/sci/ - Science & Math

I was tallying the questions and clicked the refresh page button midway on accident, hence there will be no tally.
Thank you for understanding.

>inb4 how did you even click it mid tally
I was trying to switch tabs to check my notifications.

>>15246644
Not sure how stupid this question is, but:

Given a closed/open convex subset C of the plane, with the origin not in C , is there necessarily some straight line (extending infinitely in either direction) through the origin which is disjoint from C ?

[ If the "closed/open" condition is dropped, the answer is "no" as another anon pointed out in the previous sqt thread. ]

>>15246657
thanks for telling me

>>15246683
Yes. Immediate hyperplane separation theorem consequence.

>>15246683
Found the answers; can explain if anyone would like to know.

>>15246777
Incorrect, for C convex closed (and not containing the origin) it is possible no line through the origin is disjoint from C.

However, for C convex open (and not containing the origin), there must be a line through the origin disjoint from C.

>>15246827
Sorry my mistake! Impossible in both cases.

>>15246777
Nice theorem, thank you anon.

>>15246777
Thank you for letting me know about this theorem.

>>15246593
You can speed things up slightly by using the reduction formula for powers of cos rather than integration by parts. It'll take time, still, but less time.
https://en.wikipedia.org/wiki/Integration_by_reduction_formulae#Transcendental_functions

>>15246644
Place a dipole magnet with dipole moment mu at the origin of a coordinate system.
Place a metal sphere of radius r at position vector x_1.
The metal sphere oscillates in the radial direction towards and away from the magnet with frequency f and amplitude A.
Place a magnetometer at position vector x_2.
What is the magnetic field B(x_1, x_2, t) measured by the magnetometer?

I'm wondering if there is a nice way to get an analytical expression for this using Maxwell's Laws. It's been a while since I've touched them and I am rusty.

Is there a C—C≡C—C analogue to cyclohexane? As in, would such a C24H6 be in a cyclohexane conformation, but much larger?

>>15246681
Compile the questions elsewhere (like on Notepad) next time.
Adding a maid because there was an unanswered maid question.

Unanswered questions:

Maths questions:
>>15222604
>>15223085
>>15229524
>>15231742
>>15232036
>>15235378
>>15240736
>>15241022
>>15243258
>>15245064
>>15245762
>>15246441

Physics questions:
>>15224119
>>15239421
>>15246221

Chemistry questions:
>>15230240

Maid questions:
>>15229291

Stupid questions:
>>15220043 [You get used to it.]
>>15221585
>>15223261 [Take mathematics/CS double major]
>>15226486
>>15227152
>>15232510
>>15233350
>>15235080
>>15240061
>>15242980
>>15244744

Two identical bodies are in free fall, but one of them is rotating. Our professor told us that the bodies might reach the floor at the same time, but that won't happen if the rotating body rotates in such way the gravity makes work in its rotation. I don't really get what he meant by this, could someone explain it to me please?

>>15246221
This book does suck.

2-sided bandwidth is 100 Hz, nyquist is 200 Hz.

I'm a mathematician turned AI engineer, mainly focused on language modeling. I'm not looking for a change of field yet but I'd like to broaden my expertise as I'm now working on a kinda niche part of NLP. More and more connections start talking about AI in biology/drug discovery, I'd like to learn more on that. It's not urgent so I can start from the basics. What's the shortest path I can follow to understand basic biology, computational biology and some pharmacology?

when dealing with ODE's, is it correct to say ''Our objective is to find an expression for y that also englobes the solution to the initial value problem''?

>>15222604
>What is a good book on discrete mathematics? I'm currently reading Biggs "discrete mathematics" which is horrible.
It would help if you say why your book is bad. Personally I'm a sucker for stuff by Lovász, e.g. these lecture notes: https://cims.nyu.edu/~regev/teaching/discrete_math_fall_2005/dmbook.pdf
He also has a problem book which is excellent but more advanced.
>I'd also like a recommendation for a book covering algorithms and complexity, i'm reading Kleingberg's "algorithm design" which is okay but it could be more fleshed out
I liked a grad book by this guy, and therefore assume his beginner books are good too: https://www.algorithmsilluminated.org/

>>15229524
Stein & Shakarchi

>>15231742
Youd picture doesn't give a lot of context, but the only envelope theorem I know of (economics) states that under some regularity conditions you only need to optimize over exogenous parameters.

>>15232036
>Is there a class of probability distributions that work well with geometric 2D objects or explicitly 2D distributions or an operation that works on 1D distributions to make them 2D?
Depends on your desired structure. If you want it uniform you can just use two `separate' variables for each dimension.
>For example, lets say I want a normal distribution around the origin of the xy-plane.
Bivariate normal is what you want, probably.
>On the other hand, creating the same distribution using polar coordinates (r,θ), distributing θ uniformly seems like it will 'double up' around the center.
You need to correct for this with a factor [math]\sqrt x[/math], look into the `transformation theorem'.

>>15235378
>What materials can I read to get a grasp of gambling-focused math?
Any book on elementary probability theory will do, probably. If you know how basic counting works you can answer most questions like yours, if you know what a martingale is and how harmonic functions relate to random walks you can get into ruin theory which is what casinos &c use heavily.
In any case, it seems to me that at every `time step', a player picks a random card, and so does the dealer. It makes no difference that the player can choose from 4 options, or that the dealer's card is face-up. By symmetry the probability of winning or losing is 50% and you will almost surely go broke. Look at the `St. Petersburg paradox' for some intuition.

>>15245064
>What's the point in learning to solve differential equations when almost all have no closed form solution?
You can use what you learn to help derive properties of unsolvable diff eqs.
>Are results from physical theories with exact solutions superior?
Being exactly solvable probably means your model is too simple. Still, an exact solution is superior when it can be used to calculate quantities of interest faster and more reliably.

>>15245762
>Simulating stuff in excel
ISHYGDDT
>I don't understand how to use the IF function in this context or anything
You (probably) want to generate a random number between 0 and 1 and check IF it is <=0.5.

>>15229291
>Do other kinds of math have this trick?
I wouldn't call it a trick, but rather a consequence of the fact that most math is derived from set theory. I suppose some more advanced math has the same relation to something like measure theory, for example.
>Please tell me how to draw arrows with Latex.
Tikz.

>>15221585
First prove you're not a one-to-none function.

>>15227152
At some point your textbooks start citing a lot of papers.

>>15223261
A lot of CS people I know say they wish they knew more math, and a lot of the math people I know wish they were better at CS (not the pure math people though).
I agree with trying to double major, but would advise against getting graduate degrees (in america). It's not usually worth the cost, and especially in CS you're better off having more experience.

>>15223261
I am saying this unironically, pure math is the best career choice you can make. Nothing makes you more of a generalist than having the ability to pivot into any STEM field as quickly as a pure mathematician.

You wanna do CS? It's practically discrete math and formal language.
You wanna do AI? It's practically matrix calculus, naive probability theory (non axiomatic, that is), statistics, and linear algebra.
You wanna do physics? It's practically functional analysis, group theory, representation theory and differential equations (well, this one's debatable, it's a bit more but the rest are usually easy to pick up)
You wanna do economics? It's practically game theory and differential equations
You wanna do chemistry? It's basically topology and group theory (at least the nice chemistry, the rest are memorization and practice).

Did you notice any patterns? These are the exact courses that make you a mathematician. Now, what do you think is easier in a pinch; Self-teaching organic chemistry nomenclature or group theory?

I'm trying to understand Neumann (1940)'s paper "On the commutativity of addition". If I understand him correctly, he begins by claiming:
>Let [math](S, +, 0, -)[/math] be a group in which [math]x + x = y[/math] always has a unique solution [math]x[/math] for every [math]y[/math]. Then the automorphism [math]x \mapsto -x[/math] is involutive on [math]S[/math] and fixes only [math]0[/math].
So far so good, that's not hard to show. But he then goes on to assert (without elaboration) that:
>If [math]x \mapsto -x[/math] is the only automorphism with this property (involutive on [math]S[/math] and fixing only [math]0[/math]), then [math]S[/math] must be abelian.
and I have no idea how he got to that conclusion. Why does it follow?

>>15247577
Answering my own question: the crux of Neumann's proof is to justify that the involutive mapping [math]T(x)=-x[/math] is really a group automorphism, from which commutativity follows as
[eqn]x+y = T(T(x)) + T(T(y)) = T(T(x) + T(y)) = -(T(x) \, + \, T(y)) = -T(y) \, + \, -T(x) = y+x[/eqn]

Could someone help me with this math assignment? I don't understand how to use the excel function or how to go about doing the assignment.

Probability theory btw.

>>15246644
Good numerical analysis book for pure math?

what is the intuition behind the 'r' inside the factorial in the numerator?

How would you go about showing the uniqueness of Xi? These are all linear transformations and vector spaces in the diagram.

>>15247823
What are you counting?

>>15247823
https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)#Theorem_two
with 'k' in the place of 'r'.
Each k-tuple of integers that sum to n corresponds to a tally of the number of times that each item (out of k) was chosen.

Is there a mathematical symbol for "for all but infinitely many in the context of infinite sets" (so "for almost all" colloquially). If so, what is the latex command?

>>15247903
Never heard of such a symbol personally

>>15247903
>>15247906
I made a mistake "for all but finitely many in the context of infinite sets". That's what I want to have a symbol for. Excuse me

>>15247924
It is clear what you meant. Still never heard of such a symbol

>>15247834
Flip the left morphism to work with [math]pr_i: \prod_{j \in I} V_j \to V_i[/math] ([math]\displaystyle \bigoplus _{i \in I} V_i \hookrightarrow \prod _{i \in I} V_i[/math] is actually obtained by choosing inverses to all [math]pr_i[/math] and then factoring the morphisms through the sum, so you can do this) and then argue from coordinates.

>>15248023
does your xi look like this?

>>15229291
>Set Theory has a trick where other kinds of math get defined or get proved with Set Theory
Wrong. It's all set theory

Let [eqn]\Phi: G \times M \to M[/eqn] be a free and transitiv group action. I know that [eqn]\Phi_{p}: G \ni g \mapsto \Phi_{g}(p) \in M[/eqn] is bijective for all [math]p \in M[/math]; my book now wants me to show that this map translates the "canonical group action from [math]G[/math] to itself" to the group action [math]\Phi[/math] via left multiplication. Do you guys understand this question and how it can be solved? If so, can you please tell me? Thank you.

