makes up the triangle side, then yes, the AC is subject to change because it is sensitive to halfspace redundancy, but sampling from the H-polytope itself allows you to pick points on the surface because they satisfy the inequality b-Ax >=0.

The 2d square with side 2 centered at 0,0 has an H-rep
1,1,0
1,0,1
1,-1,0
1,0,-1
and you can also write
1,1,0
1,0,1
1,-1,0
1,0,-1
1,0,-1
any other number of ways.

They all have equivalent vertex representation
1,1
-1,1
-1,-1
1,-1
and vertex center (0,0), but different analytical center. Think about it like a physics problem where we can newton's iterate to the AC and the halfspaces that comprise the triangle exert a spring-like force, if we double up the sides, you double up the force, changing the equilibrium position, but the geometric center doesn't change.
>>
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>>11810858
mathlet and brainlet here frens. pls help

I'm trying to figure out the height of 3 different positions on a 1:30 slope. Can someone tell me what formula or how to go about it so I can at least get something. thnx.

refer to image.
>>
>>11822075
it would be extremely painful
>>
>>11822372
You completely lost me with this post, but I don't care that much, so feel free to just give up on me.
Thank you very much for the insight and assistance until now.
>>
>>11823412
It drops 8" in 60" so h=8*(1-x/60). So 16/3=5+1/3" @ 20" and 8/3=2+2/3" @ 40".
>>
Math or CS?
>>
>>11823611
Math if you have iq, CS if you are smarter than most but not all that capable of creating anything interesting. Math you can do finance, some type of quantitative science, datafagging, programming, research, applied math, statistics. CS you can do programming, CS research or datafagging and that’s about it. Math grad is extremely competitive and cut throat. CS programs even at good schools are diploma/PhD mills and churn out more bad research than any field aside from cancer research. CS you could make a lot of money at a young age but want to kill yourself, Math you will likely make very little (if pure) and want to kill yourself. The redpilled choice is math+physics and to go work for Lockheed Martin or Renaissance after you graduate.
>>
>>11813380
good job, dude
>>
Reading this article about how light was captured as both a particle and a wave, however I have no idea what either would look like or even mean.

I know particle would be like a photon or something, and invisible to the eye individually.

But what does it mean wave? What does a light wave look like? Like what comes out of a lamp?

>>
>>11823943
incorrect grammar, retard.
>>
>>11813754
This is easy enough to prove using one of (forget the numbering) the fundamental homomorphism theorems. G is obviously a normal subgroup of G, so the quotient group G/G consisting of all cosets gG exists. Then, consider the homomorphism that sends all g in G to the identity of the trivial group. The kernel of this homomorphism is all of G, hence the quotient group G/G is isomorphic to the trivial group. This implies that the quotient group G/G has order 1, implying g_1G=g_2G for all g_1, g_2 in G, and therefore gG=eG=G for all g in G, with e being the identity in G.
>>
>>11820003
Im not sure about how one would define the phase of any function. But for sinusoidal functions, the phase is just the input of this function. So given the form:

f(t)=g(t)sin(h(t)) (or f(t)=g(t)cos(h(t))),

h(t) represents the phase as a function of t. (And g(t) is an arbitrary function of t as long it is not sin, cos, tan,...)
>>
>>11820003
>>11824055
Also look into Fourier Series/Transform if you haven't already, which is about switching between time dependence to frequency dependence of a function
>>
>>11814526
Consider the defining property of the delta function, which is really a distribution:

$\int_{-\infty}^{\infty}\delta(x)f(x)dx=f(0)$

Taking $f(x)=1$, we know

$\int_{-\infty}^{\infty}\delta(x)dx=1$

Then, because the delta function is only supported on the point $x = 0$, we can restrict the range of integration to any interval containing zero and get the same result.
>>
>>11816503
no. The two are not even topologically equivalent, as the sphere is a 2-dimensional manifold and the universe is 4-dimensional.

