/sci/ - Science & Math

can someone drop me a few bread crumbs here
>If [math]R[/math] is a PID, show that [math]R/(p)[/math] is a field for any prime [math]p\in R[/math]
I tried contradiction, but it just gets me that R/(p*) is a domain for some prime p* and I don't know how to work from there.
I don't know how the condition of R being a PID comes into play.

>>12417807
Sure I'll help you out >>>/c/alculator

What does it mean for an infinite set to have "no size"?

>>12415338
Saying programming language is bad is a sign of a retard, proven by experience.

The mass and radius of a sphere doesn't matter in calculating its linear acceleration rolling down a sloped surface right?

In regression analysis, it's often said that extrapolation is "worse" than interpolation. Is this just pragmatic advice for researchers, or does it have a theoretical justification (ideally, one that does not depend on a particular choice of prior)?

>>12417954
correct

>>12417807
Prove that prime ideals in a PID are maximal. It follows rather directly from the definition of a principal ideal + prime ideal + integral domain.

Does getting AIDS cures autoimmune diseases?

>>12418150
?????????????????????

>>12417796
Is there a safe way to freeze sperm at home for future use

I just learned that my sperm count is declining to the point where I will may impotent in the next 5 years. I'm only 18 so I don't want kids just yet but I'm also broke as fuck so I can't afford $200/month for sperm freezing services so I was wondering if I could just jizz into a jar and freeze it for a woman that I care about, however long that may be.

>>12417958
It just means extrapolation is harder than interpolation. If you've got a data cloud, you can probably accurately state that the data follows a linear pattern (or otherwise) inside of this cloud, but this pattern could break down beyond for all you know.

I need to implement the Runge–Kutta–Fehlberg method to get the numerical solution of ordinary differential equation, using Python. My techer sent me this:

while \(t_n\) < \(t_{FINAL}\):

while True:

\( k_1 = \)

\( \vdots \)

\(k_6 = \)

\(y4 = \)

\(y5 = \)

\(q = \)

if (q >= 1): break
else: \(h = q * h\)

\(y_{n+1} = y5 \)
\(t_{n+1} = t_n + h \)
\(h = q h \)

A i have NO IDEA what he meant by that. So I made this:

def odeRKF(f, y0, t0, NUMBER_OF_STEPS = 100, h = 0.01):

y = np.zeros( NUMBER_OF_STEPS, dtype = np.float32)
t = np.zeros( NUMBER_OF_STEPS, dtype = np.float32)

y[0] = y0
t[0] = t0

for n in range(NUMBER_OF_STEPS-1):
K1 = h * f(t[n], y[n])
K2 = h * f(t[n] + (1/4)*h, y[n] + (1/4)*K1)
K3 = h * f(t[n] + (3/8)*h, y[n] + (3/32)*K1 + (9/32)*K2)
K4 = h * f(t[n] + (12/13)*h, y[n] + (1932/2197)*K1 - (7200/2197)*K2 + (7296/2197)*K3)
K5 = h * f(t[n] + h, y[n] + (439/216)*K1 - (8)*K2 + (3680/513)*K3 - (845/4104)*K4)
K6 = h * f(t[n] + (1/2)*h, y[n] - (8/27)*K1 + (2)*K2 - (3544/2565)*K3 + (1859/4104)*K4) - (11/40)*K5

#y4 = y[n] + (25/216)*K1 + (1408/2565)*K2 + (2197/4104)*K4 - (1/5)*K5
y5 = y[n] + (16/135)*K1 + (6656/12825)*K2 + (28561/56430)*K4 - (9/50)*K5 + (2/55)*K6

#q = (1/360)*K1 - (128/4275)*K3 - (2197/75240)*K4 + (1/50)*K5 + (2/55)*K6

y[n+1] = y5
t[n+1] = t[n] + h

return t, y

I got the same y doing by Euler, Heun and Rugen-Kutta and Rugen-Kutta-Fehlberg, HUGE SUCCES, but my t...

Euler t at 10th iteration step 0.01 = -0.01465443
Heun t at 10th iteration step 0.01 = -0.01468309
RK t at 10th iteration step 0.01 = -0.01468311
RKF t at 10th iteration step 0.01 = -0.01453227

My question is: how do I implement the teacher's code? And yes, I've tried very hard

>>12418216
I think your bigger issue is non-scientific. What woman will want to inseminate herself with sperm kept in some guy's fridge?

>>12418155
Is there a possibility..
Autoimmunity is when immune system treats own cells as outsider whereas AIDS fucks the immune system,hence no autoimmune disease....

>>12418216
I'm not sure, I'm just responding to say that if this is actually the case, you should look into this elsewhere. Maybe find a clinic and ask them questions and state your situation. Most doctors will have a desire to help people even if it doesn't benefit you, so they'll answer.
how did you learn your sperm is declining at 18?

>>12418227
aids doesn't stand for "autoimmune deficiency", it stands for "acquired immunodeficiency disorder"

the problems you have will still be problems, but your body will have even more trouble managing them. because the immune system is a failure on all aspects.

>>12418224
Better ask teacher, it's his job to answer your questions.

>>12418220
>can probably accurately state that the data follows a linear pattern (or otherwise)
>this pattern could break down beyond for all you know
Yes, I think we've all heard this, and it's good practical advice (like remembering that computers have finite memory) that I'm not disputing on those grounds. But, to take your example of linear regression, the prediction error at a given regressor variable x scales with the distance from the sample mean [math]|x - \bar{x}|[/math], and is normally distributed under the usual assumptions. In particular, there's nothing special about the boundary [math]\max_i |x_i - \bar{x}|[/math] between interpolation and extrapolation. Wouldn't it make more sense to abrogate this rule and replace it with one that says "the further your regressor variable x is from the sample mean, the less reliable your forecast will be", especially since this new rule would be far less sensitive to outliers?

>>12418226
kek

how can I express the sum of dot products [math]\langle a,b\rangle + \langle c,d \rangle[/math] as a single dot product (of the form [math]\langle x, y \rangle[/math])?

I know that [math]\langle u,v+w\rangle = \langle u,v \rangle +\langle u,w\rangle[/math] but I can't see how this helps here

>>12418542
Maybe this
[math]\langle a,b \rangle + \langle c,d \rangle=\int ab + \int cd=\int(ab+cd)=\langle ab+cd,1 \rangle[/math]

>>12418542
you don't. congratulations, you've just discovered a motivation for tensors.

>>12418640
while this makes sense in the 1D case where vectors essentially "reduce" to scalars of the field, I don't think it will generalize to arbitrary vector spaces. but please correct me if I'm being a retard.

>>12418642
I'll take your word for it anon, thanks.

>>12418657
If the inner product is an integral that's gucci

>>12418640
>>12418640
[math]\langle a,b \rangle_V + \langle c, d \rangle_V = \langle \langle a,b \rangle_V + \langle c, d \rangle_V,1 \rangle_{\mathbb{R}}[/math]

Can anyone explain why to solve for this
[math]\sup_w c^Tw[/math]
this has to happen
[math]c=\frac{w}{\|w\|}[/math]

>>12418640
>>12418690
I can't believe a dot product against [math]1[/math] is the answer. That proves nothing.

>>12418748
Can't really do much at first sight. Vector axioms are few, so for abstract vector spaces anon's question seems like a doomed prospect.

>>12417796
How do I compute the chromatic complexity of the algebraic K-theory spectrum of KU without invoking redshift phenomenon technology?

>>12418754
Yeah. I'm more inclined to think that anon has a typo in the equation or is missing some extra details.

>>12418739
bump

>>12418758
oh there was no typo or missing details, this isn't a homework assignment or anything. I was just screwing around with the concept of dot products and I felt stupid for not being able to represent the sum of two products as a single product. it seemed to me as though a small algebraic manipulation should cut it. but as it turns out, the question was hopeless to begin with

>>12417796
Where does mass come from?

can anone help guide me on this

Consider the vector space [math] V = {ax + bx^2
| a, b ∈ R}[/math], which is a subspace of
[math]P2(R)[/math]. If [math]p(x) = ax + bx^2[/math]
is a general element of V , consider the linear functionals [math]f_1, f_2[/math]
on V such that [math]f_1(p(x)) = p(1)[/math] and [math]f_2(p(x)) = p(2)[/math]. Find the basis of V which makes
[math]{f_1, f_2}[/math] the dual basis.

i know i need a basis, do i find a basis such that [math] f_1(p(1)) = 1 , f_1(p(2)) = 0 [/math]
ie
[math] f_1(a+b)=1 , f_2(a+b)=0 ?? [/math]

>>12419069
you need polynomials P_1, P_2 such that

f_1(P_1) = 1
f_2(P_2) = 0
f_1(P_1) = 0
f_2(P_2) = 1

>>12419112
thanks, i think that was what i meant to put, i just find dual bases hard to wrap my head around

so is the idea of this now correct?
[math] f_1(e_1) = a+b = 1 [/math]
[math] f_1(e_2) = 2a+4b = 0 [/math]
[math] f_2(e_1) = a+b = 0 [/math]
[math] f_2(e_2) = 2a+4b = 1 [/math]

>>12419131
e_2 should use different letters. your equations says e_1 = e_2

>>12419150
thanks, but to be honest i still have no clue what im doing lmao

>>12419150
nevermind, thinking about it a bit more I think i have an idea of what to do, thank you!

