SQT thread

sqrt((-1+sqrt(5))/2)
That's what you want

So Cos(x) = Tan(x) when Sin(x) equals the golden mean?

Mind blown.

missed a negatve, my bad

Working out of Bak and Newman's Complex Analysis book. The proposition is 7.3:
If f is an entire function satisfying [math] |f(z)|\leq 1/|Imz|[/math] for all z, then [math] f\equiv 0 [/math]. I fail to see how this is at all significant or what the point of it is. It seems intuitively to be a big "well no shit" result. The proof is also kind of obtuse. They pull a [math]g(z)=(z^2-R^2)f(z)[/math] out of their ass to prove it, I understand how it follows but how they popped that up at the start beats me.
Any insight would be amazing.

>They pull a g(z)=(z2−R2)f(z)g(z)=(z2−R2)f(z) out of their ass to prove it

from what I've heard this is pretty typical for analysis

I've got about a year and a half before I graduate with a B.S in Mathematics. Is there hope for me to get some kind of research experience before I graduate or am I fucked? Thinking about applying to grad schools and my chances of getting in is making me pretty nervous, especially since I go to a small and kind of shitty school.

If humanity learns to master the universe and do anything it. Would there be a reason to keep doing anything, or would humanity just chill for an eternity doing whatever it wanted?

I'm actually curious for an answer.

Biology is science... Right?
I have been looking everywhere and I haven't been able to find the answer to this question and my textbook is total shit

Q: Which has a greater effect on the rate of immigration? (talking about species coming to islands)
A: Distance
B: Size

i would appreciate any help

Can I have a fact check on Tesla being born in an electrical storm at the stroke of midnight plz senpai

should be true, sources say yes like this one
pbs.org/newshour/rundown/5-things-you-didnt-know-about-nikola-tesla/
didn't find any myth busting

I would guess distance

How close is humanity in radically extending its lifespan, and maybe reverse aging?

Are there any governments pouring funding into things like this?

Does anybody know of a good textbook to get started with modular arithmetic?

more number theoretic point of view:
An Introduction to the Theory of Numbers - niven/zuckeman/montgomery

more algebraic point of view:
hungerford - abstract algebra: an introduction

many thanks

I can't decide.

Should I use Hoffman/Kunze or Friedberg to learn linear algebra?

bump

how do i measure the frequency of some sort of cyclic mechanical thing like a gearbox. i know i have to fourier a time signal, but how do i get the time signal?

The multiplicative can never be isomorphic to the additive group. Suppose there is an isomorphism [math]\varphi[/math] from the additive group to the multiplicative group for sake of contradiction. We can study this hypothetical isomorphism and show that it cannot exist. We know that [math]\varphi(a) = -1[/math] for some [math]a[/math], so [math]\varphi(2a) = [\varphi(a)]^2 = 1[/math]. This means that [math]2a = 0[/math], [math]a = 0[/math], and [math]1 = \varphi(0) = \varphi(a) = -1[/math]. Now let [math]\varphi(1) = m[/math] so that [math]m = \varphi(1) = \varphi(-1) = m^{-1}[/math]. This means that [math]m^2 = m \cdot m^{-1} = 1[/math], meaning that [math]m = \pm{1} = 1[/math]. Notice that [math]\varphi(1) = m = 1 = \varphi(0)[/math], so [math]\varphi[/math] cannot be injective. Q.E.D.

I'm learning Prolog at the moment, my question though is more related to logic qua science than programming.

When unification is done, from my understanding, it is simply finding a substitution that makes two expressions identical, for example, the most general unifier of:

f(X, g(Y))
f(h(U), V)

is, replacing X with h(U), and V with g(Y), and I understand this to be the most general unifier.

However, what I don't understand is why this is a valid inference, in predicate logic, X, Y, U and V are elements of the universal set, and g is a subset of the universal set, and f is a subset of (universal set) x (universal set).

So, g(Y) is supposed to be a truth value, it is either true or false, it is true if Y is an element of g, it is false otherwise.

So how can we sort of "replace" Y which is an element of the universal set, with something that is "outside" the universal set (something we call a truth value), why is that even valid?

Think about what the expression means and about what it does in the proof. If you still can't get the intuition behind [math](z^2 - R^2)f(z)[/math], try reading the proof backwards.

what if all my myelinated neurons were replaced by nonmyelinated ones but with the speed of the potential remaining constant?

durr, the question being, would I still look the same?

