Anonymous at Thu, 17 Oct 2024 16:43:19 UTC No. 16436536

For me it's MegAdeTH

🗑️ Anonymous at Thu, 17 Oct 2024 21:44:45 UTC No. 16437003

>>16436512
I assume the answer is eye color since every body has an eye color so we can generalize from a small sample?

(just assume im retarded and please tell the answer directly)

Anonymous at Thu, 17 Oct 2024 21:46:20 UTC No. 16437005

>>16437003
You didn't give the whole question retard

🗑️ Anonymous at Thu, 17 Oct 2024 21:48:08 UTC No. 16437008

>>16437005

Anonymous at Thu, 17 Oct 2024 23:50:23 UTC No. 16437155

What are the best nootropics and supplements to bolster my acuity?
I trust you all more than /fit/.

🗑️ Anonymous at Fri, 18 Oct 2024 00:37:16 UTC No. 16437238

>>16437003
>>16437008
I would have said all of them except for parental education since that is the only variable that is dependant on if they could take the survey or not (the parents' education could affect the children more likely to get into those universities).

Anonymous at Fri, 18 Oct 2024 07:37:21 UTC No. 16437546

>>16437155
caffeine and a good night's sleep

Anonymous at Fri, 18 Oct 2024 07:52:40 UTC No. 16437553

How many possible are combinations are there in a pentagram? I want to know how many shapes there are in here. Considering pic related is also a shape

Anonymous at Fri, 18 Oct 2024 13:43:05 UTC No. 16437887

Can it be solved?

Anonymous at Fri, 18 Oct 2024 14:10:36 UTC No. 16437932

>>16437887
i have a marvelous proof of the case of n=2, which is too long to fit in this post.

Anonymous at Fri, 18 Oct 2024 14:20:18 UTC No. 16437947

>>16437887

Anonymous at Fri, 18 Oct 2024 15:08:32 UTC No. 16438025

>>16437887
>inside a circle
Do circles have an inside? (They definitely have no interior.) BTW, for n=2,3 probability is 0.

Anonymous at Fri, 18 Oct 2024 15:35:11 UTC No. 16438092

There are infinite points in a circle. A probability cannot be calculated.

Anonymous at Fri, 18 Oct 2024 17:13:18 UTC No. 16438258

>Let [math]A\subset \chi(\mathbb{R}^3)[/math] be a subspace with basis [math]\{X,Y,Z\}[/math] where [math]X = y\partial_z - z\partial_y \,,\, Y =z\partial_x - x\partial_z \,,\, Z = x\partial_y - y\partial_x[/math]
Help me understand this. What is [math]\chi(\mathbb{R}^3)[/math]? Why were the basis vectors written as partial derivatives?

Anonymous at Fri, 18 Oct 2024 20:12:52 UTC No. 16438551

>>16438258
>What is χ(R3)
You could easily check on ChatGpt
>χ(R3) can denote the space of compactly supported smooth functions...

>Why written like that
Cause if you play around with them you notice you get rotations.

Those are some constant multiple of the angular momentum operators. Instead of X,Y, and Z, think of L_z, L_y, L_z, where angular momentum L = r X p, where p_x = hbar/i * d_x. That multiple hbar/i doesn't really matter. The space of these Hermitian Operators (so they represent an observable) are a Lie algebra for the generators of rotation, so the exponential map of this algebra gives a Lie group representing spacial rotations. So similar to how momentum generates spacial translation, angular momentum generates spacial rotations via the exponential map.

Anonymous at Fri, 18 Oct 2024 20:48:38 UTC No. 16438598

By Fermat's last theorem you can not split a cube into two other cubes like a^3+b^3=c^3. But can the equation hold if there's more cubes, like a^3+b^3+c^3+...+n^3 = x^3?

Anonymous at Fri, 18 Oct 2024 20:59:18 UTC No. 16438613

>>16438598
2^3=1^3+1^3+1^3+1^3+1^3+1^3+1^3+1^3

Anonymous at Fri, 18 Oct 2024 20:59:20 UTC No. 16438614

>>16437553
define different
all n-sided shapes count only once for each n? e.g. a triangle is a triangle no matter the side lenghts
if not, does rotating count as a different shape?
are you maybe confusing your question with a graph related task?

Anonymous at Fri, 18 Oct 2024 21:03:13 UTC No. 16438624

>>16438598
Assuming all the integers are > 1 and unique, then the shortest counter-example would be: [math]3^3 + 4^3 + 5^3 = 6^3[/math]

Anonymous at Fri, 18 Oct 2024 22:37:52 UTC No. 16438788

>>16438624
Is it proven that you can do that sort of thing for every power, not just for a cube?

Anonymous at Fri, 18 Oct 2024 22:48:05 UTC No. 16438798

>>16438788
We have lots of examples for different powers up to 8 (not sure about higher) but is it not proven if you can do it for every power. For example no one has found any solutions if the power = 6.

Anonymous at Sat, 19 Oct 2024 04:19:46 UTC No. 16439272

>>16436512
will analysis make me better at calculus and applying it and sheeit

Anonymous at Sat, 19 Oct 2024 18:52:46 UTC No. 16440154

>>16439272
Yes...that and two extra inches

Anonymous at Sat, 19 Oct 2024 19:50:27 UTC No. 16440225

If I have to prove that a subspace [math]A < \mathfrak{X}(\mathbb{R}^3)[/math] is a Lie subalgebra, do I really NEED to prove that it's closed under the Lie bracket? Is that the only way? Shit's getting messy over here.
For context, this is the problem:
>Let [math]A < \mathfrak{X}(\mathbb{R}^3)[/math] be the subspace with basis [math]X_1,X_2,X_3[/math] where [math] X_j = x^{\sigma(j)}\partial_{x^{\sigma^2(j)}} - x^{\sigma^2(j)}\partial_{x^{\sigma(j)}}[/math] and [math] \sigma = (1\,2\,3) \in S_3[/math]. Prove that [math]A[/math] is a Lie subalgebra of [math]\mathfrak{X}(\mathbb{R}^3)[/math]
The problem actually is a bit different at first (although my statement is equivalent to the OG statement), I just introduced some other notations and the permutation to make it more convenient and allow me to work under a summation sign.
I just took two vector fields [math] F_1 = \sum_{j}f_{1j}X_j\;,\; F_2 = \sum_{k}f_{2k}X_k[/math], put them both in the Lie bracket and then I'm just developing the algebra. The [math]f[/math]'s are functions in [math]C^\infty(\mathbb{R}^3)[/math].
Might work, but it's so fucking tiring and bothersome that there must be an easier way.
Any help is appreciated.

Anonymous at Sat, 19 Oct 2024 19:53:37 UTC No. 16440229

>>16436512
Im looking for that paper done by the black maths PhD student who wrote it like a nigger due to “avoiding eurocentric language”, anyone got the name?

Anonymous at Sat, 19 Oct 2024 19:58:58 UTC No. 16440236

>>16437887
Continuous domain? Approaches zero, effectively asking for (prob will have intersect lines)/(prob a it just doesn’t just sperg in a small area).

For discrete domains you could probably do something * resolution that covers all possible pixels of a circle (probably based on on the area).

Anonymous at Sat, 19 Oct 2024 21:03:29 UTC No. 16440312

>>16436512
How come Hamas can take armed shepards and have them fly with a motorbike and a sheet aub we get stuck in traffic all the time?

Anonymous at Sat, 19 Oct 2024 21:59:51 UTC No. 16440379

>>16437887
Sounds like a clever variant of Bertrand's paradox.

Anonymous at Sat, 19 Oct 2024 22:12:33 UTC No. 16440387

>>16437887
>>16437887
P(n) = (2/3)^((n - 1)(n - 2)/2)
In the context of the problem, n represents the number of lines formed by connecting the sequentially chosen random points inside the circle. Since you start with one initial point and then select additional points, connecting each new point to the previous one, the total number of points will be n + 1, but the number of lines connecting them is n.
P represents the probability that none of the n line segments intersect each other.

🗑️ Anonymous at Sun, 20 Oct 2024 01:05:44 UTC No. 16440546

>>16440154
>add length and girth with these simple equations
prove it.

irony is i fucking suck at maths but spivak's book is the only one i've been able to understand and recollect. i put it down because i was wondering what the point was. what the fuck is wrong with me.

Anonymous at Sun, 20 Oct 2024 01:08:12 UTC No. 16440551

>>16440154
>add length and girth with these simple equations
prove it.

Anonymous at Sun, 20 Oct 2024 02:14:13 UTC No. 16440654

>>16438614
each unique face as in each various rotation, im not sure if this is a graph task
anyway the number i came to was 282

Anonymous at Sun, 20 Oct 2024 11:20:54 UTC No. 16441026

>>16436512
any recommendation on what open source/free software to use to simulate electrodynamics? I am kinda sick of looking at formulas and never real world stuff. Was reading up on how to simulate microwave antennas but thats a bit over my head...

Anonymous at Sun, 20 Oct 2024 13:07:06 UTC No. 16441119

Why does the inner product have conjugate symmetry?

That is:

[math]<V|W> = <W|V>*[/math]

I'm coming at this as a physicist trying to understand Hilbert spaces. Conjugate symmetry is stated without proof in my notes/textbook. Is there some deep idea here, or an enforced property of Hilbert spaces?

Anonymous at Sun, 20 Oct 2024 13:31:55 UTC No. 16441154

>>16441119
it's so that the inner product of any wavefunction with itself is real, which lets you interpret it as a probability distribution

Anonymous at Sun, 20 Oct 2024 13:32:42 UTC No. 16441157

>>16441119
That comes from the fact / definition: [math]| A \rangle^{\dagger} = \langle A |[/math]

So [math]{\langle W | V \rangle}^{*} = (\sum_{i} W_{i}^{*} V_i)^{*} = \sum_{i} V_{i}^{*} W_i = \langle V | W \rangle[/math]

Anonymous at Sun, 20 Oct 2024 18:15:09 UTC No. 16441461

>>16441157
And for a continuous function, instead of a summation, it would be an integral

Anonymous at Sun, 20 Oct 2024 18:42:48 UTC No. 16441488

what does a narrow height for normal distribution indicate?

Anonymous at Sun, 20 Oct 2024 18:45:58 UTC No. 16441490

>>16441488
I think you mean narrow width, not height. It means a small variance, so most of the values are distributed around the mean.

Anonymous at Sun, 20 Oct 2024 18:48:18 UTC No. 16441496

>>16441490
>I think you mean narrow width

man this shit is confusing sometimes. Thanks

Anonymous at Sun, 20 Oct 2024 18:51:26 UTC No. 16441502

>>16441026
ElmerFEM

Anonymous at Mon, 21 Oct 2024 01:09:33 UTC No. 16441988

What really is the distribution of vector fields?
I thought it was just the span of the vector fields but apparently that definition if only locally correct (whatever that means).
And also, the definition I'm using for vector field is that a vector field on a manifold [math]M[/math] is a linear map [math]X:C^\infty(M)\to C^\infty(M)[/math] that is also a derivation. Following from this definition, how can I define a covector field? A covector field is supposed to be a differential form, right?