Can someone explain this passage for the hydrogen atom wavefunctions?

[math]\langle 310 | 320 \rangle=E\int_{0}^{2\pi} d\phi\int_{0}^{\pi}sin\theta \, d\theta \, (Y_{1}^{0})^* \, Y_{2}^{0} \langle 3 | 3 \rangle[/math]

I know Y are the spherical harmonics, with the former being complex conjugated because of the definition of scalar product, and I understand the integrals and their limits of integration. What I don't get is how the remaining integral over r can be simply represented by [math] \langle 3 | 3 \rangle[/math]. As far as I know it should be a product of negative exponentials and associated Laguerre polynomials:
[math] \langle 3 | 3 \rangle=K_{3}^1{}K_{3}^{2} \int_{0}^{\infty} dr \, e^{-2r/3a} \, L_{1}^{3}(2r/3a)\, L_{0}^{5}(2r/3a)[/math]
The source even says that [math] \langle 3 | 3 \rangle=1[/math], and I don't understand this either. I know Laguerre polynomials are orthogonal (but not orthonormal) with the weight function [math]e^{-x}[/math], but in that integral they aren't even the same polynomial, so it should be 0 if anything.

Can someone explain this passage for the hydrogen atom wavefunctions?

[math]\langle 310 |E| 320 \rangle=E\int_{0}^{2\pi} d\phi\int_{0}^{\pi}sin\theta \, d\theta \, (Y_{1}^{0})^* \, Y_{2}^{0} \langle 3 | 3 \rangle[/math]

I know Y are the spherical harmonics, with the former being complex conjugated because of the definition of scalar product, and I understand the integrals and their limits of integration. What I don't get is how the remaining integral over r can be simply represented by [math] \langle 3 | 3 \rangle[/math]. As far as I know it should be a product of negative exponentials and associated Laguerre polynomials:
[math] \langle 3 | 3 \rangle=K_{3}^1{}K_{3}^{2} \int_{0}^{\infty} dr \, e^{-2r/3a} \, L_{1}^{3}(2r/3a)\, L_{0}^{5}(2r/3a)[/math]
The source even says that [math] \langle 3 | 3 \rangle=1[/math], and I don't understand this either. I know Laguerre polynomials are orthogonal (but not orthonormal) with the weight function [math]e^{-x}[/math], but in that integral they aren't even the same polynomial, so it should be 0 if anything.

If I take any field extension [math]\K[/math] of [math]\mathbb{Q}[/math] in [math]\mathbb{R}[/math] (that isn't [math]\mathbb{R}[/math] itself) inheriting the topology from [math]\mathbb{R}[/math], then [math]K[/math] should satisfy the same topological properties as [math]\mathbb{Q}[/math], right? It should neither be open or closed, should have empty interior, should be totally disconnected?

>>12417807
>>12418042
Just don't forget about that caveat of the zero ideal being prime but not being maximal in general.

>>12417825
If you don't add any context to your question, no one can answer it. My best guess is that you are referring to "sets of measure zero", a la measure theory and analysis. For instance, the Lebesgue measure [math]\sigma[/math] has [math]\sigma(\mathbb{N}) = 0[/math], despite the fact that [math]\mathbb{N} = \infty[/math]. This is because of how we define the Lebesgue measure (i.e., in an [math]\mathbb{R}[/math]-motivated fashion). On the other hand, you might define other measures [math]\mu[/math] which have [math]\mu(\mathbb{N}) > 0[/math]. So having "no size" is a measure-dependent notion.

At least, assuming that your question is based on the framework of analysis, and not something like topology or geometry.

>>12419897
typo: obviously I meant [math]|\mathbb{N}| = \infty[/math]

>>12419722
[math]\langle \psi | \psi \rangle = 1[/math]. Dirac notation always implies normalized vectors unless the author is particularly lazy and careless.

I don't know the details of your Laguerre polynomial notation, and it's been a while since I actually looked at those, but it doesn't matter. [math]\langle 3 | 3 \rangle = 1[/math]. If you get a different result from the integral, then you've got a typo in your definition of [math]| 3 \rangle[/math]. From the looks of it though, it seems the [math]K[/math]'s are precisely the normalization factors.

Can low dopamine cause depression?

>>12417807
Let m be a MI containing (p). Since PID, m=(a) and a divides p., say ra=p. So either p|a and (p)=m or p|r. In the latter case, we get an equation of type p(sa-1)=0. Since ID, a is a unit. Contradiction. So (p)=m is MI

How do I into quantum computing? I have a CS background and a math minor.

>>12420106
There's plenty of online resources to get started, and it sounds like you have the right background already. Just make sure you haven't forgotten your linear algebra and you should be fine.

>>12419722
what book are you using? the generalized laguerre polynomials require two numbers. the radial wavefunction corresponding to n=3 l=2 is different from n=3 l=1.
could it be that your problem is supposed to be n=3,l=3,m=0 for both the bra and the ket? because then I could see this abuse of notation making sense, but as it stands your first line should equal 0 as your spherical harmonics would be orthogonal

>>12419722
also
>Laguerre polynomials are orthogonal
only between different n and same l polynomials. n=3,l=1 versus n=2,l=1 are orthogonal, but not 3,1 versus 1,0
the orthogonality comes from the spherical harmonics

>>12419928
Yes I know that that is 1 by definition, I just don't get how it pops out in this case

>>12420188
>the generalized laguerre polynomials require two numbers
But I wrote them with two numbers, the subscript which is [math]n-l-1[/math] and the superscript which is [math]2l+1[/math], right?
>as it stands your first line should equal 0 as your spherical harmonics would be orthogonal
Sorry I think I dismissed something important, there was a [math]\hat{z}=cos\theta[/math] all along, like this:
[math]\langle 310 |E\hat{z}| 320 \rangle=E\int_{0}^{2\pi} d\phi\int_{0}^{\pi}sin\theta \, d\theta \, (Y_{1}^{0})^* \,cos\theta \, Y_{2}^{0} \langle 3 | 3 \rangle[/math]
pic related is what I'm following (https://youtu.be/omX2cirpXqk?t=360))

>>12420206
>only between different n and same l polynomials
Yes you're right. Then IDK
>the orthogonality comes from the spherical harmonics
Wait what? I thought those were two indipendent orthogonalities. Spherical harmonics don't even appear in the Laguerre polynomials

where does the 3 < x < 4 come from?

Are niggers dumb dum? And kikes have big brains?

>>12420618
I don't write the laguerre polynomials, I just write the radial wavefunctions [math]R_{n,l}[/math] because I think that's the least ambiguous.
>Sorry I think I dismissed something important
ah yes that's absolutely important.
my guess is that he just completely skipped over the radial wavefunction integration because he knew that the answer was 1, but it is incredibly misleading. without doing the calculation yourself, you would have no way to know whether that was equal to 1. also the way he wrote them as just a ket |3> is bad notation, you won't see that anywhere.
> I thought those were two indipendent orthogonalities
I'm referring to your original question as it was written. Without the cosine term, you'd have just the integral over two different spherical harmonics. This will always be 0, meaning that different hydrogen wavefunctions will always be orthogonal even if their radial components aren't.

>>12420625
Nowhere in particular. It's just that the function has an asymptote at x=3 which is where it goes to infinity, so that's where the "non-boundedness" happens. There's no point in working with a bigger or more complicated interval since a neighborhood of 3 is really all you really care about, so might as well just bound the interval with 4 which is at least a nice enough number and it allows you to find a bound for the other more irrelevant terms.

>>12420697
Thanks!

>>12420701
Also, just to make sure since I worded that post really badly in the beginning, with "nowhere in particular" I just mean the upper bound 4. The 3<x is obviously very important because of the asymptote, and that one in particular comes just from looking at the factor (x-3) in the denominator, which gets arbitrarily close to 0.

Please help anons, I'm stuck on some finite group problems and I'm losing my mind.

Suppose [math]p[/math] is the smallest prime that divides [math]|G|[/math]. Show that any subgroup of index [math]p[/math] in [math]G[/math] is normal.

I get the general direction uses Cayley's theorem and a homomorphism to the Symmetric group on the cosets of [math]H[/math] with index [math]p[/math] but I have no idea how to proceed.

Is there a way we can absolutely be certain there isn't a second earth on our rotation of the sun? Like, it's just always six months ahead so it just stays behind the sun to us.

>>12420922
yes, we would've been able to observe the effects of its gravity on planets such as mars and venus, which don't have the same orbital period as us

>>12420922
We know for sure there isn't due to how mechanics work, and also because at least one of the many probes we've sent would've picked it up already if it existed.

