/sci/ - Science & Math

tip: wait till 310 replies next time.

~UNANSWERED~

Math+CS
>>11491730
>>11495716 and >>11495718 and>>11495726
>>11496221
>>11502283
>>11503466
>>11504082

Physics
>>11492809
>>11493397
>>11499600 (from Ampere's law you know that an electric current generates a magnetic field, per the right hand rule. If you have current moving in a loop, then you get a magnetic field in the center of the loop. Magnetic moment is a vector, defined to have a magnitude equal to current*area of the loop, and pointing in the direction of the induced magnetic field. It's easy to see how magnetic moment is then a measure of how strong the magnet is, given that magnetic field itself increases with current).
>>11503471 (critical point is just where the distinction between phases gets fuzzy. superhot water is likely much like a liquid at absurd pressures like that)

Chemistry
>>11492187
>>11498500

Bio+Physiology+Memevirus
>>11490589
>>11494491
>>11495091
>>11496090
>>11497721
>>11501304

Stupid
>>11487337
>>11490721 (8/10)
>>11491280 (that isn't the pacific and the atlantic ocean, it's probably the discharge of some huge river like the amazon meating the ocean; silty fresh water on the right takes some effort to mix with the denser, blue, salty water on the left)
>>11491325 (hoof dog)
>>11491800 (tin or pewter, possibly)
>>11496314 (civil engie)
>>11499313
>>11499376
>>11501041 (>actually applied)
>>11503239 (more civil engie)
>>11503585

Does anyone know where I could find the 2015 edition of Whitney's book "Geometric Integration Theory, (https://www.degruyter.com/view/title/522301).).

>>11504267
>2015 edition
>I look through the de Gruyter page
>I download the front matter and read it
>overview says "These editions preserve the original texts of these important books"
Anon, I think it's just a reprinting.

>>11491730
Just the Cauchy criterion is enough. Given [math]u = (\dot{v},v)[/math] the Cauchy problem is well posed as long as [math]u \in L^2 \oplus H^1[/math] and namely the initial condition boundary intersects the characteristics transversally.
>>11503466
Analytic geometry.

Oi mates. I did part a but I'm having trouble with part b. Any help?

>>11504614
>choose a random group
>take a random subgroup that's not normal
>check if it works
Wouldn't surprise me if there were some shitty counterexamples in [math]S^3[/math].

>>11504651
Nevermind, the counterexample is actually there.
Take [math]S^3[/math]. [math]N = \langle (1 ~ 2) \rangle [/math]. Two elements, [math]S^3[/math] has 3!=6 elements, so index is 3. But [math](2 ~ 3)^3= (2 ~ 3)[/math], so we're done.

If entropy increases with heat, 0 K defines minimum entropy, and entropy constantly increases, shouldn't the end of the universe have a higher temp than the beginning? Yet big freeze implies coldness?

How do I get rid of a frog in my throat?

I'm kind of worried it's coronavirus but I have no trouble breathing and even though I'm coughing up mucus every now and then it's not really a lot.

It's like a lump in my throat that's not so big it troubles my breathing but big enough to be a nuisance and noticeable. How do I get rid of it? Home treatments?

>>11504660
>>11504651
I learned symmetric group with the [math]n[/math] in the subscript, so reading that made me think of [math]SU(2,\mathbb{C})[/math] instead.
Maybe I forgot to lower the index: [math]S_n = g_{nm}S^m[/math]...

I am trying to manage my time effectively for maximum output. I have 5 subjects I am trying to better myself in: art, A&P, chem, writing. Corona has me jobless, what’s the maximum efficiency I can achieve in a month without drugs and how? 1 hour each daily, 3 hours each alternating daily, or is there a better method because I always get stuck in analysis paralysis and end up doing only what I need for my classes.
Is there any science to it? How do I maximize my “mental gains” in all these fields? I can enter “the zone” easily if I have a plan.
Here’s the run down:
>what is the most efficient study pattern?
>what is the science behind maximizing learning gains?
>let’s assume I want to maximize them all and I don’t care about my social life

So soap is supposed to be able to destroy viruses by washing your hand for at least 20 seconds.
How about for alcohol? How long does it take for alcohol to destroy viruses??

>>11505449
The most efficient way to study is for your brain to spontaneously arrange into the desired state.
Less autistic answer: You know best what works for you, so you likely already know your most efficient plan.
My experience is that I use time best by focusing on one subject intensely. It's nice when there are definite boundaries between concepts, like chapters, so I know when I can start on another subject. I find that if I jump to another subject before completing a concept it can be expensive.
Good luck studying. What's your fifth subject?

I need to maximize the perimeter of a shape while minimizing its area using only straight lines longer than h and angles between Alpha and Beta, any recommendations on how to proceed?

>>11505398
Isn't SU(2,C) the 2-sphere S^2?

any ideas what IC is this?

>>11505746
If [math]\beta > \pi /2[/math] and [math]\alpha < \pi /2[/math], you can probably make figures of unbounded perimeter (see pic related, extend the part marked in red arbitrarily), and if [math]\alpha > \pi /2[/math], the figure won't close, so you can assume that it's actually a convex polygon. Knowing it's a convex polygon and knowing [math]\beta [/math] tells you the maximum number of sides it can have.
I am now content with my contribution and leave the remainder to other anons.

>visible light has higher energy than radio waves
>but radio waves can go through solid matter while light can't
What subject should I read up on to understand this?

>>11506370
Higher energy = higher likelihood of interaction with matter.

>>11506375
But why does x-rays and gamma-rays pass through everything then?

>>11506385
>>11506375
Out fucking skilled.

In how many ways can you arrange numbers 1,2,3 in such a way that their sum is equal to 40?

Its length has to be from 14 {3,3,...3,3,1} to 40 {1,1,1,...,1,1,1}
Any formula to calculate that?
So for example the first possibilities are:
14
>{3,3,3,3,3,3,3,3,3,3,3,3,3,1}
>{3,3,3,3,3,3,3,3,3,3,3,3,2,2}
15
>{3,3,3,3,3,3,3,3,3,3,3,2,2,2,1} (and I think that's it?)
16
>{3,3,3,3,3,3,3,3,3,3,3,2,2,1,1,1}
etc.
how to count them all quickly?

>>11506464
anyway, I did it like this and got 82 ways

>>11505031
>If entropy increases with heat and entropy constantly increases
not true

>>11506537
if heat increases entropy and if entropy cannot decrease

>>11506539
My point was that entropy can decrease despite adding heat.

Help please

>>11505667
My fifth subject is mnemonics so I can stuff as much as possible into my head, but that’s the hardest one for a couple reasons:
>hard to concentrate because it’s creation rather than memorizing
>Feels like a waste of time because I have a phone beside me with all the answers
And worst of all is trying to construct conceptual mnemonics with stories and characters, because it’s both storytelling and memorization.

>>11506560
Pretty sure you need to know initial dimensions.

>>11506560
Use a Maxwell relation. [eqn] \bigg(\frac{\partial S}{\partial P}\bigg)_T=\bigg(\frac{\partial V}{\partial T}\bigg)_P\simeq\frac{\Delta V}{\Delta T} [/eqn]

>>11506560
Use a Maxwell relation. [eqn] \bigg(\frac{\partial S}{\partial P}\bigg)_T=\bigg(\frac{\partial V}{\partial T}\bigg)_P\simeq\frac{\Delta V}{\Delta T} [/eqn]

Is math the most popular STEM subject? /sci/ seems to be dominated by mathfags

>>11506672
Math is the patrician STEM subject. You see, 4chan attracts only a certain kind of audience.

>>11506672
math is in every STEM subject. i study medicine and i still need to take calculus.

>>11506717
>Calculus
what? are you implying you don't study the results of Dr. Mary M. Tai concerning the Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves ?

https://care.diabetesjournals.org/content/17/2/152.abstract

>>11506634
I did that but how do I get rid of 1/V term?

What does /sci/ think of computer vision as a field? Is it a worthwhile endeavour?

>>11506766
Are you positive there is not more information given?

>>11504025
How do clouds become stones? How do people harvest clouds to make pillows, do they use giraffes?

>>11506793
>Girrafes for pillow harvesting
Don't be silly. We have planes for that.

>>11504025
If antimatter is thought to behave and interact with light in the same way as regular matter, why does everyone seem so sure that there's more regular matter in the universe?

>>11506823
Because antimatter also interact with gravity the same way as regular matter, so it wouldn't make sense for them to cluster around a specific spot in the universe while regular matter is so uniformly spread.
This discrepancy between matter and antimatter is the strong CP violation, and many HEP/cosmo people have been working on this for decades. I doubt you can just sweep it under the rug with a post on 4hcan.

>>11506833
But how do we know regular matter is uniformly spread and not covering one region with antimatter covering another if they look the same?

>journal paper has typos that don't exist in any iteration of the arXiv version
What a joke. All they had to do was literally copy and paste the equations. I'm looking at a nature commun. btw, so it's not some sort of Russian Bealle's list shit.