The most common big-bang model models the universe as such a manifold with a point-like singularity far in the past. This can be seen using the FLRW metric used to model spacetime:
$\mathrm{d}s^2=-\mathrm{d}t^2+a(t)^2\mathrm{d}\Sigma^2,$

where $\mathrm{d}\Sigma$ represents the spacial metric. When we model the spacetime as homogenous and isotropic (on large scales) this spacial part must have uniform curvature, and this curvature can be negative, zero, or positive. These correspond to hyperbolic space, flat space, and spherical space respectively. If we "fill" this model with a uniform perfect fluid and solve for the parameter a(t), we get several equations called the Friedman equations, which I will not bother to reproduce here. The big-bang solution describes an a(t) that is proportional to some positive power of t, and hits 0 at t=0, meaning all of space collapses to a point.
The big bang model is actually fairly shitty, but its good for really simply modeling a lot of simple properties of the universe.
>>
>>11817496
If your field necessitates being cowardly armchairs while offering advice that has immediate and severe real world consequences and your decision making and entire body of theory would be drastically different were you to actually participate in the resultant environment of your policies you are at the very least a spineless coward and at worst a charlatan since you are altering the truth value and efficacy of your predictions by shielding yourself from blow-back. If I was to make worse my prediction that spurred the design of an experiment by not being the one to design the experiment and consistently yielding null results because I never bother to take control of my research I am effectively retarding the development of my field. It is not less unethical.
>>
>>11817773
There are two different index types, one type transforms with the coordinates, one type opposite the coordinates. When you contract one of each type of index together you get a constant that doesn't transform (is independent of coordinate system), because the transformation with the coordinates cancels the transformation against the coordinates. You get higher order tensors by combining multiple of these indices. You can get a covariant index from a contravariant index by contracting it with an index of the metric tensor (which is covariant in both indices), and vice versa by using the inverse metric.
>>
>>11818074
long magnet. Just trace the magnetic field lines
>>
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Does anyone know what the peaks in this proton NMR of ferrocene correlate to?
>>
>>11815463
Because you should be able to solve the problems independently, using the logic and lines of reasoning in the textbook.
>>
>9 minutes in

for fuck's sake

i thought the "experts" said that electromagnetic fields are completely harmless, and that people who say they're sensitive to them are hypochondriacs?

is this guy a quack or what the fuck is going on?
>>
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>>11824461
>>
Can someone confirm that pic related is correct?
>>
>>11824461
I wouldn't exactly care a lot what a Chiropractor has to say on the subject of EM fields and the human body.

Unless he tells you by what mechanism this is hurting you, you can pretty safely ignore this.

>i thought the "experts" said that electromagnetic fields are completely harmless
Nobody in their right mind ever said this.
But specifically the EM radiation from phones or electrical wiring appears to be extremely safe, due to their extremely low energy.
EM which is known to cause damage is light, it is harmful because it literally burn away your skin, something you can obviously feel.
>>
>>11822075
It depends on what exactly you do. Ideally you want to have your smashed in by the wheels of the train, which they can absolutely do at that speed.
If you are unlucky you might just end up loosing a limb or two.

Aside from that, don't kill yourself.
>>
>>11824616
are his claims about flouride bunk too? i never paid much attention to it because the water in my area has relatively low levels of flouride
>>
Are solids actually just liquids with an extremely high viscosity?
>>
>>11824640
I wouldn't trust a chiropractor about those things. I do not know what he says about flouride but I would be sceptical.
>>
hELLO everyone I need help getting the natural response of this DE of second order
y"+3y'+2y=x
I got the transfer function
Y(s)/X(s)=1/(s^2+3s+2)
I got the impulse response
1/[(s+1)(s+2)] = 1/(s+1) + -1/(s+2)
or h(t)=e^-t-e^-2t
BUT I DON KNOW HOW TO FIND THE NATURAL RESPONSE
>>
>>11824666
The natural response is the solution to the homogeneous system, i.e. with x=0. This is
y(t)=(2y(0)+y'(0))e^-t-(y(0)+y'(0))e^-2t
The Laplace transform of the ODE is
Y(s)=(X(s)+(s+3)y(0)+y'(0))/(s+1)(s+2)
This can be split into the forced response and natural response:
Y(s)=X(s)/(s+1)(s+2) + ((s+3)y(0)+y'(0))/(s+1)(s+2)
The first term (obtained by setting y(0)=y'(0)=0) is the forced response (the portion which depends upon the input), the second term (from setting X(s)=0) is the natural response (the portion which depends upon initial conditions). Dividing the forced response by the input gives the transfer function, H(s)=Y(s)/X(s) <=> Y(s)=H(s).X(s); in the time domain this is y(t)=h(t)*x(t) where * is convolution. H(s) is also known as the impulse response, as it's the response when x(t) is an impulse (X(s)=1).
>>
I need to show that if $G_0\lhd G_1 \lhd \dots \lhd G_n$ is a normal sequence and $G_{k+1}/G_{k}$ has a non-trivial normal subgroup $N$, you can make a new sequence for $G$ with compositionfactors $\{G_{i+1}/G_{i}: i\ne k\}, N$, and $(G_{k+1}/G_{k})/N$.