Anonymous at Mon, 21 Oct 2024 20:04:31 UTC No. 16443019

I’m gonna get a 0 on my eletromag test

Anonymous at Mon, 21 Oct 2024 20:11:52 UTC No. 16443026

>>16443019
good. healthy people don't do STEM.

Anonymous at Mon, 21 Oct 2024 21:10:41 UTC No. 16443088

>>16436512
So I'm stuck in Analysis 1 again.
I can't figure out the next number in this sequence: 1, -7, 9, 119, ...
9 is the difference between 1 and -7, but I have no idea how they came up with 119, chatGPT tells me it's either 323 or 393 depending on whether I ask 4o or o1. Wolfram alpha told me to fuck off.

Anonymous at Mon, 21 Oct 2024 21:21:18 UTC No. 16443113

>>16443088
>chatgpt
>stem

tell me you're an overachieving midwit without telling me you're an overachieving midwit

Anonymous at Mon, 21 Oct 2024 21:25:35 UTC No. 16443124

>>16443113
>tell me you're an overachieving midwit without telling me you're an overachieving midwit
No shit anon, but I didn't ask for social commentary. Yes, I'm a midwit. Does that satisfy your superiority complex? Yes? Then help me with this please. Thanks
>Verification not required.

Anonymous at Mon, 21 Oct 2024 21:58:28 UTC No. 16443184

>>16443088
>9 is the difference between 1 and -7
Are you really, really, REALLY sure about it?

Anonymous at Mon, 21 Oct 2024 22:09:40 UTC No. 16443205

>>16443088
Try with 2, -6, 10, 120 and add -1 to the closed form

Anonymous at Tue, 22 Oct 2024 04:22:19 UTC No. 16443581

What is the electric magnetic field made out of?

Anonymous at Tue, 22 Oct 2024 04:31:46 UTC No. 16443592

>>16443581
It isn't made of anything. It's just a property at some point in space.

Anonymous at Tue, 22 Oct 2024 04:40:57 UTC No. 16443605

>>16443592
Whoa thats deep

Anonymous at Tue, 22 Oct 2024 06:27:36 UTC No. 16443713

>>16443592
Tell me more about this property you speak of

Anonymous at Tue, 22 Oct 2024 06:32:08 UTC No. 16443719

>>16443713
The electromagnetic four-potential.

Anonymous at Tue, 22 Oct 2024 06:40:36 UTC No. 16443723

Could you give me ideas for my advanced lab final experiment? The lab mainly focus in thermal and material physics. It can't be something too long since we don't have many time to work on it.
Extra points if I could you a PID controller or a lock in amplifier on it.

Anonymous at Tue, 22 Oct 2024 06:50:04 UTC No. 16443728

>>16443719
>>16443719
>The electromagnetic four-potential.
This particular Absolute Nothing you speak of exists at points in space and posses properties?
Do go on

Anonymous at Tue, 22 Oct 2024 08:15:22 UTC No. 16443783

>>16436512
All I see is some fake ass stupid nails with the quick sticking out into nothingness. Can't these stupid bitches at least get nails that are somewhat realistic?

Anonymous at Tue, 22 Oct 2024 11:05:38 UTC No. 16443932

>>16443728
So what's a field anon?

Anonymous at Tue, 22 Oct 2024 11:14:13 UTC No. 16443938

i saw this on /gee/. what do you think?

Anonymous at Tue, 22 Oct 2024 11:22:16 UTC No. 16443945

>>16443938
The answer is zero. Cut the image in half: the 40m cable + 10m height = 50m pole. So the cable can't be any other position except hanging vertically.

Anonymous at Tue, 22 Oct 2024 13:43:12 UTC No. 16444109

>>16443938
Cables hang like hyperbolas.

Anonymous at Tue, 22 Oct 2024 13:47:11 UTC No. 16444114

>>16444109
Amazon would not ask their applicants to solve the catenary equation, there is always a trick to these kind of questions.

Anonymous at Tue, 22 Oct 2024 13:55:53 UTC No. 16444125

>>16444109
[[citation needed]]. I was learned that cables hang like cosh function.

Anonymous at Tue, 22 Oct 2024 14:38:38 UTC No. 16444170

>>16444114
Maybe something with a line integral because they give you the length of the cable.

Anonymous at Tue, 22 Oct 2024 14:41:04 UTC No. 16444175

>>16444170
Are you intentionally missing the point or just retarded?

Anonymous at Tue, 22 Oct 2024 14:41:31 UTC No. 16444176

>>16443945
Is this right? It sounds right.

Anonymous at Tue, 22 Oct 2024 14:42:42 UTC No. 16444178

>>16444175
The latter. Just noticed >>16444176

Anonymous at Tue, 22 Oct 2024 14:47:35 UTC No. 16444183

>>16444176
It's right. It's a well known question, just google it.

Anonymous at Tue, 22 Oct 2024 15:47:01 UTC No. 16444263

I am learning web dev which made me interested in going way deeper in learning programming, but to do that i would need to touch up on maths which
a) i wasn't particularly good at
b) haven't studied any math in like 10 years
what would be a good comprehensive place to relearn maths as much as i can?

Anonymous at Tue, 22 Oct 2024 15:53:27 UTC No. 16444267

Which vaccines do you recommend/not recommend for a newborn? I'm a new dad and I'm really struggling with where to approach this whole subject. I figured /sci/ would be the best place to start. I intend on doing my own digging but I figured it wouldn't hurt to get some sort of foundation here. I greatly appreciate any advice with this.

EBOK at Tue, 22 Oct 2024 16:01:57 UTC No. 16444273

Fag

Anonymous at Tue, 22 Oct 2024 17:05:24 UTC No. 16444350

If I have a 1-form [math]\omega[/math], what does it mean when it says [math]\mathrm{d}\omega = 0 \;\mathrm{modulo}\;\omega[/math]?

Anonymous at Tue, 22 Oct 2024 17:13:12 UTC No. 16444360

>>16443945
i'm retarded. why are you summing the height with the cable length?

Anonymous at Tue, 22 Oct 2024 18:07:52 UTC No. 16444432

>>16444350
I think you might have copied down the language incorrectly. Just post a screenshot of the context or something

Anonymous at Tue, 22 Oct 2024 18:19:17 UTC No. 16444463

>>16444432
I copied everything correctly. I have [math]\omega = -x^2x^3\mathrm{d}x^1 + x^3\mathrm{d}x^3[/math]. The problem at hand asks
>Verify if [math](\mathrm{d}\omega)|_\mathcal{D}[/math], i.e. if [math]\mathrm{d}\omega = 0 \text{ modulo } \omega[/math]
and I'm taking [math]\mathcal{D} = \langle\partial_{x^1}+x^2\partial_{x^3}\;,\;\partial_{x^2}\rangle[/math]

Anonymous at Tue, 22 Oct 2024 18:33:43 UTC No. 16444481

Wtf, is it normal?

Anonymous at Tue, 22 Oct 2024 18:40:51 UTC No. 16444489

>>16443723
Lava batteries

Anonymous at Tue, 22 Oct 2024 18:44:08 UTC No. 16444494

>>16443932
>So what's a field anon?
A field can be many things, a field of grass, a field of wheat, a field for football, a field of air

I kind of understand the idea of the parts of atoms

I have experienced being struck by the light of the Sun

I kind of understand that atoms are made of something

So the first question in my convo here;

What is the electric magnetic field made of

Anonymous at Tue, 22 Oct 2024 18:54:39 UTC No. 16444511

>>16443938
If you tilt the 50 pole down it goes slightly across the half way point, this implies the full length is slightly less than 100

🗑️ Anonymous at Tue, 22 Oct 2024 19:00:50 UTC No. 16444521

Lay down somewhere with the sun shining on you, and tilt your head at certain angles while squinting your eyes, you will notice rainbow effects of the light hitting your eyelashes, there is then a certain way to focus your eye and move it slightly and really focus it while slightly moving it around these rainbow visions, In which you will see what looks like a small solid white circle, pin dot, surrounded by a thin circular line. Like a bulls eye, a gap, and then 1 circular band:

What are those?

Anonymous at Tue, 22 Oct 2024 19:05:06 UTC No. 16444526

Lay down somewhere with the sun shining on you, and tilt your head at certain angles while squinting your eyes, you will notice rainbow effects of the light hitting your eyelashes, there is then a certain way to focus your eye and move it slightly and really focus it while slightly moving it around these rainbow visions, In which you will see what looks like small solid white circle, pin dot, surrounded by a thin circular line. Like a bulls eye, a gap, and then 1 circular band:

What are those?

Anonymous at Tue, 22 Oct 2024 19:15:09 UTC No. 16444547

>>16444360
Another way to think about it is subtract the height from the ground (10m) from the height of the pole (50m), this leaves you with a vertical height of the parabola = 40m. But that is the exact same length as half of the entire cable. So that can only be true if the cable is vertical.

Anonymous at Tue, 22 Oct 2024 19:16:07 UTC No. 16444550

>>16443932
>So what's a field anon?
It's a place where you can add, substract, multiple and divide (as long as you remember not to divide by zero!) Oh, and also distribute.

Anonymous at Tue, 22 Oct 2024 19:30:26 UTC No. 16444579

>>16444463
Looks like nonsense to me, since on its face the expression would seem to mean d\omega is proportional to \omega, but they are forms of different ranks.

Anyway here is someone with the same unanswered question:
https://math.stackexchange.com/questions/2327678/meaning-mod-and-differential-forms

Anonymous at Tue, 22 Oct 2024 22:45:01 UTC No. 16444864

>>16436512
bros since we are all atheists who fucking love science i'm gonna ask this one: how do you avoid the christian to woketard pipeline? i'm scared it might happen to me

Anonymous at Tue, 22 Oct 2024 22:57:47 UTC No. 16444895

>>16444489
>Lava batteries
How is that a physics experiment?

Anonymous at Tue, 22 Oct 2024 23:35:12 UTC No. 16444947

Do any math nerds know how to answer this question? It relates to the binomial and beta distributions, but I'm a bit lost as to how to use that connection to arrive at a solution and ChatGPT is no help.

Anonymous at Tue, 22 Oct 2024 23:53:31 UTC No. 16444988

>>16444947
You can prove it by induction (starting from r=n) and integrating the integral by parts.

Anonymous at Wed, 23 Oct 2024 00:27:12 UTC No. 16445035

>>16444988
Can you give me some idea on how to get started with that? I don't have a strong background in math.

Anonymous at Wed, 23 Oct 2024 00:31:59 UTC No. 16445040

Please help me, /sci/. I don't know how to search this problem in google, because I get a lot of interference from similar sounding concepts that aren't quite what I'm looking for. Also, I'm a math retard, so I don't know how to read half of the results I receive.

Basically, I'm trying to find something like a weighted average between 3 or more points. I can do it with 2 points, but 3 or more, makes it too complex. I'm hoping the illustration gets the idea across. The 3 red points are static. The green point is one that you and I can control and move around.
1. When the green point is in the middle, the 3 red points average out evenly.
2. When the green point nears one of the red points, the nearest red point increase in value in proportion, and the others decrease in proportion.
3. When the green point overlaps one of the red points, it is now at maximum value, and the other points are at zero.
4. Same as 3, but now the green point overlaps a different red point. Showing that any point should be capable of assuming max value, and zeroing out the other points.

