/sci/ - Science & Math

Unanswered questions from the previous thread:
Physics questions:
>>11276685

Math questions:
>>11276755
>>11280562
>>11281218
>>11283838

Psychology questions:
>>11284418

Stupid questions:
>>11269883
>>11278245
>>11282152
>>11282990
>>11284186

Some faggots in the board set up a discord for old men struggling with basic maths. It seems topic related enough to leave a link here: https://discord.gg/v7rTvje
Note: I haven't joined the server, and I know absolute jack about its quality. I'm putting it here in the hopes that it reduces the number of people asking for advice or tips on learning algebra.

can anyone write the reaction please? it's an amine protection

guys what are those people that stand on the road with the giant tool to make circles

>>11285775
Surveyors?
>>11278245
you would be dead
>>11282152
do NOT get into adderall

>>11285775
surveyors?
>>11283838
>catenoid
The surface of revolution of a catenary, which is the shape a uniform chain makes when it hangs. Can be described by a hyperbolic trig function.
>what is space
The thing that we move through? Idk. In math it is the span of basis.
>plane, line
2D space, 1D space
>point
a single location in a space
>>11278245
you would be dead
>>11282152
do NOT start adderall

What're the best ways to compare departments between schools?

>>11285751
It's late but I tried.

Brainlet here,

Whats a good way to efficiently learn integral & differential Calculus? I'm pretty good with math but i'm out of school and I need some pointers towards good resources.

Has the possibility of quantum mechanics being "pseudo-random" rather than true random, been ruled out? Pseudo-random meaning that, every time a particle has the potential to collide with a barrier, but instead passes through, that barrier gains an increased likeliness of colliding with future particles.

>>11285862
The quality of pubs of the faculties, or their [math]h[/math]-indices.
>>11285889
If by pseudo-random you mean induced by non-random hidden variables as in stat mech then yes, by Bell's theorem which forbids formulations of local QM with hidden variables and classical Kolmogorov probability. If one is truly Bohemian (or Bohmian, I should say) he or she may wish to discard locality; this is undesirable for the practicing physicist, however, as locality is seen in almost every quantum phases and their first order responses. Non-locality can occur only in fringe cases where you have infinitely many conserved quantities in your system.
Now this is not to say that hidden-variable QM has been ruled out completely. If we wish to discard instead our conventional understanding of probability and adopt fuzzy logic, quantum topos theory (https://arxiv.org/abs/1207.1744)) is such an alternative that keeps locality. Of course this brings into question the ontology of conventional probability but that's food for the philosophers' thoughts.

[math]\sin{\theta} = \frac{4}{5}[/math]
[math]\frac{\sin{\theta}}{\sin} = \frac{4/5}{\sin}[/math]
[math]\theta = \sin^{-1}{}4/5[/math]
because fuck you

How exactly do different bases in dna tell cells which proteins to use?
Is it comparable to a computer code?

>>11285941
I should've been more specific, the two main things I want to compare (for getting my bachelor's) are:
>Job potential directly after getting a degree
Like what kind of internship opportunities do they provide
>Potential for a post grad degree

I can't make up my mind on which path I'd like to take. I'm wondering if there are some websites that provide information. Other than the scorecard website provided by the DE, most of the big sites look sketchy.

Like how important is department size, # of undergrad courses ect,. I'm just kinda clueless

Where can I see all the concepts taught in a particular university major? For example every concept taught in statistics for a statistics major. I'm not just talking about a simple stats course from one year, but everything related to the major over the course of it.

>>11286498
Any university website will have a list of degree requirements, which will be a list of something like 20-30 courses that everyone who gets a degree in X is required to take. These are generally pretty similar at most universities so that'll give you a topic-level breakdown of what any completely generic graduate would be expected to know.

>>11285574
Let me solve
>>11276685
[math] p_2^2=(P-p_1)^2=P^2-2P\cdot p_1 + p_1^2 [/math]
[math] P= (M, 0) \Longrightarrow P^2=M^2[/math]
[math] p_1= (E_1, \tilde{p}_1) \Longrightarrow p_1^2=m_1^2[/math] and [math] P\cdot p_1=M \, m_1[/math]
In the last line [math]\tilde{p}_1[/math] is the 3-momentum.

>>11286496
Honestly it does not really matter that much where you get your bachelor's. As long as you don't go to a complete dogshit meme school you'll be completely fine.
Outside of the very, very top schools (which anyone living in the USA knows by name anyway) differences between undergrad degrees are not that wide.

How important things like department size are are subjective questions for you, not objective metrics. Some people like bigger, busier departments, some people like being able to know every single prof and grad student personally. There's no "correct" answer.
Think about the city, too. Notre Dame is in shitsville nowhere, Columbia is smack in the middle of Manhattan. There are people who love and hate both of those environments, and a surprising amount of people don't consider this until it's too late even though they'll be living there 4-5 years.

>>11285574
>Stupid Questions:
>If I get absolutely shitfaced, BAC of 1%, then have a complete blood transfusion would it sober me up completely?
I don't care how stupid this is I want to see this done in a clinic just to see what happens.

>>11286577
kek

>oral exam
>prof has a blank, emotionless face throughout the exam
like talking to a fucking wall, is this normal?

>>11286602
they just don't give a shit

>>11286613
don't they get paid jack shit? why would you do it for money.

>>11286577
Theoretically it should work, I imagine it would be a nightmare for the immune system though.

>>11285883
Read Spivak.
>>11286577
>>11286643
According to my meager and frail knowledge of biology, you aren't drunk because of the alcohol in your blood.
You're drunk because of the alcohol in your brain.
So I'm distantly sure that, even if you swapped your blood out, there would still be some alcohol left in your head, and I don't know how long it would take to fuck off. Could be very fast, could take long.

>>11285963
There's Bongaarts, that I know of.
The issue with QM is the infinite hassle that is quantization. Esposito's book on Deformation Quantization gives a general outline of the situation.

>>11286517
thank you, i had figured it out in the meantime but at least now i'm sure
i have another stupid question: in the context of a collision which produces 3 particles, how do you prove that: [math]m_{12}<E_{COM}+m_3[/math]
which should mean that the invariant mass of 2 of the particles cannot be greater than the total energy in the COM frame plus the mass of the other particle?

Having very little real knowledge about Partial Differential Equations, I have tried to implement a heat flow in Python.
I am simulating a 1D "rod", and dividing it into many equal portions, each with its temperature.
What I do is iterate over the portions, average the temperature of the neighbouring ones, subtract the temperature of the current portion, multiply by a constant, and add this to the temperature.
I treat the first and last portion as the "boundaries", only taking their single neighbour, or optionally, doing a weighted average with a constant (this will make the whole rod to eventually stabilize at that constant, or if the left and right constants are different, it will approximate the shape of a linear function)
When iterating, I always compute the new temperatures according to the current ones, and only then I update them (instead of updating on the fly, which I suspect would be less realistic).
To give initial values I can use an arbitrary function, or even random values.

This system behaves more or less (to the eye) as one would expect, but I wonder if it is actually meaningful or remotely realistic. I believe what I do is formally called "finite element method" but I am not sure.
If I am doing stupid shit, what can I do to improve it?

Dumdum question here, can you use partial density (kg/m3) as mass concentration (kg/m3--from cfd)? I meant partial density is like [math]\rho_{all} . Y_i[/math] while mass concentration is like [math](Y_i . m_{all})/V_{all}[/math].
I'm trying to connect thermodynamics with chemical reactions here. And the result of mass balance of species i equation is partial density, while the kinetic rate is requiring mass concentration to compute.

>>11287031
I see no reason that would prevent you from considering those quantities. The volume V_all is presumably the same for all species.
Although I wonder why in your forumas, there's no different masses for those species mentioned.

>>11287010
That sounds more like finite differences than anything else.
>If I am doing stupid shit, what can I do to improve it?
The usual. Pick up a book on numerical PDEs, apply the techniques in it to solve the heat equation.

>>11286404
More comparable to a set of legos flying around in water.
Each of the DNA bases deforms RNA polymerase (the enzyme that puts together RNA transcripts for protein production) such that only a matching RNA nucleotide will be added to the transcript. This continues along the whole transcribed region of the DNA.
Protein mechanics are all about electrostatic interactions. The enzymes evolved so that they could deform to certain shapes that make them useful when they interact with other molecules.
After some processing, the transcript is sent to a ribosome (protein-making complex made of proteins itself and a different kind of RNA). The ribosome moves along the transcript and uses yet another kind of RNA called tRNA to build the chain of amino acids that make the protein. The ribosome pieces, amino acids, and tRNA are floating around the cytosol. What makes them useful is that they can bind to specific sites on other molecules when they come close.
Remember that small-scale interactions are dominated by randomness.

>>11287010
>What I do is iterate over the portions, average the temperature of the neighbouring ones, subtract the temperature of the current portion, multiply by a constant, and add this to the temperature.
That doesn't sound right...The rate of change of the temperature of a single element is going to be proportional to the SECOND derivative of temperature over space. Basically the situation is this:
[eqn]\frac{\partial T}{\partial t}=\alpha\frac{\partial^2T}{\partial x^2}\implies \frac{\Delta T}{t}=\alpha\frac{\Delta(\Delta T)}{x^2} [/eqn]
The equation on the left is the heat equation for a thin rod, and alpha is the thermal diffusivity of the material. On the right, t is the time increment, and x is the size of each element. Basically, you get that the change in temperate of an element over a time increment is proportional to the *slope of the temperature gradient*, not the temperature gradient itself, all divided by x. Basically you need to find the dT/dx at each element, which is what you were already doing, but then you need to find how that value, the dT/dx changes over space.

