/sci/ - Science & Math

Consider the self-adjoint matrix [eqn]\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}[/eqn]; because it is self-adjoint, it is normal. The eigenvectors of normal matrices should be orthogonal. The eigenvetors of this matrix are (-i, 1) and (i, 1). However, the scalarproduct is of these vectors is (-i) * (i) + 1 * 1 = 1 + 1 = 2 and therefore not 0. Why? What is wrong with my reasoning?

>>15566662
That is not how you take the dot product of complex vectors: [eqn]\vec{a} \cdot \vec{b} = \sum_i a_i\ b_i^*[/eqn]

>>15566674
Thank you!

>>15566555
Good Morning /Sci/entists!

Does anyone know a book that explains how to create a system of Modular Equations where the first solution is a specific positive integer?

Or what such an effort is called if it has a name? Or how the method is operated?

I looked into Chinese Remainder Theorem and Modular Inverse and Extended Euclidean Algorithm. If these things are sufficient to complete my task then how do I use them together to do it?

For example, how can I construct a system of Modular Equations where the first positive integer solution is 703? How do I know the minimum amount of Modular Equations needed in the system to do this?

I am trying to make a Computer Program which accepts a positive integer and returns such a system. If I complete this task, the code will be released to CC0 in a Maid Card.

Thank you /Sci/entists for reading my post.

>>15566684
Additionally, is the process different if the number is prime? What if you want to make a system where the answer is 709 instead of 703? If it is different, why? If it isn't different, why?

>>15566684
Given a number n, x=0(mod n) has n as its first positive integer solution, and x+1=0(mod n+1) has n as its first nonnegative integer solution.

>>15566753
Thank you for telling me, but this specific example doesn't help me. My goal is to get a big number and convert it to a system of Modular Equations which uses less characters than the number I am solving for.

If I just have to write the number in full to use the system, then it doesn't let me work with less data.

Let [math]f:[a,b]\to\mathbb{R}[/math] be a function of class [math]C^1[/math] such that [math]f(a) = 0[/math]. How can I use the fact that [eqn]\frac{1}{(b-a)^2}\left(\int_{a}^{b}f(x)\mathrm{d}x\right)^2 \leq \frac{1}{b-a}\int_{a}^{b}f(x)^2\mathrm{d}x[/eqn] to prove that [eqn]\left(\int_{a}^{b}f(x)^2\mathrm{d}x\right)^{\frac{1}{2}} \leq (b-a)^{\frac{3}{2}}\left(\int_{a}^{b}f'(x)^2\mathrm{d}x\right)^{\frac{1}{2}}[/eqn] ?

>>15566684
>how can I construct a system of Modular Equations where the first positive integer solution is 703?
Take distinct prime factors such that their product is bigger than 703.
For example 2*5*7*11 = 770 and compute the remainders if you divide 703 by it.
703 = 1 (mod 2)
703 = 3 (mod 5)
703 = 3 (mod 7)
703 = -1 (mod 11)

So 703 solves the system
x = 1 (mod 2)
x = 3 (mod 5)
x = 3 (mod 7)
x = -1 (mod 11)
. It's also the smallest positive solution as all solutions of this system differ by 770 by the CRT.

Should you normalize your data before performing a Kolmogorov-Smirnov test if you're trying to test the hypothesis that your data comes from the same distribution as the normal distribution?

>>15566852
Thank you for telling me. I think this is exactly what I needed. If I understand your post, my process should be get a big list of prime numbers. Multiply them together until the result is bigger than the number which I want to be the solution, then present a system of equations with each prime that went into making it? That the minimum number of equations is however many primes I need to exceed the original number? I suppose one works if I pick a single prime bigger than my original number (though this would defeat my goal of using less characters to store the big number)?

Is there any reason you used -1 in the last equation of the system? I could also get away with using 10, right? Since -1+11 is 10?

Also, is there a specific anime maid you like?

I am learning organic chemistry for the first time. Why don't we consider molecules where the R in a functional group is a hydrogen? For example, acetone is the "simplest" ketone, and formaldehyde isn't considered a ketone, and carboxylic acids aren't considered esters. Feels like I've never read this rule anywhere but just had to pick it up which is annoying. I am autistic if that helps.

>>15567098
>Why don't we consider molecules where the R in a functional group is a hydrogen
*to count as being part of that functional group. Sorry, awkward phrasing.

>The set of all integers, {..., -1, 0, 1, 2, ...} is a countably infinite set.
>The set of all real numbers is an uncountably infinite set.
Why? Can't you count real numbers?

>>15567117
Have you heard of cantor's diagonal argument?

>>15567098
>>15567100
The simple answer is: because their chemical properties are different enough from the rest of the ketones/esters. It's simpler to consider aldehydes separate from ketones because otherwise they'd be part of a weird subset of ketones that has slightly different properties from the rest of the ketones.
If the functional group is just hydrogen, that means the aldehydes and carboxylic acids can have hydrogen bonding between molecules. Also hydrogens are small and tend to lead to different chemical behavior than big functional groups.

any good way to reduce radiation in let's say a bed room?

>>15567098
>I am learning organic chemistry
>I am autistic if that helps
better find a chinese kid to take your tests for you cuz you're fucked lmao

>>15567339
depends on what kind of radiation. most general way would be to put metal mesh on the walls to make a shitty faraday cage

>>15567339
Depends what the source is. But lots of materials partially block radiation. If it's radioactive gas you should probably focus on ventilation.

>>15567353
>If it's radioactive gas you should probably focus on ventilation
would just the ceiling fan work? I don't know if I should open the windows. is an air purifier a good idea, I heard some of them do emit small amounts of radiation.

>>15567379
first, get your terminology straight. radiation is not the same as radioactive gas. it's unclear what you're trying to prevent
second, why are you concerned about radioactive gas? do you live in a basement or in a high-radon area? you won't be able to do better than the typical background level of ~0.1 pCi/L without specifically designing your air circulation

>>15567379
I wouldn't expect the ceiling fan to do much without a clear entrance and exit for the air. If you're worried about losing hear look into energy recovery ventilators.

>>15567379
what kind of radiation are you talking about? you aren't doing a good job of explaining yourself.

>>15567253
Thanks, that makes sense enough for me.

>>15567342
Why? I have no tests to take, I am learning for fun.

Linear algebra just doesn't feel natural or intuitive to me. Like I think I could still pass an undergrad linear algebra exam still if I had a few hours to study, but I just don't understand what half of it's for or when it's used in application. How do I "get it"

>>15567401
the kind the jews blast at you from their 5G towers that poisons your soul

>>15567573
Phone radiation isn't actually bad for you. But if you really want to block it, a few layers of tinfoil should bounce it back.

I learnt that when you subtract a larger number from smaller number you can use a trick where you subtract the smaller the number from the larger number and giving the answer a minus sign e.g.

25 -37 is turned into 37 - 25 = 12
and then you gave the answer a negative sign so it becomes -12

Can someone explain why this works?
Or why 37 - 25 = +12 and 25 - 37 = -12

>>15567743
consider subtraction to be addition of the negative, e.g.
37-25=12 <-> 37+(-25)=12
then multiply both sides by -1 and simplify
-1(37+(-25))=-1(12)
-37+(-1)(-25)=-12
-37+25=-12
25-37=-12

>>15567761
can you give an easier explanation pls
i'm new :3

>>15567551
Watch 3blue1brown's series on linear algebra. Consider this an addendum covering inverse matrices.

Leibniz wrote a letter to L'Hopital explaining a cool pattern he found in a system of equations to determine if it has a unique solution or not. This would later be rediscovered and called the determinant. I'll restate it in a different way.

Suppose the two equations that are multiples of each other.
y = 1 + 2x
2y = 2 + 4x
Notice that 1×4 - 2×2 = 0
It's easy to show this holds in general. So if two equations determinant equals 0, then they have infinite solutions. The contrapositive proves if the determinant is not 0 then the equations are not linearly dependent (they have a unique solution).

Next is to consider matrices as representing transformations of basis vectors. 3blue1brown has a great video on this.

