Anonymous at Thu, 7 Nov 2024 12:44:25 UTC No. 16465936

>>16465871
i was the one with the question about suramin

Anonymous at Thu, 7 Nov 2024 16:10:20 UTC No. 16466124

What's the book on linear algebra that everyone here recommends? There's a particular one that's a borderline meme, I think the name started with an 's' or had a prominent 's' sound in it.

Anonymous at Thu, 7 Nov 2024 16:34:37 UTC No. 16466148

>>16466124
Serge Lang

Anonymous at Thu, 7 Nov 2024 17:02:58 UTC No. 16466173

fuck, the plasma physics general is gone, and i finally had a question to ask in it...

does anyone here do RIE for semiconductor device fabrication? i need two recipes for InAs and AlGaSb

Anonymous at Thu, 7 Nov 2024 18:18:54 UTC No. 16466223

So I just want to make sure I'm with the book so far:

A discrete probability function is when:

a) 0<=p(s) for each s in S.
b) the sum of all p(s) is equal to 1.

Now with pic related, p(s) would be a discrete probability function, but p(A) wouldn't since it doesn't add up to 1 and fails (b)? But we could still use it to say "Well, the odds of flipping a heads on an odd-numbered flip are 2/3rds? Or does it failing (b) make it useless for us?

Anonymous at Thu, 7 Nov 2024 18:37:09 UTC No. 16466236

>>16466223
P(A) is not a distribution, it is the probability of an event.

Anonymous at Thu, 7 Nov 2024 18:44:52 UTC No. 16466247

>>16466223
p(A) isnt a function like p(s) is. p(s) is "probability that first heads appears on the sth toss", which is a function of s, and p(A) is "probability that A occurs", with A being "first heads is on an odd toss", so its just a constant (equal to 2/3, as shown).

Anonymous at Thu, 7 Nov 2024 18:45:35 UTC No. 16466249

>>16466236
>>16466247
jfc

thank you, that's confusing

Anonymous at Thu, 7 Nov 2024 18:55:55 UTC No. 16466258

How hot is free floating radiation? If you refined some nuclear material could you use it for a more direct process like melting glass or heating up an oven?

Anonymous at Thu, 7 Nov 2024 19:22:02 UTC No. 16466294

>>16466258
What do you mean by free floating radiation? Also note that temperature isn't a property of single particles (such as alpha/beta/gamma radiation), it is a macroscopic property of a collection of atoms (their average kinetic energy).

Anonymous at Thu, 7 Nov 2024 19:34:08 UTC No. 16466311

>>16466124
LADR by Sheldon Axler. The new edition is free, open access

Anonymous at Fri, 8 Nov 2024 01:47:48 UTC No. 16466675

>>16466294
>What do you mean by free floating radiation
How I worded it was probably better in my head. I meant the alpha, beta, and gamma particles that are emitted. The idea was trying to grasp at was if they can use nuclear energy to power steam engines via bolling water, could you just take multiple rods or material and just use the heat to warm up material directly.

Anonymous at Fri, 8 Nov 2024 03:34:47 UTC No. 16466746

If you had two weeks to learn Analysis up until the Riemann Integral, how would you do it?

Anonymous at Fri, 8 Nov 2024 04:08:17 UTC No. 16466776

Pi equals 3

Anonymous at Fri, 8 Nov 2024 04:52:26 UTC No. 16466814

>>16466746
Read Tao's book on Analysis 1 I guess, or any other book, idk. Not a math guy

Anonymous at Fri, 8 Nov 2024 05:37:43 UTC No. 16466838

I think I'm getting filtered by linear logic exponentials. I get that ! restores structural rules for terms "on the left" and ? for terms "on the right", and I understand their duality, but what about a ? on the left or a ! on the right? Why not just have one symbol that is it's own dual?
Maybe the actual filter is Sequence Calculus. I only ever use the "classical" notation (don't know what it's called) of classical logic in undergrad and this shit is confusing me.

Anonymous at Fri, 8 Nov 2024 06:12:59 UTC No. 16466851

Anyone know of any good popsci YouTube stuff I can show my girlfriend, especially videos about plants?
She's interested in science but she's not the most academically-inclined and needs visuals to learn, which is why I'm looking for popsci

Anonymous at Fri, 8 Nov 2024 06:29:18 UTC No. 16466860

>>16466851
I don't really watch plant videos so I can't give a rec.
But for popsci with high production value and visuals, look into stuff like Veritasium, Kurgesagt, AsapScience, Mark Rober, or PBS channels like Be Smart (the PBS channels are good). Im not saying I myself love em, but they are popular to most people.

Maybe be more specific for other people to answer, like does she like gardening, or plant biology, or wtv?

Anonymous at Fri, 8 Nov 2024 06:40:33 UTC No. 16466867

>>16466860
Thank you, PBS is a good rec. She's enjoyed PBS eons in the past with me
I'd say I'm looking for videos related to plant biology, ecology, and maybe plant evolution. She's also expressed interest in learning how to identify flowers.

Anonymous at Fri, 8 Nov 2024 07:25:21 UTC No. 16466892

>>16466851
Crash Course Botany maybe?

Anonymous at Fri, 8 Nov 2024 07:31:20 UTC No. 16466896

>>16466675
> could you just take multiple rods or material and just use the heat to warm up material directly.
You would die from radiation sickness since they would be highly radioactive and since nothing would be cooling them you might die from the heat first. But sure, you *could* do that.

