/sci/ - Science & Math

I'm trying to understand isomorphs of objects and found this stackexchange about playing cards, which are easily substitutable.

I want to find the number of isomorphs for a 32 card deck (four cards from 8 ranks and 4 different suits).

https://math.stackexchange.com/questions/864116/how-to-count-different-card-combinations-with-isomorphism

I don't know how to use either explanation. The first is too mathy while the second is too computery. Please help!

can someone explain this solution. i don't understand how they came to those vectors

>>12475635
The solution is wrong. The vectors don't satisfy the equation.
The way you can actually find a good solution is to pick any two linearly independent vectors and apply Gram-Schmidt (remove the collinear component of one vector to another).

>>12475641
Thanks. So to pick two vectors to gram-schmidt would I just put in values that work like 1,1,-1 and 1,-1,0?

>>12475657
Yes, the two vectors you mentioned are good.
Then all you need to do is to fix one of the vectors, say x, and then do
y'= y - (y*x)x / (x*x)

>>12475663
Thanks

What does the electric field look like inside a linear dielectric?

Specifically, I have a point charge, then some empty space around it, then a shell of linear dielectric around that, and I want to know what the electric field looks like inside that dielectric shell. Pic related is a (very crude) drawing.

>>12475787
forgot picture

>>12475576
Can someone help me solve for x? I know all of the variables apart from x.

Please I am a software engineer but need to solve this goddamn math problem in order to do my work.

Can someone help me solve for x? I know all of the variables apart from x.
Pic related.

Please I am a software engineer but need to solve this goddamn math problem in order to do my work.

>>12475860
Multiply both sides by (b+x)(z-x)(b+x) and solve the resulting quadratic equation.

>>12475860
https://www.wolframalpha.com/input/?i=%28+x+%28a%2F%28b%2Bx%29%29%29%2F%28z-x%29+%3D+%28a-x%28a%2F%28b%2Bx%29%29%29%2F%28b%2Bx%29%2C+solve+for+x

>>12475880
Thanks, this website is really good.

If we are living in a simulation, why hasn’t anyone installed magic mods for us? Or other cool shit.

Is water wet?

>>12476024
The admin is not interested in those mods (just be glad we got QM) and nobody else has the user privileges required to install mods.

>>12475791
>>12475787
electric field matches the field due to the point charge (pointing radially outward) inside the dielectric
it is reduced a bit but the direction is the same as if there was nothing there

If I have 3 points A B C, how can I describe the points D such that the vectors DA+DC and DB are collinear?

>>12476024
Because the belief systems that you would acquire from these experiences is beyond anything you're willing to consider.

I know I'm retarded, but how would I go about finishing this? Nothing I can think of regarding logs would work because you'd always have some x in a log/exponential and some x on its own at the same time.

>>12477221
Use vectors. Translate to have B=0. Apply linear transform to get A=(1,0) and B=(0,1), then the problem becomes easy. After solving it, transform back to get your answer.

Some randos were talking about Betelgeuse, the star and how it is about ready to go supernova. Cue starboy #2 doing an "Um ackchyually" it could've blow up already, the light just hasn't reached us yet." Would I be right in "Um ackchyualling" starboy because no universal clock, speed of causality and all the shit spacetime-jew taught us? Thank you very much fellow Um-Ackchyuallers.

>>12477260
Yes, you are right. Tell us how it goes.

>>12477260
don't engage with these types of people, it doesn't make you look any better than them

>>12477263

Stupid Question:

How does AC current work if it only moves back and forth in direction? What is doing the work? If I have a rope on a box and pull it in one direction it has moved. If I push and pull the box the same amount nothing happens. I am having trouble creating intuitive understanding of electricity in general but AC current is getting me even more.

>>12477330
A good way to think about it are train cars connected on a track, whereby AC moves the train car forward and backward very fast.

The mass is the energy. Its not defined by movement. The electrons/trains are the medium.

>>12477270
>it doesn't make you look any better than them
If my goal was to be better I wouldn't be cooming my life and instead be studying or climbing the wagecuck ladder.

>>12477330
the electrons aren't what does anything, it's the EM fields in the wires.
a lot of components are powered like resistors, P=I^2*R, where the magnitude of the current is important, not the direction.

>>12477342
>>12477350

This actually makes a lot more sense. I remember learning and using P = I^2*R and V= I*R in class a lot. Are there reasons why power and voltage is dependent on resistance? When I am thinking mechanically, resistance is normally just a modifier that takes away how much work I am able to do, but in electricity having no resistance would not allow for power or voltage from what I understand from this equation (unless there are nuances for R = 0 cases).

>>12477370
[math] I = \frac{V}{R} [/math] is just the integrated form of [math] \bf{J} = \sigma \bf{E} [/math] , where J is current density, sigma is the "conductivity" of a material (determined experimentally) and E is the electric field in the material.
the power law for a resistor is just inferred from P=energy/time=E/q * q/t = V * I = I^2*R

>>12477393

Ahhh, so really the physical meaning is based on conductivity and not resistance (which mathmatically is identical) but we just use the inverse. So for something to have zero resistance it would have to have infinite conductivity. I'm not sure why I had trouble with that logic before, although it makes more sense intuitively to think of conductivity over resistance. Thank you

>>12477404
conductivity and resistivity are just inverse concepts, I could have just as easily written [math] \bf{J}=\frac{\bf{E}}{\rho} [/math] . the point is that sigma and rho represent the same idea, but seeing that "current is proportional to some conductivity constant" is easier to understand than "inversely proportional to some resistivity constant"
> So for something to have zero resistance it would have to have infinite conductivity.
Yes.

Cheers, getting a good foundation on EM is crucial to understanding it.

How would you go about finding out if this thing converges

[eqn] \sum_{n = 0}^{+ \infty} \left( \dfrac{n^{4} - n!}{3^{n} + n!}\right)^{n!} [/eqn]

I did limit comparison with [math] \sum_{n = 0}^{+ \infty} \left( \dfrac{n!}{n!} \right)^{n!} [/math] I got that it diverges, but I'm not sure if it's correct

What Finite-state transducer does look like for operation binary number x -> binary number y=x mod 3

>>12477497
Seems correct to me.

>>12477497
How did you run that comparison?
The only way I'm seeing of doing it is somehow proving that [math]\dfrac{n! - n^4}{3^n + n!} \geq {n!}{n!+1}[/math], because we have https://www.wolframalpha.com/input/?i=limit+as+x+approaches+infinity+of+%28x%2F%28x%2B1%29%29%5Ex

>>12478212
Inequality should be [eqn]\dfrac{n! - n^4}{3^n + n!} \geq \dfrac{n!}{n!+1}[/eqn]

Define an operator [math]\Phi[/math] on [math]f \in L^2[0,1][/math] as [math](\Phi f)(x) = \int_{x}^{1} f [/math]. How do I go about solving explicitly for [math]\Phi^*[/math]? I'm pretty sure it's integration by parts or something

If the price of the first product is 30 dollars higher than the price of the second product,
And both products got more expansive, the first product got more expensive than the second one by 5%.
The price of the first product got increased by 10 dollars, and the price of the second product got increased by 2 dollars.
Is there an easy way to calculate the original price?
How do you solve word problems like this one?

So from my understanding of CRISPR, it's fairly impractical to apply gene editing on adults.
How about using a delivery organism that targets mainly stem & progenitor cells, while controlling the rate of senescent cells? Won't that eventually replace your old genetic sequence with the new without having to worry about cost and autoimmune problems?

>>12478604
Gonna start typing then click post
f,s
f > 30 s
f + 10 = s + 30 + 2
f + 10 = s + 32
f = s + 22
23 = 1 + 22 | 23 is 23 times more expensive
24 = 2 + 22 | 24 is 12 times more expensive, ~8ish percent
26 = 4 + 22 | 26 is 6.5 times more expensive, ~15ish percent, increase
26 + 10 = 36
4 + 2 = 6
36 is 6 times more expensive
f is now 0.5 times LESS expensive than 26 / 4
we need to go smaller, not bigger
24 + 10 = 34
2 + 2 = 4
8.5 times more expensive, compared to 12 times more previously
okay need to go higher
30 = 8 + 22 | 30 is 3.8ish times more expensive, so like 20ish percent more
30 + 10 = 40
8 + 2 = 10
it's now 25 percent more, sounds very close, let's get exact number for before addition
Wait, 40 is 400% more than 10, I've been doing this backwards
wait, I've fucked this all up
Gonna start over

>>12478604
You just write turn the statements into equations such as [math]p_1 - p_2 = 30[/math] and solve for a set of simultaneous equations. However I've no idea what to do with the next part as the wording is terrible and not clear at all about what it's trying to state.