Lastly, to find the inverse of a matrix consider what we want to do. We want to transform our matrix so that it's diagonal row is 1's and the other entries are all 0.
Well, we know that if a system of equations has a solution, it's determinant will not equal 0. So another way to think of inverting a matrix is to find the matrix such that we get the determinant of our matrix in each of the diagonals, which we can then divide by the determinant to get 1. Note dividing by the determinant is useful because if the determinant is 0 this will lead to an error , telling us that the matrix has no inverse. The other entries should be chosen so they cancel out.

Finally divide any matrix by its determinant if it isn't 0. It's determinant is now 1. This proves that the volume of the parrallelipiped formed by a 3x3 matrix is equal to its determinant and this works for any other case.

>>15567902
All over my head, even after getting an A in my linear algebra class (couple years ago), but damn linear algebra is so sick.

>>15567339
line the walls with basalt

>>15567777
multiply both sides by -1

[math]x - y = a \implies -x + y = -a[/math]

in an Euclidean or Unitarian vector space, are the same vectors orthogonal for all scalarproducts?

>>15568659
This is true for one-dimensional vector spaces but false for two dimensional one. If it was true in two dimensions it would follow that every invertible linear transformation preserved orthogonality. Let A be a linear invertible transformation that does not preserve orthogonality. Then x,y -> <Ax,Ay> is a new scalar product with different orthogonal vectors.

I have to show [eqn]\left| \int_{I} \overline{f(x)}g(x)\ dx \right| \leq \int_{I} \left|f(x)\right|^{2}\ dx \cdot \int_{I} \left|g(x)\right|^{2}\ dx.[/eqn]At first I thought: Okay, this is just the Hölder-inequality with p = q = 2 / Cauchy-Schwarz-inequality for integrals. However I took a closer look and noticed that there's a "^2" missing on the left side of the equation.
Then I tried to prove it, but wasn't able to; so after a while I looked for a counter-example, instead, and found this
[eqn]\left|\int_0^1 x \cdot 1\ dx\right| = \frac{1}{2} \geq \frac{1}{3} = \int_0^1 |x|^2\ dx \cdot \int_0^1 |1|^2\ dx.[/eqn]I'm confused. Did the author just forget about the "^2" or am I missing something?

>>15568779
Set [math]f(x) = g(x)[/math] and you're being asked to prove [math]\left| \int_{I} \left| f(x) \right| ^2 dx \right| \leq \left( \int_{I} \left| f(x) \right| ^2 \ dx \right) ^2 [/math], which is clearly true iff the integral is larger than one.
So yeah, he did forget the ^2.

>>15566555
Here's a theoretical game:
Say you have a player on a board. The board is a node map (There are "squares", which have connections to one another). You can move to any of the adjacent squares, and you can only "see" them.

As the player, you're trying to get an idea about what the map looks like. Every time you move, however, there's a chance that one of the connections in the map will change, connecting two random squares (It can be the squares it already was on, and it can be a second, or third, or fourth connection between two nodes). You know when this happens, but you don't know what square it happened to. No matter what, though, every node is guaranteed to remain accessible.

Is it possible, as the player, to map recreate the whole map? Does it depend on the chance of the connections being randomized? What's the greatest chance of randomization that guarantees you'll be able to map it out, eventually? Is the most elegant solution to just keep restarting after every randomization, until you have a whole walk with no randomization, or is there a way to do it in fewer moves?

I need to find the scaled wind velocity for the model of a fan blade in a tunnel using the Reynold's number, which stays the same in the model and in the original. The original wind speed is 90 km/h; the model should be on the scale of 1:10 and 1:15.

My lecturer provided a solution: the scaled wind speed is 250 m/s and 375 m/s. According to his explanation "W_model = W_original / 0.1 = W_original / 3.6 m/s / 0.1 = 250 m/s". Where W is the speed. He had set the characteristic length in the model as 0.1 * the characteristic length of the original.
Where is 3.6 m/s coming from? It appears at both scales. 3.6 is double ( *10^5) the dynamic viscosity if I ignore the units (Pa*s).

>>15569017
Nevermind, my careless self just got it.

>>15566841
You copied the problem down wrong. The units of the two sides don't match.

>>15566841
Anyway, once you know what the actual problem is, probably you will do something like
[eqn] \frac{1}{b-a}\int_a^b f(x)^2 dx \geq \frac{f(b)^2}{(b-a)^2} [/eqn]
plus some other assumption about the function on the interval you failed to mention in order to complete the problem

why is G'' not induced?

>>15569271
Because G'' does not contain all the edges in G that connect vertices that are in G''

>>15569315
thank you

>>15566555
I'm trying to prove the integral in pic related is true for the hyperbola 1/x without using calculus. Is this a legitimate proof or just cute bullshit?

>>15570088
I have no idea since I can't even tell what that proof is meant to depict. The diagram is horrendously unclear.

>>15570088
I can tell that you're doing
[math]\displaystyle \int _1 ^{ab} \frac {1} {x} dx = \int _1 ^a \frac {1} {x} dx + \int _a ^{ab} \frac {1} {x} dx[/math] and then [math] \displaystyle \int _a ^{ab} \frac {1} {x} dx = \int _1 ^b \frac {1} {x} dx[/math] but the actual argument is completely incomprehensible.
Try words.

>>15570123
Wait, no, I get it now. The array maps the two graphs onto each other by stretching the base by a and the height by 1/a, so it cancels out.
WORDS KUDASAI
ALSO NO LINEAR ALGEBRA

>>15570108
>>15570128
Sorry for my shitty drawing.
The function at the top is supposed to be f(x)=1/x, and we're considering the domain [1,ab].
I then split the area of that function in two, the red and blue areas.
Notice that there is a 1x1 square on the left corner of the hyperbola.
Suppose we think of it as the basis vectors of the space. Applying the matrix transformation shown below it should preserve the area since it's determinant is 1.

My argument is this new transformed version of the red area is clearly equal to the previous one, and the function is also the same, hence the integral at the bottom.

how do I dispose of radioactive materials at home?

if you had to manually compute the roots of a complex polynomial, like e.g.
[eqn]p(x) = -\lambda^3+(3+3i)\lambda^2+(9-6i)\lambda-(3+7i).[/eqn]How would go about doing it? Would you apply Cardano, Newton or just take a guess and hope for the best? On a semi-related note: Are complex calculators are allowed at your university? What calculator do you use?

youre not smart just for posting equations

>>15571147
>if you had to manually compute the roots of a complex polynomial
I wouldn't.
>inb4 gun to your head
I would die.

How safe is working with toluene at home without a fume hood? Let's say in a garage with the doors open and a fan on.

Today I learned about the cross product for complex numbers.

>>15570088
You could prove this by "covertly" remembering that 1/x this is the derivative of log and then use the log(ab) = log(a) + log(b) identity. Technically, this is still real analysis, though.

>>15566555
Trips checked
Can someone recommend me a good and reliable rock identifier for android that is free and doesn't have ads?

>>15571409
less bad than benzene but buy a gas mask anyways
also look up the odor threshhold and compare it to the OSHA safe exposure limits

How does aluminum foil lose heat so fast? I get that it's small and all, but after being in an oven at 350F for 30 minutes its still surprising you can grab it immediately

>>15571876
A combination of factors. Aluminium has low density, can be made into thin foil, and it is also a good conductor of heat. So you have something with very low mass per area giving a relatively small amount of stored heat combined with a fast rate of heat transfer.

>>15566555

thinking of starting a youtube channel that teaches physics like you would math

I would probably spend the first couple videos going over calc 3 concepts like vectors and cross/dot products

then make a video on how to approach physics problems like list all unknowns and list relevant equations. My goal would be to approach it from the standpoint of someone who never has studied the topic before

do you guys think it would be helpful?

>>15572309
Yes but aren't there channels like that already?

Our lab uses dithiothreitol which is known to degrade over time in an oxygen atmosphere. We keep it in 1.7 mL microfuge tubes at -20 degC.

Is there a way to store it under nitrogen without resorting to specialized glassware or equipment? We store unfinished ampoules of paraformaldehyde by shooting some N2 gas into them and then covering them with parafilm. Could something similar work for the DTT?

>>15572325
no not really. They just do one or two easy examples which really isnt enough to build any sort of intuition or they go through the concepts but dont really do any examples . My goal would be to help students fill in the gaps/intuition since they havent taken higher level calculus concepts or they have the knowledge but dont understand how to apply it.