Anonymous at Fri, 8 Nov 2024 13:24:16 UTC No. 16467112

hello sqt. im a neet studying math on their own and really interested in number theory. i would like a book recommendation for cool multiplicative number theory like modern stuff sieves and shit. here are the books ive read:

steins fourier analysis and complex analysis
apostols analytic number theory
apostol modular functions and dirichlet series in number theory
chandrasekharans elliptic functions
a good chunk of whittaker watsons special functions section (havent read the classical analysis part in a meaningful way)
derek lawdens elliptic functions and applications
berndt heckes theory of modular forms and dirichlet series

so im extremely good at dealing with special functions and their applications to most things especially number theory, which probs can be seen by list above. however im kinda weak about the real analysis stuff. i struggle at non trivial estimates of contour pieces or stuff like using phragmen lindelof. im familiar with the basic stuff and the standard rigour of analysis but this might be because i havent just gotten up and taken a real analysis book yet. im worried this is gonna hurt me when studying number theory. i also wanna get into algebraic nt but my algebra background is just groups rings and modules from dummit&foote and langs undergrad algebra so i have a lot to learn.
what do i do /sci/bros?

Anonymous at Fri, 8 Nov 2024 13:53:18 UTC No. 16467140

Is there a group [math]G[/math] that contains finite-index subgroups [math]A,B \le G[/math] with [math]A \cong \mathbb{Z}, B \cong \mathbb{Z}^2[/math]?

Anonymous at Fri, 8 Nov 2024 13:59:51 UTC No. 16467153

>>16467140
If both the indexes were finite than so would be their ratios, which is index of A in B. Contradiction

Anonymous at Fri, 8 Nov 2024 14:22:11 UTC No. 16467173

>>16467153
>index of A in B
A doesn't have to be a subgroup of B.

Anonymous at Fri, 8 Nov 2024 15:05:05 UTC No. 16467211

>>16467140
OP here, I think I figured it out. Assume towards contradiction there is such a group. The intersection [math]A \cap B[/math] is a subgroup of [math]A \cong \mathbb{Z}[/math] and therefore cyclic. But [math][B : A \cap B] \le [G : A] < \infty[/math], contradicting the fact that [math]B \cong \mathbb{Z}^2[/math] has no finite index cyclic subgroups.

Anonymous at Fri, 8 Nov 2024 19:03:15 UTC No. 16467440

What is the simplest way to prove that any fraction can be written as the sum of distinct egyptian fractions?

Anonymous at Fri, 8 Nov 2024 19:34:56 UTC No. 16467471

>>16467440
I'm not sure a "simple" method exists since it involves a fair amount of number theory. I think the oldest was by Fibonacci - https://en.wikipedia.org/wiki/Greedy_algorithm_for_Egyptian_fractions

Anonymous at Fri, 8 Nov 2024 19:38:20 UTC No. 16467473

>>16467440
fundamental theorem of arithmetic
the prime factorization of a number is unique

Anonymous at Fri, 8 Nov 2024 19:59:40 UTC No. 16467497

Had to take a 2 year break for school due to family reasons, will I be okay to take linear algebra? I'm pretty good algebra side but my calculus is a bit rusty

Anonymous at Fri, 8 Nov 2024 20:04:16 UTC No. 16467505

>>16467473
How does that help? Egyptian fractions are the sum of distinct unit fractions. So 2/5 = 1/5 + 1/5 would not be correct, but 2/5 = 1/3 + 1/15 would be.

Anonymous at Fri, 8 Nov 2024 21:09:26 UTC No. 16467555

>>16467497
You need more logic, sets, functions, capital-sigma "[math]\Sigma[/math]" notation (summation) and proofs for linear algebra. Very little calculus

Anonymous at Fri, 8 Nov 2024 21:30:13 UTC No. 16467589

>>16467112
Try exploring the MAA Book Review Repository. For example:
>Multiplicative functions
https://old.maa.org/press/maa-reviews/famous-functions-in-number-theory
>A summary of the elementary number theory everyone should know
https://old.maa.org/press/maa-reviews/number-theory-an-introduction-to-mathematics
https://old.maa.org/press/maa-reviews/a-guide-to-elementary-number-theory
>The reach of number theory into other areas of math
https://old.maa.org/press/maa-reviews/number-theory-an-introduction-to-mathematics
>If you are feeling lucky
https://old.maa.org/press/maa-reviews/unsolved-problems-in-number-theory
>A popularizer of number theory
John Stilwell (not really pop-sci, just very friendly but rigorous texts)
>Three classic treatises , not for the faint of heart
https://link.springer.com/book/10.1007/978-1-4612-9957-8
https://link.springer.com/book/10.1007/978-3-642-61945-8
https://link.springer.com/book/10.1007/978-1-4684-9884-4

Anonymous at Fri, 8 Nov 2024 21:31:25 UTC No. 16467590

>>16467112
any suggestions for this?

Anonymous at Fri, 8 Nov 2024 21:32:26 UTC No. 16467591

>>16467590
>>16467589
holy shit sorry for the timing

Anonymous at Sat, 9 Nov 2024 13:17:53 UTC No. 16468247

So universe expands, but locally galaxies, objects, etc. don't expand because of gravity, electromagnetic, weak and strong forces, they bind them together. Particles themselves don't expand because they're point objects.
But the question is, why fundamental forces also don't "expand" with space? F=ma, a=v/t, v=s/t. s should expand with space, hence F also should expand.

Anonymous at Sat, 9 Nov 2024 14:22:22 UTC No. 16468286

>>16468247
s is displacement, that is a fixed distance irrespective of the expansion of space. what you are talking about is relative velocity = distance/time + speed of expansion.

