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/sci/ - Science & Math

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File: 1.75 MB, 1471x1735, __remilia_scarlet_touhou_drawn_by_satoupote__f5e2809be1eb6b42ba6182303c39f53b.jpg [View same] [iqdb] [saucenao] [google]
11522896 No.11522896 [Reply] [Original]

Previously >>11504025

I'm getting banned soon for infection edition.

>what is /sqt/ for
Questions relating to math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/diy/ohm , >>>/adv/ , etc.
libgen.is (Warn me if the link breaks.)
>book recs?
>how do I post math symbols?
>a google search didn't return anything, is there anything else I should try before asking the question here?
>where do I look up if the question has already been asked here?
>how do I optimize an image losslessly?

Question asking tips and tricks:
>attach an image
>look up the Tex guide beforehand
>if you've made a mistake that doesn't actually affect the question, don't reply to yourself correcting it. Anons looking for people to help usually assume that questions with replies have already been answered, more so if it has two or three replies
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Good charts: https://mega.nz/#F!40U0zAja!cmRxsIoiLFZ_Mvu2QCWaZg
Shitty charts: https://mega.nz/#F!NoEHnIyT!rE8nWyhqGGO7cSOdad6fRQ (Post any that I've missed.)
Verbitsky: https://mega.nz/#F!80cWBKxC!ml8ll_vD2Gbw4I1hSLylCw
Graphing: https://www.desmos.com/
Answer engine:
Tables, properties, material selection:

>> No.11522944


>> No.11522977
File: 246 KB, 669x877, __remilia_scarlet_touhou_drawn_by_mozukuzu_manukedori__d445d31a92debc8e9196af7cf5ba1616.png [View same] [iqdb] [saucenao] [google]

Unanswered questions:

Math questions:
>>11505746 (with commentary by >>11506292 )
>>11508740 (See the thread for further context)
>>11509899 (Responded with a "Probably not", asker satisfied with reasoning.)
>>11509918 (Discussion prolonged in /mg/ , still sorta open)
>>11511907 (Yukariposter answered, but I'm not sure if it counts, since I have no idea what's being asked and since Yukariposter made no actual comments on his algebra and approximations being correct or not)

Probability and Statistics:

Physics questions:
>>11512387 (arguably stupid, but he's self-aware, so he gets a pass)
>>11513900 (this one has a pass for coolness)

Chemistry questions:

>>11506560 (Part of the necessary data widely conjectured to be missing)

/g/ and related questions:

Medicine questions:

Stupid questions:
>>11515474 (I think it's in the OP pasta, Bad Charts mega)

>> No.11523065
File: 361 KB, 2048x2048, COOF.jpg [View same] [iqdb] [saucenao] [google]

The total transmissivity of a surface, defined as the ratio of irradiant flux to total irradiation, is the integral of spectral transmissivity over all wavelengths and is basically a measure of how transparent a surface is to irradiation. This spectral transmissivity is a function of wavelength, obviously, and depends on electronic valences blah blah atomic scale blah blah. So basically you can have a very low over all transmissivity, or a spectral transmissivity of zero at one wavelength, but then be transparent at another. For example, iron is transparent at 1 meter, but invisible to 500 nanometer light. This is a good question and deserves a better response. Look into optics.
Look at the periodic table and think about how much water weighs. Since the atomic mass of H2O is about 2*1+16=18, and since there is specified to be 9 grams of it, we know we have half a mole of water. But since there are two hydrogens in a water, we know we have 1 mole of H. In other words, 9 grams of water contains 1 mole or 6.022E23 hydrogen atoms.
"The Scope proved to be a haunt for electronics assembly people from Yoyodyne. The green neon sign outside ingeniously depicted the face of an oscilloscope tube, over which flowed an ever-changing dance of Lissajous figures. Today seemed to be payday, and everyone inside to be drunk already. Glared at all the way, Oedipa and Metzger found a table in back. A wizened bartender wearing shades materialized and Metzger ordered bourbon. Oedipa, checking the bar, grew nervous. There wast his je ne sais quoi about the Scope crowd: they all wore glasses and stared at you, silent. Except for a couple-three nearer the door, who were engaged in a nose-picking contest, seeing how far they could flick it across the room."
In the copypasta that starts each thread.

>> No.11523395
File: 731 KB, 1763x2696, __matara_okina_touhou_drawn_by_ma_sakasama__3c2db8dc004e553ca35d35a4aebbbbc8.jpg [View same] [iqdb] [saucenao] [google]

Fuck, I was 100% sure you'd prove it by showing [math]U \cap \mathbb{H}^n - \{p \} [/math] is contractible but [math]V - \{ f(p) \} [/math] has non-trivial homology.

>> No.11523547

that's a good intuition, but you're missing something important
limits are saying: "if x is going closer to P, then where does f(x) go ?"
if a function is defined at P, then we say that f is continuous at P if the limit of f equals f(P). it makes total sense: "if x is going closer to P, then f(x) is going closer to f(P)"
so limits are used to define continuity
in your words, the limit actually tells you "what would f(P) be if f were defined at P AND was continuous at P"

>> No.11523555

pretty much

>> No.11524403
File: 107 KB, 502x779, telescope.jpg [View same] [iqdb] [saucenao] [google]

Anyone here familiar with telescopes wanna tell me if this thing would be able to get a good look at Saturn? Google just left me confused and the seller sounds like he's senile when I tried asking him.

>> No.11524656
File: 361 KB, 700x861, __remilia_scarlet_touhou_drawn_by_60mai__09f3b9117b872965d17975fe91f8c31d.png [View same] [iqdb] [saucenao] [google]

Does anyone have an outline of what's (supposed to be) the difference between symplectic geometry and symplectic topology?
I am no longer sick.

>> No.11524666

It doesn't look very powerful. You might only be able to see the Moon and Mars and Venus clearly.

>> No.11524669

Sorry but it won't.
Ignore magnification - that's theoretical and beyond actual achieving.

It's diameter than is the factor.
Scope gathers light.
It's the eyepiece that creates magnification, and like with pixels, you need to start out with more for it to be viewable when you blow it up.

look for inexpensive dobsonian scopes / wait and save.
it's worth it to not only see the rings but the gaps, the shadow it throws on the surface, etc.

>> No.11524674

p.s. the 525 comes from how you calculate magnification.
Focal length / eyepiece

So 700mm focal divided by the most powerful eyepiece in that list, 4mm, gets 175.
Then there's a 3x Barlow, basically a 300% magnifying glass, that makes 175 into 525.

But at 60mm diameter and a 4mm piece blown up 3x, you won't see shit.

>> No.11524715

Okay, so I would want some kind of combination of large scope and eyepiece? Any numbers you would recommend for seeing the shadows like you said?
Also do you know of any particular sites that have good deals now and then?

>> No.11525350 [DELETED] 

I'm learning topology and I don't understand one thing.

Let [math]V[/math] be a normed space for simplicity, and let [math]C[/math] be some set in [math]V[/math]. For some continuous linear functional [math]f: V \to \mathbb{R}[/math], define

[math]\mu = \inf_{x \in C} f(x)[/math].

Now, this means that there is a sequence of [math]\{x_n\}[/math] in [math]C[/math] such that [math]f(x_n)[/math] converges to [math]\mu[/math]... but in what topology? Is this predetermined? Do we fix the topology at some stage? I'm lost about this.

>> No.11525373
File: 7 KB, 1014x538, 1562329375126.png [View same] [iqdb] [saucenao] [google]

How do I calculate 100 numbers in a pic related graph with the highest number being 100?
Yes, I'm retarded.
Please help.

>> No.11525379

>symplectic geometry and symplectic topology?
Same thing but local vs global perspectives.
>I am no longer sick.
Good to know!
It seems like a difficult problem.

>> No.11525541

Surely that is an answer somebody who has "absolutely zero knowledge about differential geometry" can understand...

Why bother making the post? It obviously helped nobody, except it made you feel good for showing off.
Why don't you at least *try* to make posts that could potentially help people or not reply at all?

>> No.11525543

The question doesn't make any sense.
You can't "calculate numbers in a graph".

>> No.11525557

The solution another anon showed could IMO be improved. Inverse function theorem is unnecessary for it. If f:R^n ->R^n is a diffeomorphism between an open set in the domain and some other set (open set in the subspace topology in the half-space H^n), and if f(p)=q, where q is on the boundary of the half-space, then the chain rule gives that Df(p) is invertible. Using the bare definition of what it means for a function to be differentiable, and the invertibility of the derivative, we see that it's impossible that the image of an open ball around p is contained in the half-space.
That is, we can pick a direction along which we can get outside of the half-space, using just the limit definition of the derivative.
Makes it cleaner.

>> No.11525558

Does anyone know how to carry simplifications in maple through to a next step of a calculation?


y := simplify(X)
z := something(Y)

It seems to ignore much more simple forms it easily finds...

>> No.11525565

>y := simplify(X)
>z := something(Y)
This obviously doesn't work since you got y and Y.

>It seems to ignore much more simple forms it easily finds...
In general there is no real definition of "simple" so expecting a particular form doesn't really make sense...

Just try doing the simplification in line...

>> No.11525657

I got this question: For a completely sealed air-tight parallel plate capacitor with compressible air (k = 2 ) between its plates, is it possible to approach breakdown condition in the dielectric by squeezing its plates closer to each other?

Now, I'm not sure of this, because my first thought is the expression E=V/d, which would tell me that it's indeed possible. But then I think about the electric field created by two parallel plate capacitors obtained through Gauss Law: E=Q/(S * epsilon).

In this second case, the electric field created by the plates would not depend on the distance so the answer would be NO.

What error am I making? What am I missing?

>> No.11525672

I meant
y := simplify(x) = 0
z := diff(y, something) = 0

Maple just seems afraid of getting rid of common factors and denominators which makes repeated differentiation just bloat into these huge useless expressions which is exactly why I'm not doing it by hand.

>> No.11525674

Holy fucking shit the 0.999...=/=1 retards are giving me a headache!

>> No.11525700

The issue is that maple can not know what you want.
Simplification just isn't well defined, so maple might reasonably think the expression is actually simpler.

But you can use things like collect, to try to factor things out manually.
But just have a look at the documentation for simplify, there are dozens of procedures maple uses to try to find a "simpler" form...

>> No.11525703

Why respond to obvious trolls?

>> No.11525705

They are not trolls.

