/sci/ - Science & Math

>>14484018
>be me
>take graduate real analysis
>the course is pretty difficult
>7 assignments total
>get a B
>take grad complex analysis the next semester with the same professor
>try really hard this time
>7 assignments total
>Still get a B

Usually when I put in the effort, I can always get an A, and I was really trying my best, but I still got a B. I'm into combinatorics, so I guess a B in analysis is not the end of the world, but I feel pretty bad that I was not able to get an A even with a lot of effort. Combinatorics and algebra were a lot easier.

>>14484018
You forgot the title.

Unanswered questions:

Maths questions:
>>14472547
>>14473106 [Answered in /mg/]
>>14475588
>>14477648
>>14479908
>>14479971
>>14480353
>>14482433 [His solution apparently doesn't work, but he wouldn't mind a working solution.]
>>14482973 [https://en.wikipedia.org/wiki/Bessel%27s_correction]

Physics questions:
>>14470911
>>14475173

Chemistry questions:
>>14475293
>>14476112
>>14476840

Philosophy questions:
>>14480377

Engineering questions:
>>14481793
>>14483676

Semantics questions:
>>14482462 [No.]

Stupid questions:
>>14466958
>>14468319 [Partially answered]
>>14471782
>>14472410 [Honestly it makes perfect sense. [math]d[/math] for dimension and leaves [math]n[/math] free for indexes, which is always nice. Everyone loves [math]\sum _{n = 1}^N a_n[/math]
>>14473072
>>14473263
>>14473554
>>14474318
>>14475159
>>14483892

>>14484061
>You forgot the title.
and you forgot to link the next thread for the last 50 threads, so we'll call it a wash

I don't understand induction, why do we assume the conclusion (case n) to be true and prove for the n+1 case instead? Whats the intuition behind it?

>>14484018
>formerly
Chucks.

>>14484167
>you forgot to link the next thread for the last 50 threads
No, I intentionally didn't do it.

>>14484199
well maybe i intentionally didnt put anything in the subject

How do i do this question?

I think the only reason I enjoy mathematics, is that it takes my mind off the general anxieties of life and pain I would otherwise experience through wondering thoughts.
Has anyone ever studied and searched for a relation between math majors and persons who self-harm? The reasoning and feeling brought on by self harm that many online have described, matches very well with what I experience doing math.
I am worried, since it is likely that my life situation will improve, and that would imply that around that time I will lose my focus and passion.

>>14484244
Isn't it just because A has order 4 and B has order 2? Then you take their product.
You can compute their elements explicitly if you want to. Just take the 4 powers of A and the 2 powers of B, and also take the four powers of their product AB. Each of these subgroups overlap at the identity, so the total number of elements is 4+4+2-2 =8.

>>14484274
Ignore this post, i'm wrong about the elements.
Just computer all the matrices A^nB^m with n=1, 2, 3, 4, and m =1, 2.

>>14484274
>>14484298
And AB is only order 2.

>>14484298
why specifically n = 1,2,3,4 and m = 1,2?

When does a mutation become a standard feature of a species? How many % does it have to effect to become normal?
I think i heard an exact percentage a while back, but i cant seem to find it

can I improve my lung capacity and how?

>>14484182
We could assume that it was true for [math]n - 1[/math] and prove it's true for [math]n[/math], it doesn't really make any difference except for how clean a proof looks.
>>14484232
Well if it was intentional I suppose there is no problem.
>>14484244
Let's note down the main facts you should be able to get from a cursory analysis of the problem:
[math]A^4 = I[/math]
[math]B^2 = I[/math]
[math]AB = - BA[/math] (minus as in the usual minus, not matrix inverses.)
So by performing switches and cancelling out higher powers any matrix in the subgroup can be written as [math]\pm A^n B^m[/math] where [math]0 \leq n < 4[/math] and [math]0 \leq m < 2[/math].
Except [math]A^2 = -I[/math], so we can cross out the [math]\pm[/math] and only work with positives.