>>12420930
>>12420927
Oh okay. Yay science...

This isn't a question, I'm requesting your luck for sunday. I need it for reasons.
>>12419755
>neither open not closed
Yes.
>empty interior
That one too, trivially.
>totally disconnected
Yes. It's always missing a dense set of points, hence you can split any set into two by exploiting the associated open intervals.
Proving that it's in fact missing a dense set of points is your homework.
>>12420900
Something something set [math]H[/math] as the group of index [math]p[/math], then we know that [math]H[/math] acts on [math]G/H[/math] by conjugations, except this action is necessarily trivial because of Lagrange's theorem, hence [math]H[/math] is normal.
Was definitely something like that.

>>12420964
Forgot my image for maximizing luck (very important).

>>12420964
good luck for reasons
>>12420970
okay I take it back animeposters deserve nothing

>>12420976
No takebacks, I'll give you your luck back on monday.

>>12420996
you better post it in this thread or else the luck is cursed.

>>12421000
I need it for a test. A very important test.

>>12420643
yes on average

>>12420964
[math]\mathbb{Q}[/math]-poster here, thanks a lot

>>12417796
someone pls help this problem has me suffering big time. (its from Axler linalg btw, chapter 6 exercises B)

Suppose [math]C_R[-1,1][/math] is the vector space of real valued continuous functions on the interval [-1,1] with inner product given by
[eqn]\langle f,g \rangle = \int_{-1}^{1} f(x)g(x)dx[/eqn]
For [math]f,g \in C_R[-1,1][/math]. Let [math]\varphi[/math] be a linear functional on [math]C_R[-1,1][/math] such that [math]\varphi (f) = f(0)[/math] for all [math]f[/math] on [math]C_R[-1,1][/math]. Show that there does not exist [math]g \in C_R[-1,1][/math] such that [math]\varphi (f) = \langle f,g \rangle[/math] for all [mathf[/math]

What Ive tried until now is using the cauchy schwarz inequality to show that [math]|f(0)| \leq 2K^2 ||f||[/math] if [math]K = \max_{x \in [-1,1]} |g(x)|[/math] and trying to find a sequence of functions such that [math]||f_n|| \rightarrow 0[/math] but [math]f_n(0) = 1[/math] such that assuming that such [math]g[/math] exists yields a contradiction but my TA says that doesnt work as I need a sequence that converges uniformly and I cant find one

Can science help me being happier?
I do exercise, have meaningful and intimate personal and family relationships. I do take supplements and sleep fine.
Is there some trick or life-hack like micro-dosing acid or else? What makes a mind happy?

>>12421155
Look up bump functions. Let b be bump function with b(0)=1.
Then phi(b)=1. Now take bump functions b_n with support in (-1/n, 1/n).
As |g|>=|b_ng| is integrable and b_ng converges pointwise to 0 almost surely, phi(b_n) goes to zero by the dominated convergence theorem. Contradiction

how do you read this?

please don't sue me, this is hard for me

What are the subgroups for each phase of matter?
Metals, Minerals, Ceramics, Organics, Polymers are what I could find for solids, but I can't find any info on gases, liquids and plasmas past the odd reference to oils, Solvents and acids for liquids. At first I looked at the periodic table of elements, hoping to find nice neat categories of what element groups exist but it's a complete mess. I might be going about this the wrong way, I just want nice neat little categories for things.

>>12421480
The two-dimensional (n,m) vector is part of the integer set of two-dimensional vectors. That just means (n,m) is a vector with n and m being integers.

I've seen that the formal definition of an ordered pair is [math](a,b) = \{ \{ a \} , \{a,b \} \}[/math]. Let's say for example that we are in the naturals. Since both of the sets in that definition are subsets of the naturals, would that mean that mean that [math](a,b) \subset \mathcal{P} (\mathbb{N} )[/math] is true? Which would make it an element of [math]\mathcal{P}(\mathcal{P} (\mathbb{N} ))[/math]? And if that's true, since (a,b) is arbitrary, does that also imply that [math] \mathbb{N}^{2} \subset \mathcal{P}(\mathcal{P} (\mathbb{N} ))[/math], in the literal sense of set inclusion?
Could that be extended for [math]\mathbb{N}^{k}[/math] for any natural exponent?

Is there being done any real scientific research to time travel? If so what subjects are relevant to modern day scientifical research on time travel?

>>12422117
No.
Science Fiction.

>>12422117
Time goes forward everywhere but not at the same rate. Heat, gravity and acceleration change the local rate of experienced time.
Never backwards. Everything that pretends to be backwards is a lie, such as reconstructing a previous local state and pretending that is time travel.

What was that theoretical physics thing, some sort of number or constant relating to the univers, that if it suddenly changed due to a massive release of enerrgy, it would shockwave out changing the laws of physics and destroy the universe everywhere? I also recall some sort of graph visual where it was a dot on some sort of dipped line

Can anyone explain in simple terms why i and h are present in the Schrodinger equation?

[math]i \hbar \frac{d}{d t}\vert\Psi(t)\rangle = \hat H\vert\Psi(t)\rangle[/math]

I know what they are by the way, I just don't know QM. It looks like ih d/dt is an eigenvalue of the Hamiltonian?

>>12422253
You are probably talking about the Higgs field that is currently sitting at a non-zero local minima. If in one location it quantum mechanically tunnelled through the energy gap to its true zero minima that would cause the same effect to cascade outward at the speed of light from that spot. All matter in that area would gain zero mass, all atoms would fly apart and basically the universe would be destroyed.

>>12422256
h appears because it's an equation describing the quantum scale. anything related to quantum effects contains h.
i appears because it's a wave equation. [math]e^{ix} = \cos(x) + i\sin(x)[/math]

>>12422278
Thanks. Is the Planck constant there to "quantize" the result (the energy of the system) so that the values are discrete?

>>12422278
that sounds really interesting (First reply), can you go into more detail in dumb dumb terms?

>>12422286
No. The planck constant doesn't quantize the result. I guess you could describe it as the unit size of quantization. Similar to how you can cut some distance into meters but the value of a meter depends on units we use (metric, imperial, etc).

>>12422300
Ah I see that makes sense. Thanks

>>12422293
Imagine a ball rolling down a hill to the bottom but on the way it gets stuck because it fell into a small hole. The ball can't move up or down and it's not at the bottom of the hill. That is basically where the Higgs field is today. If it could break through the walls of the hole it's in and reach the bottom of the hill then shit gets real.

Is this progression valid?
arithmetics — math — calculus — algebra + geometry

>>12422320
what sets the terms of this wall? what could cause it to roll where things get bad for us?

>>12422372
> what sets the terms of this wall?
It's called a false vacuum. iirc it arises due to the fact that the Higgs is a scalar field.

> what could cause it to roll where things get bad for us?
*shrug* the most common suggestion is that it could quantum mechanically tunnel through the wall (energy gap) but the odds of that happening are really really really small.

why is a particle's momentum related to its wavelength?

>>12422391
It's simple to show if you say the particle is a photon. The relativistic energy momentum relationship is [math]E^2 = p^2c^2 + m^2c^4[/math] but since it's a photon [math]m = 0[/math] so [math]E = pc[/math].

But we also know that the energy of a photon is proportional to its frequency, [math]E = hf[/math]. So [math]pc = hf[/math] but the speed of any wave is just its frequency times its wavelength so [math]c = f\lambda[/math]. This gives the result [math]p = h/\lambda[/math]

>>12422423

>>12421155
Assume [math]g(0) = a > 0[/math] (the larger than zero part is for convenience and not actually a vital part of the proof. Considering the other two cases by immitating the proof below is your homework.). Then there is some [math]\epsilon[/math] such that [math]|x| < \epsilon[/math] implies [math]g(x) > a/2[/math]. There is also an [math]\epsilon ' > \epsilon[/math] such that [math]|x| < \epsilon ' [/math] implies [math]g(x) > a/4[/math].
Now we consider the function [math]f(x) = 0[/math] if [math]x < \epsilon[/math] or [math]x > \epsilon '[/math], [math]f(x) = x - \epsilon[/math] if [math]\dfrac{\epsilon' + \epsilon}{2} \geq x \geq \epsilon[/math] and [math]f(x) = \epsilon ' - x[/math] if [math]\epsilon ' \geq x > \dfrac{\epsilon' + \epsilon}{2}[/math]. Basically, it's a ramp that starts going up at [math]\epsilon[/math], peaks at [math]\dfrac{\epsilon' + \epsilon}{2}[/math] and returns to zero at [math]\epsilon'[/math].
Trivially, [math]f(0) = 0[/math], but [math]\langle f, g \rangle > 0[/math], a contradiction.

How do i solve such a problem. Both A and H are two by two matrices, both invertible although A has negative determinant. I want to express the solutions u and lambda which are both 2 by 1 vectors as functions of x.