>>15572335
just want to add that i would do entire videos (maybe 1-2 hours) on problems that get increasingly difficult.

>>15572309
The standpoint of someone who has never studied a topic before is often unhelpful to others. I encourage you to make the videos but I am positive that your approach to the problems will be informed by what you already know (this is a good thing)

Someone post the chart which shows by age, females that men were most attracted to. Sometimes posted on 4chan with the girls from Fate prisma illya.

>>15572189
It's just the thinness. The conductivity would make it feel hotter, not cooler.

bump

>>15572495
I meant it cools down fast, so it's already cool by the time you touch it. But yeah you're probably right, the heat capacity is likely the main cause.

>>15567743
>why this works?
long and short stick next to each other:
-----
========
distance from short's tip to long's tip = x
distance the other way = -x

>>15571710
bumping for stupid fucking rock question.

From what height I should jump for perfect hanging?

>>15573628
I don't know the answer, but I know the formula you should use.
Figure out the force needed to break your neck. because I don't know this number, I can't help you fully.
You want that much force to be applied to stop you from falling. You need to figure out next how stretchy your neck is, to figure out how long it will take you to stop. From this you can figure out the curve of force needed to stop you from a given speed (also based on your weight, which we can assume is around 300 lbs), which has a maximum at the maximum force. This maximum should be equal to the force needed to break your neck.

From this, you can increase the falling speed to increase the size of the curve. From the falling speed, you can calculate based on 9.8 m/s/s of acceleration due to gravity to find the time you need to be falling for. From this, you can get the distance from integrating the speed curve.

After that, you should be able to hang yourself quite efficiently.

>>15573678
>lbs
But newtons are kg/m/s^2

>>15573687
figure out the unit conversion, it's not hard.

>>15566555
I need a soil moisture probe for my project. I don't need a lot of precision, but I do need something more than "red = dry, blue = wet, look it's shaped like a ladybug, isn't that cute?" Ideally, I want it to give me a moisture saturation percentage.

A shitty gauge with "red to blue gradient" isn't useful. It's a really simple machine, where can I get a scientifically useable, but still not stupid-expensive, soil moisture probe?

>>15573628
https://en.wikipedia.org/wiki/Official_Table_of_Drops

>>15573720
Yep I see it. But it's too old. And I don't know what rope I should take. I afraid it will broke and I just will suffer

>>15573734
You will suffer no matter how you try to kill yourself.
Whatever shit you are going through, being dead is worse. Imagine being unbearably cold, clammy, sore with unimagineable pain, while you feel yourself literally being eaten forever. You are totally unable to do anything about it except suffer through it. You don't loose feeling at all. You slowly become less and less able to think until your mind is consumed by your own feverish nightmares, which are augmented by the very real pain of decomposition.

There may be an afterlife, or there may not be an afterlife, but it seems pretty obvious that your mind sticks around in your dead body for quite a lot of time, giving you ample opportunity to experience the horror of death beforehand.

Don't kill yourself, it makes it much worse.

>>15573734
don't listen to this guy >>15573755
do it. your waifu is waiting for you

>>15573755
I'll die in any case, I think. So, why I don't do it now? When I will be old, every day I will be scared of the death. But now this is my own decision

>>15573792
Because life is always the lesser evil.

>>15573792
What is the reason for wanting to end it all? Chances are its temporary. If you are depressed don't forget that depression causes aborations in thinking (aka you cannot or may not be able to think logically because of how depression works.). Why not just try to overcome whatever is upsetting you? Its ironically way less painful and hassle than actually trying to kill yourself.
>I've been there man, it sucks but it will pass as long as you take the most minimal and basic steps to try to get out of it.

>>15573734
Don't do it bro, suicide is cringe.
>>15573755
Is that a motherflipping SCP-2718 reference?

>>15574528
Btw don't go read that SCP entry if you're already thinking about death. I will not feel bad for you if you regret it and can't sleep at night.

>>15574528
If it was a reference, I didn't intend it that way.

I want a gradient for a kNN regression prediction. Do I need pic related or can I get a faster/more accurate result somehow using svd?

How does earth act as a practically infinite charge sink? It’s capacitance is on the order of milliFarads. My penis has a larger capacitance than that, let alone a proper one you could build. So how is it infinite?

>>15575091
It's not infinite, the Earth is just really really big.

>>15575099
I know, but it shouldn’t even be “effectively” infinite. Cause even being really really big it’s capacitance is still very small compared to charge flowing even in a small current. Yet it somehow is

>>15575123
The capacitance of the Earth is actually 710 micro-Farads, which is actually huge and remember that is per square meter.

>>15575194
What the fuck. Has /sci/ become actually retarded or completely illiterate. One, I said relative to current flow. So even a single amp is still a lot more charge flowing than required to raise earth by a volt. And your stove uses like 30 amps. Two, even just relative to other capacitors, no that’s not fucking huge. We have capacitors that are in the thousands of farads range. Third, capacitance is not a “per square meter” quantity what the fuck??? It is DERIVED from the geometry of the object, but it is a static property.
Jesus Christ

Does a basis of orthogonal eigenvectors exists, only if the matrix is symmetrical?

>>15566555
How to approach functional analysis? Should it be study after measure theory? Or is it after pde? What is the motivation for the subject?

>>15575320
t. someone who wants to learn it

Functional analysis is important has many applications in physics. Especially in quantum physics, but also in the context of mechanics. For example, if you wanted to calculate the physics of bending a elastic stick or pipe you could use methods from functional analysis.

>>15575320
After measure theory but before PDEs.

>>15575320
Rudin 1
Rudin 2
Rudin 3
Simple.

>>15566901
https://stats.stackexchange.com/questions/156897/difference-between-the-two-way-of-performing-kolmogorov-smirnov-normality-test
https://en.wikipedia.org/wiki/Lilliefors_test
also it's good practice to always make a QQ plot when testing for normality

[eqn]M_{f}: C_{0}^{\infty}(\mathbb{R},\, \mathbb{C}) \ni \psi \mapsto (x \mapsto f(x)\psi(x)) \in C_{0}^{\infty}(\mathbb{R},\, \mathbb{C})[/eqn]where [math]f \in C_{0}^{\infty}(\mathbb{R},\, \mathbb{C})[/math]. I have to show that this mapping is well-defined? Okay, but what are the equivalence classes here?

>>15575610
fyi, the set is the set of the infinitely-differentiable functions from R to C with a compact support

>>15575610
There aren't any equivlence classes here. You just have to show that the image really is in [math]C_0^\infty[/math].

>>15575633
oh, alright. Thanks

>>15575123
>Yet it somehow is
Why are you so certain of this? You've argued pretty convincingly it can't be. Try dumping a milliCoulomb of charge in the Earth and tell us what happens

>>15575123
Here I did a wikipedia search for you:
https://en.wikipedia.org/wiki/Earth_potential_rise

>>15575717
Because that’s what’s required in electrical systems for an “earth”. For small electronics, it can be the chassis itself for example in a car or the space station as relative to what is being powered they can act as an infinite pool unchanged by charge (ideally only, of course). For larger systems this the earth is literally earth. But since capacitance is only dependent on geometry it “seems” to me that none of these things should be an adequate earth, as the capacitance of even earth is tiny in relation to the charge flowing even in small appliances. But I’m obviously missing something, since electronics don’t fry themselves from their own induced emf and me having a ground fault at my home does not electrocute everybody else on my block. My question is what am I missing? How do these “earth” absorb charge if not through capacitance.
>>15575723
That has nothing to do with what I’m talking about. This is about voltage gradients produced when a discharge to earth happens. It says nothing about what happens to the actual charges or why that gradient disappears.

>>15566555
What's this sequence called
[math]s+a, s^2+2a, s^3+3a, \dots , s^n+na[/math]
I knew it but ages ago

>>15575821
To add, there used to be an entire family of sequences where one term was arithmetic and one term was geometric
[math]s\cdot a, s^2\cdot 2a, s^3 \cdot 3a , \dots , s^n\cdot na[/math]

I have a P-Channel MOSFET, specifically an IRF4905 (Ron = 20mOhm).
I'm using it as a positive side switch in a 12V system (camper bus) with the gate either at ground or source potential.