>>15248557
Here's the background why I need this: I want to show that the definition below is equivalent to the conventional definition of affine spaces (V is a vectorspace over a field F; A is a set; and there is a free and transitive group action with A and V). I suspect that I have to use the bijectivitiy of [math]a -: A \to V[/math] to formulate the inverse [math]a +: V \to A[/math]; afterwards I have to (somehow) use the result from >>15248557 to construct (some) map, for which I can then check if it is a free and transitive group action; if it is, then the definitions are equivalent. I'm stuck at >>15248557; I tried to guess what the map could be, but it was all to no avail. I don't know how to progress from here. Any help is much appreciated.

Definition. A set A with a vectorspace V is called an affine space, if there is a mapping [eqn]-: A \times A \to V[/eqn] such that [math]a-: A \to V[/math] is a bijection for all [math]a \in A[/math], and if the identities
[math]
(i)\ \ a - b = -(b - a)\\
(ii)\ a - c = (a - b) - (b - c)
[/math]
are true for all [math]a, b, c \in A[/math]; note that [math]-[/math] has more than meaning in the context of these conditions.

Dunning-Kruger might be a parody. In other words, they accuse other psychologists of having low skill and high confidence in their statistics. If "regression to the mean" explains their data, then the study itself becomes an instance of low skill and high confidence in statistics.

>>15246644
What is it with weirdos always thinking anti-gravity or a machine that can control gravity (if you're in deep space and need gravity for humans on board to not get sick) are possible?

I'm coming here since I don't exactly know what to ask. We have modelled what we see and hear with waves, a vibration going back and forth, or up and down. If we change the hertz we change the color of light or tone of sound. If the amplitude is raised the sound gets louder and for light I'm guessing it becomes brighter. The question is I suppose, do we need an entire discrete cycle of crest to trough or vice versa to see or hear anything at all? What if we cut the wave and only get the crest for example, or cover our ears before a whole cycle enters us, do we hear something? What are we hearing? What if we imagine the smallest part of the wave reaching our eye, a single photon before covering our eye. Do we see anything, a white light? Is this different for a phonon?
I'm basically asking how am I supposed to think about this?

>>15248891
after some searching. "One phonon is the quietest sound" and "The human eye is very sensitive; but can we see a single photon? The answer is yes: sensors in the retina can respond to a single photon. But neural filters only allow a signal to pass to the brain to trigger a conscious response". Neither make much sense. How can we hear a phonon as the most quiet sound if it has is no amplitude? And the light answer basically says "yes but actually no".

>>15248919
It says it's the quietest sound, it doesn't say you hear it.

>>15248982
a quiet sound has a low amplitude, a loud sound has a high amplitude.
Shouldn't the quietest sound be a wave with an infinitesimally small amplitude?

>>15248891
The shorter a sine wave snippet gets, the broader its frequency bandwidth. IIRC, a 1ms pulse has a frequency range of 1kHz, so a 10kHz sine pulsed for 0.5ms is really a range of sines from 9kHz-11kHz.

With ultra short pulses, you're essentially only getting a burst of white noise, limited by the width of the pulse.

>>15248146
Yes.
>>15248557
>>15248682
Fix [math]p \in M[/math]. This induces a bijective map [math]\Phi_p : G \to M[/math] by [math]\Phi_p (g) = \Phi(g, p)[/math].
This bijection lets us canonically identify [math]G[/math] and [math]M[/math], hence the group action on [math]M[/math] becomes the group action by left multiplication on [math]M[/math].

Could someone explain to me this problem and what's going on in it?

It's been a month since the instructor went over this topic and the example he posted sucks.

>>15248994
A phonon is a single quantum of vibration. Yes it can have a range of energy values (amplitudes) the medium allows but since it's a quantum harmonic oscillator in nature it will always have a non-zero minimum value. I guess what the statement forgot to say is that the quietest sound will always be a single phonon but not every phonon will have that amplitude.

>>15224119
Integrate the current from time 0 to time t. And divide by the capacitance.
i(t)=Cdv/dt so v=1/C*integral(i(t)dt)

>>15248891
I think you can look at the Fourier domain of the half-pulse and see what frequencies it is composed of, then use that to determine what frequencies will be heard.

>>15246221
For a rect function, its width is from w/(200*pi)=1/2 to w/(200*pi)=-1/2
so f=50hz to f=-50hz, I get the bandwidth is 100 hertz. I think the bandwidth should be 2B instead of B.

>>15249674
Little endian will be reverse of what is in memory / on the stack. So it'll print "04030201"

>>15249786
>Little endian will be reverse of what is in memory / on the stack. So it'll print "4d3c2b1a"

>>15249771
Ignore negative frequencies. The Fourier transform of a real signal will always have conjugate symmetry. When expressed in terms of sin/cos (rather than e^jx), sin(-ωt+φ)=sin(ωt+(π-φ)), i.e. negative frequency becomes positive frequency with complementary phase.

Bandwidth only considers absolute frequencies. This becomes more obvious if you look at something which doesn't include DC. E.g. a 20 kHz signal amplitude-modulated onto a 500 kHz carrier has a spectrum which ranges from 480 kHz to 520 kHz. That's 40 kHz. If you were to include the negative part, -520 kHz to -480 kHz, you'd have a spectrum from -520 kHz to 520 kHz, i.e. 1040 kHz.

This question has been bugging me for years:

1. light energy is proportional to frequency
2. frequency is the wavelength of light
3. the wavelength of light is not amplitude
4. the wavelength extends and contracts in the same direction the light travels
5. light photons have the same surface area regardless of energy (in the direction they travel, if that matters?)

Then why does the size of a hole affect the ability of light to pass through a mesh?

Eg microwaves can have a mesh on the front that allows you to see inside them because the holes are smaller than the wavelength of microwave radiation that they emit, so the harmful radiation cant escape, but visible light has a smaller wavelength so it can pass through the holes of the mesh so you can see inside

But having a lower frequency doesnt make the photon move further away from its center, that would be amplitude, right? so why does having a higher frequency allow the light to pass through smaller holes?

>>15250083
Not really how the microwave mesh (or faraday cages) work; it's only because these materials are conductors. The energy around a certain frequency is (mostly) 'captured' or 'reflected' by the metal, rather than continuing to propagate forward. (Primarily it's reflected and interferes with the original wave.)

>>15250083
> 1. light energy is proportional to frequency
Correct. [math]E = hf[/math]
> 2. frequency is the wavelength of light
False but they are linked. [math]f\lambda = c[/math]
> 3. the wavelength of light is not amplitude
Correct.
> 4. the wavelength extends and contracts in the same direction the light travels
Completely wrong. This is not what happens at all, the wavelength does not change.
> 5. light photons have the same surface area regardless of energy (in the direction they travel, if that matters?)
I have no idea what you're trying to say here since photons don't have a surface area or a width.

> Then why does the size of a hole affect the ability of light to pass through a mesh?
See >>15250094 but they forgot to mention one thing. The holes have to be smaller than the wavelength of the electromagnetic waves you want to block.

I can't solve this little fellow here. Any help ? Severely depressing, I know

>>15250248
if you use the substitution [math]x^{p/2}[/math] then you can transform this into a cubic equation [math]x^3-6x^2+16=0[/math], it has three roots one of which is negative (so it can't be used), therefore giving you two solutions which you can find by doing the inverse substitution
there may be a simpler way but I don't see it right now

>>15249256
So [math]\Phi[/math] could be written as [eqn]\Phi: G \times M \ni (g,\, p) \mapsto \Phi_{p}(g) = \Phi_{g}(p) \in M\,?[/eqn]And with "canonical group action from [math]G[/math] to itself" the book means the map [math]\Phi_{p}[/math]? Did I understand this correctly?

>>15250352
No, no, no.
The canonical group action from [math]G[/math] to itself by left multiplication is [math]\Psi: G \times G \to G[/math] given by [math]\Psi(g, h) = gh[/math] ([math]g[/math] acts on [math]h[/math] through left multiplication, hence the name).
[math]\Phi_p[/math] just bijects [math]G[/math] and [math]M[/math], which makes these two actions equivalent.

>>15250272
This seems simple enough to me.

>>15250378
Okay, thank you!

I just got mogged by fucking jewgle. seriously tho how the fuck does grass have ALL elements of the periodic table that are necessary to make a cow and mammal herbivores in general?

>>15249970
But if you demodulate the signal, its from -20Hz to 20Hz. The bandwidth should still be 40Hz. For the digital version the fft repeats and doesn't have to have a negative part unless the signal is demodulated sk the center frequency becomes 0Hz. When you move from the laboratory frame to the rotating frame in MR physics you do consider the negative part.

what am I doing wrong here with partial derivatives? I don't think I should be getting the starting eqn back.

[math]

\dfrac{\partial}{\partial z_i}[\dfrac{e^{z_i}}{\sum^{c}_{j=1}e^{z_j}}]=
\dfrac{\dfrac{\partial}{\partial z_i}[e^{z_i}] \cdot \sum^{c}_{j=1}e^{z_j} - e^{z_i} \cdot \dfrac{\partial}{\partial z_i}[\sum^{c}_{j=1}e^{z_j}]}{(\sum^{c}_{j=1}e^{z_j})^2} = \dfrac{e^{z_i} \cdot \sum^{c}_{j=1}e^{z_j} - e^{z_i} \cdot 0}{(\sum^{c}_{j=1}e^{z_j})^2} = \dfrac{e^{z_i}}{\sum^{c}_{j=1}e^{z_j}}

[/math]

>>15250634
You are acting like [math]z_i[/math] is not present in the sum in the denominator, in which case you are just taking the derivative of some constant times exp.

>>15250641
[math]Z_i[/math] is literally not in the denominator though

>>15250647
then it's correct though

>>15250634
If [math]e^{z_i}[/math] is in the denominator, then you shouldn't be getting back the starting equation. If it isn't, then you should.

Good Morning /Sci/entists.

I am working on my book more. I have questions but to keep from junking this thread I am going to link to the one I made on the dra/g/on maid board.

>>>/g/91908562

Thank you /Sci/entists for reading my post.