[math]\begin{pmatrix}u^* \\\lambda^*\end{pmatrix}=[/math] [math]\begin{pmatrix}H&A^T\\A&0\end{pmatrix}^{-1}[/math][math]\begin{pmatrix}-(2x&x)^T\\(1&1)^T\end{pmatrix}[/math]

>>12423026
wtf does that right matrix even mean. transpose of a vector inside a matrix. that's some fucked up notation.

>>12423057
Its just a convenient way of representing the 4 by 1 matrix in compact notation

>>12423026
Also, A is diagonal, if that helps

>>12422278
The higgs field is not believed to be in a false vaccum. Rather, it is believed to be in a circular minimum of a rotationally symmetric potential, with the non-zero part meaning the minimum is not at the point it is rotationally symmetric about. False vacuums are theoretically possible but there is little evidence that the universe is in one. (Note: the rotations here are not rotations of physical space, just of the space of possible values of the higgs field)

>>12423064
It's not convenient, it's simply wrong.

As for the answer just multiply out all the components of the H and A matrices with the vector and solve the simultaneous equations.

>>12423113
How, the H and a matrix has to be inverted? How do you invert that big block?

>>12423127
You don't know how to invert a matrix??

>>12423026
>>12423072
[eqn]\begin{pmatrix}H & A^T \\ A & 0 \end{pmatrix}^{-1} = \begin{pmatrix} 0 & A^{-1} \\ (A^T)^{-1} & - (A^T)^{-1}HA^{-1}\end{pmatrix}[/eqn] Just abuse block multiplication lmao.

>>12423152
This error is new. Neat to know that /sci/'s shitty Latex can still find new ways to surprise me.

>>12423152
Thats not how you invert a block matrix retard, anyway i found a better source in wikipedia. If you didn't have any idea how to help, why did you even reply?

>>12420667
Ohhh, ok. Thank you very much. Since he just wrote it without saying anything I thought it was supposed to be obvious that it had to be 1. I hate when people treat non trivial stuff as if it was trivial, always makes me waste a lot of time wondering if I missed something

>>12423178
Sure, sure, remember to come back to apologize when you finish expanding out the wikipedia formula and it gives the same result.

>>12423199
>deleted his post

if I know a time-discreet signal b[n] and I also know the convolution between b[n] and h[n], how can I find h[n]?

Matlab is allowed.

>>12423211
That's called deconvolution. I recommend just googling for algorithms or figuring out if matlab already does it on its own.

>>12423211
https://www.mathworks.com/help/matlab/ref/deconv.html

>>12423220
>>12423229

thanks guy(s)!

What is the mechanic by which individual consciousnesses are bound to corporeal forms
Someone recently implied to me that if they had fucked my mother around the time my dad did they would be my father
This was obviously meant as a joke but the question is really fucking with me. There's some reason I am me and not anyone else. There is by implication some process that determined which whether my consciousness emerges or didn't. My friend's statement seems to imply that consciousness is bound to the egg-- that mum's egg + anyone's sperm = me. But why couldn't it be sperm that consciousness is bound to? Or if any individual egg + any individual sperm would have led to my non-existence-- consciousness is a cross-product? Please fucking help me scientists

High IQ math anons, help me

I've been working with left representations of groups in [math]S_n[/math] but I don't feel like I really understand the application of the concept. Any ideas on how I can practice with these and really learn how it works?

>>12423343
Consciousness is created by neurons, which appear partway into the pregnancy. If a different sperm had reached the egg, someone else would have been born instead.

/sqt/ measure theory guy here. Just took my final exam and aced it. Thanks for those of you who helped out with some of the problem set exercises!

Last request for luck.

let there be a closed curve and call it A; a circle rolls on the inside wall of curve A, and leaves curve B behind it's center as it rolls, are curves A and B similar?

I don't understand inertial frames of reference. The way it was explained to me was:
If the observer has zero acceleration, they're in an inertial frame of reference.
If the observer has zero acceleration, they're not in an inertial frame of reference.
But I can't really think of an inertial frame of reference because aren't we all accelerating because the earth is spinning? What am I missing here?

https://en.wikipedia.org/wiki/Hong%E2%80%93Ou%E2%80%93Mandel_effect#Mathematical_description

Why are the signs of [math]\hat{d}^\dagger[/math] different, but not [math]\hat{c}^\dagger[/math]? It sounds like it's got something to do with the electric fields, but I don't see why transmission from the b mode is any different from transmission from the a mode.

>>12424683
Any terrestrial reference frame can be approximated as inertial if the experiment duration is short enough that you can consider the effects of the Earth's rotation to be negligible.

>>12424683
There is no true, perfect inertial frame of reference. However, in the context of newtonian mechanics what >>12424708 says is true, it is good enough of an approximation for practical purposes. But obviously, newtonian mechanics has its limitations (quite a few of them), and this is one of the reasons why.

>>12424708
>>12424717
Alright, thanks. For beginning Physics then, does that mean I only need to worry about "obvious" acceleration when deciding whether or not a frame of reference is inertial?

i am happy with my performance until the last 1-4 hours or of my day or so. I just never know what to do before bed so I lie there hating myself yet being unwilling to put effort into anything. i can't just tune out and watch netflix or whatever since I'm invested in criticisizing others that do so.

i can read, but I'm too tired to sit up so can't really do any worthwhile reading, just fiction to pass the time ('worthwhile reading' involves solving problems, which requires writing, which requires sitting up). i don't want a screen around this time cos it's bedtime, not bluelight overdose time.

the only reasonable solution, it seems, is to just work until I drop into my mattress and instantly fall asleep. alternatively, I could spend $500 (an absurd amount) and get one of those writing e-ink devices.

>PEEPEE POOPOO

>>12424756
oh forgot to mention, my bedroom is too small for a recliner, so I can't just my depressed husk of a body into a reclined position and force it to work. I have to sit in this shitty fold up chair that I already spend too much time in.

How does our body create stomach acid? Is there like, acid glands in our stomach or something?

>>12424768
Yes.

>>12424768
it goes straight into the spinal fluid and never leaves, so when you crack your back, if you've had too much acid, you get heart burn

>>12424792
Like seriously? Could we modify them to spit acid or something?

>>12424854
Some of us are lucky enough to have such a modification! It's called gastroesophageal reflux disease, and I can tell you it's no superpower, buddy!

retard question that I haven't really thought through yet but have wondered about for a while now

at what point do non-asymptotic things become asymptotic? For example, x! isn't asymptotic, but it does increase remarkably fast. d/dx (x!) increases even more so. (x^x)! is practically a vertical line, yet still isn't asymptotic.

There's a similar concept with the convergence of series and integrals that I'm interested in - at what point does a function decrease sufficiently fast so as to converge in finite time?

from me playing around with it, if a function has no asymptotes to begin with, there is no way to really add a constant parameter to any of these functions that make them asymptotic, no matter what you do.

Is this something considered in analysis? Is there a concept of "asymptoticity" that I can look into?

>>12424509
Yes.

If I had a question that asked to show that every convergent real sequence is bounded above and I show that it's bounded, could i then say since it's bounded it's bounded above?

>>12424509
Only if A is a circle.

>>12424690
Why is this board incapable of doing physics

>>12424690
wow this wikipedia page fucking sucks. I'm actually convinced it's incorrect or using a different formalism.

It should read
[math] \hat{a}^\dagger \rightarrow \frac{i \hat{c}^\dagger + \hat{d}^\dagger}{\sqrt{2}}, \textbf{ and } \hat{b}^\dagger \rightarrow \frac{ \hat{c}^\dagger + i\hat{d}^\dagger}{\sqrt{2}} [/math]

This comes because the reflection and transmission probability amplitudes (the coefficients in front of c and d) for a 50-50 beamsplitter are [math] R= \frac{i}{/sqrt{2}} \textbf{ and } T=\frac{1}{\sqrt{2}} [/math]

The answer you get is the same because multiplying these terms gives you the same cross-term cancellation, but their choice of coefficients seems motivated by already knowing the solution. The above way is how I learned it. It's much more clear the way I have it written, because you know that R^2+T^2=1, and the phase between R and T has to be pi/2 (in order to account for energy conservation)

>>12425205
That does make more sense. Thanks

>>12425205
>wow this wikipedia page fucking sucks
you're free to improve it

>>12425225
I'm a grad student, I already do enough work for free
>>12425215
of course, glad to finally have a quantum optics question that made me bust out my notes.

>>12425228
Could you please give a quick rundown on the pi/2 phase from conservation of energy? I'm thinking, considering only one input mode, the reflected mode should be pi off the incident light from the boundary conditions, but don't see how that relates to the transmitted light.

>>12424987
Look into bounded vs unbounded functions. If a function is unbounded at x, then for all M > 0, if when c is close to x, f(c) > M. Basically, you cannot pick an upper bound for f near x.

what does a nigger have to do to buy some ammonia nitrate here?