Anonymous at Sat, 9 Nov 2024 17:54:53 UTC No. 16468450

>>16468247
>Particles themselves don't expand because they're point objects.
Sorta. As of now, force that expands universe isn't too powerful, but it's getting stronger and at one point it might start ripping apart galaxies, celestial bodies, molecules, atoms and even hadrons.

Anonymous at Sat, 9 Nov 2024 18:03:15 UTC No. 16468464

I'm trying to minimize the variance of the d0-d11 by controlling the v0-v11. v is constrained to positive values. This is what I've got so far, but I'm not sure what else I should be doing to it to get closer to solution.
Apologies for smoothbraining. I haven't done have-to-actually-think-about-it math in a long fucking time. Your guidance will be heavily appreciated.
d0 = (14 * (v0 + 85))
d1 = (13 * (v1 + 85)) - ((v0 + 85)
d2 = (12 * (v2 + 85)) - ((v1 + 85)
d3 = (11 * (v3 + 85)) - ((v2 + 85)
d4 = (10 * (v4 + 85)) - ((v3 + 85)
d5 = (9 * (v5 + 85)) - ((v4 + 85)
d6 = (8 * (v6 + 85)) - ((v5 + 85)
d7 = (7 * (v7 + 85)) - ((v6 + 85)
d8 = (6 * (v8 + 85)) - ((v7 + 85)
d9 = (5 * (v9 + 85)) - ((v8 + 85)
d10 = (4 * (v10 + 85)) - ((v9 + 85)
d11 = (3 * (v11 + 85)) - ((v10 + 85)

Anonymous at Sat, 9 Nov 2024 18:05:09 UTC No. 16468465

>>16468247
Empty space will expand. Non empty space will not expand. So areas inside galaxies will not, but the empty space between galaxies will, far as I know

Anonymous at Sat, 9 Nov 2024 18:27:41 UTC No. 16468489

Dumb scifi writer here zero scientific background

Would it be possible to use large amounts of light, or just light in general, to accelerate particles or matter in order to generate energy? I'm making a power plant in my story that uses a "cascading light accelerator" that accelerates matter to generate energy through the use of a geographic phenomenon in a planet, and I want to know more on how that could work. I don't plan to explain it in depth and the plant itself will be mostly mumbo jumbo but if there's anything interesting to know about this, I'd like to hear it

Anonymous at Sat, 9 Nov 2024 19:01:28 UTC No. 16468538

>>16468489
Light does have momentum, it can move things. It's the basis for how solar sails work, and solar radiation pressure has to be taken into account for satellite orbits. But scientifically speaking it's an incredibly weak force that needs the power of a sun (or supernova) to have any "oomf".

Anonymous at Sat, 9 Nov 2024 19:05:55 UTC No. 16468543

>>16468465
Occupied space also expands, objects just collapse on themselves until they're their previous size.

Anonymous at Sat, 9 Nov 2024 19:25:53 UTC No. 16468579

>>16468538
that sounds good enough. Thanks

Anonymous at Sat, 9 Nov 2024 19:30:27 UTC No. 16468584

>>16468489
yes, the photoelectric effect is basically this.You can use it to generate electric current too but it sucks compared to using like a normal battery. Someone already mentioned solar sails. Its the whole E^2=(mc^2)^2 + (pc)^2 thing, even if a particle has no mass (photon), it can still carry momentum

Anonymous at Sat, 9 Nov 2024 23:15:01 UTC No. 16468865

>>16468464
I think you have a quadratic program. I can't get the solution because maxima's lapack looks broken.

Anonymous at Sat, 9 Nov 2024 23:20:15 UTC No. 16468874

>>16468865
Continued: the smallest eigenvalue is 4e-14 the rest are around 100, so it seems like you'll have a solution.

Anonymous at Sat, 9 Nov 2024 23:47:28 UTC No. 16468912

>>16468874
v =[0.000000 6.538462 11.169872 16.469988 22.896999 30.877444 41.047181 54.435312 72.822552 99.564510 141.766128 217.255376]
var = 559636.5
But with the (near) zero eigenvalue maybe you can add something to the minimum without changing the result.

Anonymous at Sun, 10 Nov 2024 15:37:09 UTC No. 16469675

>be starting chemical engineer
>senior asks me to help him
>cost reduction project where we try to find the optimum for a specific stream
>initial model was simple
>stream A enters system 1 which costs money, then enters system 2 which nets us money
>now system 2 has been split into system 2a which costs us money
>and system 2b which nets us money
>however the fraction that goes to 2a vs 2b is dependent on stream A
>more of A means more goes to 2a
so what do I do now? because now this fraction depends on A but the costs of A depends on this fraction. Feels like I'm running into an issue here

Anonymous at Sun, 10 Nov 2024 18:15:17 UTC No. 16469821

>>16469675
The best explanation of dynamic programming is in Peters and Timmerhaus plant design book.

🗑️ Anonymous at Sun, 10 Nov 2024 20:39:09 UTC No. 16469928

There's a quarter of a unit circle. Then an infinite sequence of semi-circles are put inside, each having always three contact points. The sequence is made by putting the next semi-circle in the upper right gap like shown in picrelated.

What is the diameter of the n:th semi-circle?

Anonymous at Sun, 10 Nov 2024 20:42:46 UTC No. 16469934

There's a quarter of a unit circle. Then an infinite sequence of semi-circles are put inside, each having always four contact points. The sequence is made by putting the next semi-circle in the upper right gap like shown in picrelated.

