/sci/ - Science & Math

Fun for the entire family, this time.

Unanswered questions from the previous thread:

Maths questions:
>>11689319 elaborated on >>11689347
>>11689566 (shoddily answered in /mg/)
>>11690264
>>11692477
>>11693142
>>11699137 , with addendum >>11699245
>>11699228
>>11702395
>>11703948
>>11706537
>>11710948

Physics questions:
>>11698334
>>11703642
>>11703943
>>11706489
>>11710093
>>11710249
>>11710294
>>11716016
>>11712251
>>11719539

Chemistry questions:
>>11701206
>>11717075
>>11720592

CS questions:
>>11690218
>>11697036

Stupid questions:
>>11689640
>>11692629
>>11697943
>>11701493
>>11702565
>>11706428

Can two square matrices AB = -BA? How would you prove such a question besides from brute-force?

>>11726295
https://math.stackexchange.com/questions/1649212/anticommuting-matrices-and-their-eigenvalues

>>11726295
sure, for example A = B = 0

>>11726219
Hi OP. Just wanted to thank you for all the resources. Have a nice day.

>>11726219
Is it retarded to start learning Physics II because I became interested in entropy after watching Madoka Magica yesterday?

>>11726532
FUCK, I'VE LITERALLY JUST REALIZED THAT FURRYPOSTER DIDN'T UPDATE THE SHITTY CHARTS LINK
https://imgur.com/a/TpiinBE
>>11726542
Nah.

can someone explain to me again or in more detail as to why we say electrons pop in and out of existence. To me, intuitively, it seems to be something like my beautiful drawing. the red point moving fast enough (or faster) around the black point so that it looks like a circle. The only way to determine where it is is by taking a snapshot, the location will always seem random, so you say for example: the red circle has a probabilty of 50% of being above the blue line. I dont think electrons are actually points orbitting a point i'm just using it to illustrate a idk.. limiting factor in measuring things maybe.

>>11726609

>>11726219
Why do I keep getting the wrong results on this truss :(

>>11726248
>>>11703943
I solved that one

>>11727037
whats F1? what the fuck am I looking at, is the right picture the correct solution? Did you calculate the length of the trusses or were those given?

I have never worked with word problem like this before so please no bully the sped.

Is DARTS just deep learning phrased otherwise?

>>11726295
Pauli matrices and their many generalizations
Literally any matrix representation of fermionic operator algebras or Clifford algebras
More generally, Jordan algebras

>>11727083
the amount of smokers have dropped from 23,3 to 19,3% or 23,3 - 19,3 = 4%, the time it took to drop 4% was 2010 - 2000 = 10 years. in a function you input (x) something, it goes trough the calculations and out comes the output (y). So in this case we want to find out how many people smoke when we enter any amount of years.. I guess I would call the function P(t), now functions have a basic form of Y = AX + B, where A is Δy / Δx or in other words how much the Y changes / how much the X changes, or in other words y2 - y1 / x2 - x1 (in your example (19,3 - 23,3) / (2010 - 2000) = - 4/10 = -2/5 ). B is the value you start at (so 23,3 at 2000). this makes sense because every year that passes your initial value gets smaller (this is why the A is negative).
So in your case I think the answer would be P(t) = -2/5t + 23.3

>>11727172
Thank you so much for going over this. I actually got every piece of data right including which roles the x and y were in general. I just missed the +23.3 bit at the end of the final answer but I'll get that down right now though. I was completely overthinking this and confused myself when I was inches away from the answer. So once again yeah thank you for taking the time to go over it too.

>>11727317
np man, i'm just glad it actually helped and that you took the time to reply that it did lol. Often my answers just dissapear into the void :')

>>11727368
Well, sorry for the late reply then man. I would hate to just drop a question and run without saying anything when the answer came around. I had wanted to go back over my other problems one last time. Now, I can go on knowing everything is correct with your help anon. You rock and deserve more responses!

Can anyone recommend a book/video/website on the history of computer science?

>>11727075
F1 is the left most vertical force I forgot to write F1

>>11727075
and yes the right one should be correct it is what I got from skyciv but beats me how they got some of those results

I have a yellow rocket that can accelerate to 50% the speed of light. My friend has a green rocket that can also accelerate to 50% the speed of light. If we both get in our rockets and take off on complete opposite directions, how fast is the green rocket receding away from me?

>>11727446
>>11727037
Could be arsed to scan or read your work, but obv you did something wrong.

>>11727619
[eqn] u=\frac{v+u'}{1+vu'/c^2} [/eqn]
The absolute velocity of green is u = -c/2. The absolute velocity of the yellow rocket is v = c/2. Solve for relative velocity and [math] u'=-4c/5 [/math]. So you observe your friend moving four-fifths the speed of light in the negative x direction.

>>11727416
>history of computer science
Depending on the author you'll get completely different stories.
Choose the one that will make it the easiest to get along with the people around you.
If you are British, you probably don't want to hear about Zuse.
If you are German, you probably don't want to hear about Babbage.
If you are a feminist, no one except for Lovelace matters.

I'm in my first year of physics and I asked myself, what level do I need to start Understanding shit like this?
https://authors.library.caltech.edu/3523/1/FEYpr49c.pdf
I'm getting kinda sad and unmotivated to be real.

>>11727636
wtf that looks so neat, very nice anon, I was almost done myself but your post is literally teacher tier

>>11724090
>that are untestable but also unfalsifiable
It seems very likely that if space isn't discrete, then the universe would be strictly more powerful than a Turing machine, which appears extremely unlikely considering nothing like that has been observed in human history.
So it's at the very least falsifiable. Although in a similar sense as that entire [math]P \neq NP[/math] mess.

>>11727766
maybe i should ditch the square raster and go with blank pages for my note/workbooks

>>11727764
First of all, the article starts out by referring to a previous one, so perhaps that would be a better place to start.

Then, most papers i've worked with could be adequately understood by a person with an undergraduate degree, which is 3 or 4 years. Of course you can start reading papers relating to your narrower field earlier.

But really, you shouldn't be reading old papers like this, especially fundamental ones imo (if you're learning physics and not the history thereof) . Reason being, the material at hand is better understood (by the author or not) by the time it is rendered in form of textbooks, and also that books are written with the express goal of educating, as opposed to presenting the results to specialists.

>>11727874
So i'm at the valley of despair rn?

>>11727955
who knows. certainly not me

>>11727636
Thanks... ehh I best stop using angles

Yes serious question here that I still haven't got an answer to.

Once a deep learning model completes its goal. How is it saved exactly?

>>11727764
Freshman physics -> analytical mechanics -> electrodynamics -> quantum mechanics -> particle physics

>>11728085
>Once a deep learning model completes its goal. How is it saved exactly?
Write biases and weight matrices to a file.
You can also add information about the net itself to it, to easily reconstruct it...

how do I limit the number of meshes in Ansys?

I don't get cylindrical parametrizations /sci/.

How do I determine the volume in [math]\mathbb R^3[/math] of the region bounded from below by the paraboloid [math]z = x^2 + y^2[/math] and from above by the plane [math]z = 2x[/math]? I get that the paraboloid can be parametrized by [math]\{(\rho, \theta, z) \mid 0 \leq \rho < \infty, 0 \leq \theta \leq 2\pi, 0 \leq z \leq \rho^2\}[/math], but I'm not sure how to cast the plane to this coordinate system, or how to determine the integration boundaries in general.

>>11729976
> but I'm not sure how to cast the plane to this coordinate system,
x=ρ.cos(θ), so z=2x => z=2ρ.cos(θ) is the implicit form or (ρ,θ,2ρ.cos(θ)) is the parametric form. Similarly, z=x^2+y^2 becomes z=ρ^2. The intersection is ρ^2=2ρ.cos(θ) => ρ=2.cos(θ); substituting into z=2ρ.cos(θ) => z=4*cos^2(θ) => 0<=z<=4.

do you guys have any tips or tricks for taking very important exams?
other than studying of course, just anything that gives you some advantage

>>11730283
take a fat shot of whisky before you leave for your exam
there is a certain sweet spot where alcohol will essentially completely kill your nerves without reaching the point where it's actually impairing

>>11730295
not sure this is a good idea, it could very well be impairing you without you realizing

>>11730310
you ought to know where your personal threshold for drunk is. it's basically part of being an adult.
obviously swigging back a bunch of booze for the very first time before your MCAT is not a brilliant plan

>>11730283
Looking into exams from the previous years is a massive help.
The faculty-tier student groups usually have those available in some way or the other.

