/sci/ - Science & Math

I get = 2.24.

3.5 - 0.08+0.24+0.9 = 2.28

3A/50+4B/50 = 2.28
How do the /50s get you 114?

>>14489627
[math]2.28 * 50 = 2.28 / 2 * 100 = 1.14 * 100 = 114[/math]
Also there was already a thread in >>14484018 , they just oofed the title.

>>14489774
>Also there was already a thread in >>14484018 , they just oofed the title.

That's why I couldn't find it when I searched 'stupid'.

>>14489792
You should search for "questions", because even if we changed the thread name it would probably still work.

I'm writing a novel about a habitable planet in the Large Magellanic Cloud. Is this feasible?

>>14490272
yes, you can write a novel about any topic, novels are a fiction format. i doubt you could write an autobiography on the same topic.

When you have
(2 + 3x) / (4 - 3x) = 13

Why can't we simplify the left side to get:
(1 + 0x) / (2 - 0x) = 13

I get that cross multiplication is the way to solve this. By why is this ^ wrong?

Why can't we write [math]-\log_{3} (x^{2} + y^{2})[/math] as [math] \log_{3} (x + y)^{2} [/math] ?

>>14490441
1+4 isn't 9

>>14490449
thanks

>>14490426
simplify how? I can't even squint hard and see how you would get that.

>>14490609
Sorry, Mb. Wanted to ask why we can't do pic rel

>>14490999
That's not how fractions work, anon.

How is the standard deviation of the difference between these two 100?
I would have thought it would be 20. I there a time when you do just subtract one distribution from another?

Why is Kahn Academy taking the variance this way without dividing by N?

>>14491810
The internet says this is the formula for variance.

>>14491813
p_i is equivalent to 1/N or something like that

>>14489792
>>14489800
>just type in sqt

How do i derive the recurrence relation for the sequence a(n) = n! ??

i know a(n) = n*(a(n-1)), but i thought you're supposed to solve for a(n) - a(n-1) and use that result to create your recursive relation.

When i do that i end up with:
= n!-(n-1)!
= n(n-1)! - (n-1)!
= (n-1)*(n-1)!

I dont know how to make this be n*(n-1)!

Can someone explain something that I have found puzzling about galaxies and yet doesn't seem to be discussed much?

The angular momentum of galaxies. We observe spiral galaxies to be scattered around with the inclination of their spins in apparently random directions relative to each other.

As I understand it galaxies formed from the mutual gravitation of mass into clumps of matter. All good and well. But then where did the angular momentum to create their spin come from?
>Iit came from the primordial gas clouds.

Yeah, okay, but that just pushes the question back to where did the gas clouds get their angular momentum from?
>From the turbulence caused by bits of matter forming and bumping into each other during the initial expansion of the Universe.

In that case we would still expect an overall random distribution of angular momentum that would on large scales cancel out, unless all the matter in that gas cloud was already spinning in a uniform direction. So that means each proto galaxy gas cloud still had to acquire a huge amount of angular momentum in one particular direction from somewhere.

Then there is the matter of galaxies containing huge amount of matter that is generally all rotating the same way, while neighboring galaxies have their matter all rotating in completely different inclinations.

So how did the distribution of angular momentum across different galaxies occur and where did the angular momentum come from in the first place?

Furthermore it puzzles me that I haven't heard anyone else ask this sort of question before. Is the answer so obvious and I am just immensely retarded on a scale of retardation previously unknown to Mankind?

Where does this 2 come from?

It works, but i dont understand why.

a[n] = a[n-1] - n, where a[0] = 4

i got a[n] = (((a[n-3] - (n-2)) - (n-1)) - n)
= a[n-3] - 3n +3
= a[n-3] - 3(n+1)
= a[n-n] - n(n+1)
= a[0] - n(n+1)
= 4 - n(n+1)

but it should be a[n] = 4 - n(n+1)/2

>>14492289
[eqn]1+2+3+...+n = \frac{n(n+1)}{2}[/eqn]

>>14492343
is the way i did a[0] - n(n+1) fundamentally wrong? i cant tell if its a coincidence it looks so close to the answer except it doesnt have /2

>>14492378
or a[n-n] - n(n+1) rather, like the transition from a=[n-3] -3(n+1) to the first term

im not sure what the "formula" is to go from a[n-3] - 3(n+1) alllll the way to a[0] -n(n+1) without writing out every term

>>14491810
>>14491813
If the data is for the entire population, divide by N to get the variance. If it's for a sample, divide by N-1 to get an unbiased estimate of the variance of the total population.

>>14491596
A has stddev 80, and -B has stddev 60. The sum of these two independent variables has the standard deviation [math]\sigma_{A+(-B)} = \sqrt{\sigma_A^2 + \sigma_{-B}^2} = \sqrt{6400+3600}= 100.[/math]

what did the r-coder mean by this
also can someone explain how to factor dataframes without turning them *into* factors

How many years does it take to learn everything about quantum mechanics, relativity and electromagnetism?

Don't know if this is even the right board, but can my eyes get damaged from an infrared lamp if i keep them closed while shining it in my face or should I wear additional protection? Trying to clear my skin.

I got my math exam tomorrow and I am so fucked lads.

How can I learn general algebra before tomorrow, god I hate how teaching studies forced you to choose between mathematics or Norwegian.

>>14493806
I had a mask that shone infrared on your face, but there was slits for the eyes so I couldn't say for certain it's safe. I would just do the cucumbers on your eyes thing.

hi sqt. I was part of a group chat in my class that was posting fucked up shit, notably pornographic content and apparently someone reported the chat to the Dean.

I didn't participate in the spam but I still feel like I'm totally fucked. What's likely going to happen?

>>14489612
If you have some average probability for a class of events, is it really acceptable to use that average chance no matter how the underlying events are distributed? Take genes for example. There is some average chance for randomly picked subclass of genes to match either ingroup or between different groups so a sequence of genes can just be that average raised to the power of whatever number of genes are being compared.
I suppose this isn't the best example because matching genes implies more matching genes. But suppose they were fully independent. Does it really not matter if some genes have 99.999% match rate and other have 0.001% and any possible distribution between?

>>14492190

It's a fair question and an open one in astrophysics. There is a great deal of modern work around structure formation in the universe, mostly building computational simulations. Lots of effects (gravity, fluid dynamics) make it non trivial.

We know a fair bit about accretion disks, so if we have a clump of matter with some initial angular momentum, we can model its collapse (https://en.wikipedia.org/wiki/Accretion_disk).). So if you imagine the early universe as a "gas" with slighlty inhomogenous density and angular momentum, the overdense areas will start to collapse under gravity. Considering this area separately, it will have some non-zero angular momentum (because of the inhomogeneity) around some centre of mass. As it undergoes "collisions" or turbulence or whatever process, the matter will collapse from a sphere to a disk, rotating around the centre of mass. This effect is probably best seen in a video (https://www.youtube.com/watch?v=tmNXKqeUtJM).). As it collapses, matter goes inwards and angular momentum is transported outwards and the speed of spin at the edge tends to increase.

Good overview of AGN physics:
https://www.astro.umd.edu/~richard/ASTRO421/Netzer_AGN.pdf

But that still doesn't answer the original question of how an initial clump of matter (perhaps an active galactic nucleus) gained angular momentum. Lots of this work is open and being addressed by computational models. Most work is built on the tidal toque theory - basically that individual clumps would be set in rotation by the tidal torques from neighbouring clumps

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/532C9CB5B48453E9E0D6863CCFD747F0/S1743921308017262a.pdf/how-galaxies-gain-and-lose-their-angular-momentum.pdf

You'll have to refer to the literature if you want more information on tidal torque theory and the distribution of angular momentum in the early universe. Peebles (1969) might be good place to start.

>>14492111
Seems like overcomplication, since the factorial can literally be defined as the recurrence relation: a(n) = n*a(n-1)

But following your method:
a(n) = n! = n(n-1)!
a(n-1) = (n-1)!

a(n) - a(n-1) = (n-1)*(n-1)! as you derived

implies a(n) = a(n-1) + (n-1)*(n-1)! = (n-1)! + (n-1)*(n-1)! = n[(n-1)!] = n[a(n-1)] as required?

>>14493970
Blitz through some Schaum's Outline book.
>>14494242
Nothing.

>>14494391

What if I made a joke about Mr hands

Let [math](A_n)_{n = 0}^{\infty}[/math] be pairwise commuting, bounded, self adjoint operators on a separable, complex Hilbert space. Assume also that [math]A_0[/math] is compact and [math]\bigcap_{n : A_n \textrm{is compact}} \ker(A_n) = 0[/math]. I need to prove there exists an orthonormal basis which simultaneously diagonalizes all the [math]A_n[/math].

I know every compact self adjoint operator admits an orthonormal diagonalizing basis, but I don't see how to use the assumption on the intersection of these kernels to reduce my problem to the compact case.

