/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.11475807]

Formerly >>11454375
Make sure to visit our friends over at >>11473790 edition.

>what is /sqt/ for
Questions relating to math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/diy/ohm , >>>/adv/ , etc.
>pdfs?
libgen.is (Warn me if the link breaks.)
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
>how do I post math symbols?
https://i.imgur.com/vPAp2YD.png
>a google search didn't return anything, is there anything else I should try before asking the question here?
https://scholar.google.com/
>where do I look up if the question has already been asked here?
>>/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

Question asking tips and tricks:
>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
>ask anonymously
>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://mega.nz/#F!40U0zAja!cmRxsIoiLFZ_Mvu2QCWaZg
Shitty charts: https://mega.nz/#F!NoEHnIyT!rE8nWyhqGGO7cSOdad6fRQ (Post any that I've missed.)
Verbitsky: https://mega.nz/#F!80cWBKxC!ml8ll_vD2Gbw4I1hSLylCw
Graphing: https://www.desmos.com/
Answer engine:
https://www.wolframalpha.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
https://www.matweb.com/

[Anonymous No.11475861]

Unanswered questions from the previous thread:

Maths questions:
>>11455358 (Kinda /g/)
>>11455715 links to >>11455638
>>11455754
>>11458055
>>11459462
>>11462238 followed by a correction >>11462246
>>11469352
>>11474583

Physics questions:
>>11455696
>>11459188 followed by >>11459230
>>11463147

Engineering questions:
>>11459092
>>11459611
>>11464015
>>11464231
>>11467422
>>11467443

/g/ questions:
>>11457417
>>11460656

Medicine questions:
>>11459088 (Shoddily answered, might count)
>>11468482
>>11473081

Chemistry questions:
>>11472016

Stupid questions:
>>11464194
>>11464557
>>11464689
>>11465820
>>11466542
>>11468390
>>11470775
>>11472949
>>11472951
>>11473026
>>11473467
>>11474546 (I mean, it's too late, but you can still answer if you want to.)
>>11474588
>>11474881

Questions regarding Yukarifag:
>>11464562

[Anonymous No.11476048]

Real stupid question here
Should I be moving my money out of UK banks, given how shit the Corona situation is bound to get?

[Anonymous No.11476173]

why [math]\lim\limits_{x \to \infty}x sen(1/x)[/math] equals to 0 and 1?
when I use trig limits it equals to 1.
But with the squeeze theorem it equals to 0.

[Anonymous No.11476189]

>>11476173
x to 0, my bad

[Anonymous No.11476210]

>>11474260
Ah I see, you have used the transpose but since the Lie algebra [math]\mathfrak{so}(1,2) \cong \mathfrak{sp}(1,3)[/math] it becomes the conjugate adjoint. You had picked [math]L[/math] skew-adjoint so you do indeed got [math]\{L,\neta\}=0[/math]; I was thinking of [math]L[/math] being self-adjoint so the expansion [math]\Lambda \cong I + i\epsilon L[/math] yields [math][L,\eta]=0[/math]. Just a matter of convention, you're correct.
>>11458055
Kunze-Hoffman.
>>11474583
Write [math]\begin{pmatrix}a & b \\ c & d\end{pmatrix} = ae_{11} + be_{12} + ce_{21} + d e_{22}[/math] where [math]e_{ij} = \delta_{ij} [/math] is an orthonormal basis in [math]M_2(\mathbb{R})[/math]. Then just match coefficients.
>>11463147
Indeed, near the horizon the length of your geodesic approaches [math]\infty[/math]. That analogy is fine to an extent.

I'm afraid I can't answer the other physics questions as they are nonsense.
>>11476173
0 is correct. Whatever trig limits is, you did it wrong.

[Anonymous No.11476229]

>>11476210
why cant i go like this tough?
[math]xsen(\frac{1}{x}) \to \frac{xsen(\frac{1}{x})\frac{1}{x}}{\frac{1}{x}}\to1[/math]

[Anonymous No.11476244]

>>11476229
Because [math]\lim_{x\rightarrow0}\sin\frac{1}{x}[/math] isn't defined. You can only use [math]\sin x /x \rightarrow 1[/math] only when the limit exists.

[Anonymous No.11476259]

>>11476244
i see, thanks

[Anonymous No.11476322]

I need to decide for tomorrow, ChemE or EE? Yukri fag and the rest of you please help me.

[Anonymous No.11476341]

>>11476322
ChemE if ur a good boy and can stay employed, EE if you realistically see yourself between jobs/NEET/self-employed

[Anonymous No.11476354]

>>11476341
interesting opinion. Could you elaborate a bit more please?

[Anonymous No.11476406]

>>11476322
ChemE here. you do know it's mostly working with pipes and pumps and very little chemistry right? It's basically understanding how a chemical plant operates, the different processes dealing with fluid flow, heat transfer, and mass transfer.

[Anonymous No.11476583]

how do i subtract these equations from each other

c1: (x^2)-4x+(y^2)+(z^2)=4

c2: (x^2)+(y^2)+(z^2)=4

I want to do c1-c2

[Anonymous No.11476623]

>>11476244
Not the correct reasoning.
>>11476259
He was wrong. You CAN do that, remember, as x goes to 0 what does 1/x go to? Not to zero, but to infinity. sin y / y is 1 as y goes to 0, and it is 0 as y goes to infinity. Here, you care about y going to infinity. Be careful about using trig limits, they usually work but you need to make sure you are approaching the right location.

[Anonymous No.11476642]

>>11475807
/asg/? it has got an IQ edition!

[Anonymous No.11476811]

>>11476048
No. Anything up to a few hundred thousand is protected by state-backed insurance if the bank fails.

As for whether it's better to move it away from sterling: you already lost 30% from brexit, the Euro isn't necessarily any safer (mainland Europe is getting hit hard right now), the dollar isn't necessarily any safer (lack of public healthcare, lack of sick pay, lack of testing, overall incompetence of current administration).

[Anonymous No.11476815]

>>11476583
Every term except -4x cancels, leaving you with -4x=0 => x=0.

[Anonymous No.11476850]

can't I do like u = tgθ and get to 2ln|a+btθ|+c?

[Anonymous No.11476857]

>>11476850
I mean obviously not since the answer is wrong, but why can't I? it's not clear to me why int(2/(a+bu))du can't be ln|a+bu|+c

[Anonymous No.11476861]

>>11476857
>ln|a+bc|+c
2ln|a+bc|+c*

[Anonymous No.11476862]

>>11476857
is it because it's a sum?

[Anonymous No.11476880]

>>11476850
ffs who writes tangent like that kys,
You can do it like that you just made a mistake, redo it.

[Anonymous No.11476885]

>>11476857
n00b
[math]\int \frac{2}{a+bu}du=2 \ln|a+b\tan(\theta)|\cdot \left(\frac{d}{du}(a+bu)\right)^{-1} +C[/math]

[Anonymous No.11476887]

>>11476880
yeah redoing it I realized the mess I made. thanks and sorry about the whole spamming

[Anonymous No.11476894]

>>11476885
thank you fren. trig kinda confuses me even though it wasn't really a trig mistake

[Anonymous No.11476904]

Why was my solution, different from the textbooks solution?

Name of chapter:
2nd degree differential equations

[Anonymous No.11476905]

>>11459092
no doubt Springer Handbook of Robotics

[Anonymous No.11476916]

>>11476904
Oh dear [math] \sqrt{16} =\sqrt{4}? [/math] ?

[Anonymous No.11476918]

>>11476916
>>11476904
Nice handwriting tho

[Anonymous No.11476925]

>>11476916
Ah shit
I wrote 16 as √4
When its 16 = 4^2

[Anonymous No.11476926]

>>11476918
Thanks bro

[Anonymous No.11476931]

>>11476916
>>11476904
>>11476925
besides don't they mean with growth that the first derivative at [math](0,1)[/math] is [math]-1[/math]

[Anonymous No.11476938]

>>11476931
Find the curve to [equation], through [points] with the growth of -1

[Anonymous No.11477010]

>>11476904
I like how you skip the part where you solve the equation.

[Anonymous No.11477021]

not a question, but a blog post
>finally get past the chapter on linear differential equations and their methods of solutions in my diffeq class
>next chapter is applications of higher order linear differential equations (aka harmonic oscillators)
>undamped oscillations are modeled by
[eqn]m\frac{d^2x}{dt^2}=-k\left(x+s\right)+mg[/eqn]
>this can be simplified to
[eqn]\frac{d^2x}{dt^2}+\omega ^2x=0[/eqn]
>which, when a linear second order DE is of form [math]y''+\alpha ^2x=0[/math], its auxiliary equation always has nonreal roots m=±ki
>and its solution is of form [math]e^{ikx}[/math]
>or [math]y=c_1cos\left(kx\right)+c_2sin\left(kx\right)[/math]
holy shiiiiiiiiiiiiiiiiiit it's all coming together

[Anonymous No.11477025]

>>11477010
I just plugged in the units to where the textbook said I had to.
In the top it shows the equation, then right under that is how to solve it

[Anonymous No.11477050]

>>11459611
Hmm this shouldn't happen, at least if your modulated function is sinusoidal (or periodic in general) than the RMS as a function of the message amplitude should oscillate around some value.

[Anonymous No.11477077]

>>11477050
So I'd check if for even higher amplitudes it tightens again.

[Anonymous No.11477131]

>>11475807
I have a discrete time ECG signal, I need to make a simple algorithm that detects the QRS complex, how do I do this?

[Anonymous No.11477157]

>>11476244
> [math]\lim _{x \rightarrow 0} \sin \frac{1}{x} [/math] isn't defined
>implying
https://vixra.org/abs/1809.0234
>>11476322
Economical Engineering is clearly the better option.

[Anonymous No.11477253]

>>11477131
Someone pls?

[Anonymous No.11477526]

>>11476623
This is complete nonsense. There is no such thing as "[math]\sin y[/math] as [math]y[/math] goes to infinity", because the limit doesn't exist, which is what trig limits requires. You need the fact that [math]|\sin x|\leq 1[/math] and use dominated convergence, which is essentially what squeeze theorem is. You CANNOT use trig limits.

[Anonymous No.11477533]

I can't solve this alone, am I really retarded?

[Anonymous No.11477574]

>>11477526
the post is completely correct. what's your problem ?

[Anonymous No.11477586]

>>11477574
>the post is completely correct
It isn't.
>what's your problem ?
My problem is it isn't.

[Anonymous No.11477591]

>>11477586
>It isn't.
what exactly

[Anonymous No.11477592]

i had a question that was to fill in this table with the additive group Z_3.

would it just be, from top to bottom: 012,120,201? or do i not understand this. i assume i don't understand it because i don't know what overline means in this case

[Anonymous No.11477594]

>>11477533
In which universe will the trolley ever move left?

[Anonymous No.11477599]

>>11477591
Using trig limits or l'Hopital of trig limits require the limits (or limits of their derivatives) in the fraction to exist. [math]\sin \frac{1}{x}[/math] does NOT satisfy this property at 0. Literally the only thing you can do is squeeze theorem/dominated convergence. This is non-negotiable.