any hints?
>>
What resource should I check if I want to learn about the first predatory single celled organisms? When they appeared, what they looked like, etc.
The Cambrian is specified everywhere as the era where multicellular predator-prey relationships were established, but I'm interested in unicellular life.
>>
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>>11824841
Still dont get it
>>
Does simulation theory have any credibility? any good books on it? what about thoughts influencing the world?
>>
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How would you solve this?
>>
>>11825139
By slurping on my pp
The milk makes your brain the big brain
>>
>>11824866
You have a group $G$ and it has a normal subgroup $H$. We denote the canonical projection onto the quotient by $p_1 : G \rightarrow G/H$.
If $G/H$ has a proper normal subgroup $N$, we have another projection $p_2: G/H \rightarrow (G/H)/N$.
Then, the composition $p = p_2 \circ p_1 :G \righhtarrow (G/H)/N$ has a kernel which is a proper normal subgroup AND contains $H$.
>>
>>11810858
how do you prove from formulae that the expected value of a variable representing number of good samples in a population of k good and n-k bad is mk/n?
probabilities of y good samples from a total sample of y god and m-y bad are
[eqn] \frac{\binom{k}{y}\binom{n-k}{m-y}}{\binom{n}{m}} [/eqn]
So the expectation of Y is
[eqn] E(Y)= \sum^m_{y=1} y * \frac{\binom{k}{y}\binom{n-k}{m-y}}{\binom{n}{m}} [/eqn]
i already know the result derived from the fact that the distribution of y is equivalent to the distribution of Sm given Sn=k, where Si is a number of successes in n independent trials. But supposedly it follows if you use the formula above, the computation gets messy and im not really motivated to go with it. Maybe you know what to do with it?
>>
>>11825365
>from a total sample of y god and m-y bad are
total of k good and n - k bad

>Si is a number of successes in n independent trials
in i independent trials.
>>
>>11825001
In that pic, you're setting y(0)=y'(0)=0. Which is correct for the forced response but incorrect for the natural response. For the natural response, you set X(s)=0 which gives you:
Y(s)=((s+3)y(0)+y'(0))/(s+1)(s+2)
=(y(0)s+(3y(0)+y'(0)))/(s+1)(s+2)
Partial fraction decomposition:
A/(s+1)+B/(s+2) = ((A+B)s+(2A+B))/(s+1)(s+2)
Equate terms:
A+B=y(0), 2A+B=3y(0)+y'(0)
Solve:
=> A=2y(0)+y'(0), B=-(y(0)+y'(0))
Substitute:
=> Y(s)=(2y(0)+y'(0))/(s+1) - (y(0)+y'(0))/(s+2)
Inverse transform:
=> y(t)=(2y(0)+y'(0))e^-t - (y(0)+y'(0))e^-2t
>>
my uni is giving us the option to go online or in person for the fall. it will be the first semester of my masters but im thinking online just to save a bit of money. is this a good idea or would going in person be best for connections or something?
>>
any good books about reprogramming the brain? I don't mean subliminal or mind control like I mean changing internal responses (look on the bright or dim side) how to build habits, discipline etc.
>>
what does the derivative of the linear motion function f(t)=v0+at : f'(t)=a show? the velocity?
>>
>>11825845
yes, derivative of a motion is velocity
however since you've written v0 in f(t), are you sure f(t) is not the velocity ? in that case we're talking about uniformly accelerated motion and f'(t) = a is the acceleration.
>>
>>11825859
makes sense, thanks
>>
MMOfag here, getting hung up over varying drop rates from a boss and minions and trying to calculate the effective drop rate after 1 kill. Let's say there is a boss with 4 minions, the boss drops a weapon at a 1/150 chance, each of the minions drop the same weapon at a 1/600 chance. It is possible to get the weapon from the boss and all four minions, getting the weapon from the boss does not make it impossible to get it from all 4 minions, and vice versa. What would the probability to get the weapon from any one in that group after killing them for the first time?
>>
>>11826018
1.33%
>>
>>11820670
Chem is mostly calculations
>>
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Anons, can we agree that X is neither a subset nor a superset of Y ?
>>
>>11826107
Why wouldn't it be a subset?
>>
>>11826107
suppose a pair belongs to $X$.
Then the elements of the pair can be written:
$a, \sqrt{a}$ for some $a$, nonegative real number. since a is nonegative real number, $\sqrt{a}$ is also.
$\sqrt{a}^2 = a$ so if we write $y= \sqrt{a}$, clearly $(y^2,y) = (a, \sqrt{a})$ therefore it belongs to $Y$. And since we considered arbitrary element of $X$, every such element belongs to $Y$ which in turn makes it true that $X$ is a subset of $Y$. So no.
>>
>>11825139
a,b>0
r^2/a^2 + z^2/b^2 = 1