>>12478604
>>12478637
second attempt
100 = 70 + 30
100 is 30% more
100 + 10 = 110, 10% more
70 + 2 = 72, 2% more
got 8% more expensive
50 + 10 = 20% more expensive
20 + 2 = 10% more expensive
opposite direction
200 + 10 = 5%
170 + 2 = 0.8ish%
140 + 10 = 7ish% more expensive
110 + 2 = almost 2% more expensive
7 - 2 is 5%
but I'm not sure if I should be comparing how much they grew relative to each other, or how much more it is now compared to what it was
140 is 22ish% more than 110
150 is 25ish? more than 112
3% diff, damn that's close, up or down? down I think
100 is 30% more than 70
110 is 45% more than 72
15% diff, lets get more than halfway closer to 140 test case
130 is 30% more than 100
wait, that's wrong, well that's right but the previous 30% is wrong
100 is 44ish% more than 70
1% difference
I need calculus, but I have a better idea

>>12478639
There are two products, one product was more expensive than the second product by 30$.
Both of the products got more expensive, but the price increase of the first product was 5% more than the second product.
The price of the first product increased by 10$, and the price of the second product got increased by 2$.
What was the original price of each product?

>>12478698
Ok then the set of equations should be

[math]\begin{align*}
p_1 - p_2 &= 30 \\
p_2 (n - 1) &= 2 \\
p_1 (1.05 \ n - 1) &= 10
\end{align*}
[/math]

Solve by eliminating [math]n[/math] then [math]p_2[/math] to get the price of [math]p_1[/math]

>>12478604
>>12478637
>>12478677
>>12478698
<?php
for ($i = 31; $i < 1000; $i = $i + 0.01) {
$firstPrice = $i;
$secondPrice = $firstPrice - 30;
$newFirstPrice = $firstPrice + 10;
$newSecondPrice = $secondPrice + 2;
$firstDiff = 100 - (($firstPrice / $newFirstPrice) * 100);
$secondDiff = 100 - (($secondPrice / $newSecondPrice) * 100);
$diffDiff = ($secondDiff - $firstDiff);
// var_dump($firstDiff);
// var_dump($secondDiff);
// var_dump($diffDiff);
// echo '<hr>';
if (ROUND($diffDiff) == 5) {
echo 'first product got 5% more expensive potential match <br>';
echo 'firstPrice $' . $firstPrice . '<br>';
echo 'secondPrice $' . $secondPrice . '<br>';
echo 'newFirstPrice $' . $newFirstPrice . '<br>';
echo 'newSecondPrice $' . $newSecondPrice . '<br>';
echo 'firstDiff ' . $firstDiff . '%<br>';
echo 'secondDiff ' . $secondDiff . '%<br>';
echo 'diffDiff ' . $diffDiff . '%<br>';
echo '<hr>';
}
}
die();

original price of first item: $35.40
original price of second item: $5.40

Yes, this is how your typical programmer solves all problems, I hope this has ruined your day

Also let me know if I got it right.

>>12478637
>>12478677
>>12478749
take your meds.

>>12478765
Is there meds to teach me calculus? Because I’m perfectly fine other than not knowing proper math. Just showing my work since that’s what he asked, and posting it non filtered.

>>12478749
>php

Could someone explain to me how we know that the Covid vaccine won't have any serious long term effects? Genuinely asking out of curiosity, not trying to start any /pol/ shit or whatever. I just thought that the approval process for vaccines generally took years so that they could monitor that kind of thing.

Suppose T is an operator on an Hilbert space such that [math] \langle Tx , y \rangle = \langle x,Ty \rangle[/math] for all x and y. How do I show that T is bounded?

>>12475860

This is basic algebra

[eqn] -b \pm \sqrt{b^{2}+zb} [/eqn]

>>12477221

Because you cancelled the [math] x^{2} [/math] terms, you missed the easy root: [math] x = 0 [/math].

For the remaining roots, you could just prove you know the number of roots, and find their respective intervals.

Take a function [math] f(x) := -3 + x + e^{-x} [/math]. Sample the points [math] x = -10 [/math], [math] x = 0 [/math] and [math] x = 10 [/math]. Using the intermediate value theorem twice, you can prove the existence of at least two distinct roots (one on [math] (-10, 0) [/math] and one on [math] (0, 10) [/math]).

If there were more than two distinct roots, you could just use Rolle’s theorem twice to show that the derivative must have two distinct roots. However, [math] {f}’(x) [/math] only has a root at [math] x = 0 [/math], so [math] {g}’(x) [/math] has exactly one root on [math] (-10,0) [/math], one root at [math] x = 0 [/math], and one root on [math] (0, 10) [/math].

Any materials on database design normal form synthesis?

>>12477192
D is any point on a line which passes through B and the midpoint of AC.

Draw a parallelogram with D,A,C as three of the vertices. Label the fourth vertex P. Then DP=DA+DC.

>>12479040
First, we had a head start, as most of the Covid vaccines are based off vaccines developed for SARS and/or MERS.

Second, vaccine development is usually sequenced. After one stage is complete, results are analysed and the next stage is planned. With Covid, everything was started at the earliest opportunity. Approvals for large-scale tests were given as soon as small-scale tests produced preliminary results. Full-scale production was started before the first stage of testing was complete. The risks of expending resources on a vaccine which may not be approved are outweighed by the fact that any successful vaccine is likely to sell several billion doses (the majority of the world's population is expected to be vaccinated). Most developed nations have ordered 2 doses of every viable candidate for every person (or whatever they can get, up to that limit).

Third, vaccines generally don't have delayed side effects. They aren't drugs, in the sense of chemicals which modify biological systems. They're "imitation" viruses which provoke an immune response. While the immune response itself can sometimes be problematic, this is usually fairly immediate. Most issues are apparent within 24 hours, although there's one (can't remember the name) which may take a week to manifest. If there aren't any adverse side-effects within a fortnight, it's all but certain that there will never be any.

Am I retarded or is there no nice way to compute a formula for the sum
[eqn]S(N)=\sum_{n=1}^{N} \frac{1}{n^r}[/eqn]
where [math]r > 1[/math]? Is this problem supposed to be hard?

>>12479558
These are real numbers. Why do you need a nice formula? Just rewrite it and call it a day, like you do with e+pi.

>>12479558

[math] \sum_{n = 1}^{\infty}\frac{1}{n^{2}} = \frac{\pi^{2}}{6} [/math]

Of course this type of problem is hard.

>>12479567
I'm just trying to find a nice trick as a step in doing a proof. Can you explain what you mean by "rewrite it and call it a day"?

>>12479570
Hmm, I almost forgot about the Basel problem. I am suddenly not so confident anymore

>>12479583
>Can you explain what you mean by "rewrite it and call it a day"?
Well that's how arithmetic in real numbers looks like?
What is e+pi? The answer is e+pi.
What is e*pi? The answer is e*pi.
What is e+pi+2/3 + phi? The answer is e+pi+2/3 + phi.
This is how arithmetic in the real numbers works. To get an answer, you just repeat back what was said to you.

>>12479589
Ah, ok thanks. I guess you can't always have nice things

>>12479589

The only reason you can’t write the answer to [math] e + \pi [/math] more simply is because supertasks don’t practically exist.

If a supertask machine could exist, you could represent any real numbers as points on a ruler.

I am writing a paper about the anthropic principle.

Basically, suppose there were a such thing as a black hole, and I had a hard drive full of child pornography (CP). Could I hope to place my hard drive full of CP into a black hole, thus permanently destroying the evidence?

Does this idea work?

What's an easy way to integrate a function that contains an absolute value? Please, I don't want to split the integral in intervals, because when the limits of integration are functions it gets messy

>>12479744
piecewise function => you need to split the integral

>>12479744

There are two problems with what you are asking for.

1) Besides joining/splitting bounds of integration, applying the linearity property of integration, and using the fundamental theorem of calculus to move functions between the bounds of integration, and the integrand (u-substitution), there really aren’t broad tricks to integration.

2) Compositions of elementary functions and absolute value functions are basically piecewise functions, so there really aren’t any general tricks to it.

>>12479744
>an absolute value?
abs() is poorly defined shite. Rewrite it as a norm of a complex number
|z| -> [math]\sqrt{zz^*}[/math]
where z=a+ib

>>12479488
Thanks for the comprehensive answer, Anon.

How do I go about proving these?

>>12480213
DCT

>>12475576
Maybe too highbrow for this thread but:
Is math related to science?

>>12480240
You're obviously too highbrow for this thread so why don't you fuck off and hangout with the other pseudo-intellectuals.

>>12479288
wtf kinda retardation did i just witness

>>12480250
A non-answer. -> Ignored.

>>12480213
As a first impression, I might say that for (a) you have to use at least one version of the differentiable limit theorem and the Bolzano-Weierstrass theorem. The hard part seems to prove that there exists a subsequence of subsequence of derivatives that converges uniformly to some [math]g:[0,2] \to \mathbb{R}[/math].

>>12480305
just 'a subsequence' not 'a subsequence of subsequence'

>>12480305
Ah, probably also Arzela-Ascoli is involved at point (a).

>>12480213

Here is an attempt.

Each [math]f_n[/math] is differentiable on the interval, thus continuous. By the mean value theorem and because the derivatives are all bounded:

[math]\frac{|f_n(x)-f_n(y)|}{|x-y|}=|f'_n(c)|\leq M [/math]

Therefore [math]f_n[/math] is Lipschitz [math]\forall n[/math]. Now we will show that [math]f_n[/math] are equicontinuous. Let [math]\varepsilon >0[/math] be arbitrary:

[math]|f_n(x)-f_n(y)|\leq M|x-y|<\delta M[/math]

Setting [math]\delta = \varepsilon/M[/math] yields equicontinuity. By Arzela-Ascoli you get that there is a uniformly convergent subsequence [math]f_{n_k}[/math]. The question about nk seems like a trick but I'm not sure. What do you think?

why?