[Anonymous No.11477603]

>>11477594
The trolley is moving left under it's own initiative. They want to know how the block in the middle moves

[Anonymous No.11477607]

>>11477533
You might think you're good at cropping, but I can see that spanish on the corner, Alejandro.
>>11477591
Presumably the part about how thinking of naive "convergence to infinity" leads you to a false intuition about infinities cancelling, which is properly corrected by deep study of the great theorem of L'Hospital (Bernoulli).
>>11477594
The universe where the trolley has non-zero initial speed to the left.

[Anonymous No.11477612]

>>11476811
Jews really fucked sterling with their Brexit. Thanks brit/pol you kikes.

[Anonymous No.11477625]

>>11477533
The assumption is that block B remains level.
>Lower left pulley
[math] V_B=(50+u)/2 [/math]
>Lower right pulley
[math] V_B=(10-u)/2 [/math]
So [math] u=-20\text{ m/s} [/math] (direction was guessed wrong) and [math] V_B=(50-20)/2=15\text{ m/s} [/math].

[Anonymous No.11477627]

>>11477594
>>11477607
It moves to the right, sorry

[Anonymous No.11477631]

I feel like a total brainlet right now. Can someone explain to me how to prove that the products of two sets of integers are equal? So you have the product of the elements in set A and the product of the elements in set B and need to prove those are the same.

You aren't allowed to take the products of the sets and prime factorization is not allowed.

[Anonymous No.11477634]

>>11477599
he's saying that [math]\lim_{y \to \pm \infty}\tfrac{\sin y}{y} = 0[/math], therefore [math]\lim_{x -> x_0}\tfrac{\sin f(x)}{f(x)} = 0[/math] when [math]\lim_{x \to x_0}f(x) = \pm \infty[/math]. this is fine. (up to technical assumptions on [math]f[/math] which [math]\tfrac{1}{x}[/math] clearly satisfies).

[Anonymous No.11477642]

>>11477634
>he's saying that
How does that at all help with anything? It's circular if the original question is about the convergence of [math]x\sin\frac{1}{x}[/math] at 0.
>up to technical assumptions on f which 1x clearly satisfies
Wrong. 1/x isn't analytic near 0 so you cannot use l'Hopital to reduce 1/x to x. Again, stop talking out of your ass.

[Anonymous No.11477643]

>>11477627
>It moves to the right
impossible

[Anonymous No.11477650]

>>11477634
What if [math]\frac{1}{x}[/math] approaches zero from the left tho?

[Anonymous No.11477658]

>>11477642
>How does that at all help with anything?
apply to [math]y = \tfrac{1}{x}[/math]
>1/x isn't analytic near 0 so you cannot use l'Hopital to reduce 1/x to x
irrelevant

[Anonymous No.11477669]

>>11477658
>doesn't see how assuming what the the limit is to "prove" the same limit is circular
>doesn't see how the analyticity is required to sub into the fucking denominator of a limit
Are you actually this stupid? Or just trolling?

[Anonymous No.11477675]

>>11477627
>It moves to the right
Then V_B is 10 m/s, downward.

[Anonymous No.11477682]

>>11477631
If a|b and b|a then a = b.

[Anonymous No.11477686]

So my gf came to me yesterday all worried about this conspiracy theory video going around facebook saying not only is corvid 19 a hoax but it's to cover up the real culprit making everyone sick: NEW 5G TOWERS MAKING WAVE RADIATION FUCKING UP THE OXYGEN IN EVERYONES LUNGS

Lol I know it's a weird mix of /x/ tier anti vaxxer like bullshit. But my gf gets paranoid about it cause she's been having headaches and yadda yadda and she comes to me with facebook junk "science" so I can debunk it for her and it helps her know not to worry.

Thing is I'm just an engineer working for a research institute and not at all do I know shit about desease and pandemics enough. I can tell what smells like bullshit but that's about it. This one was easy cause the video just opens and starts with bullshit. I can't link the video and frankly don't want to but here's the gist of why they think 5g towers cause you to be sick
>5g all run at 60 hertz/mm
>60 hertz fucks w oxygen molecules
>makes their electrons spin faster
>making oxygen in your lungs fuck you up
>like this one dude in Wuhan that just collapses
>therefore it's 5g, not corvid19, making everyone sick

Now all that's wrong. But it got me thinking about how yes you can use a magnetic field to increase the energy/spin of an electron and if that did happen to oxygen on a large scale what would be the effects?

tl;Dr: what happens when you use a magnetic field to move electrons up a spin? I have only the vaguest memories from chem 1 class on this

[Anonymous No.11477695]

>>11477669
I don't care if it helps to the original problem, because that's not my point. my point is that if by any means you find yourself in a situation where you know what lim sin(y)/y is (for y going to 0 or +-inf), you can use it to compute sin(1/x)*x = sin(1/x)/(1/x) which is what the post you called is about.
and no, you absolutely don't need analycity of f. it's just a limit of a composite function, why would you need analycity for that.

[Anonymous No.11477710]

>>11477695
>I don't care if it helps to the original problem
So you're just posting random shit as if it's relevant? Need I remind you that you needed me to TELL you that your dumbass post is circular at best.
>why would you need analycity for that.
Because the only way to get convergence of ratios is to bound them with their difference quotients, which requires at least Lipschitz in both the functions involved in the composition.

[Anonymous No.11477719]

>>11477710
give me a counter example then. I want [math]f(x)[/math] such that [math]\lim_{x \to x_0}f(x) = \infty [/math], but [math]\lim_{x \to x_0}\tfrac{\sin f(x)}{f(x)}\neq 0[/math].

[Anonymous No.11477724]

>>11477719
Arcsin at 1.
I'm done. You're hopeless.

[Anonymous No.11477732]

>>11477724
[math]\lim _{x \rightarrow 1} \arcsin (x) = \infty [/math]?

[Anonymous No.11477740]

>>11477724
doesn't work. lim isn't ∞.

[Anonymous No.11477745]

Fuck, I always missed the new /sqt/ thread when it pops up.
Question from last thread: >>11477723

[Anonymous No.11477746]

Holy fucking shit i still dont know the answer guys

[Anonymous No.11477756]

>>11477592
overline here means congruence class, just think of addition mod 3

[Anonymous No.11477757]

>>11477746
>>11476189
>>11476173
it's fucking 1 or 0?

[Anonymous No.11477764]

>>11477757
it's zero, use the fact that if f(x) is bounded, then lim x f(x) as x -> 0 is 0

[Anonymous No.11477791]

I saying "x is within the reals squared" the same as saying "x is a real number >=0" ?

i.e. Is [math]x\in \mathbb{R}^2[/math] the same as [math]\{x\geq 0|x\in\mathbb{R}\}[/math]?
idk if that notation is right

[Anonymous No.11477795]

>>11477791
no, the superscript of 2 means tuples of real numbers
if you want x >=0, just specify it

[Anonymous No.11477817]

>>11477021
congrats anon, it's always a nice feeling when things start making sense

[Anonymous No.11477826]

>>11477724
embarrassing

[Anonymous No.11477898]

>>11477745
Set [math]R = G= H= \mathbb{Z}_2[/math].
Unless I'm mistaken, that's a counterexample.
Specifically, [math](0, 1) \times (1, 0) = 0[/math] in one but [math](1, 0)*(0, 1)=(1, 1)[/math] in the other one (the notation is confusing, I know).

[Anonymous No.11477957]

>>11477898
yeah the notation is tripping me up, I'll try toying with it some more

[Anonymous No.11477967]

>>11477795
I figured. But if you squared every number in [math]\mathbb R[/math], is that the same as x>=0 within [math]\mathbb R[/math]?

[Anonymous No.11477975]

>>11477967
yeah that's definitely true
maybe it's a matter of preference, but I'd rather say "let x be a non-negative real number" than saying "let x be a squared real number"

[Anonymous No.11477986]

>>11477957
>just twelve elements bro

[Anonymous No.11478376]

>stuck at home because of coronavirus
>mixture of boredom and lack of human contact
How are you lads handling it?
I'm seriously thinking about setting up a temporary /sqt/ discord server, even if it's an absolutely horrendous idea.

[Anonymous No.11478379]

>>11475807
does anyone have a good resource for a tl;dr on game theory? I need to be able to understand and solve questions like pic related. Thanks

[Anonymous No.11478387]

>>11478376
Zoom your supervisor and do some research.

[Anonymous No.11478399]

[eqn]\%[/eqn]
Why is it so ugly?

[Anonymous No.11478429]

Why is number of turns the sole multiplier in step up/down transformers? Why does it affect the voltage at all? I was thinking it had to do with total flux, but then it should be dependent on wire gauge and total length of wire not just number of turns.

[Anonymous No.11478445]

>>11478387
I'm supposed to meet a professor at thursday about research, but I don't think the university will even be open.

[Anonymous No.11478498]

>>11478429
Because the magnetic flux through a solenoid [math]p:S \rightarrow S^1[/math] is proportional to the winding number and the mutual inductance [math]M_{12}[/math] between two slenoids [math]S_2,S_2[/math] is proportional to their linking number. Let [math]L[/math] be a line bundle on [math]S^1[/math] with the [math]U(1)[/math]-connection [math]A[/math], such that magnetic flux through it reads [math]\Phi = \oint_{S^1}A[/math]. By Chern-Weil theory the curvature [math]B= dA[/math] lies in the integral cohomology class [math]H^2(D^2,\mathbb{Z})[/math] where [math]\partial D^2 = S^1[/math], hence [math]\Phi[/math] through the solenoid actually computes the first Chern number [math]c_1(p^*L) = nc_1(L) \in n\mathbb{Z}[/math] where [math]n = \operatorname{deg}p[/math] is the degree of the cover [math]p: S\rightarrow S^1[/math].
Now given [math]L_{1,2}[/math] line bundles on [math]S^1_{1,2}[/math] around the solenoids [math]p_{1,2}:S_{1,2}\rightarrow S^1_{1,2}[/math], Poincare duality [math]H^1(D,\mathbb{Z}) \cong H_1(D,\mathbb{Z})[/math] allows us to define the non-degenerate intersection pairing [math]\langle \operatorname{PD}A_1,A_2\rangle = \operatorname{lk}_{12} \in \mathbb{Q}[/math], and we are able to compute [math]M_{12} \propto \langle \operatorname{PD}p_1^*A_1,p_2^*A_2\rangle = n_1n_2\operatorname{lk}_{12}[/math]. This shows why the fluxes, and hence the EMFs, are quantized in terms of the number of turns on the solenoid.
>>11478445
Yep my campus is closed too, but I'm able to hold online meetings with my supervisor through Zoom.

[Anonymous No.11478540]

>>11478498
I didn’t really understand that, but I doubt even if I did it wouldn’t answer my question in the same way the equation for gravitational force doesn’t explain gravity. Physically, what is going on? Am I wrong in assuming that all else being equal, increasing the gauge of the secondary wire would increase the flux?