Problem is that I have a ~4V drop with a current of ~1A when the MOSFET is on.

Is the part broken or am I retarded in some other way?

>>15575817
I think the paradox is maybe resolved because the 711 μF figure is the Earth's self-capacitance, which is with reference to infinity, but in a real system the mutual capacitance of Earth and an object will be much higher because the distance is smaller and there is a connection

>>15575821
>>15575841
https://en.wikipedia.org/wiki/Arithmetico-geometric_sequence

Can /sci/ recommend books about chemistry? From absolute zero

>>15575882
https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)

>>15575817
The voltages produced when charge is discharged to the earth is exactly what you are talking about. The charge doesn't just disappear, the potential is changed appreciably and in fact the local potential is much greater than a naive calculation using the 710 micro Farads you are quoting since that value seems to come from a textbook calculation assuming the earth is a perfectly conducting sphere. But if you put charge in the earth in north america it's not going to affect the voltage in australia.

>>15575343
Is there a historical approach to it? I read on Math Stack and found that most of the motovation come from studying Fourier Analysis, so should I start by studying Fourier Analysis to motivate the subject?
>>15575350
Troll question but probability theory before functional?

>>15575864
It’s derived using a point at infinity because self-capacitance can be viewed as the amount of charge required to raise the potential of an object per volt. I don’t think mutual capacitance between the earth and some appliance would be a particularly meaningful value since I am wondering about the behavior reparative to every other system around it.
>>15576038
To be more clear, that page has nothing to do with the theoretical explanation I’m looking for. Yes, it’s another example of why I know I must be missing something but then I already knew that.y corcern is what/why
> But if you put charge in the earth in north america it's not going to affect the voltage in australia.
It obviously doesn’t. But why not.

>>15567347
>>15567383
>>15567391
>what radiation are you talking about
not radioactive gas anymore but I guess ionizing radiation

>>15576252
The details depend on the source, but basically you need mass between yourself and the source. Lead works best but water, concrete, wood etc all work if you use enough of them

>>15576305
do you think baking soda will work too?

stupid question I know

>>15576318
why are you being so evasive? you still aren't explaining what the source of this "radiation" is.

>>15576487
I meant for like contaminated things like the floor

>>15576547
And why would the floor be contaminated? From what?

>>15576318
I mean, a meter thick layer would probably be decent shielding, but it'd be cheaper to use sand or dirt.
>>15576547
If you've spilt sonething radioactive on the floor somehow, putting shielding around the floor is probably pretty impractical, so it'd be better to move the contaminated material somewhere else. Baking soda might help get it off the floor, but it absolutely won't make it not radioactive, you still need to collect it and put it somewhere. And make sure not to get any inside you or leave it on your skin for days.

>>15576798
Stop beating around the bush god damn it. This is driving me crazy. What is the radiation? What is the radiation?

>a 32-year-old mathematician named Ulrich who is in search of
>a sense of life and reality but fails to find it. His
>ambivalence towards morals and indifference to life has
>brought him to the state of being "a man without qualities",
>depending on the outer world to form his character. A kind
>of keenly analytical passivity is his most typical attitude.
they wrote a novel about me bros

>>15577142
Please, if the book was about you it would half as interesting and the character would be twice as dumb and suffer from a crippling addiction to furry porn. :^)

>>15575882
A bit advanced but clayden ochem textbook is insanely good

Is there a name for this psychology thing:

You have a thought based on old info after something huge has happened that makes it impossible for that thing to happen, and then youre like "oh that cant happen anymore"

eg: oh ill order this for x's birthday (seen while shopping). oh wait, x died a few months ago.

but its for someone really significant like a wife.

>>15576130
Stein & Shakarchi vols. I, III and IV for a mathematical POV
If you're just interested in applications for QM then any QM textbook will have enough about Hilbert spaces to get you started (assuming you have some notions of calculus and linear algebra)
Measure theory is just a tool for axiomatizing probability theory (Borel algebra and Kolmogorov axioms) in a way that's appealing to pure mathematicians, you can do advanced probability and statistics without it fine if you're interested in that. It's historically motivated by extending real analysis to integrate over arbitrary sets, not just intervals (Lebesgue integrals), and it's usually covered in an analysis course.

Could a laymen make assisted suicide drugs at home ?

can someone identify this equation? Thank you

>>15577648
Reverse Fourier Transform

>>15577667
thank you anon

does ice melt faster in air, or in liquid that it has already cooled to near equilibrium?

(my freezer is broken)

>>15577804
water, higher heat capacity and conductivity

>>15577822
even if its already cooled down? So i should drain the ice cube trays when they're sitting in their own melted water to make them last longer?

>>15576803
the source? something you ordered of Amazon that the grieger counter read the packaging as 20 CPM and you put in an aluminum tin but it definitely touched a chairs, seats, and your fingers beforehand.

yes, that was what got me all worked up.

>>15577835
20 CPM is approximately 4 microSievert per day. That is less than half than the normal daily background someone would receive and you would have to be up close to that source for all of that time. You aren't buying dangerous radioactive materials off Amazon.

>>15577878
my greiger counter does not pick up alpha particles. you have to shill out more for that

>>15577885
you think you bought an alpha particle source? kek

>>15577890
okay, the thing I specifically bought was linen socks. they were made in Poland but was in a warehouse in Ukraine. I put them (in its packaging) in an aluminum tin (along with scissors and tape) in my closet. I've been told that they check for radiation when you import stuff but I still feel uncomfortable around that thing. my mom is trying to throw it away where it will end up in a landfill and I don't know if I should call an organization to remove it. I still feel off when I enter my room

>>15577895
And why would being stored in Ukraine matter? Do you think someone took them from the warehouse, walked across the warzone to Russian occupied Chernobyl, popped them on their feet before entering the sarcophagus, then walked all the way back to the warehouse so they could be sold to some idiot on Amazon? Makes perfect sense.

>>15576547
Contaminated things need to go through a wash room and disposed of before they enter the living space. So like if you were close to a nuclear bomb going off when you got home you would strip naked outside your home and wash your entire body. All your clothes and shoes can be later bagged (wearing gloves) and put in trash bags and buried.

>>15577895
some areas of the world have high background radiation than others and different materials radiate that radition they absorbed over time. I don't think its anything to really worry about, literally the whole world is bathed in low end radiation, its just that the giger counter is made it ignore that kind of radiation.

>>15577895
> worried about deadly radioactive socks
> socks

>>15577920
so what should I do with it? put it in a landfill?

>>15577920
I remember reading a short story that humans were being naturally exposed to more radiation than other species in the galaxy. To them it was pretty deadly. For us it just made us a little wacko.

>>15577929
No, instead I recommend you go see a psychologist about your hypochondria.

>>15577932
On a similar line Asimov books said that one of the main reasons humans were like the only species in the galaxy was that Earth has more radiation that caused more mutations and life because of the constant effect.

>>15577932
>>15577937
I don't think a fictional story about aliens is helping your argument anon.

>>15577935
okay but how do I get rid of it?>>15577919
okay but what if it touches the floor or a seat?

>>15577967
that much radiation is the same as a bunch of bananas. you're being a retard.

Hi, I'm a stupid pro/g/rammer making a machine to combine fruit into groups of equal weights.

Knowing the average weight and the standard deviation of the fruit (obtained after weighing each of them individually), could I calculate how probable it is to find a combination of a given target weight?

Obviously if the target weight is 1kg and I have fruits that weigh 400 grams, it's going to be quite difficult to find a target. But I'm not totally sure how to quantize it.

Btw, the fruits probably follow a doubly truncated normal distribution.

>>15578418
I'd implement one of these approximate algorithms:
https://en.wikipedia.org/wiki/Multiway_number_partitioning
and then do Monte Carlo simulations to get the distribution of group weights

Hey guys. Im learning chemistry by myself and want to do the basic experiments listed in the book.

But where can I buy the equipment? Microscopes, beakers, ood scales bunsen burners and primarily pure elements? Any good stores? I dont want to get vanned, I just want to learn, I feel like an idiot for not understanding any chemistry. Please help

>>15577422
Forgetting or maybe denial.