How come neanderthals and shit never have crazy long ass hair? Did they used to cut their hair as well? What?

When I transfer from community college to university, will my stinky GPA follow me and stain my degree?

NOPE

your shit gets reset, you will start with a zero GPA.

don't fuck it up this time.

yes user, don't worry; you'll never die

how's your gpa?

>If you believe in special relativity, there is nothing receding faster from us than c. You can catch up to anything other than photons if you go faster than it.

I believe in SR but I also believe in observational cosmology, where we see galaxies receding from us faster than c.

From Earths PoV it's clear the ship won't ever reach those galaxies but what would it look like from within the ship?

just chill

you forgot about characteristic 2

What is similarity transformation from the geometrical pov? What is similarity coefficient?

No vectors pls

Does anyone knows how to do a linear control for a hovercraft?

HOO HOO HOO!

I'm going to explain how I can made a single core hyperthread, into six processors, due to the topic of trig.

Blazzin it in math

it means you make something bigger or smaller. the coefficient is how much bigger or smaller you make it. simple enough for you?

Thoughput to OUTput to output SHELL.

Break my streets network and analyse, like breaking into kiddie porn orgies happening by my foodstore

congrats Craig

So if we're taking ST of a plane, it's gonna be it's own invariant regardless of the k_s?

Define invariant and k_s, then I can answer your question.

Invariant of f from X to X is a subset of X that remains the same under f. k_s is similarity coefficient.

The reason we wake well is lack of decaf and a secured networking GIANT.

The Illinois economy recieved 42,000,000USD; I have a billion one third currencies today a Billion now.

Just saying we need to just take theor HugesNet box, upgrade, the destroy to secure.

My funds are prossesed.

In the next 11 years what can I most likely expect technology/medical wise Veeky Forums?

mEMe drive

Probably nothing exciting. Everything will just be slightly higher quality. Think about how things are today compared to, say, 2006. Computers are faster, smartphones are much better, internet is better, and there have been slight cultural shifts because of that, but that's pretty much it. My guess is by the end of the 2020s the big new technology will be self-driving cars.

I see. Well thanks for the reply user.

Is there by chance any huge advancement you think will most likely happen 30-40 yrs by chance?

USE WOLFRAM ALPHA YOU NIGGER

Why do poor people have more children than richer people/people who are more taken care of?

What on earth am I looking at

a test on whether or not you can apply the fundamental theorem of calculus

>taught something fucking forever ago
>not used for anything
>suddenly we need it
Why does university do this?

What are some ways an advance civilization can prevent the heat death without leaving the universe for another, or just getting out of it?

Radiating negative energy while creating positive energy maybe?

Every time you evaluate an integral
[math]\int_a^x f'(t) \mathrm{d}t = f(x) - f(a)[/math]
you're using the fundamental theorem of calculus.

If you then take the derivative of both sides
[math]\frac{\mathrm{d}}{\mathrm{d}x} \int_a^x f'(t) \mathrm{d}t = f'(x)[/math]
you get exactly what you posted.

Please explain that like I am a retarded caveman who is loudly banging two rocks together as you speak

A similarity transformation's invariants will be any linear subspace, or ray/halfsubspaces if the coefficient is nonnegative.

Suppose there is a function F(x) which when differentiated gives sin(e^x+2^x).
The fundamental theorem of calculus tells you that
[eqn]\int_a^x sin(e^t+2^t)dt=F(t)-F(a)[/eqn]
Now differentiate the LHS, that's what your picture wants you to do, then differentiate the RHS. Well, differentiating F(x) gives sin(e^x+2^x) and F(a) does not depend on x at all, so differentiating gives 0, so all you end up with on the RHS is the sine term.

jareddiamond.org/Jared_Diamond/Further_Reading_files/Diamond 1975.pdf
distance

bump

It's called the FUNDAMENTAL THEOREM of calculus. You should remember it.

One reason is poor people will be taken care of by their children.

Can someone explain the solution to this problem to me? I think I understand it.

Given events A and B are defined as follows:
A={It rains Monday}
B={It rains Monday and Thursday}
Which of the following is true?
A. B is a subset of A
B. A is a subset of B

The correct answet is B is a subset of A. Why is this? Is this because B is just a combination of A with additional events but will ultimately fall under it rains on monday?