>>11730316
as I said, just because you feel better it doesn't mean you're performing better
it's very difficult to determine how it's affecting your performance, that's why in science you have studies with hundreds of participants, blinding, etc
you have no idea how much processing in your brain is subconcious, alcohol could very well be interfering with thinking processes
>>11730325
yeah but that's what I classify as studying
I meant stuff more like pulling yourself from a problem when you can't see the next steps or something about managing your time, etc

>>11730333
>it's very difficult to determine how it's affecting your performance
it's not difficult at all to tell how it's affecting your performance. you get explicit concrete feedback on how you performed on an exam

>>11730340
>n=1, no control group, no blinding
yeah bro concrete feedback lol

>>11730345
>try it? nah bro how will I know it works just by seeing if it works or not I need a double-blind peer-reviewed study on a sample of at least 300 randomly selected students to tell me what to think

how do I deal with complex eigenvalues when using the QR algorithm?

>>11730355
dude, you're saying that your performance immediatelly tells you if the alcohol had a positive impact
are you not aware of how retarded you are? are you no aware of the fact that just because you performed well, doesn't mean alcohol had a positive effect on your performance?
why do I even have to explain it to you for the third time now? you have no way of determining the effect in this scenario, period.
don't go full retard next time

>>11730361
dude, you're saying that your performance immediatelly tells you if studying had a positive impact
are you not aware of how retarded you are? are you no aware of the fact that just because you performed well, doesn't mean studying had a positive effect on your performance?
why do I even have to explain it to you for the third time now? you have no way of determining the effect in this scenario, period.
don't go full retard next time

>>11730364
>goes full retard again despite asking him not to
lmao

>>11730359
REEEE
HOW DO I CALCULATE OCMPLEX EIGENVALUES

>>11730090
Thanks! Also, should I really let theta take on all values? Geometrically it seems like I should restrict it to [math]-\pi/2, \pi/2[/math] but I'd love some validation on this

I fusion just a meme?

stupid linear algebra question mostly about terminology

{1, x} is a basis for a subspace of all continuous functions
{x, x^2} is also a basis for a different subspace of all continuous functions

are these bases connected by a linear transformation?

you can just use the 2x2 identity matrix and declare that its domain is relative to {1, x} and declare that its range is relative to {x, x^2} and now you used a linear tranformation to go from one to the other, but I'm not sure if this counts as being "connected". the problem also says to find the "transition matrix", but I've only seen "transition matrix" used in the context of two bases that span the same space, not when they span two different spaces, which is partly why i'm doubting myself. textbook has no examples of questions like this.

>>11730359
You do not.
Where would complex EVs pop up?
https://en.wikipedia.org/wiki/QR_decomposition

>>11730504
I thought they might form a "square" on the diagonal similiar to how they behave in the jordan normal form

Why is the average value of a function defined by using an integral? I get that the integral is analogous to the discrete case by summing up all the constituent pieces, but we are not just adding the value of the function, we are also multiplying it by a small width so it's not the actual value of the function. I am just curious how we build the bridge from the discrete case to the continuous case and how the average area underneath the function relates to the average of the function itself.

>>11730616
I guess there are two ways you could think about it. Geometrically, if you draw a rectangle with base (b-a) and height the average value of the function, it will have the same area as the area under the function's graph. This is intuitively consistent with the idea of an average, e.g. if you travelled 100km in 1 hour, your average speed ought to be 100km/hour.

It also really is almost completely analogous to the discrete case.
If you want to compute a "continuous" average of a function, a natural place to start would be to take a discrete average and then see if you can take a limit. If you try averaging n equally spaced points in (a,b), then the average will be [math]\sum_{k = 1}^{n}f(a+k*\frac{b-a}{n})*\frac{1}{n}[/math] . This is just a Riemann sum that's been divided by a constant (b-a), so when you take the limit of the average of n points, what you will get is the integral divided by (b-a).

>>11730434
It should be restricted. ρ=2.cos(θ), so ρ>0 => cos(θ)>0 => -π/2<=θ<=π/2. That's assuming that you're integrating w.r.t. dρ dθ, i.e. the bounds for ρ depend upon θ. If you're doing it the other way around, then you have θ=arccos(ρ/2), i.e. the bounds for θ are -arccos(ρ/2)<=θ<=arccos(ρ/2).

It may help to note that in the X-Y plane the intersection is a circle of radius 1, centred on (1,0).

The integration bounds depend upon the order of integration. If you're using polar coordinates, you normally choose the order of integration based upon what you can actually integrate (i.e. which expressions have closed-form antiderivatives). The innermost term is ρ.f(ρ,θ,z); depending upon f, that may have a closed form anti-derivative w.r.t. some of {ρ,θ,z} but not others. Different integrating variables give different antiderivatives, and you need something which can be integrated w.r.t. the next variable, and so on.

If you're just trying to find the volume, it's likely to be simpler in Cartesian coordinates (the volume is π/2).

which one did i get wrong and why?

How important is Mars as a stepping stone for humanity to achieve interstellar expansion?
Should somebody be able to destroy the planet, would we be bound to Earth forever? If so: what would it take to destroy Mars?

>>11731288
Thank you so much anon. You've helped me a great deal.

>>11731417
not as important as the annihilation of all jewish life

>>11731417
>what would it take to destroy Mars?
Settling on it would be a good start.
Then it's only a question of time.

Is the Axis Of Evil really a big deal? What could it mean for cosmology?
Is Copernicus just a faggot?

Help me, I'm retarded

This is going to sound kind of cringe, but are there any math shirts with non-trivial math/physics on it? Trying to buy a gift for someone that's a fellow math major.

>>11732219
get a plain white shirt, and put pic related on the titty pocket

i have no idea where to ask this, so this is my best bet.

any good sources on sound generation (DSP)? going very fancy, into digital instrument creation. is this very difficult?

My friend (who's basically a theoretical quantum physicist) told me that black holes are the result of the universe trying to divide by zero. If this is the case, what prevents a black hole from forming when I try to divide by zero on a calculator? Do calculators have built-in mechanisms to suppress or prevent the formation of black holes, or is the process itself somehow different from when the universe does it?

>>11732219

>>11730515
>I thought they might form a "square" on the diagonal
Why?

>similiar to how they behave in the jordan normal form
The QR decomposition isn't the Jordan normal form.
Literally look at the algorithm, if you could calculate the EVs with that it would be an enormous discovery.

>>11732956
>My friend (who's basically a theoretical quantum physicist) told me that black holes are the result of the universe trying to divide by zero.
That is a very inaccurate description.
More accurate is something like, black holes form where our mathematical models about the universe lead to division by zero.
The universe does not think and it does not calculate and it does not understand mathematics.

>If this is the case, what prevents a black hole from forming when I try to divide by zero on a calculator?
A calculator can not divide by zero, it recognizes a mathematical error and tells it to the user.
It's just circuitry doing things, you can try to calculate by zero on a piece of paper, how could that possibly lead to a black hole?

>>11731417
>Should somebody be able to destroy the planet
Then they are also capable and willing to annihilate all human life.

I sprayed some of this stuff on the carpet of the room like a retard to clean up a roach I killed. I wiped it up after with a wet towel but
now I am having a panic attack thinking I am going to chlorine gas myself when I go to bed tonight.

Someone please just tell me I'm a hypochondriac retard and nothing is actually going to happen so I can go to bed and sleep.

>>11733243
I called poison control and they told me there was nothing to worry about. So now I will go to bed and try tomorrow to not be stupid.

>>11733061
you know you can calculate real EV with repeated QR decomposition right?
https://en.wikipedia.org/wiki/QR_algorithm

>Why?
Just a guess because everywhere I looked it didnt say anything about the QR Algorithm not being able to calculate complex EV

How do I calculate the sum of coefficients of odd powers of x's of the following polynomial?
[math]Q(x) = \left ( 7x^{3} - 5x^{2} -2x +8 \right )^{5}[/math]

>>11734204
nvm, figured it out

>>11734204
Subtitute 1 and -1, subtract them, then divide by 2

>>11726219
Have I solved this centroid correctly or did I get it wrong

Also does anybody know some free online software to do the calculations?

>>11734361
How do you get x=7+2/3 for a triangle which ranges between x=5 and x=7?

>>11734361
Also: A4 isn't a quadrant; the right-hand edge is at atan(20/2). FWIW, I get x=3.17, y=14.27.

how do I stop making arithmetic errors on exams?
I understand the material well, I know how to solve problems but they always require many arithmetic operations and I'm like 50% likely to make an arithmetic error somewhere which instantly fails my solution
this problem has been ruining my grades forever, pls help

>>11726219
Can you find the center of a polygon by breaking it down into triangles? For example, you can find the center of a triangle by bisecting the angles. So for pic-related, you could find the center of those three triangles using this method.
Then, if you connected those centers, you would have a new triangle. Would the center of that new triangle also be the center of the pentagon?