>>14484182
When I was first taught induction they used "n" in the statement you're trying to prove and a separate variable (like "k" or something) in the proof, so that this point of confusion wouldn't occur. It's not really an abuse of notation, but I do think it's more clear what's going on when you use a different variable.

Does any anon know what identity they use to go from the 2nd last step to the last step with the cosines?

who's the idiot who keeps making this threads? Take the anime spam back to /a/

>>14486091
It's just playing with the cosinus sum formula.
[eqn]
\cos{(x+y)} = \cos{(x)}\cos{(y)} - \sin{(x)}\sin{(y)} \\
\cos{(x-y)} = \cos{(x)}\cos{(y)} + \sin{(x)}\sin{(y)} \\
\cos{(x+y)} + \cos{(x-y)} = 2\cos{(x)}\cos{(y)}[/eqn]

>>14486127
So in this case they used the last identity with cos(x+y) + cos(x-y) = 2cos(x)cos(y), thank you anon T_T

>>14484182
You're forgetting the critical step of showing it is true for a specific case.

Let's say you show it is true for n = 0.
Then when you assume it is true for n and show that that imples that n+1 is true too, then going back to your first case, where you showed it is true for n = 0, so now it's true for n = 1, and so it's true for n = 2, and so on and so forth.

Did I do this correctly. A fren asked me for to help him with it, so I have to be certain. Ty

>>14486309
>Did I do this correctly.
You forgot your parenthesis on the last couple lines.
The passage
[math]2 + 3x = 52 - 39x[/math]
[math]3 + 39x = 52 - 2[/math]
[math]42x = 50[/math]
is sickening.

Can anyone verify my solution to this ODE?

[math]\displaystyle x''(t) = a\left(1-\frac{x(t)}{x_0}\right)^4 - b[/math]
With [math]\displaystyle \frac{dv}{dt} = \frac{dv}{dx}\frac{dx}{dt} = v \frac{dx}{dv}[/math]
[math]\displaystyle \int_{v_0}^v vdv = a\int_{x_0}^x \left(1-\frac{x}{x_0}\right)^4dx - b\int_{x_0}^x dx[/math]

[math]\displaystyle \frac{1}{2}(v^2 - v_0^2) = \frac{a x_0}{5}\left( \frac{x}{x_0} - 1 \right)^5 -b(x-x_0) [/math]

[math]\displaystyle v = \pm \sqrt{ \frac{2a x_0}{5}\left(\frac{x}{x_0} - 1\right)^5 - 2b(x-x_0) + v_0^2} [/math]

With my boundary condition of [math]v_0 = 0[/math]

[math]\displaystyle v = \pm \sqrt{ \frac{2a x_0}{5}\left(\frac{x}{x_0} - 1\right)^5 - 2b(x-x_0)} [/math]

Annoyingly, when I tried checking it on mathematica, I can only get the same result by setting C[1] = b*x0 using
DSolve[v[x]*v'[x] == a (1 - x/x0)^4 - b, v[x], x] /. C[1] -> b*x0

Not sure if I just don't get how mathematica does it or whatnot.

>>14486309
Yes. To further simplify it, reduce the fraction to x = 25/21

Can I get some in depth resources to learn more about fungi, particularly mushrooms, on both the cellular and macro level? I want to expand my hobby from just growing mushrooms to actually researching them somewhat.

>>14486348
To be pendantic, you haven't fully solved the ODE, you've just reduced it from a second-order one to a first-order ODE: to solve it would be to find an expression for x as a function of t.
With that said, your derivation looks good -- see if you can figure out when the original system chooses the positive vs. negative root.

>>14486579
Thanks. Fair enough.
I have no idea if there even is an analytical solution for x(t), but I'd be fine with a non elementary one.

>see if you can figure out when the original system chooses the positive vs. negative root.
I will have to take a closer look now that's double checked.

