/sqt/ /qtddtot/

[Anonymous No.10369197]

Itty bitty questions thread.

[Anonymous No.10369208]

>>10369197
There's one of these up already, dumb kurisuposter.

[Anonymous No.10369210]

>>10369208
He didn't put sqt in the title so it's horrible to find in the catalog, dumb nothingposter.

[Anonymous No.10369453]

what does the image say

[Anonymous No.10369467]

Why can't I build muscle?

[Anonymous No.10369481]

>>10369197
Ok, so I asked the code chimps over on /g/ and apparently their IQ wasn't high enough for this:

is it possible to generate 0xFFFFFFFF (32-bit word with 1s at odd positions) using only integer constants 0 through 255 (0xFF) and a limited number of the operations:
! ~ & ^ | + << >>
(where the right shift is arithmetic)

[Anonymous No.10369514]

>>10369453
"Fuck off to /fit/! Fucking building muscles faggot!"
>>10369481
Could you write it out as a math question?

[Anonymous No.10369734]

>>10369453
Language fag here
she says: die! not him.. die!
the characters to the left say: gata gata gata (sounds for typing furiously)

[Anonymous No.10370067]

So this question asks to find average and reactive powers, but all I did was use V*I.

When am I supposed to use (1/2)*Vm*Im*cos(Ov-Oi)
Where Ov is angle of voltage and Oi is angle of current?

[Anonymous No.10370088]

>>10369481
>is it possible to generate 0xFFFFFFFF (32-bit word with 1s at odd positions) using only integer constants 0 through 255 (0xFF) and a limited number of the operations:

FF is all ones retard.

for(int i=0; i<sizeof(n); ++i){
[math]~~~[/math] n<<=8;
[math]~~~[/math] n|=0b01010101;
}

or unroll the loop

n<<=8;
n|=0b01010101;//8bit chars
n<<=8;
n|=0b01010101;//16bit shorts
n<<=8;
n|=0b01010101;
n<<=8;
n|=0b01010101;//32bit ints
n<<=8;
n|=0b01010101;
n<<=8;
n|=0b01010101;
n<<=8;
n|=0b01010101;
n<<=8;
n|=0b01010101;//64bit long long ints

[Anonymous No.10370137]

not sure if i posted the wrong thread but >>10370124

[Anonymous No.10370158]

>>10370137
>>>/g/

[Anonymous No.10370160]

>>10370137
>is this an actual address
you're right, that is a dumb question
yeah you did something wrong, not sure what though

[Anonymous No.10370320]

>>10369197
Can influenza be perpetuated by ass gas?

[Anonymous No.10370753]

Is there a field in fluid dynamics that deals with how solids behave with high mechanical energy?

[Anonymous No.10370793]

>>10369208
STFU, Kurisu posting is a noble thing regardless of the stupidity of the poster.

[Anonymous No.10370795]

>>10369197
Why is mustard gas called like that?

[Anonymous No.10371141]

How do you actually specialize once you graduate med school? Looking into radiology but I don't want to graduate and realize I didn't kiss enough ass or gun enough during school to actually get the training.

[Anonymous No.10371281]

Does separability of Hamiltonian imply that the wave function is separable?

[Anonymous No.10371561]

Will someone in charge of hiring slaves for a lab know I'm a brainlet (I am, but I don't want them to know that) from reading my resume?

[Anonymous No.10371589]

>>10371561
didn't read but
>verbose subjective shit to hide lack of qualities and prestige
into le trash it goes

[Anonymous No.10371597]

>>10371589

[Anonymous No.10371723]

Are the unities Newton and m.s^-2 equivalent please?

[Anonymous No.10371724]

>>10371723
look it up

[Anonymous No.10371727]

>>10371723
No, [math]N=kg m s^{-2}[/math]

[Anonymous No.10371765]

>>10371727
ok thanks!

[Anonymous No.10372284]

I'm feeling really silly, but if we have a function defined in a punctured neighborhood of [math]a[/math], then how do we even use the difference quotient to calculate derivatives in that point? It's not possible, right? Or at least not well defined.

[Anonymous No.10372314]

>>10372284
The function can only assume one value at a and remain continuous. Evaluate that, then calculate the derivative at a normally.
Of course, if there is such a value.

[Anonymous No.10372322]

>>10372314
Nevermind, I'm retarded. I read "neighborhood of a" as "punctured neighborhood of a" in the notes. Of course if the function is not defined at a, we can't take any derivatives there.

[Anonymous No.10372336]

How do I get from the top two equations to the bottom two?

[Anonymous No.10372352]

>>10372336
Look up how to solve second order differential equation with constant coefficients.

[Anonymous No.10372394]

>>10372352
Everywhere I look, I just get this.
Do I just assume that this is the solution? I can’t find a more laborious method for solving it

[Anonymous No.10372425]

>>10372336
It's a linear ODE, the solutions to which contain only terms of the form t^n*e^kt (and n>0 only occurs if the characteristic equation has repeated roots). See also the response to this question in the previous thread:
>>10368480

[Anonymous No.10372484]

>>10372394
The systematic approach is to use the Laplace transform: L{f'(t)}=s*L{f(t)}-f(0). When applied to a linear ODE, you get L{f(t)} as a rational function of s. Find the roots of the denominator, factor it, and use partial fractions to decompose the function to terms of the form k/(s-a)^n, then take the inverse Laplace transform of each term (which is 1/(n-1)!*t^(n-1)*e^at).

So in the case of >>10372336 you get
L{d^2V/dz^2}- L{γ^2*V}=0
=> s^2*L{V}-s*f(0)-f'(0)-γ^2*L{V}=0
=> L{V}=(s*f(0)+f'(0))/(s^2-γ^2)
= (s*f(0)+f'(0))/(s+γ)*(s-γ)
= a/(s+γ) + b/(s-γ)
= ((a+b)*s + (b-a)γ)/(s+γ)*(s-γ)
=> a+b=f(0), b-a=f'(0)/γ => a=(f(0)-f'(0)/γ)/2, b=(f(0)+f'(0)/γ)/2
V=L^-1{a/(s+γ) + b/(s-γ)}
=L^-1{a/(s+γ)} + L^-1{b/(s-γ)}
=a*L^-1{1/(s+γ)} + b*L^-1{1/(s-γ)}
=a*e^-γz + b*e^γz

[Anonymous No.10372568]

>>10369197
How do I into implicit partial differentiation?
Let's say I have the equation [math]x^9z^4+sin(y^8z^4)−9=0,[/math] for which I am to find [math]\frac{dz}{dx}.[/math] Would I carry over the terms so that it becomes [math]x^9z^4=9−sin(y^8z^4)[/math]? Would I expand the terms and differentiate them separately? I'm super fucking confused

[Anonymous No.10372571]

>>10369197
>>10369197
How do I into implicit partial differentiation?
Let's say I have the equation [eqn]x^9z^4+sin(y^8z^4)−9=0,[/eqn]
for which I am to find [math]\frac{dz}{dx}.[/math] Would I carry over the terms so that it becomes [math]x^9z^4=9−sin(y^8z^4)[/math]? Would I expand the terms and differentiate them separately? I'm super fucking confused

[Anonymous No.10372633]

A good book on uncertainty of measurement and how to deal with correlated uncertainties and estimate their correlation coefficient?

[Anonymous No.10372642]

can /sci/ tell me what this integral is
pic related

[Anonymous No.10372662]

Do you know how to prove that the dimensions of R as a vector space over Q is uncountable? It's quite easy to prove that it's infinite but I have no idea on how to find an uncountable set of linearly independent vectors.
>>10370793
Based and redpilled Kurisuposter

[Anonymous No.10372670]

>>10372662
>how to find an uncountable set of linearly independent vectors
That's not the way to go about it. Suppose that there is a countable set of vectors that spans R, and find a contradiction.

[Anonymous No.10372689]

>>10371281
If by "wavefunction" you mean a generalized distribution-valued holomorphic section of the tensor Hermitian bundle [math]\mathcal{H}_1\otimes\mathcal{H}_2\rightarrow X[/math] then no, but if you mean the eigenfunctions of the separable Hamiltonian [math]H = H_1 \otimes H_2, H_{1,2}\in \mathcal{B}(\mathcal{H}_{1,2})[/math] then yes via the spectral theorem.

[Anonymous No.10372691]

For some reason I'm having a hard time proving this is true for all natural numbers n. I think it might be due to a hole in my maths knowledge I don't know. How would I even go about comparing the two in a way where their 'size' difference is obvious? ( I have to prove this with PMI)

[Anonymous No.10372941]

>>10369734
the second word also means die, it's a meme word.
not sure how to translate it exactly but the idea is she means die for real, not just as a meme
see https://www.weblio.jp/content/%E6%B0%8F%E3%81%AD

[Anonymous No.10372947]

>>10369481
>their IQ wasn't high enough
ironic considering your question is malformed
and the answer is obviously yes of course

[Anonymous No.10373202]

Do you guys use Word to write your papers/reports? I know mathfags cream over LaTex, but what about the rest of you?

[Anonymous No.10373212]

>>10373202
Libreoffice because it's free.
Some niggas I know use google doc.
The problem with both of them is they can't graph for absolute shit, so I borrow mom's pc, which has Word.
But Latex is essentially the only thing that's useable for maths. You need that [math]\mathcal{O}[/math] for algeo and nothing actually substitutes it.