>Is this because B is just a combination of A with additional events but will ultimately fall under it rains on monday?

Yes. B holds in less situations than A does, so it's a "smaller" set.

solution is

(It rains on monday)= (it rains on monday and thursday)U(it rains on monday and not thursday)

In the textbook but that notation doesn't make sense to me :/

Technically it's the golden ratio conjugate, but yes, that number is extremely prevalent.

I mean I understand what the notation is saying I just dont get how then union of those two gets rain today

union = or

I get that but I dont get how it simplifies down to just it rains on monday

If it rains on Monday, then it either rains on Thursday or it doesn't. In one of these cases you get the first set, in the other you get the other. Draw a Venn diagram and it will make more sense.

how about you just learn linear algebra through multiple sources you fucking procrastinator

dont ever get fat with a brain like yours

I see it now I guess user. I just wouldn't have made that connection I guess. Thank you

Suppose we have the seires

[eqn]\sum_{i=0}^{\infty} \frac{5}{i^{3}+2}[/eqn]

Would these two forms of the direct comparison test be equally okay to prove the convergence?

>First:

Take the convergent p-series

[eqn]\sum_{i=1}^{\infty} \frac{5}{i^{3}}[/eqn]

Then consider:

[eqn] i^{3} < i^{3} + 2[/eqn]
[eqn]\frac{1}{i^{3}} > \frac{1}{i^{3}+2}[/eqn]
[eqn]\frac{5}{i^{3}} > \frac{5}{i^{3}+2}[/eqn]

Thus the original series must converge.

>Second:

I just think of it this way:

Same p-series:

[eqn]\sum_{i=1}^{\infty} \frac{5}{i^{3}}[/eqn]

But then the relation:

[eqn]\frac{5}{i^{3}+2} < \frac{5}{i^{3}} [/eqn]

Since clearly [math] i^{3}+2 > i^{3} [/math] which implies the former grow smaller much much faster than the latter. Same answer, but less inequality work.

What type of integration do I use for something like sqrt(d^2 + x^2) ?

trig sub

[eqn] \sqrt{a^{2}+bx^{2}} \implies x = \frac{a}{b}\tan\theta [/eqn]

I'm pretty sure there was another method though.

ibp, u=sqrt(d^2+x^2), dv = dx

Please use English on this British watercress-sampling imageboard.

Integration by parts you mong.

I thought that was for two things multiplied together.

In IBP it's often useful to use dv=dx. Consider this:

[eqn] \int \arcsin(3x) dx [/eqn]

where [math] u = \arcsin(3x) [/math] and dv=(1)dx

How do interpolation periods and sample periods work? Trying to implement this algorithm:
researchgate.net/publication/258401146_Look-Ahead_Algorithm_with_Whole_S-Curve_Acceleration_and_Deceleration
I can`t figure out what Ts is supposed to be...

So what exactly does this coefficient represent?

I have absolutely no clue what you're talking about, and that still doesn't explain why you can use IBP without two things being multiplied together.

Mentally tried normal substituion, back substituion and by parts and there is no way.

Trig sub unless you have some genius identity.

Hmm, and trigonometric substituation produces a gigantic mess.
Which leads me to suspect that I'm doing this question wrong.
I assumed the answer was to integrate the function for the distance of a part of the rod from P.

Why hasn't GR been superseded yet if it doesn't fit the Standard Model in quantum physics with gravity and with other phenomena like dark energy?

He is right.

You are multiplying by dx. You always multiply by dx.

>that still doesn't explain why you can use IBP without two things being multiplied together.
Uh.... yes it does. Did you actually read what he posted?

If I could understand it when it's written in such a shorthand way, I wouldn't be posting in a SQT.

The two things you are multiplying are [math]\arcsin(3x)[/math] and [math]dx[/math].

Let [math]u=\arcsin(3x)[/math] and [math]dv=dx[math].
Then [math]du=\frac{3}{\sqrt{1-9x^2}}dx[/math] and [math]v=x[/math] (since the antiderivative of 1 is x).

So we have...
[math]\int\arcsin(3x)dx=x\arcsin(3x)-\int\frac{3x\,dx}{\sqrt{1-9x^2}}[/math]
by integration by parts.

[math]\int\arcsin(3x)dx=x\arcsin(3x)-\int\frac{3x\,dx}{\sqrt{1-9x^2}}[/math]

jfc