Hello, when can i take the derivative of an infinite sum and infinite product of a sequence of functions? I know the infinite product case can reduce to the infinite sum case by taking the logarithmic derivative, and i know the differentiability of an infinite sum has something to do with uniform convergence in its radius of convergence, but I still dont get it. An example of something say like the derivative of [eqn] \sum_{n=-\infty}^{\infty} q^{n^2} [/eqn] would be ideal. Basically i want to justify differentiating theta functions but am i just supposed to show the uniform convergence of the sequence of the terms' derivatives or what? Note these are complex functions if that makes a difference. Thanks.

>>15250701
Here is how I see it:
Assuming [math]\abs{q}<1[/math] (otherwise it blows up), note that [math]\sum_{n\in\mathbb Z}q^{n^2} = 1 + 2 \sum_{n\geq1}q^{n^2}[/math] and that [math]\sum_{n\geq1} n^2 q^{n^2}\leq \sum_{n\geq1} n^2 q^n=\frac{q(1+q)}{(1-q)^3}<\infty[/math], so that by the DCT you can say that [math]\partial_q \sum_{n\in\mathbb Z}q^{n^2} = 2\sum_{n\geq1}n^2q^{n^2-1}[/math]. Good luck computing it though because I don't think there is even an explicit form for the original sum.

>>15250677
Maids don't need to have big tits. They just need to have a deredere personality.

>>15250747
On second look this is only true under the hypothesis that $|q| < k$ for some $k<1$, which is significantly weaker.

>>15250747
On second look this is only true under the hypothesis that [math]|q|<k[/math] for some [math]k<1[/math], which is significantly stronger. (otherwise the resulting expression can blow up as [math]|q|\to 1[/math].

Does anyone know an example of a non-unital but injective "rng" homomorphism between unital rings?

>>15250701
For a general infinite sum/product of functions the general convergence behavior is probably more complicated.


However for a *complex* *power series* (centered at any point) , the convergence set is always shaped like a disk (together with some subset of the boundary) whose radius is called the radius of convergence (ROC) ; or just the center point (ROC=0), or the entire complex plane (ROC=infinity).

Determining the convergence set then comes down to 1. finding the radius of convergence , and 2. if the ROC is positive finite , then also determine which boundary points are convergence points.

>>15250901
Forgot to say, the disk of convergence is centered at the center of the power series

>>15250894
Something like
[eqn]x \mapsto \begin{pmatrix} x & 0 \\ 0 & 0 \end{pmatrix}[/eqn]

>>15250915
Ah yes thank you

I've just realized that I still use "cringe" in 2023 because I (subconsciously) find it less hurtful than outright calling things "embarrassing", is this normal?

Does someone have this paper?
10(dot)1038(forwardslash)s43587(dash)022-00183-2
>spam detection on doi string

>>15250901
Thanks that made things clearer!

>>15250956
i got it. how do i upload to scihub?

>>15250225
>>15250094

but why does the hole have to be smaller than the wavelength of light?

if its not about a certain width of wavelength managing to fit through the hole, im confused why its the wavelength that is the important thing

i'm thinking of it like a (made up numbers) photon with a wavelength of 2.1mm not managing to squeeze through a hole that is 2.09mm wide

>>15250990
U can email it to Alex (alexandra@dns.cymru) but generally the pirated scihub/libgen stuff is updated in big swaths at a time from dumps.

>>15250997
sounds like a lot of work
wow, the spam filter REALLY doesnt like anonfiles

>>15250894
>>15250915
Also I think any direct product of two nonzero rings

>>15251033
Many thanks, anon.

>>15250901
>>15250958
Also I should have added, a complex power series will not only converge uniformly to some f(z) everywhere within the interior of the disk of convergence, but also will be holomorphic in this region, and the term-by-term derivative of the power series has the same property and is the power series for f '(z) .

In full generality it's not necessarily true that term-by-term differentiation of a sequence of functions equals the derivative of the limit of the sequence

>>15251060
<3

Would anyone know an example of ideals [math] I,J [/math] in a commutative ring [math] R [/math]
such that the ring homomorphism [math] (R/I) \otimes_R (R/J) \rightarrow R/(I+J) [/math] is non-injective?

>>15250993
Think of it a bit like resonance, the material is susceptible to those particular wavelengths (and their higher order harmonics) because they "match" the material's impedance at that frequency.

Let [math] I,J [/math] be ideals of a commutative ring [math] R [/math].
If [math] (R/I) \otimes_R (R/J) = 0 [/math]
then does [math] I + J = R [/math] ?

>broke mercury thermometer next to my bed
>possibly spread some mercury around the house
>clean up visible drops
>didn't use sulfur
>toxicologist says I should be fine
>freak out every time I feel something that vaguely maps onto Hg poisoning symptoms
>sometimes wake up like pic rel with panic attack from fear I'm inhaling fumes from invisible mercury droplets
How dangerous is this shit is really?

I hate that I can't feel peaceful, because I'm afraid sleeping in my own bed will turn me into more of a clumsy retard than I already am.

>>15250993
I don't know but I'm guessing it has to do with diffraction. You should be able to calculate what angle an incident beam diffracts when it hits a hole of a certain size.
It doesn't make sense for a 2.09mm hole to completely block a 2.10mm wave, but there should be a precipitous drop that should be calculable.

>>15251093
Sorry actually this follows from the general fact [math] (R/J) \otimes_R M = M/(JM) [/math] for any module M over R

Did I make a mistake here?

would a triangle (sawtooth) wave have a higher peak voltages than a square wave and sine wave if they all have the same rms voltage?

>>15251367
Well, your math is correct, but as you've probably figured out you've made it a lot worse than you need to.
Manipulating the relation between trig functions is the right idea, but maybe consider consulting your list of identities again to see if there's anything less ugly?

>>15251105
You're going to die, sorry anon.

>>15251390
Good question, I believe it would be, but only if you assume the square wave has a 50% duty cycle. If the square wave has a duty cycle ->0 and fixed rms, it'd be ->infinity at the peak

>>15251397
I already solved it this way. But you're right, there's a way quicker solution to this.

>>15251426
time for 8 hour long session of breathing in mercury while unconscious

>>15251390
pic related, or you can do the integrals yourself if youre not a pussy

>>15251105
Just follow the directions from poison control and
you'll be okay:
https://www.poison.org/articles/thermometer

Personal anecdotes from people in contact with
mercury:
https://www.thoughtco.com/when-you-touch-liquid-mercury-609286

>>15251390
sin wave: [math]V_{rms}=\dfrac{V_p}{sqrt(2)}[/math]
derived on https://en.wikipedia.org/wiki/Root_mean_square
Bipolar square wave:
[math]V_{rms}=sqrt(\dfrac{1}{T_2-T_1} \int _{T_1} ^{T_2} V_p^2dt)=V_p[/math]
Sawtooth: derived on
https://www.youtube.com/watch?v=g9pjcTTxQIY The answer is [math]\dfrac{V_p}{sqrt(3)}[/math]

kinda lost with this one.
Any help or resource would be appreciated

>>15251602
There is one resistor and one capacitor.

R= 6.63 ohms, and c= 1.07 *10^-4

>>15251521
>when the mercury is at room temperature then the evaporation rate is only 0.063 ml per hour per cm squared of surface area exposed of mercury.
finally, I wanted to know this but I didn't know the term "evaporation rate", though that number/hour seems too high

it actually happened 7 months ago, I think I cleaned it properly, at least all that was visible so what's done is done

>Hg evaporation rate = 50μg/cm2
>worst case scenario it contained 3g of Hg (not sure)
>it seems I collected about 1g
>2g of Hg = 0.15ml = 0,15cm3
>0,15cm3 = 1.37cm2
>1.37cm2 * 50μg = 68,5μg/h
>OSHA limit is 100μg/m3

This is like best case-worst case scenario, though fortunately I think my thermometer contained less than 2g of Hg, but it's not a neat ball so the surface area is higher than in my calculation so evaporation might also be higher.
But from the paper I read mercury slows down evaporation due to oxidization so emission might be lower.
But on the other hand I might have accidentally spread around the mercury by walking, including onto my bed, which would mean it's possible I have mercury right next to my head when I sleep.

I'm just gonna get my piss tested.
If after such a long time I'm not poisoned then my rooms is safe I guess.

>>15251602
kinda weird that im a EE senior and i cant figure out how to solve this without using laplace transforms.

So I'm trying to make a controller for a robot that's like an office chair except every wheel and caster can be driven. Part of this requires determining the torques on each wheel and caster. Each caster wheel produces a planar force from the respective torque and force and these forces should minimal cancel each other out(something something null space), be less than or equal frictional forces that can be produced(which should be inside the radius of a circle), and have as small a magnitude as possible. I think I have a number of equality constraints too, IE torque should be enough to counteract rolling friction and inertia. Is this something I can solve with linear optimization or do I need to do quadratic programming?

Call me double retarded for not knowing this and not knowing latex, but how do I find the absolute entropy for something starting from 0K to some temperature? Isn't the integral Cp/T dT undefined starting from 0?

>>15251747
hmm what would the answer be if you were to use a laplace transform, i want to check myself

>>15251778
transform the voltage and current, divide the voltage by the current, replace [math]s[/math] with [math]j\omega[/math], plug in [math]\omega=377[/math], and simplify.

How is it that GHz frequencies can escape by bouncing through thin gaps, but be blocked completely by a fairly wide pored mesh?

>>15251492
Wants ipks as a function of rms, not the other way around like your picrel. those don't look like easy to invert functions

>>15251793
>those don't look like easy to invert functions
take a look at the square and sawtooth wave ones

>>15251786
hmm not sure if i did this right but i got 66.3 for the resistor, and 1.07*10^-5 for the capacitor

>>15251731
>>15251521
Given the small amounts of mercury that have been
spread around from your actions, if any bit of it
has absorbed into your body it would have been
flushed away by now. And it's your first exposure...
not really life-threatening than, say, daily mercury
creme rubs to cure syphilis (see: Tuskeegee Syphilis Studies).

So, yes, test your piss and you'll see you're okay.

>>15251769
> Isn't the integral Cp/T dT undefined starting from 0?
Yes but since that equation isn't correct it's not an issue. You would just use the usual formula for [math]\Delta S[/math] given an initial and final temperature and add that to whatever the starting entropy was.