>>12480213
We start off with some [math]\epsilon > 0[/math].
We choose a finite subset [math]A \subset [0, 2][/math] such that every [math]x \in [0, 2][/math] is at a distance at most [math]a[/math] from some point in [math]A[/math].
Then, since [math]A[/math] is finite, we choose [math]N[/math] such that, for all [math]m, n \geq N[/math], [math]x \in A[/math], we have [math]|f_m (x) - f_n (x)| < b[/math].
Now, we compare, for [math]x \in [0, 2][/math] and [math]x' \in A[/math] such that [math]|x - x'| \leq a[/math]:
[math]|f(x) - f_n (x)| \leq \sup |f_m (x) - f_n (x)| \leq |f_m(x) - f_m(x')| + |f_m(x') - f_n(x')| + |f_n (x') - f_n(x)| \leq | \int _{x'} ^x f_m'(t) \ dt | + b + | \int _{x'}^x f_n'(t) \ dt | \leq Ma + b + Ma = b + 2Ma[/math].
Your professor probably intended for you to do the Arzela-Ascoli proof tho.

>>12480367
I think it works. For part b, I'm thinking that if f'_n uniformly converges then by Differentiable Limit Theorem f is differentiable and therefore continuous. What do you think of this reasoning? Can I show this with the given information?

>>12480425
Good news.
I wrote all that shit, but then I noticed that the appropriate characterization of the result is just in terms of Lipschitz functions, and then I googled for it and found it in two minutes.
https://math.stackexchange.com/questions/2356399/given-sequence-of-l-lipschitz-functions-which-converges-pointwise-prove-unifo

>>12480436
Part (b) looks tricky, because we proved that a subsequence converges uniformly and not [math]f_n[/math] itself, which converges pointwise, so it might be a trip up question.

>>12480213
>interval [0,2]
based

is the order of the generator of a cyclic group always the same as the order of that group?

am I retarded?

I have a project for which I was given some python code that uses the freud-analysis package. Being careless, I did pip install freud, which obviously gave the wrong package and didn't work. I uninstalled freud (pip uninstall freud -y), and am currently trying to install freud-analysis but it's just thinking and thinking and not actually doing anything. I'm in Jupyter notebook, the exact command I ran is pip install freud-analysis -v -v -v, since I wanted maximum verbosity to keep an eye on what's going on.
Any suggestions would be helpful, and I can provide any other relevant info.

Which vaccine is the most promising? My country bought six.
>AstraZeneca
>Johnson & Johnson
>Sanofi/GSK
>BioNTech/Pfizer
>Curevac
>Moderna

>>12480693
I too like to ask complex medical questions on an anonymous message board full of children and schizos.

>>12480693
>t. the president of an African Country trying to choose which vaccine he'll give to his people
I have good experiences with Johnson & Johnson shampoos, might want to go with that one.

>>12480259
But you didn't ignore it, Anon

>>12475576
Where does mass come from?

>>12481000
depends, but any answer I give is just going to be more confusing because at the end of the day mass is just another property like electric charge that just "exists"
the short answer is "either the higgs mechanism or energy" depending on what type of mass you're considering
the long answer isn't really worth typing out unless you have more specific questions or truly care

>>12481000
there is more than one way bug essentially self-energy or the higgs mechanism. most of the mass in everyday matter comes from the strong force binding energy in the nucleus.

Is there any mineral that contains both mercury and lead?

Scientifically speaking, is sasquatch real?

Are all lattice vectors given in the coordinate basis and then they in turn form a new basis for the lattice? Or is every lattice defined in terms on their own basis? For example would a 2D triangular lattice have the basis vectors {(1,0);(0,1) or {(1,0);(0.5,sqrt(2))}?

>>12481618
I think I figured it out, the only way to get unique reciprocal lattices would be to first define a lattice in the coordinate basis otherwise every lattice and every reciprocal lattice would be identical.

How can you have voltage without current? For example, an ideal op-amp will have an infinite input impedance, thus blocking the current, but will allow voltage to pass? How, when voltage in the force that moves current? Also, how can you have no voltage drop-and in fact a voltage gain-from an op-amp with infinite input impedance?

>>12478558
My bad, I ended up forgetting to answer this.
Anyhow, [eqn]\langle \Phi f, g \rangle = \int _{[0, 1]} \Phi f (x) g^* (x) \ d \mu (x) = \int _{[0, 1]} \left[ \int _{[x, 1]} f(t) \ d \mu (t) \right ] g^* (x) \ d \mu (x) = \int _{A} f(t) g^* (x) d \mu_A[/eqn]
Naturally, [math]A = \{ (x, t) : 0 \leq t \leq x \land 0 \leq x \leq 1 \}[/math].
But we can also write [math]A = \{ (x, t) : t \leq x \leq 1 \land 0 \leq t \leq 1 \}[/math]. This other decomposition allows you to invert the order of integration and get the integral of this thingy multiplying [math]f[/math].
>>12479145
See https://math.stackexchange.com/questions/3587464/proving-a-linear-map-on-a-hilbert-space-is-bounded?noredirect=1&lq=1
>>12480666
Yes.
Maybe.

>>12481924
Wrote [math]A[/math] incorrectly.
Should be [math]A = \{ (x, t) : x \leq t \leq 1 \land 0 \leq x \leq 1 \}[/math] and [math]A = \{ 0 \leq x \leq t \land 0 \leq t \leq 1 \}[/math]
Unless I'm wrong again, of course.

>>12481809
> How can you have voltage without current?
By an absence of free conductors. Electric field is the force which would be applied to a hypothetical test charge. It isn't necessary for that charge to exist.

> Also, how can you have no voltage drop-and in fact a voltage gain-from an op-amp with infinite input impedance?
Input impedance doesn't come into it. The current through a FET is determined by the voltage on the gate. For any practical device, some current must have flowed in order to establish the gate charge, but no current is required to maintain that charge.

>>12481809

first you need to realize that voltage is just an arbitrary definition. it will make things easier

>>12475576
This endless stream of /pol/ fueled conspiracy garbage is getting exceedingly tiresome. It's just so fucking boring, monotonous, and unimaginative. At least put some fucking effort into your trolling you lazy cunts. Trolling is supposed to be an art, but all you fuckers do is flood this board with bottom of the barrel regurgitated and steaming horse shit. It's not even entertaining. No wonder m00t created that containment board. But unfortunately all it did was create a safe space for you mongoloids to get each other all riled up so that you build up the courage to shit all over the other boards too. Just fucking die in a nice, warm, and cozy house fire already. At least that would give us some respite from the cancer that you're spreading.

how do i apply riemann definition of integral to this? The answer is [math]\int_{0}^{2} f(x) + f(-x) dx[/math]
I let 2k/n= x and x -> 0 but what does 2/n term become?

Will the guy who solves this problem be a mathematical legend? Will he at least be a step above Stephen Hawking or if not who? Is this problem all hype?

>>12482396
It's two Riemann sums with [math]a=0[/math] and [math]b=2[/math].

https://en.wikipedia.org/wiki/Drinker_paradox
I have a problem with part 2. of the proof here:
>For any nondrinking person, the statement "if that particular person is drinking, then everyone in the pub is drinking" is formally true: [...]
I don't see how this is "continuously" true if there's 2 or more nondrinkers, because if at a point in the future only one of the two starts drinking the statement will have be proven wrong.
Should I be satisfied with the fact that the statement above only applies to the precise instant in which it's made, and has no predictive power, just like "I have my arms down, and, if my arms are up, donkeys can fly." is true?

How many numbers are there?

why does chewing stuff like airheads increase the pressure in my head

>>12483210
Yes, exactly. Implications are like that by default in math, if you want any kind of continuity or necessity you have to specify that explicitly.

Logic noob here.
I stumbled upon these two statements and they are supposed to be equivalent.
A: Make money
B: Spend money
The statements:
>You have to spend money to make money
>If you haven't made any money, you haven't spent any
Using logical connectives it should look like this, I believe.
[math]
(B=>A)<=>(\neg A => \neg B)
[/math]
Did I get it right?

>>12483863
Nah.
"You have to spend money to make money" means that, if you've made money, you have to have had spent money. Hence, [math]A \rightarrow B[/math].
Second one is correct tho.

>>12483881
Ah, it's much simpler now, it makes sense.
So it should be [math](A \implies B) \iff (\neg A \implies \neg B)[/math] and the truth value of [math]B \implies A [/math]is not known, since it should be possible to spend money without making any, right?

>>12483881
>Second one is correct tho.
The directiony
[math](\neg Q\implies \neg P)\implies (P\implies Q)[/math]
is merely classically valid

>>12483895
So [math](B \implies A) [/math] is true?

>>12483893
No.
Like, I'm kind of dazed the entire day because of this disgusting heat, so I forgot to mention that the [math]\iff[/math] in the middle should be a [math]\land[/math].
But to answer your question, [math]\lnot A \implies \lnot B[/math] is classically equivalent to [math]B \implies A[/math].
So joining everything together you have
[math]A \implies B \land B \implies A[/math], which means [math]A[/math] and [math]B[/math] are equivalent.

