/sci/ - Science & Math

do not post here post in my chad novelty thread. i got dubs. its a good time

>>11454355
>>11454355
>>11454355
>>11454355
>>11454355
>>11454355

>>11454381
what the fag does this shitty fagcunt think he's fucking doing?

>>11454387
Schizo bullshit. Ignore it. Tally coming soon.

Bogdatally:

Physics questions:
>>11437756
>>11439758
>>11439867
>>11440771

Maths questions:
>>11437861 (there is a correct explanation, but no one axiomatically proved it from muh modus ponens, etc)
>>11440690 (Applied maths)
>>11440969 (Lengthy)
>>11442903 (Can't use Silow)
>>11444654
>>11444740
>>11454322

Engineering questions:
>>11439770

Biology questions:
>>11441642

Chemistry questions:
>>11450486

Stupid questions:
>>11437929
>>11439098
>>11443690
>>11445390
>>11445535
>>11446892
>>11446914
>>11447380
>>11448974
>>11448975
>>11449318
>>11450855
>>11451813
>>11453462

>>11452800
I can't make sense of any of that, unfortunately.
I wrote my proof that way out of bad habit, but in vector calc lang, I think you'd substitute [math]G(v) \rightarrow \nabla g(0) . v[/math], and the operator norm argument becomes Cauchy-Schwarz.
Also, a bunch of norms become modulos.
>>11454322
[math]S_n[/math] is the symmetric group, [math]D_n[/math] is dihedral, and fuck if I know [math]U_n[/math]. I'd usually assume it's the unitary group, but that's normally [math]U(n)[/math].

What is a cardinal exactly?
Is it a class that contains all sets of a certain cardinality?
Is it a proper class or a set?

>>11454534
Cardinals are just ordinals

Ok lads, let's say I have a term in my Lagrangian like:

[math] -g A^{\mu} A_{\mu} \partial_{\nu} A^{\nu} [/math]

I know that the Feynman rule for an AAA vertex includes the momentum of one of the outgoing photons, but should there be an additional term of three? I mean, should the Feynman rule be:

[math] 3g \eta_{\mu \nu} p_{\sigma} [/math]

>>11455059
I think I got it lads, I think it should be:

[math] 2g( \eta^{\mu\nu}p_1^{\sigma} + \eta^{\mu\sigma}p_2^{\nu} + \eta^{\nu\sigma}p_3^{\mu}) [/math]

How do I express the type of a curried function whose codomain depends on the argument?

I got stupid questions.

Can you make up a type of dimension that's neIther a dimension of time nor a dimension of space?

Any interesting property of an universe with an infinite amount of time dimensions and space dimensions? Would such an universe be considered ponctual (space wise)?

Any good read regarding quirky dimension stuff?

Any system where instead of using "base" units to build objects, you start off from an omega object to make smaller and smaller objects eventually turning into concepts?

Any work relative to the analysis of fundamental ideas such as concepts? Like what if you had an universe made of concepts and another type of concept, like completely different yet compatible in a way?


Sorry I couldn't find anywhere else to ask, I wish I had the brains to clarofy my ideas.

>>11455551
>Can you make up a type of dimension that's neIther a dimension of time nor a dimension of space?
Yeah, look up muh quadratic forms.
In other words, [math]\mathbb{R}[/math] with the symmetric form constant zero has no timelike or spacelike dimensions.
>Any interesting property of an universe with an infinite amount of time dimensions and space dimensions?
Anon's property: It sucks.
>Any good read regarding quirky dimension stuff?
Hausdorff dimension.
>Any work relative to the analysis of fundamental ideas such as concepts? Like what if you had an universe made of concepts and another type of concept, like completely different yet compatible in a way?
Sounds like category theory.

>>11455597
t-thanks

I want to learn more about economics, but with a mathematical slant. My CC intro to economics class's textbook was interesting ish but they tried to explain what a limit was and what a derivative was, without ever using the word "derivative" or "limit". To give you guys an idea of what I don't want.

Are there any books that don't shy away from the mathematics of economics? We don't need to get into like, Black-Scholes Stochastic Calculus and Stochastic Partial Differential Equations tier math, but I definitely want a book that uses calculus to explain economics.

Say you have a particle, we'll call it a T particle. This T particle decays into a photon and a tachyon, but the tachyon adheres to the self-consistency principle and can't cause any time paradoxes. Essentially, the tachyon cannot interact with anything in the T particle's past light cone, because that potentially alters the T particle and thus the tachyon's own creation.

Is it even possible for a single observer to detect both the tachyon and the photon emitted by the T particle's decay?

I guess I probably should have asked this here: >>11455638

>>11454375
ignoring the fact that string theory is unfalsifiable, what are some conceptual contributions it has made to QFT?

Hello, this mr.Richard Dix, i work in a machine shop. I want so much to learn trig. My mind just don't uderstand it. I really want to learn it. I am at the age (63). Help.....

>>11453521
>you haven't even shown the limit exists in the first place
But that's what I'm doing, I'm proving that the limit exist and that's 0.
>why you can exchange g with it's gradient
i prove that before so i just skipped that but of course i would explain that in an actual prove
>The line below that clearly isn't what you wanted to show in the first place.
the limit that i want to prove is 0 if only if the last limit is 0 and that's true since g is differentiable

Prove that if A is a mxn matrix with linearly independent columns then A is left invertible, without using row operations.