Is the Boltzmann constant the entropy of anything in particular? Like, what system would generally have entropy of k?
Or is it just a scaling factor?
From S = k ln |W|, only a system with e microstates could have entropy k. That can't be done because e isn't an integer, right?

>>11287070
>>11287010
If you want, you can say that
[eqn]\frac{\partial^2 T}{\partial x^2}\approx\frac{T_{i+1}-2T_i+T_{i-1}}{x^2}[/eqn]
where Ti is the temperature of the ith element and x is element size. At the boundaries, you will need to use forward/backward second order finite differences (look that up).

>>11287074
statistical thermodynamics completely falls apart at the scale when you are dealing with 2~3 states. the Bolzmann equation is valid for large W.

Is [0,pi[ with addition and multiplication mod pi a R-vector space? If so, why is it not isomorphic to some R^n?

>>11287074
Seems to be a scaling factor. I think of Boltzmann distributions as basically bell curves, but bounded on one side by zero.
The constant is just a normalization factor associated with that distribution.

>>11287085
How is the multiplication by scalars defined?

>>11287070
>>11287080
Thank you anon. I think that was very clear. I really should read more on this. My implementation felt too simple to be correct.
>>11287061
>Pick up a book on numerical PDEs
That's always a good idea.

>>11287131
Regular real multiplication, just bring the result mod pi

>>11287139
Is it well defined?

>>11287085
No. [math]u = \frac{\pi}{\pi} u = \frac{1}{ \pi} \times \pi u = 0[/math] for any u.
>>11287135
>That's always a good idea.
Indeed, indeed.

>>11287168
Ah yes, thanks.

>>11285524
I need to learn the deduction of a parabola formula (using the focus, directrix, etc.). Is there any textbook that explains this for brainlets? I don't understand what exactly is the focus for example.

>>11287194
https://www.mathopenref.com/parabolafdderive.html

>>11285524
is [math]i[/math] a number?

>>11287243
Yes. It is an imaginary and complex number.

Is it weird to start off a proof by contradiction by saying "by contradiction, assume...". My professor had a proof in class that was by contradiction and I asked her if she meant for contradiction and she said it didn't matter and people say botb. Like the contradiction wasnt reached so you can't derive anything from it so saying" by" seems to make no sense. It was an econ class BTW, is this really standard practice?

>>11287268
>is this really standard practice
Sure, whatever. It really doesn't matter and I think you are reading way too much into it. People usually start those kinds of proofs with "Assume to the contrary that..." It means the same shit.

>>11287268
it doesn't make sense but people do it. that's literally all.

>>11287274
>>11287276
Fuck guess I'm autistic.

>>11287280
aren't we all~?

>>11287282
no

How do I solve x+3^x<4? I need to find the X value for which this statement is true, i.e. isolate the x.
I tried using symbolab but it did the following which I did not understand:
(it got there from 3^x<4-x)

>>11287292
let [math] f(x)=x+3^x-4=0 [/math] then use Newton's method to pin down that zero, say x0. Then notice that f(x) increases monotonically, therefore x is all x less than x0. There is no closed form inverse of f. I don't know what the fuck symbolab is doing.

>>11287292
Set y=4-x.
Then x=4-y, and we have
[math]3^{4-y}<y[/math]. Then we have [math]81=y3^y[/math], and y=3.
>>11287297
>

>>11287297
>use Newton's method to pin down that zero, say x0. Then notice that f(x) increases monotonically, therefore x is all x less than x0. There is no closed form inverse of f
I don't know anything of that, but this is supposed to be an intro to calculus book(Spivak)... Did I get memed? I was enjoying how he was reviewing basic algebraic properties so far and make you write proofs to things which seem obvious at first sight

>>11287306
Please help

>>11287458
this guy already helped you >>11287300
the last step, where he gets y=3, is inspection. Or, literally just inspect the original inequality.
>one plus three to the first power equals four
>x plus 3 to the x always increases
>so x is less than 1

>>11287475
Should I know this already if I'm just getting into calculus?

>>11287515
know what? how to manipulate exponents? yes

>>11287525
>Newton's method
>monotonically increasing functions
>closed form inverse
>inspection
I never saw any of that in high school and haven't seen any pre-calc course mention it either, what's usually covered is some trig, functions up to logarithmic and exponential functions and some geometry.

>>11285524
i was looking at the solution for a problem and thought i got it wrong, but then i used a calculator to find my answer had the same value, it was just expressed differently. In general
[math]\frac{\sqrt{x}}{x} = \frac{1}{\sqrt{x}} [/math]

is there any particular reason to use 1 form over the other? or is it arbitrary?

where other than library genesis can I find lots of books?
I need the latest edition of a certain title and they only have the one before it

Does anyone know of any books that go in depth into empirical aspects of Quantum Mechanics?
Soemthing that actually goes out of its way to explain how the Hydrogen's energy levels were measured before Schrodinger calculated them and the like.
>>11287546
Gotta remove roots from the denominator.
>>11287609
Did you try seeing if your university has open access?

>>11287546
Not really. You could argue the first is better because then there are no radicals in the denominator. You could also argue the second is better because it has 1 as a numerator so it's simpler.

so i'm reading through the first chap of Apostol Calculus, at the part where he proves why the area under a parabola is [math]b^3/3[/math], I understand how he gets to top inequality, but I don't understand why he says "this is obviously false when n > ...", where did that last inequality came from??

Obviously [math]\frac{2x-1}{\:x-1}\not= \left(2x-1\right)-\left(x-1\right)[/math], but when I do one or the other of these, they both seem algebraically valid.

Can someone point out where I'm fucking this up?

>>11287777
exp(ln(A)-ln(B)) = exp(ln(A)+ln(-B)) = exp(ln(A)) * exp(ln(1/B))

>>11287782
Alright, that's where I figured it was going south. Thanks.

>>11287777
exp isn't linear

exp(ln(A)+ln(-B)) = exp(ln(A)) * exp(ln(1/B))

>>11287777
The one on the left is fucked up.

>>11286654
As long as you don't care about the classical limit, there is no need for "quantization" in the strict mathematical sense. Von Neumann's QM text directly constructs states from the *-irreps of the Heisenberg/Weyl algebra. The reason why deformation quantization is such a rich and complex field is because you're studying how to make the CCR/ACR algebra jive well with the classical Poisson structure. There is no need for that in algebraic QM; the density distributions are exactly what you get from the *-irreps and nothing more, what's "classical" is merely a matter of opinion.
>>11287611
Try Zinn-Justin.

>>11285524
Pleb trying to learn math here.
When solving differential equations in linear algebra, how do I know if I pick the right eigenvector matrix? Lets say I have a basis for the null space with eigenvalue that is (1,0,1) and (0,1,1) but (1,-1,0) is also in the null space. I would get different results depending on which vector I pick.

>>11287715
i remember having a lot of trouble conceptualizing with that exact inequality (and the parts leading up to it)

here is my best take. keep in mind im a total amateur.

so far as i can tell, if we assume A> b^3/3 we get that inequality on the top as equivalent. in other words, we are saying n will always be less than the right side. but we are assuming n can be ANY positive integer, so we can always choose an integer n which is greater (or equal), for example consider x = b^3/(A-b^3/3)

if we say n = x+1 then we have a contradiction. n cant be both greater than or equal to and less than that value.

>>11287777
only the right hand side of ur pic is right
[eqn] t=\ln\Bigg(\frac{2x-1}{x-1}\Bigg)=\ln(2x-1)-\ln(x-1)[/eqn]
exponentiate both sides
[eqn] e^t=e^{\ln(2x-1)-\ln(x-1)}=e^{\ln(2x-1)}e^{-\ln(x-1)}=e^{\ln(2x-1)}e^{\ln\big((x-1)^{-1}\big)}=\frac{2x-1}{x-1} [/eqn]

>>11287803
thank you for reply,

>>11287787
>As long as you don't care about the classical limit, there is no need for "quantization" in the strict mathematical sense.
I know.
Anon had asked for books that derivaed results, and then asked for books about Quantum Mechanics.
My brain just naturally dragged quantization in for no good reason.

>>11287545
You need to think analytically and to understand the laws of exponents and logarithms, how basic inequalities work and how algebraic substitutions work. Newton’s method isn’t necessary for this problem. Spivak is a watered down intro to analysis text not an intro Calculus text, he expects analytical competence and will only demand more of you in the later chapters.

>>11287850
It's a fair connection to make, especially since most get their first contact with QM through classical mech considerations.

had my first linguistic course (the chomskyan program) and now I want to transfer from computer science to linguistics
thoughts?

How many generations would it take to breed chihuahuas to doberman size without adding other breeds to the mix?

HELP

An object is traveling at [math] v [/math] meters per second.
There is a stationary line [math] s [/math] meters in front of it.
With what value should the object (constantly) accelerate or decelerate, such that it passes the line in exactly [math] t [/math] seconds?

>>11287915
sounds more rewarding and less soul crushing, I support your decision. understand though that unless you plan on doing translation work your job prospects will suffer significantly.

>>11287975
remember SUVAT? Apply yourself, anon!