[Anonymous No.11478564]

>>11478540
>Physically, what is going on?
One loop = one unit of flux. N loops = N units of flux.
>increasing the gauge of the secondary wire would increase the flux?
By gauge you mean the EMF driving the current? Sure it simply increases the flux you have through the loop, but the fact that it's proportional to the number of loops on the solenoid doesn't change. With one loop you can in principle tune [math]B[/math] such that [math]\Phi[/math] is equivalent to that with multiple loops, but remember that your EMF must also fight against the eddy current generated from you tuning the magnetic field so you'll actually need a lot more power to drive the current necessary for that. This is why people just loop wires around solenoids since that gets you double the flux "for free".

[Anonymous No.11478583]

>>11477526
what the fuck are you on about? i said sin(y)/y is 0 as y goes to infinity. OVER y. LEARN TO FUCKING READ YOU FUCKING MORON.
>>11477724
good lord, unironically end yourself. you need to pass precalculus before you answer questions here.

[Anonymous No.11478601]

Please help me solve this. My hurt hurts from hitting myself too many times when I get it wrong.

If f(t)=√5 / t^3, find the rate of change function of f.

It's supposed to be a simple derivative rule problem but my stupid fucking head can't get it. I don't understand what I'm doing wrong and the website my uni uses doesn't offer hints during or the right answer after.

[Anonymous No.11478611]

>>11478564
> By gauge you mean the EMF driving the current
No I mean the wire gauge i.e thickness. Thicker wire = higher cross sectional area= higher flux( I think)
>One loop = one unit of flux. N loops = N units of flux
But the size of of every one of those units should increase if wire size increases doesn’t it? If you increase the wire size and double the area perpendicular to the field the flux should double even if it’s the same number of turns, yet the step up formula is solely dependent on number of turns.

[Anonymous No.11478617]

>>11478601
Oh my god I just figured out why I was getting the wrong answer every time. I'm a fucking idiot. Oh jesus fuck. I want to kill myself or move to the woods.

[Anonymous No.11478623]

>>11478601
Rate of change is first derivative. Factor out the root of 5 and simply take the derivative of t^-3. Phone posting cba to latex.

[Anonymous No.11478631]

>>11478611
Well those give you non-universal prefactors, yes, which aren't really important for a first order calculation. The winding number is universal, however, so it must enter your flux.
Now the problem with increasing the area is that the current generates a magnetic field that falls off algebraically away from the wire, so the full magnetic field through the doubled area would decrease. it is not a priori clear that doubling the area would double the flux, or even increase it in the first place.

[Anonymous No.11478690]

>>11478601
Do you know what the derivative of 1/t^3 is? sqrt(5) is just a constant factor in front.
The derivative of 1/t^3 is -3/t^4.

[Anonymous No.11478691]

>>11478631
>it is not a priori clear that doubling the area would double the flux
What do you mean? The equation is just B * perpendicular area. If you stay within the same area B should be the same and a doubled cross sectional area should mean doubled perpendicular. Did I assume something wrong there?
> so the full magnetic field through the doubled area would decrease
Either way, there should be some change if not exactly doubled. Yet the equation for how much the voltage is mutiplied is only ratio of turns. Is there an assumption there I’m missing, like equal wire size in primary and secondary windings? Cause every transformer I’ve seen had different sized wires on each end.

[Anonymous No.11478697]

>>11478691
>B should be the same
No. B is not uniform.

[Anonymous No.11478728]

>>11478697
Why not? Why would solely increasing the wire size in the secondary winding change the field produced by the primary winding through the same space?

[Anonymous No.11478765]

>>11478728
The entire point is that the flux is [math]\int_A B[/math]. It's only [math]B * A[/math] when the field [math]B[/math] is uniform but if you induce it from a current through the wire then ti's obviously not.

[Anonymous No.11478847]

>>11478765
Even if it’s not constant, it would still be over the same space it’s just the wire occupies more of that space. I don’t see how just changing the secondary would affect that produced by the primary. What I’m talking about is just making the blue wire in this pic thicker. That would seemingly increase the flux, but I got sidetracked from my main question focusing on that. The real point was what does wrapping the wire an extra time around this core give you that is unique to number of turns and couldn’t be explained by, say, linear length of the wire wrapped around.

[Anonymous No.11478857]

>>11478847
>What I’m talking about is just making the blue wire in this pic thicker. That would seemingly increase the flux,
Please explain how you think this would increase flux.
>what does wrapping the wire an extra time around this core give you that is unique to number of turns and couldn’t be explained by, say, linear length of the wire wrapped around
Just assume that the magnetic field is constant, for simplicity.
[math] \Phi=N\times B\times A [/math] where N is turns. Flux is a measure of how much magnetic field flows through an area [math]
as\ seen\ by\ the\ wire. [/math] If The wire is more coiled, if there are more turns, then B enters it more times, and there is more flux.

[Anonymous No.11478886]

>>11478857
>Please explain how you think this would increase flux
Because the cross sectional area of the wire is bigger. Is that not the relevant area in the equation?
>then B enters it more times, and there is more flux.
Oh, right. I wasn’t fully picturing what part of the wire would actually be perpendicular if you just kind of spiraled it around. That answers my primary question, but I still don’t see how A remains constant if you increase wire size.

[Anonymous No.11478890]

>>11478886
>Is that not the relevant area in the equation?
No lol. It's the area of the solenoid. In the pic in >>11478847 it's the rectangular x-sectional area of the core.

[Anonymous No.11478950]

>>11478890
So is the turn ratio a factor specific to transformers? The reason I thought it was the wire area is because the induction works even without the core. It also raises the question of why the core size isn’t relevant in the equation. Although in that case I can much more easily see how it could just be cancelled out since both wire share the same core.

[Anonymous No.11478959]

>>11478847
>>11478950
Anon...

[Anonymous No.11478970]

How do I improve my conceptual reasoning on more advanced topics?
It gets to a point where everything breaks down and I don't understand it intuitively.

[Anonymous No.11479001]

If I wanna define a ring homomorphism from a group ring, is it enough to specify where the "group elements" map to and make sure I didn't fuck up the multiplication? Can I do an "extend linearly" thing along with foiling?

[Anonymous No.11479007]

Why can people keep getting the flu? I know that it mutates fast but does it really manage to change so fast that every season our immune system can’t recognize whatever part it’s looking for? Are antibodies that specific? Why doesn’t our immune system ever train itself with the immutable parts of the virus?

[Anonymous No.11479019]

>>11478950
jesus dude

[Anonymous No.11479020]

>>11479001
The "group elements" form a basis for the group ring as a free module (take ten seconds to check the definition), so yes.

[Anonymous No.11479022]

>>11478959
>>11479019
WHAT

[Anonymous No.11479031]

>>11479020
Thanks, exactly what I needed
Have a classic Kurisu for my gratitude

[Anonymous No.11479037]

>>11479022
You're just so lost, it's hard to know where to begin.

[Anonymous No.11479038]

>>11479020
>>11479031
I have a sq. You two both know you’re adults right?

[Anonymous No.11479042]

>>11479037
So instead you’re going to act smug about someone asking a possibly stupid question in a stupid question thread? Whatever makes you feel better my guy.

[Anonymous No.11479050]

>>11479031
Is this about the product thing? Because I think I just came up with the shittiest counterexample in history.
Set [math]G=H=0[/math], the trivial group, and [math]R = \mathbb{Z}^2[/math].
For obvious reasons (unless I'm literally having vivid hallucinations), [math]R(G) \cong R[/math], and [math]G \oplus H \cong G[/math], but [math]R \oplus R \neq R[/math].
>>11479038
Yes.

[Anonymous No.11479053]

>>11479042
>The reason I thought it was the wire area is because the induction works even without the core.
But it doesn't work as good without the core. The core "guides" the magnetic field into the solenoid, increasing flux.
>It also raises the question of why the core size isn’t relevant in the equation.
It is relevant. The core size is exacly what is captured in the definition of magentic flux [math] \int B\text{d}A [/math]. The time rate of change of flux is relevant to Faraday's law, which is exactly how transformers work in the first place. The diameter of the wire barely matters.

[Anonymous No.11479054]

>>11479050
Typo, should be [math]R = \mathbb{Z}_2[/math].

[Anonymous No.11479064]

>>11479050
Oh thanks, same poster who asked the group ring question earlier in the thread (might as well call me group ring fag). Looks good to me.

[Anonymous No.11479094]

I'm trying to learn about the Carnot cycle, where internal energy through the adiabatic steps is [math]\int_{T_1}^{T_2} \frac32 \frac1T dT = -\int_{V_1}^{V_2} \frac1V dV[/math].
I'm used to the antiderivative of the reciprocal being the natural logarithm, but it doesn't make sense to me to evaluate the logarithm of a dimensioned quantity like a temperature or volume. I know that it proceeds to [math] \frac32 (\ln(T_2) - \ln(T_1)) = \ln(V_1) - \ln(V_2) = \frac32 \ln(\frac{T_2}{T_1}) = \ln(\frac{V_1}{V_2})[/math], where the logarithm is being evaluated for dimensionless ratios as I expected.
The intermediate step is bothering me. You can't raise e to a power and get a temperature or volume. Is it just an abuse of notation?

[Anonymous No.11479102]

>>11479094
Interesting point, haven't actually thought about this issue. I'm guessing (like all conventions in physics) that it's abuse of notation, and that we should really be writing logarithms of fractions of dimensioned quantities instead of splitting them up.

[Anonymous No.11479108]

>>11479102
>it's abuse of notation, and that we should really be writing logarithms of fractions of dimensioned quantities instead of splitting them up.
basically this

[Anonymous No.11479424]

Can someone walk me through the steps for using the legendre symbol with (105/317)? I don't get it at all. And when I use the calculators, the solutions don't really make sense to me. Need some help please.

[Anonymous No.11479438]

>>11479424
I'm answering my own question. But I'm not sure that it's right.
(105/317) = (317/105)
>(p/q)=−(q/p) if p≡q≡3(mod4). Otherwise (p/q)=(q/p)
(317/105) = (2/105)
>a ≡ b (mod p), then (a/p) = (b/p)
(2/105) = 1
>(2/p) = 1 if p ≡ 1 (mod 4).

[Anonymous No.11479609]

If an intersex man has functional ovaries and sperm would the offspring be basically no different then if he (or a hypothetical twin) knocked up his sister or basically a sibling?

[Anonymous No.11479610]

>>11479609
Eggs and sperm I mean.

[Anonymous No.11479762]

Generally, do engineering students have to take biology, chemistry, or some other bs life science as a general ed or something? What about Data Science majors?

[Anonymous No.11479808]

>>11479094
>but it doesn't make sense to me to evaluate the logarithm of a dimensioned quantity like a temperature or volume.
It's fine if the base of the logarithm has the same dimensions. And log_b(x)=log_c(x)/log_c(b) for any c.