>>12483906
So does this mean the two initial statements are indeed equivalent?
>I'm kind of dazed the entire day because of this disgusting heat
Poor you, it's cold as shit over here.

>>12483908
Yes.

>>12483909
I'm afraid I'm the one who's dazed now, does this mean the original statement
[math](A \implies B) \iff (\neg A \implies \neg B) [/math] is not the same as
(You have to spend money to make money) <=> (If you haven't made any money, you haven't spent any)?

>>12482396
The first sum you see corresponds to a constant increment partition of the interval [math][0,2][/math] because

[math]P^1_n=\left\{\frac{2}{n},\frac{4}{n},\frac{6}{n},...,\frac{2\cdot n}{n}=2\right\}[/math]

Intuitively as [math]n \to \infty [/math] the partition becomes [math][0,2][/math]. The increment is

[math]\Delta x = \frac{2(k+1)}{n} - \frac{2k}{n}= \frac{2}{n}[/math]

Similarly the second sum you see corresponds to a constant increment partition of the interval [math][-2,0][/math] because

[math]P^2_n=\left\{-\frac{2\cdot n}{n}=-2,-\frac{2(n-1)}{n},...,-\frac{2}{n}\right\}[/math]

Intuitively as [math]n \to \infty [/math] the partition becomes [math][-2,0][/math]. The increment is

[math]\Delta x = -\frac{2k}{n} + \frac{2(k+1)}{n}= \frac{2}{n}[/math]

So at this point you can use linearity of the summation and obtain two Riemann sums, which in the limit become the integral.

>>12483863
Alright, I think I figured this one out.
It's [math](A \implies B) \iff (\neg A \implies \neg B)[/math] and it turns out the two statements are not equivalent, at least not according to a truth table generator.
Thanks for the help man >>12483881.
If anybody else wants to correct me go ahead.

>>12483210

The truth table of logical inference should be interpreted as “sound or unsound,” not “true or false.”

>>12475576
cs pleb here, studying b+ trees it says the height of a b+ tree is O(logn) and I’m not sure why it’s expressed this way js it because the height depends on the lrder size of the tree?

>>12484252
It is just using O notation to state the fact that the height of the tree scales logarithmically with the number of elements. So are you asking about not understanding O notation or the scaling?

>>12482595
Stephen Hawking was not a mathematician. A better comparison would be J P Serre, Michael Atiyah, or Alexander Grothendieck. From a strictly mathematical perspective, solving the RH would be a far bigger achievement than anything Stephen Hawking has done.

>>12483980
thanks Anon, so I should consider the sequences more thoroughly

Suppose [math]f \in L^1 (\mu)[/math], and define [math]\nu(E) = \int_E fd\mu[/math]. Assuming [math]f \ge 0[/math], I proved that for any real-valued measurable [math]g[/math] we have [math]g \in L^1 (\nu) \Leftrightarrow gf \in L^1(\mu)[/math], in which case we also have [math]\int gd\nu = \int gfd\mu[/math]. (hopefully my proof is sound)

Question: can this be extended to general integrable [math]f[/math]? If so, I don't see how to prove it. My argument for the non-negative case relied heavily on monotone convergence. We've only just begun talking about signed measures in class tho so maybe there's something trivial that I'm missing here

>>12484799
I think I figured it out, would be nice if anyone can confirm this makes sense: I believe that the sets [math]\{f \ge 0\}, \{f < 0\}[/math] correspond to the Hahn decomposition induced by [math]\nu[/math], yielding [math]\nu^{\pm} (E) = \int_E f^{\pm}d\mu[/math]. We can then show that the integral is linear w.r.t. measures, namely that [math]\int_E gd\nu = \int_E gd\nu^{+} - \int_E gd\nu^{-}[/math]. And this basically concludes the proof, so the claim can indeed be extended to any [math]\mu[/math]-integrable [math]f[/math].

>>12485025
I don't really follow the specifics of the explanation, but the broad of it looks correct.
Specifically:
> I believe that the sets {f≥0},{f<0} correspond to the Hahn decomposition induced by ν, yielding ν±(E)=∫Ef±dμ.
Yes.
>We can then show that the integral is linear w.r.t. measures, namely that ∫Egdν=∫Egdν+−∫Egdν−.
And you've lost me. That's the definition that shows up in Cohn when I looked it up, actually. Page 120 of the second edition.
>And this basically concludes the proof, so the claim can indeed be extended to any μ-integrable f.
Don't follow this part either.

my brainlet brain is short circuiting here: In scheduling problems, you try to order jobs that minimize the average completion time. So for example, you can have three jobs and each take time t1, t2, and t3 respectively. The total time is fixed since these job times don't change; however, the average completion time CAN change. In this simple case, the best choice is to process the jobs by order of least amount of time it takes. My question is how is this valuable when the entire time of the process is fixed? What value is gained by a process that has lower average completion time? Is it because they can get material out on the floor quicker? What if material couldn't be moved until the last operation finishes, then would there be any strategic value in minimizing average completion time?

>>12476024
Because the magic mods are already installed. You just find them boring because you don't like wizardry.

>>12477330
Consider a piston. It oscillates, yet usable work can be extracted.

>>12486415
It's the same principle as having a "six items or less" checkout queue, or serving the person who wants to buy a pack of gum before the person with a full cart regardless of who came first.

If you have a 10 minute job and a 50 minute job, processing them in that order delays those waiting on the first job by 10 minutes and those waiting on the second job by 60 minutes (average wait: 35 minutes). Processing them in the other order delays those waiting on the 50-minute job by 50 minutes and those waiting on the 10-minute job by 60 minutes (average wait: 55 minutes).

Regardless of the order, someone has to wait until the last job is done, and that delay isn't affected by the order. But all of the earlier delays are reduced (as well as the average delay) if you process the shortest jobs first.

It becomes more complex if different jobs have differing consequences for delay. If one job holds up the entire factory while another delays one person, the former would be prioritised even if it takes longer.

>>12486513
This clears it up a lot, thanks.

To calculate a square area it's just length times width... so if I multiply my area of 60cm by 140cm I get 8400cm^2...? That can't be right because 1m^2 is 100cm x 100cm and my width isn't even 1m. What is wrong with me?

>>12486543
Oh hang on, 1m^2 is 10,000cm^2 not 1,000cm^2so my result is just under 1m^2
disregard, cocks = sucked

>>12486543
>>12486548
Putting the s into /sqt/

If microwave dialectric heating works by making water molecules jiggle around, why don't mincrowave ovens seem to heat up ants?

>>12486561
http://letmegooglethat.com/?q=why+don%27t+mincrowave+ovens+seem+to+heat+up+ants%3F

>>12485379
I see, in my course we used a different approach to define the integral w.r.t. a signed measures, so I didn't take this linearity for granted. Anyhow, I can totally pick it up from here. Thanks for replying anon, appreciate it

How do I prove that the there are exactly [math]gcd(k_1, k_2, k_3)+1[/math] integers [math]a_1, a_2, a_3[/math] such that [eqn]0 \le \frac{a_1}{k_1}=\frac{a_2}{k_2}=\frac{a_3}{k_3} \le 1[/eqn]
Obviously, it's easy to construct [math]a_i[/math] such that the fractions take values 0 and 1.
Otherwise, it's possible to enumerate other values by setting [eqn]a_i = \alpha \frac{k_i}{gcd(k_1, k_2, k_3)}[/eqn],
for [math]\alpha[/math] from 1 up to gcd.
How do I prove there aren't more of such a_i? How would I even arrive at such construction (it was somewhat a guess)? I initially wanted to count lattice points on a segment in R^n that has lattice endpoints

>>12480213
You open rudin and read

Having trouble simulating this... Should I shuffle a deck of cards, what are the odds none of the cards will be in their original position? The number of cards doesnt matter here does it?

>>12487352
There are [math]n![/math] permutations of [math]n[/math] elements and [math]!n[/math] derangements (permutations where no element appears in its original position) among them. So the probability to pick one is [math]\frac{!n}{n!}[/math]. However you can show that this can be very reasonably approximated as [math]\frac{1}{e}[/mat] for [mat]n[/math] big enough ([math]n > 10[/mat] is enough), so in short the number of cards doesn't really matter.

>>12487352
There are [math]n![/math] permutations of [math]n[/math] elements and [math]!n[/math] derangements (permutations where no element appears in its original position) among them. So the probability to pick one is [math]\frac{!n}{n!}[/math]. However you can show that this can be very reasonably approximated as [math]\frac{1}{e}[/math] for [math]n[/math] big enough ([math]n > 10[/math] is enough), so in short the number of cards doesn't really matter.

>>12487294
does he define the reals? Can he even define the reals

>>12487411
Exactly the term I needed to know about, this makes a lot of sense now

Is there any way to put this into a single statement?

∀x (s(x) t(x))
∀x (t(x) u(x))
∴∀x (s(x) u(x))

>>12487481
sorry arrow disappeared

∀x (s(x) -> t(x))
∀x (t(x) -> u(x))
∴∀x (s(x) -> u(x))

>>12487483
"and" (^) operator?

>>12487526
I don't just want to show that the first and second statements are true, but the whole transitivity thing

https://en.wikipedia.org/wiki/Bernstein%E2%80%93Vazirani_algorithm

Why does this algorithm need n queries with a classical computer? Can't you just input the max number (all 1's) and get the secret string?