>>11734888
and I guess by "center" I mean "incenter". And alternatively could you simply bisect all 5 angles? Would that work?

since rust is oxidation can you reverse rusting with electricity?

How to make sense of an equation given in spherical coordinates? E.g. [math]r = 1 + \cos \varphi[/math] (where [math]\varphi[/math] is the azimuthal angle which ranges from [math]0[/math] to [math]\pi[/math]). I can't figure out how to approach this i.e. how to plot it (ultimately my goal is to calculate the volume of the solid defined by this curve, but first I'd like to gain some basic understanding of what it looks like).

i'm having trouble with this assignment. what i have right now is:
[math]S_{1(x)} = -\frac{1}{x}\sum_{n=0}^{\infty} \frac{(-x)^{n}}{n!}[/math]
and i'm supposed to get this:
[math]S_{2(x)} = \int_0^x S_{1(x)}dx = -\frac{1}{x}(e^{-x}-1+x)[/math]
now i know that
[math]\sum_{n=0}^{\infty} \frac{(x)^{n}}{n!} = e^x[/math]
but i dont understand how they got the second part

>>11735111
well, how do you go about making sense of an equation in cartesian coordinates ? it's not really trivial

>>11735314
Except that I *am* accustomed to cartesian coordinates. I can easily visualize and plot a sketch of the graphs of many cartesian expressions, like [math]y = \exp(-x^2)[/math] or [math]y = \tan (x - \pi / 2)[/math].

On the other hand, I'm completely dumbfounded by [math]r = 1 + \cos \varphi[/math].

>>11734646
Write clearly and in an organized fashion on the page. Stay in straight lines, move in a linear fashion along and down the page. If you have to do multiple chunks of a problem, break your page into separate boxes. If your handwriting is very bad, write slower until it's less bad.
On a related note, slow the fuck down. Really try to go at like 75% or 80% of the speed you want to be going. Most dropped minus signs occur because people are writing too fast, not paying attention to what they're writing because they're rushing to the next step of the problem.
Don't do things in your head. Even bonehead simple steps. This is where "why the fuck did I think 5-3 = 3?" errors come from. It's hard to write this down on the page and not notice it, but it's very easy to let it slip through when you do 3 mental calculations and then write out the final result of them.

>>11734534
I counted in the total distance from the source, yes the right triangle is 2m wide but I think I have to factor in the offset from the source 0,0 which means which means it should have been +5 not +7 fuck i fucked up

How do you calculate the level curves of f(x,y) = ln(x-y)/(x-y)

Did I do this right? The question is: If sin(pi/9) = cos a and a is acute, what is the radian measure of a?
sin(pi/9) = cos a
cos a = sin((pi/2) - a)
(pi/2) - a = pi/9
a = (pi/2) - (pi/9)
a = (7pi)/18
I asked on another site (reddit), and I was told the answer was (8pi)/9

>>11737487
8pi/9 is 160 degrees
it's not even acute

>>11737559
Yeah, right? And when I said I got a different answer, they downvoted me!

Is there a generally accepted value for [math]p(x \in \mathbb{N}|x \in \mathbb{R})[/math]?

At first glance feels like a case similar to [math]0^0[/math].

>Let us take an angle whose radian measure is 1. Using the picture below, prove that its degree-measure is less than 60°.
How would I do this?

>>11741017
The radian measure of an an angle is the length of the arc that subtends it on the unit circle.
If you set the radius to be 1 in your diagram you can conclude that an angle of 60 degrees is subtended by an arc larger than 1.

>>11735229
Doesn't look right to me. Are you sure you didn't miss/mess anything?

>>11739179
Well, since all natural numbers are in the reals, I believe the question would be similar to asking the probability of (uniformly) picking a natural number over itself. I believe the answer is that you cannot assign such a distribution, so the question is moot and not some sort of "limit" going to 1. Measure theory would be the machinery to answer to prove the question.

>>11735229
I am pretty sure the minus sign of the x in the first Epsilon in the first series is supposed to be in the exponent. Otherwise, you get into logarithmic integrals and such, and you end up with a non-covergence.

>>11730441
It's highly improbable that fusion power will be a reality in 100 years, that is for sure. It's extremely an extremely interesting technology, and promising regardless.

>>11735229
From the definition [math]S_1\left(x\right)=-\frac{e^{-x}}{x}[/math]. If the second equality is true, then [math]S_2'\left(x\right)=S_1\left(x\right)[/math], so the derivative of the right side is equal to [math]S_1\left(x\right)[/math]. You can probably show that's not true.

>>11741617
I was likening it to [math]0^0[/math], since it's similar in that there is no reasonable way to assign a value, because the result is inconsistent either way.
Whatever you do, you break everything.
Set it to 0 [math]\Rightarrow[/math] Nonsense, since there are elements in [math]\mathbb{R}[/math] that are also in [math]\mathbb{N}[/math].
Set it to anything >0 [math]\Rightarrow[/math] Nonsense, since that would imply [math]\mathbb{R}[/math] is only countably infinite.

OK so I have this problem, I could solve it but I need some extra info.
Should I assume that, a=17, b=53 and that the angle given is the opposite of side c? and do that everytime a problem like this pops up
OR
The bitch from the course forgot to clarify something?
OR
Im retarded and there's some law that I forgot.

>>11741116
OK, so I set the radius to be 1, which would mean each leg of the inscribed triangles are length 1, and in an equilateral triangle, each angle equals 60 degrees, which equals pi/3 radians, which is greater than 1, so the degree measure of 1 radian must be less than 60 degrees. Does that look correct?

>>11742162
You're working too much. Just argue that the triangles are equilateral. Then clearly the length of a 60° arc is strictly larger than the circle radius.

>>11742162
no
you got halfway through and then gave up and converted to radians using the formula and compare numbers
the point of the diagram is to not explicitly convert between units

the fact that the triangles are equilateral is very relevant though. try comparing the length 1 base of the triangle to the circle arc with the same endpoints

>>11742156
Included angle refers to the angle between the two given sides, so yes, it would be opposite side c. Then just use 1/2(a b sinc) to get the area

>>11742231
Thanks bro, didn't knew what "included angle" meant.

What's the best book/resource a dumbass like me can learn about discrete math?

>>11735044
In general, polygons don't have an incenter. Consider a triangle with an inscribed circle. If you "cut off" a corner to form a quadrilateral, the new edge isn't required to be tangential to the circle, yet no other circle is tangential to the original three edges.

>>11735091
I dunno about reversing it, but you can prevent it; see "impressed current cathodic protection".

>>11742701

What's the best engineering discipline if I want to focus on probability and statistics in the future (I can't study math though as the university doesn't offer that course and the closest university that does is in another city and I don't wanna move). I was thinking maybe Industrial Engineering, or Electrical.

>>11742229
>try comparing the length 1 base of the triangle to the circle arc with the same endpoints
Sorry, I'm dumb and I don't quite get what you mean by this. Could I ask you to explain a little further please?

You need to build a huge mountain as cheap as possible using the least raw material that can't be obtained on site, how would you accomplish that if time weren't an issue?

Alright, so I am studying for an exam coming up monday but I am having difficulty with this one problem. It's functions.

f(x)=x^2 + 2 and g(x)=3x-1

The question itself is

(fog)(3)

I've tried f(g(3)) but going off the answer I definitely didn't do it right. Maybe you guys could help?

>>11743540
Spoiler I figured it out fucking the second I looked back. The question was actually (fog)(2). Fucking hell.

>>11743540
What did you get?

>>11743551
On the (fog)(3) , I got 66. On the (fog)(2) I got 27.

What's the reasoning behind simplifying fractions with a radical as the denominator? For example [math]\frac{1}{\sqrt{5}}[/math] is simplified as [math]\frac{\sqrt{5}}{5}[/math].

>>11743946
in the past it was way easier to divide a number than to take the inverse of it.
for example, once you look up the square root of 5, it's way easier to divide this by 5 to get your answer, than it is to take 1 over sqrt(5).
nowadays it doesn't really matter that much since computers and calculators make this all irrelevant, and fields like quantum mechanics commonly use terms like [math]\frac{1}{\sqrt{2}}[/math] because it's a clearer notation.

i heard some guy say that theres no solid delineation between (electrical) conductors and insulators, and that it was all just resistivity on a spectrum. this made sense to me as it was something that i previously thought about as a kid
but the more i think about it, the more holes i can poke in the idea, so whats the answer?

>>11744158
All physical objects have electrical resistance except in fringe cases. An insulator is just a classification of an object with higher resistance, and a conductor with lower resistance.
If you had an object that you could increase the resistance of at what point would it go from conductor to insulator?