>>11288160
>remember SUVAT?
no, I was never taught that
but I looked it up. Thanks

I had a hemipelvectomy a while ago, how do they saw bones while they're in me without getting chips of bone in me?

import re

In a Python string, how do I replace all instances of TeX brackets $foo$, as in
>bla bla $y=\sqrt{1-x^2}$ and so on

with mathJax style brackets \(foo\)
>bla bla \(y=\sqrt{1-x^2}\) and so on

Thanks.

>>11287793
If you have an eigenvalue with multiplicity N>1, the corresponding eigenspace is N-dimensional, i.e. there are infinitely-many sets of N linearly-independent vectors which form a basis for the eigenspace.

In terms of solving linear ODEs, if you have a repeated eigenvalue then you end up with c1.v1.e^λt+c2.v2.e^λt = (c1.v1+c2.v2).e^λt, i.e. you can choose any vector within the eigenspace. But you also end up with a (c1'.v1+c2'.v2).te^λt term (more generally, t^n.e^λt terms where n+1 is the multiplicity of the eigenvalue).

IOW, it doesn't matter which vectors you use as a basis for the eigenspace. When you solve for the initial conditions, the choice of vectors just affects the constants meaning that you end up with the same solution regardless of the choice of basis.

>>11288804
re.sub(r"\$(.*?)\$",r"\(\1\)",s)

>>11288823
based, thx

I can't understand what the 4-divergence is, it seems to be the same as the 4-gradient. wikipedia defines the 4-gradient as: [math] \partial_\mu= \left(\frac{1}{c}\frac{\partial}{\partial t}, \vec{\nabla}\right)[/math], while pic related is the definition of 4-divergence in my book, are they not the same?

Why don't women lay eggs?

>>11288999
A gradient of a scalar field is a vector, and the components of it are partial derivatives.
The divergence of a vector field is the sum of partial derivatives.

>>11288999
Einstein summation.

How do I get rid of old, fully healed scars?

How do I set up [math] {\LaTeX} [/math] so that:
1. every new line in the code is a new line in the document
2. every empty line in the code is an empty line in the document
?

>>11289115
scalpel, anesthetic and a mirror
you can find medical books explaining scar repair techniques online

>>11289133
>1
end every line with \\

Please tell me why can't psychiatrists consider the 6.5 billion religious people as schizophrenic

>>11289167
because psychiatry's primary goal is to control low functioning people with drugs so they don't destabilize society by killing themselves or others and ideally can get back to work

religious people are usually productive and not at risk for these behaviors, but many are indeed functionally psychotic

>>11289167
Because religious people typically don't think they can talk to god or hear his voice in their head or whatever

>>11289167
they don’t have symptoms of psychosis, most of them don’t have waking religious experiences outside of communal worship settings and even then its more emotional than the dreamlike visions of a schizophrenic mystic. Not much different from people becoming heavily invested in a tv show or sporting event.

>>11289177
but they have delusions, false beliefs and disordered thinking

>>11289182
>>11289186

>>11289186
Look, this isn't the board for being an edgy atheist. You are embarrassing yourself and atheists at large

>>11289186
And yet they dont have symptoms of psychosis

>>11289196
/sci/ is an atheist board anon

>>11289200
When you grow up, you will find that STEM has about the same portion of religious to non-religious as the general population. Oddly, I've actually had a large number of religious math teachers. Arnold's Mathematical Method's book starts with a passage from Psalms.

>>11289198
delusions, false beliefs and disordered thinking are symptoms of psychosis

>>11289200
No, we are Muslims Alhamdo lelah!
Allah akbar!

>>11289049
>>11289056
fuck i'm retarded

What the fuck is going on in spherical coordinate unit vectors? I thought I understood this stuff back in Calc 3, but Griffiths is screwing with my mind.
For example, if I have a point [math]P=(x,y,z)[/math] in Cartesian coordinates, I understand how you would express it as [math]P=(r,\theta,\phi)[/math] in spherical. But then if you want to write [math]\vec{r}=x\hat{x}+y\hat{y}+z\hat{z}[/math] as [math]\vec{r}=a\hat{r}+b\hat{\theta}+c\hat{\phi}[/math], how do I determine [math]a,b,c[/math]?

>>11289438
[eqn] a=\sqrt{x^2+y^2+z^2} [/eqn]
[eqn] b=\text{atan2}(y,x) [/eqn]
[eqn] c=\arccos\frac{z}{a} [/eqn]

>>11289453
So [math]a=r,b=\theta,c=\phi[/math] just like in the Calc 3?
I guess I'm a brainlet.

\begin{bmatrix}
1 & 0 & a \\
0 & 2 & b\\
0 & 0 & c
\end{bmatrix}

For what real values of a, b and c is this matrix diagonizable?
My answer is that for all choices of a and b if a != 2 and a != 1, if a = 2 or a = 1 then a=b=0 is the only choice. Otherwise the algebraic multiplicity will exceed the geometric.
Is this correct? Have I missed any cases?

I have an optimization problem with the following constraint

-p > x > p

where p is a positive real. That is, x must be outside the line segment (-p,p). How can I reformulate it so that I get a feasible set of linear constraints?

>>11289487
I dunno lmao, try [math]x^2-p^2>0[/math]

>>11285524

Questions cant be stupid you pleb. But we do have an epidemic of inquisitive idiots.

would you rather do a 4-year stem phd in one of the world's top universities or 1-year state university phd?

>>11289153
Thanks!
I just used :%norm \\ in vim

>>11289478
Its eigenvalues are 1,2, and c, so if c is neither 1 nor 2 then it has 3 distinct eigenvalues and so must be diagonalizable. The converse isn't necessarily true. Clearly a=b=0 is diagonalizable for any c=/=0.

>>11289672
former, you can carry that with pride for the rest of your life. i wasn't using those 3 years anyway

>>11289478
We have from wolfram alpha that [eqn] \lambda_1=2\ \Leftrightarrow\ \mathbf{v}_1=[0\ \ 1\ \ 0]^T [/eqn] [eqn] \lambda_2=1\ \Leftrightarrow\ \mathbf{v}_2=[1\ \ 0\ \ 0]^T [/eqn] [eqn] \lambda_3=c\ \Leftrightarrow\ \mathbf{v}_3=[a/(c-1)\ \ b/(c-2)\ \ 1]^T [/eqn]
All of these vectors are linearly independent, but only if c is not 1 or 2. If c is 1 or 2, then we get repeated roots in the characteristic polynomial and then the algebraic multiplicity is not equal to the geometric and all that, and only then can we not diagonalize. Constants a and b do not matter.
>>11289465
aren't we all?
>>11289679
yw

>>11289763
Yes, but lets say i pick c = 2, algebraic multiplicity = 2

1 0 0
a = 0 0 0 ax=0 for (0,1,0) and (0,0,1)
0 0 0


and case of lambda = 1 we get eigenvector (1,0,0)

It works the same if we pick c = 1, but a and b has to be 0 to "free" that col. Am I misunderstanding something?


>>11289819
If we have unique roots we are guaranteed that its diagonalizable, that is trivial. But you can have a CP with non unique roots that have AM=GM.

>>11289897
>But you can have a CP with non unique roots that have AM=GM
Interesting

>>11289897
>you can have a CP with non unique roots that have AM=GM
interesting. do you know know of any examples?

>>11289640
After concluding my education at Cambridge, I decided to travel the world and teach mathematics to the less fortunate in poor countries.
I taught brown little dipshits in Somalia, slanty-eyed illiterate brats in Nepal, and even rat thief gypsy children in Romania. I always carefully explained things, answered all their questions, and sometimes fucked the childrens' mothers to make things easier for anyone coming after me.
Throughout all of those fourty years, I agreed with you, and believed that there was no such thing as a revolting, nonsensical and stupid question.

Later, in my retirement, I found out about these threads.

>>11289905
https://en.wikipedia.org/wiki/Diagonalizable_matrix

>>11289897
> But you can have a CP with non unique roots that have AM=GM.
This isn't one of those cases, though. If c∈{1,2}, then the matrix isn't diagonalizable unless a=b=0 (i.e. it's already diagonal).

IOW, your original post was correct (apart from writing a where it should have been c).

What equation is used to calculated the probability of two different sequential probabilities?

So If I flip a coin and have a 50/50 chance of head/tails then I roll a dice and have a 1 in 500 chance of rolling a 6, what is the sequential probability of getting heads then a 6?

>>11290548
P(A and B)=P(A)*P(B)
So 1/200

>>11290567
Gosh. I'm too stupid to even understand this.

>>11290596
The probability of two independent events occuring is the product of the probabilities if they happened by themselves.

Hewwo! I was wondewing how many dicky wicckies can fit in my bucci maximum??!!

>>11290668
One at a time unless you are a complete fucking slut.

>>11289942
8.125/10

>>11290668
One at a time unless you are a complete fucking slut.

>>11290668
Hey! Where did my (you) go?!

>>11290662
So wouldn't that make it a 1/1000 chance?

>>11290687
Damn, my bad. Yeah, 1/1000.

>>11290704
ty!