How's my proof?
a, b, x and y are positive integers. Prove that if a is congruent to b modulo 5, and x is congruent to y modulo 5, then ax is congruent to by modulo 5.
Proof:
>Suppose a is congruent to b modulo 5 and x is congruent to y modulo 5.
>Then a - b = 5c and x - y = 5d, where c and d are positive integers
>ax - by = 5e, where e is a positive integer
>a = b + 5c
>x = y + 5d
>(b + 5c)(y + 5d) - by = by + 5bd + 5cy + 25cd - by = 5(bd + cy + 5cd)
>Then, ax - by = 5k, where k is bd + cy + 5cd.
>Therefore, ax is congruent to by modulo 5.

https://en.wikipedia.org/wiki/Equals_sign#History

>bicauſe noe .2. thynges, can be moare equalle

>>11439758
No, it means the spinor part is trivial, i.e. transforms under the trivial representation [math]{\bf 1}[/math] of your gauge group [math]G[/math]. Generally, a spinor transforms as [math]\psi \mapsto \rho(g) \cdot \psi[/math] with Clifford multiplication, which requires a "matrix" structure on [math]\psi[/math]. The trivial representation on the other hand literally just gives you [math]\psi \mapsto \psi [/math] so no matrix structure is required.
Given this you can build up your effective action [math]S[\psi] = \int_M \mathcal{L}(J^\infty\psi)[/math] in grand Ginzburg-Landau style with a [math]G[/math]-invariant Lagrangian density [math]\mathcal{L}(J^\infty\psi^g) = \mathcal{L}(J^\infty \psi)[/math].
>>11444654
Remember that if the Gaussian surface [math]S[/math] is given by the zero locus of a harmonic map [math]\phi[/math] then [math]\partial \phi[/math] induces an orthonormal frame on [math]TS[/math] with respect to the Riemannian metric as [math]g[/math] on [math]S[/math]. As [math]S[/math] is 2D, the two-form [math]d\phi \wedge d\phi[/math] is a top-degree exterior form and hence defines a normal form [math]n(S)[/math] in the normal bundle [math]NS[/math]. Its local derivative [math]-\nabla_s n(S)[/math] is the shape operator. As you have perhaps noticed, the matrix [math]d\phi_s \odot d\phi_s[/math] is the Hessian that tells you the curvature at [math]s\in S[/math].
Now as you move in [math]S[/math], [math]n_s(S)[/math] gives a vector normal to the surface at [math]s \in S[/math], which scales with the curvature; eigenvalues and eigenvectors of the shape operator then also scales with those of the Hessian, which tells you how much and towards where the curvature of [math]S[/math] is changing.
>>11455059
Generally you must have [math]\delta(\sum_\text{incoming}p - \sum_\text{outgoing}p)[/math] to preserve 4-momentum. Also I don't think a vertex like [math](A\wedge \ast A )dA[/math] is gauge invariant (modulo boundary terms), is it?

>>11454375

In 240v circuit running off of two 120v lines (like in the outlet for your oven [NA]), are the phases in sync or are they 180 out from eachother?

I can't tell if they're in sync because the waves compound and add to 240v relative to 0 or if they're out of phase and you get 240v because there's a difference in potential between +120v and -120v.

>>11455914
based overcomplicated answer poster

>>11455635
Read Mas-Coleil.
>>11455795
Can I just show that the associated linear map is invertible?
[math]e_i[/math] is the [math]i-th[/math] basis vector. Set [math]B(Ae_i) = e_i[/math]. If all the [math]Ae_i[/math], which actually equals the [math]i-th[/math] collumn, are independent, [math]B[/math] extends to a well defined linear map in the obvious way, and we have [math]B=A^{-1}[/math].
>>11455845
>ax - by = 5e, where e is a positive integer
Did you leave this line in the middle of the proof on accident?
Seems alright to me, otherwise.

>>11456625
They are 180° apart, each 120V from neutral. If they were in sync, the voltage between them would be zero.

>>11457031

Thanks.
I was thinking maybe for an hot+hot+neutral+ground they might be adding their potentials relative to the neutral if they were in sync.

I have a quantity that is a function of the summation of daily temperatures. Ie Y is a function of the temperature of day 1, plus temperature of day 2, and so on.

[eqn] Y = f \left \sum_1^n T \right [/eqn]

Can I just derive it for the time and say that the derivative is just a function of temperature? Basically, can I get a sort of "velocity" function which depends on temperature through derivation of a summation?