Strictly speaking near absolute zero the heat capacity would decrease to zero so [math]C_p[/math] would no longer be a constant so it would in reality be more complicated than that.

>>15251531
so it would be square wave since Vp is just the amplitude?

>>15251996
No, the saw has that vp times sqrt(3),so it is larger

Does anyone know of a good textbook for learning Finite element analysis?
Looking for something that leans more towards application instead of theory.

>question
What is a good font for lettrines? I think lettrines look nice, but only with fancy fonts. Sometimes really cool ones have so much art they look like a postage stamp with a big letter on it.

Somebody said make a font with illustrator, but I don't have that tool. Is there a good font for fancy lettrines in Latex?

>>15247119
>>15247646
>>15250378
>>15250794
I like this maid. This is the best thread on 4Chan because it has maids and research and arguing about ideas.

>>15247374
Thank you for telling me.

>>15250677
I fell asleep and my thread got expired before I woke up. A dra/g/on made a website with 2k+ AI generated maids on it so tomorrow I can look through this dataset and pull out 200-300 I like and put them in the rest of the margins.

If the dra/g/on who made maidspace.net is reading this, thank you for making so many maids. Is it okay if I thank you and link to that site in the preface of the book?

>>15250794
Why not both?

>>15251996
1/sqrt(3)<1/sqrt(2)<1.

Hello. Teaching myself differential equations. Recently been learning about the Wronskian, variation of parameters method, Cauchy-Euler ODEs, etc. One thing that I keep noticing in the textbook that I'm reading is that, for any two particular solutions to a homogeneous equation, both solutions are linearly independent. I only know what this means in a linear algebra context, but why does this fact matter for differential equations?

Anyone got books on how to become an auto-didact? And maybe something on building up discipline?

>>15252174
If they were linearly dependent, then one solution would be a scalar multiple of the other, and in most (if not all) contexts you would have a strong argument that these are really the "same" solution with just a change in units.

i beat this is an easy one but i think im overthinking this

so I = v/z , z= sqrt(R^2+wL^2) , w =2pi *f , where f is 1/pi so w= 2.

so that would leave me with 10 cos(2t) /sqrt(11)

>>15252296
whoops i meant sqrt(13) on the bottom

>>15252296
you can instantly tell your answer is wrong because theres no phase shift

>>15252296
you found the magnitude of z, but you still need the angle of it. remember, phasors have magnitude and direction.

>>15247191
Pls respond.

Let [math]X[/math] be a compact metric space and [math]\mu[/math] a regular probability measure on it. Suppose [math]T: X \to X[/math] is invertible and [math]\mu(A \Delta T(A)) = 0[/math] holds for every measurable [math]A \subset X[/math].

Is [math]T[/math] the identity map up to null sets? (i.e. must there be a full measure subset on which [math]T[/math] acts trivially?)

>>15247191

When an object falls, it experiences a force due to gravity that accelerates it downwards. In the absence of air resistance, all objects will fall at the same rate, regardless of their mass or any other properties.

However, if one of the bodies is rotating, it may experience additional forces due to its rotation that can affect its motion. For example, if the rotating body has some kind of mechanism that causes it to spin faster as it falls, it could experience a net force that causes it to fall more slowly than the non-rotating body.

The key point your professor was making is that if the rotating body experiences a net force that does work on it as it falls, then it will have a different rate of acceleration than the non-rotating body. This could cause the two bodies to hit the ground at different times.

To understand why this might happen, consider a simple example: a spinning top that is dropped from a height. As it falls, the force of gravity accelerates it downwards, but its rotation also creates a gyroscopic effect that opposes the motion. This can cause the top to fall more slowly than a non-rotating object of the same mass.

In general, any rotating object that experiences a net force that does work on it as it falls will have a different rate of acceleration than a non-rotating object. This is because the force of gravity is not the only force acting on the rotating body. The additional forces due to rotation can either assist or oppose the motion due to gravity, depending on the specific circumstances.

So, in summary, if the rotating body experiences additional forces due to its rotation that affect its motion, it may fall more slowly than the non-rotating body, causing the two bodies to hit the ground at different times.

>>15252553
Nah.
[math]X = [0, 1][/math]. Make [math]\mu[/math] the trivial probability measure and tah dah, it's regular.
>what if I straight up just ask for the measure to be Borel
Probably true then, I think.

>>15252840
Oh yeah, of course, I'm only considering Borel measures.
>Probably true then, I think.
Same, but I can't think of a convincing argument. If one comes to your mind, I'd love to hear it.

Am I understanding this correctly?
I am rusty on C and pointers, but I tried.

>p is stored in the stack, destination is in memory location of x
>f is stored in stack, destination is heap wherein f is allocated memory of sizeof(foo)
>f->bar is stored in heap, destination is in the stack at memory location of x
>weakness is in the "return f->bar(f->buffer);" line, wherein coping the contents of f->bar to f->buffer creates a buffer overflow

Also, what is meant by p, b, and e? I asked my professor to elaborate but referred me to the slides, which didn't have anything about p, b, and e on them.

>>15252404
ah okay so that would mean i would just take the arctan(wL/R).

>>15253302
right

>>15253446
thanks, my answer is 2.77 cos(2t-34) A for that one. Easier than i expected once you guys got me on the right track

problem in pic gives me two voltages, im just not sure what to do with it. I cant really find any specific example in my book

>>15247191
Ask your professor. It sounds like nonsense to me since gravity can't exert a torque about the center of mass of the rotating object and if the object is in "free fall" there are no other forces acting on it. But perhaps he had some logic behind it that he either phrased poorly or you misremembered.

why is eeg analysis so hard? I should've went to college for EE instead of biology

Not the guy above, but I too am also looking at simple RLC circuits. I understand why we need to convert from the time domain to the phasor domain , but is there any conceptual description that can helpfully describe what exactly the impedance is? Resistance for an ohmic conductor is obviously based on the resistivity of the material, length, cross-sectional area, etc., but what is impedance based on?

>>15253027
> weakness is in the "return f->bar(f->buffer);" line, wherein coping the contents of f->bar to f->buffer creates a buffer overflow
That part is wrong.

f->bar is defined as a function pointer that has the input of a char * and the output of an int. However the address of the function is set to be the value of p, which was earlier set to the be address of x. So when the function f->bar is called in the return statement the program tries to execute code at that location in memory, in other words it will try to run what ever machine code '0xdeadbeef' represents. Though this is likely to cause a crash first since the stack is typically set with no-execute protection.

I have absolutely no idea what 'b,p, and e' are meant to represent, it's certainly not common terminology. Sounds like some notation your professor personally created for his course.

>>15253500
it's just a generalization of Ohm's law to AC circuits and assorted components
resistance is, as per Ohm's law, defined by [math]R=\frac{U}{I}[/math], we extend that definition with impedance ([math]Z=\frac{U}{I}[/math]), the notable difference being that impedance has a phase on top of magnitude

>>15253493
what about it is hard

>>15253533
there's so much to learn and alot of it is difficult. even if you know what you want, the learning curve required to get the result can be long. ex: I've been trying to extract some gamma waves in python but getting a decent graph has been a weeklong hassle.

How do you solve the bernoulli differential equation y' = xy^(8) - 1 using subsitution?

Is Euclid's algorithm supposed to be obvious?

>he Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number. For example, 21 is the GCD of 252 and 105 (as 252 = 21 × 12 and 105 = 21 × 5), and the same number 21 is also the GCD of 105 and 252 − 105 = 147

Is the part where GCD(A, B) is equal to GCD(A-B, B) just plainly obvious because I don't see how you can just 'know' this intuitively

>>15253753
If n = gcd(A,B) then there exists some integers a and b such that A = na and B = nb, where n >= a,b.

You can then write A - B = na - nb = n(a - b), so n|(A-B) and n > (a - b) then n must also be the gcd of (A-B,A) and (A-B,B)

Could it theoretically be possible to communicate information with entangled particles? Or is that just pop-sci/sci-fi bullshit?

I need some help with my homework:
The question is about calculating the oscillation of the system, however what I'm struggling with now is calculating the force of the spring in the x-axis. The spring has a natural length b and b<h. Point A is the equilibrium point, The mass is free to move along the x axis without friction.
In my first attempt, I calculated the length of the spring and subtracted its natural length: F = -k(sqrt(x^2+h^2)-b). The force in y axis should be irrelevant as the mass is only free to move in the x-axis. But how do i get the force in x axis? Thanks.

>>15253753
If n = gcd(A,B) then there exists some integers a and b such that A = na and B = nb.

You can then write A - B = na - nb = n(a - b), so n|(A-B) then n must also be the gcd of (A-B,A) and (A-B,B)

>>15253789
It's pop-sci bullshit. With entanglement when you measure "0" then instantly the other particle is now "1" or vice-versa. However you cannot force your particle to be in either state so you can't use it to send information.

>>15253797
Ok, so that's out. Can photons be in two places at once? Or are they not quantized in states between emission and measurement? I'm trying to validate a conspiracy theory, but I'm starting to think it may be bullshit.

>>15253806
Your question isn't clear so I'm not sure how to answer that.

> Can photons be in two places at once?
No. No particle can. You might not be sure where a particle is until you measure it but that is different.

>>15253814
I guess the moon isn't artificial then, thanks anon.

>>15253007
Alright, broad proof strat (I haven't looked the details over and they aren't exactly trivial but w/e):
[math]\displaystyle \int _X | f(x) - f \circ T(x)| d \mu (x) = 0[/math] for any simple function hence [math]\displaystyle \int _X |f(x) - f \circ T(x)| d \mu (x) = 0[/math] for any *measurable* function. The measure being Borel guarantees you have enough measurable functions for that to imply [math]f(x) = T(f(x))[/math] a.e.

>>15253881
*for that to imply [math]x = T(x)[/math] a.e.

>>15253473
could i simplify the circuit like in pic?

i just dont know what to do with the current source or how to factor that in

How can I compute the limit [math] \lim_{n\to\infty} \frac{(n!)^{1/n}}{n} [/math] ?
Apparently it is [math]1/e[/math] according to WolframAlpha, but I have no idea how to show this.