If you take the antiderivative of 1/x w.r.t. x, you get ln(x)+C = ln(x/k), where C and k are arbitrary constants. k has the same dimensions as x.
Both antiderivatives in your example are dimensionless: the infinitesimal products have dimensions of (1/T)*T and (1/V)*V.

It's not really any different to e.g. using complex numbers in the solution of linear ODEs where the variables are physical quantities, as the imaginary components end up cancelling to give a real result.

[Anonymous No.11479831]

Let [math]p(x)=a_0+a_1x+\ldots +a_nx^n [/math] be a polynomial with complex coefficients and complex zeros [math]\alpha_1,\alpha_2, \ldots , \alpha_n, [/math] where only [math]\alpha_1, \ldots , \alpha_k[/math] are unequal to zero. What are the coefficients of the polynomial with only the roots [math]1/\alpha_1,\ldots , 1/\alpha_k [/math]?

[Anonymous No.11479833]

>>11479762
depends on the uni, so find out, next

[Anonymous No.11480090]

My mind is stuck guys, I need some help.

>doing function relations & graphs
>I can find graphs starting from functions
>I am stuck at finding the functions from graphs
>exercises give a function, its graph and 2 other graphs
>asks how the original function has changed to each of the new graphs

Any tips to unstuck? I feel stupid, it seems obvious but can't get it how.

[Anonymous No.11480103]

>>11480090
In general, that's a fairly hard thing to do. But I imagine these graphs are changed in a very obvious way, like they are either translated or dilated, or rotated, or reflected. Would I be right?

[Anonymous No.11480109]

>>11480103
ah yes, I forgot it says that whatever happens it will be +2 or -2 .
So the pondering is if it will be f(x) +- 2 or f(x +- 2)
Or the next set of graphs changes by multiplication.
picture on the next post.

[Anonymous No.11480113]

>>11480103
>>11480109
I am doing b now.
I have the answers but I care about the process.

The steps I will do to go from the first g(x) and (a) graph to (b) & (c).

[Anonymous No.11480152]

does anyone know the identity used here to turn the e part into sin?

[Anonymous No.11480154]

does anyone know the identity used here to turn the e part into sin?

[Anonymous No.11480159]

How do is solve this differential equation ?
[math] |PQ'|=|QP'|[/math]

[Anonymous No.11480168]

Just went math ssj2. Get on my level.
What are my chances for grad school?

[Anonymous No.11480173]

>>11480154
https://en.wikipedia.org/wiki/Hyperbolic_functions
By definition

[Anonymous No.11480174]

>>11478847
Magnetomotive force (mmf) is measured in units of Amp-turns. Some conversions happen (flux density, magnetic reluctance etc.) but the key point is, the mmf is conserved.
If you send 5 amps through 10 turns of your primary, you have 50 Amp-turns of mmf. If your secondary is 100 turns, you get 0.5 amps. Current steps down.
>>11478429
>Why does it affect the voltage at all?
Ultimately, it's power that's being conserved. And since P=IV, you can do the math: 5 amps at, say, 12V is 60W, so 60W at 0.5 amps is 120V. Voltage steps up.

Wire thickness is largely trivial. It's simply so the wire doesn't burn out under high current.
>>11478611
>But the size of of every one of those units should increase if wire size increases doesn’t it?
only trivially

[Anonymous No.11480177]

>>11480173
ah, I hadn't even spotted the h there. thank you

[Anonymous No.11480180]

>>11480113
f(x)+a is just f(x) shifted up by a units, f(x)-a shifted down
f(x-a) is just f(x) shifted to the right by a units, and f(x+a) is shifted to the left
a*f(x) is f(x) scaled up (if a>1) by a factor of a along the vertical axis, and scaled down by that factor if a<1
f(ax) is f(x) squeezed down along the x axis if a>1, and stretched out along the x axis if a<1
f(-x) is f(x) reflected across the y axis
-f(x) is f(x) reflected across the x axis
Play with this
https://www.desmos.com/calculator/umv4b5d1fz
>>11480159
Separation of variables
>>11480168
Ah yes, the ol' MS paint proof. They will love you.

[Anonymous No.11480187]

EE here, is AI worth going into?

[Anonymous No.11480193]

>>11480113
f(x)+a is just f(x) shifted up by a units, f(x)-a shifted down
f(x-a) is just f(x) shifted to the right by a units, and f(x+a) is shifted to the left
a*f(x) is f(x) scaled up (if a>1) by a factor of a along the vertical axis, and scaled down by that factor if a<1
f(ax) is f(x) squeezed down along the x axis if a>1, and stretched out along the x axis if a<1
f(-x) is f(x) reflected across the y axis
-f(x) is f(x) reflected across the x axis
Play with this
https://www.desmos.com/calculator/umv4b5d1fz
>>11480159
Separation of variables
>>11480168
Ah yes, the ol' MS paint proof. They will love you.
>>11479762
>biology
I had to take a "life science" so I took environmental science cuz it was easy. I should have just taken bio.
>chemistry
Two semesters of general chemistry.

[Anonymous No.11480199]

>>11480168
>if ab = i then ab^2 = i
? why is that

[Anonymous No.11480203]

>>11480173
I like how most calculus course introduce even/odd functions purely as a way to simplify integral calculations and ignore the characterization of the exponential in terms of even and odd functions.

[Anonymous No.11480214]

>>11480199
I is the identity matrix. If you read further along you would know this.

[Anonymous No.11480216]

>>11480113
>>11480193
That helps! Thank you.
I also use
https://www.symbolab.com/

[Anonymous No.11480228]

>>11475807
>receive grade for an assignment
>assistant didn't add the marks up properly, and gave me a higher grade than i deserved
would you say something?

[Anonymous No.11480249]

>>11480228
If you are applying for graduate school they review all copies of every graded quiz/exam that you took to see the grades were correct, if they were not then they will not let you in.

[Anonymous No.11480275]

>>11480228
do nothing about it

>>11480249
>they review all copies of every graded quiz/exam that you took to see the grades were correct, if they were not then they will not let you in.
grad schools get hundreds of applicants. they go by transcripts and don't review your work in individual courses

[Anonymous No.11480279]

>>11480275
Don't fucking tell him that you actual chink/Indian.

[Anonymous No.11480282]

>>11480228
Are you Jewish/Jewish last name? Chances are it is nepotism.

[Anonymous No.11480322]

>>11480159
If [math]P[/math] and [math]Q[/math] are [math]C^1[/mathg], a solution is locally a solution of either [math]PQ'=QP'[/math] or [math]PQ'=-QP'[/math].
If the latter, you use the product rule to obtain [math](PQ)'=PQ'+QP'=0[/math], if the latter, [math](PQ)'=PQ'+QP'=2PQ'=2QP'[/math], if the former, and I have no idea what to do with the last one.

[Anonymous No.11480376]

Thinking of switching from CS to EE. I'm just worried about the extra year of study this will incur. Has anyone else done something like this? Is it worth it?

[Anonymous No.11480391]

rubbing ethyl alcohol has denaturants added to it to make it toxic so it doesn't need to pay alcohol taxes. but those denaturants don't change the structure of the alcohol and ethyl alcohol evaporates at 78C. let's say hypothetically my friend has a distillation setup where he heats alcohol to that temperature and collects the vapor, would the denaturants be removed from the vapor? of course i wouldn't do such thing and this is just a question.

[Anonymous No.11480393]

>>11480376
>CS to EE
why? if it interests you/you don't like CS then go for it but if you look at it career wise, CS is much better for the foreseeable future

[Anonymous No.11480418]

>>11480391
If the denaturants have A) similar boiling points (+/- 1-5 C) and B) form something called an "azeotrope," you're fucked

[Anonymous No.11480429]

>>11480418
do you know what denaturants are generally added to ethyl rubbing alcohol?

[Anonymous No.11480538]

>>11477724
still waiting for that counter example

[Anonymous No.11480565]

>>11480193
>https://www.desmos.com/calculator/umv4b5d1fz

It says it will only do g(x) not g(x + a) and similar.

[Anonymous No.11480613]

>>11478379
bump, someone pls help

[Anonymous No.11480630]

>>11478379
wikipedia, stanford, any online encyclopedia are the best sources for tl;dr's.
i'd recommend you to never take the tl;dr route but instead read a book or take a course

[Anonymous No.11480639]

any answers to this? >>11472016
it's found in yerba mate and many other herbs.
the official statement bans it because they say it has laxative properties that could be potentially cause problems after a long time but other studies online said it is highly radioactive and carcinogenic while others said its shown to lower the chance of getting cancer, autoimmune and diabetes and to be overall healthy and very good for the body.
so which one is it? cancer, diarrhea or good.

[Anonymous No.11480652]

>>11480639
Where the fuck are you seeing that it's banned? Source ur claims

[Anonymous No.11480670]

sorry for bringing so many stupid integral questions today, I don't know anyone that could help me with them and have no perspective of when the next meeting with my calc professor will be due because of the whole coronavirus quarantine

anyways, I'm trying to understand where the -3 came from? I got to the 3/[(x-2)2 - √32] part but all I did was kick the three out of the integral and then use the 1/u2-a2 identity. in the end I have a similar answer to pic related but the fraction on the left is 3/(2√3) rather than -√3/2. which makes my solution completely wrong I guess

[Anonymous No.11480680]

>>11480670
>3/[(x-2)2 - √32]
3/[(x-2)^2 - √3^2]

>1/u2-a2
1/(u^2 - a^2)

[Anonymous No.11480689]

>>11480670
oh wait, he multiplied everything by -3, didn't he? for what purpose though? could he not just kick the nominator our of the integral since it's a constant and apply the identity?

[Anonymous No.11480698]

>>11480689
>multiplied everything by -3
multiplied the integral by -3 and then divided everything inside of it by -3 so they cancel out,* rather. only multiplying everything would mean a different integral

[Anonymous No.11480822]

>>11480652
https://www.matportalen.no/verktoy/tilbaketrekkinger/yerba_mate_te_merket_kharta_khadra_trekkes_fra_markedet (original)
https://www.nutraingredients.com/Article/2019/09/12/Yerba-mate-tea-brand-Kharta-Khadra-taken-off-Norwegian-market (English)
they say it's banned because of anthrachinon (norwegian for anthraquinone)

[Anonymous No.11481008]

>>11480322
>product rule
Why do we prove the product rule (using limits which are french and therefore gay), when it is sufficient (much easier and more beautiful) to define derivative from the rule.

[Anonymous No.11481058]

>>11480822
>norwegian
>herbal supplements
figures. Just buy it off ebay or smth

[Anonymous No.11481085]

>>11481008
imagine I'm a first year student. convince me that your *axiomatic derivative* is something worth studying.

[Anonymous No.11481115]

>>11481008
Even if (and I'm not sure it does) that works for [math]\mathbb{R}[/math] (I'm assuming you can somehow make it work because of the no exotic smooth structures thing), I'm pretty sure it collapses for [math]\mathbb{R}^4[/math], and then you need to add a bunch of autistic axioms specifying which functions are differentiable.
Also, geometric definitions are nice.