[Anonymous No.10373220]

>>10373202
If the document is a few pages then word is fine. If you're working on a thesis that's 100+ pages long with countless equations, [math] \LaTeX [/math] is the only way to go. You'd be out of your mind to use word in that situation.

t. engineering PhD candidate

[Anonymous No.10373232]

>>10372571
I don't know if this is what you're looking for, but you can solve it with finite differences numerically.

[Anonymous No.10373285]

>>10372571
>>10372571
You just have to note that [math]z[/math] is (implicitly) a function of [math]x[/math], and just use the chain rule: ie, since [math]z=z(x)[/math], then [math]f(z)=f(z(x))[/math] and [math]\frac{df}{dx}=\frac{df}{dz}\frac{dz}{dx}[/math]. Similarly for [math]y=y(x)[/math].

Applied to your function, you get [eqn]\frac{d}{dx}\left(x^9z^4+\sin(y^8z^4)-9\right)=9x^8z^4+x^9\cdot 4z^3\frac{dz}{dx}+\cos(y^8z^4)\cdot(8y^7x^4\frac{dy}{dx}+y^8\cdot4z^3\frac{dz}{dx})=0[/eqn]
Now you have to solve for [math]\frac{dz}{dx}[/math] which is just algebra, rearranging the equation: [eqn]\frac{dz}{dx}=\frac{-9x^8z^4-8y^7x^4\frac{dy}{dx}\cos(y^8z^4)}{4z^3(x^9+y^8)}[/eqn]

[Anonymous No.10373621]

>>10373212
Bro, you can get pretty cheap (and legit) m$ office licenses if you look around. I bought a 2013 one for like 10 bucks about 6 months ago, no problems so far. I also got windows years before for even less.

[Anonymous No.10373646]

why do I like to touch and flex my muscles when I have doms? surely my body would want to avoid the pain right?

[Anonymous No.10373747]

>>10373646
Shut up lanklet

[Anonymous No.10373892]

>>10373747
hold on how do you know I'm a lanklet
something's fishy

[Anonymous No.10373917]

>>10373892
It’s pretty obvious. I bet you can’t even 1/2/3/4. Probably far from it. I bet you don’t even know what that is, lanklet.

[Anonymous No.10374030]

>>10372642
Whoever came up with that expression should be shunned. Anyway, it trivially reduces to the area of half the unit circle, so it's pi/2.

[Anonymous No.10374219]

>>10369197
I have that
[math]cos(\alpha)=\frac{a}{b}[/math]
How do I find unambiguously if [math]0<\alpha<\pi[/math] or [math]\pi<\alpha<2\pi[/math]

[Anonymous No.10374220]

>>10374219
Nice one me

I have that
[math]cos(\alpha)=\frac{a}{b}[/math]

How do I find unambiguously if
[math]0<\alpha<\pi[/math]
or
[math]\pi<\alpha<2\pi[/math]

[Anonymous No.10374221]

>>10374220
Fuck it you get the idea

[Anonymous No.10374240]

>>10374219
>>10374220
you dont

[Anonymous No.10374241]

>>10374219
If you look at the graph of cos, you'll know you can't.

[Anonymous No.10374249]

>>10371723
[math] \displaystyle

\left \{
\begin{array}{l}
P=UI\\
P= \dfrac{W}{t}= \dfrac{F \cdot s}{t}= \dfrac{ma \cdot s}{t}
= \dfrac{m \dfrac{v}{t} \cdot s}{t}= \dfrac{m \dfrac{s/t}{t} \cdot s}{t}
= \dfrac{m \cdot s^2}{t^3}
\end{array}
\right.
\\\\
\left \{
\begin{array}{l}
W=V \cdot A \\
W= \dfrac{J}{s}= \dfrac{N\cdot m}{s}= \dfrac{kg \cdot \frac{m}{s^2} \cdot m}{s}
= \dfrac{kg \cdot m^2}{s^3}
\end{array}
\right.

[/math]

[Anonymous No.10374397]

Why does [math]e^{2ln(\frac{1}{2})} = \frac{1}{4}[/math]?

[Anonymous No.10374401]

>>10374397
[math]n ~ ln(x)=ln(x^n)[/math]

[Anonymous No.10374408]

>>10374401
Oh.. Yeah, forgot about that one. Thanks

[Anonymous No.10374615]

this is absolute basic physics I... and I still manage to fuck it up somehow.

average speed is displacement over time.
5689/396 is 14.37 which isn't right.
(20+25+75)/3 is apparently within 10% of the correct answer, but that shouldn't be correct either since it doesn't account for the actual distance traveled

[Anonymous No.10374618]

>>10374615
The entire trajectory gives 9,300m. Divided by the time we have 23.4848, which is within 10%.

[Anonymous No.10374620]

>>10374615
Check out the harmonic mean.

[Anonymous No.10374624]

>>10374615
>average speed is displacement over time.
It's total distance over time, which is equal to the weighted average of the speeds over each time interval i.e. (20*3 + 25*2.6 + 30*1)/6.6

[Anonymous No.10374631]

>>10374624
>>10374618
Alright, that was the right answer.
> (20*3 + 25*2.6 + 30*1)/6.6
I guess I'm just a bit confused at how this gives the correct result considering it didn't convert units, unless converting the minutes to seconds isn't necessary.

[Anonymous No.10374638]

>>10374631
To convert into seconds you just multiply both the numerator and denominator by 60, which changes nothing.

[Anonymous No.10374641]

>>10374638
That's what I was doing. Not sure how I fucked it up that bad; I'll figure it out. Thanks for the help.

[Anonymous No.10374701]

how would you prove that the sum of a rational number plus an irrational number is irrational.

[Anonymous No.10374721]

>>10374701
Contradiction.

[Anonymous No.10374728]

>>10374721
I think I got it, if x is a irrational then,
a + kx = r/s, s =/= 0, and k =/= 0
x = (r - as)/sk, which is rational

[Anonymous No.10374744]

>>10374728
What?
No, assume a and c are rational, and b is irrational in a+b=c.
But b=a-c, and the rationals are closed under sum.

[Anonymous No.10374760]

>>10374728
That's on the right path, but the k is unnecessary. If a/b+x=c/d => x=c/d-a/b=(bc-ad)/bd which is rational. IOW, the difference between rationals is always rational, so adding an irrational to a rational must yield an irrational.

[Anonymous No.10374802]

>>10373917
I DONT know what that is but can you answer my initial question.

[Anonymous No.10374849]

>>10369197
as a cs undergrad, how to get into static program analysis?

[Anonymous No.10374874]

EE undergrad here. Just started my junior year a few weeks ago.
Should I minor in CS or software engineering? Is it even worth getting a minor? I don’t know where in my schedule I can fit the classes to get a minor, but maybe during my senior year?

[Anonymous No.10374975]

>>10374874
do you plan to actually use the minor to get a more CS or software related job? if not then it is probably not worth it unless you are very very interested in CS

[Anonymous No.10375008]

>>10374975
I do plan on it. I figure most jobs nowadays use software for stuff. Professors at my uni emphasize on stuff saying software is the future since it’s taken over many jobs. My friend graduated as an EE and ended up doing CS stuff at intel and is at grad school for CS now. Don’t know really know if his situation is unique

[Anonymous No.10375043]

Given these 4 equations, how can I solve for the unknowns?

[Anonymous No.10375058]

>>10375043
do a matrix equation of it and solve

[Anonymous No.10375086]

>>10375043
>that cheeky j
>five unknowns
>four equations
Can't be solved.

[Anonymous No.10375091]

>>10375086
Nah I just solved it. j is just root -1

[Anonymous No.10375118]

>>10369197
How long should it take me to go through these books if I put aside 1 hour per day?

[Anonymous No.10375127]

>>10375118
>optics
based

[Anonymous No.10375132]

>>10375008
You should just do it then. Unless it would cost you a lot of money to do the minor. If you are just doing it for programming and software applications then really just do the quickest or easiest minor out of the two (CS and Software engineering), either one will show that you are a little more competent than an average EE for programming

[Anonymous No.10375138]

>>10375118
try it and find out

[Anonymous No.10375143]

>>10375091
>using j for root of -1
"Literally no else uses this" tier notation.

[Anonymous No.10375151]

How do I into undergraduate research? I feel like I shouldve tried to get in at the beginning of the semester, but do I just email or ask a professor or something? I cant really just approach one in person as i dont know their office hours and what not. Not even looking for paid experience, I just want some because Im about to graduate in December and have no idea if grad school is something i want to do

[Anonymous No.10375191]

>>10375143
It's used all the time especially when dealing with electromagnetics or circuits, retard.

[Anonymous No.10375220]

>>10375143
the absolute state of "math" majors

[Anonymous No.10375228]

>>10375143
You know electricity is a thing right

[Anonymous No.10375345]

>>10375143
>tier notation

[Anonymous No.10375533]

>>10375043
>[math]{\bf I}_1 + {\bf V}_1[/math]
>adding ideals and varieties together

[Anonymous No.10375562]

Where can I learn to do the meme every Youtube vid uses to explain derivatives, "For W=F*r, let's assume a tiny change in distance, dr, and that corresponds to a tiny change in work, dW, while we assume that the force remains constant over this tiny dr."

Where do I learn this in more detail? I'd like a dumbed down book on calculus explaining these concepts in much detail to an IQlet.