What is the diameter of the n:th semi-circle?

Anonymous at Sun, 10 Nov 2024 22:55:09 UTC No. 16470070

>>16469934
The radius of the first semicircle, which I will denote [math]R[/math], is [math]\sin\theta[/math] where [math]\theta[/math] is the angle of the unit circle (from the positive horizontal, increasing downwards) whose point on the unit circle is the bottom right corner of the semicircle.

It's also obvious that [math]\cos\theta=2\sin\theta[/math], which yields [math]\theta=\arctan(1/2)[/math]. Therefore, [math]R=\frac{1}{\sqrt{5}}[/math].

Next, denote [math]\varphi[/math] to be the angle from the first semicircle's positive horizontal (increasing upward) where the second semicircle's bottom left corner is. Additionally, similarly to [math]\theta[/math], denote the angle to the bottom left corner of the second semicircle from the positive horizontal of the unit circle as [math]\theta'[/math]. The radius of the second semicircle, which I will denote [math]r[/math], is [math]\sin\theta'[/math], and also [math]R-R\sin\varphi[/math]. Additionally, we have the relation

[eqn]R+R\cos\varphi+2r=\cos\theta'[/eqn]

WolframAlpha gives me a really complicated exact solution (and a numerical answer) for r, so it suffices to say that this can be repeated over and over to find the radius of the nth semicircle.

Side note, thanks for the problem anon. This was interesting to solve.

Anonymous at Sun, 10 Nov 2024 22:56:13 UTC No. 16470071

>>16470070
That eqn didn't render. In math form:

[math]R+R\cos\varphi+2r=\cos\theta'[/math]

Anonymous at Mon, 11 Nov 2024 07:59:36 UTC No. 16470521

Let [math](G, \mu)[/math] be a probability space and set [math](\Omega, \mathbb{P}) = (G^\mathbb{N}, \mu^\mathbb{N})[/math]. Let [math]X_i: \Omega \to G[/math] the projection on the ith coordinate, written [math]X_i (\omega) = \omega_i[/math], and let [math]\mathcal{A}_n[/math] be the sigma algebra generated by [math]X_1 \dots X_n[/math]. I want to prove that for any (say bounded) [math]F: G^{n+1} \to \mathbb{R}[/math] we have [math]\mathbb{E} [F(X_1, \dots, X_n, X_{n+1}) | \mathcal{A}_n] = \int_G F(X_1, \dots, X_n, t) d\mu (t)[/math].

It boils down to proving that if [math]A_n \in \mathcal{A}_n[/math] then [math]\int_{A_n} F(\omega_1 , \dots, \omega_n, \omega_{n+1}) d\mathbb{P} (\omega) = \int_{A_n} \int_G F(\omega_1 , \dots, \omega_n, t) d\mu(t) d\mathbb{P}(\omega)[/math]. How does this follow from independence of [math]X_{n+1}[/math] from [math]A_n[/math]?

Anonymous at Mon, 11 Nov 2024 17:01:59 UTC No. 16470999

Dumb question, but why does only this term survive in QFT? if <0|psi+=0 and psi|0>=0 shouldn't this term die due to normal ordering like all the others?

Anonymous at Mon, 11 Nov 2024 17:40:20 UTC No. 16471058

This probably doesn't deserve it's own thread, unless the premise is expanded to a /sci/ck/ deal. What is the optimal amount of times to flip potatoes to get as many sides fried and crunchy in the least time possible? It's an optimization problem, which I haven't done in years, and it involves probabilities, which I've never been great at. Here's some assumptions:

>The potatoes are cooked and only the sides need to be fried.
If you don't know already, baking your potatoes before you fry them gets you better results than cooking them in the pan at a low heat before you fry them.

>The potatoes have been cubed perfectly
Obviously they haven't and there will be a lot of strange shapes because you're dicing an irregular shape.

>One side on each potato is fried before the first turn

>Flipping the potatoes turns each cube to a random side

At this point I'm stuck because I've always been weak on probability. There's a 1/6 chance of each side being fried each time they're turned, but one side has already been fried, so to my mind 1/6th of the sides have been fried and there's a 5/6 chance of frying a new side on the first turning. And that's as far as I can take it with my half remembered and half-assed probability ability. What's the next step? What formula am I missing? Is this a combinatorics problem?

Anonymous at Mon, 11 Nov 2024 20:04:38 UTC No. 16471187

Is it normal for Boston fern (Nephrolepis exaltata) leaves to turn yellowish during fall and winter? I heard overwatering can cause fronds to turn yellow, but I can rule that out, since the soil has a good drainage and I'm careful with watering.

Anonymous at Mon, 11 Nov 2024 23:36:10 UTC No. 16471395

>>16470999
The psi operator isn't acting on the vacuum |0>, it is acting on the two particle state |i>. Each psi field kills off one of the b^\dagger operators on the right, and the \psi^\dagger operators kill off the b operators on the left in <f|.

Anonymous at Tue, 12 Nov 2024 08:39:33 UTC No. 16471780

>>16471058
pbinom(0, flips, 1/6) is part way there:

1 0.83333333
2 0.69444444
3 0.57870370
4 0.48225309
5 0.40187757
6 0.33489798
7 0.27908165
8 0.23256804
9 0.19380670
10 0.16150558
11 0.13458799
12 0.11215665
13 0.09346388
14 0.07788657
15 0.06490547
16 0.05408789
17 0.04507324
18 0.03756104
19 0.03130086
20 0.02608405

If you pick a face, flip it 20 times, 2.6% of the cubes will not cook that face. But if you flip it too often it won't become as crispy, because the potato surface temperature will be lower.