>>12425815
Probably depends what state you're in. Be prepared to talk to some glowniggers though.

what the fuck is quantum coherence?

my book introduces the term like this...

>A superposition state is often called a coherent superposition because the relative phase of the two terms is important. For example, if the input beam were in the [math]| - \rangle _x[/math] state, then there would be a relative minus sign between the two coefficients, which would result in an [math]S_x = - \hbar / 2[/math] measurement but would not affect the [math]S_z[/math] measurement.

>>12425119
why wouldn't it be true for an ellipse?

How do i separate geometric isomers? I need to show how i would isolate a trans methylketone from a mixture of trans and cis methylketones. The specific molecule is alpha-ionone and i have no idea where to start

>>12426214
is that in a tiny victorian bathroom?

that girl is like 5'9 in real life

>>12426214
Oh also exposure of trans alpha-ionone to UV light converts it to cis-alpha-ionone. If i did that is there a way to convert it all to the trans isomer?
>>12426224
Its shoped sadly

>>12426202
Physicists tend to be very lax in their use of language. All coherent means in a superposition is that there is an operator that convert one state in the superposition into another. For example S_x to flip between a spin-up and a spin-down state.

>>12426214
>>12426225
original

I'm trying to draw a cubic polynomial in 3D space given a set of points that the polynomial must past through. I know that I can find the coefficients for this polynomial by solving linear equations.
I can do it 2D just fine, but I don't know how to setup the linear equation for a polynomial in 3D space.

>>12426230
thank you.
>there is an operator that convert one state in the superposition into another
Is this never possible if you have a mixed state of spin-up and spin-down particles?

>>12426253
In general no but a superposition is typically created from a single source in such a way that the two possible end states are then correlated (coherent) in some way.

>>12426203
Why *would* it be true for an ellipse? In general, the equation describing an offset curve doesn't have the same structure as the original curve. In particular, if the radius of curvature at any point is smaller than the offset distance then the offset curve will have a cusp.

This is an important topic in computational geometry (e.g. CAD/CAM), as offset curves/surfaces to the types of spline curves/surfaces typically used in modelling are much less convenient to work with than the original surfaces. E.g. if x,y,z are polynomials or rational functions in s,t, their derivatives will have the same form and thus so do the tangent and normal. But to get an offset surface you have to normalise the normal which requires a square root and whatever nice algebraic properties the original surface had go out the window.

But I was wrong about a circle being the only case; involutes of a given curve form a family of parallel curves, so an offset curve of an involute is itself an involute. An ellipse isn't an involute of anything, though (involutes inherently have monotonically decreasing curvature and can't be closed curves).

Let [math]e^{inx} \in L^1 ([0,2 \pi])[/math]. I'd like to show that [math]\int_A e^{inx} \to 0[/math] for all measurable [math]A \subset [0,2\pi][/math]. It's easy to verify this in the case that [math]A[/math] is an interval. The hint is now to use the regularity of Lebesgue measure to conclude the proof, but I don't understand how.

(In my course's terminology, regularity of Lebesgue measure means that [math]m(A) = \sup \{ m(C) : C \subset A \} = \inf \{ m(U) : A \subset U \}[/math] for [math]C[/math] closed and [math]U[/math] open.)

Note: I'm aware there's a slick proof using the Riemann-Lebesgue lemma for Hilbert spaces, but I can't rely on that stuff unfortunately.

Should I take DiffEQ or Calc 3 first? I always thought Calc 3 was a prereq for DiffEQ but apparently only Calc 2 is needed.

>>12426567
Take a natural number k and approximate A with a finite union of open intervals U_i such that m(A symmetric difference (union of U+i's))<1/2k. Find N such that for n>N you have |\int_{union of U_i's}e^{inx}dx|<1/2k. Combine both facxts and get tkan for n>N |\int_A e^{inx}dx| \leq 1/k

>>12426567
Take sets [math] K \subset A \subset U [/math] that approximate A.
Write [math] U [/math] as union of open intervals.
Use that [math] K [/math] is compact and find a finite covering [math] K \subset O \subset U [/math].
Write [math] O [/math] as (finite) disjoint union of open intervals.
Note that [math] m(K) \leq m(O) \leq m(U) [/math], hence you can approximate [math] A [/math] by a finite disjoint union of open intervals and you are almost done.

>>12426666
>>12426709
Thanks very much to both of you!

I'm at a total loss here. Let [math]L[/math] be an extension of [math]K [/math], and let [math]K_0 [/math] be the algebraic closure of [math]K [/math] in [math]L [/math]. Prove that for all [math]\alpha \in L [/math] with [math]\alpha \not \in K_0 [/math] is transcendental over [math] K_0[/math]

>>12427126
Was that supposed to be "[math]K_0 [\alpha][/math] is transcedental over [math]K_0[/math]"?

>>12427165
Alpha is transcendental in [math]K_0[/math], but they might be equivalent statements

I need help with my stat homework to impress a boy.
I don't understand the last argument in example 9.19 from http://www.stat.columbia.edu/~bodhi/Talks/Emp-Proc-Lecture-Notes.pdf :(
/lgbt/ sent me since they don't rly know

>>12427187
So, I don't really remember the exact definition of an algebraic closure inside another field.
Anyhow, assuming it's a maximal extension [math]K_0[/math] such that [math]K \subseteq K_0 \subseteq L[/math], then you just have to notice that, if [math]\alpha[/math] were algebraic over [math]K_0[/math], then [math]K_0 \subseteq K_0 [\alpha][/math] is an algebraic extension, and hence [math]K_0 [\alpha][/math] is algebraic over [math]K[/math], which violates the maximality.

>>12426243
How many points do you have? And are they associated with specific values of the polynomial's independent variable (parameter)?

There are three distinct problems here. They all involve finding a cubic function f : R->R^3. This has 12 coefficients (4x 3D vectors).

1. Finding f s.t. f(t)=<x,y,z> for 4 specific <t,<x,y,z>> tuples.
2. Finding f for 5 specific <x,y,z> tuples (with t unspecified).
3. Finding f for 4 specific <x,y,z> tuples (with t unspecified).

For 1, you have 12 equations in 12 unknowns (4 sets of equations, each set having one equation for each of x,y,z). This is just linear algebra.

For 2, you have 15 equations in 15 unknowns (the 12 coefficients, plus 3 values of t; the first and last can be assumed to be 0 and 1 without loss of generality). This is non-linear and doesn't have a closed-form solution.

For 3, the system is under-determined, i.e. you have a choice for some of the coefficients leading to an optimisation problem (e.g. minimise curvature).

> I can do it 2D just fine
2D in the sense of y=f(x), or in the sense of <x,y>=f(t)? The former is simpler because it's essentially 1D rather than 2D.

>>12427225
jesus i'm retarded ty

>>12424352
A day late, I don't know what's going on cuz I haven't been here for a month but good luck bro, take my luck. I'll be waiting to hear your reply, and if it goes wrong, we're here for you.

>>12424352
i think im still range b& but good luck, remilia friend

>>12427188
Please what does it mean, that there can’t be an extension of a uniform random variable to all sets of [0,1]?

>>12427188
maybe you should first check if the boy is interested in transexuals

>>12425285
a=Rc+Td
b=Tc+Rd
|R|^2+|T|^2=1
so, for a 50-50 beamsplitter, you get [math]R=e^{i \phi_R}/ \sqrt{2}, T=e^{i \phi_T}/ \sqrt{2} [/math]
now if you impose energy conservation (energy in=energy out, where energy is related to the square of the amplitudes) then you'll get cross terms that will only cancel if you have [math] \phi_R-\phi_T=\pm \frac{\pi}{2} [/math]

>>12427626
But what if he doesn’t want to talk to me anyways, if I can’t tell him how the empirical process on the cardinal function space equipped with the supernumerary norm is not Borel measurable? :( Pls I need a Knight in shining armor...

>>12427673
Maybe I should mention I only care about the case n = 1

>>12427673
is it true that pubic hair builds up in neovaginas so that you have to routinely scoop up hair balls covered in pus from the neovag?

>>12427730
I don’t know I don’t have one. Maybe I can marry a boy who buys me one, but for that I need answers :(

>>12427740
Are you a tranny and do you have a penis

>>12427775
Ye & Ye:(

>>12427656
>>12425285
if you want the full answer, think classical electric fields
[eqn] \mathcal{E}_{in,a}=R \mathcal{E}_{out,c} +T \mathcal{E}_{out,d} [/eqn]
since energy is proportional to the square of electric fields, square both sides where we call the square of the electric field the energy (proportionality drops out since it's the same on both sides)
[eqn] E_{in}=RR^*E_{out,3}+TT^*E_{out,4}+RT^*\mathcal{E}_{out,3} \mathcal{E}_{out,4}+TR^* \mathcal{E}_{out,4} \mathcal{E}_{out,3} [/eqn]
given a 50-50 beamsplitter, we know that |R|^2=|T|^2=1/2, and write the cross terms in term of their relative phases
[eqn] E_{in}=\frac{E_{out,3}}{2}+\frac{E_{out,4}}{2}+\frac{1}{2}(e^{i \phi_{R}-\phi{T}} + e^{- i(\phi_{R}-\phi_{T})}\mathcal{E}_{out,3} \mathcal{E}_{out,4} \\
E_{in}=E_{out}+cos(\phi_{R} - \phi{T})\mathcal{E}_{out,3} \mathcal{E}_{out,4} [/eqn]
since we don't want the last term to contribute any extra/less energy, as we already have Ein=Eout, we want to impose that it's 0, so [math] cos(\phi_R-\phi_T)=0 \rightarrow \phi_R-\phi_T = \pm \frac{\pi}{2} [/math]

>>12426435
Thank for the reply I'm writing a CAM program for cutting out shapes with a cnc and was just curious if the path that the tool takes could be similar to the shape it is cutting out, it would make things simpler. Do you have any good resources on CAM and computational geometry?