>>14492190
Cheers for that. At least now I know its an open question rather than simply me being too retarded.

Incidentally, I have asked the same question several times in the past on various forums. This is the first time I received a proper answer. Thank you. I am still puzzled by the fact that very few people seem to bring this question up in pop sci discussions ( personally I have never seen it asked ) since it seems a very obvious thing to point out.

>>14494723
Yeah nah, I am retarded, replied to my own post rather than this one.
>>14494341

>>14494560
Start off choosing an orthogonal basis which diagonalizes [math]A_0[/math]. The really important thing to notice here is that the only infinite dimensional eigenspace of any compact [math]A_n[/math] is [math]0[/math]. The restriction of the diagonalization to any of the finite eigenspaces can be gradually refined by going through the the other operators and the only infinite-dimensional eigenspace gradually vanishes.

I'm not posting an entire solution because the construction is ass but I hope my schizoposting helped you.

Quantum Gravity or Quantum Field Theory, which one is the right one?

The hipnosis is real?.
If so, how can I find more information about the subject?

>>14494990
Yes.
On a site called Google.

Given the equation [math]O(q) -4.25 = 0[/math], I have to find the roots q to this equation using scipy.optimize.fsolve().

[eqn]O(q) = (R+r)\cdot\int_{0}^{2\pi}\sqrt{q^2 + 2q\cos(c\theta + \theta) + 1}\ d\theta[/eqn]
I'm given R, r, and c. They're all constants.
How do I go about this? I honestly don't understand, do I have to integrate while keeping the q as an unknown?
If so then I tried integrating by parts and ended up with:
[eqn]\frac{2}{3}\cdot\left(2\pi(q+1) + \frac{2\sqrt{2\pi}}{5}\cdot \cos\left(\frac{2\pi -q^2 -1}{2q}\right)\right)[/eqn]
Which I then turned into code and plugged into the scipy method but I keep getting wrong answers. What am I doing wrong?

>>14495040
You're obviously supposed to use scipy.integrate to integrate numerically.

>>14495065
Scipy doesn't support keeping unknowns in it's integration, I already tried.

>be me
>started learning guitar a few months ago
>starting to feel a lot less retarded, can remember things more easily

is this normal? I’m in my mid-20s

>>14495040
Why not just numerically integrate manually at this point: http://www2.math.umd.edu/~dlevy/classes/amsc466/lecture-notes/integration-chap.pdf

>>14495082
Try

import scipy as sp
import numpy as np
from scipy import integrate
from scipy import optimize

def func(q):
return sp.integrate.quad(lambda x: (R + r) * (q**2 + 2 * q * np.cos(c*x + x) + 1)**(1/2), 0, 2 * np.pi)

print(sp.optimize.fsolve(func, 0))

>>14495352
>ValueError: The array returned by a function changed size between calls

>>14495367
Fucking hate python.

import scipy as sp
import numpy as np
from scipy import integrate
from scipy import optimize

def func(q):
return sp.integrate.quad(lambda x: (R + r) * (q**2 + 2 * q * np.cos(c*x + x) + 1)**(1/2), 0, 2 * np.pi)[0]

print(sp.optimize.fsolve(func, 5))

>>14495378
I just got the same result as when I did something similar.
It's still wrong.
Using the root in the integral and computing it results in [math]O(q) = 4.1887912836568155[/math] which is somewhat far from our expected 4.25.

>>14495394
Have you fucked around with the parameters to make the result more precise?

>>14495414
I redid the math and I found an error in my calculations:
[eqn]O(q) = (R+r)\cdot\int_{0}^{2\pi}\sqrt{q^2 + 2q\cos(c\theta - \theta) + 1}\ d\theta[/eqn]
Which is:
[eqn]O(q) = \frac{2}{3}\cdot\int_{0}^{2\pi}\sqrt{q^2 + 2q\cos(3\theta) + 1}\ d\theta[/eqn]
Tried adjusting the parameters of both the integration and fsolve but to no avail.
I'll reformulate the problem in a minute and post it. I've spent several hours trying to work this out now.

>>14495489
Oh.
We're dumb, we've been forgetting to use O(q) - 4.25 instead of O(q).
import numpy as np
import scipy as sp
from scipy import optimize
from scipy import integrate

def func(q):
return (2/3) * sp.integrate.quad(lambda x: np.sqrt(q*q + 2 * q * np.cos(3*x) + 1), 0, 2 * np.pi)[0]

def funcu(q):
return func(q) - 4.25

r = sp.optimize.fsolve(funcu, 5)
print(r)
print(func(r))

Given the two equations that describe the following figures:

[eqn]x(\theta) = cr\cos(\theta) - qr\cos(c\theta)\\
y(\theta) = cr\sin(\theta) - qr\sin(c\theta)[/eqn]

Where [math]R = 0.5, N = 3, r = \frac{R}{N}, \theta \in [0,2\pi][/math].
The figure on the left has [math]q=0.75[/math] while the figure on the right has [math]q=1.5[/math].

We want to solve the equation [math]O(q) -4.25 =0[/math] by finding the appropriate q.
Given:
[eqn]O(q) = \int_{0}^{2\pi}\sqrt{[x'(\theta)]^2 + [y'(\theta)]^2}\ d\theta\\
x'(\theta) = (R+r)(q\sin(c\theta) - \sin(\theta))\\
[x'(\theta)]^2 = (R+r)^{2}(q^{2}\sin^2(c\theta) -2q\sin(c\theta)\sin(\theta) + \sin^2(\theta))\\
\\
y'(\theta) = (R+r)(q\cos(c\theta) - \cos(\theta))\\
[y'(\theta)]^2 = (R+r)^{2}(q^{2}\cos^2(c\theta) - 2q\cos(c\theta)\cos(\theta) + \cos^2(\theta))\\
[x'(\theta)]^2 + [y'(\theta)]^2 = (R+r)^2(q^2 + 2q\cos(c\theta - \theta) + 1)\\
\Rightarrow O(q) = \frac{2}{3}\cdot\int_{0}^{2\pi}\sqrt{q^2 + 2q\cos(3\theta) + 1}\ d\theta[/eqn]
>>14495510
I had already tried that with my own code to no avail. I'll try it with yours.

>>14495510
Holy shit it finally worked!
I'll have to compare my code to yours to find what exactly I did wrong.
Thanks anon.

>>14495510
>>def funcu(q):
> return func(q) - 4.25
It seems this is what made the code work, what I did was subtract 4.25 in the very same function func(q). That small difference is apparently what caused the values to differ, though I'm not quite sure why.

>>14495552
Can you post your code?
I just split funcu off so I could print(func(r)) later.

>>14495001
No

I'm good at math, what book do I need to read to learn how to use this skill to make big bank in the stock market?

For those of you that have finished an undergrad degree, I have a question. I am in a bit of a pickle in organizing my next few semesters due to the overlapping of courses during summer.

So far I have:

spring
Physics II/Linear Algebra - 8weeks
Statistical Analysis/Abstract Algebra - 8weeks

summer
Probability I/humanities bullshit 101 8 -weeks
ODE's/economics survey crouse 8 -weeeks

During the summer, these two 8 week blocks overlap by almost 2 weeks, which is why I stuck humanities for the summer.

The following fall and spring is much easier to spread the pain with real/complex analysis, probability II and the few other things I need.

>>14495659
>big bank in the stock market

Go into robotics instead.
My advice because you would be happier winning a game that is productive and creates abundance. Not a zero sum game.
Don't be a Jew.

Is there a formula for a probability problem like this?
Do you really have to make this giant chart of every possibility?

>>14495916
>>14495659
But, to answer your question... You probably want to try trend following with linear regression models. Any neural net model or something more complicated will overfit.
Just experiment with many different price histories (charts) and Python algorithms. Experiment with when to buy and when to sell.
I've heard you want to sell (or close your position) based on x amount of time without a gain instead of a stop loss. But I didn't get too far into it.

As far as books, maybe someone else can recommend. I know there were white papers written by investment banks in the 80s about trend following.

Working on a way to generate exercise recommendations based on past exercise records.
Problems:
1. It's not possible to measure strength with decent certainty. How should I represent the uncertainty involved?
2. People generally get weaker without exercise. How should I factor in that decay?
3. Since this thing will be generating recommendations, it could tweak them to learn more about the person's strength. What's a good way to implement that, while also taking care not to recommend something dangerous?

Anyone experienced with genetic algorithm could help me design my encoded chromosome?
I'm kinda running out of options.
It's a GA about scheduling college classes.
The thing is, the courses to be scheduled doesn't have a uniform duration. So the chromosome examples I find on some papers online wouldn't work.
I found one that kinda works. It creates an extra hash map for the classes that acts as a timetable reference each fitness calculation:
https://www.codeproject.com/Articles/23111/Making-a-Class-Schedule-Using-a-Genetic-Algorithm
BUT it relies on the high speed implementation of C++ so doing it on another language while inputting hundreds of classes wouldn't work.
Anyone?