I have no question, but I just want someone to wish me luck because I have no friends irl.
I have astrophysics exam in an hour anons, I am feeling pretty good. The only subject I don't feel very confident in is about equatorial coordinate system and transformations between equatorial, galactical and horizontal.

how did 9/11 cause gas prices to quadruple permanently

>>11290770
That sounds gnarly, but I know you do fine. GL, anon~

>>11285524
Is my proof correct?
Problem:
Let [math]A \subseteq \mathbb{R}[/math] ,such that [math]A[/math] is bounded above and let [math]cA = {ca: c \in \mathbb{R}, c \geq 0, a \in A}[/math]
Prove that [eqn]Sup(cA) = cSupA[/eqn]

Proof:
>As [math]A[/math] is bounded above then from its definition [math]cSupA[/math] is an upper bound of [math]cA[/math]
>Let [math]\gamma \in cA[/math] such that [math]\gamma[/math] is an upper bound of [math]cA[/math] and [math]\gamma < cSupA[/math]
> Then [math]\frac{\gamma}{c} < SupA[/math] and [math]\frac{\gamma}{c} \geq a \hspace{2mm},\hspace{2mm} a \in A[/math]
This yields a contradiction, as [math]\frac{\gamma}{c}[/math] cant be both less than [math]SupA[/math] and equal or greater than any element of [math]A[/math]
>Q.E.D??

So, I want to solve this to second order central difference.
[math]\frac{\delta{\epsilon \rho D \frac{\delta{Y}}{\delta{z}}}}{\delta{z}}[/math]
If the form is like [math]\frac{\delta^2{u}}{\delta{z^2}}[/math] then I can express it easily, but I don't know how to do that if it's like that (my question).

>>11290084
Exactly, thats what I thought. Well aren't all diagonal matrices with duplicates along the diagonal one of those cases?

>>11290781
Seems correct to me.
Slightly informal tho. So, for example, your second line should properly read " [math]Assume ~ sup ~ cA < \gamma < c ~ sup ~ A[/math] ".
No biggie, really.

Should I bring a folder to an interview?
They asked me to bring 3 new resumes for the people who are going to be interviewing me.
Don’t know if it would “look right” to walk in holding a folder. Wouldnt look right to walk in with just the papers too.

>>11291016
How do I know something is less or more formal?
I come from an engineering background where everything is done with hack and slash.

>>11290803
[math]\epsilon \rho D \partial_z Y = \partial_z \epsilon \rho D Y - Y \partial_z \epsilon \rho D[/math], by integration by parts.
>>11291076
Read lots of proofs.

>>11291575
>integration by parts
*by the Leibniz rule.

>>11285524
Define the sequence s(n) as the co-primes to 30, in order, with s(1)=7. So all the primes are in s(n), but also 49, 77, 91, 121, etc.

Is there a formula that gives all the n for which s(n) is a multiple of 11? And how would I obtain such a formula?

Summer internships vs Fall/Winter internships?
I inquired FAANG abouthem csi internship

Fall looks comfy hmm
but people be stealing them spots
worried rn that there be no more

>>11291940
f(n)=s(n)*11

>>11292076
I'm looking for the n values, not the s values. So I guess I'd want a formula for the inverse of that function you gave.

Why are factorials usually defined as products of substractions instead of additions?
So if we want n! it is usually defined as the finite product of (n-x) where x begins at 0 and ends at x-1 (or x-2, not that 1 will do anything)...
Isn't it more intuitive and simple to define it as the finite product of n, where n begins at 1 (or 2) and ends at our desired number?

>>11291940
>>11292119
it may no tbe the direct way but what if
what if you use modulus bro
f(n) = mod ( s(n) , 11)

whenever f(n) = 0, that n also the same n where s(n) result is a multiple of 0

[spoiler also how you feel about internships?? do you like summer ones or the fall ones[/spoiler]

>>11292173
it's the same shit

>>11291940
>>11292119
it may no tbe the direct way but what if
what if you use modulus bro
f(n) = mod ( s(n) , 11)

whenever f(n) = 0, that n also the same n where s(n)'s result is a multiple of 11

[spoiler also how you feel about internships?? do you like summer ones or the fall ones[/spoiler]

>>11292173
>>11292183
For the first statement: x ends at n-1 or n-2 sorry

>>11292183
Of course. I just ask why is it more commonly described as such.
I guess it is like the pi vs tau thing. Or why Euler's identity is usually written as e^i^pi - 1 = 0, instead of e^i^pi = -1

>>11292173
Multiplication is commutative

Did anybody that's a burger go to community college before getting their bachelor's? Did you feel that community college properly prepared you for the rest of undergrad and postgrad?

Why is computer science full of weebs?

>>11292431
I will have my bachelors soon enough, but I did go to CC. I would say no, but it did save a lot of money.

>>11291940
If n is coprime to 30, 11n is coprime to 30.
If n is coprime to 30, n+30k also is coprime to thirty.
Find all numbers smaller than 30 coprime to 30 and put in fifteen minutes to get something nice and easy to evaluate.
>>11292532
They have neither the physical strength nor the intelligence needed to become Touhou posters.

>>11292185
I agree that this is true. But it's kind of just a restatement of my question: I'm looking for all n such that mod( s(n), 11) = 0. Idk how to solve for n from that.

>internship
I think it depends on your weather preferences and geographical location, but generally summer is preferable. Why do you ask?

>>11292558
>put in fifteen minutes to get something nice and easy to evaluate.
It's proving to take me more than that, unfortunately. 11*s(n) will, as you say, be coprime to 30, so 11*s(n) = s(m). I'm looking for m.

>>11292610
m=n anon.

>>11292617
Actually, no idea why I wrote that.

>>11292610
Right, my mistake earlier, I misread the question.
Essentially, consider [math]Z_{330}[/math].
There are a number [math]n[/math] of elements [math]m \in Z_{330} [/math] coprime to 30.
Additionally, if a=s(x), then a+330=s(x+n), since a is divisible by 11 and coprime to 30 if and only if a+330 is, and we have n elements between a and a+330.

A chemistry question of sorts.

Where do I buy chemicals that aren't sold to final consumers? it's simple enough to buy common substances and some stores have plenty of more specialized stuff. Yet I have been looking for something (1-phenyl-1-cyclohexene, if it matters) and I can't find it anywhere other than those research chemicals sites which charge a gorillion dollars per gnat's fart. As far as I can tell, it is used in bulk in various base industries and it's not controlled seemingly anywhere in the world. So what gives? Do I have to ask chemical labs directly searching for it? How do industries find suppliers for those in the

A chemistry question of sorts.

Where do I buy chemicals that aren't sold to final consumers? it's simple enough to buy common substances and some stores have plenty of more specialized stuff. Yet I have been looking for something (1-phenyl-1-cyclohexene, if it matters), and despite it being widely avaiable at chink shit stores, I can't find any sellers here other than those research chemicals sites which charge a gorillion dollars per gnat's fart. As far as I can tell, it is used in bulk in various base industries and it's not controlled seemingly anywhere in the world. So what gives? Do I have to ask chemical labs since it's not announced seemingly anywhere? How do industries shop around for suppliers for these more obscure yet bulk-made substances in the first place?

>>11292774
>chemical labs
Assuming you've already asked the store clerks from the places where you usually buy shit, I don't see why not.
If you can't find chemical labs, try just asking the local university's chemistry department.

>>11292651
Hmm... I think I understand what you are saying, but I don't see a path from that to a formula for m. Maybe it would help if I gave a simpler example of what I'm talking about.

Define b(n) as the sequence of numbers coprime to 6. So:
b(1) = 1
b(2) = 5
b(3) = 7
b(4) = 11
b(5) = 13
b(6) = 17
b(7) = 19
b(8) = 23
b(9) = 25
b(10) = 29
b(11) = 31
b(12) = 35
b(13) = 37
b(14) = 41
b(15) = 43
b(16) = 47
b(17) = 49
etc.

Now suppose I were looking for a formula m(x) for all the m for which b(m) is a multiple of 5.
b(2) = 5
b(9) = 25
b(12) = 35
b(19) = 55
etc.
So I want an m(x) that yields the sequence 2, 9, 12, 19, etc.

I found one that works, based on the fact that it seems to be "oscillating" between numbers that end in 2 and 9:
m(x) = 5*x -2 +cos(Pi*x)
So
m(1) = 2
m(2) = 9
m(3) = 12
m(4) = 19
etc.

But I have a lot more difficulty coming up with a formula like this when the original sequence is coprime to a number with 3 or more prime factors, such as 30. I would like a function like m(x), but for the sequence s(n) of numbers coprime to 30, and picking out the m for which 0 = mod(s(m), 11).

>>11292794
Why do some substances seem to be so on the downlow tho? Does the alphabet soup tell companies not to advertise them because they might be used as a precursor yet don't control them since they're too widely used?

>>11292825
>Why do some substances seem to be so on the downlow tho?
Supply and demmand.
Also possible that there are issues with not making it to order or with contracts for constant supply, so it's hard to purchase outside of industry.
>Does the alphabet soup tell companies not to advertise them because they might be used as a precursor yet don't control them since they're too widely used?
Probably not.

>>11292853
>Also possible that there are issues with not making it to order or with contracts for constant supply, so it's hard to purchase outside of industry.
That makes a lot of sense. Industrially important chemicals with virtually no consumer demand might be made and sold just in huge, periodical batches. Good one, anon.

>>11291019
Bump

>>11293460
Bringing a folder and a pen to an interview is perfectly acceptable

Cytosin can easily deaminate into Uracil. This will be detected and repaired by a mechanism since Uracil doesnt appear in DNA. The reason why Uracil isnt found in DNA is because otherwise the repair mechanism wouldnt be able to differentiate between deaminated Cytosin turned Uracil and intended Uracil. Now in RNA we do have Uracil and it binds to Adenin, replacing Thymin. Meaning we have both Cytosin and Uracil in the RNA.
How does the body prevent mutation through deamination Cytosin in RNA? Wouldnt it make more sense for Uracil to replace Cytosin instead of Thymin? Am i retarded?