>>15253853
That's a new one. I'm now curious what schizo conspiracy theory that is.

what do you use instead of sci-hub now that sci-hub doesn't work for anything past about 2017?

>>15254325
Actually I guess this can be done with Stirling's approximation.

However this showed up in the undergraduate complex analysis I'm TAing for.
This is more than they should be expected to do right?

>>15254381
Yeah, I was just about to post a proof using Stirling. You could probably also take the log and expand the factorial terms and step through a page of algebra.

>>15254325
https://en.wikipedia.org/wiki/Stolz–Cesàro_theorem?useskin=vector#Example_2

>>15253790
You calculated the magnitude of F. But F is a vector that is directed along the spring. Simply find the x component using trigonometry

trying to finish up a lab. I was wondering how i could get the power factor for the RL circuit based on the data from oscilloscope in pic.

The yellow line represents the voltage across the resistor. The green line represents the voltage across both the resistor and the inductor. purple subtracts yellow from green leaving only the voltage across the inductor

Does the voltage across the inductor of the RL circuit always resemble the input voltage for, triangle,sine and square wave ?

i would assume no, since measurement devices display rms correct?

>>15254341
It succeeded in convincing me that the moon could not have formed naturally, but each answer it offered was more unconvincing than the next. There's a pdf readily available, if you're curious. I can't promise it will convince you but I can promise you will be entertained.

>>15254678
>voltage across the inductor of the RL circuit
it's exactly the same as the output wave (with some phase offset.) use KVL

>>15254325
Not sure, but try applying log and converting it into an integral.

(1-(1/n))^n increases towards 1÷e until around n=50,000,000 where it becomes less than 1÷e

Why?

>>15254775
*500m

>>15254768
i assume this is also true for capacitors and resistors, with capacitors having -90 degree offset while resistors having no offset?

>>15254787
anything across the same terminals as the load (same nets) will always have the same voltage as the load. anything in series with the load will always have the same current.

>>15254325
>>15254770
Yes, I tried. This gave exp (-1).

>>15254820
thanks tho just for clarities sake, im right about the offsets correct? (not trying to annoy, just trying ask stupid questions now so that it doesnt bite me later)

>>15254831
It depends on how they are arranged. Two components (or sub-circuits) in parallel won't have a voltage offset, but current might lag. One in series won't have a current offset but its voltage might lag.

>>15254841
understood thanks. My components were arranged in series. Thank you for clearing things up.

>>15254787
>resistors having no offset?
yes. Only "reactive" components (can store energy)

>>15252553
>>15253881
Alright, I think I got all the details right; still, I'd love to find a proof that's more illuminating than the following.

Any atom of [math]\mu[/math] is [math]T[/math]-invariant, so may as well assume [math]\mu[/math] is diffuse. Then [math](X, \mu)[/math] is measure isomorphic to the unit interval with good old Lebesgue measure. Now the function [math]f: [0,1] \to \mathbb{C}, f(x) = x[/math] is integrable, whence [math]x = f(x) = f(T(x)) = T(x)[/math] almost surely.

>>15254325
>1/e
only with the approximation
it's ->0 done anal-ytically

>>15246644
>stupid
Is DNA a polyester?

>>15254909
No, it's not.

Is science ever going to figure out everything in the universe? People think it's always this progressive thing.

>>15254863
I was thinking about using distance functions.
[math]d_y (x) = d(x, y)[/math], where [math]x, y \in X[/math].
Then [math]\displaystyle 0 = \iint _{X \times X} |d_y (x) - d_y (T(x))| d \mu (x) d \mu (y) = \iint _{X \times X} |d_x (y) - d_{T(x)} (y)| d \mu (y) d \mu (x) = \int_X \| d_x - d_{T(x)} \| d \mu (x)[/math], hence a.e. [math]\| d_x - d_{T(x)} \| = 0[/math]
Then you can call [math]B = B_x (d(x, T(x))/3)[/math] so [math]\displaystyle 0 = \| d_x - d_{T(x)} \| = \int_X |d_x (y) - d_{T(x)} (y)| d \mu (y) \geq \int_B |d_x (y) - d_{T(x)} (y)| d \mu (y) \geq \dfrac{d(x, T(x))}{3} \mu (B)[/math] a.s., hence either [math]\mu(B) = 0[/math] (in which case fuck [math]x[/math] who cares) or [math]x = T(x)[/math].
The issue is that although all of the [math]B[/math] have zero measure, there might be uncountably many of them, and I don't remember any Borel measure tricks for showing their union has zero measure regardless (they are all open sets so there might be some trick, I just don't remember it.)

i was wondering if someone can help me understand how to find intervals with higher order diff eq.

(the solutions are only answers, no explanations)

>>15254981
No.

if i send in a paper but it's wrong, that would be embarrasing
and now they would know my name
how i avoid this. i don't know anybody i can trust that also knows maths.

Would you guys say I have to elaborate here? Or can I assume that the reader will understand. Lambda and mu are elements from a ring.

>>15255117
I don't think so, but I think it's reasonably likely that might find out (i.e. be able to prove) that we can't know everything. With a bit of luck, we just be able to even approximate how much we can know in percentage terms.

is there notation/operator to find two closest integers that multiply to a given value? kind of like square root.

>>15255396
I doubt it. The problem is that for example two closest integers that multiply to 65537 are 1 and 65537.

>>15254775
[math]\displaystyle
\left(1 - \frac{1}{n}\right)^{n} = \sum_{k = 0}^{\infty} \binom{n}{k} \left(\frac{1}{n}\right)^{k} (-1)^k \leq \sum_{k = 0}^{\infty} \left(\frac{1}{k!}\right) \left(-1\right)^k = \sum_{k = 0}^{\infty} \frac{1}{(2k)!} - \sum_{k = 0}^n \frac{1}{(2 + 1)!} = \cosh(1) - \sinh(1) = \frac{1}{e}
[/math]
It's always less then 1/e and it's strictly monotonously increasing, since
[math]\displaystyle
\left(1-\frac{1}{x}\right)^x = f(x) \iff x\ln\left(1-\frac{1}{x}\right) = \ln(f(x))
[/math]
and therefore
[math]\displaystyle
\ln\left(1-\frac{1}{x}\right) + \frac{1}{x}\ln\left(1 - \frac{1}{x}\right) = \frac{f'(x)}{f(x)} \iff \ln\left(1 - \frac{1}{x}\right)\left[\ln\left(1-\frac{1}{x}\right) + \frac{1}{x}\ln\left(1 - \frac{1}{x}\right)\right]
[/math]
und this gives us
[math]\displaystyle
0 \neq \ln\left(1 - \frac{1}{x}\right)\left[\ln\left(1-\frac{1}{x}\right) + \frac{1}{x}\ln\left(1 - \frac{1}{x}\right)\right] \iff 0 \neq \frac{1}{x} [/math]
for all x in R.

>>15255477
1 + 1/x, sorry. You should check all of this, if that's your homework. I was in a hurry

>>15254721
Share it so we can all have a laugh.

If you actually want to learn about the moon's formation watch : https://youtu.be/wnqPqV6DdFQ

>>15247191
Pic related
>>15252666
>>15253489
t. 80 iq nigger

>>15255788
Read my post dumbass. Gravity can not exert a torque about the center of mass to transfer the translational kinetic energy to rotational. This is a simple calculation to check, and at a higher level you can just note that if this were possible then all this stuff about the equivalence principle would be wrong

Might be more of a /diy/ question, but would you know where I can get dichroic filters that dont cost an arm and a leg? Any obsolete consumer electronics I can rip one out of? I want to try making a two or three colour laser projector out of some junk I have and I think the simplest method would require both beams to be colinear, and these filters would still let me use safer low power diodes. I don't know much about optics, so if there's another way to get two beams to overlap that would be awesome.

>>15255292
make math friends or don't send in crank papers
>>15255329
[math](\lambda\mu)_1[/math] isn't the clearest notation, but if it means [math]\lambda_1 \mu_1[/math], then the first matrix is obviously equal to the product and there's nothing to elaborate on

>>15254678
>>15254768
For zero frequency (DC) the inductor is just a wire. Higher frequencies can't pass as easily. RL is called a low pass filter. Waveforms other than sine won't be the same. See pic related. But unless it's just math, your input was bandlimited to begin with, and I would say that two bandlimited square waves resemble eachother more than they resemble a square wave with infinite bandwidth.

>>15254775
>>15255477
I tried subbing in [math]x = 1 - \frac{1}{n}[/math] (which means [math]n = \frac{1}{1-x}[/math] and the derivative is at 0 only when [math]x = 1[/math] i.e. [math]n = \frac{1}{0}[/math].

>>15254775
[math]\lim_{n\to\infty}\left(1+\frac{x}{n}\right)^n[/math]
is one of the standard definitions of the exponential functions.
Your expression is that term of x=-1, meaning it will convert straight to 1/e.

[math]\left(1+\frac{x}{n}\right)^n[/math] is a natural number power of something smaller than 1, it can't be bigger than 1, so it's surely not converging towards 1+e.

Philosophynigger here. Where do you people find the discipline/strength/whatever to actually do STEM shit every day? Anyone here who has developed these habits from nothing care to elaborate?

For the record, I find maths and CS inherently interesting, but I'm too weak and sad to regularly force myself into those habits. I got into philosophy because I naturally just read a lot and argued a lot

>>15256432
>Philosophynigger here. Where do you people find the discipline/strength/whatever to actually do STEM shit every day? Anyone here who has developed these habits from nothing care to elaborate?
I get bored. The more bored I get with the world the more I shove into learning and finding new ways to amuse myself with this goddamn stupid fucking boring world.

>>15256432
>I got into philosophy because I naturally just read a lot and argued a lot
If you just naturally read a lot about whatever STEM field you are interested in, and do calculations or write programs or whatever about certain problems you are interested in, than that is all there is to it. You don't need to have it be a habit every day (although if you want it to become your job then you better get your shit together some time in grad school), it is just something you like to do.

>>15256432
>but I'm too weak and sad to regularly force myself into those habits
Sounds just like a problem of discipline. Reading stuff you know is easy, hard stuff you push out.
I'd say create yourself a space and time on the weekend, say giving yourself 3 hours to engage with a text and a piece of paper.
I think you can view physics and math as a particular subject of philosophy - one where you mostly just learn things other people before you have already understood (fewer room for innovation, since there's sharper cuts of what doesn't make sense)

I want to create an equation for the relationship between x and y, but the data is not linear and polynomial fitting didn't get close enough. Is there any other option besides making several piecewise functions?