>>11744158
>but the more i think about it, the more holes i can poke in the idea, so whats the answer?
Like what?
It's obviously true that "conductivity" isn't a binary state, how can you pike holes into something obviously true, which can be demonstrated by very basic experiments?

>>11743368
>how would you accomplish that if time weren't an issue?
Wait until one forms naturally.

>>11744158
Anything will conduct electricity(except void obviously) if you pump enough energy through it but it likely melt and catch fire as well. Ever wondered why air generally doesn't conduct electricity but tesla coils are a thing?

>>11744255
>If you had an object that you could increase the resistance of at what point would it go from conductor to insulator?
well, the idea is that insulators dont conduct electricity
>>11744256
here were my thoughts, a proof by contradiction:
a (basic) capacitor is taught as two conductors electrically separated such that electrons cannot flow from one conductor to the other. consider two coppers plates positioned very close to each other, separated by air. if the voltage across the plates is high enough, then the air will ionize and electricity will flow, and it will cease to be a capacitor. if there is no delineation between conductors and insulators, then the definition of a basic capacitor like this can be generalized as two materials separated by another material of less conductivity/higher resistance.
now, gold conducts electricity better than copper, so can a capacitor be constructed out of two plates of gold separated by copper? perhaps if the voltage across the gold plates is small enough, then the gold can have current through it without the copper having any, implying a sort of "minimum voltage requirement" for conductors, but this confuses me. when you increase the voltage from 0 to infinity across a conductor like copper, the current will increase linearly with it. but do the same with an "insulator" like air, and the current will be basically zero until sudden it starts conducting. does this same thing happen in a conductor like copper, only its not noticeable? if so, that would clear everything up

>>11741214
>>11741726
>>11741789
thats how they got the answer. here's the snippet of it. i also got to the [math]S_{1(x)}[/math] point but nothing further

>>11744289
>here were my thoughts, a proof by contradiction:
It breaks down to "air can act as a conductor under high voltages, therefore conductivity is binary", this makes no sense whatsoever.

I mean, it is totally irrelevant whether or not copper exhibits similar material properties towards conductivity, as air does.
What the fuck would it proof it were not the case?
Honestly, I have no clue whether these effects appear, in the ideal case (https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity)) they clearly are not modeled.

>so can a capacitor be constructed out of two plates of gold separated by copper?
Maybe, maybe not? But why would it matter whether or not copper exhibits the same ionization properties as air?

>but do the same with an "insulator" like air, and the current will be basically zero until sudden it starts conducting.
Certainly due to a material property of air, which changes based on current.
What the fuck is some weirdness of air having to do with anything.

>>11744463
my point is that air and other conventional insulators can conduct electricity under high enough voltages, but they dont appear to do it in the same same way as conventional conductors
if you can make a capacitor with air, could you make one with copper? if not, why? it somewhat implies that materials that you could make a capacitor out of are somehow different than materials you couldnt make a capacitor out of

should I take adderall before an exam?

>>11744475
>my point is that air and other conventional insulators can conduct electricity under high enough voltages
The electricity changes the chemical makeup of the air, which changes it's conductivity.
The conductivity of air, at least to my understanding is constant, at least to my understanding, but air can be chemically altered through the electricity and change it's conductivity.

> if not, why?
You most likely can, but it will be extremely bad since almost all of the charge is "conducted" away.

>>11744575
>should I take adderall
no.

When does the calculus in a calc III class start? I'm looking at the syllabus and it's 99% vectors and matrices. Also, any general advice for Calc III?

Can someone explain if i am being retarded or if it's my calculator? If so, how do i fix my calculator? I have to use this in a final exam in 2 days.
I'm doing

P2 = P1 V1 T2
--------------
T1 V2

On my calc pic related it equals pic. But on the answer sheet it is 0.915 atm. Even on the combined gas law calculator website it's 0.915 atm... I'm so confused... i have been using this calculator for months

>>11745376
>or if it's my calculator?
Extremely unlikely, although in general they might get ridiculously wrong results under particular circumstances, they almost never do, especially not when the numbers are very well behaved, such as here.
If you are still unsure type it into Wolfram alpha (or any other CAS) which won't do an error prone numerical calculation but a correct algebraic one.

>>11745376

degrees K retard

>>11745491
I-i knew that retard I was just testing you all

Will I ever find love?

>>11745752
No.

>>11745752
not with that attitude

>>11745752
Love isn't for everybody, that is the sad truth...

>>11744475
You can "sort of" create a binary divide between insulators and conductors based upon the presence of mobile charge carriers. Essentially, if all of the valence electrons are bonded, you need a high enough voltage to break the bonds before significant current will flow.

Ultimately, materials which are used as conductors have very low resistivity, while materials used as insulators have very high resistivity (and also fairly high breakdown voltages, as you want the resistivity to remain high). Materials with intermediate conductivity are used as neither conductors or insulators, as whichever role you want you can find something that does a better job.

>>11726219
What is the relationship between mass and age of a galaxy? Naively, one would expect the earliest galaxies to be smaller, since they haven't accumulated yet. But is this supported by the data? When I try searching it I find stuff like this: https://www.scientificamerican.com/article/astronomers-get-earliest-ever-glimpse-of-ancient-giant-galaxy/

I would really like a numerical correlation between galactic mass and age, or perhaps galactic radius and age.

I have to find the volume of the paraboloid z = - (x2 + y2) + 4. I suppose I have to use double integrals, but I'm having trouble figuring out the boundaries. Is this correct?

How do I prove/disprove that [math][0,1]^2[/math] is a 2-dimensional manifold*** in [math]\mathbb R^2[/math] ?

***Note: The definition given in our class is this: [math]M\subset \mathbb R^n[/math] is a [math]k[/math]-manifold if for every [math]p[/math] in [math]M[/math] there exists an open nbhd [math]V[/math] (i.e. open in [math]M[/math]), and some [math]U[/math] which is open in either [math]\mathbb R^k[/math] or [math]\mathbb H^k[/math], and a [math]C^1[/math] homeomorphism [math]\phi: U\to V[/math], such that its differential [math]D \phi (u)[/math] has rank [math]k[/math] for all [math]u \in U[/math].
I realize there are other ways to define a manifold - but this definition is all we've got to work with at this point.

I assume I should disprove. My intuition is that the square has pointy corners and there cannot be any such [math]C^1[/math] map, but I'm having trouble showing it.

>>11747172
That is a surface that goes on forever, I believe. Do you mean the volume below the paraboloid but above the xy plane?

>>11747338
Yes, sorry. The base of the paraboloid is at x0y.

>>11747349
It's been a while since I've done double integrals, so apologies if I mess this up. But I believe the inner integral bounds should be from x=-sqrt(4-y^2) to x=+sqrt(4-y^2). And then the outer integral bounds should be from y=-2 to y=+2. Does that make sense?

>>11747269
The nbhds of boundary points of the square aren't open in [math]\mathbb{R^2}[/math], so you can't an homeomorphism.

>>11747420
Oh, shit, that makes sense, actually. Thank you!

>>11747704
Care to elaborate please anon? Note that the definition I gave allows for a homeomorphism from a subset that's open in [math]\mathbb H^2[/math] toa subset that's open *in [math]I^2[/math], i.e. open in its induced topology. So why can't there be a homeomorphism?

My hunch was that a homeomorphism actually is possible, but that the [math]C^1[/math] condition is what would prevent the square from being a manifold..

>>11747420
Is it 25.13?

>>11748796
I believe so.

>>11748357
Oh yeah, sorry. Fuck. I forgot what [math]\mathbb{H}[/math] was. In that case, you said your only problem are the corners, right?. For [math]p=(0,0)[/math], let [math]U[/math] be the quarter of the disc with center in [math]p[/math] and radius [math]\varepsilon[/math], and let [math]V[/math] be the half of that disc in [math]\mathbb{H}^2[/math]. Now take [math]\varphi(r,\theta)=(r,2\theta)[/math]. Do a similar thing for the other corners.

I'm gonna try my luck.
Any marine biologist here?
What's a good place to get detailed info about the life cycle of Sipunculus?

Stupid question here:
[math] A =
\begin{bmatrix}
1 & 0\\
0 & 1\\
0 & 0
\end{bmatrix}
[/math]

[math] A^T =
\begin{bmatrix}
1 & 0 & 0\\
0 & 1 & 0\\
\end{bmatrix}
[/math]

Why does the product [math]AA^T[/math] is different from [math]A^TA[/math]? I mean I know left/right multiplication is different, what I don't get is why left multiplication by A transpose is the identity in this case. Any light?

>>11749819
I mean, AA^T and A^TA aren't even the same size. A 2x2 matrix and a 3x3 matrix are obviously "different" matrices, it's not clear to me what is confusing you there.