>>11505398
>Maybe I forgot to lower the index: Sn=gnmSmSn=gnmSm...
underrated

>>11505657
bump desu

p-values seem completely useless to me. surely p(a|b) doesn't tell you anything about p(b|a). when would using a p-value be of use?

>>11507109
You guess a bunch of other probabilities on intuition and use Bayes's theorem.
Ultimately, you need to understand that Bayesian statistics is studied by the insane and deranged.

>>11505364
Halp

I'm not having trouble breathing, drinking, or eating really but it clogs my throat a little and in worried about it. Every time I swallow I feel it

but if you're guessing then why find you p-value. if the null is 'b', and my data is 'a', then p(a|b) {which is my p-value} doesn't tell me anything about p(a), p(b) or p(b|a).

>>11507151
>the insane and deranged
>why do they do this
Sometimes you do have some broad data about p(a) and p(b), tho.

I have a stupid question about the forces involved in arm-wrestling.
Specifically, I tried arm-wrestling with a girl who was allowed to use two arms, one on the table in the normal manner, and the other one just freely pushing on the point where our hands were locked, like in pic related.
I'm curious how big of an advantage this is. I was able to beat her, but it was extremely difficult. It seems like pushing directly at the outer rotation point instead of having to produce torque from the elbow on the table, essentially, would be a huge leverage advantage.
But I don't even know enough elementary physics to figure out the kinds of force amplification involved.

>>11507241
It gives her an advantage because toque=force×moment arm. The extra toque on her end would be from the linear forces she applies where your hands are coupled, with the moment arm being her literal forearm. From your perspective, there is only the torque generated in your bicep itself, there being no moment arm to give you any kind of advantage.

>>11507109
You think being signed up for a Wrestling club is uncorrelated with gender (null hypothesis). You get the numbers of 30 people signed up for a Westling club. The 85% of men turns out to be men.
p-value is a statistical model-dependent % below which you have to face the facts that you didn't just coincidentally get men on the line (despite, as you initially assumed and guesses, there being a 50/50 split). The alpha % value is often e.g. 5% per convention and you must come up with either the combinatorics (if it's exactly solvable) or some statistical model that give you a condition for judging unlikelyness in terms of that p value. If p<alpha, you reject your initial guess and are smarter now.

>>11507109
You think being signed up for a Wrestling club is uncorrelated with gender (null hypothesis). You get the phone numbers of 30 people signed up for a Westling club. Of the people you get on the line, 85% turns out to be men. Intuitively, you've proven yourself wrong and p-value is the tool to formalize this more.

The p-value is a statistical model-dependent % below which you have to face the facts that you didn't just coincidentally get men on the line - despite, as you initially assumed and guesses, there being a 50/50 split.

The so called alpha % value (a choosen boundary p-value) is often e.g. 5% per convention. And you must come up with either the combinatorics (if it's exactly solvable) or some statistical model that give you a condition for judging unlikelyness in terms of that p value. If p<alpha, you reject your initial guess and are smarter now.

How do I make neat data presentations?
Things like maps with numbers and all that cool stuff.

>>11507260
ty

>>11506844
https://iopscience.iop.org/article/10.1088/1367-2630/14/9/095012/pdf

quick google turned this up. afaict the tl;dr is that if the universe were a patchwork of regions of antimatter and matter like that, in the past those regions would have to have been touching in order to expand into what we see rn. this obviously means there'd have been significant annihilation, but we don't observe any signs of annihilation in the cosmic microwave background, so there's a contradiction.

to get around this, the regions have to be at least the size of the observable universe, which instantly makes the theory unfalsifiable. i might have gotten all of this completely wrong, i'm crap at science, check for yourself.

>>11506790
No that's all thats been given. Prof may have made a mistake

>>11507383
Can we have the previous questions, just to check?

>>11507421

>>11507430
Thanks, lad.

If I were trying to correlate two variables, [math]X[/math] and [math]Y[/math],

but I could only make a limited number of observations [math]N[/math], in some interval [math][a,b][/math],

would it be "better" to take my observations as evenly spread across the interval as possible? That seems intuitively correct, but if I'm already assuming linearity, then mightn't it be better to take repeated measurements at the extrema of the interval? Put one half of [math]N[/math] measurements at [math]a[/math], another half at [math]b[/math]?

Are repeated measurements of a single value more valuable than single measurements of different values?

I'm speaking mainly from the perspective of variance in statistical parameters of a model, but other perspectives would be appreciated.

Can someone explain how B in y=sin(Bx) affects the cycle, period and why is the formula for period P=2pi/B? How does B "speed up" the cycle? I don't even understand the difference between a cycle and a period, I thought that shit was the same. Please in layman terms!

>>11507851
Putting it simply, you can think of sine as taking a line segment of length 1, pointing to the right, and then rotating it counter-clockwise around the origin by the number of degrees or radians that you give it (Bx in your example), and then returning the y coordinate of the rotated endpoint of that line segment. So sin(90 degrees) aka sin(pi/2) will rotate to point straight up, and the value will be 1.
When you multiply by B, of course you rotate B times as far.
Re. terminology.
>https://mathbitsnotebook.com/Algebra2/TrigGraphs/TGTrigVocab.html
>One complete repetition of the pattern is called a cycle. The period of a function is the horizontal length of one complete cycle.

The formula for period you posted is using radians. You know there are 2 pi radians in a circle, right?
So if you just do sin(x), then x will have to go from (for example) 0 to 2pi to complete a circle. If you multiply the angle by some scaling factor B, then x only has to change 1/B times as much to make a full circle. Hence 2pi/B.

>>11507109
Ignore the guy screeching about Bayesian statistics because he's retarded and p-values are the most frequentist thing in the world.

You're not actually trying to compute p(b|a). p(b) is 1 anyway because you're assuming your null hypothesis in the first place. What your p-value is doing is letting you say that your data 'contradicts' your null hypothesis so you can toss it out and make more statements that are inconsistent with it (ie that the parameter is equal to your estimate).

>tfw only math, CS and other meme questions get answered
where are the chem, med and bio bros? i don't want to use stack overflow or god forbid reddit

cartesian product of a family of set in which one is empty is empty, but then unique function does not satisfy the universal condition for composition when taking non-empty set

on the other hand, in the categorical definition of product we do not assume "objects are not initial" or something.

I am confused, help me.

>>11508066
heyre 4 u anon

Might be a dumb question.
So last year 2019 when I did my taxes I filed as Single. Does that count as 2018 because I used 2018 numbers?
Meaning this year 2020 when I do my taxes, it would be 2019 since I’m using last years numbers?
I ask this because when I file this year, I will be a dependent. I dont want to lose $1.2k in this crisis.

>>11506766
assume an initial volume of V=1, and give your answer as a ratio (in units of Vinit)

>>11506370
Bump.

What is the mechanic by which a non-human-transmissible virus combines with a human-transmissible one as I understand to have occurred with the novel coronavirus? I recall hearing a term for it but have forgotten.

>>11508219
yes. tax year only includes Jan 1st to Dec 31st 2019.
The only reason taxes file in April 2020 is so you can get your shit in order. Otherwise you'd file them new years' eve 2019.
Nobody gives a shit what you do this year, until next year.

>>11508066
ask and ye shall receive. Math and CS are the common man's STEAM, so they flood everyone out

>>11508441
Note that this depends where you live. Here the financial year runs July 1 to June 30.

Check whatever agency is collecting this tax's website.

1. if one set in family {X_i} is empty then prod_i X_i is empty, right?

2. therefore if I take Y another set and maps f_i: Y --> X_i then there exists a unique map h:Y-->prod_i X_i, such that f_i= pr_i h, right?

3. but h must be an empty map since prod_i X_i is empty

4. now assume X_j is nonempty then
f_j = pr_j h
LHS is some function and RHS is empty function so the categorical definition does not work when one set is empty

5. i.e. this implies that all f_i are empty functions

help! help!

>>11508660
>and maps f_i: Y --> X_i
There can be no such collection of maps as one of the X_i's is empty.
If Y is nonempty, there is no function from Y to an empty set.

>>11508660
>>11508676
Now assuming that Y is empty, there indeed exists a unique function h:Y---> prod_i X_i (the empty function).
f_j = pr_j h indeed holds since each f_j is the empty function, because Y is empty.

>>11508676

unfortunately there is an (the?) empty function

for all x\in \emptyset exists y\in Y f(x)=y

that is always true

>>11508680

ok, thanks, stupid me, if X_i is empty than Y must be empty

>>11508660
>>11508676
>>11508680
What I'm trying to say is that the only way such a collection of maps (f_i) can exist is if Y is empty and hence each f_i is the empty map. There is no contradiction.

I don't understand the difference between the Symmetric Property and the Commutative Property.

I'm confused by terminology /sci/

Is there any difference between the statements "[math]X = [X_1 \dots X_n][/math] is a normally-distributed random vector" and "[math]X_1 \dots X_n[/math] are normally-jointly-distributed random variables"?

>>11508740
Bump. Someone please explain?