>>11457596
Like dY/dt=dT1/dt+dT2/dt+...?
then yes

>>11455795
Generally we have an exact sequence [math]0\rightarrow \operatorname{ker}A \rightarrow V \xrightarrow{A} W \rightarrow \operatorname{coker}A \rightarrow 0[/math], which tells you [math]W = \operatorname{im}A \oplus \operatorname{coker}A[/math]. On the image [math]\operatorname{im}A \subset W[/math], [math]A[/math] is certainly invertible so it just suffices to show that [math]\operatorname{coker}A = 0[/math]. Now since [math]\operatorname{im}A = \operatorname{Span}_{j\leq \operatorname{dim}W}\{\operatorname{Col}_jA\}[/math] is the span of the column space, any [math]w\in W/\operatorname{im}A[/math] gets you a vector linearly independent to the [math]\operatorname{dim}W[/math]-columns. However this cannot happen if [math]\{\operatorname{Col}_jA\}_{j\leq \operatorname{dim}W}[/math] is linearly independent, unless [math]w = 0[/math]. This means that [math]W/\operatorname{im}A = \operatorname{coker}A = 0[/math].

>>11455722
String theory is a CFT, not a QFT. The observables are constructed from chiral Virasoro algebras (glorified ladders) instead of generic field operator nets, which behaves much nicer both algebraically and analytically. This is in essence due to the much larger underlying conformal symmetry CFTs enjoy, and string theory takes full advantage of that. In fact, you can leverage modular invariance to show that the OPE coefficients (conformal blocks) are all holomorphic on [math]S^2\setminis \{0,1,\infty\}[/math] so you can use Laurent expansion techniques to solve the KZ equation, for instance.
You would not be able to prove most things you encounter in CFT, such as the Ward-Takahashi or Yang-Baxter, as easily in general QFTs, but drawing inspiration from CFTs at least allows us to understand what algebraic structures for the local operator nets are necessary in order to yield a consistent QFT. They don't solve the regularity/summability issues of [math]S[/math]-matrices however.

If you have a group with sub groups A and B, is A union B also a subgroup? What about A intersection B?

What's a good book for learning linear algebra? I've already taken a course on it in university but I felt it was too numerical and not enough proofs.

>>11457956
No. Just use your brain bro.
Take all the multiples of 3 and multiples of 2 in the integers.
The union isn't but the intersection is indeed a group again, the proof isn't hard.
This is a pattern that shows up in vector spaces, topologies, etc. so I'm pretty sure it's related to category theory.

>>11458060
>No. Just use your brain bro.

I'm lost

>>11457956
There's a theorem that states a non empty subset of group is a subgroup if and only if gh^{-1} is in the subset for all g,h in the subset. A intersect B certainly passes that test. A union B fails it by counterexample.

>>11458303
since the osculating plan is normal to N, N' = tn and so t2 = |N'|2 = k12 cos2 theta + k22 sin2 theta, where theta is the angle of e1 with the tangent to the curve. And since the direction is asymptotic, we know cos2 theta and sin2 theta are functions of k1 and k2 so t2=-k1k2 but the details are confusing to me

>>11455914
No, it's not gauge invariant. It's part of the gauge fixing term: [math] -\frac{1}{2\xi}(\partial_{\mu} A^{\mu} + \frac{1}{2} g A_{\mu} A^{\mu})^2[/math]

>>11454355
>>11458641
Someone sketch me the probability it's the exact same person.

>>11454375
What does the artwork on the front of this book represent? I've encountered this structure before when messing around with permutations, but I'm interested in what it has to do with number theory.

>>11458976
Looks like a sieve.

Talk to me about Gravity.
If we go out into space, are we in free fall and falling towards Earth or the nearest large piece of mass or are we simply floating in space?

>>11458996
I believe it's 2-dimensional

>>11458999
Classically, you are accelerated in whatever direction the net force on your body is. This net force is the sum of all gravitational and electromagnetic and other kinds of forces from all other bodies acting on you. So no, it's not just the Earth's gravitational field you would feel.

So you're between the moon and the earth so whichever force is stronger, you'd be headed in that direction?
Where did this concept of "floating in space" come from

>>11459034
>So you're between the moon and the earth so whichever force is stronger, you'd be headed in that direction?
No. You are **accelerated** in the direction of the net force. That doesn't mean you are literally moving toward it. You could have lots
of momentum in the opposite direction, for example, and be traveling against the net force.
>Where did this concept of "floating in space" come from
Probably from the fact that when you are in orbit/free-fall, you don't experience a "downward" acceleration.

>>11454375
I guess this question is science related? I'm not entirely sure. Sorry if this is the wrong thread for this question.
I'm doing some writing, and have been attempting to learn about paraplegia. I've been able to skim a lot from google, but there's a specific question I can't seem to find an answer to. I'm probably just dumb, but I phrased it about five ways and it just kept telling me about normal paraplegia.
Question is: Is there a type of paraplegia (or another medical condition of another, specific name) that is similar in that you have no feeling/motor control in your legs, but it doesn't start at the waist, rather lower, around the upper thighs or so.
I figure I might not be able to find something like this, since most paraplegia is related to spinal issues, which affects everything below it to varying degrees, but if anyone knows a condition that fits the bill I'd love to know what it is!

What's the best single text on robotics and robotic engineering? Assume all requisite knowledge to fully engage with it is already possessed.

Which is better? going to college or going to /sci/?

>>11459118
Spending a lot of money on college and shitposting on /sci/ in the middle of class is best.