[Anonymous No.10375642]

I really, really hate this kinematics bullshit.
I feel like I'm flying blind 90% of the time.
I'll try and do something based on the formulas I've been shown, and get an answer.
Which turns out to be wrong.
I'll check the solutions manual and it does it in some completely ass-backwards, unintuitive way

obviously I'm the one in the wrong. Something's just not clicking. Does anyone have any advice on how to figure this shit out the right way the first time?

[Anonymous No.10375646]

>>10375562
Kenn Amdahl's "Calculus for Cats"

[Anonymous No.10375681]

I found (a) by doing 24=Vi+cos(53)2.2
I'm confused, though. Shouldn't this be just the x component of the launch velocity, and not the entire velocity vector?

[Anonymous No.10375740]

>>10375681
I'm starting to wonder if it's this textbook making it so difficult on me.

The solutions manual solution for section (c) mentions this "trajectory equation" which seems necessary to answer the question.
Nowhere in the entire book is this equation mentioned or derived.

[Anonymous No.10375764]

>>10375740
This equation is just Newton's 2nd law applied to this specific case

[Anonymous No.10375772]

>>10375764
If that's the case, we haven't gone over Newton's laws yet, so I'm still not sure why they're using it before they've introduced it

[Anonymous No.10375789]

>>10375681
Jesus fucking Christ the absolute autism of this problem.
Essentially, decompose the position into vertical and horizontal. The equation for the height at a point in time should be just a second degree polynomial, and you just calculate the apex (average of the roots).

[Anonymous No.10375819]

>>10375151
please help a local autist, will i make it to grad school with only 1 semester research

[Anonymous No.10375914]

>>10375819
yeah

[Anonymous No.10376050]

Are multiple integrals linear? Can I split up multiple integrals if two terms are added together?

[Anonymous No.10376052]

God help me...
Given, [math]\displaystyle T= \begin{bmatrix} 2 & 0 \\
0 & -1
\end{bmatrix}[/math] and [math]X=\mathbb{R}^{2}[/math], I'm trying to find the operator norm, [math]||T||[/math].

By definition, [math]||T|| = \sup\limits_{||x||\neq 0} \frac{ ||Tx|| }{||x||}[/math]. Let [math]x=(a,b)\in \mathbb{R}^{2}[/math]. Then, [math]\displaystyle ||T|| =\sup \frac{\sqrt{4a^{2}+b^{2} } }{\sqrt{a^{2}+b^{2} } } [/math] . Is this the answer? Does it simplify further? Is there an inequality I should be applying? Can I say, let [math]a=b=c>0[/math]. Then [math]\frac{\sqrt{4c^{2}+c^{2} } }{\sqrt{c^{2}+c^{2} } } \leq \frac{\sqrt{5c^{2}}}{\sqrt{2c^{2}}} = c\sqrt{\frac{5}{2}}[/math] ?

[Anonymous No.10376055]

>>10376050
You mean like [math]\iiint(f+g)dV = \iiint f dV + \iiint g dV[/math]? then yes

[Anonymous No.10376145]

>>10376052
Divide the numerator and denominator by a to see that your expression depends on only the single variable b/a. Then use calculus to find the maximum of the expression.

[Anonymous No.10376151]

hello, gigantic brainlet here, could someone explain to me why the derivative of x^4 = 4x^3

[Anonymous No.10376159]

>>10376050
>are linear operators closed under composition
Yes.
>>10376151
Because [math] Dx^n=nx^{n-1} [/math].

[Anonymous No.10376160]

>>10376151
power rule: [math]\frac{d}{dx}[x^{n}] = nx^{n-1}[/math]

[Anonymous No.10376197]

>>10376145
thanks m8

[Anonymous No.10376227]

>>10375789
so it's not just me, and the question seems needlessly contrived and esoteric?
You can see how they want me to solve it (in the solutions manual for a similar problem) here >>10375740

[Anonymous No.10376238]

>>10376160
>>10376159
yes, but WHY is this?

[Anonymous No.10376241]

>>10376238
literally a subhuman nigger animal

https://en.wikipedia.org/wiki/Power_rule

[Anonymous No.10376248]

>>10376151
from the definition
[math]lim_{\Delta x \rightarrow 0} \frac{f(\Delta x+ x) - f(x)}{\Delta x} = lim_{\Delta x \rightarrow 0} \frac{(\Delta x + x)^4 - x^4}{\Delta x} = 4x^3,[/math]
which in the general case leads to the rules listed above.

[Anonymous No.10376308]

>>10376238
From the definition of the derivative:
df(x)/dx = lim[δx->0] (f(x+δx)-f(x))/δx

The binomial expansion of (x+δx)^n is x^n+n*δx*x^(n-1)+<other stuff>. So (x+δx)^n-x^n=n*δx*x^(n-1)+<other stuff> (the x^n terms cancel). Dividing by δx gives n*x^(n-1)+<other stuff>. The limit as δx->0 effectively discards <other stuff> leaving you with n*x^(n-1).

[Anonymous No.10376829]

>tfw really shitty at geometry
Any resources for learning?

[Anonymous No.10377064]

Are all Affine functions Linear functions?

[Anonymous No.10377107]

http://www-personal.umich.edu/~pran/jackson/P505/F07_hw10a.pdf

Can someone explain the steps of #1 to me?

[Anonymous No.10377498]

>>10376829
what kind of geometry

[Anonymous No.10377522]

Trying to do some raw computations on [math]e^{T} = \sum_{n=0}^{\infty} \frac{T^{n}}{n!}[/math], where [math]T\in B(X)[/math] is a bounded linear operator ([math]B(X)[/math] is Banach).
Supposing [math]T[/math] is similar to a diagonal matrix, [math]T=SDS^{-1}[/math], [math]e^{T} = \sum_{n=0}^{\infty}\frac{1}{n!}SD^{n}S^{-1} = \sum_{n=0}^{\infty}S\begin{bmatrix} \frac{\lambda_{1}}{n!} & \dots & \dots & 0 \\
0 & \frac{\lambda_{2}}{n!} & \dots & 0 \\
0 & \dots & \ddots & 0 \\
0 & \dots & \dots & \frac{\lambda_{n}}{n!} \end{bmatrix}S^{-1} = S\begin{bmatrix} e^{\lambda_{1}} & \dots & \dots & 0 \\
0 & e^{\lambda_{2}} & \dots & 0 \\
0 & \dots & \ddots & 0 \\
0 & \dots & \dots & e^{\lambda_{n}} \end{bmatrix}S^{-1}[/math].
Does this look right? Can I simplify further?

[Anonymous No.10377527]

>>10374874
Employers don't care about minors, just learn the CS material on your own and make projects that you can discuss in interviews.

[Anonymous No.10377533]

>>10377064
An affine function is y=ax+b.
All linear functions are y=ax.
Unless you're working with some weird definition.
>>10376829
Whichsted've.
>>10377522
Yeah.
IIRC diagonal matrices are the centralizer, and powers of diagonal matrices are also diagonal, so you can: SD^nS^-1=D^nSS^-1=D^n.

[Anonymous No.10377537]

>>10377533
Thanks.

[Anonymous No.10377559]

>>10377533
Wait, nevermind, diagonal matrices only commuted with diagonal matrices.

[Anonymous No.10377609]

>>10377064
> Are all Affine functions Linear functions?
No, although all linear functions are affine.

Linearity requires f(k*x)=k*f(x) and f(a+b)=f(a)+f(b). A corollary of both is that f(0)=0 (where 0 is the additive identity).

Affinity is a weaker condition, namely that f(b)-f(a)=g(b-a) where g is linear. Thus, an affine function consists of a composition of a linear function and a translation.

[Anonymous No.10377641]

>>10369197
What's the strongest non-nuclear EMP you could fit in a car. What would the range for electronic interference, specifically telecommunications, be?

[Anonymous No.10377680]

>>10371141
You specialize in your resindency years, at least in Brazil. Dont know how it works in the rest of the world.

[Anonymous No.10377947]

Anyone have any knowledge of ranking algorithms, specifically Glicko?
How would I go about calculating Glicko results from a tournament result set? I thought calculating each match itself would result in inconsistent data (if you calculate player x once, then again, x's Glicko rating would be different), but not sure how else to do it. How would you go about it?

[Anonymous No.10378078]

>>10377498
>>10377533
Analytical mainly. Would also be interested in reading about other geometry though.

[Anonymous No.10378184]

Can someone give a simple explanation to what the 'variational formulation' of a differential or partial differential equation is? And why is it also called the 'weak formulation'? Is the variational formulation not equivalent to the original problem, and why?

I understand you basically convert the original equation into a system of integral equations, one equation for each test function of your choosing. I read somewhere the variational form should be equivalent to the original problem in the limit of infinite different test functions, is this true?

[CIA No.10378191]

>>10377641
Refrain from posting further.

[Anonymous No.10378253]

how do i show that there are [math] (p-1)/2 [/math] quadratic residues modulo [math] p [/math], by using primitive roots?
what ive got so far, in rough, is:
-there is a primitive root modulo [math] p [/math] as [math] \phi(p-1)>0 [/math]
-if [math] s [/math] is a primitive root, then math] 1, s, s^2,..., s^{p-2} [/math] are all distinct mod [math] p [/math]
-half ([math] (p-1)/2 [/math]) of these are of the form [math] (s^{k})^2 [/math] so are quadratic residues

is this correct and where do i go from here?

[Anonymous No.10378263]

If I put a point at the center of a triangle, and then drew lines from the point to each vertex of the triangle, will the angles created from those lines equal up to 360 degrees?