>>15575817
Bear in mind that earth is (usually) connected to neutral. E.g. a fault on a mains appliance (live shorted to earthed casing) causes the current to end up back at the neutral connection on the utility panel as usual; it just goes via the earth wire rather than the neutral wire, causing the RCD/GFCI to trip.

In the cases where earth is the actual connection (e.g. single-wire earth return), the connection is a combination of resistive and capacitative coupling. Charge isn't simply being dumped into the earth, it's being added at point A and removed at point B. SWER boosts the transmission voltage to reduce the current, and no-one is powering an aluminium smelter via SWER. Also, it's only being added/removed for 1/100 or 1/120 second before the polarity reverses, so 1A RMS is ~14mC over a 10 ms half-cycle.

>>15577924
>>15577969
>those socks in its packaging were contained in an aluminum tin in a corner of my closet fora little more than a week
>that corner is now noticeably warmer than the other one
spooky...
>>15577917
no but I heard that if you fly to Kiev ( where the warehouse specifically is at) you are exposed to gamma rays in the plane or something? don't know if imported items have that too.

>>15579619
You are either an idiot or 12 years old, I'm inclined to think both.

>>15579619
Dude. That's not about kiev. Black holes and pulsars are radioactive and in a plane you have less atmosphere to shield you from them. And alpha particles cannot get out of an aluminium tin. That's pure nocebo.

Basic QM question. What happened here? Where is the direct product gone? Why are there only three subscripts?

>>15579908
the direct product symbol is omitted for brevity
the last bra should have a subscripted 2, that's a typo

>>15579825
>And alpha particles cannot get out of an aluminium tin.
but gamma rays can. and I forgot to mention that ot was actually in a carboard box for a day almost until I put it in the tin and threw away the box.
and the heat in the corner of the closet, what will come of that?

>>15579908
>direct product
That's a tensor product bub.

>>15580307
> what will come of that?
nothing, you are being laughably paranoid. you clearly have no understanding of radiation, science or logical reasoning.

Alright eggs heads, I need your help to solve a real life problem:

I need make a rope with a length of 2.20 mts.
I did some tests and I was able to make a 30cm lenght rope using a total of 24mts of thread. To make the final rope I first must make 3 little ropes, i must twisted them and finally put one over each other and untwisted them against clockwise in order these 3 little twisted ropes unit together and twist each other to form the final rope, so for each little twisted rope i must use 8mts of thread so x 3=24 mts of thread to make this final rope with a lenght of 30cm.

Note: before twist each little individual rope first I must folded it 4 times in order create the thickness for the final rope.

Question:
How many meters of thread do I need to make each individual little twisted rope in order have a final rope with a length of 2.20 mts? I will use 3 little twisted ropes to make the final rope.

How come you can extract more momentum from photons by bouncing them back and forth between two mirrors vs. just absorbing the photon? Shouldn't the former automatically cut the amount of momentum you get by half?

>>15580749
I'm not sure if that is always true. It should depend on the exact nature of the mirror.

You extract some of the momentum from the photon by making it lose energy (p = Ec). So with each bounce off a mirror it is losing a portion of energy / increasing in wavelength. However absorption is an all or nothing process so it will only happen if the photon has the exact energy to be absorbed while reflection does not depend on the energy.

>>15580330
that's sort of why I came to the stupid questions thread, isn't it?

>>15580880
And you are ignoring all the answers. It is also damn odd you would think something random you bought would be dangerously radioactive.

Been stuck on 2. How do I do it?

>>15581536
Just use the definition. For any open set [math]U[/math] containing [math]z[/math], we want to prove there's some [math]N[/math] such that [math]n > N[/math] implies [math]z_n \in U[/math]. There's necessarily some [math]B_r \subseteq U[/math] with [math]r > |z|[/math], hence since [math]\lim \sup _{n \to \infty} | z_n | \leq | z | < r[/math] there's some [math]N[/math] such that [math]n > N \implies | z_n | < r \implies z_n \in B_r \implies z_n \in U[/math].
Similarly for the other way around.

Where I can buy cheap pure tungstene?

>>15581727
for what purpose?
you can get pure tungsten cubes as a novelty item from amazon

>>15581738
I don't have Amazon here.
I need tungstene for making armor. Like knight.

And an acetylene I think

>>15581740
why would you use tungsten instead of steel or titanium, it's extremely heavy and poorly malleable

>>15581745
Nazis couldn't kill me if I would wear a full tungstene armor, aren't it? Bulletproof, like a tank.
But steel can be demolished by .50 or another heavy bullet

>>15581746
That isn't true. You'd still be killed / maimed by the blunt force even if the metal held (which I doubt)

>>15581749
shit.
Well. another question.
Are SSRI really work?

>>15581707
how to do the otherway around? i dont see why must lim sup |z_n| have to be leq |z|.

>>15581787
For any [math]r > |z|[/math], [math]B_r[/math] is an open set containing [math]z[/math], hence there's an [math]N[/math] such that [math]n > N \implies z_n \in B_r \implies | z_n | < r \implies \lim \sup _{n \to \infty} | z_n | \leq r[/math]

>>15581808
Nhmm not too sure how that gets us lim sup |z_n| < |z| though.

>>15581866
I got as far as if z_n converges to z, then we must have for some n> N such that z_n in Br, and then |z_n| < r, not sure where to go from there

>>15581266
>And you are ignoring all the answers.
"go see a psychiatrist" isn't really an good answer to anything i was sayng.

>>15580307
Gamma rays can't turn stuff radioactive, it'd need to be emitting neutrons for that. And radioactivity shouldn't really feel hot, I think. And if there was radiation getting out of the box, a geiger counter would pick it up.
>>15582025
Why isn't it?

>>15582167
>Gamma rays can't turn stuff radioactive, it'd need to be emitting neutrons for that.
so you're saying is that if let's say a piece of uranium is touching or is near a stone, will that stone become radioactive or not? it's an extreme example i know but its one to keep in mind. also I've heard that contamination and irradiation is different?
that corner of my closet was near a bookshelf with a lot of books and dvds and such. when I picked up one of the DVD cases, I felt stinging and when I scaned it it went up to 20CPM. that closet also has my piggy bank. does it mean I would have to do what >>15577919 said and burry them? there's some pretty important stuff in there.
>Why isn't it?
because it doesn't answer the question of "how should I dispose of the offending item" I know 20cpm isn't much but like what >>15577878 said you have to be pretty close to it. and I fucking touched it

>>15582167
A radioactive source can generate heat but you are talking about blocks of uranium ore or nuclear reactor rods. Anything that could cause a notable temperate change would send a Geiger counter off the scale (tens of thousands of clicks a second). Why this dude has a geiger counter in the first place is sussy as hell. He writes like a child who thinks Ukraine is like S.T.A.L.K.E.R and everything there is like The Zone.

>>15582225
>because it doesn't answer the question of "how should I dispose of the offending item"
If it doesn't set off a geiger counter? Then it's not a danger to anything that isn't touching it unless it leaches into the water or something. You can just cover it in saran wrap to stop water getting at it, maybe put it in a box to stop the wrap getting torn, then throw it in a landfill.

>>15582225
> I know 20cpm isn't much
As people keep telling you it's literally nothing. Depending on the elevation and the type of Geiger counter, a typical natural background radiation level is anywhere from 5 to 60 counts per minute.

>>15582289
a bit too late for that now. my parents already put it in the garbage bin (albeit inside a the aluminium tin in a cardboard box) and it's burried with other bags. doesn't the radiation get diluted ny the ground water? should i call someone now?

>>15582396
> ignores everyone informing you it's not radioactive
> my parents
fuck it kid, your entire house it already dead, it's only a matter of time before you all melt.

>>15582410
okay, if it's not radioactive, then how am I gonna melt?

>>15577929
You can use use them and wear them. Did you know that asphalt and bananas are also radioactive? Probably more so than your socks yet you encounter it everyday. Like I said earlier I wouldn't worry about it.
>>15577932
Theres a lot of stories like that floating around, the truth of the matter is that you can't escape radiation. The sun radiates radiation onto you (sunburn and tanning), a lot of construction materials are are radioactive, bananas and other produce are radioactive, if you dig into the ground you will encounter radioactive particles. This isn't even mentioning actual man-made devices that we use and walk around with that produce radio waves or other forms of low-end radiation. Its just inescapable, that was my whole point on the matter.