Should I get
Serge Lang's Linear Algebra
or Axler's Linear Algebra Done Right ?

+ give me recommendations for analytical geometry texts please

When I'm asked to find the "Mechanical Resistance" of a material given a stress/strain graph, what the fuck am I being asked to find exactly?
I've literally seen the term referring to any of the main points on the graph, and my brainlet take is that I'm being asked to find the Highest point on the curve (Ultimate Strength), and report what the (nominal) stress at that point is., which is basically the highest stress the material can take before breaking (or literally at break point, for some ceramics)
But I also find some sources referring to the stress at fracture as "Mechanical Resistance" which makes no fucking sense. Also the maximum yield stress (or simply the stress at .2% for continuous lines) but that makes at least a lick of sense.
Which is it then?

In group theory, what does the < > notation mean? E.g. H = <a,b>. I thought it meant inner product but I think that's incorrect.

>>14495918

Well, the chart is nonsensical, because it doesn't explicitly account for the probability that a firework will work or not - it suggests every possible outcome, but assumes that work:dud is 50:50, which is never clarified.

So as a sample space, it's fine. But the probability part isn't explicit/rigorous.

Anyway, in general, this is a binomial distribution problem.

You can write the sample space using some shortcuts. If binomial distribution is not familiar to you, I'd recommend a bit of Youtube or something. Really useful piece of stats.

Short answer is that you can find the number of possible outcomes (1,4,6,4,1) using nCr - "n choose r" (this is a mathemtical operation and a button on most fancy calculators). https://www.wolframalpha.com/widgets/view.jsp?id=f704c51b68805b14b9eb223026d333ca

You give the n (number of fireworks) and r (number of duds). So you plug in 4C0, 4C1, 4C2, 4C3, 4C4, you will recover 1,4,6,4,1 as here. In general, the number of relevant outcomes is [total fireworks C number of duds]. So if we have 12 fireworks, there are 792 possible outcomes with 5 duds (12C5 = 792)

>>14496652
Subgroup generated by a,b

>>14496652
Don't listen to this anon >>14496680, it's the inner product of the two elements.
So <a,b> = b^-1ab (a^-1 ba)

>>14496535

Go to libgen or b-ok and take a look at the books. Give them a try and see what works for you. Finding textbooks isn't about finding the best one, but finding one that works for you. I'll even include links:

https://b-ok.cc/book/881225/554936
https://b-ok.cc/book/3372205/ac6013

From cursory inspection, I prefer Lang's approach, but I'm a physicist so might see it differently.

>>14496689
Good advice, thank you!

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

continuing from >>14496210
For #1, I was just gonna take the average and standard deviation of all relevant records, weighted by newness.
#2 I was thinking about somehow reducing the mean and widening the standard deviation by some constant based on how old the latest records are.
For #3 maybe it should recommend exercises randomly between the 45th and 55th percentile?

can anyone help me drawing the graph of this circuit?

>>14489612
Suppose [math]u \in L^1(a,b)[/math] with [math]u(x) = \int_{x_0}^x v(t)dt[/math] for some [math]x_0 \in L^1(a,b)[/math] then I want to show that the weak derivative of u is v but without using the fundamental theorem of calculus, with the fundamental theorem, integration by parts immediately yields the desired result, otherwise I dont see how to approach this.

>>14497694
For some [math]x_0 \in (a,b)[/math] sorry, obviously not in L1

>>14489612
any recommendations for a beginner's electronics book?
i know the basics of the components and basic applications Ohm's law but my knowledge is just built from scrapping together stuff from the internet
i'm interested in putting circuits together with a raspberry pi but struggling to put ideas into circuit designs
thanks for any help anons

>>14489612
please explain that a differential equation is

wtf is this supposed to mean: y + dy/dx = 5x?

is the goal to get rid of the :dy/dx part?

>>14498837
it means

y + y'/x' = 5x

>>14498849
yes i understand that but what exactly am i solving?

>>14498837
You're solving for a function [math]y[/math].
Like how when you solve [math]y(x) = \int f(x) \ dx[/math] you're solving for a function [math]y[/math].

>>14498837
>>14498869

>is the goal to get rid of the :dy/dx part?
kinda
the goal is _usually_ to find y(x)

this is a first order linear differential equation btw
READ the theory
because you solve it with a simple formula

>>14498837
The goal is to find y(x). There's some very well-established theory about solving linear differential equations (of which this is an example).

In this case, it's obvious that y includes a ke^-x term. y=ke^-x => dy/dx=-ke^-x => y+dy/dx = 0. It's equally obvious that it involves a linear term: y=ax+b => dy/dx=a => y+dy/dx=ax+(a+b) => a=5, a+b=0 => b=-5 => y=5x-5

So altogether, y=5x-5+ke^-x
=> dy/dx = 5-ke^-x
=> y+dy/dx = 5x

You need the value of y at x=0 to determine k.

x=0 => y(0)=-5+k => k=y(0)+5

=> y=5x-5+(y(0)+5)e^-x

Non-linear differential equations are somewhat more involved, and it mostly involves identifying that the equation fits a particular pattern for which there's a known solution.

>>14494865
Thanks, it sure has helped!

Anyone got a subscription to New Scientist and can archive this article for us?

https://www.newscientist.com/article/2320810-astronomers-question-if-the-first-picture-of-a-black-hole-is-accurate/

How is the universe not just fractals all the way down?

>>14499999
checked

anyway, why would it? You're just fantasizing, keep an eye on what's real
the world is made of matter
maybe a fractal geometry would fit it somehow but I have no clue why and probably now neither physicists are sure

How to get this relation?
[math]|\vec{k}|^2=\frac{\omega^2}{c^2} \epsilon \mu[/math]
I guess I should use [math]|\vec{k}|=\frac{\omega}{c}[/math] and [math]c=\frac{1}{\sqrt{\epsilon \mu}}[/math], but I get no [math]c^2[/math] in the denominator

>>14500263
test

>>14500263
Beware that there are multiple versions of ε and μ, one set is their values in vacuum, one set is their values in a material, and a third set is the material values relative to the vacuum values.
The relation you gave has the wrong dimensions, so I suspect you're dealing with relative values [math]\varepsilon_r=\varepsilon/\varepsilon_0,\, \mu_r=\mu/\mu_0[/math]. The same is true of the speed of light, which might be the vacuum value c0 or its value in a material, make sure you're clear which it is.

Why can't I simulate a current source in series with a capacitor? The voltage across the cap at t=0 is in the gigavolt range and does not rise any further.

>>14497729

I used Practical Electronics for Inventors by Scherz. Fairly straightforward book.

A classic is 'The Art of Electronics' by Horowitz, which is probably thorough enough to cover everything. Very well regarded.

Regardless of the book, it works best when you go through things practically. Get yourself some components and a breadboard.Or maybe someone has built a circuit emulator online that you can use? There are also some video games about building circuits which might be fun.

is it possible to have a chill job as an engineer? As in you go into work, get paid well then come home and chill? or is it high stress?

>>14489612
did the nootropics threads get moved somewhere? where?

>>14489612
If I have a sequence of sequences [math]a_k[/math] such that [math]0 \leq a_k \leq \frac{1}{k}[/math] for all [math]k \in \mathbb{N}[/math], how do I construct a convergent subsequence?

>>14502672
I forgot to add: convergence on this vector space of real sequences is defined through the norm [math]||a_k|| := sup\{|a_k| \mid k \in \mathbb{N}\}[/math]

>>14500263
ffs if you are doing EM set epsilon_0=mu_0=c=1.
Seeing all these unnecessary constants makes me ill

I throw a dice. If I get the number 4 I win.
Each throw I have a 16.67% (1/6) chance of winning.
If I throw the dice N times, how do I calculate the probability of getting a 4 at least once across all the N throws?
Do I just multiply the percentage by the number of throws (so if I throw 12 times I have a 200% chance of winning)?

>>14502987
It's a binomial distribution and the probability of getting at least one success is 1 minus the probability of getting zero successes.
[eqn]\mathbb{P}(X \geq 1) = 1 - \left(1-\frac{1}{6}\right)^N[/eqn]

>>14503050
Is this Bayesian theory?

>>14491813
Yes
This is done over a sample of N data points
Notice that xi can be obtained as many times xi occurs
So the formula is really just
Σ(xi-X)^2 * n(xi) /N
With the sum being on the individual values of xi you got
And n(xi) is the number of times xi occurred in your results
Wich n(xi)/N is just the probability of finding xi
A deeper look at that formula tells you that σ^2 = E(x-E(x)) = E(x^2)-E(x)^2
Which can be used as a norm for the space vector of the random variables on your set of points.
But that's another story

>>14495659
Good answers were given to you
My tl;dr take is :
Machine learning for economics

>>14503055
No

>>14500913
>>The relation you gave has the wrong dimensions, so I suspect you're dealing with relative values
So then [math] |\vec{k}|^2=\frac{\omega^2}{c^2} \epsilon_r \mu_r [/math] would be correct? How do I get it?