[Anonymous No.10378280]

why are these wrong?

[Anonymous No.10378288]

if the probability of one event is 8% and the other is 12% what is the probability of at least one of them occurring? how do i calculate something like this? the events are independent btw

[Anonymous No.10378310]

>>10378263
The angles formed between the new lines?
That's true for any polygon and any point inside it.
>>10378280
I can't see the question.
>>10378288
One has a chance of 92% of not happening, and the other of 88%. Multiplying we have a chance of 80.96% of neither happening. The rest gives 19.04%.

[Anonymous No.10378809]

Anyone like graph theory? I'm trying to break this down part by part, but it's just melting my brain.

[Anonymous No.10378939]

>>10378809
That is really badly worded.

It's saying that you can make it so the vertex that has the most neighbors (D = Delta) is adjacent to the D vertices with the next-most neighbors, without changing the overall degree sequence.

[Anonymous No.10378947]

Can somebody tell me why the galilean group can be written as a semidirect product and not simply as a direct product of:

[eqn] Gal(4) = \mathbb{R} ^4 \rtimes ( \mathbb{R} ^3 \rtimes SO(3) ) [/eqn]

I mean what difference does it make in terms of physics? (not very advanced on group theory stuff sory)

[Anonymous No.10378962]

>>10377064
wikipedia is your best friend

[Anonymous No.10379027]

I'm using an iterative method to try and converge on a value, how can I test if is instead diverging due to poor initial guesses?

[Anonymous No.10379042]

>>10379027
Nevermind that question really is stupid

[Anonymous No.10379360]

>>10377522
First of all not all [math]T\in B(X)[/math] are diagonalizable. Second of all [math]T^n = (SDS^{-1})^n \neq S^n D^n S^{-n} \neq SD^nS^{-n}[/math].
>>10378184
This is related to Dirichlet principle: the solution to the Laplace equation on [math]D[/math] is the minimizer of the functional [math]I[u] = \int_D dx|\operatorname{grad}u|^2[/math]. In general one can express PDE's [math]L=0,~ L \in \mathcal{B}(X) \otimes_X \bigwedge TX[/math], linear or otherwise, as the first variation condition for a Frechet and Caratheodory functional [math]I: X\rightarrow\mathbb{R}[/math] after applying Raymond-Dubois. In cases where Raymond-Dubois doesn't hold pointwise or when [math]I[/math] isn't Caratheodory, one can only obtain saddle points of [math]I[/math] in a "weak" sense, i.e. under an integral. This leads to the theory of distributions and generalized functions.
>>10378947
Because the action of rotation [math]O\in O(3)[/math] on a translation [math]T[/math] is [math]O^{-1}TO[/math], not [math]OT[/math]. If you just rotate and don't rotate back then you don't translate to the same point in space.

[Anonymous No.10379431]

>>10379360
>[math]T^n \neq S^nD^nS^{-n}[/math]
[math]T^2=SDS^{-1}SDS^{-1}=SD^2S^{-1}[/math]
which, extended to all n, such that [math]T^n=SD^nS^{-1}[/math], is the equality he actually used.

[Anonymous No.10379435]

>>10379431
>extends
Are you trying to use induction on infinitely many matrices?

[Anonymous No.10379440]

>>10379435
No, I exemplified a computation and claimed that it works for all n without proof because induction sucks to write.

[Anonymous No.10379453]

anyone knows anything about subgrid modeling ? I need to briefly explain what it is and can't for the life of me get on solid grasp on how it actually works

[Anonymous No.10379524]

I am currently taking an intro to proofs course and just have some retarded questions. As you advance through different topics of pure math how to people retain what they learn? Math seems to be do dense. Do you just remember some fundamentals and then specialize in a 2 or 3 areas like number theory, algebra and whatever ? Do you just rederive things with the problem solving skills you have when faced with problems from old topics? My bad if this is incoherent.

[Anonymous No.10379541]

>>10379524
>retain what they learn
I don't. I usually just remember learning it, and when I need it I go back and refresh my memory on it.

I'm as much of a brainlet as you can be in science tho

[Anonymous No.10379865]

is it safe to sleep with a buttplug in my ass? its silicone

[Anonymous No.10379886]

>>10379865
Depends on the lube you're using. Water based should be fine but oil based lube might erode the silicone.
Don't do this everyday though.

[Anonymous No.10379909]

>>10379886
its water based
also fuck you yukarifag, engineeringchad out

[Anonymous No.10379917]

>>10379909
>engineeringchad
>wears a buttplug so sleep
Most I've done is a prostate massager. You're more of a sissy than I am.

[Anonymous No.10379938]

>>10379917
i'll have you know I'm a 6'4" 203lb MAN
im just experimenting

[Anonymous No.10380069]

>>10379917
>>10379938
I just imagined you two having angry sex. Keep it up.

[Anonymous No.10380156]

>>10379524
Learn something once by studying and doing exercises. Then just focus on remembering important theorems and concepts. If you need to remember the little details, it should be as simple as just reviewing your old notes.

[Anonymous No.10380188]

>>10379360
So should I write [math] O(3) [/math] there?

[Anonymous No.10380193]

I really need some help with this guy, I've been banging my head for hours here. I know it's only satisfied for m = 1 aka y = x, but the issue is actually solving this disgusting creature. I keep getting really nasty fractions, and the hint seemed to only make it worse. What the am I missing here?

[Anonymous No.10380761]

Why isn't a graph with no cycles defined as having zero girth? Seems far more intuitive than infinite girth.

[Anonymous No.10380816]

>>10380193
Whenever you have some gnarly differentiation to do, it's better to use Wolfram Alpha or Octave/Matlab than to do it by hand, saves time and stops you heading down blind alleys. Either way, your general approach should be:

Use this substitution:
y(x)=xv(x)

Differentiate it twice:
y'(x)=xv'(x)+v(x)
y''(x)=xv''(x)+2v'(x)

Substitute these into Legendre's equation and simplify to get:
(x-x^3)v''(x)+(2-4x^2)v'(x)=0

Now you can divide by x-x^3 to get the first fraction in your hint. You have a standard equation of the form:
f'(x)+k(x)f(x)=0

The solution is to find a q(x) such that q'(x)=q(x)k(x), then you can multiply both sides by q(x) to get
f'(x)q(x)+f(x)q'(q)=0

And integrate both sides to get
f(x)q(x)=C for some constant C

[Anonymous No.10380830]

>>10380816
(I realise this isn't a complete solution, I'm lazy, let me know if you're still stuck)

Also the Legendre equations are well-studied and have known solutions, if you feel like being a cheeky cunt you can just rip the answer off google.

[Anonymous No.10380934]

>>10380830
God bless anon, I'm at the point where I have v'[x^2+2x]=C_1

Where do I go from here?

[Anonymous No.10380952]

>>10380934
Wait fucked up I.F., should be v'(x(x^2-1))

[Anonymous No.10380960]

>>10369197
Why aren't laser weapons a thing yet? I don't know much about lasers except the basics (mirror, cavity, amplification), but I'd guess the problem with powerful lasers is the power and heating, but both of those could be solved if it was installed in a nuclear carrier, for instance, yet there are none.

[Anonymous No.10381037]

>tfw can't solve a problem I've solved four months back
Am I growing stupider?

[Anonymous No.10381127]

>>10380952
...it should almost definitely be the 2nd partial fraction you're given, so x^2(x^2 - 1).
In case case, divide and integrate to get v.

[Anonymous No.10381169]

>>10380960
Because even a powerful laser isn't a particularly effective weapon.

[Anonymous No.10381191]

A bag contains 4 red and 2 blue balls. 4 balls are taken out at random. What is the probability that the fourth ball is red?

[Anonymous No.10381213]

I checked this thread and feel initimidated. The paradox being, I intuitively understand most of the equations in this thread without the knowledge of doing the groundwork first. Academia is an interest but I'm town at, fvk birds and gIt $$$%%%. Hub. Repositories of info unconsciously stored. No closer to the true answer in my life.. Instead I will continue to declutter my life and lifestyle and reassess at a later date. Aerospace. Aeroplane. Pilot license for instance, or skydiving license. Adrenaline is my drug of choice, how bout we start a discussion of the chemical compounds found in strains of adrenaline and how they over ride base self preservation logic.. Because this shit happens on a daily basis to most humans. See fight or flight response.

Tl;Dr grasp control of that reptilian and make it your power to drive you in your direction, but I'm definitely NOT the guy who started all this spaghetti.

[Anonymous No.10381455]

how do I set up my mesh currents for this?

[Anonymous No.10381460]

>>10380960
back to cawadoody, cracker

[Anonymous No.10382362]

>>10380934
You should get q(x)=e^integral(k(x)), where k(x)=(2-4x^2)/(x-x^3)

integral(k(x))=log(1-x^2)+2log(x)=log(x^2(1-x^2))

q(x)=e^log(x^2(1-x^2))=x^2(1-x^2)

q(x)v''(x)+q'(x)v'(x)=0

d/dx(q(x)v'(x))=0

q(x)v'(x)=C for some constant C

v'(x)=C/q(x)

v(x)=integral(C/q(x))=C*integral(1/q(x))

integral(1/q(x))=1/2(-2/x-log(1-x)+log(1+x))

v(x)=C(log((1+x)/(1-x))-2/x)

It's late but hopefully I didn't make any mistakes.

[Anonymous No.10382390]

how do scientists come with the IQ of a historical/deceased person?