>> No.11525725
File: 1.02 MB, 1768x1223, __konpaku_youmu_and_konpaku_youmu_touhou_drawn_by_pegashi__c860c80c8b84fa60a6b1f06e22fdd5d7.jpg [View same] [iqdb] [saucenao] [google]

What local perspective, tho?
It's not even a "doesn't Darboux trivialize the local theory" thing, I can't really recall any other results that properly get the title of local, beyond Moser isotopy and Duistermaat-Heckman.
>That is, we can pick a direction along which we can get outside of the half-space, using just the limit definition of the derivative.
I'm not saying it doesn't work, but I will tell you it probably doesn't. Do tell me if you somehow manage to force that out from the definition.
If you want an absolutely elementary proof, >>11522817 probably works, [math]J_h=0[/math] because it's a critical point, but [math]J_g[/math] is an isomorphism and [math]J_f[/math] is nonzero, thus by the chain rule for jacobians we have a contradiction.
Essentially just elementary results.

>> No.11525728

What makes you think that?

>> No.11525740

Assume [math]f: \mathbb{R}^n \to \mathbb{H}\cap V[/math] has invertible derivative everywhere and [math]f(p)=q \in \partial \mathbb{H} [/math].
Take [math]s = (0, \ldots, 0, -1) [/math] and take [math]d = Df(p)^{-1}(s)[/math]
[math]\lim_{h\to 0} \frac{f(p+hd)-f(p)}{h}=s[/math].
Thus, looking at the n'th component
[math]\lim_{h\to 0} (\frac{f(p+hd)-f(p)}{h})_n = -1[/math].
However, this would not be possible if f(x)_n>= 0 for all x.

Also I'm pretty sure your approach doesn't work.

>> No.11525743

Hmm, my bad, looks alright to me.
>I'm pretty sure your approach doesn't work.

>> No.11525755

to be honest the exact formulation of >>11522817 feels a bit weird, but the idea is simple and 100% correct:
if f(p) lies on the boundary, then the n-th coordinate of f attains maximum at p. easily implies that the jacobian has non-trivial kernel.
sorry to step into your discussion, I wrote >>11523032

>> No.11525798
File: 19 KB, 800x800, eigenchris.png [View same] [iqdb] [saucenao] [google]

How do people do their change of basis calculations? I want something easy to remember but also generalises nicely to tensor fields when we are changing basis of tangent vectors and the transformations are by the Jacobian.

I have temporarily settled with pic related's convention, that is if we have old basis [math]e_i[/math] and new basis [math]e_i'[/math] the matrix [math]F[/math] taking old to new is obtained by expressing each new basis vector as a linear combination of old and stacking those coefficients into a matrix. Then all change of basis calculations are done by left multiplying [math]F[/math] by row vectors.

I like this because its nice for Jacobians, for example cartesian to polar we have tangents [math]e_x, e_y[/math] expressing new in old via chain rule gives [math]e_r = \frac{\partial x}{\partial r}\frac{\partial}{\partial x} + \frac{\partial y}{\partial r}\frac{\partial}{\partial y}[/math] and doing the same with angle gives

[math][e_x, e_y]\left[\begin{array}{cc}
{\frac{\partial x}{\partial r}} & {\frac{\partial x}{\partial \theta}} \\
{\frac{\partial y}{\partial r}} & {\frac{\partial y}{\partial \theta}}
\end{array}\right] = [e_r, e_\theta][/math]

When I try this with other methods I usually end up getting transpose Jacobians. I don't like this for just normal linear algebra though, its nasty having to write vectors of vectors and then do left multiplication. Is there a best of both worlds method?

>> No.11525985

This actually works! One space has a point whose complement is contractible, other doesnt. Hence the spaces are not homeomorphic!

>> No.11526041

This approach definitely works.

>> No.11526109


>> No.11526130

80mm minimum, but 150mm if you really want to see things, especially deep space fuzzies (other galaxies, nebula, stuff outside our solar system).
this can be done for <$300 for the scope.
shop used for eyepieces.
they're more expensive then scopes though for good ones.
maybe start with a zoom eyepiece, not great but will let you find things and magnify without buying multiple eyepieces.

newtonians are better then refractors unless you have a big budget so get that refractor look out of your head.
small refractors absolutely suck and you won't use it even three times.

ideally for beginner, 150mm newtonian on a dobson mount. one eyepiece around 20mm, one around 5mm.
2x barlow

>> No.11526137

you have to understand that a scope has lenses and/or mirrors, and eyepieces you look through have multiple lenses.

you can't get all that glass in decent quality for $200.
you can barely get reasonable eye glasses for that and that's just 2 simple lenses.

>> No.11526151


6 inch diameter mirror, 4' long.
I still own this scope, was my first decent one.
incredible for the price.

>> No.11526311

I think there's an error in my textbook but I can't tell
The limit as x approaches infinity of x*sin(pi*x)
I think it wouldn't exist, but the answer key claims it's 0

>> No.11526323

If x is restricted to the integers, the limit is indeed 0 because for all x the expression is 0.
If x is just a real number, you are right, the limit does not exist.

>> No.11526338

>If x is restricted to the integers
and now it all makes sense, thanks anon

>> No.11526426

ln (100) = 4.6
If you want f(100)=100, multiply ln(100) by 1/4.6 gives [math]\frac{ln(100)}{4.6}=1[/math]
multiply ln(100) by 100/4.6 (or 21.7) gives [math]\frac{100*ln(100)}{4.6}=100[/math]
Then just plot x=1,2,3,4,...100 and y=21.7ln(1), 21.7ln(2), 21.7ln(3)...21.7ln(100) in excel or something

>> No.11526493

and if you want [math]f(1)=1[/math] and [math]f(100)=100[/math] for [math]f(x)=a*ln(\frac{x}{b})[/math]
Set [math]\frac{f(1)}{1}=\frac{f(100)}{100}[/math] and solve for the scaling constants "a" and "b"

[math]\frac{a*ln(\frac{1}{b})}{1}=\frac{a*ln(\frac{100}{b})}{100}[/math], "a" cancels out

[math]-0.0465=ln(b)[/math], [math]e^{-0.0465}=b=0.955[/math]
Knowing "b," solve for "a"


So now plot y=21.5*ln(x/0.955). Thanks for the eqn, this may be useful for me

>> No.11526817

I'm just starting to learn this, and I'm watching through professor Leonard's lectures, and on one part he fucked up explaining this proof well, he messed/forgot to mention some key points and I'm now stuck trying to reason why [math]\displaystyle{\lim_{x \to c}f[g(x)]}=f[ \displaystyle{\lim_{x \to c}}g(x)][/math] works. All the other identities make sense, but I can't accept just taking something for granted. Could someone provide an easily comprehensive proof of how we got this identity? Please no epsion-delta bullshit I'm not a math major I'm literally just trying to reason why this is possible.

>> No.11526843

This is how he tried to prove it, if it helps anyone to see where he made a mistake. Maybe I'm retarded and there is no mistake, but I'm pretty sure he forgot to mention something when he says "Is it true that if limit exists at [math]\displaystyle{\lim_{x \to c}g(x)=L}[/math] that it also means that [math]\displaystyle{\lim_{x \to c}g(x)=g(c)}[/math]? Then he says yes. But this wouldn't work if the equation weren't continuous at that point, and he doesn't mention anything about the continuity. Of course no one bats an eye in his class to ask the question because they're all mouth-breathing retards and the comment section is full of "omg i understand everything thanks mr leonard make a workout video omg super ur so hot bby send milk pix" type of shit. Like fuck.

>> No.11526850

Fuck I'm actually the mouth-breathing retard here, forgot the YT link:


>> No.11526853

this is true only when [math]f[/math] is continuous
[math]f[/math] is continuous at point [math]x[/math] if [math]x_n \to x[/math] implies [math]f(x_n) \to f(x)[/math] for any sequence [math]x_n[/math]: "if we're getting closer to x, then the images are getting closer to f(x)". try to think this through to see that it really captures the concept of continuity well.
this can be written as [math]\lim_{n \to \infty} f(x_n) = f(\lim_{n\to\infty}x_n)[/math]. and that's the rule of thumb: when f is continous, we can move the lim sign in and out.
this is basically your question, only [math]x_n[/math] is not a sequence, but another function. the point still stands though

>> No.11527096
File: 209 KB, 448x656, lain gun.png [View same] [iqdb] [saucenao] [google]

this question is VERY important for me so please answer correctly
is REM rebound(rem rebound meaning less sleep =more dreams,more vivir dreams,and even lucid dreams)a true and proven phenomenon?

I'm at a point of life where I really need to dream.
im willing to reduce my sleep because of it

>> No.11527124
File: 57 KB, 709x738, photo_2019-12-08_14-04-01.jpg [View same] [iqdb] [saucenao] [google]

Let's denote [math]S[/math] as a set of continuous monotonically decreasing functions [math]f: \mathbb{R} \rightarrow [0, 1] \subset\mathbb{R}[/math], for which [math]f(1) = 0[/math]. Find [math]\inf_{f\in S}\sup_{x\in[0,1]\subset \mathbb{R}}\frac{xf(x)}{\int_{0}^{1}f(t)dt}[/math].

Tips to approach this?

>> No.11527133

nvm found the answer

>> No.11527152

For some reason I can't stop thinking about how the numerator is the lower Darboux sum for the trivial partition on [0, x], but I get the impression this helps with absolutely fucking nothing.

>> No.11527257
File: 63 KB, 256x192, 1585333927617.gif [View same] [iqdb] [saucenao] [google]

How did the Spanish Flu pandemic end?

Most of what I found says something like "Infected/spreaders either died or became immune", but that sounds like BS with the 10% fatality rate.

Another theory was "less deadly strains emerged and had a selection bias due to the war, overtaking the previous" but doesn't that imply that previously immune people are no longer safe? (Also the theory doesn't seem to have much actual evidence)

>> No.11527358
File: 793 KB, 659x2048, Screenshot_20200403-011054_Camera.png [View same] [iqdb] [saucenao] [google]

Hey, brainlet here!
I don't know how to prove equality of these two sums.
One is from binomial distribution and the other one is from negative binomial distribution.
And I'm sure they do equal. The thing is I can not change the indexes/do algebraic manipulations/use magic/... to prove it.
I would appreciate any help.