>>15566555
[math]P(A) \cap P(\bar{B}) = \{{\emptyset}\} \Rightarrow A \subseteq B [/math]

I was trying to prove this by contraposition and i end up with [math]P(A) \cap P(\bar{B}) = \{\emptyset\} \cup \{A\cap\bar{B}\}[/math].

Is this correct? I don't know how else to prove it than by supposing A is not a subset of B and proving the powereset intersection doesnt equal the set containing the empty set.

>>15583327
[math]P(A) \cap P(B) = P(A \cap B)[/math] bucko.

>>15583483
I just went to check and somehow this property isn't on the wikipedia power set page. Sasuga.
[math]x \in (P(A) \cap P(B)) \iff x \in P(A) \land x \in P(B) \iff x \subseteq A \land x \subseteq B \iff x \subseteq A \cap B[/math]

>>15583327
If [math]A \nsubseteq B[/math], then there is [math]a \in A[/math] such that [math]a \notin B[/math], which implies [math]\{a\} \in P(B^c)[/math] so that [math]P(A) \cap P(B^c) \neq \{ \emptyset \}.[/math]

Container A and Container B contain a certain volume of ice cubes. The ice cubes in each container are identical in every single way.

Container 1 and Container 2 contain a certain volume of water. The water in each container is identical except for the temperature of said water.
Container 1 -- Y degrees (C)
Container 2 -- Y + x degrees (C)

We want to pour the water from Container 1 over the ice in Container A, and the water from Container 2 over the ice in Container B.

We then want to measure the time (t) it takes for the water poured into each container to reach the goal temperature Z (which we assume is less than Y, and also assume that Y is close enough to Z that both containers will eventually reach goal temperature Z at some point).

Is there any positive value for x that would lead to the time (t) to reach the goal temperature Z to be lower for the water poured into Container B than the water poured into Container A?

Basically I'm asking if slightly warmer water will melt ice faster and cause the water to cool down faster than water that starts at a cooler temperature and melts the ice more slowly

>>15583743
The rate of heat transfer is proportional to the difference in temperature of two bodies. This should be obvious if you pour boiling water onto an ice-cube.

I don't really know much quantum mechanics aside from the little I learned in chem. I found this image which I think is saying that when an electron drops down an orbital level, the electron releases the energy it held in the form of light(photon).

My question is there an explanation why it releases the energy in the form of light? Why not heat?

>>15583743
>Basically I'm asking if slightly warmer water will melt ice faster and cause the water to cool down faster
No, like >>15583836 said the rate is always proportional to the difference in temperature, starting with hotter water just gives the cooler water a "head start" as it converges to the temperature.

So NO and the cooler water will always reach the target temperature faster

>>15583984
>My question is there an explanation why it releases the energy in the form of light? Why not heat?
Because heat isn't a particle. The energy may end up as heat (indeed this behavior inside solids is essentially heat transfer) but heat "moves" (or statistically appears so) due to temperature difference so you would not necessarily call photon emission heat emission.

>>15583994
Man this is interesting but also confusing. I guess my next question is where exactly does a photon come from? The electron still exists after dropping down a level. But the photon just seems to come out nowhere, I don't think electrons are made up of photons.

>>15583984
Well thermal radiation is photons. It's how the energy of the sun reaches the earth after all. But you need to be careful when you use the word 'heat' because in the physics of thermodynamics that has a very precise meaning.

>>15583999
It is energy being converted from one form (the total energy of the electron in that orbital) into another (lower energy orbital + photon).

>>15582167
>Gamma rays can't turn stuff radioactive, it'd need to be emitting neutrons for that.
False. Neutron capture isn't the only mechanism for induced radioactivity. Sufficiently-energetic gamma rays can cause photodisintegration, where a neutron turns into a proton, electron and neutrino. This can convert a stable isotope into an unstable one. The rays need to have energies of at least 2 MeV for deuterium up to 10 MeV for heavier nuclei.

>>15583999
>The electron still exists after dropping down a level. But the photon just seems to come out nowhere, I don't think electrons are made up of photons.
This is way beyond the scope of your question frankly. I can only point out that electrons do not properly contain photons *as matter*.

The idea that mass and energy are interchangeable is one of the core ideas you may be missing, otherwise maybe take a course on it (bearing in mind these models remain incomplete and only partially accurate, so don't get too enamoured with the "revelations" you might encounter)

>>15583999
photons are just an oscillating electric/magnetic field pair. they are not matter.

>>15579926
It doesn't seem a typo because the guy continues to use this notation. It seems as though the second subscript is shared between the two inner bras? Pic related is the full picture

>>15580322
What do I know, the guy calls it direct product

>>15584422
>It seems as though the second subscript is shared between the two inner bras
yeah that's clear from this one with the bras having a subscript on the left for some reason, that's a nonstandard notation
>the guy calls is direct product
I think that's incorrect see https://math.stackexchange.com/a/511266

>>15566555
>Deers
>French is font way bigger than English font
>Leaf quarter
This picture was taken in Quebec did it?

Why is the answer to this problem always b/gcd(a,b)? I'm guessing it's some number theory rules, but I haven't studied that yet.

Hey, can someone explain whether or not a man working 50 years ago in a varnish factory could cause his children and grandchildren to have a neurogenetic disease and optionally elaborate on how if the anwser is yes ?

>>15585609
Yeah, you need to knew a few properties about mod and gcd.

Another way of writing [math]a \equiv r \pmod n[/math] is [math]a = r + nk[/math], where k is some integer.

There is also a theorem I will not prove stating [math]gcd(a,n) = gcd(b,n)[/math]. Some general properties of gcd are: [math]gcd(a,0) = a,\ gcd(a,1) = 1,\ gcd(a.n,b.n) = n\ gcd(a,b),\ gcd(a.b,c) = gcd(a,c).gcd(b,c)[/math]

---
So [math]ax \equiv 0 \pmod b \implies ax = bk[/math]

Which gives you: [math]gcd(ax,b) = gcd(0,b) \implies gcd(a,b).gcd(x,b) = b \implies gcd(x,b) = \dfrac{b}{gcd(a,b)}[/math]

Using substitution you can then write [math]gcd(x,b) = gcd(x,ax/k) = x\ gcd(1,a/k) = x[/math], giving you the final equation: [math]x = \dfrac{b}{gcd(a,b)}[/math]

>>15585609
Yeah, you need to knew a few properties about mod and gcd.

Another way of writing [math]a \equiv r \pmod n[/math] is [math]a = r + nk[/math], where k is some integer.

There is also a theorem I will not prove stating [math]gcd(a,n) = gcd(r,n)[/math].

Some general properties of gcd are: [math]gcd(a,0) = a,\ gcd(a,1) = 1,\ gcd(a.n,b.n) = n\ gcd(a,b),\ gcd(a.b,c) = gcd(a,c).gcd(b,c)[/math]

---
So [math]ax \equiv 0 \pmod b \implies ax = bk[/math]

Which gives you: [math]gcd(ax,b) = gcd(0,b) \implies gcd(a,b).gcd(x,b) = b \implies gcd(x,b) = \dfrac{b}{gcd(a,b)}[/math]

Using substitution you can then write [math]gcd(x,b) = gcd(x,ax/k) = x\ gcd(1,a/k) = x[/math], giving you the final equation: [math]x = \dfrac{b}{gcd(a,b)}[/math]

>>15585609
>I'm guessing it's some number theory rules
It's middle school maths.
[math]lcm(a, b) = \dfrac{ab}{gcd(a, b)}[/math]

>>15585889
I can't see how that applies to the question asked?

>>15585904
the way it's defined, ax is the least common multiple of a and b. then divide both sides by a

>>15585906
>ax is the least common multiple of a and b
damn it, you reminded me why I hate number theory.

>>15585906
Thank you for explaining my post.
>>15585921
>I hate number theory.
Same desu.