>>15256751
What makes you think an equation that fits your data exactly is meaningful? Do you think that if you go out and measure more data at half steps in x it will still fit on the piecewise function?

>>15256759
I’m attempting to model a written melody,
I’ve found sections where there are patterns in pitch changes, which I could make some calculations for. So I believe that it could be split into these sections with their own piece wide functions. But I am wondering if I could model all of the patterns with a single equation.

>>15256791
If you are trying to make functions that make music, install a Haskell compiler on your computer and use a book called "The Haskell School of Music". It says how to make sounds and music with Haskell. Haskell is a functional computer programming language. Maybe figuring out how to make your music with this tool will help you figure out how to make it with math?

>>15256843
I am analyzing a piece of music and seeing if I can make variations on it by transforming the patterns in it. My main goal is making music with math. I’ve never heard of that book but it seems helpful, thanks.

what does the gradient of a 2d circle do:
[math]x^2+y^2=k[/math]
[math]f_x=2x[/math]
[math]f_y=2y[/math]

>>15256862
This task sounds interesting. What patterns are you looking for and how do you transform them?

Is there any known way to represent music as a number or a sequence of numbers?

>>15256876
esl or retarded ?

>>15256564
>>15256531
>>15256524
thanks anons. I appreciate the responses.

>>15256900
>What patterns are you looking for
I’m focusing on patterns in note changes, the harmonic intervals between notes and note repetitions.
In terms of transforming them, I will try whatever I can do with the equations, translating, rotating etc.

>>15254678
The answer is - it depends. The voltage across an inductor in an RL circuit is a high pass filter (not a low pass as another anon stated). The voltage across the induct will be a high pass version of the input wave. Sines are made up of a single frequency so as long as frequency of the sine is in the pass band of the RL circuit the waveform will not be reduced in amplitude, but would have a 90 phase shift relative to the input . Square and triangle waves are made up of multiple frequencies (look them up). If all the frequency components are in the passband (aka above the filter corner frequency), then the input square or triangle waves would look reasonably like the input waveform, but with would have a phase shift of 90 deg.

>>15255129
>The issue is that although all of the B have zero measure, there might be uncountably many of them, and I don't remember any Borel measure tricks for showing their union has zero measure regardless (they are all open sets so there might be some trick, I just don't remember it.)
Follows immediately from inner regularity actually. The measure of the union of Bs is the supremum of the measures of compact subsets of the union, all of which are covered by finitely many B and hence have measure zero.

>>15256751
What do these numbers mean? What do the axises mean? How is the data made?

>>15256751
Try a loess regression. Pic related covers the topic and other things that might be more suitable for discrete pitches. Modeling pitch your way is claiming that octaves are far when they're almost interchangeable.

>>15255084
0 is the sum of [1/exp(n)] for n=1...inf
The approximation isn't a good one for this problem.

>>15256957
X counts every new note, it does not count when a note is repeated consecutively. Y is the identity of the note relative to how many semitones there are from the note to the base note, if the note is the base note then it is 1. The data was made from taking compositions, then noting down each note, their characteristics, and their relationships with other notes (eg. harmonic intervals).

Does a complex entire function map convex sets to convex sets?

>>15257015
I’ve tried some forms of polynomial regression but I have not tried loess, so I’ll give it a shot. Thanks for the resource.

>>15257021
I presume you mean limit and not sum. Also since the limit is e^{-1} and not e^{-n} that isn't a problem.

Also the approximation is no longer an approximation when n is infinity.

>>15257129
not in general, no

>>15257166
Could you give an example of an entire function sending a convex set to a non-convex one?

>>15257195
exp(z)

>>15257199
Right,

can it also map an open convex to a non-convex? If not is there an entire function which does so?

>>15257204
Oops ignore this

Sorry for the barrage of stupid questions but

Can the complex plane with a ray removed be the range of an entire function?

>>15257212
Oh I got the answer

>>15257212
Sorry, trivial by Picard's Little Theorem

>>15257157
>limit and not sum.
No. The big E is sum.

>>15257273
do you want to share how you add together a strictly positive series and end up with 0?

Let [math] f(z) [/math] be a complex entire function with [math] f(\mathbb{C}) = \mathbb{C} [/math].
Then do we have [math] f(\infty) = \infty [/math] ? More precisely: does [math] f[/math] extend to a continuous function from the Riemann sphere to itself, sending complex infinity to itself?

>>15257287
Not necessarily. A polynomial like z^2 can be extended to a map from the Riemann sphere to itself, but something like e^z is not analytic at infinity.

>>15257302
Bruv [math] f(z) = e^z [/math] does not have [math] f(\mathbb{C}) = \mathbb{C} [/math]

>>15257302
>>15257304
Read the question again: >>15257287

>>15257304
Fine. Try sinh z.

>>15257313
Right that would do it, thanks

>>15256274
L between input and output, R between output and ground => low-pass filter
R between input and output, L between output and ground => high-pass filter
C between input and output, R between output and ground => high-pass filter
R between input and output, C between output and ground => low-pass filter
L between input and output, C between output and ground => low-pass filter
C between input and output, L between output and ground => high-pass filter

All of those configurations are voltage dividers. L has impedance which is proportional to frequency, C has impedance which is inversely proportional to frequency, R has impedance which is independent of frequency. LC has a sharper response than RL or RC (as both parts vary with frequency rather than just one).

Sorry, new stupid question:

Does there exist a non-discrete closed subset [math] A \subset \mathbb{C} [/math] ,
and a holomorphic function [math] f : \mathbb{C} \setminus A \rightarrow \mathbb{C} [/math] , such that each point of [math] A [/math] is a (non-removable) discontinuity of [math] f [/math] ?

>>15257365
Forgot to add, also require [math] A [/math] to have empty interior

>>15257365
Also require [math] A [/math] to have empty interior, so it makes sense to talk about points of [math] A [/math] as continuity/discontinuity points, since in this case, every point of [math] A [/math] will be a limit point of [math] \mathbb{C}\setminus A = \mathrm{domain}(f) [/math]

>>15257365
>>15257377
Someone gave me an example , 1/sin(1/z)

>>15256185
Stage shit
https://www.stagespot.com/rosco-permacolor-color-glass-dichroic.html

>>15246644
I have two known points in a 2D carthesian coordinate system, A and B. And I have an unknown point C, and my only information about C is it's angle to the AB section. So basically I have a triangle with 1 known side and the angle opposite of it. What would be the equation that defines all these C points?

>>15247339
>transformation theorem
ty anon

>>15252046
>Why not both?
In my experience, big titted maids are almost never deredere. But nor are flat-chested maids (mostly tsundere). The vast majority of deredere maids are somewhere in between. Not too big or too small. They also have the best deredere maids; the rare few deredere big titted or flat chested maids can't match up to them.

>>15256957
>axises
axes.

>>15257888
I am confused by your use of deredere? I thought it was just a description of personality?

Thank you for giving me the right word. I don't usually use this kind of graph or read about it. I think probably I should though because it can help me draw data more ways and also visualization is usually more powerful than abstraction, I think. At least as a means of communicating with people.

Do you know a book about getting good at designing graphs and making them look nice and picking the right one to represent your data?

Also, I heard there is something called visual proof where you make drawing instead of writing to make a proof of something. Do you know any good books from visual proof? I want to change words into drawings in as many places as possible.

Thank you /sci/entists for reading my post.

Hello frens, how can I git good at academic writing? My uni allows us to use Grammarly, so I'm not too worried about grammar errors.
I've never written any formal reports, and struggle with academic writing. I read the academic writing slides and tried to incorporate them into my writing but the switch is taking too long. Any advice would be greatly appreciated.

In order to be able to left and right multiply two matrices, the matrices need to have the same "number" of columns and rows. So even in the infinite cases the number of columns and rows needs to be equal (so countably infinite for both matrices), right? I'm asking this, because I want to describe all cases, when matrices form a ring with the componentwise addition and matrix multiplication as inner joins.

>>15256182
waaaa waaa
I only read
>When an object falls, it experiences a force due to gravity that accelerates it downwards. In the absence of air resistance, all objects will fall at the same rate, regardless of their mass or any other properties.
and this is false

>>15257836
>AB section
What does "AB section" mean

any R chads here? pls help. /g/ doesn't use this.

>>15257979
If you're thinking abstract-algebraically, don't think about matrices in terms of "rows and columns", start thinking about matrices as e.g. Hom-sets between free modules , and the matrix multiplication arising from the natural evaluation homomorphism [math] W^* \otimes_R W \rightarrow R [/math] for free W over commutative ring R.

Also tf is an "inner join"

>>15258359
your xlim argument looks off

>>15258359
You are not using a `c` in your xlim argument

>>15258359
You need to format your `xlim` and `ylim` parameters as `c(2.5,5)` and `c(15,30)` respectively.

>>15258419
>>15258420
ahh thanks frens. I was being a baka

Given two sets [math] A,B[/math] each consisting of [math]n[/math] points in the complex plane [math] \mathbb{C} [/math], and a choice of bijection [math] \phi:A->B [/math] ,
is there a biholomorphism [math] \mathbb{C} \rightarrow \mathbb{C}[/math] of the complex plane which restricts to [math]\phi[/math] on [math]A[/math] ?

Given two sets [math] A,B [/math] each consisting of n points in the complex plane [math] \mathbb{C} [/math] , and a choice of bijection [math] \phi:A\rightarrow B[/math] ,
is there a biholomorphism [math] \mathbb{C}\rightarrow \mathbb{C} [/math] of the complex plane which restricts to [math] \phi [/math] on [math] A [/math] ?

>>15258624
assume [math]n = 2[/math].

[eqn](x - a_1 + b_1)(x - a_2) + (x - a_2 + b_2)(x - a_1) : a_1,a_2\mapsto b_1,b_2[/eqn]

>>15258641
i forgot to include the normalizing factor

>>15258246
It is not false. You're an idiot

>>15257934
>I thought it was just a description of personality?
Yes, but my point is that said personality is almost never paired with big titted maids or flat chested maids, and on the rare occasions it is, the result has been underwhelming.