How can I do this?

Anonymous at Wed, 23 Oct 2024 01:32:21 UTC No. 16445114

>>16443945
The 40m of cable length and the 10ft to the hanging midpoint would overlap, akshully.

Anonymous at Wed, 23 Oct 2024 02:07:50 UTC No. 16445154

>>16444109
>>16444125
He's confused, because comparing the equations y=f(x) for each curve they are different [catenary is hyperbolic function and hyperbola is algebraic] but the parametric equations of the hyperbola does use both hyperbolic trigonometric functions

Anonymous at Wed, 23 Oct 2024 02:23:07 UTC No. 16445180

>>16445114
What??

Anonymous at Wed, 23 Oct 2024 02:29:48 UTC No. 16445186

>>16445040
Look at this animation
https://www.mathopenref.com/coordcentroid.html

Anonymous at Wed, 23 Oct 2024 02:49:54 UTC No. 16445211

>>16445186
This is not what I need. I'm already able to find the center of 3 points. Remember I said the red points are static? I don't need them to move. The green point moves. And then by moving the green point between the red ones, a new value is extracted. A value that shows the proportional distance between red and green.

Anonymous at Wed, 23 Oct 2024 02:51:58 UTC No. 16445213

>>16444526
>Lay down somewhere with the sun shining on you, and tilt your head at certain angles while squinting your eyes, you will notice rainbow effects of the light hitting your eyelashes, there is then a certain way to focus your eye and move it slightly and really focus it while slightly moving it around these rainbow visions, In which you will see what looks like small solid white circle, pin dot, surrounded by a thin circular line. Like a bulls eye, a gap, and then 1 circular band: What are those?

Anyone?

Anonymous at Wed, 23 Oct 2024 02:55:37 UTC No. 16445215

>>16445040
Let the red points be [math]P_1(x_1, y_1), P_2(x_2, y_2), \cdots[/math] and the green point be [math]P_0(x_0, y_0)[/math]
Then, calculate the distance from the green point to each red point as
[eqn]d=\{\sqrt{(x_1-x_0)^2+(y_1-y_0)^2},\cdots\}[/eqn]
where [math]d_n[math]
Then, the total distance is [math]d=\sum{d_n}[/math], and the proportions are
[eqn]d^*=\{\frac{d_0}{d},\cdots\}[/eqn]
which should be what you're looking for.

Anonymous at Wed, 23 Oct 2024 02:56:52 UTC No. 16445216

>>16445215
ah i'm a faggot for typing that shit out wrong but the last equation is just
[eqn]d^*=\{\frac{d_0}{d},\cdots\}[/eqn]

Anonymous at Wed, 23 Oct 2024 02:58:06 UTC No. 16445217

>>16444895
You said thermal. Set up a battery factory near a very thermal very safe volcanic site, to trap the energy in large batteries then ship them out

Anonymous at Wed, 23 Oct 2024 03:23:47 UTC No. 16445234

>>16445215
>>16445216
>Let the red points be P1(x1,y1),P2(x2,y2),⋯ and the green point be P0(x0,y0)
ok

>Then, calculate the distance from the green point to each red point as
Alright.

>d={(x1−x0)2+(y1−y0)2−−−−−−−−−−−−−−−−−−√,⋯}
Not sure what that equation is, but I assume it's summing up the many distances from green to red.

>where dn[math]Then,thetotaldistanceis[math]d=∑dn
You lost me. What are you doing here? Can you explain the concept in plain terms? I'm barely math literate, and work better conceptually.

I should say that I can already get the proportions of the distances, if that's what you're doing. I add up the distances between red and green, and then divide the individual distances by the total. That's a way of getting proportions, but not the exact proportions I'm looking for.

Anonymous at Wed, 23 Oct 2024 04:33:00 UTC No. 16445313

>>16445234
>That's a way of getting proportions, but not the exact proportions I'm looking for.
oh i see what you want
just do d-d_n instead, i think you just want it inverted

Anonymous at Wed, 23 Oct 2024 04:43:32 UTC No. 16445324

>>16445234
okay i took another look at this and what i think you want is the absolute difference between the green point's distance to a red point, and the red point's distance to a red point

Anonymous at Wed, 23 Oct 2024 05:13:55 UTC No. 16445345

>>16445313
>just do d-d_n instead
What does d-d_n mean?

>>16445324
An absolute value is when you get the difference between two points, but it's always positive, right? How does that help? I can do that. But I'm not sure to what end.

Anonymous at Wed, 23 Oct 2024 09:21:46 UTC No. 16445513

>>16444481
Seems like you have an unusual personality.

Anonymous at Wed, 23 Oct 2024 16:55:38 UTC No. 16445978

>>16444263
Khanacademy. Also saw mathacademy.com shilled on hackernews but idk if it's worth the money
>>16444481
No, you're unusually autistic, but the data there might be skewed due to social desirability bias. You'll get more accurate results by combining self-evaluation with assessments from people who know you.
>>16444526
Maybe an Airy disk caused by a pinhole from intersecting eyelashes?
https://en.wikipedia.org/wiki/Airy_disk?useskin=vector
>>16444947
https://math.stackexchange.com/questions/624688
Here's for [math]X \leq r[/math], now try something similar
>>16445040
https://en.wikipedia.org/wiki/Barycentric_coordinate_system?useskin=vector

Anonymous at Wed, 23 Oct 2024 17:20:07 UTC No. 16446021

>>16445217
"Thermal physics is the combined study of thermodynamics, statistical mechanics, and kinetic theory of gases."

Anonymous at Wed, 23 Oct 2024 17:21:47 UTC No. 16446029

Is there any artificial sweetener with fluorine in chemical formula?

Anonymous at Wed, 23 Oct 2024 17:26:37 UTC No. 16446037

>>16446029
None come to mind.

Anonymous at Wed, 23 Oct 2024 23:11:03 UTC No. 16446497

>>16445978
>https://en.wikipedia.org/wiki/Barycentric_coordinate_system?useskin=vector
Holy shit. That's what I'm looking for! And pic related, is actually what I'm trying to do! This is a great lead, thanks for the link. Now I know what it's called, I can get help on it. Unfortunately, I still have to try and work it out, which is going to be hard.

If anyone is feeling generous, I would appreciate an dumbed down explanation for how this works. In the mean time, I'll read on, and see what I can glean.

Anonymous at Wed, 23 Oct 2024 23:28:35 UTC No. 16446507

If I have a sphere and n points spread evenly across the sphere, how far apart are the points from their closest neighbor? I'm looking for an equation ideally or at least some simple way to approximate it.
A specific example: If I have a sphere that is 1 micron in radius and 600,000,000 points evenly distributed across the surface of the sphere, how far apart will a point be from its closest neighbor?

Anonymous at Wed, 23 Oct 2024 23:46:51 UTC No. 16446518

If I define a subspace [math]J^k(V)\leq \mathcal{T}^k(V)[/math] spanned by all tensor products [math]\bigotimes_jv_j[/math] of linearly dependent vectors [math]\{v_j\}_j\subset V[/math], can I define the exterior product [math]\Lambda^k(V^*)[/math] as the quotient [math]\Lambda^k(V^*) = \mathcal{T}^k(V)/J^k(V)[/math]?
Furthermore, considering the projection of [math]\mathcal{T}^k(V)[/math] onto [math]\mathcal{T}^k(V)/J^k(V)[/math], i.e., a map
[eqn]
\begin{align}
\pi:\mathcal{T}^k(V)&\to \mathcal{T}^k(V)/J^k(V)\\
T &\mapsto T + J^k(V)
\end{align}
[/eqn]
can I say that by restricting its domain to the subspace of skew-symmetric tensors I'll have an isomorphism?

Anonymous at Wed, 23 Oct 2024 23:55:15 UTC No. 16446530

>>16446507
There is no exact equation and it's actually an unsolved problem (the Tammes problem). However you can generate the points using some code like the Fibonacci sphere algorithm. As a *very* rough approximation you could cut the surface area of the sphere into N squares or smaller circles and then calculate the distance between them.

Anonymous at Wed, 23 Oct 2024 23:58:58 UTC No. 16446533

>>16446530
Oh wow. Okay thanks for the info. I guess the idea is if the region of the surface is sufficiently small, it's approximately flat and can be treated as 2 dimensional?
That works for me

Anonymous at Thu, 24 Oct 2024 01:41:11 UTC No. 16446646

w-what happened to The Phenotype pic in our sticky..

Anonymous at Thu, 24 Oct 2024 01:43:27 UTC No. 16446648

>>16446646
What do you mean?

Anonymous at Thu, 24 Oct 2024 02:01:25 UTC No. 16446668

Brainlet here. I am confused about question c in pic rel. Why doesn't the argument for uncountable Omega work for countable Omega? In both cases, none of the infinite sets are disjoint, yet in the uncountable case, we can still include an infinite amount of finite sets.

Anonymous at Thu, 24 Oct 2024 02:38:48 UTC No. 16446707

When have you failed to reject your null hypothesis /sci/?

Anonymous at Thu, 24 Oct 2024 07:07:43 UTC No. 16446875

I'm missing something and I don't know what

Anonymous at Thu, 24 Oct 2024 07:34:29 UTC No. 16446886

>>16444463
They're asking you to verify if [math] d \omega = \omega \wedge \alpha [/math] for some 1-form [math] \alpha [/math]

Anonymous at Thu, 24 Oct 2024 13:08:03 UTC No. 16447122

>>16446875
Legible handwriting is what you are missing.

Anonymous at Thu, 24 Oct 2024 16:43:58 UTC No. 16447431

Is there an equation that gives out the result of a degree n polynomial being differentiated n times?

Anonymous at Thu, 24 Oct 2024 16:49:04 UTC No. 16447447

>>16447431
>Is there an equation that gives out the result of a degree n polynomial being differentiated n times?
Unless it's a very, very tricky question, the result will be [math]a_n n![/math], where [math]a_n[/math] is coefficient by [math]x^n[/math].

Anonymous at Thu, 24 Oct 2024 16:59:58 UTC No. 16447487

>>16447447
Now that i look back at it, it was quite a stupid question. Thanks!

Anonymous at Thu, 24 Oct 2024 17:00:15 UTC No. 16447489

>>16447447
>Unless it's a very, very tricky question
nta but im curious for an example where this doesnt hold.

Anonymous at Thu, 24 Oct 2024 17:33:50 UTC No. 16447560

>>16447431
Same guy. Was wondering if this would also mean that:
y=(ax^n + bx^(n-1)....+z)^c
after differentiating n\cdot c times:
\frac{dy^(nc)}{d^(nc)x} = a^c \cdot (nc)!

Anonymous at Thu, 24 Oct 2024 17:41:38 UTC No. 16447575

>>16447560
Same guy. Was wondering if this would also mean that:
[math] y=(ax^n + bx^{n-1}....+z)^c [/math]
after differentiating n\cdot c times:
[eqn] \frac{dy^{nc}}{d^{nc}x} = a^c \cdot (nc)! [/eqn]

Note: im new to this board

Anonymous at Thu, 24 Oct 2024 17:43:44 UTC No. 16447576

>>16447575
Yes that's correct.