>>12487415
Yes

what's the best deodorant type?
do you apply deodorant stick vertically or horizontally?

What it the fattest particle?

How do I do part b and on bros?

I've got an okay understanding of classical physics, atomic etc... at least by my standards, recently I've gained an interest in the quantum world. So my question is, where would one start self-learning about quantum mechanics? Any recommended reading? I don't really know anything about the subject.

>>12475860
assuming you mean a-x(..) and not (a-x)(..)

https://www.youtube.com/watch?v=shaQZg8bqUM
In this video he found that 363 is an inverse element to 27^(1) mod 392
Why then if you type it into wolfram alpha it's not equal to 1? https://www.wolframalpha.com/input/?i=27%5E%28-1%29++*+363+mod+392

>>12475576
/o/tist here. Any environmental science anons here?
I live in an area that plans to ban the sale of new gasoline cars in 15-20 years time. The reason being is that they say gas cars are the number one air pollutant. Is this true? Will banning gas cars truly result in better air quality and such on a large level? Keep in mind, old/used gas cars will still be able to be sold, and commercial companies can continue using new diesel and gas powered vehicles.
I like my car, a simple 4 cylinder. It's not a gas guzzler. Are environmentalists just trying to put blame on cars rather than other causes of air pollution? Looking on google mostly gives me non-science results from the media, so I want a better explanation.

>>12488471
Depends. If you have a major harbour the ships will emit way more than cars both in terms of volume and dire quality since ship fuel is sulphur heavy filth.

>>12488485
I actually live in an area with a large seaport, plus an international airport. The city gets huge amounts of money and pumps out jobs from these, so there's no way they're gonna start pushing those companies to be more eco-conscious.
In that case, banning new gas cars would barely change emissions in the area, I would think.

An outfielder throws to the second baseman , the distance is 125 ft, the throw is at a speed of 80 miles per hour
How would I find the angle needed?

>>12488471
Plurality of greenhouse gases come from transport and majority in transport comes from light vehicles so it's true that cars a big polluter. Look up the fifth cycle of IPCC reports on climate change (sixth cycle coming out in 2022). There's a full chapter on transport. They're usually well-regarded for summarizing the state of research to the public.

>>12488471
Plurality of greenhouse gases come from transport and majority in transport comes from light vehicles so it's true that cars are a big polluter. Industry is the next biggest polluter after transport. Look up the fifth cycle of IPCC reports on climate change (sixth cycle coming out in 2022). There's a full chapter on transport. They're usually well-regarded for summarizing the state of research to the public.

>>12488534
[eqn]z(x) = -\frac{gx^2}{2v_0^2\cos^2{\alpha}} + v_0 \tan (\alpha) x[/eqn]
FInd [math]\alpha[/math] such as [math]z(x=125ft)= 0[/math].

>>12488602
8.5 degrees?

okay is this a valid argument in first order logic?

∀x (red(x) -> color(x) ∧ color(x) -> shape(x))
¬shape(line)
∴ ¬red(line)

>>12488003
Griffiths the ultimate introduction to QM. It's so masterful that even brainlets like me grasped something. Highly recommended for self study.

>>12488745
I found McIntyre's much more intuitive since it builds from experimental data. On the other hand, Griffiths was kinda confusing for me. I guess it depends on the style of the reader.

How are angles of light rays emanating from the sun statistically distributed?
That is, assuming the sun is a perfect sphere, for any point [math]p[/math] on its surface the light rays emanating from [math]p[/math] form some angle [math]\theta[/math] in relation to the normal plane to [math]p[/math]. What statistical distribution do these [math]\theta[/math] follow?

>>12488991
*each light ray emanating from [math]p[/math] forms some angle [math]\theta[/math]

Look, I know it's a meme topic, but I'm genuinely curious. What does the sum of natural numbers equal to, if it equals something? This is a complex analysis topic, right?

>>12489031
[eqn]\sum_{i=1}^{n} i = \frac{n(n+1)}{2}[/eqn]
You can't write that sum from 1 to [math]\infty[/math] because that would assume that the series converges (it doesn't).

>>12489048
everything converges in the complex projected plane

>>12489031
taken to inf it diverges to infinity

What's the proof that particles exist in a superposition i.e in every possible location at the same time and not a definite but unknown to us location due to randomness or whatever.

>>12489104
It's a physics model, it's not "true" in the "you have feet" kind of way.

It's been 20 minutes and I feel retarded. What's the name of the general problem where you have a set of specific integers and you have to find all other integers that can be produced by only adding and subtracting a subset of them?

>>12487977
there must be a trick somewhere that makes everything easy because this one is evil

>>12489184
If it helps, my specific instance is to find all numbers that can be reached by summing any selection of items from the multiset {0, 10, 10, 30, 30, 30, 30, 50, 50, 55, 70, 70, 70, 160, 160, 160, 160, 160, 160, 165, 180, 180, 305, 310, 600, 600}. I can write a quick thing to solve it, but I have completely forgotten the name of this type of problem, and as I am writing a tutorial, it's necessary to know the name.

scientifically speaking, why am I gay?

>>12487977
For whatever [math]x[/math], choose some [math]\epsilon > 0[/math] such that [math](x - \epsilon, x + \epsilon) \cap \{ 1, 1/2, \ldots \}[/math]. Then, no matter how I look at it you still need to exaust on the two possible cases of [math]x > 0[/math] and [math]0 > x[/math], but you can get an expression for [math]f[/math] restricted to [math](x - \epsilon, x + \epsilon)[/math] as a power series, and those are differentiable.

Why do Redox reactions happen?
Low IQ individual here.
I'm not asking what are they, but why they happen.
why would an electron move places if his OG atom was already neutral? wouldn't that need energy? if so, where does it grab it from? does Redox R create more entropy?

>>12489222
*such that thingy is the empty set right in the beginning.

>>12489219
Because you touch yourself at night

>>12489222
Forgot about showing it's differentiable at zero.
My solution for that one is just computation.

>>12489224
There is a potential well at the site the electron moves to. I hated atomic physics so much that I switched to mech. eng rather than learn the details. Freight train engineering pays well though.

>>12489134
what do you mean

>>12489249
now I got more confused lmao, I'm just self-learning general Chemistry from pic rel, is that thing you are saying necessary to understand it?

>>12489270
Oh no, for general chemistry you get to a rough approximation of the potential at the redox site eventually with almost no qm. I've just forgot the details.

>>12489287
aith, thanks brah, have a flat gator

>>12487977
Most I could do, don't know if right so check thoroughly.
[math]1/2\leq x < 1[/math]
[math]f(x)=2^{-1}(-x+1)+\sum^{\infty}_{n=2}2^{-n}(x-1/n)[/math]
[math]|f_1(x)|=|2^{-1}(-x+1)|\leq 2^{-1}[/math]
[math]|f_2(x)|=|2^{-2}(x-1/2)|\leq 2^{-2}[/math]
[math]|f_3(x)|=|2^{-3}(x-1/2)|\leq 2^{-3} [/math]
[math]...[/math]
[math]|f_n(x)|\leq 2^{-n}[/math]

By the Weierstrass M-test the function converges uniformly on [math]x \in [1/2,1)[/math]. By induction (probaby) and term-by-term continuity the function is continuous on all subintervals. You should prove that it is continuous also across the 'angled' points (the same points at which it's not differentiable). e.g. informally

[math]\lim_{x\to 1}^-f(x)\approx \sum^{\infty}_{n=2}2^{-n}(1-1/n)[/math]
[math]f(1)=\sum^{\infty}_{n=2}2^{-n}(1-1/n)[/math]
[math]\lim_{x\to 1}^-f(x)=f(1)[/math]

I think a similar argument works to show differentiability on the subintervals using the term-by-term differentiability, but non-differentiability at the 'angled' endpoints.

>In Carbonara, 90% of the spaghetti is eaten with 10% of the pancetta.
Is there any scientific basis for Pareto's 90-10 law?

>>12489622
>carbonara
>pancetta
to the gulag

Is it possible to produce sugar synthetically?
Meaning, plant and animal byproducts were not used at any point in the process?
I imagine being able to replicate the cellular machinery used to turn energy and soil additives directly into sugar without the additional indirect process of agriculture, which should be dramatically more efficient
Are we even close to being able to do something like this?

>>12489629
no one sells guanciale

How can cos45 and sin45 add up to more than 1?

For example, let's say you have a 2d force equal to 1. If you break it into its horizontal and vertical components, the resulting forces will add up to more than 1. Doesn't that break the law of conservation of energy?

I want a sin (or cos) function but it has smaller waves (probably sin or cos) inside it (pic related). Any idea how its equation will look like?

>>12490256
Just add more frequencies until it just works. Look at [math] \sin(x) + \frac{\sin(9x)}{3} [/math].

All things being the same would a one mm plate really conduct twice as much thermal energy as a two mm. Retard cross boarder here.

>>12490273
That works. Thanks.

Any good resources on "hacking"? I use it in quotes as I care less about the spergy culture around it and moreso about the technical skills and tools behind it. Do I just read a bunch of textbooks on network engineering and other CS buzzwords?