>> No.11527900

Obviously he doesn't know why. It's just because f is continuous. You could take the definition of continuity to be that the lim f = f (lim) which you've seemed to reason out. Why are you watching him anyway? You seem to realize he's not the best for this

>> No.11528052
File: 1007 KB, 1079x632, guys.png [View same] [iqdb] [saucenao] [google]

Who's on the far left? I wanna say it's Leibniz but it might be some other wig-guy. For the other three it's Franklin, Edison, Einstein.

>> No.11528086

Why is this board full of people who are insecure about their intelligence?

>> No.11528380

Is it?

>> No.11528384

It's 100% Newton. Look up google images for Newton.

>> No.11528526

It's not enough for f to be continuous. g has to be continuous too.

As an example take f as the logistic function (or any continuous, bounded and monotonically increasing function) and [math]g: \mathbb R^+ \to \mathbb R, \ g(x) = \frac{1}{x}[/math].
f(g(x)) is thus still a bounded, continuous and monotonously increasing function, this means that [math]\displaystyle{\lim_{x \to 0}f[g(x)]}[/math] exists, but on the other hand [math]f[ \displaystyle{\lim_{x \to 0}}g(x)][/math] doesn't exist, since even [math]\displaystyle{\lim_{x \to 0}}g(x)[/math] does not exist.

You still need g to be continuous, to ensure that this is actually true. (Another quick way to see this is just taking f as the identity, obviously the limits don't have to exist, unless g is actually continuous.)

You can think of this as continuous function mapping convergent series to convergent series, which is also basically the proof since if g is continuous g(x_n) is just another convergent series, so f maps that convergent series again to another convergent series.

>> No.11528545

please do note, to add onto what other anons said, what f(p) actually is doesn't matter. a limit is formally defined by these little things called epsilon and delta, and this doesn't really matter to your elementary understanding but the gist of it is that the only thing we actually care about is the behavior surrounding the point and what the limit /should/ be.

as you learn more about limits you'll face many situations where a limit (on its surface) doesnt exist at a point (typically as theres a zero in the denominator) but that we determine there to be a limit there anyways. epsilon and delta play a role there again.

>> No.11528548

sir isaac newton.

>> No.11528555

Thanks, anons!

>> No.11528584

Not really. The issue with limits isn't a matter of definition and it can't, in general, help you to find the value at a missing point.

Two examples:
f(x) = 1 on [0, infinity] and f(x) = 0 on [-infinity,0)
This function is clearly defined everywhere but it isn't continuous.

f(x)=1/x for x not 0.
This function is NOT defined everywhere but there is NO possible value for f(0) such that the function would be continuous.

You are correct that sometimes the limit can sometimes help you define a function where it isn't defined, BUT that is by no means the most relevant fact about it NOR should it be your intuition.
Do you want an actual explanation?

Epsilon delta arguments are not required to define continuity. In fact you can define continuity on an arbitrary topological space.
Also, personally, I think that in a metric space you should rather think about continuity in terms of sequences, that usually will also be more relevant in more abstract areas.

>> No.11528591
File: 7 KB, 194x226, pc1.png [View same] [iqdb] [saucenao] [google]

I'm not really a math guy but signed up for some security stuff. In particular I'm confused with some encryption stuff involving permutations in pic related.
I know we start with a 64 bit key (represented in binary) to do the permutation in pic related and it returns 56 bits, but when I'm looking at websites like this one https://paginas.fe.up.pt/~ei10109/ca/des.html
What's got me is that In the example on that website, after doing the permutation with that 7x8 grid they give a 64 bit value as such: 00000000 00000000 11111111 11110000 11001100 11110000 00000000 11110000
How did they keep the entire 64 bits instead of just the 56? Where did the other 8 numbers go?

>> No.11528911

Is machine learning just a meme?

>> No.11528914

No. It's a useful tool to fit real life data to a model.

>> No.11528948

Is there any way to solve for r in this equation?

>> No.11528957

In the equation [math]3\sqrt{x}=x[/math]. Why is [math]x\left(3\sqrt{x}\right)=x\left(x\right)[/math] an invalid way of solving for x compared to [math](3\sqrt{x})^{2}=x^{2}[/math]?

>> No.11528967

One adds an additional solution.

>> No.11528992

Thank you, that's really helpful actually. I thought it would be fine as equality was maintained, but I see now that really I just creating a higher-order polynomial.
Can you explain this in more detail, point me to some resources, or otherwise give me something I can search?

>> No.11528997

what's the output speed of a full can of spray deodorant?

>> No.11529059

The issue is that sqrt(x^2) has two solutions x and -x.
When you do (3\sqrt{x})^{2}=x^{2}, you are essentially simultaneously solving two different equations, namely 3\sqrt{x}=x and 3\sqrt{x}=-x and you will get the results for both equations in the end.

More abstractly this is related to the issue of whether a function is "bijective" or not, which essentially means if you can undo your manipulations in a unique way.
For the squaring function this is not the case, since -x and x have the same square.

>> No.11529114
File: 280 KB, 921x728, 9.jpg [View same] [iqdb] [saucenao] [google]

If you have anal sex with your sister, is it still incest?
Scientifically, I mean.

>> No.11529175

Is the same

a=b then aa=ab but a=b, then, replacing, aa=bb

>> No.11529229
File: 88 KB, 1080x222, 20200402_091820.jpg [View same] [iqdb] [saucenao] [google]

Permutations. Fucking how?

>> No.11529242

It depends on the science.
Genetically, no.
Anthropologically, yes.
(Geologically, no answer)

>> No.11529267
File: 358 KB, 563x900, __seiran_touhou_drawn_by_akagashi_hagane__9ba0591099d045072657a6e7c414d176.png [View same] [iqdb] [saucenao] [google]

By the way, would you happen to have a good proof that the homology is non-trivial?
Mine sorta goes like this:
>[math]V[/math] is open, so there's an open ball [math]B[/math] around [math]f(p)[/math] whose closure is contained entirely in V
>we take the sphere [math]\partial B[/math]
> [math] \partial B[/math] has a non-trivial homology class in [math]\mathbb{R}^n - \{ f(p) \} [/math]
>Poincaré duality followed by the de Rham isomorphism gives us a differential form [math]\omega [/math] defined in [math]\mathbb{R}^n - \{ f(p) \} [/math] with [math]\int_{ \partial B} \eta \neq 0[/math]
>we restrict [math]\omega[/math] to [math]V - \{ f(p) \} [/math] to obtain [math]\eta[/math]
> [math]\int_{ \partial B} \eta \neq 0[/math], trivially, which completes the proof that homology is non-trivial
Which, while extremely simple, feels unnecessarily long, but I don't really recall what was the theorem which you used for this trick.
> [math]g[/math] needs to be continuous
Pretty sure it doesn't, the limit [math]\lim _{x \rightarrow c} g(x)[/math] just has to exist.
>do you have a proof
I have a very shitty but sort of neat proof. Set [math]h(x) = g(x)[/math] if [math]x \neq c[/math], [math]h(c)= \lim_{x \rightarrow c}g(x)[/math]. Then, [math]h[/math] is continuous at [math]c[/math] and the proof (for [math]h[/math] ) follows the way you're thinking.
But neither of the sides of the expression depends on the value [math]g[/math] takes at [math]c[/math], so it follows.

If you insist on it, I can do an epsilon-delta one, but it's kind of a pain.
>all the faces have different colours
Man, that really makes it easier.

So, imagine you're holding the cube. First, you choose a face, which you hold in your direction.
Choose another face, which can't be the opposite one, and rote the cube so that it points upwards.
This means that the cube has 6*4=24 choices of positioning, so you just compute all the arrangements and divide by that.

>> No.11529284

If i have a group of order n and a set constructed in this way,
M = {(g_1, g_2, ..., g_p) such that g_1 ... g_p = unity of G} and p is a prime that divides n, how would I go about finding the cardinality of M?
I tried looking at some examples of the form Z_n but they are too specific, in that they are cyclic and abelian, and this problem is a lot more general

>> No.11529300

Makes it obvious. Nicely done.

>> No.11529301

So basically, you have a group, you take a set [math](g_1, \cdots, g_{p-1})[/math] under no restrictions, and you set [math]g_p = ( g_1 \cdots g_{p-1} )^{-1}[/math]?
I don't think you can use that for anything, anon.

>> No.11529340

Idk what to use it for lmao, it's just part of a homework problem that I can't seem to figure out, hence why I'm posting here

>> No.11529345

>Pretty sure it doesn't
Yeah, you are absolutely right. Certainly continuity is sufficient but your argument makes it pretty clear that it is not necessary. Oh well, should have thought a bit longer about it...

And, I mean, the proof seems good.

>> No.11529361
File: 9 KB, 540x99, Screenshot_2020-04-03_18-01-31.png [View same] [iqdb] [saucenao] [google]

Any hints guys? I've been trying this one for a few hours with no success

>> No.11529384

Write [math]{n \choose k}{n \choose k} = {n \choose k}{n \choose n-k}[/math] in the sum. You can now interpret this combinatorially.

>> No.11529407


Final question from brainlet. I kinda get what you're are trying to explain but why not colour the whole cube because if you only colour 2 sides the rest of the side can be coloured the same or different ways. (checked and your answer was right btw)

>> No.11529419

If you get a simplified equation where a variable is both inside and outside of an exponent, you're almost always fucked without using special functions that are basically defined as "the solution to my equation".
Even something easier like re^r = 2 is not solvable for r in any useful sense.

>> No.11529436

Right. So, imagine you fix the painted cube and lock it from rotating. Then, the number of ways to paint it is the classical n!, that is, you choose a colour for the first face, then the second one, etc.
But if we can now rotate this cube, this produces 24 possible dispositions (which would have counted as different colorings in the previous situation), so to obtain the rotation-independent number of colorings, we obtain the number of fixed colorings, and divide it by the number of ways we can rotate (which produce different cubes by the previous convention).
Only works because of the sides have different colors thingy.

>> No.11529446 [DELETED] 
File: 15 KB, 190x290, images.jpg [View same] [iqdb] [saucenao] [google]

NVM I got it. The point of it is to count the positions (like u said).
bless you for your help.