Anonymous at Thu, 24 Oct 2024 18:34:18 UTC No. 16447644

>>16447489
in a field with characteristic [math]p[/math] it will sometimes be zero

Anonymous at Thu, 24 Oct 2024 18:40:03 UTC No. 16447660

i assume the distribution on the right is a better fit right? is it because it fits the normal better or is there a better interpretation?

Anonymous at Thu, 24 Oct 2024 18:40:59 UTC No. 16447664

>>16447644
nm this is included in the [math]n![/math] term, now I'm curious too

Anonymous at Thu, 24 Oct 2024 19:00:28 UTC No. 16447697

>>16447660
Yeah the right fits better because the left's left side is all out of whack. I'm not sure why you're mentioning the normal distribution.

Anonymous at Thu, 24 Oct 2024 19:46:42 UTC No. 16447759

>>16447697
If you look at the bar graphs there is a normal distribution overlayed on it

Anonymous at Thu, 24 Oct 2024 19:50:20 UTC No. 16447764

>>16447759
no, those are Weibull and Gamma distributions, respectively.

Anonymous at Thu, 24 Oct 2024 19:57:28 UTC No. 16447773

>>16447759
A normal distribution is symmetric around the mean.

Anonymous at Thu, 24 Oct 2024 19:58:57 UTC No. 16447775

>>16447764
.... why am I retarded

Anonymous at Fri, 25 Oct 2024 00:14:21 UTC No. 16448047

Kind of a weird question. But I know phone cameras can pick up near infrared light. So when I pointed my phone camera outside from a window I noticed it was picking up a bluish purple light that i couldnt see with the naked eye. I noticed it was only picking up the light through the glass double pane window. I'm not able to see the light through window screen. I know there is a little bit of argon gas in the double pane windows, is that gas cause some visible light source to shift towards near ir?

Last thing There are no blue lamps near me

Anonymous at Fri, 25 Oct 2024 01:17:55 UTC No. 16448145

>>16448047
Tricky question to answer. It would depend on the sensor in your phone, the exactly frequency sensitivity of the device is unlikely to be public information. Not all double pane windows use argon, and even if it has it's not going to glow like a neon lamp. That requires electricity. Rayleigh scattering might be what is happening - enhancing blue+purple would be exactly this - but maybe more likely is the fact the camera is better at picking up low light than your eye and / or it's a post-processing image artifact.

🗑️ Anonymous at Fri, 25 Oct 2024 01:22:55 UTC No. 16448151

>>16448145
This is what it looks like when I zoom all the way in on it. (I'll post the zoomed out version right after)

🗑️ Anonymous at Fri, 25 Oct 2024 01:25:21 UTC No. 16448155

>>16448151
>>16448145
Here it is zoomed out, the bluish dot in the center is what I zoomed in on. It cannot be seen with naked eye

Anonymous at Fri, 25 Oct 2024 01:32:23 UTC No. 16448165

>>16448145
Oh you know what. I just realized my camera has a laser auto focus so that was the laser reflecting back into the camera lmao.

Anonymous at Fri, 25 Oct 2024 01:45:13 UTC No. 16448180

>>16448165
Ahh, even if that's not what you originally thought it's still kind of cool.

Anonymous at Fri, 25 Oct 2024 03:42:51 UTC No. 16448326

>>16448180
nice try cia, why are you trying to cover up secret argon resonators hidden in everyday windows? What's up with that?

Anonymous at Fri, 25 Oct 2024 03:49:25 UTC No. 16448333

Allegedly there is a structure (organellum?) in human cells whose purpose remains completely unknown (assuming it has any purpose.) Is that true?

Anonymous at Fri, 25 Oct 2024 20:01:24 UTC No. 16449439

Let [math]J^k(V)[/math] be the subspace of [math]\bigotimes^kV[/math] spanned by all tensor products [math]\bigotimes_jv_j[/math] such that for at least two different indices [math]j,l[/math] we have [math]v_j=v_l[/math].
How can I prove that [math]J^k(V) = S^k(V)[/math] where [math]S^k(V)[/math] is the subspace of symmetric tensors?
I need to do this because I want to use the first isomorphism theorem to prove that [math]\bigotimes^kV/J^k(V) \cong A^k(V)[/math] where A is the subspace of skew-symmetric tensors.
I defined a map [math]\varphi : \bigotimes^kV \to A^k(V)[/math] that takes any tensor and spits out its skew-symmetric part, since any tensor can be uniquely written as the sum of a symmetric and a skew-symmetric tensor. So I just gotta prove that [math]\ker(\varphi) = J^k(V)[/math].
Refer to pic related.

Anonymous at Fri, 25 Oct 2024 20:41:10 UTC No. 16449472

I'm trying to obtain the action angle variables for a central force
problem. How do I integrate this thing?
[math]f(x) = \int_{a_{min}}^{a_{max}} \sqrt{E+\frac{1}{x}-\frac{1}{2x^2}} dx[/math]
I know you're supposed to get something similar to this
[math]f(x) = - 1 + \sqrt{-\frac{1}{2E}} [/math]
but most books just say
>trust me bro

Anonymous at Fri, 25 Oct 2024 20:54:14 UTC No. 16449482

>>16449472
I do not know where you got that integral from because it does not give a result anything close to what you seem to be expecting.

Anonymous at Fri, 25 Oct 2024 21:57:27 UTC No. 16449568

>>16449472
I'm gonna swap your notation f(x), a_max, a_min for I, b, a, respectively
[eqn]I= \sqrt{-E}\int_a^b x^{-1}(x-a)^{1/2}(b-x)^{1/2}dx [/eqn]
This looks like a hypergeometric function:
https://dlmf.nist.gov/15.6
So let's rescale the limits of the integral to be 0 and 1 to put it in a standard form.
[eqn] I = \sqrt{-E}\frac{(b-a)^2}{a}\Gamma(3/2)^2 \,F(1,3/2;3;1-b/a ) [/eqn]
Now Gamma(3/2)^2=\pi / 4, and you can simplify the hypergeometric function to an ordinary function using 15.9.17 of
https://dlmf.nist.gov/15.9

Anonymous at Fri, 25 Oct 2024 22:41:37 UTC No. 16449636

>>16449568
Yeah I worked it out to the end. You get
[math] I= \frac{\pi}{\sqrt{2}}\left(-1+\sqrt{-\frac{1}{2E}}\right) [/math]
There's probably an easier way, but this works

Anonymous at Sat, 26 Oct 2024 01:06:05 UTC No. 16449841

>>16449636
>>16449568
Thank you. Seems I had to use complex variable theory in the end

Anonymous at Sat, 26 Oct 2024 05:29:03 UTC No. 16450087

Suicide suicide suicide

Anonymous at Sat, 26 Oct 2024 09:09:32 UTC No. 16450212

Explain why this wouldn't work

Anonymous at Sat, 26 Oct 2024 09:33:57 UTC No. 16450238

>>16450212
what do you mean? it would work

Anonymous at Sat, 26 Oct 2024 09:37:54 UTC No. 16450243

>>16450212
the ball needs to have significantly more momentum than the bear, but it would work

Anonymous at Sat, 26 Oct 2024 12:25:28 UTC No. 16450388

>>16450212
The ball would need to bounce pretty well and be pretty heavy. And the bear would have to be very good at aiming to keep hitting it. But apart from that it seems like it should work.

Anonymous at Sat, 26 Oct 2024 13:45:39 UTC No. 16450543

>>16450212
Coming soon to an anime near you.

Anonymous at Sat, 26 Oct 2024 13:47:57 UTC No. 16450550

I don't understand what they mean by this. Do they perhaps mean this action [eqn]\mathbb{Z} \times \mathbb{S}^1 \to \mathbb{S}^1, \quad \quad \left(k,\, e^{2\pi i\, \cdot\, \alpha}\right) \mapsto e^{2\pi i\, \cdot\, (k\, +\,\alpha)}.[/eqn]

Anonymous at Sat, 26 Oct 2024 13:48:58 UTC No. 16450552

>>16450550
Forgot the picture.

Anonymous at Sat, 26 Oct 2024 16:38:23 UTC No. 16450909

>>16450552
[math]\mathbb{Z} \times \mathbb{S}^1 \to \mathbb{S}^1, \quad \quad \left(k,\, z\right) \mapsto e^{2\pi ik \alpha}\cdot z
[/math]

Anonymous at Sat, 26 Oct 2024 17:03:35 UTC No. 16450941

>>16450909
thank you

Anonymous at Sat, 26 Oct 2024 17:32:29 UTC No. 16450984

>>16436512
What happened to /our/ guy's channel, Norman Wildberger? His videos are all gone. Set theorist jews conspired and got him... Our hero is down.

Anonymous at Sat, 26 Oct 2024 18:00:30 UTC No. 16451023

Each line has different spacing somewhere. Which one looks best?

Anonymous at Sat, 26 Oct 2024 18:20:11 UTC No. 16451044

>>16451023
They all look the same. Stop being so schizophrenic about millimetric spacing on your equations.

Anonymous at Sat, 26 Oct 2024 19:05:44 UTC No. 16451092

>>16451023
The third one is correct and would be automatically set if you had actually bothered to use \cos{\phi} and not cos\phi

Anonymous at Sat, 26 Oct 2024 19:32:23 UTC No. 16451114

>>16451092
>\cos{\phi} and not cos\phi
These yield the same spacings

Anonymous at Sat, 26 Oct 2024 19:37:41 UTC No. 16451117

>>16450984
It says he removed them himself.
That's upsetting. I liked his stuff.

Anonymous at Sat, 26 Oct 2024 20:11:43 UTC No. 16451151

Wait WTF, so nuclei can indeed have protons that orbit around other neutrons/protons and nuclei aren't always round and can look like fucking rice grains? HOW? All my physics teachers lied to me. My whole life is a lie.

Anonymous at Sat, 26 Oct 2024 20:24:26 UTC No. 16451160

>>16451151
Nuclear physics is complicated and all models are an approximation. Also those configurations are inherently unstable and decay within milliseconds.

Anonymous at Sat, 26 Oct 2024 20:44:01 UTC No. 16451186

>>16450212
The other answers are wrong. Momentum is a vector quantity. The momentum of the bear must be to the right at all times. But the ball is the only source of the bear's momentum. This means the ball would have to be moving to the left. But the bear can only reach the ball when it's moving to the right.

This means that the only way the bear can get across is if he does this in only one step. This is the same as a rocket problem; you can only move forwards when something else is pushed behind, so you can't just throw a ball backwards and try to catch it, cause you'll just end up at the same initial spot. Notice that this is just Newton's 3rd law

Anonymous at Sat, 26 Oct 2024 20:47:23 UTC No. 16451193

>>16451186
to the right relative to the bear, btw

Anonymous at Sat, 26 Oct 2024 20:57:41 UTC No. 16451218

>>16451186
False. Yes, the bear transfers momentum down and to the left, but if the ball already has a strong up/right momentum the energy loss will be trivial enough to get him across.