>>11292798
No, no, no.
There are [math]n[/math] numbers coprime to 30 in [math]Z_330[/math], and [math]m[/math] numbers coprime to 30 and multiples of 11 in [math]Z_330[/math].
If [math]s(x)[/math] returns the x-th number coprime to 30, and [math]s*(x)[/math] returns the x-th number coprime to 30 and a multiple of 11, we have the relation [math]s(a)+330=s(a+n)=s(b)+330=s(b+m)[/math], get it?
>>11292867
You absolutely should still call the labs, tho.
>>11294305
Now listen, I'm not a biologist, and I'm answering based on what I recall from high school.
But wasn't RNA prior to DNA? First you had shitty little things with RNA, and then you had shitty little things with DNA?

>>11294533
>forgot the fucking keys
[math]Z_{330}[/math] for both.

>>11294533
Ugh, also forgot the star.
[math]s*(b)=s*(b+m)[/math]

>>11294533
I'm afraid I don't get it. How do you solve for m?

>>11294557
You solve it by hand for b<m, then you define the function recursively.

>>11294560
But in this comment >>11292798, for a simpler case I didn't need a recursive function:
m(x) = 5*x -2 +cos(Pi*x)
That's not recursive.

Does it just become impossible to get a non-recursive function when the number it is coprime to is 30 instead of 6?

>>11294567
No, you can fiddle around with this and get a solution that is gonna look like a sum of a linear function and a bunch of sines.
But the recursive definition is really, really fast, and really, really easy to calculate.

>>11294574
Hmm ok. It's just bizarre to me that there wouldn't be a systematic way to carry out that "fiddling around" as you say.

>>11294583
There is.
The linear component naturally has coefficient xn/m, because (x+m)n/m=xn/m+n, as you'd expect from >>11294533 .
Then you can just consider the period of m on the remainder and do trigonometric interpolation.

But you have literally no fucking reason to. Just let your computer look up the values in a table, 500% faster.
Ask /g/ if you doubt me.

>>11285524
Why are standard black body samples made of carbon rather than just any random material given Kirchoff law? Doesn't Kirchoff imply any cavity will work like a black body?

>>11294583
> It's just bizarre to me that there wouldn't be a systematic way to carry out that "fiddling around" as you say.
The systematic approach is detrending then a Fourier transform. This gives you

f(n) = 5+n*11+3.58343275*cos((2*n-3)*pi/8)+1.41421356*cos((4*n+6)*pi/8)+3.10789474*cos((6*n+7)*pi/8)-0.5*cos(n*pi)

Bit confused about the Higgs mechanism.
Popular science, and some legit looking sources I've looked into say it's responsible for all mass, including that of ordinary matter. But other legit looking sources say it's only responsible for a small percentage, and that only the W and Z bosons draw 100% of their mass from it.
Which is it? If it's the latter, then where does the rest of mass come from?

>>11295073
Fix the positioning of your leptons

>>11285524
Incoming retard question.

Average speed is defined as the total speed divided by the total time. Why? Wouldn't the two time units cancel each other out and leave just a unit of distance?

Example question: A man walks up a hill at 10m/s, it takes him five seconds. He then walks down the hill at 20m/s it takes him 2.5 seconds. What was his average speed?

>>11295073
Non-expert here.
From my understanding, the Higgs mechanism is responsible for 100% of the mass of the fundamental particles (except the Higgs boson, which gets its mass from something to do with the Higgs field potential shape). Most of the mass of composite particles like protons and such is from "confined" kinetic and potential energy of quarks and gluons.

>>11295115
Also, the specific mechanisms for lepton masses are different in the details from that for the W and Z bosons.

>>11295109
>Average speed is defined as the total speed divided by the total time.

Where are you getting this from? This isn’t true from a google search. You are right if this was the case then it would be a distance measurement.

Ex:
Avg. Speed = [Absolute Distance] / total time
= [10 (m/s) * 5 (s) + (20m/s) * 2.5 (s)] / [5 (s) + 2.5 (s)]
= 100 (m) / 7.5 (s)
Avg speed = 13.33 m/s

Which is different from avg velocity of 0 m/s since it’s relative displacement was 0 meters. Velocity is vector quantity and speed is just a scalar quantity.

>>11295115
Yeah, makes sense. When you add up the masses of the up and down quarks you get far less than the actual masses of the protons and neutrons.
Other question: does the Higgs boson itself have to do anything with mass generation? Or is it just a byproduct of the Higgs Field which does all the work?

>>11291019
>>11293460
Yeah folders are fine. If you want to look as professional as possible buy yourself a leather portfolio (padfolio?) and bring that.

>>11295150
Damn I see my mistake now. Thanks for the enlightenment.

how do I grow a beard, grows in fine in some places and not at all in others

Would reversing the supreme court decision made in Wickard v. Filburn have any disastrous economical consequences, or was the US just butthurt some lowkey farmer controlled the means of his own production?

>>11295166
The latter. The Higgs boson doesn't play a direct role in the Higgs mechanism.

Anyone know what website I'm thinking of?
It had reviews and a list of effects and sometimes recipes of a ton of different drugs, mostly black background iirc or at least dark looking

Is there a correlation between oxytocin and low IQ?

>>11295770
sure
>oxytocin
>more trust
>less suspicion
>lower iq

>>11295588
erowid

>>11295812
Thank you! I've been searching all day and asking everyone I know.

>>11295837
retards always forget useful things

>>11289204
I'm surrounded by STEMfags on a daily basis and the vast majority are implicitly or explicitly atheist/agnostic. Religion is thoroughly mocked and rejected by people my age in STEM and our professors seem to hold it in rather strong disdain, especially creationism, though as a biofag that is probably more pronounced than in say mathematics or other disciplines.
>>11289206
They don't present like that, only the devoutly religious of certain sects routinely display psychotic behavior and even then its high functioning.

I don't understand the radiation patter of a synchrotron accelerator. I keep seeing pictures like the one on top, where the axis of the torus is parallel to the acceleration. But I know that the pattern for a linearly accelerated partcile is like the picture on the bottom. A particle in circular motion can be thought as if it is instantaneously under a linear acceleration toward the center, so I would think that I can just rotate the pattern on the bottom so that the acceleration points to the center, but this gives a different pattern from the one on top.

I don't understand the radiation patter of a synchrotron accelerator. I keep seeing pictures like the one on top, where the axis of the torus is parallel to the acceleration. But I know that the pattern for a linearly accelerated partcile is like the picture on the bottom. A particle in circular motion can be thought as if it is instantaneously under a linear acceleration toward the center, so I would think that I can just rotate the pattern on the bottom so that the acceleration points to the center, but this gives a different pattern from the one on top.

I remember not having this question back in high school, since the teacher probably explained it, but I don't remember the explanation.

Light travels with the speed of causality, since it has no weight, right?
But light has energy, doesn't it? And energy ultimately is equivalent to mass, isn't it?
Isn't that a paradox?

>>11296461
>casualty
Light traveling a constant speed in all inertial frames is an experimental observation/axiom of relativity. Causality is defined in terms of the sign of the spacetime interval between two events. Casually related if positive, not related if negative. Intervals with zero magnitude are light-like, definition.
>energy, momentum
Objects do not need mass to have energy. Not a paradox. The E=mc^2 is only for massive objects at rest.

If i have a linear transformation from R^3 -> R^2 and the size of the basis of the kernel of the transformation is equal to 0, can I say that the basis of the image of the transformation is (1,0),(0,1)?

>>11296511
>If i have a linear transformation from R^3 -> R^2 and the size of the basis of the kernel of the transformation is equal to 0
You don't, that's impossible.
For [math]T: \mathbb{R}^n \rightarrow \mathbb{R}^m[/math] the kernel has dimension at least [math]n-m[/math].

>>11296527
my bad, I meant if the kernel is equal to 1.

>>11296548
Then yeah.
For [math]T: \mathbb{R}^n \rightarrow \mathbb{R} ^m[/math], you have [math]n= dim ~ \mathbb{R} = dim ~ ker ~ T + dim ~ im ~ T[/math]. This formula should be somewhere on your textbook.
Since the only two dimensional subspace of [math] \mathbb{R}^2[/math] is the entire vector space, we have [math]im ~ T = \mathbb{R}^2[/math]

>>11296554
Typo, should be * [math]n = dim ~ \mathbb{R} ^n[/math]

>>11296558
thank you so much anon

>>11296511
>the basis

you should say "a basis"

>>11296491
>>casualty
For a second I was worried I had made a typo.
You do know how to quote without retyping everything, right?

Thanks for the answer.

This is about social science.

Why is Kohls moral development theory respected at all when it is so incredibly flawed, I cant believe I have to study this just because of how incredibly stupid it is
Is it a feel good thing?

>>11296461
E^2 = m^2 c^4 + p^2 c^2
m = 0 for light so the energy of light is attributed entirely due to its 4-momentum.