>>15258641
>>15258647
Ah got it, it can be solved with polynomials, thanks

>>15258641
>>15258647
>>15258866
Sorry wait, I asked for a biholomorphism, a quadratic isn't a biholomorphism.

>>15258910
Oops, biholomorphisms of the complex plane are apparently only of the form z -> az+b . Forget my question lol

Graphic artist,. Who needs help explaining why you can't just go from RGB to CMYK,. Can someone help me with the numbers?

RGB swatches are determined by 3 scales,. Red, Green and Blue,. Each of which can be set from 0 to 255 in any combination.

How do I math the exact number of possible RGB combinations?

Likewise CMYK has 4 scales Cyan Magenta, Yellow and Black,. Each of which only goes 0 up to 100 in any combination.
What's the math for the exact number of CMYK valuesm?

>>15259159
Isn't it just 256^3 for the first one and 101^4 for the second one?

I believe CMYK has some overlap. for example the color with any "black" level would be identical so long as C=M=Y=0. And scaling CMY uniformly is the same as changing black.

>>15258652
You are coping.

Could someone give me an example of a system were p and E are conserved, but L is not?

>>15259625
Charged particle moving in a uniform external electric field.

I haven't checked it, but think in terms of Noether's theorem. We need space and time translation invariance, but not rotational invariance. So the external forces should be constant in space and time, but not isotropic (same in all directions).

Is it always true that if [math] f(z) = \sum_{n=0}^{\infty} a_n z^n [/math] is a complex entire function with the given Maclaurin series,
then does [math] f(1/z) [/math] have the Laurent series [math] \sum_{n=0}^{\infty} a_n z^{-n} [/math] converging to it on the whole punctured plane [math] \mathbb{C}\setminus \{0\} [/math] ?

If yes, what's the best way to show this rigorously?

>>15259235
Is it?
Artist, not mathematician. I wasnt sure if ! Had something to do with it.

>>15259272
Not quite. 0,0,0,100 is actually quite different from say 50,60,70,100
We refer to it as"pure black" and "rich black" respectively (and that's just an example, different printers have their own preferred blends for Rich black)
Newsprint is printed in pure black,
But if you had a piece of art in a book for example you'd use rich black for a really deep tone.

>>15259734
Momentum obviously isn't conserved in this case since a charged particle will accelerate in the direction of the field. You have to be careful where you apply translation invariance. Noether's theorem applies in Lagrangian descriptions and it is the potential that appears in the Lagrangian, not the electric field itself.

>>15259810
Ideally (or on a screen), they're the same color though. It's just a limitation of the inks. By that logic, CMYK and RGB also can't replicate any Pantone color with its own ink, which is technically true because it covers the entire spectrum and also has some unique influence on reflectivity. But looking just at eye color, e.g. taking a photo and inspecting pixels, would still make rich vs whole black indistinguishable.

>>15259235
I think a simple mapping can be made between the
two systems. From >>15259235 the CMYK has
more color options than RGB, so we can map the
sparser RGB to the richer CMYK. If there is a
color match between the two, that's part of the
mapping (ignoring saturation, hue, etc. I guess).

After a few matches, it may be possible to find
a pattern and build a function from there.

>>15259955
Illustrator (or Inkscape or Krita) will happily make that conversion back and forth, usually with the option (e. g. "Convert All Blacks to Rich Black" when saving.

let's suppose I did the Miller-Rabin test for a certain number on 10 different bases. The test returned 'prime' for 6 bases. what is the probability of the number actually being prime?

>>15259955

This: >>15259972

Hey >>15259159, problem's solved...I guess.

cyber apothecary topological abnegated hypnotic or submanifold de group classified sequence with respect to virtual derived motions of acting individuals universally framed at the superior shape argumentum qua probability dominated in the situation constantly domain bijective homotopy (neural grid and axil)

can it this applicative logistic integration DNA and cognitive adaptive fine tuning of biological specimens be proved? is it supreme basilisk of benign and otherwise inferior divinities?

if this post is a mutated (deforming pasta: cf oui Cthulu what you did there) sequence pls delete

stats bros, help me out
on page 5 (onto 6), how does the 8-bit XOR mask test differ from simply counting the number of times each byte occurs? i feel like i'm missing something really silly here

This is really stupid, but how do I determine the rate constant from a graph like this?

I'm in calc 2 and we started sequences so I'm looking over this youtube video and it just seems like the stuff we learned in the beginning of calc 1.

https://www.youtube.com/watch?v=XdkoTb8PEG0&list=PLHgLUBSREUPl6Ie2hq2NdVdX3z-B8ldOi&ab_channel=TheOrganicChemistryTutor

>>15260053
so what's your question

>>15259856
Oops that's my mistake. The electric field is uniform but the potential isn't.

If it's just a particle in an external potential, if the potential is constant in space then I'm not sure how it could fail to be rotationally invariant. Hence a more complicated system would be needed.

>>15260055
my question is what is the difference

>>15260126
You just started and it will get harder lol

>>15260053
Differentiation is provably easy. Integration is difficult. It's very easy to write down simple-looking functions that can't be integrated in terms of any known functions.

Sequences and series are just as difficult, if not more so. Some series, like the sum over positive integer n of 1/n^2 , require more exotic techniques like complex analysis

>>15259955
You've got it backwards though. There are many more RGB colors,. Which is why when you shift to CMYK. You can sometimes get drastic shifts and muting in color.

Sure, you can find a "closest" match,. But let me tell you, some clients go ape over their color selection,. And some of them you can't blame over just how different the swatches are.

Going from CMYK to pantone is a similar issue, as there are only a few thousand pantone swatches, vs CMYK.

>>15259972
Sure you CAN auto conver and trust Illustrator to choose what it thinks might be an appropriate CMYK match for an unapproachable vibrant RGB swatch,
But your clients gonna be ripshit that the extremely vibrant lightshow on their computer screen prints out like like a Rothco painting.

>>15255129
>>15256953
Neat solution!

>>15259159
RGB and CMYK are different parameterisations of a cube.

RGB has the origin (0,0,0) at black with coordinates increasing along the positive red, green and blue axes. (1,1,1) is white. CMY has the origin (0,0,0) at white with coordinates increasing along the negative red, green and blue axes (cyan, magenta and yellow, respectively); (1,1,1) is black. CMYK is just CMY but with the lowest of C,M,Y subtracted from each (so the lowest one becomes zero) and replaced with black; e.g. CMY (0.2,0.3,0.4) becomes CMYK (0.0,0.1,0.2,0.2). This is because blacks obtained by mixing C,M,Y will have a definite hue due to C,M,Y not being exactly matched; so the amount that "should" end up as black is replaced with actual black. So CMYK doesn't actually have any more distinct combinations than RGB.

0-255 and 0-100 are just quantisations of the 0-1 range into discrete steps. 0-255 is how most computer hardware will store the values, 8 bits per component; 0-100 is a percentage which is probably simpler for artists and other non-technical users.

>>15260300
CMYK has a smaller gamut due to the inks being less saturated than the phosphors/LEDs/whatever of a monitor. It's much easier to make something which emits a specific wavelength or a very narrow band of wavelengths than to make an ink which transmits a very narrow band of wavelengths while absorbing everything else.

"How many colours" is a question of representation. Computer systems most often use 8 bits (256 levels) per component, 24 bits per pixel for 16,777,216 distinct colours, both for RGB and CMY (it's rare for CMYK to be used internally; CMY is normally converted to CMYK only when needed). Although HDR (high dynamic range) rendering techniques may use 16 bits per component or even a 32-bit floating-point value per component). Raw images from cameras may also use more than 8 bits. Displays are typically limited to 8 bits as the human eye can't distinguish intensity that accurately.

Sci fi tier retarded question:
Is it possible for the earth to stop spinning around its axis (with its “face” to the sun remaining consistent in the anual loop)? If this would happen, what would happen to the permanent-day side and the permanent-night side? Would the cessation of the spin itself cause a huge shockwave if it doesn’t happen slowly?

>>15260692
>Is it possible for the earth to stop spinning around its axis (with its “face” to the sun remaining consistent in the anual loop)?
These wouldn't be the same thing, but I'm going to assume you're asking about the latter, in which case it's a very real phenomenon called tidal locking. In fact, the moon is tidally locked to Earth.
>what would happen to the permanent-day side and the permanent-night side?
Vegetation would get fucked, and animals might have a hard time adapting to the new conditions, but it wouldn't be the complete hell you'd find in some other cases. A non-negligible amount of the polar regions already have six months of day and six months of night.
>Would the cessation of the spin itself cause a huge shockwave if it doesn’t happen slowly?
It would be extremely painful, to say the least. Even at the equator, the slowest-moving part of the planet, you're looking at a rotation of some 1600 km/h. Now suppose that you were moving at that speed and came to a less-than-gradual stop.

let [math]l:\mathbb{R}\rightarrow\mathbb{R}[/math] be the function representing the love I receive from girls at some time t. Is there a measurable set on which [math]l[/math] is nonzero? How can I find such a set of measure greater than 0?

Is science another religuh?

So the person who ran I Fucking Love Science is a crazy woman? How does it feel?

is there a quick fix for how I can make the entries of this matrix look more centered?

>>15261206
Centered how? If you want to align the binomial coefficients in a column you can add a \phantom{-} in front of the positive ones.

>>15261211
>how
How \phantom{-} would align them but without having to copy the expression before every non-negative entry. That was the idea basically

Why do men overestimate how big a dick has to be for women? Is it cultural bias from porn or something? I get that a longer dick might help insemination, so I guess it's got evolutionary backing to think a longer dick would work.

Should I just sit alone in uni?
I'm currently hanging out with two guys I know from the uni prep sem. I'm a 23 yo freshman.
The guys I hang out with are the class clowns. One of the guys said that the prof can't even do division when she made some arithmetic mistakes.
Today, I behaved like a child, which made me evaluate this. One of our TAs is a young grad with short haircut. These guys were calling him badly behind his back all week. Anyways, during the attendance check, this TA asked if one of the students were absent. One of these guys kept saying he was sick. The TA didn't respond (maybe he didn't hear) so they asked me to tell him. I said that he was sick a bit loudly, and TA looked at me for a few secs.
When the TA was in the opposite side of the class, our group wanted to get his attention. I actually said "hey badly". I'm pretty certain that he didn't hear us, but it was incredibly childish, especially for a 23 yo. I got home and couldn't believe that I acted this way. I never do shit like this.
Most of the other students have their fren groups and I don't really know them. I was thinking of asking another guy I know to sit between us so I'm not close to them. I feel disgusted about how I behaved. I'm bad at social stuff, so is it better be alonish in uni than this.