Anonymous at Sat, 26 Oct 2024 21:11:51 UTC No. 16451242

>>16451218
What has energy got to do with conservation of momentum? Pushing the much heavier bear to the right will have a greatly increased change in velocity of the ball to the left. And if the velocities don't match, how are they meant to stay in sync??

Anonymous at Sat, 26 Oct 2024 22:49:16 UTC No. 16451340

I don't get why this guy (Steven H Simon in Solid State Physics chapter 15) acts like k is periodic for a free electron perturbed by a periodic potential. Since there still is an electron with [math] E_0 = \frac{(k \cdot \hbar)^2}{2 m} [/math], shouldn't the energy for [math] k = 3\pi/a [/math] always be bigger than for [math] k = pi/a [/math]?

Anonymous at Sun, 27 Oct 2024 04:24:49 UTC No. 16451692

>>16451340
A free electron has energy [math]E \propto k^2[/math] but inside the band that is instead something like [math]E \propto \cos{ka}[/math]. This is a fairly standard result in an quantum system with boundaries (the gaps). It might be covered later in the book.

Anonymous at Sun, 27 Oct 2024 07:51:49 UTC No. 16451866

>>16451242
>Pushing the much heavier bear
This is where your claim falls apart

Anonymous at Sun, 27 Oct 2024 15:35:52 UTC No. 16452289

>>16451866
You sound like the type of person that has sex with incels

Anonymous at Sun, 27 Oct 2024 16:08:11 UTC No. 16452332

>>16452289
Lol just ignore him

EBOK at Sun, 27 Oct 2024 16:12:53 UTC No. 16452339

>>16452332
Fag
>>16452289
Fag
>>16451866
Fag

Anonymous at Sun, 27 Oct 2024 19:32:36 UTC No. 16452625

why do magnets attract each other if they have zero relative velocity

Anonymous at Sun, 27 Oct 2024 19:38:10 UTC No. 16452635

>>16452625
never mind i read that it's because of particle spin

Anonymous at Sun, 27 Oct 2024 19:38:13 UTC No. 16452636

>>16452625
That is what attraction or any other force does. It causes a change in velocity.

Anonymous at Sun, 27 Oct 2024 19:39:40 UTC No. 16452640

>>16452636
but the magnetc force is the cross product of velocity and the field, so it needs to be moving?

Anonymous at Sun, 27 Oct 2024 19:52:32 UTC No. 16452663

>>16452640
You are talking about the classical EM force. You are right that the magnetic field of magnets is due to spin, and that is a quantum mechanical effect.

Anonymous at Sun, 27 Oct 2024 23:15:42 UTC No. 16452932

How to measure the volume of a fluid from a spray nozzle
I'm using minoxidil and it came with a spray nozzle and a dropper. I want to use the spray nozzle because it's more sterile I guess but nowhere on the packaging is it mentioned how much one spray is. Is there any way of calculating it, I don't have the tools to measure accurately. I'm guessing it would be something like pipe area*swept length right?
Supposed to use 1ml twice a day

Anonymous at Mon, 28 Oct 2024 00:33:10 UTC No. 16452996

>>16452932
Fill the spray with water. Do full sprays for N reps, and M sets. You can calculate the water loss by weight loss (prob not accurate) or by volume (maybe little more time consuming depending if you're collecting the water or measuring what's left). Find the average loss per spray.

Anonymous at Mon, 28 Oct 2024 00:37:45 UTC No. 16453002

>>16436512
I flunked maths in high school and I feel like I’m mathematically illiterate (aka I’m retarded). How can I improve my maths skills at home / as a hobby? Are there any specific types of maths I should focus on learning (besides add/sub/multi/divide)? Any websites I should check out?

Anonymous at Mon, 28 Oct 2024 02:57:50 UTC No. 16453153

>>16452996
I figured doing that but again I want it to be sterile
Then again, 95% of the solution is isopropyl alcohol so it really wouldn't matter since that's antibacterial right?
>>16453002
Look up knot theory. I suppose it would be the easiest math field where a layperson could make actual advancements

Anonymous at Mon, 28 Oct 2024 03:28:09 UTC No. 16453164

/sci/ is probably not the right board for this but here goes
What's that psychological bias where every piece of evidence is used as confirmation of ones beliefs
I remember this clip used to illustrate where something was happening was used as evidence for both X and not X by two different people

Anonymous at Mon, 28 Oct 2024 03:31:33 UTC No. 16453165

>>16453164
confirmation bias

Anonymous at Mon, 28 Oct 2024 03:32:24 UTC No. 16453166

>>16453164
Confirmation bias, social media algorithms thrive on it.

Anonymous at Mon, 28 Oct 2024 07:08:11 UTC No. 16453295

What is the amplitude of a photon? Can it be predicted? How many nanometers wide are they?

Anonymous at Mon, 28 Oct 2024 07:26:23 UTC No. 16453309

>>16453295
Photons do not have an amplitude, they are not that kind of classical wave. As for their width or size, that depends on what precisely you mean. Since a photon is an excitation in the quantum electromagnetic field they do not a physical size. However you can talk about what affect they have on their surroundings and calculate something like their cross section in scattering processes. That result would be related to the wavelength of the photon.

Anonymous at Mon, 28 Oct 2024 11:02:48 UTC No. 16453416

Does anyone have that reddit post from a teacher telling how bad his students are as they fail to comprehend and apply basic concepts and even do basic tasks?

Anonymous at Mon, 28 Oct 2024 12:20:48 UTC No. 16453444

Does anyone have a link to the proof that two differentiable structure on [math]\mathbb{R}[/math] are necessarily diffeomorphic.

Anonymous at Mon, 28 Oct 2024 17:10:31 UTC No. 16453737

I'm not a math guy so there's prob details missing. Idk but here's what I feel is the gist of it:

If f(x) = x^2 and f(c) = 4, you can't tell if c = 2 or -2. If you're working with homeomorphic functions, it should work then. Notice that this fucks up where f'(x) = 0, cause that's when the curve goes back up (or down) and retraces over the same values of f(x).

Given f(x) and g(x), the diffeomorphic map between the two is the continuous function (f o g^{-1}) and inverse (g o f^{-1}), and not past f'(x) = 0 or g'(x) = 0. So for something like f(x) = x^3 and g(x) = x^5, the first map works for p \in (0,\infty). Something like p = 32 you can put into g^{-1} to get 2 and you can cube it to get 8. So 32 maps 8, and the differentiable function that maps it is p^{3/5}. Diffeomorphism just means (f o g^{-1}) and it's inverse are differentiable and a bijection. You can just do chain rule on (f o g^{-1}) and inverse (g o f^{-1}). Composition of homeomorphic functions are homeomorphic, so it's a bijection.

>misc
The use of the jacobian when talking about diffeomorphisms is because this means that when it's determinant is non-zero at some points, the inverse function exists around those. The way to show that it's a diffeomorphism is to use the Inverse Function Theorem (IFT), which shows that the inverse map for a differentiable function is differentiable around those points (so locally). For one dimension the Jacobian is just the derivative, which you can use chain rule on (f o g^{-1}).
We intentionally chose the domain to exclude when the derivatives of f and g equal 0, which means (f o g^{-1}) won't be zero either. The IFT then guarantees the existence of the differentiable inverse function we want.

You can prob look up details on google, like How to prove the IFT, or the proof of composition of homeomorphic/cont. functions are homeo/cont too, or why nonzero jacobian determinant (the inverse of the jacobian matrix exists) implies an inverse func, wtv you really want.

Anonymous at Mon, 28 Oct 2024 17:11:32 UTC No. 16453741

>>16453444
oh woops, somehow the @ was missing in >>16453737

Anonymous at Mon, 28 Oct 2024 17:18:30 UTC No. 16453751

>>16453309
>Since a photon is an excitation in the quantum electromagnetic field they do not a physical size.
That doesn't make sense. Why wouldn't they?

Anonymous at Mon, 28 Oct 2024 17:23:59 UTC No. 16453758

>>16453751
All fundamental particles are point-like. Their 'size' comes about from how we measure them.

Anonymous at Mon, 28 Oct 2024 17:25:55 UTC No. 16453762

>>16453758
>All fundamental particles are point-like.
How do you distinguish between an electron and a black hole of the same mass and charge, then?.

Anonymous at Mon, 28 Oct 2024 17:32:32 UTC No. 16453770

>>16453762
You wouldn't have to. A black-hole that small would instantly evaporate due to Hawking radiation.

Anonymous at Mon, 28 Oct 2024 17:54:34 UTC No. 16453804

find all [math]z \in \mathbb{C}[/math] such that [math]z^4=\overline{z}[/math] . Can someone solve this?

Anonymous at Mon, 28 Oct 2024 18:32:55 UTC No. 16453842

>>16453804
Convert to polar coordinates, z = Re^(i*theta). Or ask Chatgpt for hw help. Remember that theta + 2pi*n == theta to get the general solution

Anonymous at Mon, 28 Oct 2024 18:54:21 UTC No. 16453864

>>16453804
>find all [math]z \in \mathbb{C}[/math] such that [math]z^4=\overline{z}[/math] . Can someone solve this?
WolframAlpha can https://www.wolframalpha.com/input?i=z%5E4%3Dconjugate+%28z%29

Anonymous at Mon, 28 Oct 2024 20:19:19 UTC No. 16453943

warosu.org is down, can anyone remind me what the other /sci/ archive is?
I don't mean archived.moe, it was something that also archives /3/, if I remember correctly.

Anonymous at Mon, 28 Oct 2024 20:21:10 UTC No. 16453944

>>16453943
Fuck me it's literally in the OP. I don't remember seeing it there in the past, my bad.

Anonymous at Mon, 28 Oct 2024 20:24:49 UTC No. 16453949

>>16453864
analytically how am i supposed to reach the solution without using polar coordinates?>>16453842

Anonymous at Mon, 28 Oct 2024 20:36:33 UTC No. 16453963

>>16453949
first look at the modulus, taking a complex number to some power takes the modulus to the power as well and taking the complex conjugate does not change the modulus so we have [math]|z|^4=|z|[/math], so the modulus is 1
next use the fact that [math]z\cdot\overline{z}=|z|[/math] and substituting that in you get [math]z^4=\frac{|z|}{z}=\frac1z[/math] or [math]z^5=1[/math]

Anonymous at Mon, 28 Oct 2024 21:01:25 UTC No. 16453998

>>16453963
>so the modulus is 1
Ahem, modulus is 1 or 0.
>>16453949
Substitute z = a + b*i, expand left side, get real and imaginary parts of resulting equation, have fun solving system of equations of fourth degree for a few hours.

Anonymous at Mon, 28 Oct 2024 21:56:55 UTC No. 16454056

>>16453758
>All fundamental particles are point-like.
NTA but how exactly do we know this?

Anonymous at Mon, 28 Oct 2024 23:05:01 UTC No. 16454129

>>16454056
Because that is what quantum field theory tells us, that every fundamental particle is an excitation in their associated field and has zero volume.

Anonymous at Tue, 29 Oct 2024 00:58:06 UTC No. 16454253

Why is the human brain so slow at math? I guess at language too now that AI is a thing. AI might not get facts right but it has good grammar. Calculators solve problems faster than anyone but they dont know what the problem is.