>> No.11529465
File: 11 KB, 442x104, prev.png [View same] [iqdb] [saucenao] [google]

Huh, thanks!
This actually ties to the previous question (as I suspected but couldn't tie together), pic related.
Cool stuff

>> No.11529481
File: 15 KB, 190x290, images.jpg [View same] [iqdb] [saucenao] [google]

God bless you

>> No.11529673

microneedling and worship of Ishtar

>> No.11529698

If you want medical information, look it up on pubmed: https://www.ncbi.nlm.nih.gov/pubmed/
In my personal experience, you get more vivid dreams if you live an exciting and emotionally turbulent life. Also, setting an alarm in the middle of the night to disturb your sleep is a much better method than sleep depriving yourself.
ask 420ch's /dr/ for more techniques and personal takes

>> No.11529807
File: 62 KB, 1624x122, para.png [View same] [iqdb] [saucenao] [google]

[G,G] is the commutator subgroup of G, and [H,H] is the commutator subgroup of H. It's not really even intuitive to me that commutators of H will necessarily be commutators of G.
Any help is appreciated.

>> No.11529814

Trivially (check), [math][H, H] \subseteq [G, G][/math].
Also trivially [math][H, H] \subseteq H[/math].

I honestly don't know what's confusing you.

Just in case, remember that [math][G, G] = \{ xyx^{-1}y^{-1} : x, y \in G \}[/math]

>> No.11529830

Ya I guess I just don't really see the top line. That's not clear to me at all.

>> No.11529834

how are babby made?

>> No.11529873

If [math]a \in [H, H][/math], then there's [math]x, y \in H[/math] such that [math][x, y] = a[/math].
Because [math]H \subseteq G[/math], then [math]x, y \in G[/math], and thus [math]a = [x, y] \in [G, G][/math].

>> No.11529881

Ok that makes sense. Sorry about that.

>> No.11529957
File: 3 KB, 125x123, 1585768287243s.jpg [View same] [iqdb] [saucenao] [google]

When I was learning proofs, I recall my professor telling me that
[math] P(n-1) \Rightarrow P(n) [\math]
was a better or more robust or more educated way to do induction proofs than
[math] P(n) \Rightarrow P(n+1) [\math]

but I don't remember how he justified that. Can anybody provide input, re: how that might be the case?

>> No.11529976
File: 283 KB, 480x473, 1585939520102.gif [View same] [iqdb] [saucenao] [google]

fuck, can't LaTeX and posted the thumbnail too

>> No.11529996
File: 158 KB, 602x535, 1581184500699.png [View same] [iqdb] [saucenao] [google]

It's not the case. If anything, it's the other way around.

>> No.11530000

They are obviously totally equivalent. Depending on the situation one might lead to nicer notation than the other.

>> No.11530004

Hey, lets say I define a sequence as a function [math]x: \mathbb{Z} \rightarrow \mathbb{X}[/math] with [math]\mathbb{X}[/math] a metric space.
Can you give me an example of a sequence [math]x[n][/math] with more than 1 limit point?

>> No.11530009

1,0,1,0,1,0,1,0,.... in the reals

>> No.11530011

[math]X = \{ 0, 1 \} [/math] has the discrete metric (or whatever fucking metric, really).
[math]f(n) = n \mod 2[/math].
Fuck he's fast.

>> No.11530016

That has less than one limit point my dude

>> No.11530019

Define a limit point.

>> No.11530022

If you're using "limit point" for "accumulation point", you're wrong and need to reread your definitions.
If you're using "limit point" for "limit", limits are unique for metric spaces.

>> No.11530023

Take a sequence a_i to a and b_i to b.
Then the sequence a_1, b_1, a_2, b_2, a_3,... had two "cluster points". Which is what I assume you meant.

There is also the issue what exactly you mean by "limit point" usually a set has a limit point and a sequence a "cluster point".
The important distinction is that e.g. {0,1} has no limit points, but >>11530009 has two cluster points.

>> No.11530026

I dont see how this works.
Lets say we take a 1 as a candidate por a lomit point. And we consider a neighborhood of radius [math]r < 1[/math] that there isnt any [math]N \in \mathbb{Z}[/math] such that [math]n \geq N \implies x[n] \in \mathcal{N}_r(1)[/math]

>> No.11530027

Limits of sequences in metric spaces are unique. You cant have more than one limit

>> No.11530028

>limit point
>different things

>> No.11530030

The requirement is that for every neighborhood you can have a point...

A cluster/limit point isn't the same as a limit ...

>> No.11530034

Hmm. Sorry dude, it's still not entirely clear to me to be honest.
The solution to [math]3\sqrt(x)=x[/math] is apparently [math](3\sqrt{x})^{2)=x^{2}[/math] where [math]x=0[/math] and [math]x=9[/math], which you're saying introduces an additional solution?

I don't really understand why multiplying both sides by x breaks the original equality. More specifically, if it DOES break equality, then why does squaring both sides not do that? I'd always thought that multiplying both sides by some factor (say x) was completely legitimate. Here it's not, but squaring both sides is?

>> No.11530038

fk u

>> No.11530046

Ok im clearly not making myself very clear and have something mixed up, i apologize about that.
What im looking for is for a sequence that very clealry converges if its defined as a function [math]x:N \rightarrow X[/math] but if we "extend" the function such that its defined as [math]x:Z \rightarrow X[/math] then the limit point "reflects" itself in the negatives and the function ends up being divergent.
Is this more clear?

>> No.11530051

>Is this more clear?

>> No.11530053

Please define what a limit point of a sequence from Z to X is.
I have no clue...

>> No.11530057

Set [math]X = \{ -1, 0, 1 \}[/math] with the discrete metric, and [math]f(n) = sign (n)[/math], the good ole "1 if it's positive, 0 if it's zero, -1 if it's negative".
Is this what you want?

>> No.11530078
File: 2.89 MB, 4128x3096, 15859423079346340456927632278859.jpg [View same] [iqdb] [saucenao] [google]

Lets see if this helps

>> No.11530082

>the good ole

>> No.11530095

There always is an issue of adding another solution.
Look at:
1 = 2
Obviously this equation has no solution. Now let's multiply both sides by x.
1x = 2x
This equation DOES have a solution, namely x=0.

The same goes for squaring.
This equation has one solution, let's square both sides.
x^2 = 4
As you can surely verify x=2 and x=-2 are BOTH solutions.

What you have to do in general is do the manipulations which add solutions anyway and after the fact check whether your solutions actually solve the equation or if they are "fake".

To be honest, I misunderstood your original question. In fact both manipulations you did are equally valid.
Doing the squaring will result in you having to find the zeros of a degree two polynomial.
Multiplying by x, while valid, won't help you since you will be stuck with the x*sqrt(x) term.

>> No.11530102

See >>11530023, but
a_1, b_-1, a_2, b_-2, a_3,...

But, to be honest I think you are confused about your subject.

>> No.11530115

>To be honest I think youre confused
Its likely, the issue is that were trying to see why usually in analysis you consider sequences as functions between the naturals and a metric space and not between the integers and a metric space, to make this point the prof asked us to find a sequence that has more than 1 limit point when defined over the integers.
I replied that that cant happen as limits are unique but he said this wasnt a rigorous question and that I should try to find one honestly I dont understand what the fuck he means :/

>> No.11530128

I wouldn't know what the limit of a sequence in the integers even means.

But I *think* my example is what you are looking for, but I could definitely be wrong.

But still, sequences do not have limit points, they have cluster points, but I also wouldn't know what a cluster point for a sequence in the integers would be.

>> No.11530132

Ahh... and there's my mistake: when I multiplied both sides by x I did [eqn]x(3\sqrt{x})=3x^2[/eqn]. What a pleb. Ty, anon. Very helpful.

>> No.11530359
File: 9 KB, 1280x672, Equal-Sign-Transparent-Image.png [View same] [iqdb] [saucenao] [google]

I'm making an elaborate political compass meme, and I need help from ppl who know calculus.
For the left label of the compass (where economic-left would normally be) I want to put some math that represents "equality approaching infinity."
The concept being that the further left you go on the political spectrum, the closer to total economic equality you get.

Would it be something like:

f (x) = Equality
x ထ

does that make any sense?

>> No.11530367

the symbols didn't all show up, but i know there's supposed to be an arrow inbetween the x and ထ and that there should be "lim" somewhere in there

>> No.11530409

could this be it?

lim [Equality^x]
x ထ

>> No.11530474
File: 291 KB, 640x550, yukari_smile3.png [View same] [iqdb] [saucenao] [google]

That forbids homotopies, not diffeomorphisms. Your argument relies on Brouwer's: maps on an open set [math]V[/math] minus one point can have no fixed points, which implies the same for [math]U[/math] if a homotopy exists, but that's a contradiction since you're sending a boundary point of [math]U[/math] to the fixed point in [math]V[/math]. This is in fact not sufficient to prove that there is no diffeomorphism between [math]U[/math] and [math]V[/math] however, since homotopies need not be diffeomorphisms and taking out a point changes more than just the smooth structure. I wanted to emphasize why corners (and only corners) matter in [math]{\bf Diff}[/math] but not in [math]{\bf Top}[/math] or even [math]{\bf hTop}[/math] precisely due to this fact.
This follows from standard results in homotopy theory [math]\mathbb{R}^n\setminus \ast \simeq S^{n-1}[/math] and [math]\pi_n(S^n) \neq 0[/math]. In particular by just taking a cellular decomposition [math]S^n = \ast \cup_f D^n[/math] it follows that [math]H^\ast(S^n,\mathbb{Z}) \equiv \mathbb{Z}[e_0,e_n][/math] with free generators [math]e_0,e_n[/math] at degrees 0 and [math]n[/math]. This is more refined than using de Rham, since Poincare duality (in the way you're using) requires [math]\mathbb{R}[/math]/char-0 field-valued-coefficients, which kills all torsion.

>> No.11530550

Consider a particle at x=0
There is a probability p that the particle will jump one unit to the right, and probability q=1-p that the particle will jump one unit to the left. What is the probability that the partcle will be at position x=x* after n jumps?
I'm assuming that you need to define two discrete random variables, one that counts how many steps to the right were taken, and one that counts how many steps to the left. Both would follow a binomial distribution, right? But after that I'm not sure how to proceed...

>> No.11530553

It's just binomial.
Consider jumping to the right to be a success with probability p. Then, it only returns to the original position if, after n trials, it succeeds in n/2 of them.