How can I synthesize/extract/purchase pure isoprene? I have some basic chemistry glassware but can't buy from places like sigma.

>>14484018
Anyone has some material to learn about the SU(2) and U(1) groups and their application to SM theory ?

You know how you can add two sine terms like this:
sin(A)+sin(B)=2sin((A+B)/2)cos((A-B)/2)
How do you do this for three:
sin(A)+sin(B)+sin(C)?
I tried to follow the analogs from the derivation and break the angles down to addition terms for the sine
(A+B+C)/4,(A+B-C)/4,(A-B+C)/4, (B+C-A)/4 but it just makes a huge mess.

(Basically I want to find the envelope equation for a major chord but I don't know any math beyond trig and algebra)

Can anyone make the new /mg/? The title should be /mg/ - maths general, the image should be pic related, and the body should be:

Formerly >>14461881

Systolic Geometry edition.

Talk maths.

Just completed an entire experiment on amplitude modulators grounding the components like this. Was this a good idea?

>>14484018
Can someone explain how negative modulo operations work? I can "calculate" them in my own way, but don't really understand the principles.

For example, why is:
-1 mod 3 = 2 or
-8 mod 6 = 4?

>>14487952
Lol you got banned from making new threads. If I make the new /mg/ I get to choose the picture and the stupid bullshit it says.

>>14488214
>you have asked me to do X, but I may instead use the free will imparted onto me by our Lord and Savior Jesus Christ to instead do Y lol
Amazing, whod'a thunk.

>>14486309
Stop rushing things and write things out nicely. It's correct, but step 3 looks odd to me, were did the 3 come from?

2 + 3x = 13 (4 - 3x) <=>
2 + 3x = 52 - 39x <=>
3x + 39x = 52 - 2 <=>
42x = 50 <=>
x = 50/42 = 25/21.

>>14486339
>>14486348
Thanks anons.
>>14488230
It should be 3x, I forgot to write the x. Thank you fren.

>>14488359
Ah, makes sense then. Yw fren.

What is the hardest mineral that contains calcium cations [math]Ca^{2+}[/math]?

>>14488201
[math] a \mod b[/math] is defined as the smallest positive difference between [math]a[/math] and any integer multiple of [math]b[/math]
[math] \displaystyle 15 \mod 7 = 1 \; \; \; \; \; \; \to \; \; \; \; \; \; 15-(2)7=1[/math]
[math] \displaystyle -1 \mod 3 = 2 \; \; \; \; \; \; \to \; \; \; \; \; \; -1-(-1)3=2[/math]
[math] \displaystyle -8 \mod 6 = 4 \; \; \; \; \; \; \to \; \; \; \; \; \; -8-(-2)6=4[/math]
in math, there are these things called "rings". in the ring of 10, for example, 4, 14, 24, 34, ... are all "equal" to each other because they all have the same remainder upon division by 10, so you can replace them with each other when youre doing arithmetic. for example, if you want to know what the last digit of 423521095 + 1564725623 is, all you have to do is add the last digits of each. positive 3 and negative 7 are equivalent to each other as well, because they both have the same reminder upon division by 10: positive 3 divided by 10 is 0 with a reminder of postive 3, and negative seven divided by 10 is negative 1 with a remainder of positive 3.

>>14487929
There isn't a simple way to do this for more than two waves. You can get something similar by taking the absolute value of the sum of the original waveform with its complex Hilbert transform, but that may be too complicated. For pure sine waves you could probably simplify it significantly because a Hilbert transform is essentially just a π/2 phase shift.