Anonymous at Tue, 29 Oct 2024 01:20:08 UTC No. 16454272

>>16454253
General vs Specialised. A calculator is built to do only math and do it fast. The brain is built to do anything, including building a calculator or an AI.

Anonymous at Tue, 29 Oct 2024 06:54:18 UTC No. 16454535

>cant seem to force myself to want to do what it takes to succeed in school
>no other obvious avenues in life
how did you do it /sci/fags? ive failed core classes in my cs degree path several times now, and every single day i tell myself i will do things differently, and then i just regress and continue to do the same shit day after day. i haven't been able to convince myself that any of this shit matters. i sit down for a couple hours, struggling with my coursework only to get so frustrated with being completely unable to learn what im supposed to, and start making mistakes and losing points, or i'll do great on homework assignments for an entire chapter, then bomb a test because it turns out i don't actually know how to do the problems, i only know how to look up textbook examples or watch youtube lessons. it's like learning a language with a pocket dictionary in your hand at all time or something. i simply can't grasp this shit at the rate im expected to and i have poor retention

it just kills whatever motivation i have, and all of this is coupled with a constant deluge of horror stories i hear from STEM industries of graduates not being able to find employment with their degree. let's say i did put my shit together and graduate. i wouldn't have anything higher than a 3.0, guaranteed. i have virtually zero chance of finding employment anywhere.

Anonymous at Tue, 29 Oct 2024 07:30:22 UTC No. 16454547

>>16454535
lord have mercy, i promise you anon, you will get a job with a CS degree.
what classes have you had success in? what did you do differently in those?

Anonymous at Tue, 29 Oct 2024 07:58:55 UTC No. 16454561

Any Medfags out there?

What blood type am I?
I do not understand how to read this secret medical code.

Pretty sure it says I'm type A (child)
But I specifically wanted to know if I'm Rh negative or positive.

Also anything else you can decode from this medical gibberish is appreciated.

Anonymous at Tue, 29 Oct 2024 08:06:27 UTC No. 16454564

>>16454561
>>>/sci/med/

Anonymous at Tue, 29 Oct 2024 08:31:50 UTC No. 16454578

>>16454561
It's the line labled Rh.
D = D antigen gets produced
d = D antigen does not get produced
C = C antigen gets produced
and so on...

Anonymous at Tue, 29 Oct 2024 08:40:48 UTC No. 16454581

>>16454561
> But I specifically wanted to know if I'm Rh negative or positive.
Having the Rh D antigen (which you do) make you Rh positive (+), without the D antigen you would be negative.

Anonymous at Tue, 29 Oct 2024 09:02:28 UTC No. 16454592

>>16454581

I slightly came to that conclusion earlier in a Google search but I was not positive that I was correct in my assumption. Thank you anon.
A quick google search does not really quickly get you a black and white definition of what they are explaining here.

/x/fag here.

I wanted to know because a majority of supposed alien abductees are RH Positive. Supposedly.

Thanks /Sci/ my business with you here is done for now. I'll be back. Biology nerd here. I bet you guys hate on us for some gay 4chan hater reason. I like trees,cells and soil science fuck you math nerds.

Anonymous at Tue, 29 Oct 2024 12:04:43 UTC No. 16454673

d fug happn'd?

https://imgur.com/gallery/fuuuuuuuuuucccckkk-Q3U7xFs

Anonymous at Tue, 29 Oct 2024 12:11:49 UTC No. 16454677

>>16454592
>/x/fag here.
Are you stupid?
>I wanted to know because a majority of supposed alien abductees are RH Positive. Supposedly.
IIRC 85% of Homo sapiens is Rh+.

Anonymous at Tue, 29 Oct 2024 12:53:19 UTC No. 16454698

if a=o(r^n-1) where r=sqrt(h_1^2+h_2^2+...+h_m^2), how is it that a* h_i=o(r^n)?

Anonymous at Tue, 29 Oct 2024 15:00:27 UTC No. 16454803

>>16454677
Yes. Yes I am. Stupid that is. That's why I've frequented 4chan since 2007.

Anonymous at Tue, 29 Oct 2024 18:50:11 UTC No. 16455078

Help on, t-desgin + graph, can someone enlight me, I do not get it.

> How do you generate a non-infinity block
> Are there more than one block containing infinty

I tired everything, and manage to obtain blocks of size 6... but I think it's wrong, to do so I have removed all edges incident to the vertices forming the edge to encode, it gives me 6 edges but it is not two distinct triangles. I'm kinda lost.

Anonymous at Tue, 29 Oct 2024 22:42:54 UTC No. 16455356

>>16454698
You might want to give a bit more context than a dry ass equality with n numbers we know nothing about

Anonymous at Tue, 29 Oct 2024 23:24:55 UTC No. 16455379

>>16454698
what is o? big O?

Anonymous at Wed, 30 Oct 2024 06:19:58 UTC No. 16455650

>>16455379
Probably small o.

Anonymous at Wed, 30 Oct 2024 07:20:04 UTC No. 16455666

>>16455078
Where is the problem? Label the vertices 1,2,3,4,5,6. The pairs of two triangles are
123 + 456
124 + 356
125 + 346
126 + 345
134 + 256
135 + 246
136 + 245
145 + 236
146 + 235
156 + 234
All those blocks contain 6 edges. Three from each triangle. Then you have 6 other blocks with the claws and points of infinity for a total of 16 blocks just as needed.

Anonymous at Wed, 30 Oct 2024 17:33:10 UTC No. 16456034

>>16454673
someone mined a sand block and the gravity physics kicked in.

Anonymous at Wed, 30 Oct 2024 18:29:40 UTC No. 16456091

>>16454673
Probably a cavern collapse

Anonymous at Wed, 30 Oct 2024 22:30:20 UTC No. 16456345

Find two numbers x >= 1 and y >= 1 such that xy = 50 and 2x + y is a maximum.

Anonymous at Wed, 30 Oct 2024 22:40:36 UTC No. 16456355

>>16456345
Am I missing anything or is this simply (x, y) = (50, 1)?

Anonymous at Wed, 30 Oct 2024 22:41:33 UTC No. 16456357

>>16456355
Ok but why? How did you get the answer?

Anonymous at Wed, 30 Oct 2024 22:42:18 UTC No. 16456359

Why do men smell worse than women?

Anonymous at Wed, 30 Oct 2024 22:50:09 UTC No. 16456363

>>16456357
By guessing, I guess? You look for maximum of 2x+y so you want x to be as large as possible. Given the conditions (xy = 50 and y>=1) the largest possible x is 50. (It's midnight. No idea if it makes any sense.)

Anonymous at Wed, 30 Oct 2024 23:57:32 UTC No. 16456413

Find the dimensions of a right triangle of maximum area whose hypotenuse has a length one.

Anonymous at Thu, 31 Oct 2024 00:14:34 UTC No. 16456423

>>16456413
I got it, its width and height equal [math]\sqrt{1/2}[/math]

Anonymous at Thu, 31 Oct 2024 08:36:15 UTC No. 16456748

Why doesn't blackbody radiation go green? It goes from red to white to blue, but never green for some reason

Anonymous at Thu, 31 Oct 2024 08:43:34 UTC No. 16456754

>>16456748
The frequency range the human visual system sees as pure green in incredibly narrow and when black body radiation peak is within that range (~6000K) there is still enough blue and red light being produced that our brain ends up seeing white instead.

Anonymous at Thu, 31 Oct 2024 10:19:55 UTC No. 16456794

This is an exercise from a book I'm reading. Let [math]T[/math] be the (torus) group of matrices of the form [math]\left(\begin{smallmatrix}e^{i\theta_{1}}\\
& e^{i\theta_{2}}
\end{smallmatrix}\right)[/math]. Let [math]S[/math] be the subgroup of matrices of the form [math]\left(\begin{smallmatrix} e^{it}\\
& e^{it\sqrt{2}}
\end{smallmatrix}\right)[/math]. I need to show that the closure [math]\overline{S}[/math] is not 1 dimensional, and conclude that [math]\overline{S} = T[/math]. The hint is to use the fact that a continuous, bijective homomorphism between matrix groups is a homeomorphism.

I'd appreciate any ideas or hints, I'm rather clueless.

Anonymous at Thu, 31 Oct 2024 12:22:06 UTC No. 16456857

>>16456345
you can find the single variable function you are trying to maximize by combining the equation and function you have and get [math]f(x)=2\cdot x+\frac{50}x[/math]
now you can put this into any graphing calculator and read the result from the plot or if you want to do it analytically you can see that the function is continuous in the range that you care about so take the derivative of the function and find its roots, which is just x=5, so that is the only local extremum, now check the function value at the extremum and both ends of your domain, or x={1,5,50} and find that x=50 gives the maximal value

Anonymous at Thu, 31 Oct 2024 13:13:40 UTC No. 16456887

All these mean people in society who conspire against us are truthfully experiencing a three body problem and have been stripped of their ability to be concerned. If you can be concerned, you are likely here experiencing the mess of these people. One day it will fix itself and they'll start to be kind again and will give you lots of money and take away all of your problems.

IS IT NOT CLEAR TO SEE THAT THERE IS AN ERROR IN THE WORLD. THE SAME KIND OF MEANNESS PER PERSON... THE SAME KIND OF MENTAL PROBLEM.

It will subside soon and everything will be ok. There's more to life than what is visible in the universe.

ASSGJD

Anonymous at Thu, 31 Oct 2024 13:17:59 UTC No. 16456893

>>16456887
A simulation disaster is occuring. You will eventually be saved.

Anonymous at Thu, 31 Oct 2024 13:19:10 UTC No. 16456895

>>16456893
I can communicate to you now with my mind but I seldom do for the pain it would cause, but this could be your big break. You could learn everything in this mess and become super rich.

Anonymous at Thu, 31 Oct 2024 13:20:35 UTC No. 16456897

People have approached me admitted they were NPC and just laughed at me out of character. Trust me. I know what's going on. A few years maybe six months.

Anonymous at Thu, 31 Oct 2024 13:48:54 UTC No. 16456921

>>16456887
Do YoU eXpErIeNcE a StRaNgE sErEnItY aRoUnD tHiS pOsT? IT BECAUSE THEY AGREE AND THEY ARE REASSURING YOU THEY CARE FOR YOUR TROUBLES.

YOU ARE BEING SCAMMED AND YOU ARE IN A HELL CAUSED BY SIMULATION DISASTER. IT WILL SOON CEASE AND YOU WILL BE REWARDED AND NO MORE REALITY TROUBLE. ITS JUST A MATTER OF MONTHS OR FEW YEARS.