>>11458406
Oh I guess you're looking at ghost vertices then? No wonder it looks weird

Am I missing something about the hypothetical behavior of tachyons? The faster something moves, the slower it ages, with things moving at the speed of light having their age frozen. Continuing that logic, tachyons would age backwards. If a tachyon passes through a barrier that slows particles down, it would instead speed up, because it was already born into the world having experienced the slow down, and is aging backwards to before it was slowed down.

Is that all right?

Actually, using speed for the analogy was probably a bad idea.

If a tachyon interacts with a barrier that saps energy from particles that pass through it, will the tachyon first pop into existence having already been sapped, then take energy FROM the barrier when it passes through? Or does the time-reversed nature of the tachyon not affect its interaction with the barrier in this way?

>>11454534
Afaic a cardinal is an ordinal that cannot be injected into any smaller ordinal.

Is there any reason to believe that ZF(C) or PA is consistent besides the fact that we couldn't find a contradiction so far?

Are the elements in the first two groups all acids since they donate protons?

>>11457673
I don't understand

I don't get it, why does my RMS spectra widen for a single tone FM signal if I increase my message signal's amplitude?

>>11459088
Something like this?
https://medlineplus.gov/ency/article/000687.htm
>>11459118
College, definitely.
>>11459462
>Is there any reason to believe that PA is consistent
https://en.wikipedia.org/wiki/Presburger_arithmetic

>>11459505
you mean bases, which donate electrons? yes, except for hydrogen.
>>11450486
Yes, all that matters is the carboxylic acid is deprotonated, while the carbon tail remains greasy. You might get shitty soap though

You guys are butt nuggets.

When mapping complex coordinates (a+ib) to polar coordinates [math](re^{i\theta})[/math], which polar variable becomes imaginary? radius, or angle?

Does converting from a+ib to phasors map [math]\mathbb C \rightarrow \mathbb R^2[/math]?

Why shouldn't I go on a cruise rn? Prices are low af

Y=-2x^2
If X is -2 then how is the correct way to solve it? And why?
A) Y=-2×(-2)^2
Y=-8
B) Y=-2×-(2)^2
Y=8

And what about Y=-X^2
If X=2 will Y be 4 or -4?

>>11459908
[math] Y=-2X^2=-2\cdotX\cdotX [/math] for [math] x=-2 we find [math] Y=-2\cdot -2\cdot-2 = -8 [/math]

>>11459872
>Presburger_arithmetic
Yes? What about it? I obviously meant Peano Arithmetic.

>>11459891
the angle

in matlab, i have 1 vector that's of 1xn size with zeros only and a 2nd one that contains indexes that should be set to 1 in the first vector
the braindead way is to just iterate over the 2nd vector and for each number, set the index to one but can this be vectorized?

Any smart person knows a way to download all the trillions of books from LIB GEN at the same time or a working torrent that has at least a Terabyte of books in one file online?

>>11460752
>all the trillions of books from LIB GEN at the same time
>at least a Terabyte of books in one file online
it's tens of terabytes, roughly 10GB apiece across 2000 torrents, last I checked, and it's under downloads>torrents
If you want sci-mag's database too, and any of their other sister projects, it'll run you another ~65TB or so per pop

>>11460800
wow thanks

>>11459895
Once your ship arrives at the end of the trip you'll find out old mr. Shang, the dude in the room next to yours, was in Wuhan once when he was 5 years old, and now the cops have quarantined the entire cruise and you're stuck there for two weeks because muh corona.
>>11460378
>what about it
If Presburger arithmetic is consistent, Peano arithmetic should also be consistent.
>do you have anything better than analogies
I don't, naturally.

>>11458976
hint: factors

Probability question (not a homework, just something I'm curious about, from a game):
>You have a deck of 40 cards
>3 cards in a deck are red, and 37 cards in a deck are blue
>You draw 4 cards from the deck, you can do it 2 times (with returning them to deck)
>So you draw twice from a deck of 40 random cards, 3 of which are red
>What is the probability of drawing at least 1 red card after the second draw?

I figured out the answer to similar question, which has drawing 4 cards just ONCE, and it's:

[math]1-\dfrac{37\choose 4}{40\choose 4} \approx 0.277[/math]
1 minus the probability that you don't draw it, basically. Or, equivalently:

[math]\dfrac{{3\choose 1}{37\choose 3}+{3\choose 2}{37\choose 2}+{3\choose 3}{37\choose 1}}{40\choose 4} \approx 0.277[/math]

So you have about 27.73% of drawing at least one of red cards, IF you draw 4 cards ONCE.

But what if you draw twice? I thought that [math]2\times0.277=0.554[/math] could be about it, but that's not the case.
I wrote a python script and after a lot of iterations of such "games" the answer is about 47-48%, not 55%.

Here's the script: https://repl.it/repls/TidyWickedIntegers

What should I take into account calculating the second draw?

Probably the fact that you sometimes don't go into the second drawing phase? But how to write it mathematically?

>>11461029

>>11458303
help

please help with this

>>11461121
Toponogov's Differential Geometry of Curves and Surfaces has a full proof written out.

>>11461029
You want the hypergeometric distribution.

>>11461145
Do you happen to know what page?

>>11461158
128
Just Ctrl+F Beltrami, tho.