>>11285524
How can current after a resistor be the same as before the resistor when a circuit is in series? From what I understand the resistance of an object is how much it impedes flow (amps) despite the pressure to flow (volts). Hence R = V / I. But after it goes back to the regular resistance would the current not be capped at the amount it was at whilst in the resistor? Like water in a pipe wouldn't changes in the diameter continue to affect the stream?

https://math.stackexchange.com/questions/192452/whats-the-proof-that-the-euler-totient-function-is-multiplicative

In the accepted answer here, what exactly is meant by "units" and
[math]
\mathbb{Z} / \langle a \rangle
[/math]
?

>>11296622
Social science is neither math, nor science (despite the name).

>>11296739
pic related

I don't understand why

regressor = LogisticRegression()
regressor = regressor.fit(x_train, y_train)
predictions = regressor.predict(x_valid)


yields an array full of zeroes, and of course the confusion matrix and the AUROC show that the model always predicts zero--but

regressor.predict_proba(x_valid)


outputs a nonzero array.

Train-test split was done correctly and both label sets have an 18% of ones. Correlation between features and targets is nonzero.

>>11296798
>unit
Element of the ring which divides the identity.
>[math]\mathbb{Z}/ \langle a \rangle[/math]
[math]\mathbb{Z}[/math] modulo the ideal generated by [math]a[/math]
>what's the idea generated by a
For an arbitrary ring with unit [math]R[/math], it's [math]RaR[/math]
[math]\mathbb{Z}[/math] is commutative, so in this case it's just [math]\mathbb{Z}a[/math]

>>11296853
What's the relationship between [math]\mathbb{Z}_n[/math] and [math]\mathbb{Z} / \langle n \rangle[/math]? Is there even one? I know the Chinese remainder theorem says that
[equation]
\mathbb{Z}_{ab} \cong \mathbb{Z}_a \times \mathbb{Z}_b
[/equation]
if a and b are coprime, but I haven't seen it in the form where we speak of these "units".

>>11296858
That second equation is meant to say

[math]
\mathbb{Z}_{ab} \cong \mathbb{Z}_a \times \mathbb{Z}_b
[/math]

>>11296858
[math]\mathbb{Z}_n=\mathbb{Z} /n \mathbb{Z} = \mathbb{Z} \langle n \rangle[/math]
Emphasis on the equality. They aren't isomorphic, they're the exact same thing.

>>11296864
Forgot a slash in [math]\mathbb{Z}/ \langle n \rangle[/math]

>>11296864
What is meant by [math]\mathbb{Z}/n\mathbb{Z}[/math]? I've never seen multiplication between a set and an integer before.

>>11285524
hello my friends
Does anybody have a copy of Donald McQuarrie's Mathematical Methods for Scientists and Engineers from 2003. I have scoured library genesis and torrent sites for it and I need it to begin one of my math classes soon and the cheapest options are $81 and by god I am so poor. Any help would be greatly appreciated, even if it's just a referral. Thank you anons

>>11296882
For an arbitrary ring [math]R[/math], we set
[math]aR = \{ x \in R ~ : ~ x = ar ~ where ~ r \in R \}[/math]
[math]Ra[/math] is defined analogously, and so is [math]aRa[/math] or even [math]AB[/math] for [math]A, B \subset R[/math].
You know how the quotient construction goes, right?

>>11296739
>How can current after a resistor be the same as before the resistor when a circuit is in series?
There is no built up of charge in a wire, so the conservation of charge implies the current at any point in a straight wire is the same (equivalent to Kirchoff's current law).
It's exactly the same principle as water flowing through a pump or a venturi: there may be a head or pressure differential (analogous to voltage) over the device, but the mass flow rate of water is identical at each point along the pipe.
>>11296802
This is absolutely not how water in a pipe behaves. The mass flow rate (and volume flow rate) in the top portion would be identical as the bottom. The only difference would be a change in flow velocity as the cross section changes, and a corresponding increase in dynamic pressure and decrease in static pressure. However, you do get HEADLOSS, which is exactly analogous to the voltage drop over a resitor.

>>11296801
there is no other board I can discuss this on
Please accept me as a refugee /sci/entists

>>11296913
Literally >>>/his/

>>11296923
>/his
>wojaks and misinterpreted or outdated eugenics theories
I have a better chance of discussion at /b/ even or /v/

Ill try asking mods to fo a social science board or to moderate /his/ but its probably beyond saving by now

Anyone have the compsci textbook chart?

>>11296933
>/sci/
>a better board than /his/
Are you balls to the wall insane or are you specifically referring to /sqt/?

The jannies have been a bit lax lately, since this post >>11289942 is still up, so you can probably get away with it.

>>11296900
>change in flow velocity
Does it increase when the pipe gets smaller to compensate? Is this what makes the current the same at the top and at the bottom?

>any p-norm is convex
Then, if each component of a vector is a linear function of other variables (e.g., x=[x1,x2]'), shouldn't the norm of this vector be a convex function of x?

>>11296988
>balls to the wall
thats an expression I havent heard in a long time

Well if nobody here cares about that stuff then its of no use
There's no 4chan place to discuss social sciences (besides popculture popular ones) unfortunately would be nice to reflect on studies sometimes

I find physics boring but really enjoy reading all things nuclear and radioactive. If I wanted to pursue a career based in this, how much physics based stuff am I going to have to put up with? Will I have to actually study physics?

>>11297082
>I want to study a subfield of physics without studying physics
I don't understand anon
Also, are you in high school?

>>11297082
You ever look into being a rad tech? Doesn't sound like a perfect fit but from what I hear it pays decent and doesn't require exceptional intelligence

>>11297024
Let [math]C \subset V[/math] be a convex subset of the vector space [math]V[/math].
Then, for any [math]\lambda \in K[/math], and some [math]T \in End_{Vect}(V)[/math], we have that [math]T( \lambda u + (1- \lambda) v)= \lambda T(u) + (1- \lambda)T(v)[/math], which, if [math]u, v \in C[/math] implies that [math]T(C)[/math] is also convex.
>>11297025
>thats an expression I havent heard in a long time
I'm old like that.

Maybe /pol/ in a couple of years works.
You can also try creating a social sciences board in another imageboard.

>>11297116
My bad, I forgot that affineness generalizes but convexity doesn't.
You get the idea, tho.

Is it weird to show up to a phd defence or to a candidate presentation for a tenure track job? I’m sort of worried there would be less people than at a regular seminar, making me awkwardly stand out

>>11297019
>Does it increase when the pipe gets smaller to compensate?
Yes. This is because mass is conserved and also water is pretty much incompressible.
>current
Yes. This follows from conservation of charge. Basically, the net charge inside a control volume is equal to the flux into the control surface, minus the flux out (because charges dont spontaneously pop into existence). Because charges are not accumulating (we aren't playing with capacitors), we hence know that the current is the same at all points.

>>11297090
I'm actually in the medical field, I never studied physics in school and opted for chemistry and biology instead. I've wondered if physics just wasn't appealing because it was taught poorly.
I find the effects of radiation on the body fascinating, unfortunately radiography in the UK isn't paid very well compared to the States.

>>11297141
srry, phrased that poorly
**The rate of change of net charge inside a volume is equal to the integral of current density over the surface that encloses the volume

>>11297152
Oh, you probably should of specified this ahead of time. You sounded like an I Fucking Love Science type in your first post. Unfortunately, I don't know how to help you

>>11297116
>>11297124
I'm not sure I understood. Is T(C) representing the norm of a vector in C? It looks more like some linear transformation.
>>11297134
If there's only a few people in the room (which is likely), you may be the only one the candidate doesn't know, making it kind awkward for him. It may be a good idea introduce yourself to him and explain why you are interested before the presentation.

>>11297152
Become a nuclear technician. Tip: this is an extremely difficulty position to obtain. Have you sucked the dicks of any AFL-CIO affiliated industrial labor unions lately?

>>11297169
Thanks, I was afraid of that. I guess I’ll just have to pass on them since I’m an avpd loner

>>11297134
No.
This one time, I didn't have anything to do at university, so I watched this random lad's bachelor's thesis presentation. Besides him and the professors, I was literally the only person in the room.
Once he finished up, the professors told us to fuck off out of the room so they could discuss his presentation, and I talked with him outside the door.
We talked about the presentation, I asked what he would do after this, he told me he'd go back to his hometown, I told him about family I have in his hometown, etc.
Now, I understand that not everyone can be as extroverted and charismatic as me, but you still shouldn't worry about this shit.
>>11297169
You were asking if [math]f(T(x))[/math] is convex if f is convex and T is linear, right?
I'm sorry, but the image is really hard to read.
>>11297185
Don't be a faggot, anon.

>>11297185
Dude, just come to the presenter before he starts and say "I'm anon, a student/researcher here (or wherever) and heard about your defence from X. It took my interest since I study Y, so I came to watch. Nice to meet you, and good luck." or something along these lines.

>>11297141
Thanks man this cleared it up

>>11297218
>You were asking if f(T(x))f(T(x)) is convex if f is convex and T is linear, right?
Not exactly, but I realized my question is contained in this question, so thanks, anon.
Would f(T(x)) also be convex if T was an affine transformation?

>>11297218
>>11297220
I appreciate the advice, but I’m not a normalnigger. I’m socially retarded and showing up to an unfamiliar room or situation is sufficient to frazzle my nerves to hell

>>11297240
For T affine, we decompose it as [math]T(x)=L(x)+a[/math], where L is linear.
[math]f(T( \lambda u + (1- \lambda) v))= f(L(\lambda u + (1- \lambda) v)+a)=f(\lambda (L(u)+a) + (1- \lambda)(L(v)+a)) \leq \lambda f(L(u)+a) + (1- \lambda)f(L(v)+a)= \lambda f(T(u))+ (1- \lambda)f(T(v))[/math]
Looking through this for typos and mistakes is left as an exercise to the reader.