Anonymous at Tue, 12 Nov 2024 15:04:04 UTC No. 16471994

>>16471780
That's not quite what I'm after. The average number of cooked faces per cube is more germane because then you can set it up as an optimization problem to maximize the cooked sides per flip.

>But if you flip it too often it won't become as crispy
I should have listed the assumption that the amount of time spent on each face was sufficient to crisp it, but you have a point. What if the flips are only sufficient to cook it halfway to crispy so that each side needs to be fried twice to actually crisp up. You could flip it nearly twice as often and you'd have less of a chance of burning a face.

Anonymous at Tue, 12 Nov 2024 18:27:20 UTC No. 16472205

Do books get checked for accuracy? I lost points for paraphrasing a book answer

Anonymous at Tue, 12 Nov 2024 18:30:22 UTC No. 16472208

>>16471994
8 flips is ideal. If you keep flipping the burned side will get more burned faster than the average number of cooked sides increases 6*pgeom(flips, 1/6). But your burned-raw preference may be different, and I might be off by 1 since the first side starts out cooked already.

Anonymous at Tue, 12 Nov 2024 18:35:14 UTC No. 16472215

>>16471058
Fry them in oil for the quickest results. In general, the closer to sphere shape the more even the cook, but gradation actually adds complexity to texture. Any conceivable goal could min-maxed, such as shoe string fries to maximize crunchyness, and steak fries for nice body.

Anonymous at Tue, 12 Nov 2024 18:38:15 UTC No. 16472218

>>16472205
No. What gave you the idea they would be?

Anonymous at Tue, 12 Nov 2024 18:40:35 UTC No. 16472219

>>16470521
Stripping away some details of your question, I think you essentially want to prove that [math]\mathbb E[f(X,Y)|X]=g(X)[/math], where [math]g(x)=\mathbb E[f(x,Y)][/math].
I'm not really sure how your intermediate step plays into this (not a fan of the notation tbdesu), but I would prove the above first for indicator functions and then use the ``standard machinery'' or a monotone class argument.

You have, for example, for [math]A,B \in\mathcal B(\mathbb R)[/math], [math]\mathbb E[1_A(X)1_B(Y)|X]=1_A(X)\mathbb E[1_B(Y)][/math] by measurability and independence, while [math]g(x)=\mathbb E[1_A(x)1_B(Y)|X]=1_A(x)\mathbb E[1_B(Y)][/math] (also by independence), implying the above holds for [math]f(x,y)=1_{A\times B}(x,y)[/math].

🗑️ Anonymous at Tue, 12 Nov 2024 18:42:14 UTC No. 16472220

>>16467497
Linear Algebra is about solving for n variables in a system of n linear equations using equations that contain matrices as their objects instead of values and whose operators are a bit different than the standard +-*/ operators you know.

It's not a hard class. A matrix is just the coefficients of the variables in the linear equations (in the system) written in a rectangular grid form.

All of it is just a time-saving mechanism.

Anonymous at Tue, 12 Nov 2024 19:56:55 UTC No. 16472299

>>16472218
It is the class's textbook

Anonymous at Tue, 12 Nov 2024 20:28:11 UTC No. 16472334

>>16472299
Of course textbooks can be wrong, why do you think errata or new editions exist? But was the textbook wrong or was your paraphrasing of it incorrect?

Anonymous at Tue, 12 Nov 2024 21:11:58 UTC No. 16472392

How much time elapses for a person who attempts partial hanging to actually decease? Help me write my thesis.

Anonymous at Tue, 12 Nov 2024 22:08:49 UTC No. 16472452

>>16472208
Thanks, anon. I'll take your word for it and brush up on probability so I can do this myself next time.

Anonymous at Tue, 12 Nov 2024 22:25:07 UTC No. 16472471

What are the values of the limits [math]\lim_{x\rightarrow 1} \left(\frac{2-x}{x}\right)^{\frac{1+\sqrt x}{1-x}}[\math] and [math]\lim_{x\rightarrow 0}\frac{1-\cos x\cos 2x}{x^2}[\math]

🗑️ Anonymous at Tue, 12 Nov 2024 22:30:41 UTC No. 16472477

>>16472471
Let me fix that for you:

What are the values of the limits [math]\lim_{x\rightarrow 1} \left(\dfrac{2-x}{x}\right)^{\dfrac{1+\sqrt{x}}{1-x}}[/math] and [math]\lim_{x\rightarrow 0}\dfrac{1-\cos{x}\cos{2x}}{x^2}[/math]

Anonymous at Tue, 12 Nov 2024 22:31:56 UTC No. 16472479

>>16472471
Let me fix that for you:

What are the values of the limits [math]\lim_{x\rightarrow 1} \left(\dfrac{2-x}{x}\right)^{\dfrac{1+\sqrt{x}}{1-x}}[/math]
and
[math]\lim_{x\rightarrow 0}\dfrac{1-\cos{x}\cos{2x}}{x^2}[/math]

Anonymous at Tue, 12 Nov 2024 22:33:01 UTC No. 16472480

>>16472479
I blame moot

Anonymous at Wed, 13 Nov 2024 01:39:18 UTC No. 16472700

>>16472471
>>16472479
nta, here's the second one:

[math]\lim_{x\to 0}{\frac{1-\cos{x}\cdot\cos{2x}}{x^2}}[/math]

Anonymous at Wed, 13 Nov 2024 02:00:30 UTC No. 16472724

>>16472700
Use L'Hospital's rule twice, that should give you 5/2

Anonymous at Wed, 13 Nov 2024 02:21:40 UTC No. 16472749

If I have a son and put in effort to ensure he always has his highest possible natural testosterone growing up (age appropriate exercise, good diet, blood tests to check for possible lack of micronutrients, etc.) will that make him have a larger dick? What about trying to maximize his testosterone while he's still in his mom's placenta? Would it be about increasing the mother's testosterone?