>>14502682
It's my professor notes, I have no choice

are forces on an object applied simulataneously or applied consecutively

>>14503604
Depends on the forces and the timing?
If you're exerting two different forces on an object then their normals are simultaneous.

>>14503611
ok thank you, so it is possible for them to be simultaneos

can someone explain me naming in neural networks correctly? assuming simple dense ones now
for example in this image, there's input layer with 3 neurons, 1 hidden layer with 5 neurons and an output layer with 3 neurons
there's 3x5 = 15 weights between input and hidden layer (20 if we add in bias)
do we say that that the hidden layer has these 15 / 20 weights? or does the input layer?
and then there's another 15 weights between hidden and output layer, do we say that these belong to the output layer then?
also looking at some examples, i saw some "simple" networks, that had like 1024 -> 512-> 128 -> 16 neurons
do they then have 1024x512 + 512x128 + 128x16 weights? that's 591872 weights, i know there are networks with billions of parameters, but do even simple ones get that huge?

>>14503125
Thanks anyways for the formula.

hello can somebody please re-arrange this to solve for B? i am a software engineer and need this for my work. but im too fucking brainlet to solve this. please please help

My discrete math book briefly talked about the set of real numbers being an uncountable set, and the "Cantor diagonalization argument" and "decimal expansion."

Can someone put this into words why "every real number has a unique decimal expansion" and "the assumption that all the real numbers between 0 and 1 could be listed must be false"?

My brain melts trying to follow the r1=0.d(ij),... matrix-looking notation.

>>14504495
this is the paragraph on it in the book

>>14504495
it's so simple

I don't understand part of one of my homework questions.

λ = 0.8
If Y is a Poisson random variable with parameter λ, determine the general expression
for the conditional probability of P(Y = y | Y ≥ 1), for y = 1,2,3,....

It's the (Y = y | Y ≥ 1) that confuses me; what does the | mean?

>>14504495
It's a bit of a setup to get to the point it's trying to make: if you can derive a new unique real number from a list of all real numbers, that list does not contain the number you just made and you just proved you can't count all the real numbers. The key phrase there is that all real numbers would generate a unique real number using this method, and its existence proves you can't list all real numbers (because all real numbers would have a unique real decimal expansion, and those would too, and so on).

>>14504892
you're joking right?

>>14504984
ty for explaining anon, i'll keep trying to understand

>>14489612
>archive.wakarimasen.moe/sci
it's gone

If I have a poisson distribution for probability of some event, assuming λ=0.8 where event number is any y=0,1,2,3...

How do I recalculate λ if I want to excluse y=0 (y=1,2,3...)?

>>14505217
I'm trying to work out what the average number of events would be ONLY considering the days where the number of events > 0 (ie 1, 2, 3...).

>>14505157
They deleted a decent thread today too, some essay on tensile mechanics.

>>14505157
Shit, hopefully it's on maintenance.
>archived.moe doesn't have search enabled
>fireden isn't updating

>>14502672
>>14502680
Just adapt the Bolzano-Weierstrass construction.

Does anyone know where I can buy a 5000 ml volumetric flask calibrated to deliver?

My prof defined complex permittivity as:
[math]\hat{\epsilon}=1+\frac{4\pi i}{\omega}\sigma[/math]
But this doesn't make sense since it should be:
[math]\hat{\epsilon}=\epsilon'+\frac{4\pi i}{\omega}\sigma[/math]
Where [math]\epsilon'[/math] is the real part of the absolute permittivity. We are spcifically inside of a material so [math]\epsilon'[/math] can't be 1. What am I missing?

>>14505217

https://en.wikipedia.org/wiki/Zero-truncated_Poisson_distribution

how do I make zotero citation clicks take you to the bibliography entry in the final pdf? unlinking doesn't do that and just removes the zotero edit that pops up.

Let [math]K/E/F[/math] be field extensions where [math]E/F[/math] is algebraic. Let [math]\alpha \in K[/math] be algebraic over [math]E[/math]. Must [math]\alpha[/math] be algebraic over [math]F[/math]?

i've got this old jug of hydrogen peroxide i found in the garage, and it says it's 32% peroxide but it's degraded since then.

i was looking up ways to determine how much peroxide remains, but the most practical option involves reacting it with potassium permanganate, and measuring the volume of oxygen produced by bubbling it into a grad cylinder.

i don't have any potassium permanganate, and no stores sell it, so i'd have to order it.
are there other chemicals i could use in place of permanganate to fully react the hydrogen peroxide in order to determine the concentration?

So a Newton is defined as 1 * kg * m/s^2, this means that when I work with Newtons I should always make sure mass is in kg, correct?

>>14505878
Yes

>>14505892
Thanks bro

Any tips on computing Bezout coefficients in a commutative ring? Can't use extended Euclidean because the ring has zero divisors (the ring in question is [math]\mathbb{Z}_4[x][/math]). The coefficients I need to compute always exist.
I think using extended Euclidean ver [math]\mathbb{Q}[x][/math] and projecting to [math]\mathbb{Z}_4[x][/math] should work? Any other ideas?

>>14505901
You can try to look into discrete Fourier transforms for arbitrary rings. Fourier transform everything, solve there, inverse Fourier transform everything.
Those apparently exist according to the second reply in https://www.reddit.com/r/algorithms/comments/72a7lb/fast_fourier_transform_algorithm_for_rings_in/

Why can’t we harness the earth’s magnetic field for energy?

>>14505939
We can't harness any magnetic fields at all for energy. Magnetic fields don't do work.

>>14505939
you can make a dc motor that uses the earth's magnetic field

>>14505939
It's very weak.

>>14505965
what if we made trillions of dc motors orbiting around earth that use the earths magnetic field and connect them to power something?

would it be unlimited energy or would it eventually cause the earth to stop spinning?

>>14489612
What's the best way to learn higher math from the internet?
I want to be able to read all Machine Learning papers.
I'm going through Calculus and Statistics & Probability on Kahn Academy. Then what? Or what else?
I've tried books but math books are very strange to me the way they are written. The are so rigorous and autisticly written that I leave each page with more questions than answers.

>>14506038
That's a different kind of math. Machine learning is likely using set theory and discrete math, mixed with differential equations.

>OP posts his homework
>someone solves it in like five posts
>thread basically goes on with people coming in and posting "you're all STUPID" and then following up with a solution that's already been posted five distinct times
Why is /sci/ like this?
>>14505169 could have died after >>14505187, OP's an adult and can mechanically apply solution methods from google.
>>14506038
>Then what? Or what else?
Linear algebra.
Besides that, how are you going to read papers if you can't even read books?

>>14506033
The earth's spin comes from its orbit. I don't think the quantity of energy you could gather could impact its orbital speed. Also it's painfully slow, trying to find a resonance with an orbiting magnet that produces net energy would likely require something humongous, like a magnetic moon. You'd probably be better off wrapping coils around the moon to be honest. There's a fun math problem.

>>14504401
Matlab can do that in a few seconds. As can Wolfram alpha. Also since I think this came from another digitized solution (since it includes erf), it might be worthwhile to manually work with it some so erf doesn't get included.

Why is the set A × Z+ where A = {2, 3} countable and not countably infinite?

The set of the odd negative integers is countably infinite because (n) in Z+ is mapped to -(2n-1) in this set to produce the set of odd negative integers right?

Doesnt AxZ+ also do the same thing?

>>14506052
>how are you going to read papers if you can't even read books?

The papers are usually describing something that happens. I don't understand what is happening in a math book. It looks like moon runes to describe other moon runes ad infinitum.

>>14489612
Alright so this question might be kind of weird.

So when sleeping if I receive a phone call (through WhatsApp) I wake up (during the call or at most 10 mins after) despite my phone being silenced. I always leave the phone facing down so light won't bother me if notifications arrive.

The question is: Why does this happen? Is it a wifi thing (router is in my bedroom)?

What is this top equation?
You might not want to break down every detail, but can I has a clue?
>I see there is the 'proportional to' symbol there.
What is proportional. Why?

This is from a paper for a policy gradient reinforcement learning algorithm.

https://arxiv.org/pdf/1806.06920.pdf

>>14506086
Does somebody actually claim that your set isn't infinite? Or are you confused, and think that a countably infinite set isn't countable?

>>14506156
Without reading the paper I'm sort of guessing here, but it looks you have two different conditional probability distributions, q_i( a|s ) and pi(a|s, Theta_i), and an assertion that to get from pi to q, you multiply by the exponential expression, and then rescale (so that the new total probability is 1..0).

>>14506120
Have you ever actually popped open a machine learning paper?