[Anonymous No.10382668]

when someone says the solution to a differential equation can be multiple functions
do they mean in a "family-of-functions, integral + C" kind of way
or radically different equations can model the same differential equation

[Anonymous No.10382680]

How do you calculate $50 per minute?

If I provide a service at this rate, how much would I pay if I did it for 72 seconds for example?

Sorry I'm really dumb, I'm from r9k

[Anonymous No.10382692]

>>10382680
it's right in the phrase
$50 per minute
$50 / minute

divide 72 seconds by 60 seconds to get what percentage 72 seconds is to a minute. In this case, 72 seconds is 1.2 minutes

so you get the expression: (50/1)=(1/1.2).
then just multiply 50 by 1.2 to get $60 (this is technically cross multiplication)

[Anonymous No.10382727]

>>10382692
tyvm

[Anonymous No.10382791]

What kind of math do you need to understand an undergraduate-level course in quantum mechanics? I am in engineering and will take up to calculus with complex variables and a basic course in linear algebra (up to vector spaces and linear transformations). What kind of math would I have to learn on my own to understand QM well?

[Anonymous No.10382847]

>>10382390
By comparing their achievements with the achievements of people who had their IQ measured.
>>10382668
The latter.
>>10382791
>up to the first subject in linear algebra
If I were you, linear algebra and then wait until further requirements show up.
But it depends a lot on the exact uni. They could expect you to know babby functional analysis, or babby differential geometry, but they probably won't.

[Anonymous No.10382873]

I know what everything on this graph is, just curious if any data scientists or statisticians know whether it has a name? If it does, I'd rather label it with its proper name in my paper than "MSE vs -log(lambda)"

[Anonymous No.10382882]

If an iterative algorithm is said to have "monotone convergence", does that mean it will eventually converge no matter how it is initialized?

[Anonymous No.10382943]

Is there a way to get wolfram to recognize ±?

[Anonymous No.10383088]

are not these both correct?

[Anonymous No.10383206]

How big would an o'neil cylinder have to be before it would be difficult to tell you are within an o'neill cylinder without observing the "sun"?

How would one even go about calculating such a thing?

[Anonymous No.10383858]

>>10382847
What should I study in linear algebra afterwards? What is the normal "progression" once you understand vector spaces and linear transformations?

[Anonymous No.10383968]

>>10383858
Determinant and properties, the relation between multiplying matrices and composing linear transformations, eigenvalues, eigenvectors, eigenfun, change of basis, diagonalization, pfaffians, tensor products, covectors, modules, etc.

[Anonymous No.10383973]

"Applicants for the Astronaut Candidate
Program must meet the basic education
requirements for NASA
engineering and scientific positions, specifically,
successful completion of standard professional
curriculum in an accredited college or university
leading to at least a bachelor’s degree with major
study in an appropriate field of engineering,
biological science, physical science, or
mathematics."

So, bioinformatics is considered biological science by NASA, right?
I gotta know before continuing my major

[Anonymous No.10384005]

>>10381037
No you just forgot something and are being too hard on yourself most likely.

[Anonymous No.10384093]

Is this correct?

[eqn] < x \, | \, \hat{p} \, | \, x' > = -i \hbar < x \, | \, \frac{\partial }{\partial x' } \, | \, x' > = -i \hbar \frac{\partial }{\partial x'} < x \, | \, x ' > = -i \hbar \frac{\partial }{\partial x'} \delta (x - x' ) = i \hbar \delta ' (x - x' ) [/eqn]

I fell like i'm abusing notation here, can the derivative move around like this?

[Anonymous No.10384099]

>>10384093
i mean the bra [math] < x \, | [/math] acts on the ket [math] \left( \frac{\partial }{ \partial x ' } \, | \, x ' > \right) [/math]

[Anonymous No.10384174]

[math]\int \frac{1}{x^{t}} = \frac{x^{t-1}}{t-1}[/math] for [math]t \neq 1[/math] since that would divide by zero.

So why is [math]\int \frac{1}{x^1} = ln(x)[/math] (meaning t=1)?

[Anonymous No.10384197]

>>10369481
>>10369514
>>10370088
t. brainlets
just do ~0

[Anonymous No.10384200]

Will taking anxiety meds reduce my cognitive ability?

[Anonymous No.10384207]

>>10384200
anxiety medications are not a long term solution to having too much on your plate. Neither is ADHD medication, or antidepressants. Take some off your plate, and give yourself the time that it takes to think.

[Anonymous No.10384209]

>>10384093
this mix of notation is giving me aids

[Anonymous No.10384216]

>>10384207
I'm not anxious because I have too much on my plate, I'm anxious because I get panic attacks when I go to the gym and I literally can't get fit. Trust me, I know how to handle stress from being busy.

[Anonymous No.10384283]

Is there a limit to how energetic electromagnetic radiation can be? I always see gamma rays listed at the top of wavelength charts or lists whatever as if there wasn't anything with a shorter wavelength

[Anonymous No.10384295]

>>10384197
That's not "32-bit word with 1s at ODD positions"

[Anonymous No.10384313]

>>10384295
0xFFFFFFFF is all 1's

[Anonymous No.10384329]

>>10384209
what are you talking about?

[Anonymous No.10384333]

>>10384283
bump

[Anonymous No.10384346]

>>10384093
https://en.wikipedia.org/wiki/Momentum_operator#Fourier_transform

[Anonymous No.10384349]

>>10384333
Why do you bump my question
Anyway I did some googling and it looks like there are more energetic forms of radiation but they're just called high energy gamma rays instead of a unique name

Could EM radiation have a wavelength shorter than the planck length?

[Anonymous No.10384544]

>>10384346
Yeah I know that this is the answer, I’m asking if I have abused notation. (My prof proved it using the commutation relations)

[Anonymous No.10384588]

In in junior year for my math bachelor's. I think I want to get a PhD and do research, but I haven't looked into how to do that at all. I think it's fear holding me back, but regardless is it worth looking into at this point? Are there specific sites to look at? I wanted teaching but that's hard without further degrees unless I go to some really bad school for work.

[Anonymous No.10384590]

>>10384200
Bump for an actual answer to this question that isn't asking if I've tried calming down?

[Anonymous No.10384593]

>>10384590
It depends. Medicine isn't binary, it's trial and error.
I doubt there would be lasting effects unless you really fuck it up, but there's always the short-term risk like any other drug.

[Anonymous No.10384595]

>>10384588
https://4chan-science.wikia.com/wiki/Universal_Material#Academia_and_Graduate_School

[Anonymous No.10384642]

>>10384313
Assuming he's a brainlet that doesn't know hex is more likely than him being such a brainlet that he doesn't know the difference between "odd" and "all"

[Anonymous No.10385433]

Anyone mind explaing how the Axiom schema of specification doesn't imply the axiom schema of replacement?

[Anonymous No.10385615]

HOW THE FUCK DO I INTO BASIC RINGS I THOUGHT I KNEW THIS SHIT BUT CAN'T EVEN CALCULATE A BASIC HOM QUESTION (part 2, the first hom is easy)

[Anonymous No.10385658]

>>10385615
>describe
I hate those exercises.
Just pretend k is R, solve it for that, and try to generalize later.
Also keep and eye on whether n|m, m|n, etc.

[Anonymous No.10385699]

>>10384093
>>10384099

[eqn]\left\langle x \right| \hat{p} \left| x' \right\rangle = -i \hbar \left\langle x \left| \frac{\partial }{\partial x' } \right| x' \right\rangle = -i \hbar \frac{\partial }{\partial x'} \left\langle x \right| \left. x' \right\rangle = -i \hbar \frac{\partial }{\partial x'} \delta (x - x' ) = i \hbar \delta ' (x - x' )[/eqn]

[Anonymous No.10385712]

>>10384099
Look, this is what you write:

>>10384099

Did you mean?:
[eqn]\left\langle x \right| \hat{p} \left| x' \right\rangle = -i \hbar \left\langle x \right| \frac{\partial}{\partial x' } \left| x' \right\rangle = -i \hbar \frac{\partial }{\partial x'} \left\langle x \right| \left| x' \right\rangle = -i \hbar \frac{\partial }{\partial x'} \delta (x - x' ) = i \hbar \delta ' (x - x' )[/eqn]

[Anonymous No.10385724]

>>10384093
>>10384099
Look, this is what you write: >>10385699

Do you mean?

[eqn]\left\langle x \right| \hat{p} \left| x' \right\rangle = -i \hbar \left\langle x \right| \frac{\partial }{\partial x' } \left| x' \right\rangle = -i \hbar \frac{\partial }{\partial x'} \left\langle x \right| \left| x' \right\rangle = -i \hbar \frac{\partial }{\partial x'} \delta (x - x' ) = i \hbar \delta ' (x - x' )[/eqn]

[Anonymous No.10385830]

Physics undergrad here. What's your method to learn new shit ? I feel like such a brainlet struggling with solid state physics.

[Anonymous No.10386219]

Anybody good at statistics?

[Anonymous No.10386230]

>>10385615
Use linearity. In both cases, any morphism is determined by the image of 1.

[Anonymous No.10386337]

Why isn't spin (quantum mechanical spin) always conserved?

[Anonymous No.10386663]

>>10385724
Yeah what’s the difference? My question is if I can move the derivative like that.

[Anonymous No.10386765]

>>10386230
Image of 1 and image of x.