>>11508740
What do you mean by symmetric property and the commutative property?
Property of what? Give the definition.

>>11508740
Usually abelian refers to a map [math]A \times A \rigtharrow A[/math] and symmetric refers to [math]A^n \rightarrow B[/math].

>>11508810
I mean equality (=) is said to be symmetric because a=b is equivalent to a b=a. Addition (+) is said to be commutative because a+b is equal to b+a.
I don't understand the distinction between these to concepts, and why equality isn't said to be commutative or addition isn't said to be symmetric.

>>11508827
Nonsensical question anon.

How can I calculate a percentage error if the actual value is zero?

>>11508826
To me that looks like abelian is just a special case of symmetric.

>>11508836
Just divide by 0 bro.

>>11508830
I don't know how to make it more sensical.
I'm unwilling to accept "It just is because I said so" as an answer.

Do we expect the universe to be flat, in terms of space? If so, why?

>>11508875
No?
What gave you that impression?

>>11508912
Do we know it's not flat?

>>11508920
Can you jump?

>>11508922
Yes. How is that relevant?

>>/wsr/795140
[eqn] \mathbf{F}_{24}=k\frac{q_2q_4}{r_{24}^2}\hat{\mathbf{r}}_{14}=k\frac{q_2q_4}{(\sqrt{2}d)^2}\big[(\sqrt{2}/2)\hat{\mathbf{i}}-(\sqrt{2}/2)\hat{\mathbf{j}}\big]=\frac{k}{d^2}q_2q_4\big[(\sqrt{2}/4)\hat{\mathbf{i}}-(\sqrt{2}/4)\hat{\mathbf{j}}\big] \\
\mathbf{F}_{14}=...=\frac{k}{d^2}(q_1q_4/4)\hat{\mathbf{i}}\\ \mathbf{F}_{34}=...=\frac{k}{d^2}q_3q_4\hat{\mathbf{i}} [/eqn]
so
[eqn]\sum\mathbf{F}=\frac{k}{d^2}\Bigg[\bigg(\frac{\sqrt{2}q_2q_4}{4}+\frac{q_1q_4}{4}+q_3q_4\bigg)\hat{\mathbf{i}}-\bigg(\frac{\sqrt{2} q_2q_4}{4}\bigg)\hat{\mathbf{j}}\Bigg][/eqn]
you do the rest

>>>/wsr/795140
[eqn] \mathbf{F}_{24}=k\frac{q_2q_4}{r_{24}^2}\hat{\mathbf{r}}_{14}=k\frac{q_2q_4}{(\sqrt{2}d)^2}\big[(\sqrt{2}/2)\hat{\mathbf{i}}-(\sqrt{2}/2)\hat{\mathbf{j}}\big]=\frac{k}{d^2}q_2q_4\big[(\sqrt{2}/4)\hat{\mathbf{i}}-(\sqrt{2}/4)\hat{\mathbf{j}}\big] \\
\mathbf{F}_{14}=...=\frac{k}{d^2}(q_1q_4/4)\hat{\mathbf{i}}\\ \mathbf{F}_{34}=...=\frac{k}{d^2}q_3q_4\hat{\mathbf{i}} [/eqn]
so
[eqn]\sum\mathbf{F}=\frac{k}{d^2}\Bigg[\bigg(\frac{\sqrt{2}q_2q_4}{4}+\frac{q_1q_4}{4}+q_3q_4\bigg)\hat{\mathbf{i}}-\bigg(\frac{\sqrt{2} q_2q_4}{4}\bigg)\hat{\mathbf{j}}\Bigg][/eqn]
you do the rest

Sanity check: does it follow from the universal coefficient theorem that if the chain complex of X is finitely generated,
H_k(X, Z_2) = H^(k)(X, Z_2)

>>11509528
>universal coefficient
You mean Poincaré duality?

>>11509555
No I don't. This has nothing to do with Poincare duality.

can I state the following?
[math]\int |\sin x| dx = \begin{cases}
\cos x, \frac{\pi}{2} \geq x \geq \frac{3\pi}{2} \\
- \cos x, \frac{\pi}{2} < x < \frac{3\pi}{2}
\end{cases}
[/math]

I have n convex sets in the euclidean plane, I take the first and second, a and b respectively, and rotate and translate them over each other such that their intersection is maximized, now their union is a new set, call it (ab), we take the third set c and rotate and translate it such that it's intersection with set (ab) is maximized, this new set we call (abc), we take the fourth set and do the same process with the previously generated set, and we do this with all n sets, and end up with the set(abc... n) which within itself contains all sets from a to n, the question is is the set (abc... n) the same as the set that has minimum area but also contains any set from a to n?

>>11509918
No. I will show you a counterexample with n=3 once I get off the toilet.

Does anyone know if someone's stitched together a mega folder or whatever with recommended texts for the full Verbitsky curriculum?
I think it might make it easier to trick people into falling for it with one of those.
>>11509918
The set isn't going to necessarily be the same. You can prove this through highly shitty counterexamples where [math]B, C \subset A[/math] and we just choose a suboptimal embedding of [math]B[/math] in [math]A[/math] on the first step (in the corner, for example, while [math]C[/math] is long-ish, so it can't properly cover the entirety of [math]B[/math] and maximize area unless it's in the middle). (an explicit example would be A being a disk, B being a really small disk, and C being a square inscribed on A)
The problem of whether the optimal full intersection can be achieved by some intersection which maximizes at every step is evading me, though.
I think no.

>>11509899
Probably not. |sin θ| has no antiderivative. Its better to just talk about definite integrals.

>>11509918
As the other anon has show, if the maximum intersection for any two sets is not unique, then the answer to the problem is negative.
So we're left with the version of your problem that requires (ab) be unique for all a,b (that restricts the choices of figures you can take. In that case, the problem reduces to proving the associativity of the operator (..): if (abc...n) is optimal, at least one of them is an optimal position, so (abc...n)=(ab..)(x) for some x.
So it suffices to prove it for the case n=3:
If A,B,C are convex plane figures, we want to show that (AB)C = A(BC).

>>11509918
>>11510004
Here you go. If you do orange->green->red there is a unique maximal way to do it in each step but you get a smaller area overall if you do red->green->orange.
Although only the first way is unique. I'm not sure about an example were two ways would be unique and one will be smaller than the other.

>>11509945
>>11509918
>>11510004
I guess a good formulation of the question is:
Given an intersection of maximal area of x_1, x_2, x_3,.... and any sequence of x_i's, is it always possible to reach this intersection by adding one by one of the figures in the sequence that every subsequent intersection in the sequence is maximal. I don't know the answer.

>>11510004
>>11510048
I've figured out a way to rephrase the problem that might or might not be convenient.
Assume anon's conjecture is true for [math]n=3[/math] (specifically, that there is at least one way of arranging [math]A, B, C[/math] such that the triple intersection maximizes area and any of the individual intersections also maximizes area).
Assume that we've placed [math]A[/math] and [math]B[/math] somewhere on the plane, and call [math]A \cap B = C[/math]. Then, the area of the triple intersection (under motions and rotations) is at least [math]C[/math], which implies that [math]C [/math] admits some embedding in [math]D[/math], where [math]D[/math] is some solution of the problem of maximizing the area of [math]A \cap B[/math], by anon's conjecture.
Conversely, if any intersection of [math]A[/math] and [math]B[/math] arranged somewhere in the plane can be contained in some intersection which maximizes area, we obtain anon's conjecture back.

I might have made some mistake somewhere, tho.

>>11510061
In retrospective, I get the impression that the second proof doesn't work as is but it can somehow be brute forced into working.

>>11509945
I don't think I get it, if b and c fit entirely into a then the set with minimal area is achieved, where b is put into a doesn't matter in your explicit example because after we take the union of a and b, that union is actually equal to a, and for c it doesn't matter where b was placed if it was placed entirely inside a. maybe my notation is confusing. PicRelated

>>11510124
>I actually completely misread the problem
>the other anon also completely misread the problem
Amazing.

given the data we have on the corona virus having a higher mortality rate as BMI increases, would it be smarter for someone on upper end of healthy BMI to diet in anticipation of infection or to maintain weight?

yes its a corona virus post, i just dont wanna bother an actual doctor right now or make another thread just for this. im skinnyfat as fuck, so im likely carrying a higher amount of fat than most people at my BMI. I would love to be able to deal with my excess fat, but i do believe generally speaking dieting weakens the immune system, and i do not want a weak immune system right now.

I'm puzzling over the Binomial Formula. As far as I can tell n! gives the number of terms you would get from the full expansion. Dividing by (n-r)! then removes most of the terms.
Are these the terms that don't contain the exponent we are looking for? If that is the case then why also divide by r! ?

>>11510140
>Minimal union
>Maximal intersection
Sounds dual

>>11509528
Close; UCT says that only the free part is identical, while the torsion part is shifted by one. [math]\operatorname{tor}H_k(X,\mathbb{Z})\cong \operatorname{tor}H_{k-1}(X,\mathb{Z})[/math], so their [math]\mathbb{Z}_2[/math]-torsors differ (up to a shift in grading).
>>11509555
Poincare duality relates [math]H^k[/math] and [math]H_{n-k}[/math] honey.