[Anonymous No.11481128]

>>11481115
Why care about R or R^n in particular
any field is good enough
see complex analysis

[Anonymous No.11481135]

>>11481128
missed the point completely

[Anonymous No.11481143]

>>11481135
You missed the point entirely. Any reasonable (read "non-indoctronated") student is only interested in calculus not in playing with autism toys such as limits
infinity does not exist btw

[Anonymous No.11481148]

>>11481143
missed the point completely

[Anonymous No.11481398]

>>11480630
thanks anon, found a good stanford online course which is helping me come to terms with the fundamentals

[Anonymous No.11481513]

>By Lagrange’s Theorem any subgroup of S_3 must have size 1,2,3 or 6.

Can someone explain this to me. I don't understand how you can have a subgroup bigger than its group

[Anonymous No.11481520]

>>11481513
S_3 is size 6.

[Anonymous No.11481584]

does -1 divide 3

also why cant negative numbers be prime

[Anonymous No.11481728]

>>11481584
1. depends on your definition of divides
2. cause -n "divides" n and the other way around, so there would be no primes

[Anonymous No.11481752]

Is the reason why people say to have a 2 week quarantine because it takes at most 2 weeks to exhibit symptoms?
Celebrities like NBA players came out positive but have have not shown any symptoms.

[Anonymous No.11481868]

>>11481728
>cause -n "divides" n and the other way around, so there would be no primes
as in, (-3)=(-1)*3? If that's the case, then there are no positive primes either

[Anonymous No.11481886]

>>11481584
Yes.
Negative numbers aren't natural, so in some definitions (i.e. wikipedia's) they aren't natural trivially.
>>11481868
A prime [math]p[/math] is a natural number whose natural divisors are [math]1[/math] and [math]p[/math].

[Anonymous No.11481889]

>>11481886
>they aren't natural trivially.
Aren't prime.

[Anonymous No.11481895]

My plants are cuttings less than 30cm tall. Will they die to frost if I put them outside. South east England.

[Anonymous No.11481898]

>>11481895
'pends entirely on the plant in question

[Anonymous No.11481911]

>>11481898
Let's say tomatoes. I know it would be sensible to keep them indoors but I'm hoping to get them planted as early as possible..

[Anonymous No.11482092]

What is the sum of the all the products of all distinct subsets of {1,2,3,4,5,6}?
I brute forced it by doing like, 1*2*3 + 1*2*4 + 1*2*5... 4* 5*6, and got 735.

Is there a nicer, closed form way of finding this out?

[Anonymous No.11482097]

>>11482092
distinct subsets of length 3*

[Anonymous No.11482627]

>>11480168
>Virgin latex
Uses latex as a "2nd check" to make sure his proof is accurate.
Isn't autistic in his wants for a perfect typesetting, but is only using latex because that's what everyone says he should use.
>Chad Gimp
Doesn't care if he can read his proof. Knows it's correct.
Gets into graduate school based on sheer output knowing most math papers go unread anyways.

[Anonymous No.11482958]

>>11475807
I'm trying to evaluate the constant of a 3D wavefunction for a free particle. The first assumption is that in 1D the constant is 1/sqrt(pi), but I can't get that. Any advice?

[Anonymous No.11483093]

Any book recomandations for the following subjects?
-Abstract Algebra
-Multivariable Calculus
-Afine and Projective Geometry

[Anonymous No.11483100]

>>11482092
>all distinct subsets
Assume we've evaluated it for our previous set without one element. Then, our new subsets split up into the old ones, old one times the new element, and single element from the old one times the new element. Any of those is easy to evaluate (first one is trivial, second one is the previous sum times the new element, third one is the sum of all elements in the old set times the new element), so you can compute it inductively.
>>11482097
>distinct subsets of length three
For length two, we'd use [math](\Sigma_i a_i )^2 = \Sigma_{i \neq j} a_ia_j + \Sigma_i a_i^2[/math] (note how [math]a_ia_j[/math] is "kinda sorta doubled.")
For lengthy three, you can try fiddling around with [math]( \Sigma_i a_i )^3[/math] and cancelling things out.
>>11483093
>wanting to study affine geometry
What for?

[Anonymous No.11483139]

>>11481058
that's not my point, i don't even live in Norway. i just want to know about anthraquinone, what is its function in plants and if it's toxic

[Anonymous No.11483156]

>>11483093
Geometry by Brannan for Affine and Projective geometry.

[Anonymous No.11483162]

>>11483100
I feel like my teachers is moving too slowly with the course; cute Remi pic
>>11483156
thanks

[Anonymous No.11483174]

no question but i've had this image lying around since forever and i never got around to using it, so here it is in the hope that maybe one of you can.

[Anonymous No.11483247]

>>11482958
Are you sure you have the right wave function?
>[math] \Psi(x)=A\exp(jk_xx) [/math]
isn't square integrable.

[Anonymous No.11483271]

Why are spacings of 1/10 of a wavelength solid to electromagnetic waves? where does this property come from?

[Anonymous No.11483287]

>>11483247
This is the assignment, I was not able to get anything coherent, so I started to see if I could even get the 1st dimensional constant. I've browsed youtube a little and now know that the constant comes from a Fourier transform, I'll look into this exercise again in the evening.

[Anonymous No.11483315]

So I had an understanding once that is now lost, I used to think of division in terms of "grouping". Let me give you an example, and if you understand where I'm trying to get at, please explain it to me. I want this intuition back.

For example, dividing 36 months by 12 groups months into 3 years. I "sort of understand" this, but not fully. Full understanding unfortunately eludes me.

[Anonymous No.11483326]

>>11483287
Ah, you just have to compute the n-dimenional gaussian.
IIRC you used something like [math]\exp(k r) = \exp(k_1r_1 + k_2r_2 + k_3r_3) = \exp(k_1r_2) \exp(k_2r_2) \exp(k_3 r_3)[/math] and Fubini to split up the integral into the product of the the integrals along each of the three axis, which were all equal.

[Anonymous No.11483334]

>>11483326
Ah, you used a formula that looked like [math]\int_{X \times Y} f(x)g(y) d \mu _{X \times Y} = ( \int_X f(x) d \mu_{X} )( \int_Y g(y) d \mu_{Y})[/math].

[Anonymous No.11483341]

What's some good outsourcing sites where I can pay some genius chink to do my homework?

[Anonymous No.11483383]

is it likely that integrals have many equivalent answers that at a first glance look nothing alike? trigonometric integrals, more specifically. for example, this website has 3 different approaches with different (or are they?) answers to the same integral, but I can't tell whether they're equivalent or only one of them is correct
https://socratic.org/questions/how-do-you-integrate-int-cos-3x-dx

[Anonymous No.11483531]

>>11477533
you could do this formally, like >>11477625 . But to me the problem is clear. The cart is moving the rope at 50 m per second and the weight 10 m per second. So so in a second 60 m of rope is lost between 4 layers. 60/4 = 15 m/s.

[Anonymous No.11483535]

>>11483383
Ask ya boy wolfram to differentiate them answers.

[Anonymous No.11483570]

>>11483326
>>11483334
I actually used the gaussian integral in >>11482958 when solving the integral for the 1D case. It seems that in this case you can't normalize the function, so you ahve to do a Fourier transform on it to get the 1/sqrt(2 pi) constant.

[Anonymous No.11483586]

why does cervix exist and what function does it actually serve?

inb4 wikipedia

[Anonymous No.11483654]

>>11483535
that's a good idea, thanks!

[Anonymous No.11483709]

>>11483139
>what is its function in plants
As a highly symmetric molecule, the diradical could be useful for some novel metabolism. It appears to be used industrially to convert O2 to hydrogen peroxide; so my guess is some enzyme catalyzes the production of some pretty exotic plant peroxides/difficult oxidations
>and if it's toxic
consensus appears to be "maybe," but probably not

[Anonymous No.11483734]

>>11483709
thanks.
btw do you know any website that could be used to search the properties of chemicals especially ones that aren't popular?

[Anonymous No.11483781]

>>11483287
[math]\int\frac{dx}{\sqrt{2\pi}} e^{ikx}\delta(x)= 1[/math]. The plane wave is the Fourier transform of the delta function. It's not square integrable in the conventional sense but only as a distribution.

[Anonymous No.11483785]

would it be okay to wipe down this boxes of candies i got my mother for her birthday with alcohol? dont want to accidentally give her the covid from some candies... but i dont want the alcohol to leech through the cardboard either... oh bother...

[Anonymous No.11483795]

>>11483734
I just used wikipedia, plus several years of college I guess

Chemspider is decent for obscure industrial chemicals. Merck Index should have drug and health info.
I think you're shit outta luck for biomolecules/enzyme catalysis though. Just gotta comb through the literature for species name/enzyme class and pray you get a hit

[Anonymous No.11483816]

>>11483781
Is it valid to say that Dirac delta convolved with itself is Dirac delta, and in what sense?

[Anonymous No.11483834]

>>11483816
Yes. Take [math]\mathcal{S}[/math] the (tempered or compactly supported) test functions, complete it in the convolution product then take the topological dual [math]\mathcal{S}'[/math], you'll find that the Dirac delta is the unit in the algebra of distributions [math]\mathcal{S}'[/math] in the sense that [math]f\ast \delta = f[/math].

[Anonymous No.11483836]

>>11483816
IIRC you defined convolution of a function with a distribution and then convolution of a distribution with another distribution by associativity (i.e. for any f, [math](g * h) * f = g *(f*h)[/math], so we have [math]( \delta * \delta ) * f = \delta * ( \delta * f) = \delta * f= f[/math].

[Anonymous No.11483943]

If n is odd natural number with exactly k distinct prime factors. How many solutions modulo n does x^2 ≡ 1 mod n have?
Kinda lost on this one.

[Anonymous No.11483947]

>>11481513
The size of S_n is n!

[Anonymous No.11483949]

>>11483943
chinese remainder theorem

[Anonymous No.11483953]

>>11483943
>>11483949
Yup. This formulation is probably the most convenient one:
[math]Z_n \cong Z_{p_1} \times ... \times Z_{p_k} [/math]

[Anonymous No.11483958]

>>11483949
>>11483953
Can you elaborate on that? I figured I had to use that in some way, but I'm not really sure how.
Is it just k? And why?

[Anonymous No.11483966]

>>11483958
The isomorphism sends [math]1[/math] to [math](1 ~ \mod ~ p_1, 1 ~ \mod ~ p_2, \cdots, 1 ~ \mod ~ p_k)[/math] , so you compute the pointwise square roots.
>Is it just k?
Nah.
Also, watch out if one of the primes is 2.

[Anonymous No.11483967]

>>11483966
> \mod already adds in a space
T-Thanks LaTeX.

[Anonymous No.11483978]

>>11483966
So what would the answer be? This isn't for homework or anything, I just don't really see what the answer is in general.