DERp. Who farted? They/them did

Anonymous at Thu, 31 Oct 2024 14:34:27 UTC No. 16456968

>>16456857
Ok that makes sense.
I got x=5 y=10 which was wrong and I didn't know how to move forward until I read your explanation.
I didn't think it would be appropriate to use x=50 because the derivative isn't 0 there.

bean at Thu, 31 Oct 2024 18:51:50 UTC No. 16457288

i need to find the Fourier transform for the given signal (picrel)

is it just me or is it impossible for [math]e^{at}[/math] to equal [math]1[/math] if [math]T\neq0[/math] (and [math]T\in\mathbb{R}[/math]?

if that is that case, what do you reckon the expected answer is supposed to be? i got [math]\frac{1-e^{(a-j\omega)T}}{j\omega+a}[/math]

(image from B. P. Lathi's 1998 Signal Processing & Linear Systems, Fig. P4.1-4, page 310)

bean at Thu, 31 Oct 2024 18:55:20 UTC No. 16457289

>>16457288

correction: [math]\frac{1-e^{(a-j\omega)T}}{j\omega-a}[/math]

question still remains

bean at Thu, 31 Oct 2024 19:20:14 UTC No. 16457312

>>16457288

correction: is it just me or is it impossible for [math]e^{aT}[/math] to equal [math]1[/math] if [math]T\neq0[/math] (and [math]T\in\mathbb{R}[/math])?

question still remains

bean at Thu, 31 Oct 2024 19:23:47 UTC No. 16457317

>>16457288

correction: is it just me or is it impossible for [math]e^{aT}[/math] to equal [math]1[/math] if [math]T\neq0[/math] and [math]T\in\mathbb{R}[/math] and [math]a\neq0[/math] and [math]a\in\mathbb{R}[/math]?

question still remains

Anonymous at Thu, 31 Oct 2024 20:57:00 UTC No. 16457381

how come the sun's reflection on water increases and vanishes despite the sun barely moving? Obviously itll be nearer or farther depending on its angle in the sky, but I go to this nearby lake at least once a week and Ive noticed the sparkling on the lake seems to vanish when it was there just 10 seconds ago. Sometimes it looks like its moving from the far end of the lake towards me in the span of 5 minutes or so

Anonymous at Thu, 31 Oct 2024 21:08:36 UTC No. 16457395

>>16457381
For the same reason stars twinkle at night, the light is passing through moving pockets of air at slightly different temperature & pressures hence causing it to be refracted.

Anonymous at Thu, 31 Oct 2024 21:19:22 UTC No. 16457405

>>16457395
but stuff like the reflections of trees or clouds stay visible at all times

Anonymous at Thu, 31 Oct 2024 21:22:12 UTC No. 16457410

>>16457405
You are seeing those due to reflection, not refraction. There is always some ray of light striking them and being reflected into your eyes.

Anonymous at Thu, 31 Oct 2024 21:35:52 UTC No. 16457422

>>16457410
the sun isnt a constant stream of light?

Anonymous at Thu, 31 Oct 2024 21:36:23 UTC No. 16457424

>>16457288
my guess would be that they meant it to be [math]f(t)=e^{a\cdot(t-T)}[/math], so it would be the mirrored version of the (a) part of the problem and either left out the shift operator because it was obvious or because they forgot (im not too familiar with the field so not sure what the standard is)
and with that function i got [math]X(\omega)=\frac{e^{-j\omega}-e^{aT}}{a-j\cdot\omega}[/math]

Anonymous at Thu, 31 Oct 2024 21:41:18 UTC No. 16457431

>>16457422
The sun may be taken to be a constant but the refraction isn't.

Anonymous at Thu, 31 Oct 2024 22:42:01 UTC No. 16457510

>>16444895
you try making fucking lava in a lab without physics

Anonymous at Fri, 1 Nov 2024 12:57:05 UTC No. 16458095

I'm trying to find an article (I think it was published on an .edu webpage) about writing a thesis or academic article.
I remember it distinctly because the main advice was not straying from the main topic thesis - and the advice the author gave was in the lines of (paraphrasing) "this paper makes no claims about the ethical, moral or economical considerations of using gerbils instead of hamsters for energy, my only claim is 22% of increase in output on a treadmill"
Maybe someone remembers the article - google gives back nothing.

Anonymous at Sat, 2 Nov 2024 15:56:04 UTC No. 16459732

Some of my Adderall is about to expire. Its only been 1 year since I got it.
I've barely opened the bottle, maybe 4 or 5 times.
will its efficacy actually be affected? how badly?

Anonymous at Sat, 2 Nov 2024 17:01:11 UTC No. 16459773

>>16459732
it's fine

🗑️ Anonymous at Sat, 2 Nov 2024 20:54:57 UTC No. 16460020

How do you turn cazy infinite series into integrals or vice versa like in picrelated? How do you learn al this stuff?

Anonymous at Sat, 2 Nov 2024 21:00:48 UTC No. 16460022

How do you turn crazy infinite series into integrals or vice versa like in picrelated? How do you learn all this stuff?

Anonymous at Sat, 2 Nov 2024 23:53:49 UTC No. 16460244

>>16460022
Probably by using a shit load of factoring and trig identities, and knowing what the answer to the bottom integral actually is.

Anonymous at Sun, 3 Nov 2024 00:06:00 UTC No. 16460258

how would I go about making this chemical: C51H40N6O23S6

Anonymous at Sun, 3 Nov 2024 01:56:23 UTC No. 16460403

>>16460258
If you want to know anything meaningful about any organic compound, you're going to need to post either a name or a skeletal diagram
There are an absolutely ludicrous number of compounds with that as an empirical formula

Anonymous at Sun, 3 Nov 2024 04:27:24 UTC No. 16460526

How does Algebraic Geometry different from Differential Geometry? How does Algebraic Topology different from Differential Topology?

Anonymous at Sun, 3 Nov 2024 05:13:08 UTC No. 16460575

>>16460022
I dont know if that's even true. Can you easily find the antiderivative of that function to be a polynomial times sin plus a polynomial times cos, and the polynomials doesn't seem to fit this answer.

Anonymous at Sun, 3 Nov 2024 06:18:02 UTC No. 16460612

>>16460022
>>16460244
>>16460575
Taylor series

Anonymous at Sun, 3 Nov 2024 06:25:05 UTC No. 16460613

>>16460022
>>16460612
Alternatively, you can find the antiderivative of the bottom using repeated integration by parts, and rewrite in Taylor series after integration

Anonymous at Sun, 3 Nov 2024 07:06:41 UTC No. 16460632

It's getting chillier this time of year, and it made me wonder;
what's the warmest temperature an adult person could freeze to death in?
Like, it's 35F (2C) out right now; if I were to sleep outside naked, would I freeze to death? If so, how much warmer could it be until I don't freeze to death? If not, how much colder until I do?
This is something I couldn't even really begin to guess at. I don't know a whole lot about freezing to death other than little anecdotes like paradoxical undressing and shit like that.

Anonymous at Sun, 3 Nov 2024 10:13:23 UTC No. 16460730

>>16460632
0F is roughly defined as the freezing point of brine, which was meant to be a stand-in for the freezing point of the human body. So roughly around there, maybe higher with wind chill.
Hypothermia can of course set in at 60F if you're in water, iirc

Anonymous at Sun, 3 Nov 2024 10:25:31 UTC No. 16460736

>>16460575
>Can you
*You can

Anonymous at Sun, 3 Nov 2024 17:32:45 UTC No. 16461135

>>16460730
Thank you.
I wonder how high it could be if you factor in wind chill, though. Like, I feel like I could die if I was in the buff at something like 20F for a day.

Anonymous at Sun, 3 Nov 2024 18:20:47 UTC No. 16461184

>>16461135
I have definitely gotten frostnibble at 20F with a strong wind so probably yes

Anonymous at Sun, 3 Nov 2024 18:48:53 UTC No. 16461232

Will solving puzzles like these actually raise G, or will it just increase the test score?

Anonymous at Sun, 3 Nov 2024 19:12:13 UTC No. 16461263

>>16461232
Just raise the test score, duh. It's like asking if playing more basketball will increase height.

Anonymous at Sun, 3 Nov 2024 20:34:27 UTC No. 16461365

There's two quarter circles, one of which is rotated 180 degrees and is tangent to the other one in three points while being inside it. What is the ratio a/b?

Anonymous at Sun, 3 Nov 2024 20:42:21 UTC No. 16461372

>>16461365
Well, the radius of the larger circle is b*sqrt(2). I feel you can do the rest of the work

Anonymous at Mon, 4 Nov 2024 00:51:18 UTC No. 16461610

Not sure where to ask
Has anyone here experienced tinnitus?

For the past week I thought there has been a mosquito living in my room, only now I realized that I can hear this faint buzzing sound in other rooms too. It's so weird, it starts around 2 am every night and persists until I fall asleep. I also feel that at the same time my blood pressure goes up (feel slight increase in pressure iny ears/head).

Anonymous at Mon, 4 Nov 2024 02:32:57 UTC No. 16461689

>>16461610
>Not sure where to ask
There's a >>>/sci/med thread, Ned.
>it starts around 2 am every night and persists until I fall asleep.
Not the MD, but have you tried going to sleep at 10pm?

Anonymous at Mon, 4 Nov 2024 07:51:14 UTC No. 16461889

>>16461689
Going to bed at 10pm is for chuds.

Anonymous at Mon, 4 Nov 2024 16:05:07 UTC No. 16462262

Does the Gogny interaction include the electric repulsion between protons? It does involve the isospis, meaning there's an obvious component tied to whether the nucleons have charge or not, but does the usual electrostatic repulsion need to be taken into account separately?

Anonymous at Mon, 4 Nov 2024 16:48:07 UTC No. 16462329

Relearning calculus, specifically discontunity and differentiability. I just want to see if understand correctly, pic related is a piecewise function I thought of, does it have a jumping discontunity at x =-1, since [math]\lim_{x\to-1^+}e^{-x^2}=e^{-(-1)^2} \not=[/math][math]\lim_{x\to0^-}\frac{1}{1-x}=0.5[/math]. Removable discontinuity at x=0, since [math]\lim_{x\to0^-}e^{-x^2}=1[/math] and [math]\lim_{x\to0^+}x^x=1[/math] which gives us continuity and for differentiability,
[math]\lim_{x\to0^-}-2xe^{-x^2}=0[/math] and [math]\lim_{x\to0^+}x^xlnx+x^x=\infty[/math], obviously [math]x^x[/math] isn't differentiable at x=0, but if it was a differentiable function whose limit would be different from 0 it wouldn't be differentiable, right? We could substitute with [math]y=x^x[/math] with [math]y=x[/math] and it's derivative would be defined at 0 but different from [math]-2xe^{-x^2}[/math] and thus, the piecewise function wouldn't be differentiable at x=0.

Hope I make sense, feels like I just threw up word salad

Anonymous at Mon, 4 Nov 2024 16:49:22 UTC No. 16462331

>>16462329
Replace [math]y=x^x[/math] with [math]y=x+1[/math] is what I meant since they limit of the functions are the same at 0 but not the derivative...