>>12427875
hopefully with my formatting errors it's still understandable

Scientifically speaking, how would one restore anal plasticity? Asking for a friend.

What is the set of all points that can be reached by a projectile shot at an constant speed at different angles. Is this set bounded by a parabola from above?

>>12427188
Oh wait is the answer because this would also include non measurable sets on [0,1] such as the classical cantor set? What would be an example of a non measurable set for the new measure [math]\mu[math] ?

>>12427901
OMG this is so easy lol
We find a open ball construction such that we can connect our uniform random variable with any random set which we can simply choose outside the sigma algebra...
I just messed up about my domains and didn't understand the what we actually wanted to show.

lol a dumb tranny is smarter than this even dumber board. I will impress that boy tomorrow, but now I wish you a good night....
My b

where exactly is it proven that inf(b) exists? it just talks about lower bounds

>>12427977
This really was not made very clear. In L2 we find a decreasing strictly decreasing sequence with a lower bound in B. Then by the monotone convergence theorem this limit exists and is the infimum. :)

>>12427977
(L1) proves that [math]\frac{1}{a}[/math] is a lower bound of B, (L2) proves that it is the greatest lower bound that exists and therefore is an infimum of B.

In this phasor diagram, it compares the phase angle between Eo and the voltage across the load.

Does the diagram say that the voltage across the load is lagging Eo by 36.9 degrees?

Sorry to ask, but what exactly is meant with the O(t^2) terms of a Taylor series expansion? The Taylor series cut off after x^1?

What kind of maths is this and what will I need to learn to understand it?

>>12428128
pretty much, the O(t^2) collects all the higher order terms starting with t^2

>>12428128
big O means "order" and O(t^2) reads "on the order of t^2 (or greater)" referring to the power. so if t is small then when you square it the terms get even smaller, meaning that terms of higher order than t^1 are so small that they're negligible in this application
>>12428132
this would be multivariable calculus mixed with some kind of physics, I have no idea what a fovea is

>>12428128
The Big O notation means, that these terms have very little influence near the point where we approximate a function. x < 1 => x^n < x, so in the tailor expansion these terms become very small. Formally the big O means the following:

O(f(x)) is the space of functions like g s.t. g(x) <= f(x) for x large enough.

There are some more equivalent definitions. You can find them if you google big O notation <3

>>12428132
it looks like we simply go from Cartesian to spherical coordinates. This is useful in a many areas of science and maths. You may good coordinate transform and find more on this topic :)

>>12428137
>>12428141
>>12428145
Thank you very much!

>>12428128
basically the intuition behind
[eqn]f(x) = a_0 + a_1 x + O(x^2)[/eqn]
is "if [math]f[/math] was a polynomial, there would be only higher order terms after [math]a_0 + a_1 x[/math]"

>>12428141
>>12428159
Awesome, now I have a concrete starting point, thank you very much!

It's from an article discussing how information from the retina is projected upon cells in the visual area of the brain in representative coordinates.

water expands when freezing into ice, but what if you froze the ice under pressure? like, if you had some sealed incompressible container, totally filled with water, and froze it, what happens?
i assume that with a low enough temperature, of course it would freeze into a solid, and of the same volume as the water. if so, if you remove it from the container, would it stay the same volume or would the ice cube expand under standard pressure?

>>12428210
That is a really cool question (pun intended) if you basically what you are looking for is a phase diagram to look up what exactly would happen, but basically yes the water would freeze and the ice would be under higher pressure.

>>12428210
there are 19 different phases of ice, each distinguished by their crystal structure. freezing water under pressure (requiring colder temperatures to reach the solid phase) can produce ice in one of these additional phases.
unless the pressure is high enough, however, the freezing process will still lead the water to expand and the ice will push apart on the outside of the container

>>12428210
idk but I know they heat oil to created high pressures enough to make diamonds from carbon

>>12428191
Thank you!

>>12428243
>unless the pressure is high enough, however, the freezing process will still lead the water to expand and the ice will push apart on the outside of the container
how strong is this force? what mediates the strength? of course it comes from the hydrogen bonding in the water, but, it makes me think about the practical uses. lifting very heavy weights by freezing water underneath. how would you calculate the force of expansion?

>>12428260
you still have to put in a lot of effort to freeze the water. this isn't a case of "free energy," and even though I don't know the exact answer to your question I can say you need to put in more energy to freeze the water than you'll get from raising the object

>>12428210

>>12428260
you look it up in a phase diagram

>>12428269
of course but some things are not practical to move by other means. like, consider a glacier moving on a thin layer of water. i cannot envision a machine capable of lifting a glacier without damaging it.

>>12428260
>>12428244

does anyone have more graphs/studies like this? im looking for energy source production per time of day

>>12425105
please answer

>>12428437
yes, a real sequence can't be bounded if it doesn't have an upper bound in the first place

>>12428437
I don’t fully understand your question, but in order to show that is bounded above, assume the opposite s.t. for every a in \R \exists n_0 \in \N : x_n > a, \forall n > n_0. Now for any \epsilon > 0, choose a > |x| + \epsilon. Then that implies that there exists a n_0 \in \N : |x_n| > a > |x| + epsilon, \forall n > n_0. Rearranging and noting that \epsilon > 0 yields ||x_n|-|x|| > \epsilon and this by reverse triangle inequality yields |x_n - x| \geq ||x_n|-|x|| > \epsilon. So x_n does not converge to x. This is a contradiction.

If I wanted to find the PPM of these values, would I need to divide by whatever its time first, then multiply it by 24.45 then the total divide by its molecular mass?

>>12428505
redpill me on using /R instead of /mathbb{R}

>>12428359
Does the country matter? If I recall correctly one of the energy authorities in the Canadian Ontario province has hourly data on energy production (or is it usage?).

>>12428556
no anything is good

>>12428090
What's the frequency of E0?

i don't know much about electricity outside of what i learned in physics, and DC wiring of car stereos.

i'm trying to make a heating mantle of a particular shape, and heating mantles are expensive for what i perceive to be a very simple device, from documentation i've read.
would pic related be safe to do? if not, why?

i plan on stripping a 3 prong grounded wire, and wiring the neutral and hot wires to a bare resistance wire (nichrome). this is woven through a fiberglass sheet, like a basket. i'll probably put an extra layer above and below to minimizing the risk of short circuits. this basket is surrounded with glass wool, and sits in an aluminum container. i'll take the ground wire and attach it to the outer wall of the aluminum with a bolt.

my understanding is that this is safe, so long as the ground is high quality. like, even if i shorted the heating wire directly to the aluminum container, i could touch the container with my bare hands and not be in danger, because the ground is a preferable return path.

additionally, what happens if i were to get this wet, like, what if a container full of water shatters in the mantle? would this be safe, because of the grounding? if i filled it with water and stuck my hand inside, would i be electrocuted?

this seems to match the construction of older "glascol" mantle designs, though some of those do not even have a grounded exterior.

would it be useful to install a GFCI between the mantle and the variac? what about mineral insulated heating cable?

i am not confident enough working with AC power, and i want to avoid killing myself or burning my house down, but, this seems very simple from the patents i've read.

>>12427885
It is, thanks a lot

>>12417796
some help pls quick.
Need a sequence of functions such that [math]f_n(0) = 1[/math] (or any constant > 0) for all positive integers and such that the integral [math]\int_{-1}^{1} f_(x) dx[/math] yields a sequence that converges to 0

>>12428674
ffs the integral is [math]\int_{-1}^{1} f_n (x) dx[/math]

>>12428638
60 hz I believe, it is a 3 phase generator

>>12428674
>>12428680
shit i think ive found it, pls someone confirm that it works.
let [math]f_n(x) = \frac{1}{(1+x)^n}[/math] then:
[eqn]\begin{align*}
||f_n|| &= \sqrt{\int_{-1}^{1} \left( \frac{1}{(1+x)^n} \right)^2 dx}\\
&= \sqrt{\left[ \frac{(1+x)^{1-2n}}{1-2n} \right]_{-1}^{1}} \\
&= \sqrt{\frac{2^{1-2n}}{1-2n}} \rightarrow 0
\end{align*}[/eqn]

>>12428674
Do you need the function to be continuous? If not then you can define a piecewise function that is 1 at the integers and the constant 1/n everywhere else.