>>12490623
Pentest is the word you are looking for. Too bad I don't know about this to give any recommendations

>>12490623
What you call hacking is just "programming", and "recognizing faults" in other programmer's code and environments.
Except instead of notifying the developers of the issue, you take advantage of it like a douchenozzle.

Certainly there are standard techniques like port knocking which aren't in the usual programmer's toolkit, but there's nothing you can't figure out yourself given time and dedication.

How to solve?

>>12490844
(x-1)(x+1) = x2-1

>>12488991
uniform distribution

>>12490070
what is the physical meaning of "adding the horizontal and vertical components" ?

>>12490844

[math] \left (x + 1 \right )^{2}\sqrt{x^{2} - 1} [/math]

>>12490844
1. Square it:
=> (x+1)*(x^2-1)^4/(x-1)^3
2. x^2-1 = (x+1)(x-1)
=> (x+1)*(x+1)^4*(x-1)^4/(x-1)^3
3. Cancel powers of x-1
=> (x+1)*(x+1)^4*(x-1)
4. (x+1)(x-1) = x^2-1
=> (x^2-1)*(x+1)^4
5. Square root
=> (x+1)^2*√(x^2-1)

>>12480213

This one is pretty easy. In fact, you can prove a much stronger conclusion. You want to prove the contrapositive.

The negation of the conclusion is basically, “for any subsequence [math] {f}_{n_k} [/math], there exists some [math] \epsilon_{0} [/math] such that [eqn] 0 < \epsilon_{0} \leq \sup_{x \in \left [ 0, 2 \right ]} \left | {f}_{n_k}(x)- f(x)\right | [/eqn] for infinitely many [math] k [/math].

Fix [math] {f}_{n_{k}} [/math] and [math] 0 < \epsilon_{0} [/math], and choose [math] {f}_{i} [/math] as an infinite subsequence of [math] {f}_{n_{k}} [/math] such that [eqn] 0 < \epsilon_{0} \leq \sup_{x \in \left [ 0, 2 \right ]} \left | {f}_{i}(x)- f(x)\right | [/eqn] for all [math] i \in \mathbb{N} [/math].

Choose a sequence [math] x_{i} [/math] by choosing each element such that [math] x_{i} \in \left [ 0, 2 \right ] [/math] and [math] \epsilon_{0} \leq \left | {f}_{i}(x_{i}) - f(x_{i})\right | [/math].

Because [math] \left [ 0, 2 \right ] [/math] is a compact set, and because [math] x_{i} \subset \left [ 0, 2 \right] [/math], there must be an accumulation point [math] A \in \left [ 0, 2 \right] [/math] of [math] x_{i} [/math] (you could use the Bolzano–Weierstrass theorem here instead).

Construct a neighborhood around [math] A [/math] with radius [math] \frac{\epsilon_{0}}{2M} [/math]. The rest of the steps are pretty mechanical from here.

Can someone please give me an example of a linear system of ordinary differential equations that can be solved as an initial value problem and models something ocurring in the real world (like a mechanism with harmonic excitation or things such as)?

>>12491407
harmonic oscillator

>>12477260
based on current information (light) and distance we can infer the current state of the star.

For example, if the wavelength of light implies that it will go supernova in 2 million and 1 years, and the star is 2 million light years away, you can infer that it will go supernova in 1 year.

as someone pointed out, don't engage with these people. it's often a sign they have false senses of superiority and just want you to feel down so they can feel better about themselves.

>>12488471
> being this attached to cars that you can't adapt to electric

Yes, it's that bad. Your intuition might be that there are greater pollutants including the meat industry but imagine trying to convince people that they can't eat meat.

There's definitely bigger fish to fry than automobiles but it's a great first step and psychologically primes you into more sustainable options. In burger land, cars are peoples identity and livelihood and nothing will get people to be on board with green solutions than LARP'ing as a cyberpunk eco warrior with a self driving electric car.

is there a biological or scientific difference between muscles that can be worked out in a "natural" movement as opposed to an "unnatural" movement. For instance pectorals can be worked out by lying down a pressing a way, which feels like a normal movement whereas to workout your triceps you have to put your body in a position it would normally never be in or you have to do something you would never normally do like hold a weight behind your head while lying down.

>>12490623
Hacking: the art of exploitation
Yurichev - reverse engineering for beginners
check out the GBAtemp archives for examples

>>12489224
a neutral atom isn't that important. A salt is neutral enough to be stable.
Redox happens b/c the electron being moved moves to a lower electronic potential energy. Like in a battery, or a chunk of sodium blowing up in water (Na + H+ ions)

>>12490909
Hmm.. I guess you would have to have two tools that measure force in a given direction and set them perpendicular to each other (one vertical and one horizontal). Then you would apply a force at an angle which has a magnitude of one. Together, the tools would read numbers that add to more than one meaning that you have more force than you started with.

I don't understand this thing

[eqn] \dfrac{\partial f}{\partial \overline{z}} [/eqn]

What does it mean, how is it derived?

>>12492355
https://en.wikipedia.org/wiki/Partial_derivative

>>12492361
I understand derivatives, what I don't understand is that this one is with respect to [math] \overline{z} [/math], the conjugate of a complex number, how does it work?

>>12492355
https://en.wikipedia.org/wiki/Wirtinger_derivatives#Functions_of_one_complex_variable
>>12492361
Don't be daft.

>>12492373
Oh yeah I missed that. It's a Wirtinger derivative, aka:
[eqn]\frac{\partial}{\partial\bar{z}} = \frac{1}{2} \left( \frac{\partial}{\partial x} + i \frac{\partial}{\partial y} \right)[/eqn]

>>12490070
>>12491753
Firstly the magnitude of the force doesn't change. Basic Pythagoras.
Secondly why do you even think the force applied is linearly related to the energy of a system?

When using a PLA as a ROM, does this mean that there is a logical mapping from every address to every entry? Isn't this really hard to implement for a large ROM? Is this impossible to generalize?

Help a brainlet out on this one:

Let [math] \mathcal{A} = [-1,0] \times [1,2] [/math] and [math] f(x,y) = \frac{1}{y-x} [/math], does [math] \int_{\mathcal{A}} d \mathcal{A} [/math] exist?

The answer is that it does, which I don't get since that A area contains the point (1,1) which is out of the domain of f

>>12490899
Really? Nice, thanks.

>>12492706
Meant this:
[math] f(x,y) = \frac{1}{y-x} [/math], does [math] \int_{\mathcal{A}} f(x,y) d \mathcal{A} [/math] exist?

>>12492706
is this an exercise in calculus, or measure theory?

>>12492723
Real Analysis, so calculus

can i draw a circle and say it's a non-euclidean triangle?

>>12492706
> that A area contains the point (1,1)
No it doesn't, go to sleep, you desperately need some sleep.

>>12492706
Bruh, you may be retarded

>>12492729
only if you draw three points on it

>>12492738
>>12492731
Yep I'm thinking I'm a sleepless retard. Sorry, going to bed and an hero thx

>>12492742
das cool. thanks.
my friend told me he would pay me a lunch if i gave him a round triangle, so i guess this is it. i'd give you half if i could, anon

>>12478814
Well you shouldn't have done that because now we know you are mentally ill.

A child on a sled is on an icy hill that angles up at 15 Degrees above the horizontal, she is going at 10m/s at the bottom. Assuming negligible friction, what vertical elevation did she start at?
Is this just final velocity/9.8? As if they are in free fall?

>>12492876
Not quite.
The potential energy mgh is converted to kinetic energy 1/2 m v^2 so you cancel m and solve for height h.

>>12492355

Complex differentiability is strictly stronger than real differentiability.

A function is complex differentiable iff both its real and imaginary parts are real differentiable, and that it satisfies the Cauchy-Riemann condition.

The Cauchy-Riemann condition looks pretty ugly, so Wirtinger did a change of basis from real and imaginary to default and conjugate. The conjugate term produces ill-defined limits iff its non-zero; the conjugate term is exactly the Cauchy-Riemann conditions, so the Wirtinger derivatives are the shorthand for it.

https://hips.hearstapps.com/pop.h-cdn.co/assets/16/32/1470939110-feynmansdoub.png?crop=1xw:0.7467532467532467xh;center,top&resize=480:* Regarding “the double slit” experiment— does anybody know whether or not the camera was contained during the experiment? The light creates a particular pattern when shone through the double slits but then that pattern changes when you turn a camera on to view the individual atoms and their journey. The idea is that the act of observation from the camera on the atoms causes them to be confined to this reality, eliminating its potential to behave differently, creating a different pattern. And when the camera is turned off, the atoms go back to their original pattern of diffraction. It doesn’t however, mention if the camera is contained in any way to avoid potential interference with the experiment. This is relevant because the atoms behave differently whether the camera is connected to a power source or not... this is perceived as whether or not the atoms are being observed or not. The answer to whether or not the camera is contained in a way that could prevent electrical interference and whether or not they tried switching out a camera for a different electrical appliance, could potentially solve one of the most polarising questions of quantum physics.

A 0.5 Kg mass is in the middle of a 0.1 cm diameter wire . The wire is 10 m long and is straight, without the mass . If the wire deflects 6 cm when the mass is in the middle, what is the Youngs modulus of the wire?