If you are taking physics measurements, how do you calculate the uncertainty in a formula? like if you have Vo = [(M+m)/m]V

All my measurements for distance were ±1mm and my mass measurements were ± .1g. If you have a formula that has both mass and distance in it, how do you add the two different units of uncertainty together? Normally for multiplication and division you add the uncertainties, but all the examples in my guide use the same units.

>>11461124
Notice that [math]K(s) = \kappa_1(s)\kappa_2(s) = \operatorname{det}df[/math] is the determinant of the differential the Gauss map. Using cylindrical coordinates along [math]x[/math], we can write a point on the surface as [math]s= (y(x),\phi,x) \in S[/math]. We define the Gauss map [math]f: S\rightarrow S^2[/math] by sending [math]s\mapsto \hat{\bf n}(s)[/math] to the unit normal at [math]s\in S[/math]. The Gaussian curvature is then defined by [math]K = \operatorname{det}\nabla_i \hat{n}_j(s)[/math].
Explicit computations are left to the reader.

there is a lottery, where are 1000 tickets
only 3 tickets win
my friend bought 4 tickets
what is the probability he has 2 winning tickets?


is it
[math]4! \times \frac{4*3*2}{1000*999*998} + 3 \times \frac{4*3*996}{1000*999*998}[/math]
??

>>11462238
sorry, the first number it's not 4!, it's 3!

what magnet are they talking about? are there strong magnets in a fridge? the stuff holding the door shut is very weak

>>11462246
huh?

>>11457710
ty

From Mr. Spivak's famous book. Why is the curve on the wrong side of y axis?

>>11463132
Probably to save room

>>11463132
I should add the question was to graph f(x) = ax^2 + bx + c. When b is negative, this graph is accurate, but when b is positive it is not correct unless the x-axis is opposite of how it normally is (decreasing in value to the right than increasing).

>>11463138
That doesn't make sense to me, how would it save room to have the curve on the left rather than the right? The graph takes up the same amount of space regardless.

>>11454375
are supermassive black holes pulling in space like pulling on a rug? Like do they drag more and more spacetime into them as well as particles?

>>11463146
>When b is negative, this graph is accurate, but when b is positive it is not correct unless the x-axis is opposite of how it normally is
So what's the problem?

>>11463168
It is weird to give an example of the graph without specifying this, especially given that on an initial example most people, when looking for a trivial example to draw, will assume b is either 0 or a positive integer. I understand it's 'not wrong', but that's almost like asking someone to draw a triangle and then the answer key displays a degenerate triangle (a line segment).

can someone help me with this simplification? It's just algebra, I know, but I can't seem to gather up all the y's, whenever I try they cancel out :/

>>11463504
add y^2 to both sides, add 2By to both sides, should be ez from there.

>>11463515
thank you, wise one

>>11463178
Why would you assume b is positive?
There are as many positive numbers as negative ones.
And no, the degenerate triangle would be like saying a = 0 and just having a line. Sure, it's ax^2 + bx + c but it's not a quadratic.
You are thinking the right way, "hmm what conditions make this the right graph," so keep thinking that way. But the textbook is going to save space and include one possibility and not both. I mean you'd hope for a quadratic to have 2 real roots right? This one isn't wrong just because it's above the x axis.

>>11463536
>two real roots
good point, I see that this maybe was the better example. I just thought when choosing numbers a, b and c, most people when drawing the graphs themselves would, initially at least, naturally select 0 or some positive integer, so deviating from the laziest/most expected path without explanation seemed odd to me, but you're right. Thanks!

>>11463536
Also, fwiw, it was not the fact it was above the axis that triggered me, but that it was to the right of the y-axis.

I see the minimum is obviously 0 (minimum distance cannot be negative), but I do not see how to arrive at |cm-d|/sqrt(m+1)^2, specifically I don't see where cm-d comes from.

>>11463681
The minimum is not zero. I'm not sure you know what minimum means.
Minimum = smallest value it can take.

>>11463681
The function is a quadratic in x. Surely you know how to find the minimum value of a quadratic in x?

>>11463726
>>11463728
How can it be less than zero? The expression is equal to (c-x)^2 + (d-mx)^2, clearly the minimum value of this expression is 0. I'm under the impression the 'minimum value' is not the minimum value in it's domain, but the minimum value the expression will yield (in the case of functions, the minimum y, or f(x) - not the minimum x..).

>>11461999
>>11461124

I'm still confused about this :(

>>11461124
>>11463960
Literally google "formula for the curvature of a surface of revolution".