>>12428737
yeah it needs to be continous, also, I misstated the problem, the norm over [-1,1] should tend to 0, not the integral, see what I wrote here >>12428733

>>12427359
Thanks bro, the luck came in just in time.
>if it goes wrong
It'll take a good while before I know if it worked out or not.
>>12427398
>i think im still range b& but good luck, remilia friend
Thanks lad.
>>12428514
It doesn't work here but it works in places like quora.
>>12428733
I'm not looking through that computation, but that example does work because Lebesgue convergence.

>>12428768
Wait, no, it doesn't, my bad. Shit explodes on the negatives.

>>12428733
>>12428772
The explanation I gave was shit so I graphed it on desmos for you.
https://www.desmos.com/calculator

>>12428674
Oh, and for the sequence of functions, take the normalized Gaussian [math]f[/math] and go [math]f_n(x) = f(nx)[/math]

>>12428674
Everyone is giving all these needlessly complicated answers, just use this.

>>12428768
>It'll take a good while before I know if it worked out or not.
Sounds like it worked out well, let us know how it turns out in the future

>>12428674
[math] cos^n(x) \rightarrow 0 [/math] pointwise a.s.
So [math] \int_{-1}^{1} cos^n(x) dx \rightarrow 0 [/math] with the dominated convergence theorem.
Or just google bump function and take one with support in [math] (-\frac{1}{n},\frac{1}{n}) [/math].

>>12428820
If x=0 then f(x) = 1-n not 0

>>12428862
This is elegant, i like it

>>12428090
Well, the diagram just says that the phase angle is 36.9°. It doesn't actually say that it's lagging (although it will be, because that's what you get from an inductor). FWIW, it's preferable to use atan(Im(Z)/Re(Z)) (i.e. atan(144/192)), as acos(Re(Z)/|Z|) is inaccurate for small phase angles (and for a phase angle of zero, you might get a domain error caused by rounding error resulting in evaluating e.g. acos(1.000001)).

>>12428638
The frequency doesn't matter. It just states that the reactance of the inductor is 144Ω.

>>12428919
Thank you for the explanation!

>>12428642
> would pic related be safe to do? if not, why?
Seems safe enough. I'd suggest putting a fuse or breaker between the variac and the element. If the variac isn't at 100% the current drawn from the mains will be lower than that drawn by the element, so you can't rely upon the mains fuse/breaker to deal with over-current conditions.

> would it be useful to install a GFCI between the mantle and the variac?
It doesn't matter where the GFCI is; the variac should pass the ground straight through.

>>12428862
>>12428820
>>12428789
>>12428778
OK so you fags ive found it.
[eqn]f_n(x) = \begin{cases} 0 & -1 \leq x <0 \\
-nx+1 & 0 \leq x \leq 1/n \\
0 & 1/n < x \leq 1 \end{cases}[/eqn]

>>12428940
>fuse or breaker between the variac and the element.
i hadn't considered this, so thanks. i'll look into specifications from mantle manufacturer's to see what the maximum draw is for similar mantle designs, and i'll determine an appropriate value given the length of heating wire.

>>12428948
Pretty sure smoothness is implied. Your shit isn't even continuous (could be fixed) or differentiable. You could just set f(0)=1 and zero everywhere else if you don't care about continuity.

MATLAB/Simulink question: Need the signal too look like above pic but not sure exactly how.
Bottom pick is all I have. How do I place the inputs/outputs?

>>12428985
Yes it is continuous wtf are you going on about?

>>12428993
I think you need to retake some high school classes

>>12428509
I think I have it I just want confirmation I’ve done it correctly

What do I do when I'm trying to take second partial derivatives and there's a mixture of independent and intermediate variables? Do I just convert everything to the independent variables after my first differentiation?

>>12429013
Shit you're right lmao its late as all hell.
I'm just gonna use [math]f_n(x) = e^{{-nx}^2}[/math]

Why is blood a fucking connective tissue? shouldn't Arteries/Veins be the tissue?

I'm pretty bad at basic statics (force, moment, dry friction, frame/machine analysis) and I have an open book, open resource final coming up. Is there any software I can use to my advantage?

>>12429148
As a matrix, blood is essentially establishing connections throughout the body.
>Connective tissue is the tissue that connects, separates and supports all other types of tissues in the body.
Blood is vital in the support role, it connects indirectly by delivering hormones (and oxygen), and it certainly separates as only specific compounds will be transmitted via bloodstream.

Let G be a group. Let A be a neighborhood of the identity. I want to prove [math]\bigcup_n A^n =G[/math]. The inclusion [math] G\subset \bigcup_n A^n[/math] is giving me trouble. Any help?

>>12429170
makes sense, thanks brah.

>>12429173
I should mention G is connected which also means [math]\bigcup_n A^n[/math] is connected.

Is this shit even real? I had this stuff hammered into my head during my HS environmental class, and have heard every old person I know dispute it. Is it just boomer shit, or is it true that in this situation, the needs of the few ended up outweighing the many?

>>12429273
Environmental regulation used to be nonexistent

>>12429286
I mostly mean pertaining to DDT, and its side effects as this book recognized them. I'm wondering how they could have possibly been so bad and so widespread that it would outweigh the threat of things like malaria and other mosquito-borne diseases.

Has anybody ever had their self esteem affect their math skills?

>do problem in my head
>know the answer almost instantly
>immediately start to doubt myself and slowly go through it in my head
>look smooth brain as fuck, even though I had the answer straight away in my head

How do you get past this? I even do it with really simple stuff as well.

>>12429309
It's a good skill to have to be able to interrogate your own answers. The worst people to work with are the people who aren't able to do this themselves.

>>12429309
Assuming you were right the first time, you might need to work on understanding that intuition is your strong point, and that questioning your intuition may be counter productive. This is generally an issue when reasoning is time sensitive, but if you find yourself challenging your own conclusions after the fact (I do the same thing) sometimes it is best to understand that you made those choices based on all the information available, and you'll often be right.

Could particles not exist and just be energy moving reality around?

>>12429374
how do you distinguish "energy moving reality around" from a particle?
if it walks and talks like a particle, who cares what it's called

>>12429414
>how do you distinguish "energy moving reality around" from a particle?
We technically already don't. If every particle that has mass has energy, but not every particle with energy has mass how don't we know that particles aren't just a state of pure energy instead of having energy?

>>12429433
once again, what would the difference be? to a certain point, it's just semantics. our description of things is valid regardless of what's "actually happening"

>>12429437
If all is just energy it means that possibly there's only ONE possible element on the whole universe.

I want to prove something isn't possible to resolve by saying that I have only one equation but three unknowns. This is super obvious and everything, but is there a specific theorem or corollary of algebra that I would cite to say
>More unknowns than equations can't be solved due to ............

dumbass incoming

How do you read 1.1! + 2.2! ? Google doesn't recognize the dot and exclamation point

>>12429558
1 times 1 factorial plus 2 times 2 factorial

>>12418216
Just go to sperm banks

>>12418216
You can't do it at home. Sperm freezing is done using liquid nitrogen and iirc they treat you cum in such a way as to stop ice crystals forming that would destroy the sperm cells. Sticking it in the freezer is not cold enough for long term storage and would make it sterile.

>>12428514
Have my own command set up for for common sets... old habbits

How do I prove/argue that [math]\lim_{n\to\infty}(n+1)|x|^{(2n+1)}<1[/math] for [math]x\in(-1,1)[/math]?

>>12429961
lhospital

>>12429969
Forbidden for this problem, but I still don't see how even with it.

>>12429982
in principle, you need that polynomials go to infinity slower than exponentials go to zero. squeeze theorem should do.

>>12429961

>>12430011
putting series into logarithms can be really helpful if you try to show things without using l'hopital

>>12430011
actually no there is a mistake you need to argue that |(2n+1)ln(|x|)| > ln(n+1), you may do so using series expansion maybe

>>12429961

[math](n+1)|x|^{(2n+1)}=n|x|^{(2n+1)}+|x|^{(2n+1)}=f_n(x)|x|+g_n(x)|x|[/math]
[math]f_{n+1}/f_n=\frac{(n+1)|x|^{2(n+1)}}{n|x|^{2n}}=\frac{(n+1)|x|}{n}<1 \Rightarrow |x|<\frac{n}{n+1} [/math]
So [math]f_n[/math] is eventually decreasing and positive and bounded below by 0 for all [math]x \in (-1,1),n \in \mathbb{N}[/math], so it eventually converges to 0.
[math]g_n(x) \to 0, \forall x \in (-1,1)[/math]
Both converge to 0 so eventually the sequence converges to 0<1 for all x in the interval.