Anonymous at Mon, 4 Nov 2024 20:55:50 UTC No. 16462651

>>16462329
It's continuous at [math]x=0[/math] since the left and right limits are equal, but it's not differentiable at [math]x=0[/math]. If the left and right limits in a point both exist and are equal, the function is continuous. Do you know the epsilon-delta definition of continuity and the definition in terms of open sets? It can be helpful to learn these to know multiple ways of reasoning about continuity.
>if it was a differentiable function whose limit would be different from 0 it wouldn't be differentiable, right
If it was a differentiable function *whose derivative* had a limit different from 0
Also, the limit [math]\lim_{x\rightarrow0^+} \frac{d}{dx} x^x = x^x (\ln x + 1) = -\infty [/math], which you should be able to see by plotting the function

Anonymous at Mon, 4 Nov 2024 22:32:35 UTC No. 16462779

i have a device that can detect single photons, maybe a photo-multiplier tube. i also have a 2um laser that outputs ~5mW, or about 50 trillion photons per second. if i put the laser through three 40dB VOAs in series and pointed it at the device, could i theoretically detect 50 photons per second? ignore the specifics of the device itself, my question is mainly about whether i could get "discrete" photo output using a bunch of attenuators in series.

Anonymous at Tue, 5 Nov 2024 00:26:24 UTC No. 16462930

I'm adding up a series. It's not alternating but there are runs of negative numbers. How do I find an upper bound on the truncation error?

Anonymous at Tue, 5 Nov 2024 02:11:25 UTC No. 16463001

Is chatgpt the equvilent of splitting the atom?(while achieving a true a.i is the equivalent of a nuclear bomb)

Anonymous at Tue, 5 Nov 2024 02:57:29 UTC No. 16463064

>>16463001
No, it's on the level of the Mechanical Turk.

Anonymous at Tue, 5 Nov 2024 03:04:07 UTC No. 16463075

>>16462779
Yup, adding a bunch of attenuators would reduce the photon count. But it would not be an exact number per second and so not the same thing as a true single photon source.

Anonymous at Tue, 5 Nov 2024 03:07:16 UTC No. 16463079

>>16463064
Interesting

Anonymous at Tue, 5 Nov 2024 03:59:42 UTC No. 16463136

spivak calculus is about the only maths book i understand. do i need another maths book? i originally started it so i could learn to speak maths rather than just crunching techniques and equations (physics). is it complete enough for my purposes?

asking for a friend (who is me)

Anonymous at Tue, 5 Nov 2024 06:34:01 UTC No. 16463237

>>16463136

Pick up an introductory stats book. It will help you develop logic

Anonymous at Tue, 5 Nov 2024 11:56:09 UTC No. 16463446

>>16463136
Linear Algebra - Hoffman, Kunze

Anonymous at Tue, 5 Nov 2024 14:14:59 UTC No. 16463547

I need some wrinkled brain energy.

Wolfram says this integral is ~0.394294 but I can't verify it. I just need to prove it's not one.

integrate (tanh x)^2*exp(-x^2/2)/sqrt(2*pi) from -inf to inf

but I get 1 if I let u = (tanh x)^2 and 1 - some nasty laplacian if I let u = exp(-x^2/2)/sqrt(2*pi)

For some context, X is a standard normal random variable, and I'm calculating E[tanh(X)^2].

Anonymous at Tue, 5 Nov 2024 14:50:31 UTC No. 16463574

>>16463547
tanh(x)<=sinh(x), but this just shows the tanh integral is less than 3.2 assuming both limits exist.

Anonymous at Tue, 5 Nov 2024 16:16:20 UTC No. 16463714

>>16463547
Simulating in Python with
[math]\texttt{import numpy as np}\\
\texttt{np.mean(np.tanh(np.random.standard_normal(10000000))**2)} [/math]
confirms that the value is ~0.394. There is no closed form:
https://math.stackexchange.com/questions/4131589
Your substitutions give the wrong results, did you forget to change [math]dx[/math] to [math]du[/math] when substituting?

Anonymous at Tue, 5 Nov 2024 16:18:16 UTC No. 16463719

>>16463547
tanh^2 x < 1 since sinh^2 is strictly less than cosh^2.

Anonymous at Tue, 5 Nov 2024 17:05:32 UTC No. 16463787

>>16463714
Not u-substitution, integration by parts. Which one is wrong since I gave two? I trust the latter one

Anonymous at Tue, 5 Nov 2024 17:09:09 UTC No. 16463793

>>16463787
It's definitely not 1

Anonymous at Tue, 5 Nov 2024 17:32:01 UTC No. 16463817

>>16463787
Just in case you missed it >>16463719
This is the proof your integral is less than 1. The Gaussian factor integrates to 1, and the tanh^2 factor can only decrease that

Anonymous at Tue, 5 Nov 2024 17:35:31 UTC No. 16463820

>>16463075
thanks fren <3
if i were to keep a running average, how long would i have to record before my measured photons/second was within, say, 5% of the expected value? theres probably some weird statistical quantum calculation that im not privy to; a guesstimate would suffice.

Anonymous at Tue, 5 Nov 2024 18:51:40 UTC No. 16463924

I'm retarded and can't understand surface integrals, any help/good sources etc etc?

Anonymous at Tue, 5 Nov 2024 19:32:07 UTC No. 16463994

>>16463924
1. do you understand regular integrals, specifically the Riemann definition?
2. if so, do you understand path integrals?

Anonymous at Tue, 5 Nov 2024 20:13:23 UTC No. 16464031

>>16460526
>How does Algebraic Geometry different from Differential Geometry?
"Algebraic geometry combines the algebraic with the geometric for the benefit of both. Thus the recent proof of "Fermat's Last Theorem" -- ostensibly a statement in number theory -- was proved with geometric tools. Conversely, the geometry of sets defined by equations is studied using quite sophisticated algebraic machinery. This is an enticing area but the important topics are quite deep. This area includes elliptic curves".

"Differential geometry is the language of modern physics as well as an area of mathematical delight. Typically, one considers sets which are manifolds (that is, locally resemble Euclidean space) and which come equipped with a measure of distances. In particular, this includes classical studies of the curvature of curves and surfaces. Local questions both apply and help study differential equations; global questions often invoke algebraic topology. "

Source: https://web.archive.org/web/20140331014340/http://www.math.niu.edu/~rusin/known-math/index/beginners.html

Anonymous at Tue, 5 Nov 2024 22:57:50 UTC No. 16464207

>>16462651
I do remember epsilon-delta proof but never really did much with it, should probably brush up on that. thanks.

Anonymous at Wed, 6 Nov 2024 23:57:48 UTC No. 16465492

why is bessel's correction n-1 and not n-(1+df)

Anonymous at Thu, 7 Nov 2024 00:30:30 UTC No. 16465515

I want to measure nV ionization through a coil of hairstrand thin enameled wire. The instrumentation amplifier should be able to register it given enough turns on the coil.
Biggest doubt is if the He2+ ions cause an ionization in the correct orientation to induce a current, moving through a coil?
The alpha particle being a condensation kernel in fog chambers is proof of some physical effect but
it's the direction of ionization I'm unsure of. Perhaps it's a fluctuating EM field? Or pulling electrons in sideways to the alpha particle's trajectory?

🗑️ Anonymous at Thu, 7 Nov 2024 00:58:10 UTC No. 16465535

>>16465492
You can look up the proof online. The point is, when you are only taking information from a sample of the population, the sample's mean, X, and sample's standard deviation, S, probably aren't going to be exactly the same as the entire population mean, M, and entire population standard deviation, D, where M and D are constants. You should then ask, is the average of X going to be equal to M? The answer is yes. But is the average of S going to be equal to D? The answer is no, and will actually always going to be less than or equal to D. I think the equation is like D^2 = S^2 + (X-M)^2.

But instead of calculating S, is there another number you can find whose average IS equal to D? The answer is Yes, and that is S_{n-1}, or the bessel's correction to the standard deviation formula. The average of this number over all possible samples is equal to D.

>why is bessel's correction n-1
Do the calculation, and show that the average of S_{n-1} = D. Or look it up on wikipedia. That's what I did a long time ago.

Anonymous at Thu, 7 Nov 2024 01:04:14 UTC No. 16465544

>>16465492
You can look up the proof online. The point is, when you are only taking information from a sample of the population, the sample's mean, X, and sample's variance, S^2, probably aren't going to be exactly the same as the entire population mean, M, and entire population variance, D^2, where M and D^2 are constants. You should then ask, is the average of X going to be equal to M? The answer is yes. But is the average of S^2 going to be equal to D^2? The answer is no, and will actually always going to be less than or equal to D^2. I think the equation is like D^2 = S^2 + (X-M)^2.

But instead of calculating S^2, is there another number you can find whose average IS equal to D^2? The answer is Yes, and that is S^2_{n-1}, or the bessel's correction to the variance formula. The average of this number over all possible samples is equal to D^2.

>why is bessel's correction n-1
Do the calculation, and show that the average of S^2_{n-1} = D^2. Or look it up on wikipedia. That's what I did a long time ago.

Anonymous at Thu, 7 Nov 2024 01:11:07 UTC No. 16465550

>>16465544
You'll have to explain like I'm a retard. The idea that it's just n-1 seems totally arbitrary to me. It doesn't seem to take anything into account other than 'it will be less accurate, so let's make it n-1'. As you said, check the formula, but I'm a brainlet

Anonymous at Thu, 7 Nov 2024 01:20:44 UTC No. 16465558

>>16465550
There's legit no other reason other than that the average of S^2_{n-1} = D^2. It's intuitive to see that using n alone is wrong because the average of S^2 <= D^2, since D^2 = S^2 + n(X-M)^2. But why specifically we change n to n-1 and not n-2 or n-3 is just a calculation thing. Just look up the proof of Bessel's Correction online. Just be glad it's a simple number like n-1, and not something crazy unmemorizable

Anonymous at Thu, 7 Nov 2024 01:23:33 UTC No. 16465561

>>16465550
>>16465558
Maybe you can chalk it up to degrees of freedom or some other mathy reason. Idk I didn't do too much stats. Yeah, there's prob some "degrees of freedom" reason to rationalize the n-1, but I don't know it

Anonymous at Thu, 7 Nov 2024 01:30:24 UTC No. 16465573

>>16465550
btw, you also can't do the same thing for standard deviation. Like, the average of the sample standard deviation isn't the same as the population standard deviation (a constant number). But there's no simple thing like bessel's correction for the standard deviation. I think a bunch of things could be used like n-1 or n+1 or something, but it'll never be perfect.

So, the fact that a simple correction like n-1 for sample variance is neat

Anonymous at Thu, 7 Nov 2024 01:50:06 UTC No. 16465587

>>16465573
idk, I'm a tard and started up with the wikipedia and will try and digest it later. I ran GPT through a sample and population and the n-1 got it closer but wasn't accurate. So, to me, n-1 seems like yeah it gets closer, but again it just seems arbitrary in that we just have one less degree of freedom, but why should it be that that in particular is the defining metric. Why don't they just run simulations on populations and samples to find out where it more commonly lies?

btw, I get you're giving me an example with that formula, but I am just too stupid to get it and hence why I am here.

Anonymous at Thu, 7 Nov 2024 02:56:51 UTC No. 16465642

>>16460403
Its suramin.

Anonymous at Thu, 7 Nov 2024 03:01:37 UTC No. 16465650

>>16465515
is there a name for the set-up youre making? or could you provide a diagram of sorts?

Anonymous at Thu, 7 Nov 2024 09:01:01 UTC No. 16465872

new thread:

>>16465871
>>16465871