[Anonymous No.10386769]

>>10386765
Nope, my bad.

[Anonymous No.10387165]

Could someone give me an easy explanation of what homotopy colimits are? No (inf, 1)-fuckery like in nlab, please.

[Anonymous No.10387183]

>>10387165

[Anonymous No.10387198]

>>10387183
Thanks! Where is this from?

[Anonymous No.10387230]

Is this proof retarded?
>prove f(n) = n^2 + n + 1 is injective (one to one)
I assume f(x) = f(y)
therefore
x^2 + x + 1 = y^2 + y + 1
and then I just say that x and y must be the same because it's the same equation, only the variables change
sorry i'm new at this

[Anonymous No.10387245]

>>10387198
Strom's Modern Classical Homotopy Theory.
It is a text for giga-autists, tho.

[Anonymous No.10387248]

>>10387230
Yes.

[Anonymous No.10387272]

>>10387245
That¨s what I am, so thanks again.

[Anonymous No.10387274]

>>10369481
the string you described an element of [math]L = \{(10)^n | n \geq 0\}[\math], which is described by the regular expression [math]R = (1 \circ 0)^*[\math] where [math]\circ[\math] is the concatenation operation and [math]*[\math] is the star (wildcard) operation. I'm pretty sure that the operations you gave in your post can be used to simulate a finite automata, so that set of operations should be able to decide that language, including your string.

[Anonymous No.10387344]

I finally got through all my anatomy exams and dissection courses.
How hard will the upcoming Pathology exams fuck my asshole?

[Anonymous No.10387353]

Why is the speed limit of the universe 300000 km/s and not 98000 km/s or 68750000 km/s or any other number?

[Anonymous No.10387355]

>>10369197
What am I doing wrong?
[math]\lim_{n -> \infty} \sum_{k=1}^{n} \frac{2}{3^k} [/math]
[math]\lim_{n -> \infty} 2 + \frac{2}{3} +\frac{2}{2^2} + \frac{2}{2^3}+...+\frac{2}{3^n}[/math]
[math]2\cdot (\frac{1}{3^0} + \frac{1}{3^1} + ... \frac{1}{3^n})[/math] geometric series becoming [math]\frac{2}{1-\frac{1}{3}} = \frac{2}{\frac{2}{3}} = \frac{6}{2} = 3[/math]

The answer should be 1, not 3, but i've been searching hectically to find where i do something wrong. (the answer to this is also the answer to 0.999... = 1, so it would be fun to know).

[Anonymous No.10387376]

>>10387355
You're mixing up an L-series with a power series. For the former, we fix the power, and sum along the base. For the latter, we fix the base, and sum along the powers.
See Apéry's constant for the solution.

[Anonymous No.10387380]

>>10387355
Don't listen to the other retard. It's a basic mistake, the formula for geometric series starts at k=0 but your limit starts at k=1, so you're essentially just adding an extra 2

[Anonymous No.10387406]

>>10387230
Your proof is retarded. Indeed, the function is not generally injective for, say, the real numbers, or even the integers (check x=-1,0). The catch is that (assuming the formula is over the naturals, since you write n), over the naturals it is indeed injective.

Suppose f(x) =f(y) as you said. Rearranging, you get x^2-y^2 +x-y=0. Factorising, (x-y)(x+y+1)=0, that is, x=y or x+y+1=0. The latter can't happen over the naturals since x and y are bigger than 0. Qed

[Anonymous No.10387412]

>>10387230
Yes, it's retarded. You could use the same "proof" to show that any function is injective, regardless of whether or not it actually is. In general
> x^2 + x + 1 = y^2 + y + 1
has solutions other than x=/=y. Specifically, y=x OR y=-(x+1).

Note that while the function is injective over the natural numbers (non-negative integers), over the integers, you have f(-1)=f(0).

A more realistic attempt at a proof would note that f(n+k)-f(n)=k^2+k+2kn. For n>=0 and k>0, this can't be zero (k and k^2 are positive, 2kn is non-negative), thus f(a)=f(b) iff a=b.

[Anonymous No.10387426]

>>10387412
>>10387406
What the fuck, you even copied my example

[Anonymous No.10387775]

Help a brainlet out with basic kirchhoff's law.
I have this circuit and I want to find the current on 1, 2 and 3 (all of them going out of the node). The current on 4 is 2A (up) and the current in 5 is 5A (down). No resistor values are given.

How do approach circuits with current sources?

[Anonymous No.10387777]

>>10387775
>do
to

[Anonymous No.10387779]

Considering the normal of a tangent plane to the graph of a function [math]f(x,y)[/math] is always
[math](\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},-1)[/math](evaluated at whatever point we want to find the plane at) wouldn't that imply that the gradient of any surface in 3-space (level surface), or at least those that look like the graphs (i.e. only one z-coordinate per (x,y) coordinate), also be exactly that? Considering both the normal vector and the gradient vector are both orthogonal to the surface. I know it's not, but I don't know why. These two pieces of information seems very conflicting.

[Anonymous No.10387798]

>>10387779
>gradient of a surface, but not gradient of the level set function associated to the surface
What do you mean with that?
If you're referring to the gradient of a function defined on the surface, then it isn't orthogonal because it points in the direction where the function grows the most within the surface, since it de facto isn't defined on the whole space its immersed.

[Anonymous No.10387818]

>>10387798
No, I'm talking about gradients of level sets of functions. Sorry if I'm being a bit unclear.

http://graphics.cs.ucdavis.edu/~joy/ecs277/other-notes/Gradients-and-Normals.pdf
>Thus, the gradient is normal to the curve

This holds for say, level sets of functions like f(x,y,z), but I've been told their gradients are [math](\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})[/math], and this gradient will then be normal to this surface in 3-space. However, I was also taught that tangent planes to graphs in 3-space has normals with the vector I wrote in the previous post. But that would imply df/dz = -1 always, which doesn't make any sense.

[Anonymous No.10387841]

>>10387775

sum the current going into the 5 nodes, you can label your current by the resistors.

so
i1+i2+i3-i4 = 0 (center)
10 + i5 + i1 = 0 (you know i5 so this give you i1)
i5 - i4 - 2 = 0 (bottom, this give you i4)

and so on

[Anonymous No.10387850]

>>10384588
You need to talk to actual people. Find a professor who taught a reasonably advanced course (300-level or higher is fine) that you really enjoyed and stop by their office for half an hour to discuss your thoughts on grad school. 95% of profs are more than happy to give advice to anyone who's legitimately interested. You'll get more localized advice than the Internet can give you, they can help you towards opportunities you might not otherwise know about/have access to, and you may be able to get some graduate school letters that are more impressive than "he aced my class".
If you are a typical turboautist this might be uncomfortable for you but academic mathematics is a heavily social endeavour, and your choices are to either adjust to that or gtfo.

[Anonymous No.10387859]

>>10387818
We have f(x, y), a function from [math]\mathbb{R^2}[/math] to R. We want the 2D surface in 3D space given by f(x, y)-z=0. We set up a dummy function F(x, y, z)=f(x, y)-z, and the gradient of F at the surface is the gradient of the surface.
If we have f(x, y, z), we would have to take a 3D level set in 4D space given by f(x, y, z)-w, set up a a function F(x, y, w, z)=f(x, y, z)-w and calculate its gradient there to obtain something that resembles the formula you have, except for 3-surfaces in R^4.

[Anonymous No.10387888]

>>10387859
Except I'm talking about 3-surfaces in R^3. But yes, we acquire them by taking level sets of functions F(x,y,z,w). But regardless, the gradient [math](\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})[/math] will be normal to the surface (The level set) at all points on the surface. But so will the normal of the tangent plane at all points on the surface, and that vector is [math](\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})[/math]. This implies that df/dz = -1 always. But this is obviously not the case.

[Anonymous No.10387894]

>>10387888
>3-surfaces in R^3

[Anonymous No.10387916]

>>10387894
Yes? Maybe I'm not using correct terminology here. I'm talking about stuff like x^2 + y^2 + z^2 = C. I would consider this sphere to be a 3-surface in R^3, but again, maybe that's incorrect terminology.

[Anonymous No.10387924]

>>10387888
you're confusing level set and graph of a function

[Anonymous No.10387927]

>>10387888
I'll try to explain again, from the beginning.
The gradient is defined for functions and only for functions, specifically fuctions from [math]\mathbb{R^n}[/math] to [math]\mathbb{R}[/math]. Gradients of surfaces don't exist.
When a surface is defined as a level set of a function f from [math]\mathbb{R^n}[/math] to [mat]/mathbb{R}[/math], we can calculate its normal vector by taking [math]f(x_1, x_2,..., x_n)-y=F(x_1, x_2,..., x_n, y)[/math] and calculating the gradient of F.

[Anonymous No.10387936]

>>10387916
if the "3" in "3-surface" stands for dimension, then it's supposed to be "2-surface". surfaces in R^3 are two dimensional

[Anonymous No.10387952]

>>10387924
I can describe the graph of a function as the level set of another function though.

>>10387927
Ah, so that's where the -1 comes from. But still, can't just get the normal vector to a point of the surface by just taking the gradient of the function describing that function? I'll demonstrate what I mean by an example.

Suppose we have a sphere x^2 + y^2 + z^2 = 1. I then want to find the normal vector of a point on this sphere. The gradient (and here I know I'm abusing this word, like you said) will be (2x,2y,2z), meaning at say, the point (0,0,1) on the sphere the normal vector will be (0,0,2). But also note here that this is not the (0,0,-1) that I thought the tangent plane would necessarily have.