[Anonymous No.11483983]

>>11483978
Dude, basic combinatorics. Pointwise, any root is always either 1 or -1.
[math]2^k[/math] if all primes are uneven, [math]2^{k-1}[/math] otherwise.
Reminding you that [math](x^2-1)=(x-1)(x+1)[/math] and that [math]Z_p[/math] is always an integral domain.

[Anonymous No.11484033]

>>11483983
Right. Thank you. I wasn't sure what you meant by pointwise here. And it's not altogether clear why it's not 2(k-1) and 2k.

[Anonymous No.11484049]

>>11484033
Because [math]1 \cong -1 \mod 2[/math].

[Anonymous No.11484181]

Could anyone help me with this problem?

https://cs.stackexchange.com/questions/121864/prove-product-partition-is-np-complete-in-the-strong-sense

[Anonymous No.11484192]

Why did they decide 1 click in a web browser was sufficient when people were already trained to double click when using their operating system?

Who decided this, and why?

[Anonymous No.11484324]

Why should I go to college if I have the internet? is there is anything I'm missing there as a rich person who doesn't have to work a shitty job?

[Anonymous No.11484373]

>>11484324
validation by a professional
that, or a portfolio of worthwhile projects/history of worthwhile endeavors

[Anonymous No.11484377]

Doesn't the gamma function prove that 0! is not 1, but infinity (within the extended reals)?

[Anonymous No.11484381]

>>11484373
this is totally worthless shit if you think about it

[Anonymous No.11484393]

>>11484381
Demonstrating competence is not worthless.
Though yes, I agree the current system is broken

[Anonymous No.11484403]

>>11484377
Are you stupid anon? [math]\Gamma(n+1) = n![/math] so plug in [math]n=0[/math].

[Anonymous No.11484521]

Can vectors be infinite?

[Anonymous No.11484529]

>>11484403
so, then what, gamma(0)=(-1)!=infty? Did I just read it wrong?

[Anonymous No.11484549]

>>11484521
https://en.wikipedia.org/wiki/Projective_space

[Anonymous No.11484560]

>>11482958
|e^(iw)|=1

[Anonymous No.11484561]

I have the following graph, as you may see, this graph doesn't have the values for both X and Y axis.

I'm being asked if there are repeated values in any [math]a_j[/math] and in any [math]b_j[/math] i suppouse that both [math]f_1, f_4[/math] have the same value in [math]b_j[/math] because they intersect in the same place in the Y axis, right? how do i solve this crap?

[Anonymous No.11484563]

>>11484529
In what universe does [math] (-1)! [/math] mean [math]0![/math] anon?
>gamma(0)=(-1)!=infty?
Yes? Why does this surprise you? Factorials aren't defined for negative integers.

[Anonymous No.11484570]

>>11484521
Any vector necessarily has finite norm by definition.

[Anonymous No.11484576]

>>11484561
I also have to "compare" [math]a_j[/math] with 0, what does this mean? i should simply replace [math]a_j[/math] with 0?

[Anonymous No.11484579]

>>11484561
>bj

[Anonymous No.11484595]

>>11484570
That's neither true nor helpful.
Not every vector space is a Banach space and indeed there's non-metrizable vector spaces.
But generally, of course even if the answer to the literal question is formally no, he's asking for extensions of the notion to include those objects.

[Anonymous No.11484600]

>>11484595
>that's neither true
>not true
>every vector has finite norm isn't true
You're working with some pants on head retarded definitions, aren't you?

[Anonymous No.11484606]

>>11484595
>>11484600
Also, every real/complex vector space is metrizable by a norm.
Take a base. The norm of an element is the sum of the modulos of it's coefficients in the base.

[Anonymous No.11484614]

Is there a formula for dividing a sum unequally along a linear curve based on a growth rate equal to the first number in the sequence?

e.g., 1 across 4 places = 0.1, 0.2, 0.3, 0.4

[Anonymous No.11484622]

>>11484600
It's extremely cheap disingenuous to go down that route. If "not every vector has a norm" is factually true, one doesn't need to get emotional about it and start moving goalposts.

[Anonymous No.11484625]

>>11484614
hard to parse that sentence

[Anonymous No.11484639]

What is the definition of phase in the electrical sense? I can’t articulate the difference between split-phase, which I understand is a single phase system, and a two phase system with phases 180 degrees apart other than by appealing to the number of transformers used.

[Anonymous No.11484649]

>>11484625
I need to be able to divide a number into x places unevenly in such a way that they increment by the same amount each step, preferably with the amount they increment being equal to the lowest number.

[Anonymous No.11484654]

>>11484649
>unevenly
>same amount
We want to help you anon

[Anonymous No.11484659]

>>11484639
How many phase you have, separated by 360 deg / line count

[Anonymous No.11484664]

>>11484649
Ah, then you want [math] n [/math] weights [math] w_k [/math], such that for [math] k<n [/math],
[math] w_k = k / \sum_{j=0}^{n-1} [/math],
which simplifies to
[math] w_k = 2\cdot k / n / (n-1) [/math],

E.g. for n=4, you get
[math] w_0 = 2\cdot 0 / 4 / 3 = 0 [/math],
[math] w_1 = 2\cdot 1 / 4 / 3 = 1 / 6 [/math],
[math] w_2 = 2\cdot 2 / 4 / 3 = 1 / 3 = 2 / 6 [/math],
[math] w_3 = 2cdot 3 / 4 / 3 = 1 / 2 = 3 / 6 [/math]

If you don't want to start it at 0, compute the thing for
[math] w_l = l / \sum_{j=1}^{n} [/math],
instead.

The above are the partitions of 1 you look for, if you want to ramp up to a higher number, just multiply the thing

[Anonymous No.11484666]

>>11484595
What? All vectors in a normed linear space, Banach or not, have finite norm; I don't know why you think mentioning non-metrizable things is relevant. Just because a space doesn't have the conventional notion of a norm doesn't automatically mean it has vectors with infinite norm, which was what Remi's was saying.
Most non-metrizable spaces people encounter (in the e.g. weak or Mackey topology) can still be endowed with semi-norms. The problem there isn't with vectors having "infinite norm", it's that they can't be specified by a single norm.
>>11484606
>The norm of an element is the sum of the modulos of it's coefficients in the base.
In general Zorn guarantees a basis in a generic vector space but it doesn't have to be countable. Secondly, you can't really say [math]|v| = \sum_a |\lambda_a|[/math] unless you have a notion of orthonormality, which not even separability guarantees, and this is modulo convergence and completeness issues.
Though it's true that if you want a useful notion of a norm/semi-norm it better be finite.

[Anonymous No.11484668]

[math] w_k = k / \sum_{j=0}^{n-1} j [/math]
resp.
[math] w_l = l / \sum_{j=1}^{n} j [/math]
is what I meant, of course

[Anonymous No.11484672]

>>11484614
>>11484649
[math]D = n*x + T_{n-1}*x[/math]
Where D is some number into n partitions and T_x is the triangular number of x.

[Anonymous No.11484674]

>>11484666
He didn't say "vector in a normed linear space", he said vector.
I'm fully aware that non-metrizable spaces are autistic. Doesn't mean it's wrong, especially if you adopt standard math axioms.
Nice get

[Anonymous No.11484683]

>>11484659
Sorry, what??

[Anonymous No.11484705]

NOT EVEN KIDDING, I'M A15 YEARS OLD ENTHUSIASTIC MAN WHO WANTS TO FIND A CURE FOR CORONA, HOW CAN I START MY JEURNEY AS A THERIOTICAL BIOLOGIST?

[Anonymous No.11484708]

>>11484614
>>11484649
>>11484672
Sorry forgot to mention though it should be evident, x will be your initial number/increment

[Anonymous No.11484719]

I'm having trouble proving the following problem.

H is a subgroup of G. X is the set of left cosets of H. For all a\in G, p_a: X--> X is defined as p_a(xH) = axH. Let h: G --> S_X defined by h(a) = p_a.

I've managed to prove that p_a is a permutation. I've also managed to prove that h is a homomorphism. Likewise, the set {a\in H: \forall x\in G, xax^-1 \in H} is the kernel of H.

Here is where I am running into trouble. I need to show that if H has no normal subgroups other than {e}, G is isomorphic to a subgroup of S_X. I'm trying to use the fundamental homomorphism theorem but it doesn't get me where I want to. I know that if H contains no normal subgroups other than {e}, then H is precisely the kernel. However, the fundamental homomorphism theorem gives me that S_x is isomorphic to G/H which is not what I want to show.

Please help a retard out.

[Anonymous No.11484724]

>>11484705
Any introduction to biology book will be a good start. But this is a math thread, no?

[Anonymous No.11484752]

>>11484666
>it doesn't have to be countable
Any element is written uniquely as a sum of finitely many elements of the base, so the sum is always well defined either way.
>Secondly, you can't really say |v|=∑a|λa| unless you have a notion of orthonormality, which not even separability guarantees, and this is modulo convergence and completeness issues.
I have literally no idea what you mean.

[Anonymous No.11484758]

>>11484719
>H is precisely the kernel
Oh? Normal subgroups [math]N[/math] of [math]G[/math] satisfies [math][g,N] = 1[/math] for every [math]g\in G[/math] hence [math]p_a[/math] is trivial for every [math]a\in N[/math], so [math]h(N) = 1[/math]. Normal subgroups in fact fit into the kernel of [math]h[/math].
>>11484752
>Any element is written uniquely as a sum of finitely many elements of the base
Really? For [math]every[/math] vector space? Think harder sweetie.

[Anonymous No.11484766]

>>11484758
>of [math]G[/math]
Of [math]H[/math] of course.

[Anonymous No.11484776]

>>11484758
Anon, you can't sum infinite vectors on an arbitrary vector space because it has no topology.
Any element can be given as a finite linear combination of basis vectors by definition. See the wikipedia page to refresh or something.

[Anonymous No.11484780]

>>11484758
I'm unfamiliar with the notation '[g,N] =1'. Could you explain what this means? Also, how does the h(N) =1 help me show that G to some subgroup of G?

[Anonymous No.11484795]

>>11484776
>finite linear combination
They're called formal* linear combinations, and endows a specific topology on the space; namely the topology inherited from the direct limit [math]\lim\limits_{\rightarrow} V[/math] of finite-dim vector spaces. This is a specific choice of topology, not sure why you thought you don't need any for this in the first place.
>>11484780
[math][g,N] =1[/math] it means they commute, so [math]gNg^{-1}=N[/math] for every [math]g\in H[/math].
>Also, how does
Subgroups [math]N\subset H[/math] are normal iff [math]N\in \operatorname{ker}h[/math]. First isomorphism theorem then gets you [math]G \cong \operatorname{im}h/\operatorname{ker}h = S_X/\operatorname{ker}h[/math]. If there are no such normals then [math]\operatorname{ker}h=1[/math] so [math]G \cong S_X[/math].

[Anonymous No.11484841]

Are the tuhu posters getting into a fight? This shall be a sufficient source of entertainment.