Question regarding DSP
I understand why a perfect FIR filter can't be constructed in the time domain by why not make a perfect one in the frequency domain and work there, like let's say [1 1 1 ... 0 0 0 ... 1 1 1] in [0, 2*pi)

Ok, as I'm typing this I realize that in order to do that your filter would need to have length exactly the same as your signal, is that it or am I missing something more obvious?

>>12493483
Your 'filter' is basically a truncated Fourier series. Can this be applied to streaming data?

>>12493483
> I understand why a perfect FIR filter can't be constructed in the time domain
What do you mean by "perfect"? One which completely discards frequencies outside the pass band? Aka a "brick wall" filter.

> your filter would need to have length exactly the same as your signal, is that it
It is. A brick-wall filter is non-causal, i.e. the current output sample depends upon input samples from the future. Such filters can be constructed by delaying the output relative to the input so that "future" inputs are available "now". But a perfect filter has infinite impulse response (IIR), and truncating it to a finite impulse response means that it's no longer a perfect filter, i.e. frequencies outside the pass band will still be present in the output at some level.

With analogue filters, increasing the number of poles results in a sharper roll-off but also increases the delay.

I need 1 point for my grade to go from an A- to an A. The TA who corrected my last assignment gave partial marks for a few questions which he had never done in the past. Not sure if he did it on purpose but I would get an A if he didn't do that.
I'm writing an email currently but I'm not sure how to write it in a way that will make him understand. He could be an asshole if he really wanted to.
Can you guys help?

>>12493932
This is typical Asian immigrant student behavior. It's obnoxious because you are trying to play some 'fairness' card as you haven't been spoonfed the exact questions from the homeworks or mock exams, and you want to be tested only on memorization like a machine. Go back.

>>12493962
My guy, I hate internationals probably more than you. I'm a local student in Canada just trying to get a few more points so I can get the GPA prerequisite for the program I want to enter (the GPA skyrocketed because of the university bringing in more internationals than locals btw).
But it's whatever, I wrote that post because I panicked at the time. I just finished writing the email.

I have 2 values
A = 10000
B = 5000

Right now I have a ratio of 2:1
What is the math required to redistribute the values so I have a 10:1 ratio instead?

I feel like this is fucking easy but its not coming to me right now

>>12494183
If 2/1 = 10000/5000
then (2/1)*5 = 10/1 = (10000/5000)*5

>>12494221
That's not what I'm asking. I want to redistribute the total (15000) into a 10:1 ratio instead. Now that I typed it out I figured out how to solve it I'm retarded.

>>12494232
>I want to redistribute the total (15000) into a 10:1 ratio instead
divide by 10? lmao

>>12494238
yeah im dumb lol

>>12475576
How might one solve for x? where..

100 = 20(1.1)^x

>>12494270
Logs.
> 100 = 20(1.1)^x
= > 5 = (1.1)^x
=> log(5) = log((1.1)^x) = x*log(1.1)
=> x = log(5)/log(1.1) ~= 16.886

>>12494338
Fantastic. Thanks

>>12490880
Wow, I’m so dumb

Is there a program or website that has a full 3D map (including current exoplanets) of the galaxy, or at least the nearest 500 lightyears?

>>12494740
pro tip: go to academic search engines and type in "thing I'm looking for dataset"
https://academic.microsoft.com/search?q=exoplanet%20dataset

>>12494759
I want an actual 3D star map though

>>12494770
that sucks bro, I hope you're ok with pandas data frames lmao

>>12493596
Couldn't you take blocks of data as they come in and do they same thing on them?
>>12493709
>A brick-wall filter is non-causal, i.e. the current output sample depends upon input samples from the future.
Yeah, I understand that. That's why you go through all the motions with windowing/least squares/approximation algorithms. But in the frequency domain it is a perfect rectangle.
My question was why not work there instead and then inverse fft the result back to the time domain.

>>12494183

[math] 5000(2) : 5000(1) [/math], [math] 5000(2) + 5000(1) = 5000(3) [/math].

[math] x(10) : x(1) [/math], [math] x(10) + x(1) = x(11) = 5000(3) [/math].

So, [math] x = \frac{5000*3}{11} [/math].

>>12494940
>Couldn't you take blocks of data as they come in and do they same thing on them?
The Fourier coefficients depend on all data..

>>12495036
Don't spectrograms work like that though? Wasn't most signal processing in the past done in the frequency domain?

Also, ok, assuming that you can't do it for streaming data (and I agree that's probably the majority of applications) couldn't you do it if you have the entirety of the signal? I guess you would have to construct a new "filter" for every signal.

>>12495132
Spectrograms create fictional signals (using windows) that are always summable/integrable over the integer/real line.

You can always truncate the Fourier series for any signal thus creating a perfect brick wall, but yes, in real world applications we need a sequence that we can use as a filter that approximates this procedure.

Hey /sci/, bong dental student. I'm looking to buy a Dental Anatomy book and I've found one on Ebay. However, I'm not sure if there's a significant divergence between nomenclature/phrasing between American and British dentistry. Teeth are teeth but words can differ. Anyone got any experience of the anglophone issue?

>>12495302
Alright, thanks for sticking with me for all my questions.

>>12494940
> But in the frequency domain it is a perfect rectangle.
> My question was why not work there instead and then inverse fft the result back to the time domain.
Bear in mind that the FFT is ultimately just an efficient algorithm for discrete convolution. Anything you can do with FFT-multiply-iFFT can be implemented as a FIR filter of the same size as the FFT. If you want a small window so that you can perform real-time processing with minimal delay, you inevitably get something which differs from a perfect filter (the FFT of a perfect filter has infinite impulse response).

>>12495132
> I guess you would have to construct a new "filter" for every signal.
It depends upon the length of the signal, not the data. But you could also do the same thing with a FIR filter. Using a FFT just reduces the time from O(n^2) to O(n log n).

Remember, a DFT of a given size is just a matrix multiplication. Given a vector of N time-domain samples, you multiply it by a NxN matrix to get a vector of N frequency-domain samples. The inverse DFT is just the inverse of the matrix. Applying a filter in the frequency domain is just element-wise multiplication, which is equivalent to multiplication by a diagonal matrix.

So the whole process is y=F^-1.(D.(F.x))=(F^-1.D.F).x where F is the DFT matrix and D is the filter matrix. This is equivalent to just doing y=A.x where A=F^-1.D.F, i.e. circular convolution (the nature of F means that A will always be circular, i.e. all columns of A are circular permutations of each other). The FFT just takes advantage of the structure of F to perform the calculation faster. Overlap-add/save effectively use the FFT to efficiently perform convolution with a matrix which is the same size as the entire signal but where most of the elements are zero except for a finite-width strip which follows the main diagonal. IOW, eliminating the "circular" aspect.

Scientifically speaking, why am I 17 years and eleven months old?

>>12475576


be frank, what are my odds of starting the path to becoming an MD at 24

When doing diagonalization of matrices, or finding the Jordan normal form, is there a specific order to the matrices? I mean, is
[eqn]
A = PDP^{-1}
[/eqn]
equivalent to
[eqn]
A = P^{-1}DP
[/eqn]
If not, what's the criteria? or is it just the formula?

>>12495993
They're equivalent.

I am looking for a purely mathematical motivation for choosing the signature (-, +, +, +) for the Minkowski metric. I think I read somewhere that choosing either this signature or (+, -, -, -) is required to guarantee the action of the Poincaré group leaves proper times invariant, is this true? If so, why would this be desirable over other possible invariants retained under diffeomorphism?

>>12496115
There is no mathematical reason since they are isomorphic. There is no physical difference between the two, it is purely a convention. Both produce an invariant proper time. -+++ seems logical to people moving from a flat 3d space to a 4d space-time since the space-like distance between two points is always positive. However iirc +---- always ensures the proper time is positive which seems more logical to others.

Two questions.

1) How come we don't feel the Earth is spinning? When I look it up, all answers claim it is because we're spinning along with the Earth. I understand that, but shouldn't we be able to tell that the Earth is spinning since it's not an intertial reference frame due to its rotation?

2) Is the air inside a tire rotating or static when a car is moving?

>>12496220
1: We can tell because we see the sun move across the sky (obviously the sun is at rest locally, and the earth spins).

2: Tire at rest: air at rest.
Tire accelerates: air starts spinning up.
Tire remains at constant RPM: air attains same speed over time.
Tire brakes: air starts spinning down.
Tire stops: air spins down until at rest.

Just fill a glass with water and see what happens when you rotate the glass.

>>12496220
1) Either you or the person answering have confused 'feeling the spin' and 'observing the spin'. We can't tell (see) the Earth is spinning because we are rotating at the exact same speed. We can't feel the Earth spinning because the centripetal acceleration, even at the equator, is only something like 0.3% of g. It is too small of an effect for us to notice compared to gravity pulling us downward.

2) Yes it rotates since the inner walls of the tire will affect the air touching it. I'm not 100% if it will end up rotating at the same speed as the tire though.

>>12496265
>>12496294

Thanks. So the Earth is indeed not an inertial frame and if we were sensitive enough, we'd be able to feel it spinning due to the non-inertial forces that do exist, but are much weaker than the gravitational force. Is this correct?

>>12496308
Correct. With something like a sensitive electronic gyroscope you can directly measure it.

>>12496328
I see, thanks man.

If I'm forced to solve lots of captchas while masturbating, will I eventually condition myself to get hard while solving captchas?