>>15567462
As much as I applaud you for your endeavour I do need to ask you to apply it. You must take the MCAT, or DAT or teach/tutor, or make a home lab/lab job. Because it is information that has no connection to reality if you are not doing one of those 4. Information for the sake of information is a useless god.

t. ex-breast cancer researcher gone dentist

>>15583743
Imagine a reverse Mpemba effect. Warmer water has a lower viscosity, leading to a better heat transfer coefficient. Natural convection might be greater with a bulk temperature of 4C. If water had zero viscosity, the currents set up by the mixing of 0C water with 4C water might continue after the water reaches 0. Currents will survive longer if ice cubes are ice bergs. Salt concentration could be another variable to adjust in the search for exceptions to the rule.

>>15566555
that deer looks like he does not have time for this shit

>>15566555
Why do planets rotate around the sun. I mean I know it's gravity. I mean the sun is exerting a pull. Is the rotation caused by the planet's own counter gravitational pull on the sun?

>>15566555
what does creatine scientifically do for the body? what exactly is it? my younger brother wants to start taking it but parents don't like the idea, I take it myself.

>>15586590

>>15586510
no, the sun's attraction is what causes rotation of the planet
the gravitational attraction generates an inward acceleration and consequently a tangential velocity

Let [math]k,\ell \ge 1[/math]. Is the cup product [math]H^k (S^k \times S^\ell) \times H^\ell (S^k \times S^\ell) \to H^{k+\ell} (S^k \times S^\ell)[/math] surjective?

([math]H[/math] denotes singular cohomology with integer coefficients, [math]S[/math] denotes spheres.)

>>15586613
What is the etard method? Structurally the same as what? Angel's delight is a dessert, right? You should not mix paint thinner with dessert. That's not healthy.

>>15586904
Answering my own question: The Kunneth formula implies that every cohomology class in [math]H^{k+\ell} (S^k \times S^\ell)[/math] is a linear combination of such cup products (good enough for me).

>>15566555
>stupid
If one day Charon crashes into Pluto then will the resulting object be considered a planet?

>>15587232
... Haven't they already collided once?

Why would v be constant here? Would it be L = C*v after you integrate by dv?

>>15578713
Ngl, she's kinda cute. I see some of the stuff you want on ebay.

>>15587398
They are not assuming anything about the functional form of L(v) at that point. But if you have the equation
dL/dv = constant
and the left hand side is some function of v alone, and the right hand side does not depend on t, then this means v does not depend on t.

(I) A*A = AA* + BB*
(II) B*A = DB*
(III) B*B + D*D = DD*

These are all matrices * denotes the complex conjugate. How can I show that either A/D is normal or that B = 0? (if A/D is normal, then B = 0 follows)

>>15587648
>* denotes the complex conjugate
Are you sure? Do you mean complex conjugate transpose?

>>15587476
Couldn't you get a time dependent by integrating by dv then by dt? Or is velocity not dr/dt in this case?

>>15587772
then you get that r is time dependent

>>15587772
v and t aren't two dependent variables on an equal footing. v is a function of t, so your question does not make sense to me.

To see how it works concretely, suppose L=(v^2)^2.
(d/dt)(dL/dv)=0 means
4(v(t)^2)*v(t) = p_0
where p_0 is some constant vector, and v(t) is a function of time. Dot the equation with itself and we have
16 (v(t)^2)^3 = p_0^2
v(t)^2 = (p_0^2/16)^(1/3)
So the norm of v(t) is constant, which means
v(t) = p_0 / (4v(t)^2) is constant.

>>15587719
Sorry, complex conjugate transpose ofc

>>15583483
>>15583490
>>15583505
Thank you anons! Much appreciated :)

Why doesn't propyne spontaneously turn into propadiene?

What will death feel like? How much in pain would I be if I make a cut underneath my arm pit?

>>15587876
I see now, thank you very much.

>>15588090
It does. And back again too.

What are some good science and tech news sites? I like Quanta Magazine, but what else is there?

>>15588090
it does. that's why MAPP gas lists both. they appear to be in a 2:1 equilibrium under standard conditions

Can you guys show me how to do this using numpy? I have the coordinates of a rectangle and I want to find the transformation matrix (T) that when multiply with will get me the new coordinates like in picture

Thx bruhs

>>15588986
too lazy to google?

https://www.petercollingridge.co.uk/tutorials/3d/pygame/matrix-transformations/

>>15589002
Not quite what am looking for! I want to solve for this matrix from knowing these coordinates.

Of course I can start with an identity matrix, mirror by x axis, and translate up, but I want numpy to solve it for me.

>>15588986
You need to use homogeneous coordinates. Matrix multiplication is a linear operation, so it will always map (0,0) to (0,0). Also: you appear to have x/y swapped.

Does cyclopropane spontaneously turn into the more stable propene on long timescales? I can't find any mention of it happening.

Any good YouTube channels for math with white men teaching? I can't focus listening to Indian accents or female voices

>>15589488
yes

I don't wanna make my family sad because of my death. How can I prevent it? Became jerk?

>>15589567
Not a /sci/ question, try /adv/

>>15589713
k

>>15587648
>>15587930
Do you also have:
(II.b) B*A*=D*B* ?

If so I can prove it. BB* and B*B are both diagonalizable with non-negative eigenvalues. If v is an eigenvector of BB* then B*v is an eigenvector of B*B, and you can use the non-negativity and relations (II) to prove the eigenvalue must be zero. If (II.b) is not given, then maybe focus your efforts on trying to prove it.

>>15587648
Actually if A and B are finite dimensional matrices, you only need (I). Just take the trace of both sides and you can see it is only valid if B=0.

If you are talking about something fancier it sounds like you are getting in to the territory of the Stone-von Neumann theorem.

Why is /sci/ moving so fast is it just summerfags or are /pol/laks looking to branch out since I see a lot of blatant /pol/ threads not even attempting to be a /sci/ thread.
It's not usually this bad.

>>15590519
Ingenious idea, thanks a lot

>>15590519
Slick.

>If you are talking about something fancier it sounds like you are getting in to the territory of the Stone-von Neumann theorem.
For any [math]u[/math]:
[math]\langle A^*A u, u\rangle = \langle AA^* u, u\rangle + \langle BB^*u, u \rangle[/math]
[math]\| Au \|^2 = \| A^*u \|^2 + \| Bu \|^2[/math]
That should *somehow* get you [math]B = 0[/math] but the specific argument is escaping me.

>>15591007
If you are talking about infinite dimensional representations you can't argue along those lines. If you know what creation and annihilation operators in quantum mechanics are you will see that they provide a counterexample to what I did taking a trace. That's why I mentioned the stone-von neumann theorem, which deals with such representations.

>>15591019
Oh, I see what you mean.
Yeah, what I posted doesn't work for unbounded operators, I thought anon was working over bounded ones, even though they might be finite dimensional.

>>15591031
*infinite dimensional.

>>15587648
what "*" here is even supposed to represent? All the other school i went used "*" to mean entirely different things.

>>15591040
if I had to take a crack at it, I would go out on a limb and suggest that it might be the complex conjugate transpose. just call it a hunch

>>15584550
It do.

What the heck is going on when they say they put a bunch of molecules in superposition?

>>15591059
A superposition is the combination of all the possible states a system could be in, it is not in a single definite state until you measure it. Mathematically speaking it is the linear combination of all possible solutions to the Schrödinger equation. This superposition / general wavefunction can be shown to exist as it affects the probability of which final state the system will be in once measured and that is a different probability to that of the system being in that state from the start.

How you actually create a superposition and what quantum property is being measured depends on the experiment or system. The simplest example would be measuring the spin of a spin 1/2 particle along a particular axis, this would put it in a two state superposition of spin up and spin down. The experiments using molecules are similar but more complicated versions of this.

>>15591620
I clearly have much to learn, thanks for the reply

a parametrized curve is a curve that can be written as [math]\gamma = (X(t), Y(t))[/math].
Can I state that [math] X:I\to I_1[/math] and [math]Y:I\to I_2[/math] where [math]I,I_1,I_2\subseteq\mathbb{R}[/math]?

How is Atomic mass unit and Atomic mass different from each other ?
And relative atomic mass to
If we say
5gram oxygen atoms
Th no. Of particles are - (5/16)*avogadros number

But if we say 5amu oxygen atoms ?

And how is relative atomic mass is used in question solving ?