>> No.11530555
File: 209 KB, 1277x811, o1uO5Q0.png [View same] [iqdb] [saucenao] [google]

Does anyone have a Python script that plots the domain coloring of the Mandelbrot set? Like pic related

>> No.11530563
File: 85 KB, 1080x778, 20200404_004617.jpg [View same] [iqdb] [saucenao] [google]

Ok so obviously light travels at the speed of light and when we use the speed of light as v in pic related it would mean that t=t' and l=l' meaning that light is constantly everyone at every moment (if being uninterrupted) how the fuck does that work and if one were able to stop it somehow where would it end up?

>> No.11530588

What's the best book to learn linear algebra?

>> No.11530599

watch the essence of linear algebra by 3b1b

>> No.11530606
File: 35 KB, 196x361, weird_goblin.png [View same] [iqdb] [saucenao] [google]

>gamma factor vanishes at [math]v=c[/math]
>this somehow implies [math]t=t'[/math] and [math]l=l'[/math]

>> No.11530931

Is any subgroup [math]H \subset \mathrm{SU}(d)[/math] compact? More generally, is any subgroup of a compact Lie group also compact?

>> No.11530957
File: 713 KB, 787x1114, __remilia_scarlet_izayoi_sakuya_flandre_scarlet_hong_meiling_mickey_mouse_and_3_more_touhou_and_1_more_drawn_by_noya_makoto__0d0874ebfc6c78358ac37e97545b965f.png [View same] [iqdb] [saucenao] [google]

>More generally, is any subgroup of a compact Lie group also compact?
Nah, unless I've forgotten everything. Take the 2-torus [math]T = \mathbb{R}^2 / \mathbb{Z}^2[/math], choose your favorite [math](a, b)[/math] with [math]a/b \neq \mathbb{Q}[/math], let it generate a subgroup. Dense subset of the torus, wasn't it? Not closed, thus not compact.
There's probably a shitty analogous example for [math]SU(2)[/math].

>> No.11530960

this seems obvious

especially since Lie groups even have a measure on them

also, you use the word any in a wrong way

>> No.11530975

I enjoyed Linear Algebra with Applications, by Steven J. Leon

>> No.11530992
File: 405 KB, 777x831, __kaenbyou_rin_touhou_drawn_by_kagari6496__ca721dc58e2ffa14c129f0c492996d45.jpg [View same] [iqdb] [saucenao] [google]

>that counterexample
My bad.
Consider [math]\mathbb{R} / \mathbb{Z}[/math] as the circle group [math]S^1[/math] and choose some irrational number [math]a \in [0, 1][/math]. Let [math]a[/math] generate a subgroup. It's a dense subset of [math]S^1[/math], naturally, and since it's not the entirety of [math]S^1[/math] (since it's countable, for example), it's not closed.
Now, the circle group is compact and Hausdorff. Thus, we can use this https://math.stackexchange.com/questions/83355/how-to-prove-that-a-compact-set-in-a-hausdorff-topological-space-is-closed to conclude it's not compact.

>> No.11531023

Wait a second.
SU(n) has a nontrivial maximal torus, doesn't it?
Because then you can just use the counterexample above to generate a non-closed subgroup of SU(n).

>> No.11531164

Why do statisticians use log graphs to show exponential functions? Is it simply because the data looks nicer filling up the entirety of the chart space instead of most of the data being bunched near the bottom until it shoots upwards?

Because I feel like it's poor form from a science communication standpoint. Unless people know what a log graph is, they will misinterpret a "flattening" graph as one that is actually flattening. When in reality, it's still exponential.

>> No.11531175

Hoffman&Kunze, Lax, Hubbard and Hubbard, Roman, Kostikin&Manin, Dieudonne, Lang
kill yourself brainlet

>> No.11531344
File: 8 KB, 402x161, sin.jpg [View same] [iqdb] [saucenao] [google]

how do you make a sine wave with really long peaks and valleys? (marked in red)

>> No.11531482

If I take the free product of two groups [math]G[/math] and [math]H[/math], are [math]G[/math] and [math]H[/math] subgroups of their free product (up to isomorphism)?

>> No.11531525

Log plots are common in physics and engineering too. What's wrong with them? They are concise, give all the same information (if not more at a glance), and have better aesthetic.

>> No.11531582

>Why do statisticians use log graphs to show exponential functions?
Because it is really easy to figure out if a growth is exponential in a log graph.

Distinguishing between some polynomial and exponential growth in a traditional plot can be very hard to do visually.

>Is it simply because the data looks nicer filling up the entirety of the chart space instead of most of the data being bunched near the bottom until it shoots upwards?
That is another factor. It usually makes more information available when the growth is somewhat close to exponential.

>Unless people know what a log graph is
It should be enough to just look at the labels of the y-Axis to understand the basics of what is going on.

>> No.11531585

Min ( max( sin(a*x), -0.9),0.9)
Or something like this...

>> No.11531902
File: 160 KB, 1200x857, ES1d9CZXsAE0AZc.jpg [View same] [iqdb] [saucenao] [google]

A log scale plot where it is appropriate is much more informative and user friendly for people who know what it is while a linear plot for exponential data is usually impossible to use. Whether it's a failure of communication depends on the audience - I use log plots in reports for finance and linear ones in reports for marketing lel.

If you're specifically talking about covid-19 case count plots for a general audience then it's a tough problem because the linear one is useless and inflammatory but the log one is going to be meaningless or misleading to a lot of people. I'd probably go with a log scale but include some example explainer right there on the plot itself like this image.

>> No.11532018

I need help for my bachelor thesis please

It's a statistics/probability question first and programming - python question second.

>> No.11532706


>> No.11532760

Of course.

>> No.11533202
File: 300 KB, 856x1400, 80558064_p0.jpg [View same] [iqdb] [saucenao] [google]

I'm working on an unconstrained nonconvex optimization problem. However, when I include a particular set of linear constraints, the problem seems to become convex (it always converges to the same solution for any intial guess, and this is the case for all the methods I tried).
How do I prove the constrained case is convex (or how I disprove it, if my conjecture is wrong)?

>> No.11533218

>How do I prove the constrained case is convex
By demonstrating it fulfills the necessary conditions to be convex.

> (or how I disprove it, if my conjecture is wrong)
Find a counter example to convexity.

As optimization problems can be arbitrarily complex (remember they are in general equivalent to a PDE) I am afraid I have no better answer.

>> No.11533259
File: 360 KB, 891x1400, 80490285_p0.jpg [View same] [iqdb] [saucenao] [google]

The function is twice continuously differentiable, so I know that for the unconstrained case I have to check whether the hessian matrix is positive semidefinite, but I don't know how to deal with the inequality constraints.

>> No.11533270

>but I don't know how to deal with the inequality constraints
They will probably restrict the domain on which the requirement for the Hessian has to be fulfilled.

Imagine the function sign(x)*x^2, that function obviously isn't convex, but it is convex on the part where x>=0, just as an example.

>> No.11533320

>inequality constraints
Akshually, it's easier to deal with those, because the Hessian is the same as the unconstrained one.
If it was an equality you'd be pretty much fucked into learning differential geometry, tho.

>> No.11533387

How do I show that a topological space is the coproduct of its connected components if and only if the space of connected components is finite?

>> No.11533424

or perhaps I should say, homeomorphic to.

>> No.11533432

>a topological space is the coproduct of its connected components only if the space of connected components is finite?
Are you sure?
Put the discrete topology on [math]\mathbb{N}[/math]. Then the connected components are all [math]\{ n \} \subset \mathbb{N} [/math], and every connected component (read natural number) is still an open set in the disjoint union topology, so we still have the discrete topology.

Maybe you're just supposed to find some space which isn't homeomorphic to the coproduct of the connected components?

>> No.11533453

Sorry, I'll be more exact. That was a separate question that looked along the same lines as this
>Let [math]X[/math] be a space and [math]\{X_{\alpha}\}_{\alpha\in I}[/math] its collected components. If [math]I[/math] is finite, show there is a canonical homeomorphism [math]\coprod_{\alpha\in I}X_{\alpha}\cong X[/math]

>> No.11533464

fuck i'm tired

>> No.11533471
File: 295 KB, 944x1400, 80548596_p0.jpg [View same] [iqdb] [saucenao] [google]

So I got the hessian and a nonlinear equation for its eigen values. I'm trying to figure out whether or not the eigen values will always be non-negative for a set of linear inequalities. I'm not quite well versed in math, is there a general approach to do that?

>> No.11533513
File: 1.57 MB, 4096x2912, __konpaku_youmu_and_konpaku_youmu_touhou_drawn_by_suguharu86__8b3300c7c156423d2cf5669ee4386e98.jpg [View same] [iqdb] [saucenao] [google]

Assume you have a bunch of maps [math]f_{ \alpha } : X_{ \alpha } \rightarrow Y[/math]. They induce a set theoretical map [math]f: X \rightarrow Y[/math] the classical way.
If we have a closed set [math]A \subset Y[/math], then, for any [math]\alpha[/math], [math]f^{-1} (A) \cap X_{ \alpha }[/math] is a closed set. But [math]f^{-1} (A) = \cup _{\alpha \in I} (f^{-1}(A) \cap X_{ \alpha})[/math], which is a finite union of closed sets, and thus closed. Consequently, the preimage of closed sets is closed, and [math]f[/math] is a continuous map.
>what about the canonical part
No idea.

Maybe instead of the coproduct it's the disjoint union with the disjoint union topology? Then you could have a canonical map, I think.

>> No.11533524
File: 61 KB, 482x427, 1503412563162.jpg [View same] [iqdb] [saucenao] [google]

that looks like something we've done a while ago, i'll have a read to it once i get some sleep. cheers.

>> No.11533578
File: 15 KB, 153x177, yukari_hoho.png [View same] [iqdb] [saucenao] [google]

There's a simpler way. Since [math]\pi_\ast(X) \cong \times_\alpha \pi_\ast(X_\alpha) \cong \pi_\ast(\coprod_\alpha X_\alpha)[/math], by Whitehead's theorem [math]X \simeq \coprod_\alpha X_\alpha[/math]. In particular at degree [math]\ast = 0[/math] any map [math]f:X\rightarrow Y[/math] factors into a disjoint product of maps [math]f_\alpha:X_\alpha\rightarrow Y[/math], at least homotopically (since constant maps from [math]S^0[/math] into [math]X[/math] must stay constant in the connected component it lands in). Consider the identity [math]id:X\rightarrow X[/math], then it is homotopically a product of [math]id_\alpha:X_\alpha\rightarrow X[/math], but [math]\operatorname{im}id_\alpha = X_\alpha[/math] hence [math]id[/math] is homotopically a product of identities on [math]X_\alpha[/math]. Now since its homotopy inverse is [math]id[/math] and hence invertible in [math]{\bf Top}[/math], it is a homeomorphism.