Anonymous at Wed, 13 Nov 2024 04:24:42 UTC No. 16472943

>>16472749
Teach him to take care of his hair because hair loss is on the rise due to lifestyle/enviroment. You will want a high level of testosterone only up to that age which is associated with the male baldness pattern

Anonymous at Wed, 13 Nov 2024 04:32:33 UTC No. 16472953

>>16472943
don't care, baldness is non-existent in my family + being very successful in your youth counts way more than being bitter about hair when you're 45

Anonymous at Wed, 13 Nov 2024 05:03:53 UTC No. 16472967

What body has ever been observed to move in a way that is continuous? Regular algebra is what holds when limits aren't going to zero, so velocity is only the derivative of position in theory, as a simplified ideal model.

Anonymous at Wed, 13 Nov 2024 05:13:22 UTC No. 16472974

>>16472967
This is exactly what differential equations are for; the Navier-Stokes equations are perhaps the most infamous example.

Anonymous at Wed, 13 Nov 2024 08:10:19 UTC No. 16473122

>>16472974
I don't understand. If no bodies move continuously how can dif eq be a solution? Is there some kind of dark math correction that can make it differentiable?

Anonymous at Wed, 13 Nov 2024 10:30:31 UTC No. 16473206

>>16472967
Infinities do not exist in nature. Our physical laws are tools to *describe* reality, that doesn't mean they are reality.

Anonymous at Wed, 13 Nov 2024 11:08:41 UTC No. 16473232

>>16472471
>>16472479
The fist limit you can write in the form [math]\lim_{x\rightarrow 1} f(x) = \lim_{x\rightarrow 1} e^{\ln{f(x)}}[/math]. You can then write the logarithm section as:

[math]
\dfrac{1 + \sqrt{x}}{1 - x} \ln{\dfrac{2 - x}{x}} \\
= \dfrac{1 + \sqrt{x}}{1 - x} \left(\ln(2 - x) - \ln(x)\right) \\
= \dfrac{1 + \sqrt{x}}{1 - x} \left(\ln(1 + (1 - x)) - \ln(1 - (1 - x))\right) \\
= \dfrac{1 + \sqrt{x}}{1 - x} \left( ((1 - x) - (1 - x)^2/2 + (1 - x)^3/3 - \ldots) - (-(1 - x) - (1 - x)^2/2 - (1 - x)^3/3 - \ldots) \right) \\
= \dfrac{1 + \sqrt{x}}{1 - x} ( 2(1 - x) + 2(1 - x)^3/3\ + \ldots) \\
= 2(1 + \sqrt{x}) ( 1 + (1 - x)^2/3\ + ...) \\
[/math]

And so in the limit [math]{x \rightarrow 1}[/math] this simplifies to 4. So the final answer is [math]e^4[/math].

The second limit is just L'Hospital until the denominator no longer contains x.

Anonymous at Wed, 13 Nov 2024 14:53:17 UTC No. 16473411

>>16472334
It said shells become minerals in the ground

Anonymous at Wed, 13 Nov 2024 14:58:15 UTC No. 16473419

>>16473411
Limestone can be formed from shells over geological time periods but that is a rock not a mineral.

Anonymous at Wed, 13 Nov 2024 15:07:28 UTC No. 16473431

What is a proof in mathematics?

I don't get the idea, is it about coming to the same place from two different sides? Like, if we are on corner and I tell you about a store in the opposite corner of that same block, then either walking left or right around the block without crossing streets should get you to the same place, proving that the store is indeed on the opposite corner.

I want to understand the philosophy, the logic behind it. Any references? Like, how do people actually get to the level of math to go on problems like "prove 2+2=4"? All I can think is:
>2+2=4
>Because
>2=1+1
>4=1+1+1+1
>So
>(1+1)+(1+1) = 1+1+1+1
>Therefore
>2+2=4
But then again, what the fuck am I doing? Going around in circles.

Anonymous at Wed, 13 Nov 2024 15:15:38 UTC No. 16473439

>>16473431
You have to start from somewhere, assumptions that are so basic they cannot be proven - they are simply taken to be true. Those are the axioms of mathematics.

> how do people actually get to the level of math to go on problems like "prove 2+2=4"
You can do such things using fields like symbolic logic and set-theory (ZFC) but again they each have axioms. Even more basic that 1 + 1 = 2 (which they can then later on prove).

Anonymous at Wed, 13 Nov 2024 22:48:35 UTC No. 16473975

>>16473431
If you really want to know pick up the text Journey Into Mathematics: An Introduction to Proofs by Joseph J. Rotman (2006), you dont need ZFC at the beginning like the other anon said.
>2+2=4
A proof of this fact involves defining what "+" is. This definition is non-trivial but once you prove (an argument that most likely will go over the beginner's head) that it has the desired properties, that fact is easy to get, somewhat like your argument.
Look at this too:
https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/

Anonymous at Wed, 13 Nov 2024 22:49:06 UTC No. 16473977

>>16473431
Real any mathematician's first analysis book. Terrence Tao's Analysis I is very accessible.