z = (b sqrt(a^2 - r^2))/a

d/dr((b sqrt(a^2 - r^2))/a)
= -(b r)/(a sqrt(a^2 - r^2))
= slope of tangent
= m

slope of normal line = -1/m
= (a sqrt(a^2 - r^2))/(b r)

phi = atan(a sqrt(a^2 - r^2)/(b r))
>>
>>11826131
Thanks
>>
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The system is formed by connection of three systems in parallel.
y(t)=3x'(t)
H(s)=s
h(s)=δ'(t)
Find the impulse response h(t) of the overall system
How is this supposed to be solved
>>
One byte is a sequence of 8 bits : (b0,b1,b2,b3,b4,b5,b6,b7) or {0,1}^8
X is 256 different bytes (2^8)

s : X -> N | (b0,b1,b2,b3,b4,b5,b6,b7) = b0+b1+b2+b3+b4+b5+b6+b7
And x R y <=> s(x) = s(y)

how many equivalence classes are there and how many elements do they contain ?
>>
Hi there
what does sci think about ECT?
>>
>>11826716
K is a straight line in R4 defined by :
x1-x2 = -1
x3-x4 = 1

I need the explicit formula guys
>>
>>11826716
shit didn't mean to reply to you
>>
Does anyone have an example of a subset N of a module M such that it is a subgroup under addition, but the scalar multiplication isn't closed and thus isn't a submodule? I've read from the definition of submodule that it being a subgroup isn't enough and it also requires closure of scalar multiplication, but every example I come up with meets that last condition pretty easily.
>>
>>11826861
>line
>implying the intersection of two hyperplanes in 4 dimensional space is a line
$x(t_1, t_2) = (t_1, 1 + t_1, 1+t_2, t_2)$
>>
>>11826878
What is t tho
>>
>>11826897
$t = (t_1, t_2) \in R^2$
In other words, $x : R^2 \rightarrow R^4$ is an affine bijection onto the solution set of your system.
>>11826873
The subgroup of integers in the $R-module$ $R$.
>>
>>11826919
Yeah ok ok but I mean, where did x1,x2,x3,x4 go ?
>>
>>11826919
Well that ended up being much simpler than whatever example I was trying to build, thank you.
>>
>>11826878
But that's a parametric equation anon not an explicit equation
>>
does anyone have a recommendation for an introductory control systems/control theory book? One oriented more towards EE?
>>
>>11814647

This is what I got
>>
>>11820996

Yes.
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>>11827174
Just pirate Looptuner Pro
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>>11825682
getting a degree, especially online, sounds like a total meme, i don't know what employer would be impressed just by you passing some online tests
if it's a libtard kike school you are there purely for the (((connections)))
>>
I am a brainlet, can someone tell me what formula you'd use to solve this question?

How many kWs of heat energy would be contained in 8 US gallons of liquid propane?

a 2673.80 b 0.38 c 211.52 d 5.86
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>>11827653
well considering kW is a measure of power I don't know how you'd solve it.
but basically you'd calculate how much energy is given off in the combustion reaction for one molecule of propane and then multiply by how much is in 8 gallons
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>>11827539
well it would just be the first of four semesters that would be online, not the whole degree. the standard track is just classes for the first semester anyways so im not that interested in spending money to move and live there just for some classes and no research, but maybe the connections in the first semester would be worth it idk
>>
I have a disability, I can't read books, because they have too many words I don't need, which distract me, thus fuck of with your book list, you can shove those into your anus.