>>11510004
>>11510140
does it still suffice to prove the case for n=3

How do you learn self-control?
I just spend the last 3 days playing video games while I have work to do. Now I feel like shit.

>>11510201
You sure about that bro?

I have a Cambridge interview for physics next week. Any tips?

How do I find the intersection between y=-x and y=Aexp(x+A) with A a real number graphically?

>>11510430
Aren't the interviews supposed to be in January?

>>11510489
there's a second admissions round

>>11510269
Unironically? Two answers.
1) Don't feel guilty about slacking off, ever. Guilt is just part of the vicious cycle. If you fail, you fail. Play like you mean it.
2) Keep feeling like shit. You're the kind of hopeless consoomer that needs to learn your lesson the hard way.

In the first chapter of Topics in Algebra, Herstein asks the reader to verify a number of rules involving multiplication and addition, where addition of two subsets A and B of a set S is defined as their symmetric difference (A-B)U(B-A), and multiplication as their intersection. While I found parts b) through e) straightforward, the first part, a), asks the reader to verify the associativity of addition as defined by the symmetric difference for three sets A, B and C. However I tried to express (A+B)+C or A+(B+C), it always resulted in cumbersome expressions which didn't fit their being part of the first section of an otherwise simple problem. Is there any way to write these out more compactly, or does Herstein expect you to write everything out in it's full length? Thanks.

>>11510991
Pretty sure you're supposed to conjecture and prove that [math]A*B*C = \{ x \in A \cup B \cup C ~ : ~ \text{x is not in two of} ~ A, ~ B, ~ C. \}[/math].
Definition could be wrong, tho.

>>11504025
So how come it seems like Atomic Numbers increment so perfectly, on the periodic table of elements.
Certain assumptions I would have as an outsider:
>It would be the most remarkable if every single element had the exact same number of protons. The fact that they all have COMPLETELY DIFFERENT numbers of protons (and thus different atomic numbers), seems to me, no less remarkable. Why is this?
>The fact that from end to end, every atomic number is filled is also remarkable. One would expect there to be a few empty slots. Historically were there empty slots in the periodic table of elements? Looking at the included picture, and seeing Element 116 (year 2004), and Element 118 (year 2006), where all the Element 117 inbetween was discovered AFTER 2006, it seems to me that at 2006, there must have been a blank slot on the periodic table of elements for four years.

Are new elements being discovered in linear order, of atomic number, given that they have to be engineered in labs where they can not sustain continued existence for more than a few seconds, and that the higher the atomic number, the more difficult it is to engineer.

And why is the proton number the main focus of the periodic table of elements, and not the number of electrons or neutrons?

>>11511024
>And why is the proton number the main focus of the periodic table of elements, and not the number of electrons or neutrons?
proton# directly influences the chemistry of the atom - go review your lewis dot structures, bonding theory, and basic chemistry
Neutrons don't affect much, most isotopes are drop-in replacements for each other.
Electrons are inconsistent as fycj, it wouldn't make sense to let them be the standard of anything. Flighty little shits. Look up the term "isoelectronic" anyways

>>11510269
This working from home shit is killing me and my work ethic. I don't know how people can do this.

Could papers ever be published semi-anonymously with a public key assigned to a pseudonym?

So i know the answer to this 9.0g of h2o but i'm just so confused about how my lecturer went about figuring this out? Did a whole lecture on Avogadro's number but i got no idea how to solve this problem and 3 others. I've watched a few videos and searched up the process of getting this number but no questions seem to be like this.

>>11511468
Of course

So I was looking at the product rule on wikipedia and found this "argument" for the formula (pic related). What I'm confused about is the last term on the first line: where does [math]-u*v[/math] come from?

>>11511705
pic

>>11511705
>>11511707
change is the difference between uv and (u+du)(v+dv)

>>11504025
What the fuck is ∠COD. Had this in my test

>>11506370
Visible light is visible to you because it is interacting with the matter.

is there more to this? I feel like there is hidden meaning in it, factorials and hoe it interacts with other math always fascinate me

>>11511724
I think I need to brush up on my geometry LOL.
if you're not colorblind my steps are in rainbow order.
∠APB must be 52 by opposite angle
AO and BO are radii and congruent
∠OAB and ∠OBA are congruent since they are opposite congruent sides
Given ∠AOB = 80, they must be 50
∠OAP + ∠OBP + ∠OAB + ∠OBA + 52 = 180
∠OAP + ∠OBP = 28
Let ∠OAP = x, ∠OBP = 28-x
CO and DO are radii
Triangle COB and Triangle AOD are isosceles and therefore have two equal angles opposite the equal sides
∠OCB = ∠OBP; ∠ADO = ∠OAP
80 + ∠AOD + ∠BOC = 360 + ∠COD
80 + 180 - 2x + 180 - 56 + 2x - 360 = ∠COD
24 = ∠COD

>>11511724
solve for CD. Find the area of CDO. Find the length of O to CD, then use that to find the length from CD to the circle from the radius, and use that and CD's length to find the area between the arc and CD. Now you know the area of the pizza slice CDO, and you take the ratio with the area of the circle to find the angle COD.

>>11511867
how do you find CD with only one angle

Not strictly a /sci/ question, but when is it appropriate to send e-mails to my university professors?
Would it be rude to just write a list of questions to them (provided that I am sure there aren't answers in the textbooks)?
Can I ask what topics I should study if I want to get a better understanding of something that was just mentioned in class or would I be wasting their time?

>>11511872
from the internal angle theorem, you can use the arc AB to find arc CD, and the ratio of that with the circles total length is the angle, thats an easier proof. i tried thinking about it but seems CD is pretty hard to figure out

>>11511894
simp
would it be rude to ask a business provide a service that you, a customer are paying for or have already paid for?????

In the last thread, I've shared some algebra work I made to see if my reasoning was correct. I would appreciate if anyone can check.

I'm trying to trace back through algebra why an Ising model would have bifurcation points as conjugates, and I use algebra because these bifurcation points can be represented as trigonometric values. The end result shows that these points are indeed linked to the cotangent squre, which you can trace by adding ln to the both sides of the exponential equation and the silver ratio. Taking the natural logarithm of the silver ratio and dividing it by two, leaves the parameter u being equal to coupling factor J.

In my cellular automaton, I have inserted an inequality in the format of a logistic map. That inequality, when factored on the left leaves the equation as p^2 - p + 1/8 = 0. The roots of this equation are the bifurcation points. This is the remarkable result - that one can enter an equation inside this cellular automaton's transition function and receive phase transitions at the roots as a result.

>>11495716
>>11495718
>>11495726

>>11511903
Yeah, but I mean like writing something like this once or twice every two weeks:

1) Why is...
2) How is...
...
11) What is...

I am pretty damn retarded when it comes to social cues and I don't know if eventually they are going to think that I am a fucking idiot and treat me harsher during the oral exam.

Is OpenStax good enough for a brainlet to learn his way to college-level maths?

>>11509948
I see, thank you lots

help me with this crap, i have to find the error in the reasoning, i think the error comes up when doing [math](x+5)^2+3 \leq 292[/math] because you end up with a quadratic inequation that gives you two values for [math]x[/math], but still it is most likely wrong pls help.

>>11512220
I already answered it in our thread, anon.
>>/sci/thread/S11511046#p11511049
[math]x=-5[/math] satisfies the first and second inequalities, but it doesn't satisfy the third one because [math](-5)^2 = 25 > (-5+5)^2 = 0[/math].

>>11512238
but why [math]x=-5[/math]? where does the [math]-5[/math] comes from?

>>11512253
I found it in my back pocket.

trying to find a paper mentioned in a video, all I have are names and a date assuming I have the spellings correct.
Is there a trick to getting more out of google scholar or are there other better open resources I could use?
I think it's Upton & Cooke 1977 but he spellings could be different it may or may not have statistics in the title but it seems to be related to regression to the mean
2:45
https://www.youtube.com/watch?v=Rf59iSANMe4
any Idea which publication?

Tell me how stupid this simplification for the purpose of my small brain that just wants some basic understanding but isn't willing to actually spend years studying physics and math. In other words, is this good dummy understanding, or too dummy?

>everything is made of particles (particle model)
>these particles might be vibrations of one continuous string (string theory - only one could somewhat explain gravity)
>together each type of particle has its own field (quantum fields)
>the basic smallest particles on their own are not tied well within these fields and have highly uncertain position (quantum tunneling)

>>11511862
Thank you

>>11511867
Thank you. Haven't learnt this way in school.

bump for:
>>11512220

Why do black people smell bad?
I want the scientific explanation.

>>11511907
bump

>>11512621
coconut oil goes rancid very fast
dreadlocks aren't supposed to be washed

>>11512621
It's different pheromones I think, I don't personally find it to be a bad smell.