>> No.11533581
File: 33 KB, 1600x864, COVID-19-NaivePredictions.png [View same] [iqdb] [saucenao] [google]

I'm trying to model the COVID-19 spread as a logistic curve.

At the moment I have a script that guesses how far we are along the logistic curve and draws it out based on that (for example, if we're halfway through the pandemic, then our peak will be at <current_n_cases> / 0.5). The script then does a binary search for the ratio that matches the best.

I have very little idea if what I'm doing is statistically sound. For example, Right now, my model says we peak at about 15M cases, but I'm not sure how much faith I should have. If I include some data from February, this number drops to like 4M (but again, should I be including data from two months ago?)
I know that you use R^2 as a statistical significance test in linear regression, but don't know how that applies to a logistic curve. Specifically, I'm not sure what my objective function should be.

Any and all help is appreciated.

>> No.11533598
File: 2.27 MB, 1334x750, X.png [View same] [iqdb] [saucenao] [google]

Beautiful, graceful, and masterful.
One of the best proofs I've ever seen.

>> No.11533654
File: 294 KB, 760x901, 1528115064543.jpg [View same] [iqdb] [saucenao] [google]

Bumping this.

I keep reading about other epidemics just "ending" (Encephalitis Lethargica, amongst others).
The fuck? How does that work? If it's replicating so effectively why would it just "end"?

>> No.11533750
File: 186 KB, 600x600, 6778.jpg [View same] [iqdb] [saucenao] [google]

I need a spanning set of the power set [math]\mathcal{P} \{ a,b,c \}, \ K=Z_2 [/math], please could you give me and example? I don't totally get it.

>> No.11533786
File: 2.62 MB, 2002x1438, yukari_pranked.png [View same] [iqdb] [saucenao] [google]

Note that for any group [math]G[/math], [math]P(G) \cong 2^G[/math] is the space of functions [math]G\rightarrow\mathbb{Z}_2[/math]; in other words, it is a group ring [math]\mathbb{Z}_2[G][/math]. Now we know that the complex group algebra [math]\mathbb{C}[G] = \widehat{G}[/math] is the Pontrjagyn dual, which is spanned by the space of complex irreducible characters [math]\chi[/math]. Define the map [math]\operatorname{det}:\mathbb{C} \rightarrow \mathbb{Z}_2: z\mapsto \operatorname{det}z = \operatorname{sgn}\operatorname{arg}z[/math], where [math]\operatorname{sgn}\theta = \begin{cases}1 &; \theta\in [0,\pi] \\ -1 &; \theta\in [\pi,2\pi]\end{cases}[/math], we can send [math]\mathbb{C}[G]\xrightarrow{\operatorname{det}} \mathbb{Z}_2[G][/math]. By projecting the space of characters [math]\{\chi\}\xrightarrow{\operatorname{det}} \{\chi\}_{\mathbb{Z}_2}[/math], we obtain a span of [math]\mathbb{Z}_2[G] \cong 2^G[/math]. For discrete Abelian [math]G[/math], we can find the [math]\chi[/math]'s by Fourier transform.

>> No.11533807

I'm sorry anon I'm a brainlet, could you please explain it in a more simple way? I started this linear algebra course but due to corona-chan we haven't have any virtual class yet, they just send us a pdf with theory and exercises, and they don't even properly explain what a power set is, I had to google it.

>> No.11533830

> Now we know that the complex group algebra [math]\mathbb{C}[G]=\widehat{G}[/math] is the Pontrjagyn dual
Is this true? I don't see why an element of the group ring would take its value in the unit circle.

>> No.11533846

Not for generic groups no.

>> No.11533870

I am not sure what you mean here by generic. Even for abelian (finite) groups I do not see how the statement is or can be true.

>> No.11533894

I meant that [math]\widehat{G}[/math] spans the ([math]L^2[/math]-completion) of the group algebra. Sorry I forgot a few words

>> No.11533910
File: 48 KB, 640x360, 1580834986374.jpg [View same] [iqdb] [saucenao] [google]

I don't know exactly what it is you're asking, but:
Let [math]x, y \in P \{ a, b, c \} = A [/math]. We set [math]x + y = x \Delta y[/math], their symmetric difference, and multiplication by [math]\mathbb{Z}^2[/math] is the unique one.
Up until now I've basically been guessing the vector space structure on [math]P \{ x, y , z \} [/math], so feel free to correct me if I got it wrong.
Now, if I've gotten everything right, [math]\{ \{a\} , \{ b \}, \{ c\} \}[/math] is a spanning set.
>inb4 anon why did you guess this specific vector space structure
[math]Hom _{Set} ( \{a, b, c\} , \mathbb{Z}^2 )[/math]

>> No.11533965
File: 15 KB, 898x104, NMT.png [View same] [iqdb] [saucenao] [google]

i'm reading an article by the USP about compounding. there's an abbreviation, "NMT", and i can't figure out what it stands for. in context i understand the meaning conveyed.

>> No.11533971
File: 498 KB, 700x689, __fujiwara_no_mokou_touhou_drawn_by_akagashi_hagane__6e11ba96f42a0469e8c1e52a94c1139e.png [View same] [iqdb] [saucenao] [google]

No more than, probably.

>> No.11533976

that sounds reasonable to me. i'll accept that.

>> No.11534044
File: 92 KB, 640x853, image0 (13).jpg [View same] [iqdb] [saucenao] [google]

Got this in revision.

If X varies directly as Y and inversely as Z and when X= 6, Y = 10 and Z = 15. Calculate Z when X = 92 and Y = 107

>> No.11534047

am brainlet with these problems

>> No.11534076

Is CS undergrad into grad school for math feasible?

>> No.11534192

What they mean by "trivial" here is an identity morphism, correct?

>> No.11534216

lol no. the opposite is, tho

>> No.11534468

>is there a general approach to do that?
Yes, there is a small side issue that the part of the domain where the Hessian fulfills the convexity property needs to be convex too.
But that should be the case anyway with your linear inequality constraints.

>> No.11534487

If you assume the total number of infected, then you can easily do a best fit line in logit space.

But that obviously doesn't answer the question. I think what you are doing is not feasible, since we are still growing basically exponentially, which means that you are trying to fit the exponential part of expit. There you run into scaling issues, since the exponential part really tells you nothing about *how far* you are in an epidemic.

>> No.11534558
File: 120 KB, 648x800, 783dac73602b4db969d9f618ff1e1975.jpg [View same] [iqdb] [saucenao] [google]

x proportional to y and inversely prop. to z means [math] x=k\frac{y}{z} [/math] with k being a constant of proportionality. [math] 6=k\frac{10}{15}\implies k=9 [/math]. So [math] 92=9\times\frac{107}{z}\implies z=963/92 [/math].
[math] v\approx\sqrt{2P/\rho} [/math]. Velocity, gauge pressure and density, respectively.
E definitely does increase as the plates are brought together (and voltage is maintained). Remember that Gauss's law only applies to closed surfaces.

>> No.11535156

what does it mean that a fourier transform is "one to one"?

>> No.11535191

There are no two functions with the same fourier transform, likewise no function is the inverse transform of more than one transformed function. That is, there is a unique relation between a function and its transform.

>> No.11535193

thank you anon

>> No.11535264

Can you approach breakdown condition in a dielectric inside a parallel plate capacitor by squeezing the plates together?
So my logic is that it is not possible since with Gauss' law we can infer that the electric field created by two parallel planes does not depend on the distance between them. Therefore pulling them close would just increase their capacitance but would not create a breakdown. Now this seems counter-intuitive, and I can't help but think that there is something I'm missing ...

Is my assumption right?

>> No.11535277

>What they mean by "trivial" here is an identity morphism, correct?
That's what trivial usually means.

Right, so there are Baesz lecture notes on the references at the end (actually, the only reference), and there he gives the definition "An (n,m)-category is an n-category all of whose j-morphisms for j > m are invertible."
He later gives another definition:
"Definition 8. An (n,m)-category is an [math]\infty[/math]-category such that
>All j-morphisms for j > n + 1 exist and are unique wherever possible. In particular, this implies that all parallel (n + 1)-morphisms are ‘equal’.
>All j-morphisms for j > m are invertible."

In conclusion, I don't get it. The first definition and the stackexchange one are clearly compatible (by making a passage from an n-category to an infinity-category by adding in all the identities), and you can make both definitions on the reference compatible by making an appropriate passage from an n-category to an infinity-category (adding in all j-morphisms for j>n+1), but I have genuinely no idea how Definition 8 and the nlab definitions are supposed to be the same.

>> No.11535317

when you want to check orthogonality between two vectors, when do you do just that by calculating the scalar product and when do you instead calculate their cross product?

>> No.11535328

You calculate the scalar product, correct.

>> No.11535338

but can't you calculate their cross product and if you get the null vector that would confirm they are orthogonal? if so, which method is preferred?

>> No.11535343

>but can't you calculate their cross product and if you get the null vector that would confirm they are orthogonal?
No anon, the cross product doesn't work like that.

>> No.11535353

I realized I was thinking about cross product returning the null vector, not if the vectors are orthogonal but if they are parallell. is confusing ok? uwu

>> No.11535358

>when do you do just that by calculating the scalar product

>when do you instead calculate their cross product?

>> No.11535375

>>when do you instead calculate their cross product?
Uuhhhmmmm akshyually, you can check for orthogonality by taking the length of the cross product and comparing it with the product of the lengths of 2 vectors. if they're the same, the vectors are orthogonal.

>> No.11535385

>checking if two vectors are parallel
Dividing the coordinates is easier in all but exceptional cases.

>> No.11535387
File: 304 KB, 1280x720, bchd.jpg [View same] [iqdb] [saucenao] [google]

Dedicated effort, actually.

Here's some Sunday afternoon and chill


>> No.11535420 [DELETED] 

Sup /sqt/, I am a mad scientist wannabe, and am thinking about methods in genetic engineering. I was thinking, what about creating so called "eigen viruses", so that to get DNA related information on a subject, you test how well it responds to these "eigen viruses", and use that information to develop things like biological weapons targeted to that subject? Would this work?

>> No.11535424

>if they're the same, the vectors are orthogonal.
Two vectors can be not-orthogonal and not-parallel.