Any good calculus cheat sheets? 1, 2, and 3 semester, because I'm fucking lost at this point. Good cheat-sheet may contain graphs, examples, and formulas, and up to 250 chars of text per topic.
>>
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Eventually, the cold pipe will make the hot cylinder cold, but is the heat transfer when directed at a single point like this particularly efficient?

I know that it would work much better if the cooling pipe coiled around the hot cylinder. Does touching a single point really do anything?

I'm wondering because I'm curious if I can cool a glass of hot water any quicker by prodding the glass with something cold or if it would be negligible at best.
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>>11824623
>Aside from that, don't kill yourself.
But I have every reason to kill myself. My life is hell and I want to end it.
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>>11827680
seems fine to do online
maybe if you have good social skills you could try to scoop up some marriage worthy nerdy girl who most people overlook because she doesn't dress up for school and they don't realize that she has a natural beauty and great tits and a sweet personality but i wouldn't count on it
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>>11823416
you're a big guy
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>>11827710
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>>11827785
I wouldn't count on it either, mainly because sweet and nerdy natural beauties with great tits considered ugly because they wear glasses exist only in movies
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>>11827807
i know one irl who met her husband in her mid twenties at college but yeah they're rare as fuck
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Can someone tell me why the derivative of sin(x) is -cos(x), and why the differential of cos(x) is -sin(x)? It's not mentioned in the content I'm learning and I don't know how to phrase it for google searches
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>>11827862
Whoops, I meant put differentials and derivatives in the wrong order. Fucking annoying how you can't edit on here.
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>>11827862
>>11827867
And I meant integrals, not differentials ffs
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>>11825311
Thanks babe
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In Tao's Analysis, there is an exercise where we prove the existence and uniqueness if the integer part of reals(i.e., for every real number x, there is exactly one integer N such that N <= x < N + 1. The catch is he hasn't developed the Well Ordering Principle yet and he is developing the real numbers using the equivalence class of Cauchy sequence.
What I've tried so far is divide it into three cases by the trichotomy of reals and I couldn't get further when I've reached the positive case. And the other one that I've tried is since the definition of the real numbers in Tao's book is a formal limit of some cauchy sequence, I applied some property of the absolute value. Too lazy to type out the other method that I tried.
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>>11827862
>Can someone tell me why the derivative of sin(x) is -cos(x)
It's cos(x) not -cos(x).
A "non proof" version is looking at the series expansion and differentiating every individual term, then you will see that the derivative of sin is cos.

Alternatively you can look at the definition exp(ix) = cos(x) + i sin(x). And differentiate both sides, the right side is i exp(ix), if you plug in the definition again you will get the right result. Again, not perfectly rigorous, since it requires complex derivatives.

>cos(x) is -sin(x)
It's +sin(x) and a direct consequence of the above, since integration "reverses" differentiation.
>>
I'm asked to find v such that u+iv is holomorphic.
u is given as 2x^2+x+1-2y^2

I use Cauchy Riemann equations, I get the result that no such v exists. Is this correct or have I made a mistake somewhere?
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>>11827862
Consider the curve $c(t) = (\cos t, \sin t)$. This is a counter-clockwise parametrization of the unit circle. The derivative $c'(t)$ is the tangent vector to the curve at time $t$. If you consider $c(t)$ not as a point on the circle, but rather as a vector emanating from the origin with its tip on the circle, it's geometrically obvious that the tangent vector $c'(t)$ must be $c(t) = (\cos t, \sin t)$ rotated 90 degrees counter clockwise (see pic related). Therefore $c'(t) = (-\sin t, \cos t)$.
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>>11827943

Nevermind this, I think I solved it myself.
I get y=0, v = some constant and u+iv holomorphic in (x,0)
>>
I'm going through a MIT online course on calculus and I get to this point:

" If we multiply copies of the identity function together, we get powers of it, like x*x (which is x squared), or x*x*x, which is x cubed, and so on. Any function consisting of a positive power multiplied by a constant is called a monomial. If we add or subtract a finite number of these, we get what are called polynomials.