>>11749819
>Any light?
AB is in general NOT BA for matrices A and B.
Never assume this to be true unless you are truly sure that this is a special case where this is actually true.

ESPECIALLY important is it in a case like this A is a mapping from R^2 to R^3 A^T is a mapping from R^3 to R^2.
So we have that:
AA^T goes from R^3 to R^3 (it is a 3x3 Matrix)
A^T goes from R^2 to R^2 (it is a 2x2 Matrix)

Not only does the equality not hold, both things are actually totally different types of objects which can not be meaningfully compared.

Does my ballsack/ballsack sweat only smell good to me or would it smell good to others?

>>11749859
>>11749869
I think I found what I was looking for: the concept of semi-orthogonal matrices. They are any non-square matrices where all columns are orthonormal, and multiplying it by the transpose on the left OR the right yields the Identity.
But thanks for the answers, anons.

Any of you know a good place to get a paper translated from chinese?

>>11749979
only you

>>11750157
How do you know? Have you smelled other people's ballsacks?

>>11749979
maybe if they're sexually attracted to you
otherwise I doubt it

>>11750163
yours :)

>>11727092
are you talking about this?
https://arxiv.org/pdf/1806.09055.pdf
it's a neat idea, but i wouldn't even say it's phrased as non deep learning. they basically treat architecture search as a discrete optimization problem, and find solutions by continuous relaxation

>>11739179
not unless you specify a distribution on R. For any continuous distribution the answer is 0, but there are also distributions where the answer is >0.

>>11742027
>that would imply R is only countably infinite.

How?

>>11726219
https://www.youtube.com/watch?v=ZRzyN0wK32Q

Could someone give more information on signalling and counter-signalling? any good books or lectures on it?

>>11726219
Can someone pls explain how I would generate a plot like this in latex? Need to for my analysis homework

>>11751306
I would recommend making the plot in python and then using a latex package that can import python plots
I've never natively plotted anything in latex for this reason

>>11751329
How would I make the plot using python?

>>11751434
first make it in latex and then use a package to import it to python

I know this is a fuck-stupid place to ask this but I literally have no idea where else to post that won't get 404'd faster than a premature ejaculation.
I have crazy-bad brain fog and derealization like 99% of the time, had it for all my life but it's gradually gotten worse.
But for some reason when I drink alcohol it sometimes gets better and I have no idea why, can't find anyone with a similar experience online.
I'd really like to figure this out so I can stop permanently feeling like I reside in the void of obliteration every nanosecond.

>>11751509
how do you know what you call "derealization" isn't the real reality, in other words you got knocked out of a delusional perspective?

>>11751532
Ive thought that too, but if this is what real reality feels like then it's garbage.
Really though it's more based on how I've had other people describe their feeling of existence, and by how I know things used to be more clear for me.

>>11751509
Anon, you're dissociating. See a psych. inb4 pseudoscience

>>11751509
Lots of things can cause that.
I have something similar and apparently it may be because I'm a lardass with sleep apnea

>>11726219
Bros theres a detail in a proof from Rudins chapter into integration that I simply dont get why the fuck is true.
The fact is used to prove both theorem 6.10 and 6.11. It goes like follows:
Let [math]f:[a,b] \rightarrow R[/math] the if:
[math]M_i = \{ supf(x) :x \in [x_{i-1},x_i] \}[/math]
And
[math]m_i = \{ inf(x) :x \in [x_{i-1},x_i] \}[/math]
Then [math]M_i - m_i \leq 2sup|f(x)|[/math]

I Mean, its rather intuitive but other than that just wtf

>>11727764
>pdf name
ooooooooooooooh you just doxed yourself the hacker known as 4chan is gonna come after you now

>>11751601
sup |f| >= Mi (this is obvious
sup |f| >= -mi ( since - mi is also the sup over -f)

>>11751306
Pgfplots or tikz.
The plot in the image is actually not very well done.

>>11751434
Don't. It will look like shit.

why are strang's books so bad

>>11727764
Everything up to and including a graduate course in QFT. That's typically the last sort of formal course any physics department offers anyway, after that it's all reading seminars and special topics seminars.
You're in your first year, I don't understand why you'd be sad that you don't understand this stuff. What the fuck do you think school is for? Did you expect to walk into mechanics 101 and start doing path integrals by the second week?

What's the specific reaction when you boil basic water in an aluminum pot and the pot turns dark on the inside?

>>11750337
If [math]p>0[/math], then [math]|\mathbb{R}| = \frac{1}{p} \cdot |\mathbb{N}|[/math].
But if there was only a "linear" discrepancy in size, you could count all elements of [math]\mathbb{R}[/math] through diagonalization.
We know [math]\mathbb{R}[/math] is uncountable, so [math]p>0[/math] is wrong.

>>11750336
How could it get 0? [math]\mathbb{N} \subseteq \mathbb{R}[/math] with [math]\mathbb{N} \neq \emptyset[/math].
Whatever you are talking about doesn't sound like standard set theory.

how do you solve this?

>>11742027
>Nonsense, since there are elements in
what ? probability 0 doesn't mean it can't happen

>>11751957
guess i should've posted my attempt to not leave a bad taste, i'm just not sure if this is the right way

>>11751970
fuck

>>11751963
>probability 0 doesn't mean it can't happen
Sorry, you will need to explain this to me.
Is that some frequentism?

>>11751672
Yeah but how do I add the lines specifying the deltas and epsilons and shit?
Pls give me a code example, literally cant find anything online

>>11751991
it's the same principle as the area of a line in the plane is zero. the line is not the empty set, but the two-dimensional lebesgue measure of it is zero.
P(A) = 0 only means that A is a negligible set compared to the whole sample space, not that A is necessarily empty set.
and it also doesn't mean that A is in some sense impossible. for example consider shooting at a disc target, what's the probabilty of hitting exactly the center ? it's zero. but it can definitely happen.

>>11751991
the easiest way to understand it is by calculating probability with real time in play
let's say a train comes to the station between 8:10 and 8:20 with an uniform distribution i.e. any time between 8:10 and 8:20 has the same probability
the integral of the probability of the train coming to the station over 8:10 and 8:20 is equal to one, but the probability of the train coming at a single point in time is so small, we say it's equal to 0, just like integral over a single point is equal to 0

Please for the love of god, help me.

>>11751991
If you have an infinite set, the probability that a randomly-chosen element belongs to a finite subset is zero, but that doesn't mean that it can't happen. Similarly for a countably-infinite subset of an uncountably infinite set (e.g. the probability that a randomly-chosen real is rational).
https://en.wikipedia.org/wiki/Almost_surely

>>11752067
raise both sides of your assumed equation to the power of n
then take the logarithm of both sides

>>11752039
>>11752049
>>11752080
Thank You for explaining it so diligently to a retard like me.
The comparison to the disc target worked best.
Every single day I hope our universe is rational, while it may very well not be.

>>11726219
Is anyone else really good at concepts but terrible at arithmetic?
I was tutoring mathematics today and the person I was tutoring was at my level of calculating arithmetic, but struggled to understand the concepts?
Is there something about the brain I am missing? The more I explore theory, the more I loose in the practical?
or is it I have a low brain capacity and I can't remember everything because of that?

>>11752163
i'm same, if you get over calculus and start doing more theory, you stop practicing calculus (atleast it's like that in my case) and just forget some of it and lose the proficiency in it

>>11752169
I have been studying theoretical computer science for 2 months and I completely understand what you're saying.
When you don't work with numbers for a while, I think you genuinely loss that ability over time.

>>11752163
"Conceptual" understanding is an excuse people make up when they have to face the fact that they don't know something but don't want to admit they don't know it. It's bullshit.
If you can't actually do anything with the theory, you don't understand it.

>>11752176
Maybe.
But I was good at the arithmetic before, and now I'm not as good.
I know the concept well.
I was wondering why this is. Honestly I think it's something you have to keep practicing, or you loose it (like a muscle).

Anyone here with some python experience? I'm just starting out and getting an error, was wondering if someone had the time to take a look

>>11752195
Post code froggy

>>11752203
I'm just trying to install a program called obspy via the anaconda prompt.
The problem is that when I try to run the obspy-runtests command at the end, to verify that everything is installed correctly I get:

>Fatal error in launcher: Unable to create process using '"d:\bld\obspy_1584613250076\_h_env\python.exe"
>"C:\Users\Anon\anaconda3\envs\obspy37\Scripts\obspy-runtests.exe" ':
>The system cannot find the file specified.

I have no D drive on my laptop and python.exe is actually located in "C:\Users\Anon\anaconda3\python.exe".

Do you have idea if there is a way to make it look the right place for python.exe instead of trying to find it in the nonexisting D drive?