>>14506206
the answer said it was "countable", which i thought meant "countable but not countably infinite".

i think i confused the terms finite, countably infinite, and uncountable. so i was taking "countable" to mean finite, when it meant countably infinite in the context of the answer

i hope anyways

Is there some form of relationship between Gamma Matrices and 4x4 Matrix Representation of Quaternions? Can I work with the Klein-Gordon Equation in Quaternion basis instead of Gamma Matrices?

Taking the means of samples of a distribution and putting them in a distribution.
>Why would anyone want to do this and why is it called the 'Central Limit Theorem'?

Is there a name for Heaviside times two minus one?
Like in [math]\int _a^b f(x) \ dx = (2H(b - a) - 1) \int_{[a, b]} f \ d \mu[/math]

Can a mathchad please help me solve this logarithm? I gave up halfway through the last line.

>>14506413
>[math]2x + 3 = (2x^2)(2x - 4)[/math]
That's a basic quadratic, just review that stuff from your book and finish it off on your own. Put it into normal form and then use Baskhara or some hack method.
BTW [math](2x)^2 = 4x^2[/math]

>>14506401
>Why would anyone want to do this
It has a couple of handy uses (AWGN for instance).

I hesitated to expand it because it'd produce a cubic equation.

>>14506479
>AWGN
White noise.

Thank you. I don't need any white noise. Do you have a more simple use you can give me?

>>14506413
>>14506483
Going to sleep. Would be great if someone can help me.

>>14506413
>>14506483
>>14506632
You might have made a typo somewhere when stating the problem because the solution is some random real number.
https://www.wolframalpha.com/input?i=log+%282x+%2B+3%29+-+log%282x+-+4%29+%3D+2+log+%282x%29
https://www.wolframalpha.com/input?i=2x+%2B+3+%3D+8x%5E3+-+16x%5E2

if light bounces off of matter,
could tiny bits of matter bounce off of a very strong beam of light?

if not, why not?

How does the multiplication symbol work? Yea 4 * 4 = 16, but like how does a computer programming language know what that means? Do we say take 0 - 0 - 0 - 0 and for each 0 add 4 more 0's inside that group?

>>14506866

a simple way is:


var result = 0
var num1 = 3
var num2 = 4

for (int i = 0; i < num2; i++)
{
result = result + num1
}

but i'm sure some mathematical/programming genius has a better way

>>14506706
Holy Shit!
If you are thinking what I think you are thinking...

>>14507015

>>14506706
Yeah. Photons have momentum, so they can push things.

Gonna ask the dumbest question:

(x/2y) * y

Why is the simplification x/2 instead of x/y?

Any idea how the first FOC is derived? I can get the second one but I don't understand the derivative wrt w

>>14507215
[math]2y = y + y \not = y^2 [/math]

>>14507215
x/2y = x*(1/2)*(1/y)*y

>>14507215
[eqn]\left(\frac{x}{2\cdot y}\right)\cdot y = \left(\frac{x}{2}\right)\cdot \left(\frac{1}{y}\right)\cdot y = \left(\frac{x}{2}\right)\cdot \left(\frac{y}{y}\right) = \left(\frac{x}{2}\right)\cdot 1= \left(\frac{x}{2}\right)[/eqn]

>>14507229
should equal x/2 my bad

>>14507216
Such cancerous notations, jesus christ.

>>14507216
[math]\dfrac{\partial}{\partial w} \left[ s F(e(w)L) - wL \right] = L \left[ se'(w)F'(e(w)L) - 1\right] = 0[/math].
So [math]se'(w)F'(e(w)L) = 1[/math]. Plug in the second equation (from differentiating by [math]L[/math]) for the result.
>inb4 shouldn't they have given the conditions in the opposite order then
Yeah.
>>14507236
Seems normal to me.

>>14507244
Oh wow thank you

>>14506866
ALUs have special logic in them that implements multiplication. its all proprietary so you cant know whats being used in modern chips, but an easy example is repeated addition like you suggested. if you want to know how computers add numbers, google "full adder".
and that only goes for integers. for floating point numbers, a special circuit called an FPU is used, and FPUs are a whole fuckin other level of complexity.

>>14507244
> [math]e'(.) F'(.)[/math]

>>14507249
Whataboutit.

>>14507252
It's ugly, it's cancerous, it triggers my autism and confuses me.

>>14507253
Why is it ugly and cancerous? Is it the [math]e[/math] function?
That's normal. Nine times out of ten inflation is [math]\pi[/math]. Statiscians abuse pi the same way. Physicists do way worse.
The only actually jarring thing is using [math]w^*[/math] but not [math]L^*[/math] for the steady state solutions, but that's very minor.

Maybe I'm going crazy here, but has standardized testing become ridiculous this past decade? Its almost as if these people who want to destroy this method of testing went into positions where they develop them, and made them as ridiculous as possible. With brutal time constraints and arbitrary requirements. High school Calculus II exams now require you to format your exam answer like a fucking essay with an intro, a body, and a conclusion? Since when? I took this class almost 20 years ago, and I have no idea what to tell my nephew. Why are we writing sentences and describing things with words for basic integrals again?

>>14507258
I meant the dot in the parenthesis.
>That's normal. Nine times out of ten inflation is π. Statiscians abuse pi the same way.
Jesus fucking christ.

>>14507259
>Why are we writing sentences and describing things with words for basic integrals again?
I'm guessing it's to evaluate whether the student actually understands what he/she is doing and not just copy pasting what they saw before?

>>14507261
>I meant the dot in the parenthesis.
That's way normal, how come you've never seen it before?

>>14506406
Signum function, sgn(b-a)

>>14507272
I've never really come across it until now.
Not in any physics, math or chemistry book I've read.

if i have a solution, say a bottle of vodka, that's 40% ethanol. lets say it's 100 mL.

is that by weight, or by volume, or even moles? like, if i were to cleanly separate it totally, am i going to have 40mL of ethanol and 60mL water?
but ethanol is less dense than water, so that would be like 31.6 grams of ethanol and 60 grams of water. so, a 40% by volume is only 34.5% by mass.

is there some sort of standard? like, is 3% hydrogen peroxide by mass or volume? is 8% bleach by mass or volume? etc.

Let A be a basis of ker(M), for M a real matrix (doesn't have to be a square matrix).

Are all basis of ker(M) of the form AX, with X invertible ?

>>14508019
Alcohol for consumption is usually marked by ABV (Alcohol by Volume).

>>14508023 (me)
My guess :
It is true.
By contradiction, if there's a basis B of ker(M) such that B=/=AX, then it means that at least one of the columns of B can not be expressed as a linear combination of the columns of A. Note v this column.
Then v is not in span(A), absurd.

Is that correct ?

i. Can I turn polyester into fuel?
ii. If I siphon heavy metals or toxic chemicals from the soil using certain plants, will the bees that land on those flowers transmit the chemicals?

Can the periodi function [math]u(\mathbf{r})[/math] that appears in Bloch theorem:
[eqn]\psi(\mathbf{r}) = e^{i \mathbf{k}\cdot\mathbf{r}} u(\mathbf{r})[/eqn]
be a complex valued function?

>>14508474
Yes, of course. For instance if you start with a real u, multiply psi(r) by an arbitrary complex phase and you have a new u that still satisfies the wave equation

>>14508019
> am i going to have 40mL of ethanol and 60mL water?
No, because 1L ethanol and 1L water produces 1.98L of 50% ABV mixture. So you'll have slightly more than 40+60.

>>14508481
Thank you!

>>14507273
Thanks anon.

What does the psi mean hear?

From a paper for multi objective reinforcement learning.
Link.
https://www.mdpi.com/2079-9292/11/7/1069/htm

In optimization, I often see multivariate optimization being done in multiple steps. It seems like the implicit assumption is that [math]\max_{x,y} f(x,y) = \max_x \left\{\max_y f(x,y)\right\} [/math]. Is it always true that we can do multivariate optimization in steps? If so, by what mathematical principle?

Why does uncanny valley work backwards for singing?
I literally cannot get enough of almost human sounding vocaloidshit.

I am trying to calculate the mean velocity of a fluid in a rectangular pipe.
Height is [math]h [/math], width is [math]w [/math], so a cross section of the pipe is [math]S=h×w [/math]. My velocity is an Hagen-Poiseuille thingy like this : [math] v(y) = -\frac{G_1}{2 \rho \nu}y^2 +\frac{G_1}{2 \rho \nu}hy [/math].
The maximal velocity is [math] v(\frac{h}{2}) = v_{max} = \frac{3G_1}{2 \rho \nu}h^2 [/math]
To compute the average value over the cross section [math]S [/math] , I did :
[math] \displaystyle v_{avg} = \frac{1}{S} \iint_{[0,w]×[0,h]} \left (-\frac{G_1}{2 \rho \nu}y^2 +\frac{G_1}{2 \rho \nu}hy \right ) \,dy \,dw' = \frac{G_1}{12 \rho \nu}h^2 = \frac{1}{18}v_{max} [/math]
Am I retarded? Why is the average speed is so low compared to the max?
When I did the same shit for a tube flow, I got [math] v_{avg} = \frac{1}{2}v_{max} [/math] which seems much more reasonable. I can't believe it changes that much if you add four corners in your pipe. Can anyone confirm if my approach is correct?