[Anonymous No.11484864]

>>11484668
I had to do n+1 for the bottom formula but other than that it seems to work like a charm, thank you kindly

[Anonymous No.11485597]

>>11484752
what if you can't even find a base?

[Anonymous No.11485821]

>>11484758
>Really? For everyevery vector space? Think harder sweetie.
yes

[Anonymous No.11485910]

>>11485821
>Any element is written uniquely as a sum of finitely many elements of the base
Not the guy you respond to, but the statement is trivially false.

Take R^2.
In the base e1=(1,0), e2=(0,1), the vector (sqrt(2),0) is written sqrt(2)*e1 in that base.
But in the base f1=(1,1), f2=(-1,1), the same vector is written as f1+f2.

So no, it's basically never unique.

[Anonymous No.11485913]

nevermind, misread claim

[Anonymous No.11486053]

If I have [math] f(x) \in C^{\infty}_c(\mathbb{R}) \subseteq \mathcal{S}(\mathbb{R}) [/math], then I can take its Fourier transform [math] \mathcal{F}(f) = F(\xi) \in \mathcal{S}(\mathbb{R}) [/math].
My question is: can I make sense of [math] \mathcal{F}^{-1} \left \{ F(\xi)/\cos(k \xi) \right \}[/math]? Where does it belong?
And what would happen if f is not a test function but something bigger like [math] L^2 \cap C^{\infty} [/math]?

[Anonymous No.11486054]

>>11484795
Let [math]V[/math] be a vector space over a field [math]K[/math]. We say that a set [math]L[/math] is linearly independent if, for any [math]\{ l_1, \cdots , l_n \} \subseteq L[/math] and [math]\{ k_1 , \cdots , k_n \} \subseteq K[/math], [math]\Sigma_{i=1}^n k_il_i = 0[/math] imples that [math]k_i=0[/math] for every [math]i[/math].
We call a maximal linearly independent subset of [math]V[/math] a basis.
Theorem One: For any basis [math]B[/math], any element [math]v \in V[/math] can be written as a finite linear combination of elements of the basis.
Proof: Assume [math]v[/math] cannot be written as a finite linear combination of elements of [math]B[/math]. We will show that [math]B \cup \{ v \}[/math] is a linearly independent set.
Assume that, for some [math]\{ b_1 , \cdots , b_n \} \subseteq B \cup \{ v \}[/math] and some [math]\{ k_1 , \cdots , k_n \}[/math], not all [math]k_i =0[/math], we have [math]\Sigma_{i=1}^n k_ib_i = 0[/math]. If [math]v = b_j[/math] with [math]k_j \neq 0[/math] for some [math]j[/math], we then have [math]\Sigma_{i=1, ~ i \neq j}^n k_i b_i = -k_j v[/math], and [math]v =[ \Sigma_{i=1, ~ i \neq j}^n k_i b_i ]/k_j[/math], and thus [math]v[/math] can actually be written as a finite linear combination of elements of [math]B[/math], which violates the hypothesis.
Assume none of the [math]b_j=0[/math] or that [math]b_j = v[/math] and [math]k_j = 0[/math]. Then, by removing [math]v[/math] from the sum if necessary (since it doesn't actually contribute to it), we have [math]\Sigma_{i=1}^n k_ib_i = 0[/math] with all the [math]b_i \in B[/math], and thus, by the linear independence of [math]B[/math], all [math]k_i[/math] equal zero.
Theorem two: For a vector space [math]V[/math] and a basis [math]B[/math], any element [math]v \in V[/math] can be written as a unique finite linear combination of elements of [math]B[/math].

[Anonymous No.11486057]

>>11486054
Proof. Assume that [math]v = \Sigma_{i=1}^n k_i b_i[/math] and [math]v = \Sigma_{j=1}^l k_j b_j[/math]. Then, [math]0=v-v = \Sigma_{i=1}^n k_i b_i - \Sigma_{j=1}^l k_j b_j[/math], and linear independence guarantees all [math]k[/math] zero.
Theorem three: Any non-trivial vector space admits a basis.
Proof: We order the set of linearly independent subsets by inclusion. Because the vector space is non-trivial, it contains some nonzero v, and then [math]\{ v \}[/math] is a linearly independent subset, which shows that the set of linearly independent subsets is non-empty.
Assume we have a chain [math]B_{ \lambda}[/math], [math]\lambda \in \Lambda [/math]. We claim that [math]B = \cup _{\lambda \in \Lambda} B_{\lambda}[/math] is linearly independent. Assume it isn’t. Then, for some [math]\{ b_1 , \cdots , b_n \} \subseteq B[/math] and [math]\{ k_1 , \cdots , k_n \} \subseteq K[/math], we have [math]\Sigma_{i=1}^n k_ib_i = 0[/math]. Because [math]\{ b_1 , \cdots , b_n \} [/math] is a finite set, there is some [math]\eta \in \Lambda[/math] such that [math]\{ b_1 , \cdots , b_n \} \subseteq B_{ \eta}[/math]. Then [math]\Sigma_{i=1}^n k_ib_i = 0[/math] implies all [math]k_i[/math] zero because [math]B_{ \eta}[/math] is linearly independent, and [math]B[/math] is linearly independent.
By Zorn’s lemma, there’s a maximal linearly independent subset of [math]V[/math], a basis.

[Anonymous No.11486061]

>>11486057
Theorem 4: Any real or complex vector space admits a norm.
Proof: We choose a basis [math]B[/math] of V. For [math]v \in V[/math], we can write [math]v = \Sigma {i=1}^n ki b_i[/math]. This is well defined, because the linear combination exists, is unique, and is finite. Set [math]f(v) = \Sigma_{i=1}^n |k_i|[/math]. [math]f(v)=0[/math] if and only if [math]v=0[/math] follows trivially. Similarly, [math]f( \lambda v) = \Sigma_{i=1}^n | \lambda k_i| = \lambda \Sigma_{i=1}^n |k_i|[/math]. Finally, we have [math]u = \Sigma_{i=1}^n u_i b_i[/math] and [math]w = \Sigma_{i=1}^n w_i b_i[/math], where we’ve hidden the process of reindexing, etc. Then [math]f( u + w) = \Sigma_{i=1}^n |u_i+w_i| \leq \Sigma_{i=1}^n |u_i| + \Sigma_{i=1}^n |w_i| \leq f(u) + f(w)[/math].

[Anonymous No.11486071]

>>11486057
Theorem 4: Any real or complex vector space admits a norm.
Proof: We choose a basis [math]B[/math] of V. For [math]v \in V[/math], we can write [math]v = \Sigma_{i=1} ^n k_i b_i[/math]. This is well defined, because the linear combination exists, is unique, and is finite. Set [math]f(v) = \Sigma_{i=1}^n |k_i|[/math]. [math]f(v)=0[/math] if and only if [math]v=0[/math] follows trivially. Similarly, [math]f( \lambda v) = \Sigma_{i=1}^n | \lambda k_i| = | \lambda | \Sigma_{i=1} ^n |k_i|[/math]. Finally, we have [math]u = \Sigma_{i=1}^n u_i b_i[/math] and [math]w = \Sigma_{i=1}^n w_i b_i[/math], where we’ve hidden the process of reindexing, etc. Then [math]f( u + w) = \Sigma_{i=1}^n |u_i+w_i| \leq \Sigma_{i=1}^n |u_i| + \Sigma_{i=1}^n |w_i| \leq f(u) + f(w)[/math].

[Anonymous No.11486278]

Hello my friends, do dilution ratios change to scale? I use 6% sodium hypo chloride bleach at home to sanitize tile floors. The ratio is 1 1/2 cup per one gallon of water. I use this to clean my 2000 square foot home. If I needed to sanitize a 10000 square foot warehouse that has concrete instead of tile would I need to double the dilution ratios or just make more bleach when solution is saturated with dirt? The person I'm working with is of the mindset that because you're you're cleaning concrete instead of tile and the facility is larger then 2000sqf you have to double or triple the amount of bleach. Is that correct or just a waste of bleach? It absolutely reeks of bleach for half an hour after he cleans.

[Anonymous No.11486352]

I want to start studying graviton scattering and gravitational corrections in QFT processes without touching supersymmetry or strings. Does anyone have a good paper/book/notes that i can look at? Thanks

[Anonymous No.11486380]

How do I compute limits like these with Landau notation.

[math]\lim_{x\rightarrow 0} \frac{e^{2x}-e^{2x^2}-\sin{2x} }{\sin{x} - x}[/math]

[Anonymous No.11486544]

Explain Asymptomatic diseases to me? Does not showing any symptoms also mean the disease won't hurt you? Will symptoms show up later on? Or will my body get fucked without showing any symptoms? Or am I immune to the disease while being a carrier?

[Anonymous No.11486590]

Disclaimer: I also posted this on /fit/

All pools are closed, so I'm thinking of going swimming in my local lake. The water is still pretty cold, it's my understanding that a neoprene wet suit is very suitable for this situation. However, I don't have a neoprene wet suit and I won't be able to get one now because of Corona...

Are there any alternative clothing articles that can be used for warmth?

[Anonymous No.11486653]

Should I minor in csse? I've got 2 year left in my mathematical visualization major and a mo minor would add like 2 more quarters? I fell for the programming meme so that's what I wanna do.

[Anonymous No.11486849]

>>11486054
You're missing the point sweetie. I did not object to the fact that every vector can be written as a finite linear combination [math]in~the~direct~limit[/math] [math]\mathcal{V} =\lim\limits_{\rightarrow}V[/math], that's obvious to anyone that's already taken intro linear algebra. My point was that this endows the direct limit topology on [math]\mathcal{V}[/math], namely the weakest topology in which the projections [math]p:\mathcal{V}\rightarrow V= \operatorname{Span}\mathcal{B}[/math] are continuous; and indeed we must have a topology, as the moment you endow a norm the boundedness of [math]p[/math] becomes synonymous with continuity of [math]p[/math]. I'm saying this is a specific topology that absolutely does [math]not[/math] encompass "all" normed linear spaces. If you wanted to bring in topology in your objection you have to understand what it entails first.
>>11486053
>can I make sense of
Yeah, you can compute it with residues. Starting with a test function its Fourier transform also ends up a test function; using Faltung theorem [math]\mathcal{F}^{-1}(F(\xi)/\cos(k\xi)) = f(\xi) \ast \mathcal{F}^{-1}(\cos(j \xi))[/math] we know that this is also compactly supported and smooth. Though note that [math]\mathcal{F}(\cos(k\xi)) =\int\frac{d\xi}{2\pi}\cos(k\xi) = \delta(k)[/math] in the sense of distributions so you have to evaluate the convolution in [math]\mathcal{S}'[/math].
>what would happen if f is not a test function
Then you land outside of it, until you hit [math]L^2[/math]. By Parseval [math]\mathcal{F}[/math] is an automorphism and preserves the [math]L^2[/math]-inner product, so in a sense [math]\mathcal{S}'[/math] is the "biggest" space you can evaluate [math]\mathcal{S}[/math] and their Fourier transforms on. If you enlarge [math]\mathcal{S}[/math] you shrink your corresponding [math]\mathcal{S}'[/math].