>>11752213
It sounds like you have installed a library and the library is using absolute pathing.
Try intalling the require software via pip or the apt package manager if you're using linux.

>>11752081
>>11752067
Okay, but then I get
a^n = (e^ln a)^n = e^(n ln a)
And taking logs of both sides:
ln(a^n) = ln(e^(n ln a)
I don't know how to progress from this point on :/

Can someone explain to me what antifa is without any bias?

>>11726219
Hello /sci/now I havent come a cross a break problem before, I mostly dealt with beams and trusses, so I would like to know how to solve this, how do I factor in the friction

>>11752271
ln(e^x) = x

>>11752236
Thanks, the test actually runs now but is returning some errors.
If I install the primary package via pip install, will it work if my other packages are install via conda install ?

>>11752293
breaking as in rupture of the rope or what?
I assume that friction acts on the pulley as a percentage of a centripetal component of a force.

>>11752329
Yes friction is between the rope and the wheel, I guess the force when pushed acts like a break since the rope is of certain length and friction adds to fhe breaking

>>11752291
Part without bias:
"Anti-Fascists" - They go on the street claiming to be against fascism.
And absolutely everything is justified, if it's against fascism. The end justifies the means.
Biased:
They don't even agree on what fascism is. In the end, anything they don't like becomes fascism.
Even mathematics may be fascist in the eyes of some of them.

>>11752311
Appreciate the help, but I really don't get it.

>>11752444
If you don't get that ln(e^x) = x you need to go re-read your notes, because if you don't understand that you can't really be understanding anything, and there's no point in trying to do problems yet. It's literally the definition of the logarithm.

are thermodynamics laws falsifiable?

>>11752491
I understood both separately, but not how you got from A to B, or how it answers the question.

But, I guess: ln(a^n) = ln[e^(n ln a)] = n ln(a)
Therefore ln(a^n) = n ln(a)

Thanks.

>>11752613
Obviously. Build a perpetual motion machine...

>>11752291
The issue is that anybody can "be" antifa.
In the broadest sense it is a very loose group of people who believe that to stop a Fascist (that term is *extremely* important, since it's definition is entirely inconsistent between antifa "members") regime any means to stop it should be employed.

The actual different antifa groups have a more solid core of anarcho communists who believe that all government (especially their police) is inherently Fascistic and thus they feel justified in whatever actions they use towards thus supporting "government" in general.

>>11752312
Possibly. Try it and hope for the best.

This is actually the reason why you should be using linux, because things like that *do not happen*.

>>11752648
>Build a perpetual motion machine...
those don't exist...
i can't find anything that opposes thermodynamics and it seems that the general consensus is that if something violates thermodynamics then it's not real.

>>11752731
>those don't exist...
Exactly! Which is why we still assume that the laws of thermodynamics are true.

>i can't find anything that opposes thermodynamics and it seems that the general consensus is that if something violates thermodynamics then it's not real.
That is why they are still called "laws". Granted, Newton's ""laws"" have been disproven and are still called such. But obviously there has been no evidence that the laws of thermodynamics are wrong.
But so what? That does not make them unfalsifiable.

Falsifiable does *not* mean "false". It means that if they were wrong, then you could construct an experiment to disprove them.

>>11752736
No, they're called laws because if you break them the physics cops come after you.

>>11752736
>tfw entropy is 100% real and irreversible

What are physicists doing right now on a day to day basis? What kind of experiments are people running and what are they trying to figure out?
I'm pure maths and I've never looked into physics beyond what I was required to. In my head I'm just picturing the physics professors dropping apples on the floor and going "yep, still 9.8 meters a second."

>>11750569
please lads

>>11752784
>What are physicists doing right now on a day to day basis?
constantly trying to figure out the universe's biggest mysteries like
least painful suicide method
how to accept mediocrity
how to reverse previous decisions
is Buddhism real
best jobs for a physicist that aren't min wage
jobs that hire a physicist
how to not be overqualified for everything yet still without a job
best programming language for a physicist
how to learn programming quick

>>11752777
It is reversible, but only locally.
In the end, it only means the universe will probably have an end.
>inb4 quantum fluctuations

>>11752821
Would this sum that up accurately?
>"Why haven't I majored in Computer Science?"

>>11752428
>>11752673
So why are normalfags against both fascism and antifa

Why does from

0<arg(z+1)<pi/2

follow
Re{z}>-1 and Im{z}>0

and how do I prove it? I have a strong suspicion it has something to do with tan or arctan, but I'm not sure how I would go about it

>>11752860
>It is reversible, but only locally.
you mean in a closed system where you have energy exchange (like earth for example)?
entropy is still very relevant for humans and earth. the energy from sun only maintains life on earth as it is through the carbon cycle but it has little to no room for expanding.
keep in mind that most of society today, information age and all of modern technology were built on energy that took millions of years to accumulate and will be inaccessible for millions of years if not forever.

>>11753020
I mean, it's geometrically clear. 0<arg(z+1)<pi/2 means z+1 is in the first quadrant, which implies Re{z}>-1 and Im{z}>0

>>11753026
Oh damn, right. So if it was pi<arg(z+1)<3pi/2 it would imply Re{z}<-1 nad Im{z}<0 ?

>>11726295
look at their trace

>>11753038
3pi/4 instead of 3pi/2

>>11753038
yes

>>11753044
Holy shit it's so obvious when you say it like that, I completely dissociated an angle from the "actual" number, what a fucking fool.
Thanks a lot man!

>>11753038
Yes

I'm looking for the name of the algorithm things like a CNC tool path generator or a robotic combine harvester would use to optimize a path to cover an irregular area. I recognize it can be solved applying traveling salesman to a node grid the size of the "tool" (think, like the width of the combine harvester header, or a CNC mill bit), but I'd like to check previous literature in the subject.

How do you prove that a problem is weakly NP-complete?
You prove that it is NP-complete as usual, then find a pseudo-polynomial algorithm for it?

>>11752784
Obviously that picture in your head is wrong, they would say 9.8 meters per second per second.

>>11752821
>how to not be overqualified for everything yet still without a job

>A circle of radius 7 units rolls along a straight line. If it covers a distance of 20 units, what is the radian measure of the rotation it has
made?
Is the answer 280pi?

>>11753355
No

>>11753355
Did your brain malfunction?
it has rotated 20/7 radians

>>11753403
No, I'm usually this stupid. Thanks.

theoretically, the worse someones allergys are, the better their immune system is? (to an extent) from what i understand allergys are caused from your immune system basically fucking your own body because it detects pollen which is seen as a "threat" so you immune system goes crazy. i assume the immune system falls under the science catagory.

>>11753087
Im programming my own 3D printer slicer in python. Maybe what i do can help you out. (I replied to your previous question a week or so ago if you are the same guy but your question was 4 axis or more so i had no experience with that, in a planar problem i have experience)

I get the cross-section image of the 3D model (white image in my pic), i get the contour with marching cubes. I offset (this operation also goes by the name of inflate/deflate or buffer or erode/dilate) the contour by the amount of plastic extruded (or tool width in your case) to produce the perimeters of the printed layer. Then i fill the bounding box of the model with diagonal lines with an appropriate spacing and angle. I take the most inside contours and get the intersection of this contour and the previously generated diagonal lines. Basically i cut off everything from these lines thats outside the contour to produce the infill. The result is a bunch of lines and polygons. From here you have to think of a way to traverse these with the least amount moves spent not pushing out plastic (or milling in your case). I have hit a couple of snags in this step. My initial idea was traveling salesman aswell. Except solving the TSP for 20+ points on my PC takes a minute or so. Imagine solving pic related. TSP is not feasible for my problem, a greedy algorithm is way better in my case. I would think milling would produce the same amount of points to solve.

What is it you are trying to achieve?

What does this "choose" notation in probability actually mean? And how do you translate it to an actually solvable math problem? I'm pretty sure whoever wrote this stack exchange answer is an idiot and by turning every number into a factorial and multiplying it is wrong

I have no experience in optics.
Say you have a lazer with some wavelength and output power. And a target with some amount of reflexivity that you aim your laser at.
Is there an optical building block that can prevent the reflected light getting back in the laser emitter preventing its "self" destruction?

Trying to find work done. Force F=<-2, 3, 1>, and the distance vector D=<8,-1,3>.

So the dot product is D*F=-16-3+3=-16, is that right? Seems odd for it to be negative here.

>>11753546
https://en.wikipedia.org/wiki/Binomial_coefficient
read the introduction, before the table of contents

I don't know what the notation in the image you posted is, I've actually never seen that before

How can we do conditional probability with continuous distributions? [math] f_{x|y}(x|y)=P(X=x | Y=y) [/math] but the probability of [math] { Y= y } [/math] is 0 right? How does this work?