Can someone help me understand the answer?

Why does the question talk about f:A->B if in the answer B is never even mentioned?

This answer is so alien to the actual material the book presents i dont even know how to interpret it.

What is g:f(s) -> S? is f(s) B or the range of B?

It only ever talks about f:A->B and g:B->A or g:B->C including in other questions. I've never seen g:f(s)->S before.

Why do they have to introduce new material as answers to the questions? Sometimes this stuff is so demotivating.

>>14509250
Also the author is a piece of shit for saying shit like "clearly" right after delivering some rain man answer that i cant even decipher.

How do I get women? Serious question. People far less attractive and funny than me have done so. People talk about "just go outside and socialize" but that does not exist, it's considered weird to just go up to people and talk to them, and you don't see girls just roaming the streets(during the day). I'm not going to go to a bar nor an online dating site like tinder.

>>14509255
You are stupid. When the author says that it is clear, it means that you can figure out the
correctness of the claim instantly. If she says that it is not clear, it means that you may
need additional study and consult other sources. Either way it is helpful to you.

Given the position of a particle in a magnetic field [math]r(t)=(x(t),y(t))[/math]. We then have:
[eqn]\ddot{r} (t)= c\cdot\sum_{i=1}^{N} \frac{r-p_i}{||r-p_i||^3}[/eqn]
Where [math]p_i[/math] is the position of the charges and [math]c \in \mathbb{R}[/math].
We have to rewrite this into an ODE by introducing the help function [math]q(t) = \dot{r} (t)[/math], we'll then create a vector [math]y(t)= (r,q)[/math] which satisfies the system of differential equations [math]\dot{y} (t) = f(t,y)[/math].
Formulate this system of differential equations.

Where the FUCK do I even begin?

>>14509299
I know im stupid i dont need to be reminded twice now.

>>14509344
https://www.youtube.com/watch?v=zdJC-3ejmSE

>>14509347

>>14509250
>Why does the question talk about f:A->B if in the answer B is never even mentioned?
Generality.
>What is g:f(s) -> S?
A function from [math]f(S)[/math] to [math]S[/math] defined in the solution.
>is f(s) B or the range of B?
The range of [math]f[/math] restricted to [math]S[/math].
>Why do they have to introduce new material as answers to the questions?
There is no new material man.
>>14509328
Did you actually forget the ebin trick for turning a high degree ODE into a system of first degree differential equations?

>>14509365
okay thank you anon, i will go back and try and review that material and then go over that question again

>>14509365
>Did you actually forget the ebin trick for turning a high degree ODE into a system of first degree differential equations?
Yes, I haven't touched ODEs in a while.

>>14509328
r'' = g(r, r')

q := r'

(q', r') = (h(r, r'), g(r, r'))

where h(r, r') = r'

>>14509383
do post your progress

>>14509424
i went back and tried to refresh on my definitions and i found it, it was defined and mentioned in a short sentence and i must have read it but didnt understand it.

I kept thinking of f(S) was a function.

So f(S) a set, and is the image of the set S under the function f. And if f:A->B then S is a subset of A. And if S != A, then f(S) will be less than B?

so does f(g(x))=x have nothing to do with the composition which they define as (fog)(a) = f(g(a))?

this terminology is really upsetting.

>>14509568
also in this answer, it says let X = {x e A. Then says at the bottom a e X.

Is this a typo or is it saying a is an element of A and also X?

>>14509266

>>14509424
i made a drawing to try and understand and also rearranged the books definitions to try and make them make sense to me

does my drawring correct?

>>14509419
So I understand that [math]\dot{y}(t) = (\dot{r}(t),\ddot{r}(t))[/math], but I still don't understand how I can construct an ODE using that information.
I genuinely don't understand what I have to do, I haven't touched ODEs in years and reading up on it now is still not usefull, it only gave me a general idea of what to do.
I don't think I've ever encountered an ODE of that form.

>>14509623
>>14509266
>>>/adv/

>>14509631
I don't want to go there they post on reddit and there are people that claim to be women. I ask here because I think you can understand my situation more and could tell me what to say or share if you've had any success.

>>14509328
What does it mean to rewrite the [math]\ddot{r}(t)[/math] as a system of first degree equations?

>>14509629
>I still don't understand how I can construct an ODE using that information.
It's already a (system of) ODEs.
We only ever differentiate once with regards to time, hence it's an ODE.

>>14509682
So
[eqn]
r = (x,y)\\
q = \dot{r}\\
\dot{q} = c \cdot\sum_{i=1}^{N}\frac{r-p_i}{||r-p_i||^3}\\
y = (r,q)\\
\dot{y} = (q,\dot{q})
[/eqn]
becomes my system of ODEs?

https://en.wikipedia.org/wiki/Agrawal%27s_conjecture
What does [math](modn,X^{r} - 1)[/math] mean if n and r are integers?

can you combine functions using a logical connective to get one single function?
like if there was a square, and one function was to move it and another was to rotate, and i wanted one that did both at the same time.
could i write something like f ∧ g, if f and g were two functions. Or is that just dumb, and there's a much better way to do it.
I can't use function compisition because it involves applying two functions, one after the other, i just want write a single function that is made up of other functions.

>>14509682
>>14509419
>>14509365
>>14509328
After spending much more time than I should have I finally arrived at:
[eqn]\dot{y} = (\dot{r},\ddot{r}) = c\cdot\left [\sum_{i=1}^{N}\left(\int_{0}^{10^3}\frac{r-p_i}{||r-p_i||^3}\ dt + \frac{r-p_i}{||r-p_i||^3}\right)\right] [/eqn]
Is my answer right?

Is there any way I could safely harvest my own brain cells?

is it possible to have a 3d line function without using vectors or parameters? something like f(x)=ax+b

>>14509755
Yes.
>>14509946
What am I even looking at.
http://www.math.chalmers.se/Math/Grundutb/CTH/mve041/1415/material/mve041_ode.pdf

>>14510966
I was asked to find the [math]\dot{y}[/math] and turn it into code.
And that's what I got for some reason last night.
I'll try again today.

Let [math](X,\mu)[/math] be sigma finite. Given [math]k \in L^2 (\mu^2)[/math], the induced integral operator [math]A = A_k[/math] on [math]L^2 (\mu)[/math] is defined via [math]Af(x) = \int_X k(x,y) f(y) d\mu(y)[/math]. It is known that [math]A[/math] is compact and [math]|| A || \le ||k||_{L^2 (\mu ^2)}[/math]. Let [math]s_1 \ge s_2 \ge ... >0[/math] be the singular values of [math]A[/math]. I'm trying to show that [math]\sum_i s_i^2 < \infty[/math]. My attempts were futile tho... so I'd appreciate any ideas.

>>14511294
Do you have that [math]A[/math] is self-adjoint?
It doesn't make the problem easier, it just makes it less stupid. Expand it out by the eigenvalues and try to compute [math]\int_{X^2} k^2 \ d \mu^2[/math] and you'll get it.

Can I say a function is one to one if: for every b e B there is only one a e A that maps to it by function f? Or do I say "is mapped to it"?

And how come you can define it as VxVy(f(x)=f(y) -> x=y)?

I thought when you use an exclusive term like "only one" you have to include a Vz(f(x)=f(z) -> x=z) type of thing?

Ty for your patience

>>14511567
>Can I say a function [math]f: A \to B[/math] is one to one if for every [math]b \in B[/math] there is only one [math]a \in A[/math] such that [math]f(a) = b[/math] (read: "[math]f[/math] maps [math]a[/math] to [math]b[/math]")?
Not quite. What you're saying here is that the function is a bijection. There may be functions which are one-to-one (AKA injective functions) but not bijective.

Being one-to-one means [math]\forall a_1 \forall a_2 (f(a_1) = f(a_2) \Rightarrow a_1 = a_2)[/math]. If you think about it, this just means that the function never maps two different elements of the set [math]A[/math] to the same element in the set [math]B[/math].

Can someone explain to me how to understand the Y-axis of the following graph in the tweet?

>>14511636
okay thank you very much anon

Is this anywhere near an acceptable derivation of the chain rule?
[math]
h(x)' = \frac{f(g(x + \epsilon)) - f(g(x))}{\epsilon} \\
= \frac{f(g(x) + \epsilon g'(x)) - f(g(x))}{\epsilon} \\
= \frac{f(g(x)) + \epsilon g'(x)f'(g(x)) - f(g(x))}{\epsilon} \\
= g'(x)f'(g(x))
[/math]
My reasoning was that f and g would behave as if they were linear for a sufficiently small epsilon, and that I could exploit the fact that f(a + b) = f(a) + f'(a)*b when f is linear. It makes sense for an approximation, but I have no idea if this is actually valid for an infinitesimal epsilon.