>>11512276
bruh

>>11511907
The "bifurcation values" you have computed are the conformal factors of the spin expectations.
Remember that near-critical Ising is a CFT in the unitary series [math]c = \frac{1}{2}<1[/math] with a single non-trivial primary field, the holomorphic spin expectation [math]\sigma[/math] and its antiholomorphic partner [math]\overline{\sigma}[/math] in its OPE. Their conformal factors [math]\Delta,\overline{\Delta}[/math] under a reparameterization [math]\sigma(z) \mapsto (w')^{\Delta}\sigma(z)[/math] can be expressed as [math]\Delta = c + \eta[/math] and [math]\overline{\Delta} = c - \eta[/math], where [math]\eta[/math] labels the Virasoro-Witt rep it is in. Interpret these as the eigenvalues of the descendants of [math]\sigma.\overline{\sigma}[/math] under the ladders [math]L_n,\overline{L}_n = L_{-n}[/math].
Now since [math]\sigma,\overline{\sigma}[/math] form the only fields in the Witt algebra, factorization and the reality conditions on the partition function [math]Z = \sum_{\eta,\overline{\eta}}\chi^{c+\eta}\overline{\chi}^{c-\overline{\eta}}[/math] forces [math]\Delta\overline{\Delta} = 1[/math], or equivalently or [math]\eta\overline{\eta} = 1-c^2[/math] (here we see why the CFT is physical iff it is in the unitary series with [math]c<1[/math]). This allows us to parameterize [math]\Delta \in S^1\subset\mathbb{C}[/math], and in particular [math]\eta = \frac{\sqrt{3}}{2}e^{i\theta}[/math] for some [math]\theta[/math]. Algebraic conditions, arising from the fact that the Witt algebra is an affine Lie algebra centrally extended from the [math]A[/math]-series by [math]c[/math], gives you specific values of [math]\theta[/math] on the unit circle over which [math]Z[/math] is summed over.

>>11512728
Okay I'm going to need some time to digest that. Do you have any reading materials or papers to suggest?

>>11512950
https://www.springer.com/gp/book/9783540653219

>>11512984
Thank you very kindly dear Yukariposter.

[math]x^2+4x=0[/math]
[math]x^2=-4x[/math]
[math]\frac{x^2}{x}=-4[/math]
[math]x=-4[/math]

Is this valid?

>>11513045
didn't mom warn you not to divide by zero

>>11513045
Yes, also x=0

>>11513045
That's one of the solutions, yeah.

Sorry for deleting, i wanted to do it correct
[math]x^2+4x=0[/math]
[math]x^2=-4x[/math]
[math]x^2/x=-4[/math]
[math]x=-4[/math]

>>11513048
?
>>11513054
why?

nvm i'm a brainlet

>>11513073
x = 0 is a second solution to your equation, and the third line is not valid for x = 0, because you can't divide by 0

how does one improve its math skills? this quarantine I'm trying to solve indefinite integrals like there's no tomorrow

>>11513120
you're doing the right thing
the only way to get good at doing integrals is to practice a whole bunch of them

Engineerlet here, is this correct?

Please someone help me with this piece of crap >>11512220

>>11512220
>>11513170
The third line is wrong. You can't blindly square inequalities when one side is negative.
e.g.
-5 < 2
but
(-5)^2 > 2^2

>>11513170
Doesn't matter anymore guys, i connected two braincells and discovered the error.

Let's say I have a regular curve [math]c : I\subset\mathbb{R} \rightarrow \mathbb{R}^2[/math] parameterized by its arc length and [math]\kappa(s) \neq 0\;\forall s\in I[/math] is its curvature.

I'm trying to prove that [math]c_1(s) = c(s) + \frac{\mathbf{N}(s)}{\kappa(s)}[/math] is regular, but I end up that it is regular iff [math]\kappa'(s) \mathbf{N}(s) \neq 0[/math] which I can't prove.

N is the normal unit vector. Any takers?

Aight I'm gonna learn how to do math like you smart fuckers, this place is cool.

>>11513259
I haven't studied curves in an extremely long while, but I'm confused about one thing.
If you take [math]c[/math] as the unit circle, then the curvature is one at every point, and [math]c_1 = (0, 0)[/math] everywhere, isn't it?
The definition of regular was non-zero derivative everywhere when parametrized by arc length, wasn't it?

>>11513320
That's what I got, if κ'(s) is 0 anywhere(its everywhere on the unit circle, any circle) then it's not regular.
Am I trying to prove a negative?

What is a reduced row echelon form in a matrix for? isn't it enough with the triangular form?

>>11513425
I'm not sure what you mean by "enough". Enough for what?
If you want to actually solve a system in echelon form, you can, but you have to back-substitute as you go. Putting it into RREF is just getting all the back-substitution out of the way beforehand so you can read off the solution from the matrix with no work.

>>11513428
I mean, it takes more time to do a RREF, you could just do back-substitution and that's it right?

if so, why is there a RREF in the first place?

>>11513419
Right, I get you.
Maybe we just interpreted the circle counter-example incorrectly. It's constant, so the arc parametrization is just [math]\{ 0 \] \rightarrow \mathbb{R}^2 [/math], and since the derivative doesn't exist (by definition), it's not zero, so it's regular in an extremely degenerate sense.
So you've got three cases:
>[math]k'[/math] zeroes in an open set means it degenerates in a regular way
>k' doesn't zero is done
>k' zeroes in one point or in [a, b] are still up for the corners

I'm pretty sure (although I might have made a mistake somewhere) that the only prime ideals of the ring of smooth compactly supported functions in [math]\mathbb{R}^n[/math] are the maximal ideals of all the functions which zero at some point.
But my proof is absolutely horrendous. Does anyone have a good proof or a counterexample?

>>11513442
I don't think that's correct. You can't parameterize by arc length if it's not regular, you need the existness of the derivative. But that doesn't matter since curvature isn't defined at all for that curve.

Strictly speaking if k' zeroes in a set of measure 0 you could transform it to being regular but it wouldn't be the original curve. Third case is included in the first.

>>11513782
Can you tell me what text your class is using for me to double check the definitions?

How do you find a a one-one and onto mapping from the integers to the rationals without using the diagonal argument? If you let q=m/n, where m and n are elements of Z and q is in Q, then you get repeats (1/2, 2/4, 3/6, etc.) so the mapping isn't one-one. If you choose only relatively prime integers for m and n then the mapping is no longer onto. Is their an explicit function that is bijective between Z and Q? Also, Herstein is a fag.

>>11513840
*there

>>11513840
What do you mean diagonal argument? Are you seriously proving that the rationals have cardinality smaller than the continuum and deriving the naturals bijecting with the rationals from the continuum hypothesis? Have we truly reached this point?
By the way, just google "bijection naturals and rationals" and open some link (i.e. this one: https://mathoverflow.net/questions/200656/is-there-a-natural-bijection-from-mathbbn-to-mathbbq )

I've only been here a couple times and got intimidated because I've never, ever, ever done well with mathematics. I need some help visualizing a bit of science fiction. It's a problem to do with some force, and any help you could give me will help me to move forward with fleshing out a motorcycle/weapon combo I'm putting in a novel. I'm trying to come up with a futuristic equivalent to jousting. I was thinking a high powered motorcycle, going at sub-speed of sound, uses a railgun to fire a long, thin projectile. What kind of damage would that do to buildings? Other vehicles? Is there a degree of explosive force that comes out of that? If it uses lead as the projectile material, will the softness of the lead cause it to expand outward, creating a 'larger' area of damage?

I input some brainlet calculations on a force calculator site. I looked up railguns, saw that the speed of projectiles coming out of them could reach upwards of 3 km/s. A motorcycle going just below the speed of sound is going approx. 0.5km/s. The difference in joules of a motorcycle firing vs. a standing cannon firing seems negligible, and I was hoping for some advice since you guys can visualize this kind of stuff better than I.

I was hoping that there was a way for a fast moving vehicle to somehow multiply the force of something that it's shooting, but that's apparently not how physics works. I think a speeding bike with a gun on it works great for intimidation effect, for coolness, and for a general ability to set up a cannon in just about any place within mere seconds, but how the heck can I made it more impressive in terms of effect too? A fast moving vehicle would have to go ridiculous speeds in order to create significant difference in projectile force.

Please /sci/. Help me.

Everyone knows about the Japanese guy that grabs his dick during earthquakes and gets handjobs from the Earth. How many years will it take before thrill-seekers are able to afford a trip out to a black hole and a suit equipped with thrusters that will keep their relative velocity at 0; except for the dongus? It'd be a bj from the universe. You have to give exact answers

>>11513856
This is the problem verbatim:
Prove that there is a one to one correspondence between the integers and the rational numbers.

>>11513856
>>11514146
Also, by diagonal argument I was referencing Cantor's diagonal argument that the positive integers and positive rationals have equal cardinalities.

I found this extremely tiny creature on my bathroom floor, any idea what it is?