>>14487929
[eqn]
\sin x + (\sin y + \sin z) = \sin x + 2\sin{\left(\frac{y+z}{2}\right)}\cos{\left(\frac{y-z}{2}\right)} \\
(\sin x + \sin y) + \sin z) = \sin z + 2\sin{\left(\frac{x+y}{2}\right)}\cos{\left(\frac{x-y}{2}\right)} \\
\sin y + (\sin x + \sin z) = \sin x + 2\sin{\left(\frac{x+z}{2}\right)}\cos{\left(\frac{x-z}{2}\right)}
[/eqn]
Sum all three and regroup:
[eqn]\sin x + \sin y + \sin z = \sin{\left(\frac{x+y}{2}\right)}\cos{\left(\frac{x-y}{2}\right)} + \sin{\left(\frac{y+z}{2}\right)}\cos{\left(\frac{y-z}{2}\right)} + \sin{\left(\frac{x+z}{2}\right)}\cos{\left(\frac{x-z}{2}\right)}[/eqn]
It's ugly as fuck but you won't get anything more simple. The only way for it to look nice is to consider the series expansion instead.

>>14488414
Idk but probably something like CaF2 or CaO due to the large lattice energy increasing stability

Why do some people hate Terrence Tao's Analysis?

how do i solve log3(81)?

i know what the answer is but what if i didnt know that 81 is the same as 3^3?

is there a formulaic way to figure out what the big number must be based on the base?

i looked online and all the solutions to these problems just turn 81 into 3^3 without explanation.

>>14488946
divide by three until you cant anymore
eg log_3[105]
105/3 = 35
log_3[108] = log_3[36 x 3] = log_3[36] x log_3[3]
= log_3[36] + 1
now you can try repeating this on 36

>>14488962
woops, meant 108 and 108/3 = 36
its a better example than 105

>>14488962
>>14488969

ty anon, what am i doing when i turn log3(x)=4 into x = 3^4? does it have a name or justification?

I just had my first in-person exam in 2 years, one thing I noticed is that I was MUCH slower to do it than I used to before the pandemic. How do I train to do exams faster?

>>14489094
i think i can help with that anon.
1. before starting the exam, quickly flip through and see how many questions there are, which are multi-part, which want long writing sequences, proofs etc, and estimate how much time you have for each question.
2. read over each question, gauge how easy it will be to solve, or if you can solve it or not. if you aren't sure, mark it with an asterisk and go to the next question, and do the same.
3. after the last question you now have an idea of which questions you can easily solve and which you cant.
4. do the questions you can quickly solve first, then the ones that look a little more time consuming, then the ones you are unsure of for last. while doing this always be making sure that if you hit your self-imposed time limit on the x minutes/question, you will leave it there and move to the next.
5. once you have the easy questions done and the longer ones, finish any that you ran out of time to do before and had to move on.
6. then attempt to solve the ones you marked with an asterisk, but make sure to give time to try and solve each one, so dont go to your first asterisk question and sit there pondering for 20 minutes on that one question. move between them and try to solve as much as you can from each of them.

as for finishing exams faster, you should try printing out a series of easy, medium, and hard questions from the book, arrange them into an exam format, then try to solve them while sticking to the alotted time. use the same principles above for prioritizing questions.

then just try and be mindful of yourself while doing it. try and notice where you are spending a lot of time, and how you might be able to improve it. eg instead of reading the question over and over, write everything you know and is given, and all the relevant ways to manipulate that data that could get you your result.

try and make a habit of checking the time at least every 5 minutes, and force yourself to move on to the next question

>>14489094
I've always been partial to clearing my head of all thought, stilling my heart and working through the exam in order without doing anything that even resembles what >>14489129 is suggesting.

>>14488978
thats just how logarithms are defined
lhs=rhs
3^[lhs] = 3^[rhs]

>>14489129
Thank you anon

>>14487952
Didn't see this until now. I guess almost everyone is banned from making threads haha

>>14484576
Eat healthy and exercise. Exercising improves the state of your organs including the lungs, and getting your vitamins, particularly Vitamin D, the lungs.

>>14488978
As the other anon said, logarithms are defined as the inverse of the exponential.