[Anonymous No.10387979]

>>10387952
That's not a function. Essentially, that's already the F you'd have gotten by taking f(x, y)=\sqrt{x^2+y^2}[/math] for half the sphere, and f(x, y)=- \sqrt{x^2+y^2}[/math] for the other half, except it would've been F(x, y, z)=x^2+y^2+z^2-1 to be exact.

[Anonymous No.10387986]

>>10387775
Mesh analysis. Create variables for the current in the lower-left loop (the other 3 loop currents are set by the current sources) and for the voltage across each current source.

The current through each interior edge (r1-r4) is the difference between two loop currents (one in each direction), the current through each exterior edge (r5 and the three current sources) is a single loop current.

This gives you four equations in four unknowns:
(10-i)*r1 + (10-8)*r3 = v10
(8-10)*r3 + (8-2)*r2 = v8
i*r5 + (i-10)*r1 + (i-2)*r4 = 0
(2-8)*r2 + (2-i)*r4 = v2
These can then be solved for v2, v8, v10 and i. The expressions for v8 and i are fairly straightforward (each occurs in an equation with no other variables), those for v2 and v10 can be solved by substituting for i.

This is simpler than using KCL+KVL directly. Mesh analysis gets a bit more tricky if the graph is non-planar.

[Anonymous No.10387991]

>>10387979
>forgetting the one and forgetting the [math]
I need a doctor.

[Anonymous No.10388015]

>>10387952
you're confusing level set and graph of a function. if you have a function of two variables f(x,y), then its graph is a surface given by the equation f(x,y)-z = 0. taking partial derivatives of this equation you get the normal vector (df/dx,df/dy,-1). it is a special case of the general situation: a general level set surface has equation F(x,y,z) = 0 and its normal vector is (dF/dx,dF/dy,dF/dz). a graph just means that F(x,y,z) = f(x,y) - z for some function of two variables f(x,y).

[Anonymous No.10388030]

>>10387991
OK, I found the equation for the normal of the tangent plane of [math]f(x,y) = \sqrt{1-x^2-y^2}[/math] and the gradient of [math]F(x,y,z) = f(x,y) - z[/math] and they are just multiples of each other.

>>10388015
Yes, I know. The confusion came from the fact that I knew I could describe the graph of a function using a level set, just like you point out, and I knew both the normal of the tangent plane to the surface, as well as the gradient of the function, were both supposed to be orthogonal to the surface. The fact then that they didn't seem to always agree made me confused, but of course, they do.

[Anonymous No.10388040]

>>10387952
> I can describe the graph of a function as the level set of another function though.
Sometimes. E.g. given z=f(x,y), it may be possible to find some g such that g(x,y,z)=0 defines the same set of points. Or it may not. Or one may be a subset of the other. E.g. the points <x,y,z> defined by z=sqrt(1-x^2-y^2) are a subset of those defined by x^2+y^2+z^2=1 (the former is a hemisphere, the latter a sphere).

> Suppose we have a sphere x^2 + y^2 + z^2 = 1. I then want to find the normal vector of a point on this sphere. The gradient (and here I know I'm abusing this word, like you said) will be (2x,2y,2z)
That's the gradient of f(x,y,z)=x^2 + y^2 + z^2. The gradient at a point will always be normal to a surface defined as a level set which passes through that point.

> meaning at say, the point (0,0,1) on the sphere the normal vector will be (0,0,2). But also note here that this is not the (0,0,-1) that I thought the tangent plane would necessarily have.
If a vector v is normal to the surface, then so is k*v for any scalar k. The gradient won't necessarily have unit length or the desired direction. E.g. consider g(x)=-(x^2 + y^2 + z^2). At any point, the gradients have the same value except for opposing signs (∇g=-∇f), but g(x,y,z)=-k and f(x,y,z)=k define the same surface.

Also, f(x,y,z)=x^2+y^2+z^2 and g(x,y,z)=2*x^2+2*y^2+2*z^2 are different functions with different gradients (at any point other than (0,0,0)), but f(x,y,z)=1 and g(x,y,z)=2 define the same surface.

[Anonymous No.10388093]

What are some molecular species of proteins? Everything google gives me makes no sense.

[Anonymous No.10388342]

>>10369197
Say I have an objective function to minimize cost by changing some parameter [math]\theta \in \mathbb{R}^N[/math]. How could project this N-dimensional space onto a 2-D manifold?

[Anonymous No.10388935]

If U is a subspace of a vector space V with a complementary subspace W_1, then if for any other complementary subspace W_2, how do I show dim(W_1) = dim(W_2)?

[Anonymous No.10388950]

Did I do these right? How to do the last one? Thx

[Anonymous No.10389060]

>>10388935
The dimension of the complementary subspace is dim(V/U) which is independent of the W's.

[Anonymous No.10389065]

Can someone help me find some practice sheets for statistical mechanics/ theoretical thermodynamics? Prof told us to look for old grad school admission tests since thats what he takes inspiration from but didnt specifically tell us where to find them except a vague hint that some chinese websites have them. Havent been able to find them so far so would appreciate a link or any other repository of practice tests that covers just about this list:
>pure statistics (kolmogorov axioms, bayes theorem, jaynes principle)
>thermodynamic potentials/ legendre transforms
>partition functions for microcanonical,canonical and grandcanonical ensembles
>Ising spin interaction model
and probably some other stuff I already forgot...

[Anonymous No.10389070]

>>10369197

I got a 3.0GPA in my programs (double majored) but didn't participate in any research and didn't really put together a working relationship with my professors. Now I'm trying to get into a graduate program and I need letters of recommendation. This is my last undergraduate semester. Am I just fucked? What do I do?

[Anonymous No.10389111]

how the fuck do you ace a uni interview
help

[Anonymous No.10389238]

>>10389111
Are you physically present or is it via Skype? I aced my Skype interviews by cleaning my room, taking a shower and being myself without any fake humility or positivity or anything like that. If I could do it, then so can you.

[Anonymous No.10389344]

Is a uniformly picked subset of a normally distributed population normally distributed?

[Anonymous No.10389347]

So uhh.. Why do they assume i'm smart enough to figure this out? Please help

[math]\sum_{k=1}^{\infty}\frac{1}{k(k+1)(k+2)}[/math]

I get to:

[math]\sum_{k=1}^{\infty}\frac{1}{2k}-\frac{1}{k+1} + \frac{1}{2(k+2)}[/math]

I tried extending the series and playing smart (like, every even number created by 1/(k+1) takes out all of 1/(2k)), but i didn't succeed very long. Am i even on the right track?

[Anonymous No.10389362]

>>10389347
https://en.wikipedia.org/wiki/Telescoping_series

[Anonymous No.10389540]

>>10389347
[math]\frac{1}{k+1} = \frac{2}{2(k+1)}
\Rightarrow \sum_{k=1}^\infty \frac{1}{k(k+1)(k+2)} = \sum_{k=1}^\infty \frac{1}{2k}-\frac{1}{2(k+1)} - \frac{1}{2(k+1)} +\frac{1}{2(k+2)}\\ = \sum_{k=1}^\infty \frac{1}{2k}-\frac{1}{2(k+1)} - \sum_{k=1}^\infty \frac{1}{2(k+1)} -\frac{1}{2(k+2)}
[/math]
With telescoping series this is 1/4

[Anonymous No.10389704]

>>10389344
Are you asking if the means of random samples of a fixed size from a normal distribution still follow a normal distribution, or are you asking if a random sample will itself follow a normal distribution?

[Anonymous No.10389715]

>>10389704
The latter

[Anonymous No.10389719]

>>10389715
Then no

[Anonymous No.10389742]

My website (that uses a wordpress template) lately shows a very strange error. Sometimes, completely at random it seems, the page won't load correctly. Instead it shows a white background with the code in black text. After a few refreshes it shows normaly. What could be causing this and how do I fix it?

[Anonymous No.10389827]

>>10374701

Assume [math]\frac{n}{m}+t[/math] is rational for some rational number [math]\frac{n}{m}[/math] and some irrational number [math]t[/math].

That is, let [math]\frac{a}{b}=\frac{n}{m}+t[/math], where [math]a,b,n,m\in\mathbb{Z}[/math], [math]b,m\neq0[/math], and [math]t\in\mathbb{R}\setminus\mathbb{Q}[/math] (i.e. [math]t[/math] is irrational).

[math]\frac{a}{b}=\frac{n}{m}+t[/math]
[math]t=\frac{n}{m}-\frac{a}{b}[/math]
[math]t=\frac{nb-am}{mb}[/math]

Thus [math]t\in\mathbb{Q}[/math], but [math]t\nin\mathbb{Q}[/math].

Under the assumption that the sum of an irrational number and a rational number is rational, we reach a contradiction.

Therefore the assumption is false.

QED

[Anonymous No.10389850]

>>10389827
>>10389827
whoops

Assume [math]\frac{n}{m}+t[/math] is rational for some rational number [math]\frac{n}{m}[/math] and some irrational number [math]t[/math].
That is, let [math]\frac{a}{b}=\frac{n}{m}+t[/math] , where [math]a,b,n,m\in\mathbb{Z}[/math], [math]b,m\neq0[/math] , and [math]t\in\mathbb{R}\setminus\mathbb{Q}[/math] (i.e. [math]t[/math] is irrational).