Anonymous at Wed, 13 Nov 2024 23:49:06 UTC No. 16474041

Chemistry chads, will bleach have any sort of reaction with petroleum jelly (Vaseline)?
I am going to bleach some warts on my foot, and I plan on protecting the surrounding skin with Vaseline.

Anonymous at Thu, 14 Nov 2024 05:06:09 UTC No. 16474360

Tl;Dr what I want to learn about is the intersection of electricity and chemistry.
Is electrochemistry a thing?
Would it be better to investigate QED and chemistry seperately or is there literature specific to electricity doing things to molecules?

Anonymous at Thu, 14 Nov 2024 08:26:46 UTC No. 16474499

when taking the std deviation of a series of measurements of a physical quantity >=0 (say, a time duration), I'm getting that the result is x+-y with y > x, implying that there's a chance for the value of being negative. is there a better way to model random errors taking into account that my quantity can't be negative?

Anonymous at Thu, 14 Nov 2024 09:12:02 UTC No. 16474539

>>16474360
>electrochemistry
Sure, it's a thing. Do you have any portable device? Is there a battery in that device? Electrochemistry is a science behind that battery.

Anonymous at Thu, 14 Nov 2024 17:34:17 UTC No. 16474993

>>16474499
I would try the Box-cox transformation where you may end up depending on log(length+1) being normally distributed.

Anonymous at Thu, 14 Nov 2024 20:59:02 UTC No. 16475229

I just want someone to check my Nernst equation here. So I'm wanting to electrochemically reverse the reaction of ferric chloride with copper metal:
[math]Fe^{3+}_{(aq)} + Cu_{(s)} \longrightarrow Fe^{2+}_{(aq)} +Cu^{1+}_{(aq)}[/math]
The standard potential for this is 0.77-0.52 = 0.25V, polarity be damned.
The Nernst equation simplifies to this:
[math]E_{cell} = E^0_{cell} - 0.026 * ln(Q_r)[/math]
Doing some simple math, Q can never be greater than 15000, because that would make E cross 0V, and my 5V supply will easily be able to push Q beyond reasonable concentrations (153E-69). But actually calculating Q is a bit stranger. If I understand:
[math]Q_r = \frac{[Fe^{2+}][Cu^{1+}]}{[Fe^{3+}]}[/math]
But I think I can assume both that [math][Fe^{2+}] = [Cu^{1+}][/math], and that [math][Fe^{3+}] = k - [Fe^{2+}][/math], where k is the maximum/final concentration of unconsumed ferric chloride, which I'll assume has a maximum value of about 7.86mol/L.
That gives:
[math]Q_r = \frac{[Fe^{2+}]^2}{7.86-[Fe^{2+}]}[/math]
And I can feed this into the Nernst equation:
[math]E_{cell} = E^0_{cell} - 0.026 * ln \left( \frac{[Fe^{2+}]^2}{7.86-[Fe^{2+}]} \right) [/math]
Which is something I can plot a graph of.

Pic related is the graph with a logarithmic X axis representing the magnitude of the concentration of Fe2+ ions, and the Y axis is the cell potential. If chemistry class has taught me anything it's that concentrations below 10^-7 don't exist (lol), so I can assume I'll need no more than 1.2V for my cell.

Is this correct? As a physicist, having something that isn't unitless inside a natural log gives me the heebie jeebies.

Anonymous at Thu, 14 Nov 2024 21:47:25 UTC No. 16475251

>>16475229
The units are in the E0. 100 year old chemistry journals pleasantly leave out most units: they had a convention. The unit police haven't taken my Nernst equation. Assuming you did the half-cell calculation correctly, you need to apply more than 1.2V because there's an anode reaction, ohmic loss in the electrolyte, and electrode kinetics.

Anonymous at Thu, 14 Nov 2024 22:34:29 UTC No. 16475295

>>16475251
>The units are in the E0
But it's a measure of the voltage?
I think in reality, the concentration of each species is being divided by its standard concentration (i.e. 1mol/L), so the units all cancel out inside the logarithm. Because concentrations have to be relative to something. Maybe that's what the square brackets implied all along.

>Assuming you did the half-cell calculation correctly
That's mainly what I'm posting for. Does the [Fe3+] = k-[Fe2+] make sense? I'm getting second thoughts since concentrations are generally multiplicative and not additive.

>you need to apply more than 1.2V
If I understand, the E_cell value from the Nernst equation for my given reactant concentrations is what it takes to bring the cell to a steady-state, with no reaction progressing either way. 1.2V is the highest that will ever go, give or take another 5% from temperature variations. Since I'm going for a trickle-charging reactor, I figure I can just run my reaction from a ≥1.5V regulator with some series resistance and call it good. The important part is having enough voltage to prevent my copper cathode from corroding in any circumstance, while being able to push the reaction through to completion.

But I'm pretty sure some O2 and maybe CO2 have dissolved into my spent etchant, so I've no clue what the hell is going to happen when I put it all together. So long as it doesn't eat up my chinese "platinum" electrode I guess.

Anonymous at Thu, 14 Nov 2024 22:43:40 UTC No. 16475303

>>16474041
Use duck tape, Mongoloid.

Anonymous at Fri, 15 Nov 2024 07:56:39 UTC No. 16475809

Hey guys, I need help finding an identity I lost some time ago. Unfortunately, I can only be vague about this as otherwise I would have found it again myself.