So for some [math]\log_n(x)[/math]
[math]\displaystyle n^{\log_n(x)} = x[/math]
Or inversely
[math]\displaystyle \log_n (n^x) = x[/math]

Just like
[math] \sqrt[n]{x^n} = x[/math]
or vice-versa
[math]\left(x^{1/n}\right)^n = x[/math]

or
[math] \arcsin(sin(x)) = x[/math]

etc.

>>14489292
ty anon. do you know what it means to find the upper and lower bound for a log? eg if x = log3(31)?

>>14489307
i think i have an idea, but when i try to google it i get only things about algorithms and computation time

is it like the range x can be in to be >= log3(31) and <= log3(31)? its for when x is an integer

>>14489307
It means finding numbers which the result can't be greater or less.
As for what lower and upper bounds you want, it depends on what your constraints are, like for example if you want integer lower and upper bounds,

3^2 = 9 and 3^5 = 243
So for [math]2 < \log_3(31) < 5[/math]

Do note that in the case of integers, there is also the Greatest Lower Bound and the Least Upper Bound, which for the example above is

3^3 = 27 and 3^4 = 81
So [math]3 < \log_3(31) < 4[/math]

Like I said, the specific bounds you might be looking for depend on your problem, you might instead want something like this
3^3.1 = 30.14
3^3.2 = 33.63

[math]3.1 < \log_3(31) < 3.2[/math]

The inequalities don't have to be strict either, especially for problems where you don't know the answer.

>>14489398
Of course, for the reals, the answer itself is the least upper bound and the greatest lower bound, similarly if the actual answer was an integer such as in [math]\log_3(27)[/math] which is 3^3.

That's the implication of the inequalities not being strict.

>>14489313
So yeah, the range your answer can be in.

>>14487474
>SU(2) and U(1) groups
This is basic stuff you learn in a second quantum mechanics class since SU(2) is a double cover of the rotation group and U(1) is equivalent to charge conservation. Any graduate level quantum mechanics textbook covers this stuff.

Georgi has a book Lie algebras in particle physics that might be exactly what you're looking for though.

For a more mathematical perspective I liked Brian Hall's textbook on Lie Groups and representations.

>>14488727
He does stuff like using [math]n++[/math] to denote the successor of [math]n[/math] and 80% of mathematicians feel physically ill when they see this.
>>14489251
Were you the one who make the new one?
Thanks.

>>14489398
>>14489431
thank you very much anon, i appreciate your help

>>14489398
for an integer bound does 3 < log3(31) < 4 mean there is no solution since a number cant be an integer between 3 and 4?

>>14489494
log_3[31] is not an integer
maybe the questions are more about which integers are less than/more than log_3[31]?

>>14489524
oh sorry i think i meant the series (3,4) or 3< x <4

how many kids does my sibling have to have for them to pass on equal genetic information as if i were to have a kid

>>14489561
so if you have been given that x is equal to log_3[31] then yes it is between 3 and 4
if you are given log_3[x] is between 3 and 4, then you have a different question
to solve the second one, think about what happens if log_3[x] = 3 and when log_3[x] = 4

>>14484018
I'VE JUST FUCKING NOTICED BY LOOKING AT >>14489612 THAT THE PREVIOUS THREAD WROTE QTDTTOT INSTEAD OF QTDDTOT LMAO
I wonder how came up with QTDDTOT, they're such horrendous initials. I needed to stop and say it out loud in my head every thread to make sure I didn't fuck it up.

Was the valence band supposed to the the 1s2...3d10? I had previously thought that the valance band is the most oxide (was that the word?) so it's the easiest ring for electrons to be pulled out so I picked 4s2 4p2.

I do have a quick question on the side.

For a GaAs semiconductor, if we replace Ga with Silicon, then Silicon would be an donor right? Since it comes with an extra electron (relative to Gallium). If we replace Ga with Zn, then Zn would be an acceptor? (I know that we can't do group 2 with group 3 but just for the sake of the question).