If you buy a meal and it comes with two fortune cookies, which one counts?

>>11297230
yw~
>>11297653
All fortune cookies count

So what the fuck do you guys think this is supposed to mean.

>>11298095
Pretty clear and obvious, do what it says in the text.

>>11298101
I do and It doesn't make any sense.

>>11298116
What doesn't make sense? The instructions? Linear regression? Seems extremely straight forward.

>>11298117
What's linear regression? My professor didn't explain it.

>>11296707
Now that you mention it, I faintly remember seeing a formula like that. (I obviously haven't continued physics after high school.)
That explains everything. Especially how that question didn't occur to me back then.

>>11285524
what motivates a man to write several hundred pages of abstraction. for instance, higher topos theory. how do they do it?

I am retarded
Is the molar mass of CnH2n+3N (general formula of amines) equal to 14n+45 g/mol?
Also could someone explain how to name amines? Stuff like N-ethyl N-methylpropylamine makes my head spin

>>11298508
Nevermind it's not 45 what the fuck was I thinking

How the fuck can you solve this poisson equation for getting pressure field [math]\nabla P^{n+1}[/math] in this equation tho? In discretization please.

>>11298576
Wait, [math]R^n_c[/math] is a source term.

Anyone got a PDF of Aerospace Propulsion Systems by Ward?

So I have a few doubts regarding orthogonal projection. If I wanted to project a vector over a whole subspace, I would need a basis for that subspace, but does any basis work? or does it need to be orthogonal or orthonormal?

>>11298134
Linear regression is essentially approximating a set of points by a line.
Further info is available in wikipedia.
>>11298469
>higher topos theory
Sometimes mathematicians come up with generalizations or reformulations of concepts, and then they have to write thousands of pages long bricks where they adapt and rewrite some of the theorems for the previous case to the generalization, plus give some autistic basic results and insights.
I'm fairly sure HTT is one of those cases.
>>11298691
You want to project [math]v[/math] onto [math]P[/math].
There are essentially two ways to do this:
If you have an orthonormal basis [math]p_i[/math] of P, you set [math]u= \Sigma_i |p_i \rangle \langle p_i | v \rangle[/math], where we use Dirac's maymay notation.
Alternatively, if you have a normal(elements have norm 1) basis [math]p_i[/math] of [math]P^{\perp}[/math], you can just gradually remove the orthogonal components.
That is, [math]v_0=v[/math], [math]v_i=v_{i-1}-|p_i \rangle \langle p_i | v \rangle[/math], and the solution is the last one.

>>11298821
Wait, no, the basis also needs to be orthonormal in the second one.
My bad.

>>11298576
>>11298577
Wait, I'm so retarded right now. I should just do [math]P^{n+1}=R/L[/math] in matlab with R as the right side of term and L as the divergence.

>>11298880
Listen, your question is really boring, so I'm not typing a full solution out.
BUT, even if Wolfram is the kind of software that would
>actually return something when you tell it to divide by the divergence operator
You still can't guarantee that the solution you get is the gradient of some function.

Do cell phones cause health problems?
I understand that they emit non ionising radiation but surely having one right next to your skin 24/7 for years is going to have some kind of effect?

>>11299456
Whatever effect they have is fucking miniscule in comparison to being in sunlight.

>>11297653
You have to average the fortunes using the Stanislaus-Cattafi algorithm, which consists of an appropriate embedding of each fortune into a conplex vector space of dimension between [math]N [/math] and [math] 2N[/math] where [math]N=\mbox{rank}(\mbox{Fortune A}) + \mbox{rank}(\mbox{Fortune B}) - 4[/math]; You then consider a direct sum of two copies of this vector space, where the first fortune is considered as an element of the first copy, and the second fortune an element of the second copy, you consider the segment joining the two thus obtained vectors, and individuate the point on this segment that minimizes the fortunal cross-entropy.
In case you have three or more fortunes, you consider the obvious generalization where you have a simplex instead of a segment. For infinitely many fortunes, the problem is still open; although Nakamura [Nk16] and Brainstead-Aaronson-Johnson [BAJ18] performed conclusive computations in a few instances of the numerable case.

Can someone explain moments of inertia to me? If I had, say, a ladder, how would I find its moment or inertia given its mass and size?

>>11299456
>Do cell phones cause health problems?
Not paying attention where you are going, because you are playing around with your phone, can easily end up killing you.

Give an example of a function f(x), continuous except at 1, 2 and 3,

and when limit approaches 1, 2 or 3 for f(x), it diverges to infinity

>>11299708
[math]
f(x) = \frac{1}{(x-1)^2(x-2)^2(x-3)^2}
[/math]

>>11299667
Can you guide me through a practical computation?
One of them said:
>Appreciation of art is key to wisdom.
And the other one said:
>Your good humour is the cause of your elevated spirit.
>>11299728
F-fast.
I was literally typing that.

>>11299732
>F-fast
To add insult to injury, I was using a phone.

>>11299732
>Can you guide me through a practical computation?
>One of them said:
>>Appreciation of art is key to wisdom.
>And the other one said:
>>Your good humour is the cause of your elevated spirit.

Let us call these fortunes F and F' respectively.
F has 7 unigrams (words), 6 bigrams (pairs of words), 5 trigrams, and so on--for a total of 7+6+5+...+1 = a lot of n-grams. Likewise for F'. Consider the set S of all n-grams included in either fortune, and consider the complex vector space C[S] freely generated on S. Let ker(F, F') be the kernel subspace of C[S], and let V be the quotient space. V is our candidate space. It is easy to check that the inequality involving ranks and dimension holds.
Let's denote with [math]
e_F
[/math] and [math]
e_{F'}
[/math] the equivalence classes of F and F' respectively in V, and let's consider two copies [math]
V_F
[/math] and [math]
V_{F'}
[/math] of V, with [math]
e_j \in V_j
[/math] for all [math]
j\in {F, F'}.
[/math]
It is easy to check that [math]
e_F
[/math] is a linear combination of the equivalence classes corresponding to 'appreciation of' 'art is' and 'wisdom', while [math]
e_{F'}
[/math] is a combination of 'Your', 'good' and 'of your elevated'. Minimizing the fortunal cross-entropy is computation you can give to your undergrad students, if you have any. The result is an equivalence class generated by a combination of all the n-grams listed above. By the Kashiwagi embedding theorem, one can uniquely identify said equivalence class with the fortune [math]
F_{F, F', \mbox{Kashiwagi}, \omega}
[/math] equal to:
>Your appreciation of good art is the cause of your elevated wisdom

>>11299828
>Minimizing the fortunal cross-entropy is computation you can give to your undergrad students, if you have any.
Good idea, that one's going to their next linear algebra test.
>>Your appreciation of good art is the cause of your elevated wisdom
The chinese are truly a wise people.

Thank you very much for the assistance. I'll later have one of my better students write a haiku in your honor.

>>11299886
The student said he's done.
>Old Kashiwagi
>Flows from him your gay wisdom
>Guided through talent

Can someone help me with this? I know it's stupid simple but I just don't know what its asking. What does [math]N_{kl}[/math] mean? Am I supposed to write a definition where there exists an inverse from Nkl to Nk x Nl?
By the way, the cross product is a typo and is supposed to be [math]N_k \times N_l[/math]

>>11287546
The important thing is for you to understand why they're equivalent.

sqrt(x) = x^(1/2)

So

x^(1/2)/x^1 = x^(1/2 -1) = x^(-1/2) = 1/x^(1/2)

>>11296820
presumably regressor.predict works by computing the probability of each class and then picking whichever one is bigger. so it could be that a non-zero probability is assigned to class 1 for each sample, but that the probability of 0 is always >.5.

Has anyone ever published research they've done independently, not affiliated with an institution? Which journals did you submit to?

>>11299683
Ez mode:
The angular momentum of a point mass is displacement crossed with momentum, [math] \mathbf{L}=\mathbf{r}\times\mathbf{p} [/math]. However, if you have a rigid body (a collection of point masses whose relative distances never change), you can do a little bit of math and manipulation to show that [math] L=I\omega [/math] where I is a derived quantity called the moment of inertia, and omega is the angular velocity of the rigid body about some axis, say z. Moment of inertia is to angular acceleration as mass is to linear acceleration and is defined as
[eqn] I\equiv\sum r_i^2\cdot m_i=\int r^2\rho\text{ d}V [/eqn]
where ri is the distance of the ith particle to the axis of rotation and mi is its mass.The second equality is for a continuous body, with rho being density.
>how would I find
For something with a difficult shape, like a ladder, you will probably end up using the discrete form above (first equality) as an approximation. Break the ladder down in to a large number of very small elements and let 'er rip.
If you are dealing with something continuous but thin, like a plate that is rotating about an axis that is perpendicular to its flat side, you can use a similar quantity called the second moment of area. SMoA is a purely geometric thing defined by [math] I'\equiv\int r^2\text{ d}A [/math]. Look can look up this quantity for a whole multitude of different shapes in tables, or you can compute them by hand if you like. Then, if [math] \sigma [/math] is the mass of the plate per unit area, we get [math]I=\sigma I'[/math]. There is also something called the parallel axis theorem and perpendicular axis theorem, which are geometric statements and trivial to prove. Look them up. I will explain only if you don't understand.
Hard mode:
Moment of inertia is a tensor.