Help me. This Vgs source is throwing me off.

it's like no matter how matter integrals I do, I just don't get it
I still get completely stuck in front of new integrals and I don't know what to do
then I check the steps on an integral calculator and it makes sense
but then I get stuck again

holy FUCK

>>11464135
what is hard about integrals? theres a few different ways to solve them, just check each method in your mind quickly and see if it fits

Let [Math]E[/math] be a neighborhood of [math]0[/math] in [math]\mathbb{R}^n[/math] amd let [math](Y,d')[/math] be a metric space. Let [math]f:E\setminus \{ 0 \} \rightarrow Y[/math]. I need to proof

[math]\lim_{h\rightarrow 0}_{h \in \mathbb{R}^n} f(h)=y \implies \forallx \in \mathbb{R}^n \setminus\{ 0\} \ \lim_{t\rightarrow 0}_{t \in \mathbb{R} } f(tx)=y. [/math]

Let [math]E[/math] be a neighborhood of [math]0[/math] in [math]\mathbb{R}^n[/math] amd let [math](Y,d)[/math] be a metric space. Let [math]f:E\setminus \{ 0\ }\rightarrowY[/math]. I need to proof

[math] \lim_{h\rightarrow 0} f(h)=y :h \in \mathbb{R}^n \implies \forallx \in \mathbb{R}^n \setminus\{ 0\} \ \lim_{t\rightarrow 0} f(tx)=y : t \in \mathbb{R} [/math]

>>11464143
if this was true then there wouldn't be whole autistic competitions about solving integrals

Let [math]E[/math] be a neighborhood of [math]0[/math] in [math]\mathbb{R}^n[/math] amd let [math](Y,d)[/math] be a metric space. Let [math]f:E\setminus \{ 0\ }\rightarrow Y[/math]. I need to proof

[math] \lim_{h\rightarrow 0} f(h)=y :h \in \mathbb{R}^n \implies \forall x \in \mathbb{R}^n \setminus\{ 0\} \ \lim_{t\rightarrow 0} f(tx)=y : t \in \mathbb{R} [/math]


FFS

>>11464144
>>11464164
>>11464170
use the preview, retard.
That or
mathb.in

How do I solve B=m+msg for s. I putting it in to Wolfram Alpha and I doesn't work.

>>11464170
IIRC, that didn't work as stated.
Set [math]E = \mathbb{R}^2[/math], [math]Y= \mathbb{R}[/math].
Take polar coordinates, and then [math]f(r, \theta ) = r\frac{1}{2 \pi - \theta}[/math]. Since [math]\theta \in [0, \2pi)[/math] it's actually well defined, and for any [math]x \in \mathbb{R}^2[/math], we naturally have that [math] \lim _{r \rightarrow 0} r \frac{1}{2 \pi - \theta} = 0[/math] for fixed [math]\theta[/math], but it's fairly intuitive why there are sequences which converge to zero whose images explode (finding one explicitly is left as an exercise to the reader).
Note: this kind of proof is exactly the kind I'd completely fuck up. Reread everything five times.
Is [math]f[/math], dare I guess, continuous?

What 4th year EE courses should I take? Should I go into electronics, communications/signals/controls, power or software?

>>11464170
Hint: take [math]t[/math] small enough so that [math]d(tx,0) < d(h,0)[/math]. Remember that metrics are homogeneous so [math]d(\lambda x ,\lambda y) = |\lambda| d(x,y)[/math] for any scalar [math]\lambda\in\mathbb{R}[/math].
>>11464210
I'm confused. [math]t[/math] scales both [math]r[/math] and [math]\theta[/math] so you still approach [math](0,0)[/math]. The function you defined is by definition multivalued, so you cannot use the identification [math]0 \sim 2\pi[/math] on [math]\theta[/math] in the image. This means that [math]t\theta \xrightarrow[t\rightarrow0]{}0[/math] unambiguously, not to [math]2\pi[/math].
Think of it as [math]\ln[/math] being a conformal transform from the Riemann sphere [math]\overline{\mathbb{C}}[/math] to the semi-infinite strip [math]\mathbb{R}\times [0,2\pi][/math] on the principal branch. You only get back the entirety of [math]\mathbb{C}[/math] if you glue every single branch of [math]\ln[/math] together.

>>11464265
My bad, I literally had audiovisual hallucinations and assumed he wanted to prove the converse.
>The function you defined is by definition multivalued
I specified [math]\that \in [0, 2 \pi)[/math] tho.

>>11464297
*that [math]\theta \in [0, 2 \pi)[/math]

>just spent 3 hours on a problem just to find out the solution is trivial

>>11464297
>I specified
Doesn't matter. You need to identify the boundary points to get [math]S^1 = [0,2\pi]/\sim[/math]. You [math]must[/math] unfurl this angle and pick a branch if you want to write your function as anything other than a [math]2\pi[/math]-periodic function in [math]\theta[/math]. This means you have implicitly mapped the blow up [math](\mathbb{R}^2)^\sigma[/math] to the infinite strip when you defined your [math]f[/math]. By construction your function has no periodicity so [math]t\theta \xrightarrow[t\rightarrow 0]{} 0[/math] unambiguously. It doesn't blow up near [math]0[/math].

>>11464265
> t scales both r and θ
That's not true. Look how anon defined it again. At 0, t scales only r but not θ.
>yukari retardposting again

>>11464265
>>11464351

>>11464366
Ah yeah that part is wrong, my mistake. It just means that [math]\theta[/math] doesn't move but also the function isn't defined on [math]2\pi[/math] anyway while [math]r \rightarrow 0[/math] so the image gets suppressed. Point still stands though, that the image doesn't blow up.

>>11464396
Pretty sure it does, but I might have fucked it up.
Set [math]x_n = (r_n, \theta _n) = (\frac{1}{n}, 2 \pi - \frac{1}{n^2})[/math]. Then [math]f(x_n)= \frac{1}{n} \frac{1}{2 \pi - 2 \pi - n^{-2} } = n[/math].