>>14489787
>I wonder how came up with QTDDTOT
*who.

>>14489787
My wife can't be this retarded
>>14489789

>>14489094
You're also just not used to taking in person exams, generally you start it off easy freshman year before getting quicker on your feet, don't beat yourself too hard over it.

Given [math]m[/math],[math]n[/math], and [math]q[/math] are integers greater than zero such that [math]m<n[/math] and [math]q\cdot(\frac{1}{m}-\frac{1}{n})>1[/math], can I always find another positive integer [math]p[/math] such that [math]\dfrac{q}{n} < p < \dfrac{q}{m}[/math]? I just can't see it.

>>14489804
>My wife can't be this retarded
I'm not your wife.
And that's not a spelling mistake.
>>14489815
You have to be fucking with me.
[math]\dfrac{q}{m} - \dfrac{q}{n} > 1[/math]
Ignoring actually proving things for a second, isn't it obvious there's an integer between them?

>>14489826
if you're not his wife are you my wife

>>14489826
I'm retarded, mind to elaborate how is it 'obvious'?

>>14488229
cute wemi <3
>>14489153
cute ciwno <9
>>14489787
its not that funny bro

>>14489850
If [math]\dfrac{q}{n}[/math] is an integer then [math]\dfrac{q}{n} + 1[/math] works. Otherwise [math]\left \lceil \dfrac{q}{n} \right \rceil[/math] works.

>>14489859
Isn't [math]\left \lceil \dfrac{q}{n} \right \rceil \geq \dfrac{q}{n}[/math]? Would it be more appropriate to choose [math] \left \lfloor \dfrac{q}{m} + 1 \right \rfloor[/math]?

>>14489788
Valence band should be the most outside band. Although the electron filling order follows that graph (based on the energy level of the orbitals), electrons are lost from the most outside band first.
Also yes, Si would be a donor if you substitute Ga and Zn would be an acceptor if you substitute Ga. Apparently it is possible to dope Zn into GaAs but I am not familiar with the subject to explain it.

>>14489942
Yes it is. No it wouldn't. q/n is the lower bound, q/m is the upper bound.

how do I lose my virginity without having sex with men or paying prostitutes

is the board being raided or something? what's going on

Does someone know how to show the surjectivity? The rest seems to be straightforward but I can't quite figure out the "onto"-part.

Note that I could show it on compact (metric) space for [math]\lambda\ge 1 [/math] or if we had actual coercivity (then it's a direct consequence of Breuwer's fixed-point theorem).

Also would be great if someone knew the reference, just saw the screenshot on twitter and it bugged me.

any chemfags around?
is there commonly aviable solvent that will dossolve acetic acid but not copper acetate?

>>14491222
Seems so.
>>14491253
Assume it's not onto. Choose some point [math]y[/math] on the boundary of [math]F( \mathbb{R}^n[/math] that isn't in [math]F( \mathbb{R}^n)[/math] and a sequence [math]x_1, x_2, \ldots[/math] such that [math]F(x_n)[/math] converges to [math]y[/math].
Then the sequence of [math]F(x_n)[/math] is bounded, hence the inequality shows that the sequence of [math]x_n[/math] is bounded, hence convergent, hence [math]F( \lim x_n) = y[/math], a contradiction.
>inb4 what if [math]F( \mathbb{R}^n)[/math] is closed
It isn't and that's your homework. Geometrically speaking, the issue is very simple. Practically speaking I don't want to write down a proof.

>>14491461
Thanks. Thinking about your answer I realized one could also just apply the invariance of domain theorem to [math] F [/math] as a mapping from the compactification of [math] \mathbb{R}^d [/math] into itself.

>>14491578
How can you use invariance of domain on the compactification of [math]\mathbb{R}^n[/math]?

>>14491593
Never mind, forgot invariance of domain works for manifolds without boundaries.