>> No.11535461

>Gauss' law we can infer that the electric field created by two parallel planes does not depend on the distance between them
No, anon.

>> No.11535473

Read the post again, this time more carefully.

>> No.11535478

>dot product and orthogonality:
u, v are orthogonal if and only if their dot product is zero:
<u,v> = 0

>dot product and parallelism
u, v are parallel if and only if their dot product is equal to the product of their lengths (up to a sign):
|<u,v>| = |u|*|v|

>cross product and orthogonality
u,v are orthogonal if and only if the length of their cross product is equal to the product of their lengths:
|u×v| = |u|*|v|

>cross product and parallelism:
u,v are parallel if and only if their cross product is the zero vector:
u×v = 0

>> No.11535486

Okay. Thank you. I'm gonna read into how to model diseases more robustly.

Worst comes to worst I just fit a line on that shit and call it a day.

>> No.11535490

>Worst comes to worst I just fit a line on that shit and call it a day.
You can always fit an exp, that should currently work somewhat okay.

>> No.11535492

Oh sorry. I meant "Take the log of the data, fit a line to it."

>> No.11535575

yo bitches, why do we need both product and quotient rules? If x*y has some derivative, then x/y = x*y^-1 and product rule gets it

>> No.11535585

>yes, why, the quotient rule IS proved from the product rule

>> No.11535596

Because calculus is taught to snot-nosed high schoolers and college freshmen who have the mental capacity of a goldfish.

>> No.11535668

Both, as well as linearity and so on and so forth follow from the limit definition. A "Rule" like that isn't formally distinct as a logical concept anyway. After axioms and inference rules, which concern basic connectives, there's really only definitions and theorems.

>> No.11535761

>why do we need both product and quotient rules?
Because sometimes you want to calculate the derivative of a quotient, without deriving the quotient rule again.

>> No.11535880

is there any software or script to separate .pdf files by similarity of content? i've got too many files, it would be painful to sort them by scratch...

>> No.11535887

I'm having a brain shart right now and drawing a complete blank on a simple problem
[math]\sum _{n=1}^{\infty }\frac{\left(-1\right)^{2n+1}}{n}[/math]

how do I test this for convergence? The ratio test is inconclusive
for the alternating series test, every term in the associated sequence is less than the subsequent term and the limit is 0 which implies that it converges, but the series is divergent

>> No.11535892

>[math]\sum _{n=1}^{\infty }\frac{\left(-1\right)^{2n+1}}{n}[/math]
[eqn] \sum _{n=1}^{\infty }\frac{\left(-1\right)^{2n+1}}{n} [/eqn]

>> No.11535895

Lol ur a brainlet son

>> No.11535898
File: 288 KB, 758x564, S9.jpg [View same] [iqdb] [saucenao] [google]

[math](-1)^{2n+1}= (-1)[/math] for all integers [math]n[/math].
Now, does the harmonic series diverge or converge?

>> No.11535900

oh god fucking damn it I really am retarded

>> No.11535901


>> No.11535934
File: 286 KB, 759x413, z10.jpg [View same] [iqdb] [saucenao] [google]

Oh no.

>> No.11535935

Oh yes.

>> No.11535937

based anon for making this super clear without math autism
so the easiest way to check orthogonality is to check if the vectors' dot product is 0, and the easiest way to check parallelism is to check if their cross product is the null vector. gotcha.

>> No.11535940
File: 397 KB, 759x580, u17.jpg [View same] [iqdb] [saucenao] [google]

Oh no.

>> No.11536177

Is there a better notation for the parity of a completely inverted permutation? By that I mean, consider an ordered length [math]k[/math] word, i.e. [math]w = (1,2,\ldots,k)[/math]. Basically by definition it has even parity. Now I define the "completely inverted permutation" [math]\pi[/math] (I don't know if this has an "official term", I don't care so much if it does) as [eqn]\pi(w) = (k,k-1,\ldots,1).[/eqn] The parity of [math]\pi[/math] seems to be even if [math]k-1 = 0 \text{ or } 3 \text{ mod } 4[/math], and odd if [math]k-1 = 1 \text{ or } 2 \text{ mod } 4[/math]. Is there a way to express this behavior without defining the function via {cases}?

>> No.11536246

Thanks dude very helpful.

Eat shit.

>> No.11536291

just ignore him. he likes to use big words to stroke his ego, not to help you.

>> No.11536957 [DELETED] 

You can hide cases in the floor function, if you want:
[eqn]\sigma = (-1)^{\lfloor(k+2)/4\rfloor-\lfloor{k/2}\rfloor}[/eqn]

>> No.11536961

You can hide cases in the floor function, if you want:

>> No.11536980

fucking dammit
I'm not deleting my post again

>> No.11537122
File: 113 KB, 900x1200, __karasuma_fran_to_aru_majutsu_no_index_and_1_more_drawn_by_haimura_kiyotaka__b462fd76c85358dff20b66e7d15a2fd4.jpg [View same] [iqdb] [saucenao] [google]

>seems to be
The completely inverted permutation is given as the composition of all the transpositions of the form [math](m \quad k-m)[/math], where [math]m < k/2[/math], and m can be zero.
So the parity should be [math](-1)^{ \lfloor k/2 \rfloor }[/math], which seems to check out for 1, 2, 3, 4 and 5 when I manually computed them.

Although I wouldn't put five or six typos past me.

>> No.11537362

Does searching "yellowstone supervolcano" on google news always gives somewhat worrying results?

>> No.11537402

Can a single strip of polarizing film turn from completely transparent to completely opaque via some sort of electronic control? How miniaturized can an array of geometrical structures made out of such strips be?

>> No.11537448

I have no idea what you're trying to do, but it's wrong. His original answer is correct.
Every pair of elements is an inversion; the sign is [math](-1)^{n \choose 2}[/math], which is even exactly when either n or n-1 is divisible by 4.

>> No.11537698

He probably though I was asking for a more complex stuff.
Thanks anon! I actually though in that one at first but as I said I feel pretty lost so I supposed I was wrong.

>> No.11537728

Is substituting sin(x) ~= x (and vice versa) a valid technique to use?

Like if I have some function of x, and I suspect it's a really big sine function, can I just hotswap in something ridiculous like [math]x=10^9*sin(\frac{x}{10^9})[/math]?

>> No.11537739

>the easiest way to check parallelism is to check if their cross product is the null vector
No, that's the hardest way to check parallelism
The easiest way to check parallelism is to divide componentwise and see if you get the same number for each entry.

>> No.11537743

>Is substituting sin(x) ~= x (and vice versa) a valid technique to use?
As long as you know x=0, yes. Otherwise, no.

>> No.11537755

He's a mentally ill homosexual manlet with an inferiority complex, he didn't think you were trying to ask anything its just an opportunity to perform for an audience.

>> No.11537860

btw [math] \mathbb{Z}_2 [/math] aren't all the integers with modulo 2?

>> No.11537871

Yes, it's called small angle approximation

>> No.11537874

in america's colleges does having a 4.0 gpa mean you score perfectly in every single test? how do people even manage that

>> No.11537901

No it means you're black.

>> No.11537927

Oh shit yeah, this is exactly it. I remember now; you can also express it as something like [math]\sqrt{2}\cos(-\pi/4+n\pi/2)[/math]. Thanks a ton.

>> No.11537932

Yeah, no, he understands perfectly well what level of complexity you're at. He's fully aware that his "answer" was completely useless to literally anyone. He's just an ass.

>> No.11537939

i dont understand

>> No.11538146

I could literally never memorise a fucking thing in so I did rederive it every time.

>> No.11538159

did you also rederive product rule every time ?

>> No.11538165

>the easiest way to check parallelism is to check if their cross product is the null vector.
the easiest way is to divide coordinates:

u1 / v1
u2 / v2
u3 / v3

these need to be the same number.

usually you can tell if two vectors are parallel just by not being retarded and looking at their coordinates for a few seconds. if it's not immediate, then the coordinates probably include ugly fractions and square roots, in that case computing the cross product would be tedious as fuck anyway.

and also cross product works only in dimension 3.

>> No.11538167
File: 176 KB, 462x582, __fujiwara_no_mokou_touhou_drawn_by_shangguan_feiying__64ff7b01ecddc076fbf6aa8d31819d78.jpg [View same] [iqdb] [saucenao] [google]

Typo: [math](m+1 \quad k-m)[/math]
>I have no idea what you're trying to do
I'm decomposing the permutation as a product of transpositions and counting the transpositions to obtain the parity.
>His original answer is correct.
His original answer coincides with my formula, anon. [math](-1)^{ \lfloor (4n+m)/2 \rfloor} =(-1)^{ \lfloor 2n + m/2 \rfloor } = (-1)^{2n + \lfloor m/2 \rfloor } = (-1)^{ \lfloor m/2 \rfloor }[/math], which lets you see the four period explicitly.
Yeah, I made a typo with [math]\mathbb{Z}^2[/math]
>Yeah, no, he understands perfectly well what level of complexity you're at.
To be entirely honest, I had no idea what the fuck anon was asking until he mentioned linear algebra a couple posts later, and even then half of my post was literally guessing what he meant.

>> No.11538208

Can I use statistics to solve some of my problems in life?

>> No.11538217
File: 4 KB, 400x353, Untitled-1 copy.png [View same] [iqdb] [saucenao] [google]

Could someone find me the area of this shape? Thank you

>> No.11538222

You can use Bayes' theorem (or at least the idea behind it) in many real life situations. For example, when you ask someone how you look, you should not expect them to give the right answer because the probability that they'll compliment you given that you look bad is very high.

>> No.11538293

Two triangles + one rectangle...

>> No.11538295

I can't do maths man.

>> No.11538315

Me neither, but without you giving us precise measurements of the rectangle its basically impossible to calculate anything at all

>> No.11538318

in pixels.

>> No.11538328

if a number that can be all numbers but only one at a time is called a variable, what is a number that can be any number at the same time called?
i'm an ESL foreign student so i might have misunderstood something

>> No.11538332

can you give an example of what you consider "variable" and what you consider the second thing ?

>> No.11538358


If you want to check it, here is my python script
import numpy as np
from PIL import Image
im = Image.open("a.png")
p = np.array(im)

>> No.11538380

Thanks a lot.