>>11514146
A classical result of set theory is that a countable union of countable sets is again countable.
Then [math] \mathbb{Q} = \cup _{m \in \mathbb{N} } A_m [/math], where [math]A_m = \{ \frac{n}{m} \in \mathbb{Q} , ~ n \in \mathbb{Z} \} [/math] . The fact that each [math]A_m[/math] bijects with the integer is trivial and left as an exercise to the reader.

>>11514199
Thanks.

>>11514169
A termite

>>11512000
openstax's calculus books are great.

>>11514169
psocid
u got fungus growin

Does a physical equation of the form [math](a^2+b^2)[/math] imply that the norm of a complex number is being taken? That is, zz*, or [math](a+ib)(a-ib)[/math]?

Likewise, does an equation of the form [math](a^2-b^2)[/math] imply the norm of a "split-complex" number is being taken? where [math]zz^{*}=(a+jb)(a-jb)[/math] and [math]j^2=+1[/math]?

>>11513771
>the ring of smooth compactly supported functions
What's the identity of this ring?

>>11514400
>Does a physical equation of the form (a2+b2) imply that the norm of a complex number is being taken?
No. Complex numbers are not physical things. They're just models. Sometimes it makes things easier to model things with complex numbers. But if you can model it with complex numbers, you can also model it with regular 2d vectors.

>>11513771
https://math.stackexchange.com/questions/1577985/smooth-manifold-m-is-completely-determined-by-the-ring-f
https://mathoverflow.net/questions/224940/spectrum-of-ring-of-smooth-functions-on-mathbbrn/224941

>>11514199
Your "classical result" that countable union of countable sets is countable depends on countable axiom of choice.
Anon's problem doesn't actually depend on it. The rationals are bijective, in an obvious way, with a subset of ZxZ. ZxZ is countable (prove it). Hence Q is countable.

>>11514583
>They're just models
okay yeah no shit. But does an equation of the form [math](a^2+b^2)[/math] imply that whatever's being modelled behaves like a complex number?

>>11514660
That really depends on the context.

>>11514702
In what contexts would it not be true?
I know one case where the assumption seems consistent with reality (relating the lorentz factor to the hyperbolic split-complex numbers), but in what non-trivial situation would [math](a^2-b^2)[/math] not imply the norm/behavior of complex numbers?

>>11514714
Sometimes a^2 + b^2 only implies the behavior of complex numbers in that it looks like a norm of complex numbers but nothing beyond that.
For example if a and b are sides of a right triangle, a^2 + b^2 is the square of the hypotenuse. Sure we can take a, b to be the real and imaginary parts of complex numbers, but that doesn't tell us anything new (about the triangle) and is effectively useless.

how do I get homework templates for LyX? I downloaded one off the internet and opened it and it just came up with \start on the document.

Why does higher category theory read like schizo nonsense?

>>11514772
It could be a problem with the way your brain works.

>>11514660
not at all. for example you may be looking for all integer solutions of a^2 + b^2 = 50. that's a diophantine equation, nothing about complex numbers going on.
>inb4 what about analytic number theory lol

>>11514772
all math that's far from what you currently understand sounds like schizobabble
go try to read a paper on Langlands, you can barely recognize it as English unless you've spent years studying it

>>11504025
Why does Greenland look bigger than Australia on a map even though it's not?

>>11514580
But anon, I said ring, I didn't say ring with identity.
>>11514607
Could you elaborate? Neither of the links really helps.
>>11514954
Because of how the Mercator projection works.

Should I worry about Asteroid C/19, ATLAS.

>>11514954
>Why does Greenland look bigger than Australia on a map even though it's not?
because there is no map from a sphere onto the plane which would preserve all metric properties

>>11514976
Can I see your proof?

>>11504025
I'm going through Spivak's calculus now, and he says that the principle of the existence of a multiplicative inverse for any element in the set that is not 0 does not hold for integers.
I don't see why that is, I can't think of an integer (other than 0) that does not have a multiplicative inverse.

>>11515135
Oh fuck, I'm dumb
Just realized it, sorry for the stupid question

>>11515135
He means that there isn't a multiplicative inverse **in** the integers. 3 has a multiplicative inverse in the rationals, 1/3, but not in the integers.

consider the following function

[math]\int_{-2}^5 |2t - 4| dt = \int_{-2}^5 (-2t+4) dt + \int_{-2}^5 (2t-4) dt[/math]

why didn't the person evaluating this example use 0 as the upper bound for the first summand integral and 0 as the lower bound for the second?

consider the following:

[math]\int_{-2}^5 |2t-4|dt = \int_{-2}^2 (-2t+4)dt + \int_{2}^5 (2t-4)dt[/math]

why didn't the person evaluating this example use 0 as the upper bound for the first summand integral and 0 as the lower bound for the second?

>>11515194
because t=2 is vertex of the abs value

>>11515028
This is actually substantially better than what I was thinking of yesterday.

We consider a prime ideal [math]I \subset C^{ \infty}_c ( \mathbb{R}^n )[/math], the ring of smooth, compactly supported functions.
We take [math]N(I) = \cap _{f \in I} f^{-1} (0)[/math]. Assume [math]N(I)[/math] contains [math]a, b[/math] with [math]a \neq b[/math]. Then, because [math]\mathbb{R}^n[/math] is Hausdorff, we can take two disjoint open sets [math]A[/math] and [math]B[/math] with [math]a \in A[/math] and [math]b \in B[/math]. Then, we take bump functions in [math]A[/math] and [math]B[/math], which respectively aren't zero in [math]a[/math] and [math]b[/math], and we multiply them to obtain the zero function. By [math]I[/math] being prime, one of the two functions is in [math]I[/math], and we reach a contradiction. We then have either [math]N(I) = \{ \alpha \} [/math], or [math]N(I) = \emptyset[/math]. We'll assume for a while that we have the first case. This is, in some sense, "the fundamental reason why it should work".
We take [math]\overline { B_1 \alpha } = B[/math].

>>11515214
Now, it's easy to show that if [math]supp ~ h \subset \mathbb{R}^n - B [/math], then [math]h \in I[/math], we just take any bump function [math]j[/math] in [math]B[/math] which doesn't zero in [math] \alpha [/math], and we naturally have that [math]hj=0[/math], but [math]j \notin I[/math] by hypothesis, and then [math]h \in I[/math] by primeness. We take the restriction map [math]C^{ \infty} _c (\mathbb{R}^n ) \rightarrow C^{ \infty} (B)[/math]. Because the kernel (functions with support in [math]\mathbb{R}^n - B[/math] ) is already in [math]I[/math], and because the map is surjective, the image is a prime ideal, and thus the ideal of all functions which vanish in [math]\alpha[/math], and we should be done (note: this argument comes from the stackexchange).

For the case where [math]N(I) = \emptyset [/math], we have some [math]f \in C{\infty}_c ( \mathbb{R}^n )[/math], we include it's support in a compact set, and then we throw the result in the stackexchange again for prime ideals of smooth functions on compact sets.

>>11515198
got it, thanks fren

>>11515214
You can take a set of compactly supported bump functions f_i such that the intersection of all f_i^-1({0}) is empty. What's stopping you from extending the ideal generated by them to a maximal ideal?

>>11515321
nvm just realized that without unity you don't have maximal=>prime

>>11515321
The intuitive issue with that is as follows: For any smooth compactly supported function [math]f[/math], it's support is inside a compact set [math]K[/math], and this compact set is covered by [math]supp ~ f_i[/math]. Take a finite subcovering and torsion your way into getting a partition of unity out of the finitely [math]f_i[/math].

>>11515217
>For the case where N(I)=ON(I)=O, we have some f∈C∞c(Rn)f∈C∞c(Rn), we include it's support in a compact set, and then we throw the result in the stackexchange again for prime ideals of smooth functions on compact sets.
Can you elaborate on this? What is f?

>>11515348
Basically, we have a random [math]f \in C^{ \infty}_c ( \mathbb{R}^n )[/math], and we want to show that [math]f \in I[/math], that is, [math]I[/math] is the trivial ideal.
The trick is taking a compact [math]K[/math] such that [math]supp ~ f \subset K[/math], and considering the restriction map [math]\rho C^{ \infty}_c ( \mathbb{R}^n ) \rightarrow C^{ \infty} (K) [/math]. Not, [math]\rho [/math] is surjective, and thus [math] \rho (I)[/math] is a prime ideal (note: I might have hallucinated this theorem into existence, will check later). Then [math]\rho (I)[/math] is characterized as in the stackexchanges from earlier, but since it can't be any of the prime ideals of all the functions which zero at one point, it's actually the entire space of functions. Then, [math]\rho(f) \in \rho(I)[/math], we take a preimage, and also multiply by another bump function to remove the fat if necessary.

>>11515377
Right, one thing.
Regarding the prime ideal thing; We have that, if [math]g \in C^{ \infty}_c ( \mathbb{R}^n )[/math] has [math]supp ~ g \subset \mathbb{R}^n - K[/math], then [math]fg=0[/math]. If [math]f \in I[/math], we're done, and otherwise [math]g \in I[/math]. But the set of all such [math]g[/math] is precisely the kernel of [math]\rho[/math], and I'm pretty sure that the "sends prime ideal which contains kernel to prime ideals if surjective" thing worked.