>>12496201
Thanks

>>12496308
Yes. The spin can be observed on a macroscopic level through the Coriolis effect, such as north-flowing rivers on the northern hemisphere gradually going eastwards (same with a bullet going far), and the rotation of low pressures (cyclones).

>>12496328
In perhaps 10 years mobile phones will have solid stated gyros of this sensitivity for better dead reckoning.

>>12496404
I conditioned myself to get horny as fuck while writing in [math]\LaTeX[/math], if anyone ever catches me masturbating in front of my pc they'll see me grunting while writing page-long partial differential equations. Checkmate coombrains, I ascended.

>>12475576
Omg, based. This is a thread where I can ask my shizo questions.

If the new mRNA vaccine had some secret ingredients for gene manipulation, would it be enough to take drugs for hiv that are based on reverse transcriptase inhibitors?

If gravitrons react with themself, would black holes have a maximum gravity?

>>12496568
No. Reverse transcriptase inhibitors only stop the method HIV uses for replication. That doesn't prevent any other methods for gene editing.

What do mean by a maximum gravity? The heavier a black hole simply means a larger event horizon.

>>12496613
>No. Reverse transcriptase inhibitors only stop the method HIV uses for replication. That doesn't prevent any other methods for gene editing.
Isn't the gene modifying technique we use based on HIV?

What do mean by a maximum gravity? The heavier a black hole simply means a larger event horizon.
Wouldn't that keep gravitrons inside aswell if it can catch light?

>>12496642
Now that I think about it, why isn't all the gravity caught in the event horizon?
Why do black holes have gravity?

>>12496815
Blackholes have a gravitational field around them generation by its mass. That is not the same thing as gravitational radiation (gravitons) which cannot escape from inside.

>>12496553
You will no doubt want to know that over in >>>/s/latex they were so tired of [math]\LaTeX[/math] jokes the TeX extension was removed. A few seem conversant in both, as it were.

>>12496861
Will read into this. I'm a bit confused now.
It rather sounds to me that gravitons are rather normal is, but with negative mass.
That would explain why things get closer to each other in case of collision.

>>12497262
> but with negative mass.
why would you think that??

gravity field is just like an electric field. it has a source and an infinite range.

What anime do you like to watch in background while doing math

>>12497416
i watch lectures or news or audiobooks
sometimes minecraft videos bc im autistic

>>12497416
I don't watch anything with subtitles. How can I read two things at once?

>>12496220
Can you tell the difference between sitting in a car going 50 mph and sitting in an airplane going 500 mph? Considering only the feeling of motion.

>>12497416
Reviewbrah
He even does thematic podcasts and that's very nice

>>12495993
Well, [math]PDP^{-1}[/math] is [math]Q^{-1}DQ[/math] where [math]Q=P^{-1}[/math]. But if you use [math]A=PDP^{-1}[/math], then P is the matrix whose columns are the eigenvectors of A, so that's the more usual form.

If you collect the solutions of Ax=λx into a matrix P whose columns are the eigenvectors and a diagonal matrix D whose diagonal entries are the eigenvalues, you have AP=PD (post-multiplying with a diagonal matrix scales the columns); post-multiplying both sides with [math]P^{-1}[/math] gives [math]A=PDP^{-1}[/math].

If the matrix is defective (lacks a complete eigenbasis, i.e. has repeated eigenvalues whose algebraic multiplicity exceeds their geometric multiplicity), then P isn't invertible and the matrix can't be diagonalised.

>>12491456
It's not that I can't adapt to electric, it's more that an electric car doesn't seem like the best option for where I live. I live in cold, nothern Canadaland where I hear the electric battery may not do as well in the colder temperature. I also do a 3 hour drive to uni classes weekly, unsure if the range will last me the travel. There are no charging stations available on the road I drive on. I also know how to do basic repairs for a gas car than all the electric stuff in the electric car.
I understand the need to be more sustainable, but I just feel banning all new gas cars wouldn't make much of a dent in net emissions here.

>>12498083
> I live in cold, nothern Canadaland where I hear the electric battery may not do as well in the colder temperature.
Capacity will likely be reduced compared to a mild climate. But you don't have the issue of the engine not starting in cold/damp weather. If electric cars become ubiquitous, it's likely you'll see specific models for colder climates. The batteries inherently generate some amount of heat when charging or discharging; normally you aim to dissipate as much of that as practicable, but for a colder climate you'd retain some of it.

> I also know how to do basic repairs for a gas car than all the electric stuff in the electric car.
An electric drivetrain is far more reliable, so that's largely a non-issue. Even on a gas car, you have electronics (ECU etc) which aren't user-serviceable (if it breaks, you replace the unit).

Probably the biggest factor against an electric car in your case is the efficiency means that they don't generate (much) heat. So you'd probably have to expend some non-trivial fraction of the battery charge on electric heating, or have a dedicated gas heater. Whereas ICEs are basically heaters which generate some mechanical power as a by-product.

I'm about to finish Calculus. When should i get to learn Complex Analysis and Number Theory? Where and how do I get started? Any free book recommendations that's available?

I'm about to finish Calculus. When should i learn Complex Analysis and Number Theory? Where and how do I get started? Any free book recommendations that's available? PDFs?

>>12498574
>When should i learn Complex Analysis
After you learn real analysis
>Number Theory
You can study elementary number theory with minimal knowledge. If you mean analytic number theory, you could probably start now with Apostol.
>Where and how do I get started? Any free book recommendations that's available? PDFs?
The book recommendations in the sticky is good.

Let [math]f,g \in L^1( \mathbf{R} \to \mathbf{R})[/math]. Define [math]\mu(A) = \int_A fdm, \nu(A) = \int_A gdm[/math] where [math]m[/math] denotes Lebesgue measure. What condition must [math]f,g[/math] satisfy to ensure that [math]\mu \bot \nu[/math]? (one that's not a complete tautology of course. I hope my question is not too vague)

>>12498735
> start now with Apostol
I do not understand why his book gets recommended. It's awful at explanations and clears poofs. It's more like a reference guide than something to learn from.

I am having trouble with the mechanics of the Kepler problem. There is the "hidden" symmetry generated by the LRL vector A: this is one of the conserved quantities: {A, H} = 0. Conversely, this implies that the energy is constant under the action of the LRL vector. From John Baez's notes "Mysteries of the gravitational 2-body problem" I have seen how this transformation corresponds to a change in the eccentricity. While this very intuitively shows that E is indeed conserved under the LRL transformation, what's strange is that it seems to affect the LRL vector itself. Since the eccentricity only depends on A, it seems inevitable that it changes. But can that be right? Wouldn't that imply that {A, A} != 0?

I'm relearning high-school algebra (fuck me for being a retard thinking that shit was useless at the time)

Watching some online videos/courses, I liked Professor Leonard best so far, so I went with his courses.

One thing that concerns me is that he teaches the "diamond problem" to solve trinomials. I remember doing it differently in highschool (in Europe though so the approach might be different), something that was maybe a bit more direct to solve the problem, but I can't remember for the life of me.

IS there a less... "gimmicky" way of doing these, something more straightforward and intuitive you can do in your head or make it so you can use solving these problems in an actual scientific setting (I'm working up from algebra to calculus for elementary neuroscience)

Are there solstices on Venus?

>>12498944
You can solve x if your equation is a (ax^2+bx+c). You should also learn the foil method which I was too lazy to bother with, but that too is a bit of a gimmick. Sometimes I did estimated guesses until i got it right for some.

>>12498944
The common approach is "completing the square" aka reducing to depressed form, noting that (x+b/2)^2 = x^2+bx+b^2/4 => x^2+bx = (x+b/2)^2-b^2/4. This lets you eliminate the linear term, leaving you with a quadratic term and a constant term. A degree-n polynomial whose x^(n-1) term is missing is termed a "depressed" polynomial; the solution of cubic and quartic polynomials also starts by converting to this form.

First divide through by the quadratic coefficient:
ax^2+bx+c = 0
=> x^2+(b/a)x+(c/a)=0
then move half of the linear coefficient inside the square:
=> (x+b/2a)^2-(b/2a)^2+(c/a) = 0
=> (x+b/2a)^2 = b^2/4a^2+(c/a) = (b^2-4ac)/4a^2
=> x+b/2a = ±√(b^2-4ac)/2a
=> x = (-b±√(b^2-4ac))/2a
You can either apply this formula directly, or perform the above steps with a specific polynomial.

The term b^2-4ac is termed the discriminant. If it's positive, the polynomial has two real roots; if it's zero, it has a repeated root (i.e. the curve is tangent to the x axis), if it's negative it has two complex roots which form a conjugate pair (p+qi and p-qi). The graph is symmetric about x=-b/2a.

>>12498969
>>12499131
Fucking thank you

This is exactly it and both your explanations are exactly what I needed.

How is it possible to take a high dose of ayahuasca and not experience any effects?
https://www.youtube.com/watch?v=7I2jO1DDpJ4

>>12498806
I posted the question, consider this answered.

>>12499420
He did not take a high dose of ayahuasca. Ayahuasca is a brew that takes hours to make.

>>12498503
Thanks for your response anon. I'll admit that I'll keep my gas car until it dies, then buy an electric when they ever make one for colder areas.