>> No.11538533
File: 1 KB, 125x110, 1586172774427s.jpg [View same] [iqdb] [saucenao] [google]

it's the full rectangle minus the 4 small triangles

so (g-r)*b

where g, r and b are the pixels along the green, red and blue line in the picture

>> No.11538546

Give me more examples please.

>> No.11538561

No. It means you got an A in every class. The grade of a class is not just the final exam. Some classes have midterm exams. Some classes grade the problem sets. Some classes have papers.
The grades in a particular class are all averaged for the final class grade (with appropriate waitings). So to get an A in every class, you need to do very well on MULTIPLE exams per class and on weekly problem sets, but you also have a bit more leeway in that if you fuck up on a few things on one exam, but perform well enough on everything else, you can offset that. And it isn't as though you need to be perfect. At my school, getting a 93 or above grade in a class is a 4.0 (so A or A+). I've certainly gotten 80s and 85s on a few exams, but then I do well on everything else and a single bad day doesn't impact me so much.
People like to laugh at the American system but it really makes a lot more sense than just a single, uncurved final exam.

>> No.11538586
File: 2 KB, 142x79, roots.png [View same] [iqdb] [saucenao] [google]

Is it possible to remove irrationality from denominator in pic rel?
Because it's possible in the case of [math]\dfrac{1}{\sqrt{2}}[/math], [math]\dfrac{1}{1+\sqrt{2}}[/math] and [math]\dfrac{1}{1+\sqrt{2}+\sqrt{3}}[/math]

But with 3 roots it's a lot harder, or maybe even impossible. Is it possible?

>> No.11538602

Removing irrationality is always possible.
Q[sqrt(2), sqrt(3), sqrt(5)] is a Galois extension of Q of degree 2^3 = 8.
In every algebraic extension K of Q, there exists a norm N_K/Q(x) for every element of x.
To define it, you take all the embeddings of K into the complex numbers C, apply them at x and multiply them together.
For example, in the case of Q[sqrt(2)] the embeddings are the identity and
a+bsqrt(2) -> a- bsqrt(2)
In the case of Q[sqrt(2), sqrt(3), sqrt(5) ] there are 8 embeddings. Multiply them together and you'll get a number of the form
P(sqrt(5), sqrt(2), sqrt(3)) where P is a polynomial with rational coefficients.

>> No.11538612

Thank you

>> No.11538946

Does a researcher earn money for a particular citation? Like a paid premium per citation?

>> No.11539365

I need to use the method of undetermined coefficients to solve y''' - 4y' = t + 3cos(t) + e^(-2t).
I'm not sure where to start since all the examples I've seen start out in the form (polynomial)*e^(at)*sin(bt), any tips?

>> No.11539501

Why is everyone on (math) stack exchange such an insufferable, pedantic cunt?

>> No.11539714

how much energy do we get from food? Say I eat a standard apple. I know about calories and such but do we get 100% of the available calories from food we eat?

>> No.11539851

No. But if you have more citations, you can get funding more easily. Of course it is relative w.r.t each field.
For example, in niche theoretical math area, 100 citations for a paper means a lot. Meanwhile in machine learning, it should be around a few hundreds to a thousand.

>> No.11539857

It varies from person to person. What you can do is keeping track of all the calories and weigh your body in the morning.

>> No.11539868
File: 24 KB, 875x100, Screenshot 2020-04-06 at 6.09.51 PM.png [View same] [iqdb] [saucenao] [google]

I don't have any idea about this question. Any help?

>> No.11539875

Are Michel van Biezen's engineering lecture videos reliable?

>> No.11539901

>do we get 100% of the available calories from food we eat?
No one's digestive system is 100% efficient (2nd law of thermodynamics). I do not believe there is a clear answer on specifically how efficient the digestive system is on average because of how many extraneous factors there would be (type of food, time of day, person, health of person, etc).

>> No.11540042

I'll take a different approach this time and just list out the results and constructions that should be useful to formally doing the thing.
If [math]A = \prod _{i=1} ^n A_i[/math], there are canonical maps [math]i_{A_j}: A_j \rightarrow A[/math] given by [math]i_{A_j} (x) = (0, \cdots, 0, a, 0, \cdots, 0)[/math], where the [math]a[/math] is in the [math]j[/math]-th coordinate, and the map is a group homomorphism. There is also a projection map [math]p_{A_j} : A \rightarrow A_j[/math] defined by [math]p_{A_j} (a_1, a_2, \cdots, a_j, \cdots, a_n) = a_j[/math].
There's an isomorphism [math](G \times H) \times J \cong G \times (H \times J)[/math], and it generalizes the way you'd expect.
If we have [math]G= A \times B[/math], then [math]ker ~ p_B = im ~ i_A[/math], which you can combine with the homomorphism theorem for [math]G / im ~ i_A \cong B[/math].

>> No.11540047

Typo, should be [math]i_{A_j} (a) = (0, \cdots, 0, a, 0, \cdots, 0)[/math]

>> No.11540161
File: 365 KB, 1721x1786, gabriela-dea-julia-disguise.jpg [View same] [iqdb] [saucenao] [google]

>Consider a rectangle limited by y = 2 and x = π. What is the area between the function y = 1 + cos(x) and the line y = 2?

>> No.11540166

How do you actually build logic gates within a circuit? They are not electrical components by themselves, so how do you get a circuit to perform a NAND operation, for example?

>> No.11540209

2pi - pi - sin(pi)
pi - sin(pi)?

>> No.11540212
File: 1 KB, 66x160, 88.png [View same] [iqdb] [saucenao] [google]

Fuck, I just realized I attached the wrong picture. These are the options:

>> No.11540222

so just pi

>> No.11540266
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look up diode logic
AND and OR are the simplest I think

>> No.11540315
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stuck on this basic ass mechanics question
in pic related, what are the relevant reaction forces at A? obv along the z axis, but what else? are there any relevant reactions at B and C? how would you set up the equations to solve for the normal forces?

>> No.11540369
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Got a combinatorics question that should be straightforward but I fucking suck with combinatorics. I'm thinking about drawing various combinations from the set [math][n] := \{ 1, \ldots, n \}[/math]. Fix some [math]\ell[/math]-length combination [math]t \subset [n][/math], i.e. [math]|t| = \ell[/math] for [math]1 \leq \ell \leq n[/math]. Now consider the set of all [math]m[/math]-length combinations, [eqn]S_m := \{ s \subset [n] \mid |s| = m \}.[/eqn] There are [math]\binom{n}{m}[/math] element in each [math]S_m[/math].

My question is: for how many elements of [math]S_m[/math] does [math]t[/math] have an odd number of overlaps? That is, for how many [math]s \in S_m[/math] is it true that [math]|s \cap t| = 1 \text{ mod } 2[/math]? (Equivalently, one could calculate it [math]0 \text{ mod } 2[/math]. and subtract that answer from [math]\binom{n}{m}[/math].) Keep in mind that [math]|t| = \ell[/math] and [math]m[/math] and [math]\ell[/math] are completely independent of each other.

Even just a potentially useful combinatoric method to attack this problem would be much appreciated.

>> No.11540402

Okay, upon testing with small numbers, it seems the answer is highly dependent on the actual choice of [math]t[/math]. The fact that it's length [math]\ell[/math] isn't enough information. Fuck me.

>> No.11540419
File: 110 KB, 650x800, cb6d9408dc1bf0780a06038a33032c7c.jpg [View same] [iqdb] [saucenao] [google]

Basically just consider the forces on point G. There are four forces: There is weight, whose direction and magnitude are known; then there are the reactions from A, B, C, and whose directions are all known (along the supports), you just need to find magnitude. Sum the four force vectors together, and you get a system of three equations for the three coordinates with three unknowns (two unknowns, if you consider symmetry).

>> No.11540438

Why should it depend on the choice of t? You're not using any order properties of the naturals here, wouldn't you just be able to relabel any t to match any other?

>> No.11540453

Whats the difference between an exosome and a virus?

>> No.11540467
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Seconding the other anon, the exact t is irrelevant.
The obvious method is the good old split it up, so that [math]s = (s \cap t) \cup (s \cap ([n]-t))= a \cup b[/math], where [math]|a| = 1 \mod 2[/math]. So it's now two classical combinatorics problems, sum along odd k smaller than l, choose k out of l times choose m-k out of n-l.
I'll tell you if I come up with anything better. Probably won't.

>> No.11540470
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Heres a couple very stupid questions:

1)is this a tree (if so is it a binary tree?
2) why or why not?

>> No.11540489

Yes, every unary tree (list) is trivially a binary tree.

>> No.11540517

Recall the definition of a tree:
A graph is a tree if it is nontrivial and contains 0 cycles. A binary tree consists of a tree for which each vertex has at most 2 children. The graph you presented meets all those criterion.

>> No.11540560
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Write down the auxiliary equation to get the homogeneous solution: [math] y_h=k_1e^{-2t}+k_2e^{2t}+k_3 [/math]. For the particular solution, I just guessed that it had a form of [math] y_p=At^4+Bt^3+Ct^2+Dt+F\sin t+Gte^{-2t} [/math] (don't worry about the constant term, it will just get absorbed into k3 anyway). Now you just compute the third derivative of the particular solution form, subtract four times the first derivative, and solve for the variables by looking at the RHS of the ODE. You should get [math] y_p=-(1/8)t^2-(3/5)\sin t+(1/8)te^{-2t} [/math]. Finally, [math] y=y_h+y_p [/math].
I didn't recognize the name, but I looked him up and I've seen a couple videos before. There isn't any reason I can imagine that they aren't okay.

>> No.11540614

what is the intuition behind the product rule? I get the proof, but what is the geometric intuition?

>> No.11540620
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>> No.11540622

Not the product rule idiot

>> No.11540623
File: 1.74 MB, 2953x1924, LCD_4_0-13.png [View same] [iqdb] [saucenao] [google]

I don't know of any, but I'm willing to bet it's an active field of research.
Liquid crystals would be a good place to start, since they're a milder version of what you're describing. Whether it's "completely" opaque/transparent is subjective

>> No.11540624

Not the product rule idiot

>> No.11540745

biochem sucks ass, is there a sort of chart for all net amounts of products and intermediates and etc for all major pathways. something that can help answer such quesitions like, "how may moles of NADH are produced from 1 mole of glucose in glycolysis" ( i know its 2 but like for other products and pathways?)

>> No.11540780

I wonder if I should write this pop maths self help book.

>> No.11540819


>> No.11541208

why is the product of two vectors a scalar?