>>11464416
Should be a plus on the [math]n^{-2}[/math], my bad.

>>11464396
It's a good counterexample for the converse, a point which you attacked.
It's defined on the whole plane and there are arbitrarily close points to 0 that map to arbitrarily large points.
>that the image doesn't blow up.
If you mean the balls around 0 don't get mapped consistently far away from zero, you're right, but the poster never claimed that.
>the function isn't defined on 2π anyway
The fuck do you mean, retard?
It's defined on R^2.

>>11464416
> but I might have fucked it up.
No lol, yukariposter is just being yukariposter. Your example is good, don't listen to that fag.

>>11464416
No you're fine. You're right that you need [math]f[/math] to be continuous on [math]\mathbb{R}^2[/math], which is what I assumed; sorry about the confusion, I thought you were doing the same.
Though your function would've been continuous on the strip but you can make your image do whatever you want there.

>>11464461
Reminder that this person has a phd lmao

in physics the other day, while studying wave interference, i noticed that it seemed like the superposition of two or more equally spaced sine waves was always zero. that is:
[eqn]\overbrace{\sin(x)+\sin(x+2\pi\frac{1}{n})+\sin(x+2\pi\frac{2}{n})+\dots+\sin(x+2\pi\frac{n-1}{n})}^n=0[/eqn]
for all values of x.
i wasnt able to prove this however, and i couldnt find anything with google. is this equation true? can anyone here prove it? i dont remember any of my trig identities

What's the reason behind the existence of the stupid meme that the more you know the more you feel that you don't know? does that have anything to do with idiots only majoring in one small field? for me the more I know the more I feel that I know more!

>>11464504
Use sin(a+b) = sin(a)cos(b) + cos(a)sin(b), and break it up into real and imaginary parts of the sum of the powers of the nth root of unity.

>>11464461
Eh, no biggie.
>>11464504
I think it works.
Inscribe an n-sided regular polygon into the unit circle.
Then, the barycentre coincides with the circle's center, and we're done.
>>11464532
>What's the reason behind the existence of the stupid meme that the more you know the more you feel that you don't know?
It's kinda true when you're young, tho.

>>11464541
>barycentre coincides with the circle's center, and we're done.
what even

>>11464547
that's a way to visualize how summing up the powers of a root of unity gives you zero

Considering that there are stem cells produced by the testicles, does that mean that masturbation reduces or increases stem cells?

>>11464476
wait, yukarifag has a phd confirmed?

>>11464556
It's not a way to visualize, that's the actual geometry happening in the problem.

>>11464504
Let f(x) be your expression.
Then note that f''=-f so f(x) =A sin(x+b) for some constants x, b.
but by symmetry in the original expression f(x)=f(x+2pi * k/n) for any k=0,..., n-1. So f(x) = 0 everywhere.

What is a cool, /sci/ related field to get into as a hobby? I'm not pursuing any /sci/ based fields of employment right now and don't think I'd be cut out for that kind of academia anyway, but I've always liked science and learning cool things. I'd love to do something practice with this interest- I love the idea of buying a telescope to do astronomy but my area has too much light pollution for it to be worth doing. Perhaps microscopy is the way to go, or maybe geology? The main thing is that it's fun and I can sound smart in that field

>>11464590
>can sound smart in that field
go fuck some niggers anon

>>11464590
>something practice
Meant practice.

>>11464504
Another, simpler proof that the sum for x=0 is zero:
Let f(x) be your expression.
[math]f(-x)= \overbrace{\sin(-x)+\sin(-x+2\pi\frac{1}{n})+\sin(-x+2\pi\frac{2}{n})+\dots+\sin(-x+2\pi\frac{n-1}{n})}^n=0 = \\
= \overbrace{\sin(-x)+\sin(-x-2\pi\frac{1}{n})+\sin(-x-2\pi\frac{2}{n})+\dots+\sin(-x-2\pi\frac{n-1}{n})}^n= -f(x)[/math]
so f(0)=-f(0). So f(0)=0.

>>11464591
I was being slightly facetious. I just want someone to recommend me a fun science based hobby.

>>11464590
Competitive programming

>>11464605
Also you can exploit this property of f: f(-x)=-f(x) to find f'(-x)= f'(x), and so by continuity f'(0)=0. But f'(0) is precisely the f(0) but with sines replaced with cosines.
Once you have the sum of sines 0 and cosines 0, for general x the angle addition formula takes care of the rest:
f(x) = sin(x) f'(0) + cos(x) f(x) = 0

>>11464615
I'd rather have a hobby that doesn't tie me to a computer like 90% of my waking life. Didn't know competitive programming was a thing though, that's interesting

>>11464637
Geology sounds like a good one for you then. Doing field work gets you out of your seat and away from you computer.

>>11464642
Yeah I think I'll go for it. Gonna tell people I'm a rock expert and then bore them to death with facts about actual rocks

Are we even remotely close to a vaccine for Covid?

>>11464504
>>11464541
>>11464569
>>11464605

Am I missing something? Just compute the sum up to arbitrary n for various values of x and you can see it isn't generally true. Pic related.