The simplest polynomials are the linear functions we have already mentioned. The next more complicated ones are quadratic functions; these have the form, ax^2+bx+c, where a,b, and c are numbers. "

I understand what it's saying but I don't get how the identity function ties into the quadratic function; Surely changing the identity function means that it's no longer the identity function? Is it just a bad segue?
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>>11828118
>but I don't get how the identity function ties into the quadratic function
Multiplying the identity with each other is the square function.

>Surely changing the identity function means that it's no longer the identity function?
Of course. The identity multiplied with itself is not the identity.

>Is it just a bad segue?
It is actually quite an important point, demonstrating why polynomials are quite important, as they are the sums and products of identity functions (* scalars).
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>>11827950
v=4xy+y+C
∂u/∂x = 4x+1, ∂u/∂y = -4y
∂v/∂x = 4y, ∂v/∂y = 4x+1
=> ∂u/∂x=∂v/∂y, ∂u/∂y=-∂v/∂x

f(z) = 2z^2+z+(1+Ci)
=> Re(f(x+yi))=2x^2+x+1-y^2, Im(f(x+yi)=4xy+y+C
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Does the derivative of G*m1*m2/r^2 have any meaning in physics? I know the integral of the gravitational law gives the potential energy, however I can't find any units that tie derivative's units kg/s^2 to any properties of gravitation.
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>>11810858
answer for the pic is cot(pi/8)
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>>11827950
This isn’t right. They are not asking you to find a value for y. You need to use the Cauchy Riemann equations
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>>11814847
interesting question, no?
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>>11828402
I think he flipped a sign, which can end up with having y=-y as a constraint.
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If you are morosely obese whats a way to sloe weight and not have stretched out flabs of skin or is that unavoidable since the years of fat stretched it out and you need surgery to trim it down.
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>>11828522
y=-y is basically saying y=0 => Z∈R. Any polynomial is holomorphic if its argument is constrained to the real line.
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>>11827907
Assume that the integer part function is well-defined for rationals, $l : \mathbb{Q} \rightarrow \mathbb{Z}$.
Then you can extend to reals by the stupidest way possible: the limit of the sequence of integer parts EXCEPT at the equivalence classes of integers.
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>>11810858
Does the earth's magnetic field affect fusion reactors to a significant degree?

To my knowledge every tokamak fusion reactor is a horizontal torus. So can the earth's magnetic field counteract or possibly, reinforce the magnetic containment?
>>
do i take pde or gr next semester? mathfag btw.
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>>11814847
>>11828473
>
Playing around with this, I got 10^(2*203)+1 = 0 mod 29^2. Since 10=5*2, I figured we could find p such that 2 is a quadratic non-residue and 10 is a quadratic residue mod p. They would then be the same for p^2. Then maybe we could apply Euler's theorem a^phi(p^2) = 1 mod p^2, where a=5 and a=2 and phi(p^2) = p*(p-1). The hope was then that 2^(p*(p-1)/2)=-1 mod p^2
and 5^(p*(p-1)/2)=1 mod p^2, giving
10^(2*(p*(p-1)/4))=-1 mod p^2.
We need -1 to be a quad residue mod p, so p = 1 mod 4.
We need 2 to be a non-residue, so p = 3 or 5 mod 8.
We need 5 to be a residue, so p = 1 or 4 mod 5.
Solving the congruences gives
p = 40 u + 29 or p = 40 u + 21
Putting u=0 in the first one gives p = 29, whence p*(p-1)/4 = 203. Checked with Wolfram alpha. It works!
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>>11829080
no they produce their own magnetic fields that are so strong that the earth's looks like a miniscule fluctuation
>>11829086
pde, unless you're absolutely sure you'll never need them in which case take whichever sounds more fun
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>>11828240
yes the derivative of the gravitational force is the gravitational potential energy. useful in physics for calculating escape velocity
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Why does wood creak? I'm told it's caused by things rubbing together, but what's happening microscopically that makes a slow groaning noise?
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>>11829237
vibrations, and stop namefagging i only decided on a whim to expand your filtered post.
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>>11829339
Not that dude but his name is literally 'Anonymous'. Your filter is broken or some shit.
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>>11828995
https://taoanalysis.wordpress.com/2020/05/06/exercise-5-4-3/