I need to compute the Laplace transform of [math] t \int_0^t \tau^3 e^{2(t-\tau)} d\tau [/math]. Is there a way to do it without actually computing the integral.

>>14511814
Just integrate by parts a few times. If you can't do that and learn the pattern yourself, there's tables for engineers like you

>>14511359
Thanks remi. Not sure I catch your drift - doesn't [math]A[/math] being self-adjoint imply that [math]k(x,y) = \overline{k(y,x)}[/math] a.s. (which need not be the case)?

>>14511821
It's not that I can't integrate. I was wondering if there's a more "elegant" way to solve it.

>>14511840
The result is just simpler for self-adjoint [math]A[/math].
Otherwise you need to do basically the same thing but with extra steps: expand [math]A^*A[/math], write it out as an integral operator, "the sum of the squares of the singular values equals the L^2 norm".

How do I integrate:
[eqn]\int \frac{(x(t),y(t))-(p_1,p_2)}{\left(\sqrt{(x-p_1)^2 +(y-p_2)^2} \right)^3} \ dt[/eqn]
A better question at this point would be
>>14509328
How do I solve this?

>>14512033
>>14509328
I finally managed to understand what is going on.
https://math.stackexchange.com/questions/4457975/rewriting-system-of-second-order-differential-equation-as-system-of-first-order
for anyone that is curious

Is there any way to show

[math] E_{2}(-1/\tau)\tau^{-2} = \frac{12}{2\pi i\tau}+E_{2}(\tau) [/math]

without using conditional convergence property of [math] E_{2} [/math]?

I have an issue with my financial calculator: every time i try to calculate the standard deviation of the yield it gives me the wrong result.
Every other calculation is spot on.
it's an hp 10b, i've read the manual 10 times but i don't get what i'm doing wrong: to calculate the standard deviation you need to press the orange botton and then press the sigma x,y.

for example, this was a simple exercise i was doing a few hours ago.
there are 5 pair of variables: the x represent the yield, the y represent the chance
-25%, 10%
-15%, 20%
0%, 15%
15%, 25%
25% , 30%

the result it's around 17. something but the calculator says 18.43%.
i'm 100% sure i've computed the variables correctly because the first task is to calculate the expected yield (basically a weighted mean for x) and i get the correct result.

ps. i'm aware of the differences between population standard deviation and sample standard deviation.

If one spaceship goes 2/3 the speed of light and another spaceship goes 2/3 of the speed of light in the opposite direction that means that from the perspective of an observer in either one of the spaceships there's another spaceship going faster than light. Does this make sense?

>>14512207
https://en.wikipedia.org/wiki/Velocity-addition_formula

>>14512179
What on earth is [math]E_2[/math]?

>>14512281
>https://en.wikipedia.org/wiki/Velocity-addition_formula
true, thanks

>>14512282
oh sorry

[eqn] E_{2}(\tau) = 1-24\sum_{n=1}^{\infty}\frac{ne^{2\pi in\tau}}{1-e^{2\pi in\tau}}[/eqn]

See https://fungrim.org/topic/Eisenstein_series/ for more.

>>14512308
Is this about >>14508839 ?
Are you trying to use [math]E_{2}\!\left(\tau\right) = -\frac{12 i}{\pi} \frac{\eta'(\tau)}{\eta(\tau)}[/math]?
Did something go wrong with >>14508912?

>>14512356
*[math]E_2 ( \tau ) = - \frac{12 i}{\pi} \frac{\eta'(\tau)}{\eta(\tau)}[/math]

>>14496682
I've read more than one graduate level group theory book and have never seen that.. >>14496680 is a valid and useful concept

>>14511814
[eqn]\mathcal L \left \{ t\,f(t) \right \} = - \frac d {ds} \mathcal L \left \{ f(t) \right \} [/eqn]
More generally
[eqn]\mathcal L \left \{ t^n f(t) \right \} = (-1)^n \frac {d^n} {ds^n} \mathcal L \left \{ f(t) \right \} [/eqn]

What does it mean that "the momentum operator commutes with the vector operator B":
[eqn]\left[ \hat{p}, \vec{B} \right] = 0[/eqn]
How do I even unpack the commutator?
[eqn]\left[ \hat{p}, \vec{B} \right]\psi = -ih\nabla\vec{B}\psi+ih\vec{B}\nabla \psi[/eqn]
Is clearly wrong because what does it even mean to take the gradient of a vector??? A gradient wants to be fed a scalar function

>>14512166
:D

>>14512533
Usually [math][p, B] = \sum_n p_n B_n - B_n p_n[/math]
>Is clearly wrong because what does it even mean to take the gradient of a vector???
[math]\nabla \to \nabla \cdot[/math]

>>14512562
But you can't just replace a gradient with a divergence. Where is the mathematical legitimacy of this? Shouldn't the commutator for 3D operators be completely redefined?

>>14512533
>what does it even mean to take the gradient of a vector
just treat it like a scalar and it'll take the gradient of each element of the vector.

>>14512615
You really zeroed in on the second part of my post to the detriment of the first.
[math]\nabla \to \nabla \cdot[/math] is just a thumb rule.

my question about findom in the last thread went unanswered

A function f is piecewise continuous on the interval [a,b] if we can divide [a,b] into a finite number of subintervals such that:

1. f is continuous on each subinterval, and
2. f approaches a finite limit as the endpoints of each subinterval are approached from within

A function f is piecewise continuous on the interval [0,+inf] if it is piecewise continuous on every interval of the form [0,b].

Now define f(t) = t, if t is an integer, and f(t) = t^2 if t is not an integer. Is f continuous on [0,inf]?

My book says no, but I say yes. Who is right? It seems perfectly reasonable to say that a function with a finite number of removable discontinuities (one for each integer) on an interval [0,b] is piecewise continuous. The only explanation I can think of is that the second part of the definition isn't met because you can't approach a singleton subinterval from within. But then 2 should just hold vacuously, right?

>>14512822
>Is f continuous on [0,inf]?
I meant *piecewise* continuous, of course.

for x and y in G does <x,y> denote the cyclic group generated by x and y and does <x> denote the cyclic group generated by x?

>>14512514
Thank you man.

>>14511789
pls halp?

>>14511789
[math]g(\varepsilon) = \varepsilon g'(x)[/math]
How is this true?

>>14513064
I don't think it is... I don't think I did that... what step are you talking about?

>>14489612
Are stellate cells found in the liver? I know they’re mainly attributed to neurons and nerves but it was a question I missed on the test but I was told by my tutor and a few medical journals they are found in the liver but my professor said they were not and I told him it was his class and test so I would take his word

Is there a way for a brainlet to learn how to make a stupidly unfair, biased dice game that appears somewhat fair? Like, are there any good probability lectures for that?

>>14513281
Unfair in what way?

Am i retarded or is the course retarded?
Question is in the picture, supposed solution is O(n^2) since the outer for loop takes n steps and the inner one takes n^2 + n, so the total result is n^2 + 2n

But shouldnt it be n * (n^2 + n) ?? since the inner loop is called n times?

>>14513293
In a way that makes it very very improbable for a player to win against the house, but seems innocently fair. The kind of game that's meant to trick mathlets in a sham casino into going in for more and more rounds.

>>14513355
Create a "skill-based"/"competitive" game where each participant needs to put down some money to particiapte in a match, and the winners get the pot (through whatever means of redistribution). Program a match-making system that ostensibly matches players according to their skill level. Take some percentage of the pot as a matchmaking fee. Now, under a fair matchmaking system, all of the participants will only keep losing money on average -- now who wants to play that?? But here's what you do instead: you track the suckers who dump significantly more money into it than the average and match them up with people who they will most likely win against, giving them artificial winning streaks, thereby encouraging them to play more and put more money in. Of course, under this scheme, you are fucking over a majority of players who put in little money in order to entertain the minority of people who put in a lot of money, but that's okay, because you just use a fraction of the profits to advertise your junk and draw in new victims. There you go. You can unironically make hundersd of millions with this scheme.