It involved finite series, where each term was the product of a^i and b^j, with i and j being the parts indexed.

The identity showed a way to refactor the equation, which could be useful for further proofs/simplifications.

The identity was first proven by a famous marhematician/physicist.

I can't remember more than that and it is really killing me. Please. Help me /sci/, you are my only hope.

Anonymous at Fri, 15 Nov 2024 08:00:49 UTC No. 16475812

>>16475809
Should add, this identity doesn't show up in any general lists on common infinite/finite series equations.

Anonymous at Fri, 15 Nov 2024 09:06:51 UTC No. 16475849

>>16475809
>>16475812
Your description is incredibly vague and could match any number of series.. If its not on this list then good luck remembering.

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

Anonymous at Fri, 15 Nov 2024 10:40:18 UTC No. 16475901

>>16475849
Yeah, I know. Thankstho.

Anonymous at Fri, 15 Nov 2024 14:43:31 UTC No. 16476156

>>16474041
Depends on the presence of unsaturated hydrocarbons. Aromatics especially can form some nasty compounds in the presence of bleach. All this information should be available through the company's SDS, or possibly PubMed.

A quick test to see if anything is reacting is to simply mix them, and feel if the vessel gets warm. A good demonstration of this phenomenon is to drip bleach on white vs brown paper towels, in case you don't trust your judgement.

Anonymous at Fri, 15 Nov 2024 14:55:32 UTC No. 16476177

>>16473431
>What is a proof in mathematics?
It is a game where you use certain agreed upon rules to go from one set of statements ('axioms') to another ('theorems')

Anonymous at Fri, 15 Nov 2024 14:58:10 UTC No. 16476182

Why is IQ so incredibly resistant to positive change?

Anonymous at Fri, 15 Nov 2024 15:01:53 UTC No. 16476191

>>16476182
IQ is Jewish cess

Anonymous at Fri, 15 Nov 2024 15:07:08 UTC No. 16476211

>>16476191
Got any proof? Ashkenazis meming their way to the top is funny but not indicative that the psychometrics are bunk

Anonymous at Fri, 15 Nov 2024 15:35:15 UTC No. 16476277

>>16476156
Thanks, I'll mix a little bit first then.

Anonymous at Fri, 15 Nov 2024 17:12:37 UTC No. 16476429

>>16475809
Does this look right?
https://www.wolframalpha.com/input?i2d=true&i=Sum%5BSum%5BPower%5Bx%2Ci%5DPower%5By%2Cj%5D%2C%7Bj%2C1%2Cm%7D%5D%2C%7Bi%2C1%2Cn%7D%5D&lang=es
Simply the product of the closed form for each geometric series, a=1.
https://en.wikipedia.org/wiki/Geometric_series

Anonymous at Fri, 15 Nov 2024 19:52:06 UTC No. 16476693

>>16476429
Yes thank you very much

Anonymous at Fri, 15 Nov 2024 21:35:07 UTC No. 16476879

If you have a container with liquid in it and you tilt the container and the water level always stays the same during the tilt, is it possible that the container walls are not circular in shape?

Anonymous at Sat, 16 Nov 2024 01:54:52 UTC No. 16477354

Can someone tell me if this proof is correct?

[math]
\begin{aligned}
\lim_{x \to 5} \frac{1}{x-3} & = 1/2\\
0 < |x-5| & < \delta\\
|\frac{1}{x-3} - \frac{1}{2}| & < \epsilon\\
|\frac{2}{2(x-3)} - \frac{x-3}{2(x-3)}| & < \epsilon\\
|\frac{5-x}{2(x-3)}| & < \epsilon\\
\frac{1}{2}*|x-5|*\frac{1}{|x-3|} & < \epsilon\\
-\delta < x-5 & < \delta \\
5 - \delta < x & < 5 + \delta\\
|x - 3|\ & \text{has an upper bound of}\ |5 + \delta - 3|\\
|x - 3| \in & (2 - \delta, 2 + \delta) \ \text{Now assume \(\delta < 1\)}\\
|x - 3| \in & (1, 3) \ \text{Use 1 since it has the greater reciprocal}\\
\frac{1}{2}*|x-5|*1 & < \epsilon\\
|x-5| & < 2 \epsilon\\
\delta = 2 \epsilon
\end{aligned}
[/math]

🗑️ Anonymous at Sat, 16 Nov 2024 03:32:45 UTC No. 16477435

>>16477354
If epsilon is 1000, then does that mean delta is less than 1? The proof needs to work for every possible epsilon. You're good up to that statement. Instead, find what is the maximum possible 1/|x-3|, and use this

Anonymous at Sat, 16 Nov 2024 04:49:00 UTC No. 16477489

>>16477354
With your answer, if epsilon is 1000, will delta be less than 1? Your answer for delta has to work for every positive epsilon. Instead, multiply everything by |x-3|, then use the triangle inequality on |x-3| to compare to delta.

When you maneuver around to get to a point with f(delta) < epsilon, solve for delta, but be wary of dividing by a negative number in an inequality.

Anonymous at Sat, 16 Nov 2024 04:52:48 UTC No. 16477492

>>16477489
or dividing by 0 too

Anonymous at Sat, 16 Nov 2024 05:43:04 UTC No. 16477512

>>16477354
x can't be 3 since you'd be doing 1/0, so you have the options of 3 < x < 5 or 5 < x < 7. Just do inequalities for both, solve for [math] delta < 2 [/math], and choose the minimum.