This solution says that it does not work. I'm not sure if he's right though.
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>>11829237
it's like when carbon fiber delaminates
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>>11829522
Boy I sure wonder why did I specify that the definition is different (and trivial) for equivalence classes of integers.
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>>11829371
>>11829124
Very nice.
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H is an affine space in R^3

I need the corresponding implicit function or a way to find it
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MAJOR mathlet here, I was about to course Linear Algebra but then quarantine happened so I don't have anyone else to ask this very stupid question, sorry about it.

anyways, do matrices have any use outside of thinking of them as a function, or a representation of functions? I guess this kind of answers itself if you switch "matrices" by "numbers" but I wanted to make sure since I've only ever seen matrices in the context of matrix transformation
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>>11829917
Sorry no an affine plane in R3
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>>11829926
linear transformation* nor sure if there are any other sorts of matrix transformations
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If I want to filter out all threads, except /sqt/, is this the right regex?
/^((?!.*\/sqt\/.*).)*\$/i
It didn't work for me.
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>>11829917
If you have a plane $H= \{ v \in \mathbb{R}^3 : v = w + \lambda u + \mu z$, its normal is naturally $u \times z$, the cross product.
Then you can just evaluate $\langle w, u \times z \rangle = \alpha$ and tah dah, $\langle v, u \times z \rangle = \alpha$ is your condition.
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>>11830164
But where's alpha tho
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>>11811585
2 lines per point, 3 points per line, so for every line generated there will be 2 copies... 18/3= 6 + 2 diagonals =8. Unless it's a torus then methinks it's 12
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How strong an electromagnet do you need for it to be about as strong as neodynium permanent magnets?
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>>11820670
chemistry is just the physics of electrons
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>>11816240
start with something on overleaf if you feel like being a script kiddie
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>>11815909
You should not use a template.
Either make one your self or use the default.
Using things you do not understand will make your life very hard.
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What am I missing here?
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>>11811585
This isn't going to have a neat formula. You can place the first two anywhere, which gives you N^2(N^2-1)/2 distinct cases. The third one is constrained to the line through the first two but it's also constrained to the grid so it will depend upon the factorisations of the differences (in x and y) between the two. If x and y have common factors there will be more grid points which lie on the line than if they are coprime.
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>>11831476
For a start, you're missing a factor of 2π. X_L=ωL=2πfL, X_C=1/ωC=1/2πfC.
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>>11831831
there we go I knew I forgot something. thanks, I'll hopefully not forget it during my physics final.
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Maybe a dumb question, but what's the 'undergraduate' and 'postgraduate'? Are they just dumb names for Bachelor's and Master's, or something else? I'm not from an Anglo country
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What should my exponential function look like if I want a graph like this?
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>>11832164
-exp(-x)
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>>11832164
log(x)
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>>11832150
An undergraduate student (vulgarly, an undergrad) is a college student who doesn't have a bachelor's.
A grad student is someone who has a graduate degree, so he's doing a postgraduate degree like a Master's or a PhD.
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How low a temperature can you get a peltier device to run a fan at?
Can it be done at room temp if I keep the other side at absolute zero?
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>>11832164
If it's -5V at t=0 and tends to 0, it should be -5*exp(-t/T) where T is the time constant. At t=T, V will be -5V/e ~= -1.84V. From the graph, I estimate that to be ~2ms.

So: V=-5*exp(t/2) with t in milliseconds or V=-5*exp(500*t) with t in seconds.
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Do diodes emit light because the energy for an electron to cross the band gap is higher than the energy to stay at the new orbital or how does this work?
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Academia related question. Is it possible for someone with a science related degree (like math or physics) to get into a philosophy of science/epistemology postgraduate program?
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>>11829190
wrong. Its the other way around
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What are some average-guy-tier (in their explantions)guys like sean caroll and roger penrose, which discuss history of the universe and conciosuness?
Can be books but id prefer talks and interviews

>i also need an entry-level book on inflation,big bang and the possibility of aeonic cycles of the universe
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Why is it that after you look at something bright, you can see a ghostly imprint after you close your eyes?
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>>11833038
IIRC one of the excuses the Journal's editors gave for the Sokal incident and basically not even reading the hoax paper before approving it was that he was an actual scientist.
So yeah, probably.

Might want to ask somewhere else, tho. Maybe even mail some university's philosophy department to ask for their opinion.

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