I have a newb math question over here in the other stupid questions thread. Thank you.

>>14491810
>>14491813

>>14491834
The formula in the first post is the "theoretical" one whereas the formula in the second post is the "experimental" one where x_i represents the value of X you got in the i-th sample of your sampling data. In the limit N -> infinity, the two would be equal because in the second formula, [math] x_1 [/math] would occur [math] p_1* N [/math] times and similarly for x_2, x_3, etc.

>>14491922
Sorry, what would occur p1 * N times?

Is it just me or did the person fuck up on his units.

I'm trying to convert 6.261 * 10^18 / meters^2 to cm^2 so I'm pretty sure I just add 2 to it so it becomes 6.261 * 10^20...

>>14492928
It's just you. Think about it. There are 100x100 = 10^4 square centimeters in a square meter. So if you have some quantity S in one square meter, you are going to have 10^4 times *less* of that quantity if you only look at a square centimeter

>>14492934
Crap, I need to review my units. Thank you anon!

When X ~ N(0,1), what is the probability of X being -1.96 or less?
When X ~ N(0,1) and the probability of X being less than a is 0.591, what is the value of a?
When X ~ N(12,4), what is the probability of x being 14 or less?

Would be grateful to get not just the answers, but the process too.

bump

Have a question on semiconductors, particularly (E).

I know how to calculate the minority current carrier at a distance inside of N type but I don't know how to calculate the majority. A friend said we could just calculate the entire diode current and then at the same given Va and then calculate the minority carrier current at the same given Va, then the diode current subtracted by the minority should give me the majority which makes sense, however it seems too easy to be true. Is it?

>>14495276
that method would work.

>>14495571
Don't post this image a third time, there's something almost lewd about Satoko's bare shoulders and it irritates me.

>>14495576
what a perv

>>14495571
Thanks anon! Have a test tomorrow. Do you by chance know if this is the correct method for finding electric field at x distance from the center of the junction?

>>14495615
np fren.
looks right. since the charge density is constant on both sides of the depletion region, the E field simply linearly goes to zero on either side, real easy.

>>14495627
Thank you again anon, and yeah you should be careful while posting that image, I have the other variant of it that you posted and it has me acting up.

>>14495663
>it has me acting up.
yall need jesus
but im glad to see im not the only one that saves all the cutes images in here

>>14495580
Nonsense.

>>14495676
Save this Sakuya.

>>14495685
its not that cute, bro. sorry.

>>14495691
No way, it's cute as hell.

>>14495695
now THATS a cute wemi <3

>>14495713
This is my favorite Remi.
I can't explain why. When I first saw it I went "Cute! Cute!" and couldn't stop smiling for half an hour.

Any anons that have taken the FE and PE exam here? Any anecdotes about it?

>>14495741
thanks for sharing <3
my favorite satoko is anything by this artist, he draws the best faces (even if she has a flesh fang despite her teeth being closed in this one).

>>14495800
That guy's art is very consistent, I'm pretty sure ~70% of what you post is by him.

Lads I've never had to do any geometry proofs in high school and my sister is asking me for my help, does anyone know what the answer is here?

>>14495821
>I'm pretty sure ~70% of what you post is by him.
50% of new satoko art is by him
>>14495827
hint

>>14495834
>50% of new satoko art is by him
Sad.

scientifically speaking, why does findom get me so hard?

Is there a good cheat cheet for Tensor Calculus, possibly including General Relativity and the Tensor formulation of EM somehwhere? I'm tired of never remembering how to deal with tensors every single time.

>>14495902
READ THE BIBLE

>>14495827
This one is pretty easy.
The two areas in question are both four times the area of triangle ABE

>>14495928
close, but read the question carefully. you cant assume that ADBE is a square.

>>14495925
I read Pslam 121 every night

Physicists know damn well that you can't contract two covariant or contravariant indices because the result is non-physical, so was the deformation of Einstein summation that you sum along any two repeated indices actually invented by mathematicians?

may as well ask here since it got bumped
>>14496597
What the fuck is "Mechanical Resistance"?