>>14512615
[math]\displaystyle \nabla (f(x, y, z), g(x, y, z), h(x, y, z)) = \left(
\begin{array}{ccc}
f^{(1,0,0)}(x,y,z) & f^{(0,1,0)}(x,y,z) & f^{(0,0,1)}(x,y,z) \\
g^{(1,0,0)}(x,y,z) & g^{(0,1,0)}(x,y,z) & g^{(0,0,1)}(x,y,z) \\
h^{(1,0,0)}(x,y,z) & h^{(0,1,0)}(x,y,z) & h^{(0,0,1)}(x,y,z) \\
\end{array}
\right)[/math]

https://en.wikipedia.org/wiki/Gradient#Generalizations

>>14512615
[math]\displaystyle \nabla (f(x, y, z), g(x, y, z), h(x, y, z)) = \left( \begin{array}{ccc} f^{(1,0,0)}(x,y,z) & f^{(0,1,0)}(x,y,z) & f^{(0,0,1)}(x,y,z) \\ g^{(1,0,0)}(x,y,z) & g^{(0,1,0)}(x,y,z) & g^{(0,0,1)}(x,y,z) \\ h^{(1,0,0)}(x,y,z) & h^{(0,1,0)}(x,y,z) & h^{(0,0,1)}(x,y,z) \\ \end{array} \right)
[/math]
Which is the Jacobian.

https://en.wikipedia.org/wiki/Gradient#Generalizations

>>14513377
I suppose I should've been more specific. I want this game to work in the house's favor even when there's only a single player going up against the host. I'm not planning to create a mass scheme, just to trick a single player with lower than average math skills.

>>14511789
G-guise? Halp? I know this is probably wrong, but I just want to know under what circumstances that reasoning becomes invalid.

>>14495198

i think developping abstract thinking is corelated with memorising part of the brain

>>14512664
>You really zeroed in on the second part of my post to the detriment of the first.
You are right. With that definition, it makes sense I guess. That however would mean that the commutator can be zero even if the single "components" (i.e. [math] p_i B_i - B_i p_i [/math] for [math] i=x,y,z [/math]) aren't zero. Is that right? Seems kinda weird

>>14512627
But then how do I treat the other term, that is, the application of a vector operator (which is supposed to multiply a scalar) to another vector (the gradient of the wavefunction)?

Are smoothbrains always differentiable?

>>14513425
What you have is, more or less, a proof of the chain rule for linear functions. Derivatives are usually defined in terms of limits rather than infinitesimals, but the argument with infinitesimals can guide the direction of a proof with limits.

>>14513622
Am I correct in assuming that differentiable f and g can be approximated by linear functions for the purpose of approximating h, and that the approximation will converge on the true value as epsilon gets smaller? If so, is there a straightforward way to state this in terms of limits?

How did tsmc and Taiwan gain such a monopoly on chips? Why is it so hard for other countries to catch up and how will they catch up?

>>14513007
No <x,y> need not be cyclic, take the dihedral group where x is a rotation and y a reflection

>>14513730
>is it so hard for other countries
playing catch-up is too expensive since while you're learning, the chips you make aren't as desirable as they were years age when tsmc made them.
so you can't get your investment back by selling your catch-up product, and you just have to swallow the losses until you're as good as tsmc. No one can take those losses.

>>14513730
>is it so hard for other countries
Playing catch-up is too expensive since while you're learning, the chips you make aren't as desirable as they were years ago when tsmc made them.
So you can't get your investment back by selling your catch-up product, and you just have to swallow the losses until you're as good as tsmc. No one can take those losses.

If I roll a 1d100 and my result is higher than 60, then roll another 1d100, what are my chances to roll above 0 if I subtract my previous result from said die roll?

What's with these artificial intelligence bachelors popping up ? Why are they supposed to diverge from CS ? t. mathchad

>>14513745
39/100

In this passage by Gottlob Frege, is he saying that logic seeks to find truths about truth?

>Just as “beautiful” points the ways for aesthetics and “good” for ethics, so do words like “true” for logic. All sciences have truth as their goal; but logic is also concerned with it in a quite different way: logic has much the same relation to truth as physics has to weight or heat. To discover truths is the task of all sciences; it falls to logic to discern the laws of truth. [Frege, 1918–19, 351]

>>14513760
Same reason there are ‘future planet studies’

>>14513745
40/100 - (PrevResult-60)/100

>>14513768
Come again? What even is future planets ?

>>14513767
No

>>14513763
Nvm

>>14513769
That formula shows the logic I used to answer the question. A simplification gives (100 - PrevResult)/100 = 1 - PrevResult/100

>>14513781
Which shows that choosing 60 as your cutoff doesn't impact the solution

>>14505863
>hydrogen peroxide
measure its density?
https://www.usptechnologies.com/density-specific-gravity-of-hydrogen-peroxide-solutions/
E.g. with an accurate pipette and scale?

>>14513769
I guess I'm an idiot. I thought the chances would be against me.

>>14513810
i decided to tear open a couple D-cell batteries and use the magnesium oxide in them.
it's impure, with things like zinc and carbon, but an excess fully reacted with the H2O2.

where can I download more ram?

>>14513822
They are against you, the best chances you're gonna get are 4 in 10. (Actually I fucked up the formula a little bit, I acted like you said greater than OR EQUAL TO 60. This causes a small change in the formula (60 becomes 61, 40 becomes 39), but after simplifying you end up with the same 1 - Prev/100 from before. But since you assume PrevRes > 60, this means the best chances you're going to get is when PrevRes = 61, and your chances are 39/100. That is not in your favor.

Maybe I misunderstood your statement of the problem?

>>14513995
You didn't misunderstand, I worded it badly in both of my posts and asked a completely different question from what I had in mind, which was the probability of both of those rolls happening in sequence (Both the chance of rolling higher than 60, and then immediately needing to subtract it from the next result). I was wondering if the odds would turn worse than 60/40, but I think(?) I figured it out on my own. Thank you for the answer.

Testing:
>a
>a
>a

>>14514142
Bonus test:
[math][/math]>a

so im a graduate from a low tier uni that found employment at a very high tier one because of my niche knowledge and my boss is encouraging me to take classes on campus.

are there any relatively 'safe' stem classes I can take? To emphasise how poor my uni education is, it was commonly known that all you had to do to pass a class was make sure you were not in the bottom 10% of the class and the profs would curve the grade so hard it effectively becomes orthogonal.

I asked the math thread and they said fuck off so im hoping that there's something out there that I can take that I wont absolutely get butt fucked in

>>14514569
Have you posted before? I think I remember you from abt a week ago, wondering if you were in over your head...

>>14514606
in the math thread yeah, there were a few hopeful voices but im convinced I'd just get in the way. I'm hoping maybe something in biology, but that has its own headaches I assume

>>14514569
What even happens if you fail a class?
Just nut up and go for it.

>>14514569
Drop periods exist for a reason, enroll in a handful you're interested in and narrow it down later. Sometimes just getting a look at the syllabus is enough to tell if you're not prepared for a course.

>>14514569
biology is pretty braindead.
i don't know what type of course you're taking but any course that a freshman would take, you could obviously take. anything without prereqs implies that you don't need to know anything in order to take it.

chemistry is usually pretty difficult in the sense that there is a lot of memorization and rules to learn. i enjoyed the calculus i took in college but i also like math.

take something you're interested in. you have the opportunity to learn, so you might as well pick something you might enjoy.
for my chem E program, there was a mandatory materials science course. i think it was under the school of mechanical engineering, but it was one of the most interesting courses i took.
i thought "fuck me this sounds dry and boring" but the professor talked about shit like strength and toughness, and how they differ. how different steels have different properties. how the crystal structure of a material changes it. how materials are tested, etc.
it even sounds dry to talk about it but it was very interesting because of how applicable it was to home projects, like building a shed and how different materials will behave differently, and how to interpret material properties.
like, buying a power tool, and it's 15% glass filled nylon. i wouldn't think about it before, but i now know about how it would be molded and what the glass fiber does to increase the durability of the product. really neat course.

mechanics: find v avg of a biker hitting 50km/h in the first part of the travel and 75km/h in the second

why the book impplies that the answer is 60km/h if the results show 75km/h?

Δt = s/v avg > s(first part)/50
s(second part)/75

travel's total:
s(total, or 2, the travel's two parts)/3750 = 75km/h

what happened here?

>>14515123
oh shit you are supposed to add? this way we have 125÷2=62.5 rounded down to 60, thats how you do it?

Anon, I want you to make a new thread.
Don't forget the thread subject and to link the previous thread.
Also, remove wakarimasen and fireden from the archives list because the former is offline and the latter hasn't updated for a month now.
Thanks.

>>14515147
Ok >>14515149

>>14515150
Very nice, thanks a million.

>>14506284
>Klein-Gordon Equation
You mean Dirac equation

>Is there some form of relationship between Gamma Matrices and 4x4 Matrix Representation of Quaternions?
Sort of.
The gamma matrices are connected deeply to the Lorentz group SO(3,1). The imaginary part of quaternions is connected in the same manner to the rotation group SO(3).

The 2x2 matrix representation of quaternions is essentially the same thing as Pauli matrices, and tensor products of the Pauli matrices can be used to construct the gamma matrices. So probably you can write the Dirac equation in terms of quaternions in some convoluted way.

The 4x4 matrix representation is not literally the same thing as the gamma matrices though. The only point of going from 2x2 to 4x4 is that the matrix becomes real, and the gamma matrices are not real.

I'm getting only b) is linearly independent only for x ≠ 2 and a), c), d) is linearly dependent. Is this correct?