>>11515217
>>11515377
>>11515388
My bad, I have no idea where I got the idea that the only prime ideals were maximal for compact sets.
I'll try to prove it and talk to you lads later.

How can I count the number of triangles in this picture?

Can someone post the /sci/ reading list? The one with How to Prove It and Linear Algebra Done Right

>>11515422
>this fucking problem
Never mind, I give up. I am content with the result working for maximal ideals.

is there a universal method to distill/split any azeotrope mixture or is it different for each mixture?

>>11516519
latter

>>11507241
depends on wrist positioning, and how close your arms are relative to your body. Closer to your body + wrist internally rotated will recruit pectoral muscle support, which can provide significant advantage

>>11515448
I get 35: 7 distinct cases, 5 rotations of each.

How come beaches sometimes have cliffs, then the cliffs stop and you have gentle slopes for about 10 km or so, and then you have cliffs again, all in the span of less than 50 km?
In other words, what could make the cliffs be eroded in just one part of the beach?

I'm just trying to get this straight. So, in simplified terms the DNA splits apart and the RNA is read by ribosomes which go on to make certain proteins in accordance with the sequence. So my main question is (and bare with me because this will be difficult for me to ask) After the Ribosome creates the proteins, the proteins are just floating around inside the cell membrane. Are the molecules that go on to be assembled just based on chance? I mean, there is no way for a molecule to actually THINK that it should assemble in a certain way. So the RNA is in essence just making a large pool of molecules that have a certain chance of arranging a certain way and these randomly assembled molecules drift throughout the body and affect whatever they have their next chemical reaction with? Sorry if that was convoluted. Hopefully someone can make sense of what I'm asking.

I'm watching Professor Leonard now, and I'm learning limits. But he caught be off guard with the whole "domain issue" thing. In the video (I timed exactly where he says it) he mentions "simplifying out the domain issue" and "not actually getting to 2", with that I guess he means we're not actually supposed to plug 2 in but get really close to it. What I dont understand is why does he proceed to plug in the 2 into the simplified equation even though the domain of the unsimplified function clearly states it's not defined at 2? Why can he do that?

https://youtu.be/VSqOZNULRjQ?t=1837

I've watch every single video prior to this (including prealg) and this is the first time I've been stuck. Please explain this to me out so that I can continue learning for the test...

>>11504614
>>11504651
>>11504660
>>11505398
what is this

>>11517003
I don't really know what you mean. Proteins certainly aren't random, they are like sophisticated machines on a molecular level.
Two proteins made from the same gene are usually exactly identical up to differences in isotopes.
Enzymes usually only catalyze a single type of chemical reaction, from compounds particular to the enzyme, to other compounds, also particular to the enzyme, not just random ones.
If you need an example look at this: https://en.wikipedia.org/wiki/ATP_synthase There doesn't need to be any thought involved for something to be synthesized, like how a planet doesn't have to think in order to form an approximately spherical shape.
It just happens because the universe has gravity. Or if you burn hydrogen the result is just water molecules, no thought involved.
If you mean "how does an enzyme find the compounds whose reactions it catalyzes?", well that is actually random up to an extent.
The compound has to bump into the enzyme just from thermal movement.

>>11516867
positive feedback
small erosion sites -> medium erosion sites -> large erosion sites -> beaches surrounded by cliffs
The rest of the cliff is untouched b/c gravity draws the water into the partially eroded area

>>11517269
I think he means folding
>>11517003
Some of it is semi-random, some of it is assisted by helper proteins. The semi-random folding is influenced by hydrophilic sites drifting towards the outside, and hydrophobic parts drifting towards the center of the protein mass. Chelation sites may also play a role, though I'm not sure.
Protein folding is a very complex and not completely understood field.

Once the protein is properly assembled, it works like a well-oiled machine.

>>11517269
I think this anon is kinda getting what I am saying. >>11517319

Let me put it in simpler terms. Say you have a bag full of legos. You put a certain amount of each type of lego into the bag per the instructions. What I'm asking is, if you shook the bag and the legos connected, would that be the same concept behind how more complex molecules are assembled in the body? The Ribosomes make a certain amount of amino acids, proteins, etc according to the RNA and from those randomly assorted molecules, they have the chance to form certain more complex forms.

>>11506273
That is IC which was used in old models of Japanese citizens.

>>11504025
Hello, I need help with finding out the forced response of y'(x)+2y(x)=u(x) now I dont know what that means I only managed to get the general solution at least I hope I did
here it is
y=[ue^(2x) + 2C] / [2e^(2x)]
what is a forced solution I have been looking for an explanation online but there is nothing that explains it in layman terms

How do i compute P(A=1 | S=1,B=1) and P(W =1 | S=1, B=1)? i'm not even sure where to begin

I'm thinking of making a shitpost about gigachad telling you about how much he likes the torus and about the wealth of Torus theory, including:
>maximal tori of Lie groups
>Torus actions on symplectic manifolds
>complex tori
>abelian varieties
>toric varieties
>harmonic analysis on the Torus
>Riemannian metrics on the Torus
How he believes that several open problems will be solved through the Torus, and that mankind must "Leap through the hole within the Torus towards the future" or whatever autism I come up with when actually writing it.
And so on, but it's missing something.
Also, my harmonic analysis is weak as fuck.

My textbook states that, when adding series, "if one series starts with a multiple of, say, x to the first power, then we want the other series to start with the same power".

[math]\sum _{n=2}^{\infty }\:n\left(n-1\right)c_nx^{n-2}+\sum _{n=0}^{\infty }\:c_nx^{n+1}[/math]
in the above example, with regards to what the textbook says, does this mean I need to manipulate both series such that x is raised to the same power?

Or, does it mean that in either series, the x can be raised to whatever power, so long as they both evaluate to the same x at their respective index values?

>>11517156
bump..

>>11518148
No, I think it means that you should reindex series so that you can sum coefficients, and the ideal case is when they both start with the same powers since the result is cleaner.
So, for example, we can set [math]j=n-2[/math], and then the first sum becomes [math]\Sigma_{j=0} ^{ \infty} (j+2)(j+1) c_{j+2} x^j [/math], and by setting [math]k=n+1[/math], the latter series becomes [math]\Sigma_{k=1}^{\infty} c_{k-1}x^k[/math].
Now, we used [math]j, k[/math] to make the reindexing easier to read, but by just swapping [math]n[/math] back in for both of those, we get [math]\Sigma_{n=0} ^{ \infty} (n+2)(n+1) c_{n+2} x^n + \Sigma_{n=1}^{\infty} c_{n-1}x^n [/math]. The sum has a small "delay" in the first one, which we split off for [math](0+2)(0+1)c_{0+2} x^0 + \Sigma_{n=1} ^{ \infty} (n+2)(n+1) c_{n+2} x^n + \Sigma_{n=1}^{\infty} c_{n-1}x^n [/math], which is easy to sum, and we get [math]3c_2 + \Sigma_{n=1} ^{ \infty} [ (n+2)(n+1)c_{n+2} + c_{n-1}]x^n[/math].

>>11517156
>>11518204
Even though the two _functions_ (x^2-4)/(x-2) and x+2 are not the same since they have different domains, they have the same _limit_:
[eqn]\lim_{x\rightarrow2}\frac{x^2-4}{x-2} = \lim_{x\rightarrow2}x+2[/eqn]

The process, broken down, is
>1. I know my function has the same limit as the different function x+2
>2. I know the limit of x+2 at 2 is 4, because I'm allowed plug 2 inside this one
>3. by 1, the limit of my original function at 2 is also 4
Nowhere does it matter whether or not the original function is defined at 2.

>>11518032
Unit function?

>>11517156
A basic theorem about limits states that if two functions [math]f,g[/math] agree on a neighborhood of [math]x_0[/math], BUT NOT necessarily AT [math]x_0[/math] and [math]\lim_{x\to x_0}f(x)[/math] exists, then [math]\lim_{x \to x_0}g(x)[/math] also exists and these limits are equal.

As an example, take [math]f(x) = x[/math] and [math]g(x) = \tfrac{x^2}{x}[/math]. These functions are not equal, because the second function has a different domain: it's not defined at zero. However these functions agree on a neighborhood around zero (obviously not at zero, but we don't care) and we know that [math]\lim_{x\to 0}x = 0 [/math] simply by plugging in [math]x = 0[/math]. Therefore [math]\lim_{x \to 0}\tfrac{x^2}{x} = \lim_{x\to}x = 0[/math].

Of course in practice when you solve the limits, you just simplify the expression until you can plug in, but this is the reasoning why you can do that.