>>11753560
yeah, there are optical components that are basically the equivalent of one-way mirrors. they're called optical isolators

>>11753546
>>11753713
[math]{52 \choose 13, 13,13,13}[/math] is a multinomial coefficient. You have 52 items and you want to label 13 of them A, 13 B, 13 C and 13 D.

>>11753721
probabilities for any continuous distribution only make sense if you're talking about a range of values.
the probability that you pick a specific integer from 0 to 1 is exactly 0, but the probability that you pick an integer from 0.3 to 0.4 is well-defined.
you only ever deal with terms like [math]P(y_1<Y<y_2)[/math] when dealing with continuous distributions.

>>11753702
force dotted into distance is work. negative work is a well-defined concept. you get values of negative work when dealing with things like applying a force to slow an object down. in this case, your force is applied against the direction of motion, so there's a relative minus sign.

>>11753727
Okay but how do I solve a problem with this notation mathematically

>>11753745
https://en.wikipedia.org/wiki/Multinomial_theorem#Interpretations

>>11753546
He actually gave you the most efficient answer that should offer the greatest insight possible for this retarded otherwise stupefying exercise. You should be grateful.

>>11753731
So how do we alter [math] P(X=x|Y=y) [/math] for the continuous case of conditional probability?

>>11753759
if both x and y are continuous random variables
[math]P(X\in [x_1,x_2] | Y\in [y_1,y_2])[/math]
is this not what you mean?

"what is the probability that the value of the normal distribution is greater than 0.25 given that you're considering values from x=0.5 to x=1"
"what is the probability that a number ranges from 0.3 to 0.4 given that you're picking from numbers from 0 to 5?"

>>11753767
Yes I think I am just getting confused on my textbook's notation. Thank you

>>11753768
of course. stats notation is probably the worst out of any popular field.

Suppose we are in ZF + R is the countable union of countable sets. Wouldn't this imply that the Lebesgue measure of R is 0?

What is energy? Why is it that I can move my arm and throw something, or when something is raised it falls to the ground? What causes the movement on a fundamental level?

>>11753747
What I don't understand about this is 4 choose 2 is 6, but if you do 4!/2! you get 12

>>11753781
I like to think about energy as the ability to do work, or the ability to cause a change in something.
gravitational potential energy that arises from raising an object up has the potential to speed up the object as it falls
chemical energy has the potential to release heat due to a reaction
kinetic energy of a fast-moving object has the potential to speed up another object through a collision, etc.
these are just a few examples. my definition is obviously not rigorously correct, but in general it is true.

when you raise something up, you are putting energy into the system. this energy comes from the energy expended by your muscles, which comes from the food you eat. when this object falls it turns this energy into motion. when it hits the ground, it turns the energy into sound and heat, which just dissipate away.

>>11753786
the choose terminology only applies for binomial coefficients, for which there is a different formula that I linked >>11753713
for multinomial coefficients, it's assumed that the numbers on the bottom sum to the numbers on the top. thus there are no extra terms in the denominator.

think about it this way: for the binomial distribution, you have a denominator that goes as [math]k!(n-k)![/math]. but if n=k, then the term in parentheses is just 1, so we don't need to write it.
this is the idea behind the term you linked. it's just a product of factorials because they all add to the quantity in the numerator, which means there are no extra degrees of freedom and there doesn't need to be any other factors.

>>11753737
thanks

>>11753796
Okay so Im sorry that Im so fucking retarded, but if I see a notation where it is just one number above another number, like 4 over 2, that is just 4 choose 2 which is always 6? But if I see multiple numbers on the bottom, then I have to covert it all to factorials which are multiplying/dividing each other?

Yes Im a fucking retard please just spoonfeed me how to get the answer Im a helpless undergrad just trying to keep my head above water in these stupid summer classes while everything outside is chaos

>>11753806
yes. if there are two numbers n, k it's always n choose k which is given by the binomial coefficient formula.
if there are multiple numbers on the bottom, it's given by the multinomial coefficient formula.

they are both "converting all to factorials." since the "n choose k" is written [math]\frac{n!}{k!(n-k)!}[/math]. it is very helpful to memorize this formula if you don't know it.

the multinomial case is similar, except you convert it to (assuming n on the top, and k1, k2, k3 on bottom) [math]\frac{n!}{k1!k2!k3!}[/math] which is a similar form to the binomial coefficient. the caveat here is that k1+k2+k3=n, which means there are no terms like (n-k1)!. just as in the binomial case where if k=n then you wouldn't need to write (n-k)!=(n-n)!=0!=1 because it's just equal to 1.

>>11753816
thank you for simplifying what I was unable to understand after several lecturs

This is probably a bad place to ask but if i'm writing a mostly formal paper and I want to visually show the steps that are involved in a particular process that I got from a paper, can I just copy it and put it in my paper?
If not would basically copying the steps and then making my own identical diagram be ok?
I could just write out the steps but I feel like that would not be quite ugly.

>>11753869
Fuck, excuse the broken english.
Also should add that this is just for the background and overview, i'm only focusing on one single step in the process but I'd like to give some wider context about what I'm writing about.

Stupid questions about representations of groups. Everything is finite-dimensional.

1) Going off the notation of the wiki article https://en.wikipedia.org/wiki/Subrepresentation : I'm trying to understand what they really mean by [math]\pi(g)|_W[/math]. I'll take the simplest case: [math]V=\mathbb{R}^n[/math] spanned by the standard basis [math]e_1,\ldots,e_n[/math], and let [math]W=\mathbb{R}^{n-1}[/math], constructed by taking the span of [math]e_1,\ldots,e_{n-1}[/math]. The representation (images) [math]\pi(g)[/math] are invertible [math]n \times n[/math] matrices. Is the object [math]\pi(g)|_W[/math] literally the matrix [math]\pi(g)[/math] but with the last row and column thrown away (so now it's an [math](n-1) \times (n-1)[/math] matrix)? If so, is there some guarantee that [math]\det[\pi(g)|_W] \neq 0[/math], or is this something extra we have to check when constructing the subrepresentation?

2) Also assuming the above interpretation is correct: Suppose I have now a unitary representation [math]\rho : G \to \mathrm{U}(V)[/math]. For ease of my feeble brain, take [math]V[/math] and [math]W[/math] same as before, and construct the subrepresentation [math]\rho|_W[/math] also as before. If we simply throw away a row and column, it seems that this new matrix isn't even unitary anymore, as rows/columns no longer have unit norm (except in some special case, e.g. all diagonal unitaries). Is this still really a representation, or are there additional properties one needs to check?

I ask this because it seems like you can always construct irreps in this fashion (the action of the subreps on their subspaces are always closed, no?). But then this would imply that all irreps are 1D and that's certainly not true, so there's some fatal misunderstanding I have here.

>>11753869
Ask your boss if you are allowed to copy. Usually you can as long as you cite them.
Does the original paper diagram is a PDF pic? You can use pdf crop tool to crop it and it will still look nice.
Also, if you can redraw it quickly then just do so.

As a black person do I deserve to live?

>>11754039
>>>/pol/

Do y'all fellas know of a way to view a private Instagram account? Through an app or website?

Some one made a fake account pretending to be me, I want to see what they've posted before I report it.

>>11754281
what have you tried?

>>11754289
All the online sites seem to be scams. Just send you on an endless "verification" loop of surveys, etc.

Google tells me of apps that say they might, but any video I see about any seem like bullshit, and the comments are all flooded with bots. Idk if I want to try any of them, might not want it on my phone

Not sure what else I could try, but thought maybe someone might be aware of something more likely

>>11751682
he is a brainlet enginigger faggot

if an over the counter drug doesnt explicitly mention on the package not to combine with alcohol, its probably safe right?

>>11754294
any "app" claiming to bypass facebook security directly is clearly a scam and you have to be pants on head retarded to even think they could be real. Your best bet is to exploit the account recovery / verification system in some way, either by phishing the account owner (probably your best bet) or finding a weakness in one of the blindspots of facebook's verification process (good fucking luck). Either of these options would be incredibly time consuming and it is unlikely that it would be worth the effort.

>>11753726
Thanks.
Do these work with high power laser emmiters? 100-500W?
What happens to the reflected and blocked light? Does it go in a beam dump or just heats up the isolator?

>>11754281
Instagram is owned by Facebook, an enormously large company with thousands of technically skilled people, many of them being payed large sums of money to keep their services exploit free.

Do you think that, even if today there were any enormous oversight which broke their "private" setting and that exploit would be available to the public, it would be there tomorrow?

Just think before you ask retarded questions, obviously you only find scams...

why can't I just load a bunch of wire onto a truck and keep driving perpendicular to the earths magnetic field and use the induced voltage to keep my engine going?