[Anonymous No.11486852]

>>11486590
>However, I don't have a neoprene wet suit and I won't be able to get one now because of Corona...
You can't order a wet suit online? The postal service isn't shutting down, and I can't imagine wetsuits are a high-demand item right now.

[Anonymous No.11486857]

>>11486849
Oops, of course I meant [math]\mathcal{F}^{-1}(\cos(k\xi)^{-1})[/math].

[Anonymous No.11486908]

Is this graph Hamiltonian, with each VERTEX being visited exactly once, on an open walk/trail/path? It's a representation of a puzzle game level which, If I've interpreted and modeled everything correctly, must be Hamiltonian. I keep getting stuck, with multiple vertices left out. 43 vertices, 57 edges. Any useful properties/lemmas here?

If anyone cares to look, the level is #14 in this. https://armorgames.com/connecty-game/18884?fp=ng Tedious to load and skip levels, but you can arrow to the level after a few minutes. The level also does have an extra condition on certain locked tiles/vertices and previous steps, but I ignore that for the purpose of the present question.

[Anonymous No.11486909]

>>11486852
I heard something about Amazon only delivering essential items now, but I didn't check if that's actually true. Guess i should go check it out.

[Anonymous No.11486923]

>>11486852
AHAHA look at this fag, he make mistakes!
I bet Jacob Lurie doesn't make mistakes.
Mmm Jacob, give me your cummies; slurpslurpslurp

[Anonymous No.11486943]

>>11486909
They're not ONLY delivering essentials, they're just prioritized over non-essentials. It'll take a couple more days than usual to get it, but it will arrive.
Or you could just order from a sporting goods store who is probably experiencing minimal demand right now and doesn't have the "millions of food orders a day" issue to deal with.

[Anonymous No.11486955]

>>11486908
You know that tail on the right has to be the beginning of a path, so follow it to the first intersection.
From there, it can either go down, or to the left. In either case, the path not taken is left behind as a dead end. You know that will have to be the end of the path.
Your first problem is that triangle at the top: whether it's part of the beginning or the end path doesn't matter. It has to be a third end.
If you can only draw one non-branched path, this problem is impossible.

[Anonymous No.11486961]

I'm having a derp moment: how do I construct the projection matrix onto a given subspace?

So let's say I have two Hermitian matrices which don't necessary commute, [math]A, B \in \mathbb{C}^{n \times n}[/math]. I diagonalize [math]B = V \Lambda_B V^\dagger[/math] and pick a subset of its eigenbasis as the spanning set of the subspace I'm interested in. To "project" B, I can simply use its diagonal representation [math]\Lambda_B[/math] and do something like numpy.delete to remove the rows and columns outside the subspace.

How should I do this for [math]A[/math]? I thought maybe you can do something like [math]V^\dagger A V[/math] to rotate it into the [math]B[/math] eigenbasis, then remove the same rows and columns. But this seems to be plagued with tons of numerical fuzz and I don't even seem to preserve Hermiticity of the (basis changed) matrix. (For the record, I have confirmed that [math]V[/math] is as unitary as I can get it, i.e. up to numerical precision.)

Furthermore, I don't know how to get back into the "standard basis". Say my subspace has dimension [math]m < n[/math]; then my new projected, truncated matrices [math]\tilde{\Lambda}_B[/math] and [math]\widetilde{V^\dagger A V}[/math] are [math]m \times m[/math]. I can't invert the unitary transformation now, since the dimensions don't match up, and something like truncating [math]V \mapsto \tilde{V}[/math] doesn't work either, since [math]\tilde{V}[/math] won't even be unitary anymore.

I'm sure the answer is supposed to be something like an orthogonal projection [math]\Pi_S[/math] onto the subspace [math]S[/math], and I should compute [math]\Pi_S A \Pi_S[/math] and [math]\Pi_S B \Pi_S[/math], and then delete rows and columns "accordingly" (that part is also unclear), but I can't recall how to construct this matrix.

[Anonymous No.11486968]

>>11486955

Yes, I've been having similar thoughts. Thanks for the reply at least. It's possible I'm missing/misrepresenting an edge or two, but I doubt it, I've been looking at the level carefully for over a day now.

[Anonymous No.11486976]

>>11486908

Well fuck my ass, I think I just solved my own problem. Stand by, I may have something, maybe not.

[Anonymous No.11486979]

Yes, I've solved the level, stand by for a Hamiltonian path of the above, thereby answering my own stupid question.

[Anonymous No.11486993]

>>11486961
I don't really remember the classical method, but here's what I would do.
Compute an orthonormal basis for the subspace through Gram-Schmidt.
Notice that [math]P_w[/math] (the projection on [math]span(w)[/math] ) is a classical computation of [math]P_w(u) = w \langle w, v \rangle = w w^T v = (ww^T)v[/math].
Then you just sum the matrices [math]ww^T[/math] along the orthonormal base.

[Anonymous No.11487033]

>>11486993
Okay, so it really is just the sum of rank 1 projectors. Thanks, I'll try it.

The eigenbasis of [math]B[/math] that I use to construct the projector *should* be orthonormal, since I'm just taking them from the columns of [math]V[/math], which is unitary. So I think I can just use those.

[Anonymous No.11487042]

>>11487033
>it really is just the sum of rank 1 projectors
I'll emphasize again that the base needs to be orthogonal, but yes.

[Anonymous No.11487047]

>>11486849
>>11486857
Thank you, but I have some problems with your answer.
>Starting with a test function its Fourier transform also ends up a test function
If I start with a test function, its transform is never a test function (except for the constant 0).
-I'm interested in the transform of [math] \cos(k \xi)^{-1} [/math], not [math] \cos(k \xi) [/math]
>you can compute it with residues
How can I do it?

[Anonymous No.11487051]

Answering my own above stupid graph question:

The model given above has several mistakes. Its left hand side is completely wrong, it misses one edge on the top right tail, and certain points are imagined within the central large square region. Once these are straightened out, it becomes straightforward to walk a an open path in the correct model, a demonstration that the graph is Hamiltonian, a requirement of the game's levels, all of which can be similarly modeled as various graphs.

[Anonymous No.11487075]

>>11487047
By a standard result the regularity of [math]f[/math] determines the (polynomial) boundedness of [math]\mathcal{F}f[/math], but yes, it is generally not compactly supported; this is why Schwarz picked to work with the tempered test functions instead.
>I'm interested in the transform of [math]\cos(kξ)^{−1}[/math], not [math]\cos(kξ)[/math]
I'm aware. I merely wanted to illustrate that, with how ill-behaved [math]\sec[/math] is on [math]\mathbb{R}[/math], it can't be more well-behaved than [math]\cos[/math] and even just Fourier transforming [math]\cos[/math] takes you into the distributions.
>How can I do it?
By residue theorem [math]\int_\mathbb{C} dz f(z)\csc \pi z = \sum_{n\in\mathbb{Z}}f(z) [/math] for holomorphic [math]f[/math] that vanish at (complex) infinity. Complexify [math]x\rightarrow z[/math], shift [math]z \rightarrow z+\frac{\pi}{2}[/math] then evaluate the Fourier transform with a Poisson-like sum [math]\sum_{n\in\mathbb{Z}} f(n)e^{in\xi}[/math]. This is just a sketch btw, you can work out the details.
>how do I evaluate the sum
Depends on what [math]f[/math] is, but in general dunno.

[Anonymous No.11487134]

>>11487075
Wait a second right there.
The Schwartz space contains non-trivial analytic functions?

[Anonymous No.11487139]

>>11487134
Nevermind, it doesn't.

[Anonymous No.11487142]

>>11487075
>[math]\sum_{n\in\mathbb{Z}}f(z)[/math]
Meant [math]f(n)[/math] obv fuck

[Anonymous No.11487230]

>>11487134>>11487139
of course it does. any polynomial is in the Schwartz space. Also the typical example of function in the schwartz space [math] e^{-x^2} [/math]

[Anonymous No.11487241]

>>11487230
sorry not polynomials

[Anonymous No.11487242]

>>11487230
>polynomial
>literally always unbounded on the real line
>in the Schwartz space
Good point on [math]e^{x^2}[/math], tho, I completely misapplied the maximum principle.

[Anonymous No.11487283]

Continuing the autism, for a moment...

The next level (15) calls for the same thing, another Hamiltonian path. This time, I drew it out first, and used the graph first to produce the in-game result. Once applied, the extra conditons worked out, and the solution worked. Idea: drawing the planar (an abuse of notation) graph beforehand can be a relief for the imagination, once the structure/topology is understood properly.

The game under consideration is part of a family of "Hamliton-path-like" puzzle games, often involving cubes and paths of square tiles, which are to be walked continuously with certain other constraints.

[Anonymous No.11487298]

>>11487075
do you have any reference where I can find an example of a similar application of the residue thm?

[Anonymous No.11487585]

>>11487283
you made a little error in the top left but its fixable

how do u know if paths are hamiltonian without testing?

[new No.11487590]

CHECK out the NEW thread

>>11487588
>>11487588
>>11487588
>>11487588
>>11487588

checked

[Anonymous No.11487703]

>>11487585

Yes, you're right, but I actually solved the level, which actually has that structure, so I must have fixed it unconsciously. At that point, it solves itself since choices are eliminated.

To answer your question, the reason why I know that such-and-such graph is hamiltonian without testing, is because I'm modeling video game levels which are supposed to be solveable, i.e. isomorphic to hamiltonian graphs. I've been trying to model them in simpler, 2D terms (cosmetically, the game appears 3D but really isn't). Thanks for catching another goof.

[Anonymous No.11487723]

>>11487703
i meant how do u know a graph is hamiltonian

[Anonymous No.11487741]

>>11487723

By being able to "take a walk" along it, that visits each of its edges exactly once. The notion of a Hamiltonian graph is complementary to that of the Eulerian graph where in the latter each /edge/ is traversed exactly once. These notions entail precise definitions of "walk", "trail", "path", "closed" (starting and ending at the same spot), "open" (stard and end at two different spots), and various closely related species of cases. I even pulled a Chartrand book of the shelf last night when I was thinking about this (productive quarantine learning). I know almost nothing about graph theory beyond meme popsci basics but applying it to puzzle games is proving to be a nice exercise. Here is an example of another "hamiltonian-like" game:

https://armorgames.com/play/4458/on-the-edge

I just never thought of these games in terms of graph theory before, it's useful.

[Anonymous No.11487772]

>>11487741
i knew that i meant how you could doit without outright testng the path, but oh well

as far as eulerians, i know there are some conditions to excise it from possibility like a mismatch in numbers. theres also, the septagon. did u know you can hamiltonianally walk a septagon, but not a hexagon, or octagon, or any even n-gon (at least i think thats what it was but i forgot but its an ez proof)