[math]\frac{a}{b}=\frac{n}{m}+t[/math]

[math]t=\frac{n}{m}−\frac{a}{b}[/math]

[math]t=\frac{nb−am}{mb}

Thus [math]t\inQ[/math] , but [math]t\not\inQ[/math] .

Under the assumption that the sum of an irrational number and a rational number is rational, we reach a contradiction.

Therefore the assumption is false.

QED

[Anonymous No.10389853]

>>10389850
fuck me

the proof is there, whatever

[Anonymous No.10389861]

>>10374701
assume rational = irrational + rational
so irrational = rational - rational = rational
contradiction
qed

[Anonymous No.10390097]

Are all the stars in the galaxy attracted to the black hole in the center?

[Anonymous No.10390124]

Guys, am I retarded? I've been reading the proof for the chain rule for about half an hour and I still don't get it. I see pic related in the proof but I don't understand what that notation means.
Also, I do good in the class (always get high As on tests) but I feel like my comprehension of calculus is lacking, What text books would you recommend to increase understanding?

[Anonymous No.10390132]

>>10390124
You take the derivative of y with respect to x, and then you evaluate that at x=0. Simply y(x), then y'(x) and then y'(0).

[Anonymous No.10390137]

>>10390132
So does the line simply mean evaluate? That's supposed to be an a sorry.

[Anonymous No.10390152]

>>10390137
Yes. Read it as "at", e.g. "dy/dx at x=a".

[Anonymous No.10390169]

>>10390124
Read Rudin's principles of mathematical analysis

[Anonymous No.10390415]

>>10386663
Yes, you can. There is also a more or less rigorous way to show this: insert
\int dq |p> <p|, which is the untity operator, between the bra and \hat p and a similar expression between \hat p and the ket. Now exploit that <x|p> is e^{-ip} and <p_1|p|p_2> is is the delta function of the momenta times p_1 or equivalently p_2. Take the integrals and you end up with the expression on the right, involving a derivative of the delta distribution in position space. (which is only formally written as a function but should, of course, be understood as a distribution acting on a function space via integration)

[Anonymous No.10390427]

>>10386663
the unity operators were meant to be \int dp_1 |p_1><p_1| and the same with p_2, you know what I mean, anyway

[Anonymous No.10390446]

>>10382873
Looks like kind of a Morse potential curve (but has nothing to do with your graph I guess, I'm just using this as an excuse to bump my old question, the only one which matters)

>>10369467

[Anonymous No.10390461]

Is time really a 4th dimension or is it just a meme? Can't find the answer.

[Anonymous No.10390542]

>>10390461
Spacetime can be thought of as a 4 dimensional lorentzian manifold, so no, it is not a meme.

[Anonymous No.10390593]

What are the prerequisites for learning Calculus of variations? What kind of material can you use to study it on your own?

[Anonymous No.10390629]

Why are these equations equal to 1?
Shouldn't it be 0 since 1/(2n+1) = 0 when n approaches infinity?

[Anonymous No.10390639]

>>10390629
Does n/n tend to 0 because 1/n tends to 0???
Retard

[Anonymous No.10390646]

I'm trying to prove the logical equivalence of two statements using a truth table but both statements have implications and I'm not sure how that affects the outcomes.

The two statements are:
(P^Q)->R
(P->R)V(Q->R)

If P and Q are True but R is False then is the statement False or True?
Am I thinking about this correctly or am I misunderstanding something?

[Anonymous No.10390653]

>>10390639
where did n/n come from? isnt that indeterminate where as 1/n -> 0?

[Anonymous No.10390783]

>>10390653
God you're dumb

[Anonymous No.10390828]

>>10390783
Thanks for explaining in the stupid question thread. Why are you even posting here?

[Anonymous No.10390854]

>>10390828
He probably failed an undergrad test and comes here to pretend he isn't failing at life.

[Anonymous No.10390855]

>>10390629
Just calculate the sum
[math]\sum_{-N}^N ((1)^2)^k = \sum_{-N}^N ((1)^2)^k = 2N +1[/math].

[Anonymous No.10390859]

>>10390855
should be
[math]\sum_{-N}^N ((1)^2)^k = \sum_{-N}^N ((-1)^2)^k = 2N +1[/math].

[Anonymous No.10390879]

Anons how would you calculatelateral force of water on the walls around it we are creating a portable pond in our construction class and trying to figure out how much cable we need as support for the frame. its a hexagonal shape but lets just say that the the radius of the circle that fits in in is roughly 3 feet

[Anonymous No.10391989]

By what reasoning can I determine that the derivative of f(x) at x=0 is twice the derivative of f(x/2) at x=0 ?

[Anonymous No.10392003]

>>10391989
Chain rule

[Anonymous No.10392087]

>>10372633
https://4chan-science.wikia.com/wiki/Universal_Material#Error_Analysis

[Anonymous No.10392137]

Why do all linear definitions have variables which aren't ever explained?
E.g.
w1 * feature 1 + w2 * feature2 +...
What are the w's meant to be here?

[Anonymous No.10392150]

>>10392137
You mean, like, 1 kilometer = 1,000 meters? Great question! No, I do not think that the meaning of this has ever been truly explained.
You must be one of the sharpest tool in the box, right?

[Anonymous No.10392189]

>>10392150
Rude.

[Anonymous No.10392265]

>>10392137
what the fuck are you asking?

[Anonymous No.10392300]

>>10392137
W usually stands for weights which are determined experimentally or theoretically.

[Anonymous No.10392339]

>>10392137
> What are the w's meant to be here?
Coefficients. They aren't variables, they're constants. While their precise values will determine the specific solution, they don't affect the nature of the solution nor the method for obtaining it. E.g. the solution to a*x+b=c is x=(c-b)/a. It isn't necessary to know the values of a, b and c (or where they come from) to understand the reasoning behind that solution.

[Anonymous No.10392350]

>>10369197
How exactly is summation defined?

If
[math]X = \{2, 4, 6\}, Y=\{1, 8\}[/math]

then what does
[math]\sum_{x, y \in X \times Y} x = ?[/math]

[Anonymous No.10392369]

>>10392350
Using this notation seems to be used in a deliberately confusing fashion in this example, but basically:

list the pairs (2,1), (2,8), (4,1)... Then add up all the first coordinates. Basically, the elements of Y are irrelevant here, and it just has the effect of saying "sum the elements in X, then multiply by 2 (the cardinality of Y)." But this is a really non-representative example.

[Anonymous No.10392519]

Why does the ground state in the slater-condon rules mix with doubly substituted wavefunctions but not with the singles?

If I have to solve the integral
[eqn]\langle\Psi_{ijk...}^{abc...}|\hat{H}|\Psi_0\rangle[/eqn]

Why can't I just use the fact that in a case of the ground state, the hamiltonian acting on my ground state returns the ground state energy, and that the remaining integral is per definition equal to zero:
[eqn]\langle\Psi_{ijk...}^{abc...}|\hat{H}|\Psi_0\rangle
=E_0\langle\Psi_{ijk...}^{abc...}|\hat{H}|\Psi_0\rangle
=E_0{\cdot}0=0[/eqn]

[Anonymous No.10392641]

>>10390124
i would recommend looking at spivak's calculus if you want more of a rigorous understanding of calculus, or rudin's principles of analysis if you want to go in deep and formalize your understanding of calculus fully.

[Anonymous No.10392655]

>>10390629
Come on dude. 1^{2k} = 1. what is the sum of -N to N 1's? How many numbers are there from -N to N? there are N numbers from 1 to N, N from -N to -1, and 1 between (0). So there are 2N+1 numbers total. Thus we add 2N+1 1's, which is just 2N+1.
Now, what's the limit of (2N+1)/(2N+1) as N goes to infinity? Well, considering this is always 1 for every N, the limit had better be 1.
The second one is the same exact thing, because (-1)^(2k) = ((-1)^2)^k = 1^k = 1.
You should probably be going over the definitions and working on a more intuitive understanding of limits and sums, because posts like this >>10390653 make me think you are just blindly trying to follow rules without actually thinking about the problems.

[Anonymous No.10392783]

In the AB-Pruning algorithm, does it matter if the initial AB values are positive or negative infinity?

[Anonymous No.10392955]

>Lie in tub
>Make waves with my feet
>While I do this, I feel little to no waves by my upper body
>As soon as I stop, waves reach my upper body
>Why?
Not sure if I’m expressing myswlf clearly. I can explain in more detail if need be.

[Anonymous No.10392966]

>>10392955
>I can explain in more detail if need be.
Please don't.

[Anonymous No.10392981]

Why is the inverse of anything, ex. Ł, 1/Ł?

[Anonymous No.10393056]

>>10392966
>Please do...
Ok, stay put. Making figures

[Anonymous No.10393224]

CS and math double major here. What are some applications of topology?

[Anonymous No.10393492]

>>10392981
it's not

counterexample: inverse of the exp function

1/L is the multiplicative inverse of L because L times 1/l is the identity element (1) of the space you're working in

[Anonymous No.10393574]

>>10392981
That's the reciprocal, aka the multiplicative inverse. If f(x)=k*x then the inverse is f^-1(x)=(1/k)*x. But the concept of an "inverse" is far more general.

[Anonymous No.10393754]

>>10392339
Okay, thanks.
But if I were to implement such an equation, how would I go about it if I don't know the values (or at least the "recommended" values) of the coefficients?
I get that some features should be weighted more than others, but I don't know to what extent.