Guys, what would be the most eye-catching subject for an email where I ask for an intenrship, sent to a prof? it's not apaid internship, just a research 9 months one.
I just want him to open the email, for now I thought of: "Possible internship at your lab"
is it clear enough? I need urgent help I'll post it here too

>>14497192
Looking for Information about an Internship at X.

>>14497192
"Will Suck Dick to Work (For Free) (Not Clickbait)"

How can one know if their research is on the right track?

if you have a function [math]f(x,y) : \mathbb{R}^2 \to \mathbb{R}[/math] and youre trying to find [math] \frac{ \partial f}{ \partial y}[/math] on a specfic line [math]x=x_0[/math], does it matter whether you first plug in [math]x[/math] and then take the partial or vice versa?

So for a project, we're trying to figure out how well our model fits our data. The data is in half-hour increments per day, and I have a month of days. I found % error for each interval, then averaged along the days (e.g. 11:00AM has avg 5% error over the month). I also took the standard deviation of the error. In my perspective, to find times when our model is consistently poor, we should look at times with high error and low standard deviation, right? I think about it and it seems to check out, but it just feels very convoluted and like I went too far down the rabbit hole. Any advice?

>>14484182
>I don't understand induction
IIRC, it's basically a way to generalize a result. if the hypothesis applies to case 0 and also applies to case n, then it should apply to n+1 too. then you'd have to prove case 0 and that there is some pattern where case n+1 is somehow related to case n.

>>14496861
"deformation"? Not sure what you're asking but when the metric is trivial people often don't give a damn about distinguishing upper and lower indices

>>14497599
If it leads to interesting results once you've completed it

>>14498535
The usual is just take the partial derivative and then evaluate on x.

>>14499076
but does it make a difference in general?

>>14499118
Not really. Think about it, you are taking a partial derivative [math]\frac{\partial f}{\partial y}[/math] [math]x[/math] will be a constant, but to be mathematically formal you should derivative first and then evaluate.

>>14499127
i see, ty fren

Any fren mind to verify my triangle inequality proof?

For [math]x+y \geq 0[/math], [math]|x+y| = x + y[/math].
[math]|x| \geq x[/math] and [math]|y| \geq y[/math] so [math]|x| + |y| \geq x + y[/math].

For [math]x+y \leq 0[/math], [math]|x+y| = -(x + y)[/math].
[math]|x| \geq -x[/math] and [math]|y| \geq -y[/math] so [math]|x| + |y| \geq -(x + y)[/math].

>>14500350
Fine and dandy.

how do I become infertile

>>14500771
you already are if you post here.

>>14500899
no Im really not I can masturbate 14+ times per day and the first 6 will always produce pearly whites
I want nothing to come out

>>14500930
>14+ times
Those are rookie numbers, lad. Push it higher.

>>14500935
I cant it rips my foreskin
please just answer my question

>>14500989
Use lube.
As for your question, you need a massive trauma in your testes that breaks off the seminal duct that connects to the prostate. A friend a of mine went into ball busting fetish for a few years and ended up infertile.

>>14500995
cool
if that duct breaks do I have to worry about any kind of (serious) internal bleeding or infection?

>>14501501
That much I can't guarantee. It will be extremely painful
>inb4 you are a big guy
But why not go with a vasectomy? Given how cucked is modern society they will give it out to you like candy.

>>14501504
Im a third worlder from a small country they dont do that shit here let me just smash my nuts in peace, god bless

How do I get into /sfg/? I tried but too dumb to understand the topic. What's the required reading?

>>14502038
Good luck, anon. Hope you don't die of the pain.

>>14502121
unironically play Kerbal Space Program. its a hell of a learning curve, but its a really fun game and it teaches a fuckton about plane and rocket flight.