>>11513148
Looks good to me. You can double-check with the residue theorem. Function [math] f(z)=(z-2j)^{-3} [/math] has only one singularity in the region bounded by C, namely at [math] z_0=2j [/math]. Now compute [math] \text{Res}_{z=z_0}\{f(z)\}=...=0 [/math]. Finally you get [math] \oint_Cf(z)\text{ d}z=2\pi j\sum \text{Res}\{f(z)\}=0 [/math].
>>11514983
no
>>11518032
You've got a constant-coefficient linear non-homogeneous ODE with the form [math] ay'+by=f(t) [/math]. You can think of this as the governing equation for some kind of linear system, like the voltage over a capacitor in an RLC circuit or the displacement of a mass in a spring-mass-damper system, etc., all as a function of time. When [math] f(t)=0 [/math], you actually have a homogeneous ODE. Engineers don't say homogeneous, though, they say "unforced." That's because [math] f(t) [/math] is the "forcing function," i.e. is represents the power source in your RLC circuit or the applied external force in your spring-mass-damper system. Solving for this homogeneous or unforced solution gives you something called the transient solution. Solving for the non-homogeneous gives you what is called the steady-state solution, because as time goes to infinity, the homogeneous part of the solution to the ODE in general is going to go to zero because of exponential coefficients and all that.

Use a Laplace transform to solve the ODE in question. You will get [math]
sY-y_0 +2Y=\frac{1}{s} [/math]. Do some re-arranging and apply the inverse Laplace transform to get [math] y=y_0e^{-2t}-\frac{1}{2}e^{-2t}+\frac{1}{2} [/math]. Here, the first term is the homogeneous/unforced/transient solution for y. The second two terms compose the non-homogeneous/forced solution.

Hey /sci/

We place a book of mass 3 kg on a spring of spring constant 800 N/m , how far does the spring compress ?

>>11518690
first I want 1-2 paragraphs detailing specifically why you can't compute this right now without help

>>11518694
Of course , i can do it , i am asking because it's a set up for my real question


You gonna study the energies end up with an expression:

U = 0.5Kx^2 =mgx

My question is that of we study it from a forces perspective when the force are in equilibrium you get :

Kx =mgx

These two expressions don't give the same answer

>>11518701
Common guys plz ?

>>11518701
Force method:
[math] F_s=F_g\implies kx=mg [/math] so [math]
x=mg/k=(3\times 9.8)/800=37\text{ mm} [/math]

Energy method:
PE stored in spring = work done by gravity - work done by sping, so [math] kx^2/2=mgx-kx^2/2\implies kx=mg [/math]. Same shit. Your energy balance was wrong.

>>11518711
impatient faggot, feel embarrassed

>>11518720
What about this though ?

https://www.slader.com/discussion/question/a-spring-of-negligible-mass-has-force-constant-k-800-nm-a-how-far-must-the-spring-be-compressed-for/
>>11518725
Sorry , i'm not used to slow boards

>>11518733
what about it

>>11518736
He didn't include the work of the spring in his analysis , i use this answer in master physics and it worked.

Anyhow you're welcome , i feel stupid , of course the work done by the spring is gonna decrease the energy stored

>>11518748
Because they are talking about maximum displacement, not the equilibrium displacement where the book comes to rest. The book lands on the spring and compresses it twice as much as it would be in equilibrium.

>>11518766
Thanks for the help but Die you degenerate furry fag !

>>11518766
Will the book start oscillating just by placing a book on it ?
Also how do the equations work out that way ?

>>11518786
>thankful
>hates degenerates
Holy based.

>>11518789
Not necessarily. You could carefully compress the spring to equilibrium before hand, place the book on top, and release. There will be no motion.
>how do the equations work out that way ?
Newton's law and Hooke's law. [math] F=m\ddot{x}=-kx [/math]. You get a clean little second order LTI ODE. Solve for x and oscillatory motion pops right the fuck out.

>>11518803
But if you don't calibrate it , if you just place a book on top of a spring and let go , would is oscillate ?

And i meant the equation for maximum compressing distance ?

>>11518817
Calibrate what? You can get the maximum compression a couple ways. You could do it directly, by solving the ODE in the previous post and finding the maximum x, or you could use energy. I don't understand your question.

>>11518826
>You could carefully compress the spring to equilibrium
If you don't compress it carefully and just place the book , will it oscillate ?

>>11518834
>If you don't compress it carefully and just place the book , will it oscillate ?
yes

>>11518826
Thanks

Can I choose [math] A, B \in \mathbb R [/math] (not identically zero) such that [math] A J_0(x) + B Y_0(x) \in L^2 \left ( (1, +\infty) \right) [/math]?
[math] J_0 [/math] is the Bessel function of the first kind and [math] Y_0 [/math] is the Bessel function of the second kind.

>>11519032
In fact, I don't even know if J_0 or Y_0 are in L^2 but I'm not able to find anything.

>>11519032
Remember that the Bessels form an ONB on [math]L^2_r((0,\infty),rdr)[/math], namely [math]\langle J_n,J_m\rangle_r = \int_0^\infty dr rJ_m(r)J_n(n) = \delta_{nm}[/math] (up to normalization).

am taking Trigonometry and this week we are discussing Lissajous figures. I have to write a 500-word summary along with graphs, and for the research, I have to find two interesting facts about them. Apart from searching online and finding the usual answers (which I still have to source), I figured I would come to /sci/ and see if there are any unique perspectives in regards to Lissajous that are not online. I looked through the sticky and couldn’t find anything related.

Would the wim hof breathing technique help us against this blasted virus? It helped against a controlled e coli injection (not a sciencefag)

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4034215/

What fat tail is taleb talking about?
I know it is some sort of a skewed normal distribution. But what about it?

>>11518062
Use Bayes' Rule.

ok, really stupid question here, but if you have a topological space (X,tau), can you put a topology on tau itself? is that even a worthwhile thing to do?

>>11520762
>can you put a topology on tau itself?
Yes.
>is that even a worthwhile thing to do?
No not really.

>>11520796
Großwachsen!
>>11510441
The intersection of [math] f(x)=A\exp(x+A)+x [/math] with the x axis.
>>11507288
Excel or Octave (MATLAB). R if you are a chemical tranner.

>>11507288
matplotlib in python and ggplot2 in r are really good tools for making nice plots. If you're interested in maps specifically then your best bet is a full on mapping tool like QGIS.

I'm not sure if it spreads if an infected person quotes you. I think it spreads if you quote a greeny. Do you get infected if you enlarge a pic by them?

How would you go about this integral? Hyperbolic substitution and solving [math](1-(sinh(u))^2)^(-1)[/math]

>>11521777
it starts doing a lot of weird steps and i'm pretty sure there's an easier way to do it.

>>11520762
>can you put a topology on tau itself? is that even a worthwhile thing to do?
If it's a metric space, you can put the Hausdorff distance on the topology and let it induce a topology.
I don't know of any neat constructions for an arbitrary topology.

Let [math]\mathbb H^n = \{(x_1...x_n)\in\mathbb R^n : x_n \geq 0\}[/math] and denote its boundary by [math]\partial \mathbb H^n = \{(x_1...x_n)\in\mathbb R^n : x_n = 0\}[/math]. Let [math]p\in\partial\mathbb H^n[/math]. Show there cannot exist any open sets [math]U,V\subset\mathbb R^n[/math] such that [math]p\in U[/math] and [math]U\cap\mathbb H^n,V[/math] are [math]C^\infty[/math]-diffeomorphic.

Note: I have absolutely *zero* knowledge in differential geometry, manifolds etc., and was basically just introduced to the concept of diffeomorphisms (of which I know nothing of, too). I tried playing around with the limited tools I do have in my possession: the inverse function theorem, the open mapping theorem, etc., but to no avail.

Any guidance is appreciated

someone do this for me

PROJECT:
In News, from doctors or mayors or governors, we hear that in some places this
virus is growing very fast and the number of affected people doubles in every
three days. That means, 100 after three day becomes 200 and after 6 day 400
and after 9 days 800 and so on.
(a) Suppose theses are true facts that in a city we have 200 corona virus
patients and this number will be doubled in every three days. Write a
simple formula in terms of P the number of patients after n days from
the day when we have 100 patients. (write P= a formula in terms of n).
(b) Use your formula and find out the number of affected patients after one
month. Check your answer by counting the sequence 200, 400, 800,,,,.
(c) Graph your function.

>>11522752
i already flip burgers
just do it

>>11522797

>>11522334

Just because your loved ones ventilated your brain away that doesn't mean it's possible for others to ventilate as well.

>>11522795
me?

>>11522155
Aaaachoo

>>11506370
It's not about energy it's about wavelength.
Radio waves have a much longer wavelength than any structure within crystals or molecules so can only get diffracted and dispersed by much bigger structures like hills.

Gamma/x-ray do pass through mostly but x-ray diffraction is commonly used to study crystal structures since there is some scattering. The scattering angles and wavelength (might be wrong on wavelength dependence) of x-ray used is how we know what the crystal structure of many solids is.

You might find this interesting
https://en.wikipedia.org/wiki/X-ray_crystallography

>>11523032
Thank you kind anon, this seems to do the trick!

>>11522817
Kudos to you too!