50 + 10 / 8 + 2

What is a good argument I can use to make the above equation equal 60 without changing or adding any operators such as parentheses

>>12430159
There is no good argument. You can only say
> I am going use the convention of working from right-to-left for all operators in all equations
which works but is a stupid convention.

>>12430166
Wouldn't that give you 51 though?

>>12430159
Rounding up x to the nearest multiple of 10 higher than x. In this case f(x)=f(50+10/8+2)=f(53.25)=60

>>12430192
my bad for trying to read on a tiny phone screen. thought it read 1 not 10.

Is it possible to titrate a mixture of two strong bases with a strong acid if the equivalence points are separated enough? Like that you get two equivalence points?

where does cos come from?

this is from richard feynman book on qm

>>12430291
i don't get this explanation

(don't have the math backgroung obviously)

>>12430291
It is the law of cosines. It applies to the h's because they are complex numbers, and any complex number can be viewed as a vector in the plane R^2

>>12430291
[math]|z_1+z_2|^2=|e^{i\pi x+\phi_1}+e^{i\pi x+\phi_2}|^2=Re(e^{i\pi x+\phi_1}+e^{i\pi x+\phi_2})^2+Im(e^{i\pi x+\phi_1}+e^{i\pi x+\phi_2})^2=[/math]
[math]=(cos(\pi x+\phi_1)+cos(\pi x + \phi_2))^2+(sin(\pi x+\phi_1)+sin(\pi x + \phi_2))^2=[/math]
[math]=(cos(\pi x + \phi_1)^2+sin(\pi x +\phi_1)^2)+(cos(\pi x + \phi_2)^2+sin(\pi x +\phi_2)^2)+[/math]
[math]+2(cos(\pi x + \phi_1 )cos(\pi x + \phi_2)+sin(\pi x + \phi_1 )sin(\pi x + \phi_2))=[/math]
[math]=|z_1|^2+|z_2|^2+2C[/math]
[math]2cos(\pi x + \phi_1 )cos(\pi x + \phi_2)=cos(\pi x + \phi_1 + \pi x + \phi_2)+cos(\phi_1-\phi_2)[/math]
[math]2sin(\pi x + \phi_1 )sin(\pi x + \phi_2)=cos(\phi_1-\phi_2)-cos(\pi x + \phi_1 + \pi x + \phi_2)[/math]
[math]C=cos(\phi_1-\phi_2)[/math]

there's something wrong methinks, figure it out

>>12430342
maybe it's because I didn't put it the wave amplitudes. In any case the argument is this one

Made it in thanks to your patience /sqt/, taking EE next year as my first university experience.
What should I refresh my memory on the hardest during these free 3 months?

>>12430376
trig & calc + precalc like an autist and some HS physics refresh

>>12430379
On it, any books you can personally recommend?

>>12430385
Not really, there's many. Maybe some anon specialized in math education can answer optimally.

In QM why is <x|y>=y(x)? I figure that postulates says that the probability of finding y in the state of x is some constant and y(x) happens to equal that constant. But is there a mathematical proof for this?

>>12430259
you want to neutralize a basis twice? When you mix the two bases they"ll assume a new pH value.

>>12430385
not a book but I found this website to be pretty indispensable through my undergrad:
https://tutorial(dot)math(dot)lamar(dot)edu/

>>12430433
Bookmarked, thank you.
This board is an oasis in a sea of shit.

>>12430417
literally definition of the symbol <x|y>

>>12430460
So its only a definition and cannot be derived from say, |y>=sum<yn|y>|yn>?

>>12430456
Also I havent used this all that often but you might be able to use Volume 1 for some classical mechanics. What is also really important is that youre completely comfortable with the math involved. The difficulty in undergrad, at least from my experience, is the formulation of the problems and its possible, and desired, for the math to be piss easy. You just have to work on the math till its second nature. Website for mechanics: https://www.feynmanlectures(dot)caltech(dot)edu/

>>12430291
>>12430342

[math]
\begin{align*}
|z_1 + z_2|^2 &= (z_1 + z_2)(z_1 + z_2)^* \\
&= z_1.z_1^* + z_2.z_2^* + z_1.z_2^* + z_2.z_1^* \\
&= |z_1|^2 + |z_2|^2 + \ ...
\end{align*}
[/math]

RHS expands to (settings [math]r=1 \text{ in } z = r.e^{ix}[/math] to keep it clean, magnitudes can be added later)

[math]
\begin{align*}
... &= e^{i\theta_1}e^{-i\theta_2} + e^{-i\theta_1}e^{i\theta_2} \\
&= e^{i(\theta_1-\theta_2)} + e^{-i(\theta_1-\theta_2)} \\
&= \cos(\theta_1-\theta_2) + i\sin(\theta_1-\theta_2) + \cos(\theta_1-\theta_2) - i\sin(\theta_1-\theta_2) \\
&= 2\cos(\theta_1-\theta_2)
\end{align*}
[/math]

FUCK THE 4CHAN ESC BUTTON.
>>12429173
I'm not writing the whole proof again, use the fact that [math]\bigcup _{x \notin \bigcup_n A^n}A^{-1}x[/math] is open and disjoint from [math]\bigcup _n A^n[/math].

>>12430498
thanks for this. didn't know the relationship between e^ix and trig functions

>>12430517
>didn't know the relationship between e^ix and trig functions
bruh

Does anyone a good course on high school statistics and probability. Also exam questions.
Need to write a didactical course.

>>12430011
what do you use for drawing?

I just finished an exam, the last question was proving GLS was more efficient than OLS. I didn't have much time, so I just copy pasted my Gauss-Markov proof from an earlier question, and just started pasting in [math]\Omega^{-1}[/math] where necessary.

It was a 10 mark question. Am i likely to get any credit or should I just forget about it?

>>12430647
Explain why CX = I

>>12430745

>>12430745
Oh poop. Under CLRM it's I -> [math](X'X)^{-1}X'X[\math]. Under GLRM, it's something much different.

That being said, its a BLUE. So it is unbiased one way or another, I should've just followed that through

any help on this one? not really sure how to set up the torque equation

>>12430478
there are no <x| eigenstates, because it is a continuous spectrum
the best way to think about it (which is still wrong but less wrong) is that the position eigenstates are an infinite set of delta functions centered on each point along the position axis. when you bracket <x|y> you're integrating over an infinite number of delta functions at every point, with each integral giving you y(x0) at a specific point x0. doing this for all points x0 recovers the full y(x)

>>12430790
pls

For a Fabry-Perot cavity filled with an arbritary number of different dielectric layers, how do I calculate the cavity resonance?
I know the resonant wavelength of the cavity reduces as the dielectric constant increases, but how do you deal with multiple layers with arbritary positioning of the dielectrics?

How come I've been chewing nicotine gum at a pace of one 2g gum per day but have developed literally no addiction and need to consciously remind myself that I need to chew the thing for muh iq?

>>12430421
apparently not in some cases
https://byjus.com/jee/titration/

I hate online quizzes. I made one dumb sign error and lost all credit. I'm almost ready to pay someone to help me with my finals exam. Anyone have any experience with this? Are the websites that show up on Google safe?

I don't want to give them my password. I just want to send them pics of my exam and they could work on it while I work on it and we'd compare answers.

why am i so stupid

Anyone aware of a study of the correlation between subjective happiness and the frequency of sex?

>>12431090
same thinghappens to me but some anon said nicotine causes heart issues/palpitations so I stopped

the IQ/focus gains were diminished when I was doing it routinely anyway IMHO

How do I go about showing that the spectrum of a idempotent operator P on a Hilbert space is contained in {0,1}?

>>12431578
Have you considered that if you make simple sign errors in your future job and fuck up something major you will be fired?

>>12431653
You answered your own question by asking it.

What does [math]f:\mathcal{P}(\mathbb{Z})\rightarrow\mathcal{P}(\mathbb{Z})[/math] mean? Having a hard time picturing what a function from a power set to a power set is supposed to be.

can i say x = y for the system [math]\begin{cases} y - \frac{k}{x^2} \\ x - \frac{k}{y^2} \end{cases}[/math], k being a constant?

>>12432233
of course i forgot the most important part lmao. both formulas equal 0, so [math]\begin{cases} y - \frac{k}{x^2} = 0 \\ x - \frac{k}{y^2} = 0 \end{cases}[/math]

>>12432214
it's just another function from a set to another set, i'm not sure what else you would need to understand. subsets of the integers get mapped to other subsets of the integers, it could just be the identity map, maybe a function that maps sets to their complements, etc.

Do some profs make shit more difficult than it needs to be on purpose? It seems like my QM prof is making shit harder than i needs to be by switch around variables and doing other pointless shit that i then have to spend a good deal of time figuring out.

>>12432239
more specifically, how can i solve [math]\begin{cases} y - \frac{64}{x^2} \\ x - \frac{64}{y^2} = 0\end{cases}[/math]? is this is even a possible system?

>>12432413
Substitution.

>>12432467
got it. thanks