>>15592746
1 amu is defined as the mass of 1/12th of the mass of a Carbon 12 atom. It's an arbitrary value used for convenience to compare the relative weight of atoms. So for example a single hydrogen atom would weigh 1.00784 amu but it's not an SI unit like the (kilo)gram.

Help me out, algebra chads. Is the [math]n[/math]-fold tensor product [math]\mathbb{Z}[x_1]/(p_1) \otimes_\mathbb{Z} \dotsm \otimes_\mathbb{Z} \mathbb{Z}[x_n]/(p_n)[/math] isomorphic to some well known ring?

(I doubt that it matters, but in case it does, may assume [math]\deg p_i = 2[/math] [math]\forall i[/math].)

>>15566555
Given that all I know is precalc, and I want do become decently versed in math, physics, chem and a little engineering, how much can I progress given I study 10 hrs/day for 365 days? What can I expect to know and how good of a foundation will have have to learn what excites?

Where do forces get the energy from to attract or push things away? Did any scientist even ever dip their feet into this topic?

I'm trying to study more rigorous math, coming from an electrical engineering background. The more mathematical texts use notation in a different way, where my intuition tells me "there's more to this that a mathematician would see, but since I don't have that background, I don't know what it is"

specifically I'm studying variational calculus right now. The book mentions some "functional form" given as [math]F(x,y,p)[/math]. Obviously, x, y, and p are "just" arguments to F, but that's where my confusion kicks in.
They then give [math]I = \int_{a}^{b} F(x, y, \frac{dy}{dx})dx[/math]
What, if any significance is there to the arguments being y and y's first derivative, to the overall meaning/interpretation of F? Am I supposed to interpret y as just being a dumb variable, or am I supposed to understand it as "y, the dependent variable of x" as we do in single-variable mathematics? The text does mention "we don't know the functional relation between x and y".

>>15594172
Think of I as a map from functions y(x) to real numbers (it is a "functional"). Once you specify the function y, then you know F(x,y,y') for each point x and can integrate.

Example: Say F(x,y,y') = (1+(y')^2)^(1/2)

If I input the function y(x) = x^2,
F= (1+2x^2)^(1/2)

If I input the function y(x) = x.
Then F= 2^(1/2)

>>15594207
Sorry (1+4x^2)^(1/2) but you get the idea

>>15594207
>>15594211
It's a lot more clear. In your example, y doesn't explicitly appear in the functional. Is it an argument simply by virtue that its derivative does appear in the functional, so y must be included as an argument?

>>15593510
what do you mean by "decently versed in"? It's an unreasonable goal you're setting for yourself, especially with this 10 hours thing. Look up coursework for an undergraduate degree or minor in each of those fields and set a goal accordingly.

>>15594334
I just chose a functional in which x and y don't explicitly appear, only y' did. But in a more general case all three will explicitly appear

Example: (y' - A(x))^2 + y^2
where A(x) is some function of x alone. (I picked this example because it shows up in QM as a gauged harmonic oscillator)

I know how to program and stuff, but I wanna learn how to actually use it for real world applications. I wanna build a little lighthouse with a solar panel thing that will turn toward the sun. I don't know where to start though.

>>15594937
Break it down into smaller problems

>>15595457
Right, but what subjects? What books?

>>15595499
no book will teach you everything. The best way to learn is "i want to do X", look that up, figure it out, then move forward. Don't know something? Look that up. That's how professional programmers do their work lol.
Books are good for a crash course or learning the fundamentals of the language, starting out from zero, but that's the extent.
I'm not a programmer but I program a lot of things for myself and for work, never opened a book. All I took was a single semester of highschool java.

>>15566555
I can recognize that beaver vending machine anywhere, this picture was taken in quebec.

I want to source chloroform. I can learn if it's safe to smell it myself, and prep later
I'm looking for a way to source it from somewhere - I prefer plants the most. Can they make it and are a decent source for what I'm trying to get?

>>15594937
I'm confused. If you already know how to program then what is stopping you precisely?

I have trouble understanding the solution here.
Can anyone help break this down? Assume I have no idea of improper integrals.

>>15595507
>>Books are good for a crash course or learning the fundamentals
Not even. A good lecture is way better than parsing through hundreds of pages of vague, inapplicable midwittery.
All you need are the basic vocab and concepts of a field, which should only take a few hours, to start researching things on your own.

>>15595507
>>15596030
they both have their ups and downs but realistically you have to use both if you actually want to get anywhere with anything.

>>15595549
You have no (zero) chance of synthesizing chloroform from "plants", whatever the fuck you think that means. This is one of the simplest substances to prepare in an amateur context, too, as all haloforms can easily be prepared through haloform reaction in a literal ice bucket.

Chloroform also does not knock people out like you see in the movies and television, that is pure fiction. So there's no point anyway, sorry!

>>15595549
>I want to source chloroform.
Might want to check up on your local laws about that first, in a lot of places manufacturing of chloroform regardless of what its used for, even if its used legally, can still get you a felony and behind bars.

>>15595572
Well I am not educated on things like circuit boards or microcontrollers. Any books on those? I wanted to start even smaller and make something that could simply turn on a light when I press a certain combination of buttons.

>>15596240
you could literally just get a raspberry pi and put it all together. components are fairly simple because most of them these days are just plug and play, unless you are trying to make everything by yourself out of scratch?

>>15596240
Almost all components use the same simple computer logic gates as your actual computer does, its just lacking the software to direct it. So its just figuring out where software input goes, what type of software input, make sure your computer outputs that same input command and there you go. I would honestly just jump in and solve problems as they come up, its probably the most frustrating way to do it but that is how I figured out AI for the most part. Gonna be learning python this fall, pretty excited about that.

>>15596018
I don't think you even need to know about improper integrals to understand that solution. It walks you through it step by step. Which part(s) don't you understand?

>>15596240
https://www.arduino.cc/en/Tutorial/HomePage/

Can nitric acid and lime slane be combined to create calcium nitrate (instead of using lime stone), to create ammonia? One is cheaper than the other

>>15596655
the point where they substitute tanh^2(x) to rewrite the integrand. I don't get it at all and I can't see how [math] \frac{e^x - e^-x}{e^x + e^-x} [/math] turns into that

>>15597508
because [math]\tanh(x)=\frac{\sinh(x)}{\cosh(x)}=\frac{\frac{e^{x}-e^{-x}}{2}}{\frac{e^{x}+e^{-x}}{2}}=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}[/math]

>>15597519
Yes, but after that how do you get to here

>>15597521
Simply substitute and expand the terms.

[eqn]\begin{align}
1 - \tanh^2(x) &= 1 - \frac{(e^{x} - e^{-x})^2}{(e^{x} + e^{-x})^2} \\
&= \frac{(e^{x} + e^{-x})^2}{(e^{x} + e^{-x})^2} - \frac{(e^{x} - e^{-x})^2}{(e^{x} + e^{-x})^2} \\
&= \frac{(e^{2x} + e^{-2x} + 2) - (e^{2x} + e^{-2x} - 2)}{e^{2x} + e^{-2x} + 2} \\
&= \frac{4}{e^{2x} + e^{-2x} + 2}
\end{align}[/eqn]

>>15575845
I could be something else too. Can you confirm that the 12 V power supply is capable of sourcing 1 amp without a significant voltage drop?

>>15597526
ahh ok
thank you

>>15577831
What's the goal? Keep the box the same temp as long as possible or keep the ice as long as possible

What does a changing magnetic field mean?

>>15598490
Faraday's Law: A magnetic field that has enough magnetic force lines flip in polarity within an area over time.

I just ate some fish and my mood has improved. Am I having a placebo or is there an actual reason that I'm too retarded to notice

>>15599472
healthy omega-3 fatty acids and you might be deficient in something. Could be dopaminergic too, its hard to say. If you aren't getting good sleep, sunlight, exercising (stretching, cardio, strength building), and eating a healthy diet, I would start there.

>>15599472
Fish that are lower in the food chain are the healthiest. Sardines are my favorite. They don't accumulate mercury and give you all the benefits of fish.
>>15599512
when i first tried sardines, I would have intense cravings throughout the day, every day for probably a week straight. I ate nothing but sardines like a ghoul at 3am. There's actually a bit of a joke that when you eat sardines you'll go crazy for them for a while. My body was definitely deficient in whatever they have.