This is to the molecular biologists:

What are key differences between the DNA template being transcribed in eukaryotes versus prokaryotes?

I can't find any concise answers on google or in my books.
thanks for the help guys

>>11754871
Firstly, because that would require a closed loop, and anywhere that the magnetic field is uniform the total generated voltage would be zero. Secondly, even if you did it at a magnetic pole (where you can get net flux inside the loop), drawing any current would exert a force which resists motion, and the energy required to move against that force would be no less than the energy you could extract from it. IOW, it's the same reason why you can't just attach a generator to a motor, using the mechanical power of the motor to drive a generator and the electrical power from the generator to drive the motor. A bunch of wire on a moving truck is just an inefficient generator.

>>11754985
wait how does motional emf work then (V=Blv)? shouldn't just moving a length of wire through a magnetic field generate a voltage?

Let [math]U \subset \mathbb R^n[/math] be open and [math]f: U \to \mathbb R^n[/math] be smooth. Suppose also that the differential [math]Df_u[/math] is a linear isomorphism for all [math]u \in U[/math]. The inverse function theorem implies that [math]f[/math] is a local diffeomorphism.

If [math]f[/math] is also injective, does this imply that [math]f[/math] is a global diffeomorphism (between [math]U[/math] and [math]f(U)[/math])? It seems trivial but it eludes me...

>>11755051
bby's first advanced calculus

>>11755051
continuous <=> continuous at each point

this implies

bijection + local homeo/diffeo = homeo/diffeo

>>11754871
Because that would invalidate basic thermodynamics.

You can do the exact same experiment at home, with much less effort. Wire a generator and a motor together and have the motor power the generator.

>>11754003
I know nothing about representation theory, but from what I understand:

>what they really mean by π(g)|W
It means the restriction to [math]W[/math]. No more and no less.

>is there some guarantee that det[π(g)|W]≠0
That article doesn't mention it, but obviously you need [math]W[/math] to be invariant under [math]\pi[/math], so, in general, since [math]\pi(g)[/math]
is an automorphism of [math]V[/math], the restriction to [math]W[/math] will also be a well-defined [math]W[/math]-automorphism (hence [math]det[\pi(g)|_W][/math]).

I'd advise you, in order for you to clear up your doubts, to think of explicit examples. You're just thinking about particular spaces, but you're not thinking about how the actual representation have to look like.

>>11755319
>(hence det[π(g)|W]).
*hence [math]\det(\pi(g)|_W)\neq0[/math]

>>11755036
> shouldn't just moving a length of wire through a magnetic field generate a voltage?
Yes. And the other length generates an equal and opposite voltage (it's in the same direction in physical space but it's the opposite direction around the loop). To get a net voltage out of it, the total flux enclosed by the loop has to change, so linear motion of the loop within a constant magnetic field doesn't generate net voltage.

Moving a conductor through a field generates a potential difference between the ends of the conductor. But it won't push current around a loop; it will push charges in both halves of the loop to the edges.

>>11726219
Guys, is it possible to build a "seasonal" hidroelectric dam or a temporary lake with hidroelectric power?
what is the name of that kind of dams?

The stuff in red is the amount of water lost every year, thanks in advance

i'm not sure if i get it right:
polynomial interpolation gives us a single function that goes exactly through all the points we give to it and it shows more or less what the function outside these points looks like; n points means that we'll get a function of n-th degree
(runge's phenomenon is a problem though with simplier methods like Lagrange)

spline interpolation gives us many small functions that only describe what the function looks like betweend individual points, the splines are most often of 3rd degree. n+1 points gives us n different spline functions
(no runge's phenomenon)

and approximation gives us a single function that doesn't always go through all the points, but tries to minimise the error as much as possible with the degree we approximate with
(runge's phenomenon is a problem with higher degrees of approximation)

do i understand it correctly?
also if we have n points, does polynomial interpolation and approximation of n-th degree give more or less the same result then?

>>11755725
>and it shows more or less what the function outside these points looks like
What it *might* look like.

>n points means that we'll get a function of n-th degree
n-1th degree. E.g. take 2 points, you can fit a line through them, a line has degree 1.

>the splines are most often of 3rd degree
Not really. Other choices are perfectly reasonable and wildly used.

>and approximation gives us a single function
There are many, many different approximation methods.

>does polynomial interpolation and approximation of n-th degree give more or less the same result then?
What do you mean by "approximation"?

>>11755783
my bad, should've specified that
i just got into all this stuff and so far the only approximation method that i know (that isn't interpolation since approximation seems to be the more general therm) is least squares method

Can someone tell me am I "allowed" to use trig. substitution with [math]\int{(\sqrt{x}-1)^4}[/math], by setting sqrt(x)=(x^1/4)^2 which is basically the same thing, and making a triangle out of x^1/4 and 1? I keep getting a wrong result according to Wolfram.

>>11755893
>trig substitution
>no trig function
I think I found your problem

>>11755834
Least squares and interpolation are totally different.
Image a dataset with 1000 data points, you look at it there is a very clear trend which looks like a cubic.

If you do any form of interpolation you will get an extremely jumpy, wildly varying function which basically captures nothing about the original data.
A least squares approximation will try to find the general behavior, e.g. the best cubic polynomial which fits these points.

In general interpolation is used to guess the values of a function, while least squares approximation tries to extract the fundamental behavior. Usually with few data point and large gaps interpolation is more useful while many data points with small gaps require approximation, e.g. by least squares.

>>11755921
>>11755921
Not the trig substitution you're thinking of, where you got say sinx^mcosx^n, but the one where you got sqrt(x^2+1) and then you make a triangle out of it and do the sub, idk maybe it's got a different name.

>>11755938
aha i think i've got it now, thanks

I need to find a [math]\delta[/math] such that the three following inequations:
[eqn] 0 < x_{0} <1 \\ 0<y_{0}<1 \\ (x-x_{0})^{2}+(y-y_{0})^{2}< \delta [/eqn]
Implies that:
[eqn] 0<x<1 \\ 0<y<1 [/eqn]
How do i start to approach this problem? Can i really come up with a delta or shoud i learn a bunch of particular deltas for different situations? Is there abook where i can learn about those inequalities found in topology and analysis, focusing in the resolution of the inequalities and not the formal terminology?

Is the earth getting heavier because of the rising population? What would happen if there are too many of us and our orbit becomes stronger?

>>11756020
Yes. We become a black hole.

>>11755976
>How do i start to approach this problem?
Geometrically. Just draw the thing if you can't see it in your mind. You should be able to tell that what you have there is a disc of radius [math]\delta[/math] whose center is inside the square [math](0,1)^2[/math]. All you have to do is give a condition on [math]\delta[/math] that makes the disc stay inside said square.

>>11756020
no, you monkey. the atoms in your body come from food that was made here on this earth. no matter enters/leaves the earth on a large scale. it's all recycled, just like your bones will be turned into dirt which then grows plants which then is eaten by homo homo homo sapiens in 5000 years

>Tidy large, medium, or small items first.

Is there a way of finding the answer to this mathematically?

>>11726219
hey lads
so i am building this little circuit and i was wondering what the best way to manage a battery lithium battery and charge it. there seems to be ICs that charge a battery and ICs that manage a battery to make sure so that it doesnt over voltage or under charge or whatever. do i use 2 different ICs to manage the battery or what?

>>11755893
No. The antiderivative isn't an arc-trig function. Just use the binomial expansion of (a+b)^4 where a=sqrt(x) and b=-1, then integrate the terms.

Do I need to cite something if I read it and then realised it was just a conference transcript that wasn't peer reviewed and had bad sources but gave me the ideas to go find other sources which had better information?
The transcript basically says what I do in my work but there's no theory behind it and is partially wrong and is just something mentioned offhand.

>>11756346
Ask /diy/ohm

I remember seeing all in one solutions ICs for that so you will just have to keep looking for one.

I need help with a question. It's a prbability question and I for the life of me can not figure it out. This is it.

To make a non-vegetarian fajita at Lopez’s Grill, you must choose between a flour or corn tortilla. You must then
choose one type of meat from 4 types offered. You can then add any combination of extras (including no extras). The extras offered are fajita vegetables, beans, salsa, guacamole, sour cream, cheese and lettuce. How many different fajitas can you make?
pls help

>>11755976
Trivial solution: Make [math]\delta \leq 0[/math], so the inequations are always false.
Then they imply literally everything, including the inequations you want to have implied.

If that's a task in a logics course, that's probably the answer. Otherwise probably not.

Is there a similar trick with levers to multiply mechanical advantage? I know you can increase the advantage arm to get more force but are there other ways to do it?

>>11757443
Yes. It is known as "gears".
That is the way any bike or car works...

>>11757588
Thanks smartypants but i was asking about levers.