>>11285524
When looking at the discrete counterparts for derivatives, what would the nth discrete derivative be?
For example, if n = 1
[eqn]\frac{d}{dt}y(t) \rightarrow \frac{y(nT)-y(nT-T)}{T}[/eqn] where T is the sampling period.

Bonus question:
Im trying to graph sampled functions in matlab, how do I make the continuous function and the discrete function appear on the same figure? The idea is to be able to see how increasing the sampling frequency better aproximates the analig signal by direct comparison.

>>11292173
You wrote the second option wrong. It should be "finite product of x, where x begins at 1 and ends at n".

The reason it isn't written this way is probably because usually you have at least one variable other than the iterator in the expression.

It might even be considered non-sense to have a variable appear outside of the main expression but not inside it. If you write out the product of the finite number of expressions that this notation is shorthand for, and it only has x in it, what the fuck is n? It doesn't exactly make sense.

>>11299683
Moment of inertia is the rotational analogue of mass. For linear motion, you have F=ma (F=force, m=mass, a=acceleration); for rotation you have τ=Iα where τ=torque, I=moment of inertia, α=angular acceleration.

Consider a point mass m rotating about an axis with rotational speed ω, where the distance between the mass and the axis is r. Its linear speed is v=rω and its linear acceleration a=dv/dt=d(rω)/dt=r(dω/dt)=rα. So the force is F=mrα and the torque is τ=Fr=mr^2α=Iα where I=mr^2.

For a distributed (non-point) mass, you need to integrate over its volume, effectively summing infinitely many δm.r^2 point masses. For a 1-dimensional object (conventionally termed a "rod"), you integrate ρr^2 w.r.t. r over [-l/2,l/2] where l is the length and ρ=m/l is the mass per unit length. The antiderivative is ρr^3/3 so the definite integral is ρ(l/2)^3/3-ρ(-l/2)^3/3 = ρl^3/12 = ml^2/12.

This can be used for objects with one dimension much larger than the others, so the (radial) distance from the centre of mass can be approximated as the linear distance measured along the "length" axis.

This also assumes that the axis of rotation is perpendicular to the length (i.e. you're basically dealing with rotation in the plane). In 3 dimensions, the moment of inertia is replaced with a matrix and the math becomes somewhat more complex (for an object not at rest, you have to allow for precession, which is what makes gyroscopes work).

See the wikipedia page for "moment of inertia" for more information.

>>11292173
You wrote the second option wrong. It should be "finite product of x, where x begins at 1 and ends at n".

The reason it isn't written this way is probably because usually you have at least one variable other than the iterator in the expression.

It might even be considered non-sense to have a variable appear outside of the main expression but not inside it. If you write out the product for which the notation is shorthand, and it only has x in it, what the fuck is n? It doesn't exactly make sense.

>>11300562
read this https://en.wikipedia.org/wiki/Finite_difference

>>11292173
You wrote the second option wrong. It should be "finite product of x, where x begins at 1 and ends at n".

The reason it isn't written this way might be that it's improper to have variables appear outside of the main expression but not inside it. I think the variables outside of the main expression are references to the ones inside it.

Why is the variable x written curly and not normally as an x?
Also, just out of interest, how many of you write your x's algebraically in normal life? I study medicine but haven't kicked the habit since my A Levels.

>>11300610
All variables are written in an italic font to distinguish them from operators and basis vectors
[eqn] \text{d}x\\ \partial f\\ \mathbf{e}_i [/eqn]

What kinda beetle is this. It is in my house and I hate it.

>>11297134
In general defenses are open to the public, it wouldn't be too bad if you introduced yourself a little before everyone starts; however if you are not affiliated with the institution you might be construed as a crackpot.
>candidate presentation for a tenure track job
These are typically packed with grad students, so it'd be fine.
>>11298576
What's the domain and boundary condition? Assuming Dirichlet, you can generate solutions to the Poisson equation by convolving [math]G\ast f[/math] with the propagator [math]G([/math] satisfying [math]\nabla^2 G = \delta[/math]. However, without knowledge of [math]\Omega[/math] this convolution operator [math]G\ast \bullet : H^1(\Omega) \rightarrow L^p(\Omega)[/math] may not be defined. You'll need a Hardy-Sobolev-Littlewood-type inequality to embed the image into some nice [math]L^p[/math]-space.
>>11298691
If the framed vector space [math]V[/math] is over a field then ON and OG are equivalent. In general, you can interpret any linear map [math]P\in \operatorname{End}V[/math] as a "projector" if it is idempotent and completely determined by its image [math]\operatorname{im}P[/math]; of course an explicit form for [math]P[/math] as a matrix must be done through a basis, from which the isomorphism [math]\operatorname{End}V\cong V^*\otimes V[/math] arises.
>>11299683
Moments are generators of the compact part [math]SO(n)[/math] of the Euclidean group [math]\mathbb{E}(n)[/math]. Given a moment map [math]\mu:M\rightarrow \mathfrak{so}(n)[/math], the non-degenerate bilinear form [math](\cdot,\cdot) = \langle \mu(\cdot), \mu^*(\cdot)\rangle: M^2 \rightarrow \mathbb{R}[/math] pulls-back to a metric [math]g=g(\mathfrak{so}(n))[/math] on the adjoint orbit [math]T\mathfrak{so}(n)[/math]. Using [math]g[/math] we can identify [math](\cdot,\cdot)[/math] with a tensor [math]I[/math], commonly known as the moment of inertia.

>>11300664
very based

>>11300635
I don't know, but I suggest to squash it immediately and then smell the remains.

>>11300704
It is a stink bug, isnt it?

What does the concavity of a line represent on an acceleration-time graph?

>>11285524
If a stream of positrons strikes a metal plate floating in space, does the plate develop a positive charge from losing electrons?

>>11300711
Maybe.

>>11300635
it's a type of stink bug. if you live in an area where there are a bunch of them, and open a window in winter time, you can sometimes find a disgusting amount of them in the window track. Be sure to close your windows tight.

>>11300714
If the vertical axis is position and the horizontal is time, then concave up indicates acceleration and concave down indicates deceleration.
If the vertical axis is acceleration and the horizontal is time, then concave up indicates the second derivative of acceleration is positive and concave down indicates the second derivative of acceleration is negative.
It really isnt physically meaningful.

Is this real or fake? If it is real is it possible to make a circular track so the ball bearing can go in circles

https://www.youtube.com/watch?v=gJhBpnlmoJ0

>>11300554
>>11300576
>>11300664
Thanks, this helped.

>>11299953
Thanks. Kashiwagi was the kabuki robot from mystical ninjas. And that little omega was added because it looks like tiddies.

>>11300453
That's probably the case, I'll check. In fact I remember that ones are about the 18% of the set. It's weird that you can't choose a threshold for .predict, but I can work around that. Thank you.

>>11300539
I have collected all my wisdom about fortunal crossentropy in a website with very colorful characters, and a different color for each variable, and anime titties on the backround as well as used as mute variables in summations and integrals. I also published all that garbage in book format thanks to an independent sci fi publishing house. I sold three copies since my publication in 2007.

>>11300711
You can imagine the smell, or you can smell

>>11300610
>Completing the squere
>Thio
At least it's cute

>>11300354
To define a bijection [math]\mathbb{N}_k \times \mathbb{N} \longleftrightarrow \mathbb{N} [/math]
let f(n,m)=(n-1)+k*(m-1)+1

>>11300354
I'm guessing Nkl is {1,2,...,kl}. The bijection is easy, as Nkl has l times the elements in Nk. You should define it in a way such that (1,1),(2,1),...,(k,1) are sent to 1,2,...,k and (1,2),(2,2),...,(k,2) are sent to k+1,k+2,...,2k and so on. In formulese:
[eqn]
f(a,b) = a + (b-1)k
[/eqn]
with inverse g(c) = (r,q+1) with q and r obtained by euclidean division of c by k. (I.e. c=qk +r)

>>11300736
>Is it real?
Yes. The magnets are arranged so that the magnetic field is strongest at the end, so the ball flies to the end.

>Can you make a circular track? (And have it run forever)
With just magnets? No. That would violate conservation of energy. Lots of people have tried and inevitably the ball stops.

... But ...
If you make the ball become non-magnetic at the end of the track then it is possible.

That is how thermomagnetic motors work. https://youtu.be/81lEgQs45z8

The ball (or wire in this case) runs to the end of the track, gets heated past its curie point, becomes non-magnetic, and is pushed off the end of the track by the next ball or wire.

>>11293460
Also put some examples of your work in the folder so you have something to pull out when they ask what you get excited about. "I build things" has less impact than "I built these".

>>11294305
You are not stupid but you are naive. Firstly there are repair pathways for DNA: base excision, nucleotide excision and mismatch repair.
Secondly, look up CpG islands.

>>11295464
Not /sci, but this case really wasn't about wheat. It was about defining the limits of Federal power. The economic impact of pushing crop subsidy programs down to the states would have been a hiccup, not a tsunami.

>>11296900
I‘m not a furry but is there a /sci/entific reason as to why my dick feels funny?

what happened to moot
i havent seen him since last time

>>11301043
Ohhhhh I didn't realise "kl" meant k times l. That makes it really simple, thank you.

>>11296511
you most likely meant that the linear transformation is surjective
otherwise this would not be true