>>15261386
They are 18 and 19 yo

>>15261386
jfc anon.
I assume you're not paying to be in uni?

>>15261386
if you think they affect you yeah try sitting alone, if that bothers them they are clowns, and you should avoid them

>>15260023
update on this. i counted 100,000 bytes and performed what i believe to be the correct XOR mask on them, but the results are exactly the same. but im pretty sure my XOR mask implementation must be incorrect, because where the heck are they getting this line from?
>The 0th mask will always resolve to a value of -0.5, which is merely a consequence of the XOR operation and in no way representative of bias on that mask.

hello everyone I usually browse /vg/ but they couldn't help me with this

I play a game where killing a specific monster has a 1 in 32768 chance to give a specific rare drop X
it also has a a 1 in 42.67 chance to drop another item Y, this item Y can be rolled to get another drop and in this second drop table you can get the rare item X with a 1 in 256 chance

how can I calculate the amount of monsters I need to kill to get the item X on average?
please dont just give me the answer I need to know how to do the math so I can use in other parts of the game too

thank you

>>15261918
The odds per kill is the odds of the 1st drop + the odds of no 1st drop * odds of the 2nd drop * odds of the roll. So:

P = 1/32768 + (32768 - 1) / 32768 * 1/42.46 * 1/256 = 1.23*10^{-4} = 1/8162

> how can I calculate the amount of monsters I need to kill to get the item X on average?
That isn't clear what you're asking. What do you mean by average?

>>15261918
>killing a specific monster has a 1 in 32768 chance to give a specific rare drop X it also has a a 1 in 42.67 chance to drop another item Y
Are those probabilities independant? This is very important.

In either case first caclulate the probability [math]p[/math] to get the item in a given kill either directly or through the second roll.
Then let [math]N[/math] be the number of monsters you have to kill to get the drop.
[eqn]E[N] = \sum_{k=0}^\infty P(N > k) = \sum_{k=0}^\infty (1-p)^k = \frac{1}{p}
[/eqn]

This function is continuous at the origin. I'm asked to determine whether or not it's also differentiable at the origin. I think it is, but I'm not 100% confident in my work:
[math]
\lim_{(x,y) \to (0,0)} \frac{\left| \frac{x^2y}{\sqrt{|xy|}}-0-\begin{pmatrix} 0 & 0 \end{pmatrix} \begin{pmatrix} x-0 \\ y-0 \end{pmatrix} \right|}{\| (x,y) \| }
= \lim_{(x,y) \to (0,0)} \frac{\left| \frac{x^2y}{\sqrt{|xy|}} \right|}{ \sqrt{x^2+y^2} }
= \lim_{(x,y) \to (0,0)} \frac{x^2\left|y\right|}{\sqrt{|xy|(x^2+y^2)}}
= \lim_{r \to 0^+} \frac{r^2\cos^2(\theta)\left|r\sin(\theta)\right|}{\sqrt{|r^2\cos(\theta)\sin(\theta)| \cdot r^2}}
= \lim_{r \to 0^+} \left|r\right| \frac{\cos ^2\left(\theta\right)\sqrt{\left|\sin \left(\theta\right)\right|}}{\sqrt{\left|\cos \left(\theta\right)\right|}}=0.
[/math]

Thoughts?

>>15261918
There are two ways of obtaining X with probability of each being
[eqn]p_1 = \frac{1}{32768}\\
p_2 = \frac{1}{42,67\cdot 256}[/eqn]
Since the two ways of obtaining the item are independent of each other, the combined probability of obtaining X is [math]p = p_1 + p_2[/math]

The probability of obtaining the item after first try is
[eqn]P(n=1) = p[/eqn]
The probability of obtaining the item after second try means you failed to obtain the item after first try, but succeeded in the second try.
[eqn]P(n=2) = (1-p)\cdot p[/eqn]
The probability of obtaining item after third try means you failed to obtain the item the first try, you failed on the second try, but you succeeded in the third try
[eqn]P(n=3)=(1-p)\cdot(1-p)\cdot p = (1-p)^2\cdot p[/eqn]
Therefore the probability of obtaining the item after [math]k[/math]-th try is the probability you failed k - 1 times but succeeded in the last try is (called the Geometric distribution https://en.wikipedia.org/wiki/Geometric_distribution))
[eqn]\boxed{P(n=k)=(1-p)^{k-1}p}[/eqn]

>how can I calculate the amount of monsters I need to kill to get the item X on average?
The expected value (a.k.a. average) is calculated summing the number of tries you needed to succeed times the probability that you would succeed for that number of tries
[eqn]
E = \sum_{k= 1}^\infty k\cdot P(n =k )= \sum_{k=1}^\infty k\cdot p (1-p)^{k-1} = \frac{1}{p}
[/eqn]
Which means you have to kill around [math]1/p = 1/(p1 + p2) \approx 8129[/math] monsters on average in order to obtain X.

any neurofags? im trying to learn eeg. why are these two ica sources in the opposite direction of the eye noise? using mne btw.

>>15262051
clarification: the last equality follows since the quotient involving strictly [math] \theta [/math] is bounded. (right?)

>>15262130
is that real data you took? Did you set the probes?

Could just be cross-coupling noise with the polarity reversed.

>>15262136
it's someone else's data. im just going through raw eeg datasets to help learn.

>>15261918
binomial distribution.
n = # of kills
p = probability of drop
c = % confidence that you'll get it

n = ln(1-c) / ln(1-p)

TL;DC:
50% confidence = 69% of average (1 in 2 players get it in <5600 kc)
90% confidence = 2.3x of average (1 in 10 need to kill 18,700)
99% confidence = 4.6x of average (1 in 100 need to kill 37,500)

>how can I calculate the amount of monsters I need to kill to get the item X on average?
that's just the average, 1/32k + 1/(43*266) = 1/8162

this subject's eeg ica seems better though it has a mix of the same direction and opposite direction...

>>15258657
I guess my contention is that personality isn't required to be a decoration in a book? It isn't telling a story so you can't really discern a personality beyond that some of them seem slightly shy.

I am debating rewriting To Mock a Mockingbird but change all the birds into maids and make the story about maids. That is unrelated to current projects, but if I do it later I might try to give maids a story and a personality to make the story part more interesting.

Replacing birds with maids will make it easier to study the topic I think. It is hard to imagine birds doing things but easy to imagine maids doing things. That would be a place to give maids personality.

>>15261942
>>15261952
>>15262121
>>15262143
thank you bros, very informative and easy to understand even for my small brain

>>15246644
Are the units:
kg*pg/mL/mg
and
pg/mL/(mg/kg)
equivalent?
I've tried to reconcile them algebraically to arrive at the latter from the former, but can't seem to do it (although it's been a while since I've done anything like this)

>>15262167
what is the QT inverval? have you applied bazett and fredricia's formula?

>>15262476
kg*pg/mL/mg
and
pg/mL/(mg/kg) -> pg/mL * kg/mg -> pg*kg/mL * 1/mg -> kg*pg/mL/mg (also -> kg*pg/(mL*mg)
so yes

>>15262490
Hey thanks anon!

>>15262490
just out of curiosity, would this be a valid thing to do:
kg*pg/ml/mg = (kg*pg/1) * (1/(mL/mg)) = kg*pg*(mg/mL) = (kg*pg*mg)/mL?

>>15262521
no, because (1/(mL/mg)) is not equivalent to mg/mL
(1/(mL/mg)) -> 1 * mg/mL
you change a division by a fraction into the multiplication of its reciprocal

Why is x/y/z = x/y*z? Or is that correct?

>>15262521
>>15262552
i am retarded
those are equivalent, but you can't do that because it's 1/ml/mg and (1/(mL/mg)) which are not equivalent

>>15262560
i mistyped, sorry. you can think of multilayer fractions as being "squishable"
that is, x/y/z can have the denominator squished down into x/(y*z)
you can do this as much a you want
a/b/c/d/e/f/g = a/(b*c*d*e*f*g)

>>15262566
Thank you anon. I'm trying to prove why it is true to myself now. would it be because you can always factor out something in a denominator position to 1 / (something)? For example
x/y/z = x/y*(1/z) = x/y*z?

>>15262583
yeah pretty much, though personally, i think it's easier to look at it like x/y/z = (x/y)/z = (x/y)*(1/z) = (x*1)/(y*z) = x/(y*z)
that is, include the implied parentheses in the first couple steps

>>15262590
much appreciated!

>>15261397
>>15261420
I am. Student debt

What are the roots of [math]x^{15}-1[/math] in [math]\mathbb{Z}_{16}[x][/math]?

>>15262642
Sorry, should be [math]\mathbb{Z}_17[/math]

>>15262167
i had to look up a qt interval and it seems to be related to the heart? there isnt any heart monitoring in this eeg. if it shows up in the eeg then i haven't recognized it (yet).

>>15262176
I don't think there's much point. I don't remember even seeing more than one bird in that story.

>It isn't telling a story so you can't really discern a personality beyond that some of them seem slightly shy.
I do research on maids and their personalities by checking out the source material they're from.

>>15262051
>>15262133
bump

>>15263241
>>15263241
>>15263241

>>15262701
It has a lot of birds and all the birds are combinators who yell at eachother in the woods.

I need to know more good maid shows. I have been having trouble finding a good one and somebody tricked me into watching Chainsaw Man by telling me it was a maid show.

The AI maids don't have a source material, unless you count Stable Diffusion? Attached is an SD swimsuit maid for the fanservice chapter in my book.

Does anyone know about Reverse Polish LISP? In the 1980s, HP calculators had this language and I want to look at it to see what LISP looks like when it uses postfix instead of prefix? Prefix notation is one of my largest complaints about LISP and it seems this already got fixed 40 years ago and I need to know more about the grammar and implementation of this language.