>>11464690
n (the nth term) and n (the number of terms) are different numbers

>>11464605
cool proof

>>11464690
Should be
[math]\sum\limits_{n = 0}^{N-1} \sin \left(x +\frac{2\pi n}{N}\right)[/math],
you're using [math]n[/math] instead of [math]N[/math] in the denominator

>>11464698
>>11464723

Ah, I see. Thank you.

Can anyone recommend an undergraduate/intro level algebraic geometry textbook that actually offers solutions to some exercises? I want to understand wtf is happening. Even ones that work through examples amidst the chapters would be fine. I'm currently using Fulton's algebraic curves and he constantly peddles very important results off as exercises which of course have no solutions.

>>11461961
You come up with distributions for all of your uncertainties and then throw it all into some MCMC software.

Does this make sense?

>>11465104
Conics and Cubics.

>>11465563
Yes

Which one uses more math, physics or chemistry?

>>11465584
why?

>>11465696
Do you realize how stupid you sound?
>why does this make sense
It just does. It's a valid mathematical expression.

>>11465563
[math]((x^2+y^2(3x-19)/28)[/math]

Are atomic bombs capable of killing spores? Bacteria? Is the radiation strong enough to kill viruses? I know that in the old days humans used to genetically manipulate things by throwing some radiation at it and then selecting the best results, but how much rad is that compared to the amount that lingers after an atomic bomb?

>>11464566
geometry is just a way to visualize

>working in C
>if n = p(z) where z is an eigenvalue of t then n is an eigenvalue of p(t)
makes sense
>now prove that if n is an eigenvalue of t, it = p(z) for some z eigenvalue of t
how prove this?

icing on the cake it no longer holds if we are working on R and not C. helps pleez?

>>11465613
I'd say overall physics, but it also depends on the specific topics in physics or chemistry that you're comparing. From my experience, in general the theoretical physics gets math heavy quicker and uses more of it than chemistry. Past undergrad though this distinction may not hold. Some areas in chemistry (Pchem in particular) look very much like physics, so they're more evenly matched there. If you're in experimental for either one, then you're not using much advanced math past statistics.

dont really know where else to ask this:
my EE prof said that in order to solve a symbolic system of equations (we're doing Laplace transforms) you need to use Kramer's rule. if i put the equations into my ti-89, though, it spits out an answer just fine. is this a valid answer? do i have to somehow tell the calculator that the system is symbolic?

>>11466085
Could you actually state the problem?

>>11466210
>in order to solve a symbolic system of equations (we're doing Laplace transforms) you need to use Kramer's rule.
Nah, you can use row operations just like any other system. He probably just didn't know hand-held calculators had that feature. The result is valid.

>>11466227
i see, thanks furry-kun

what's the best free place to find sources and studies online? i want something professional that can be included in a paper

>>11466234
I use freefullpdf.com for my geology work and it's done me well.

>>11466217
for n, z in C, prove that n is an eigenvalue of p(t) if and only if n = p(z) where z is an eigenvalue of t

, then show that this does not hold true if n,z are in R

>>11466217
>>11466284
the first part seems intuitive, that if n = p(z) then its an eigenvalue of p(t) for R and C, but its the bit about logical equivalence, the iff statement that im struggling with

This is a very retarded question about field operators but here it goes. What's the commutation relation between a creation operator, a+ with the Fourier exponential exp(i k x). I know it should be zero but when I think of it it isn't right. Can anyone explain me why? I believe the creation operator has a d/dx inside it so it shouldn't commute with a+. I know I'm wrong but what's wrong with my reasoning?

>>11466294
*so it shouldn't commute with the exponential.

why do i keep getting only two zeros for this? shouldnt it have 4? no combination of 24.96 and 0.06 multiplies out to 600

>>11465578
thank youuuu

So sometime people say stuff like "using choice, we can prove that such an x exists, but we can't explicitly construct x".
What do they mean by "construct" in this context? Do they mean supplying a predicate p such that [math]\forall y(p \iff y \in x)[/math]?

i want to understand reality, why is math so much harder than humanities? how do i make it easier? i tried sleepin normally but truly sleep deprived makes me clear. but then fatigue gets me falling asleep, but it stops the chatter. and psychedelic drugs amp the patterns. i just wanna know and be fast, help me please?

>>11464590
microbiology and various cultivation related things like yeast (for homebrewing) and mushrooms. you can apply the scientific method to your cultivation attempts, and if you git gud you can have your own sterile lab in your home. also, needing to control environmental paramaters quickly leads one into diy electronics, another /sci/ hobby.

Learning about generators of the Lorentz group O(1, 3) today; lie algebra in general. I got the requirement for transformations must be of the form [math]\Lambda^\intercal \eta \Lambda = \eta[/math] and then reaching [math]L^\intercal \eta + \eta L = 0[/math] by setting [math]\Lambda = \delta^{\mu}_{\nu} + \epsilon L[/math].
For L, I get that it's a matrix of form [math]\begin{bmatrix}
0 & b & c & d \\
b & 0 & g & h \\
c & -g & 0 & l \\
d & -h & -l & 0
\end{bmatrix}[/math]
Is this correct so far? Pretty sure I can work out the basis generators from L and work out the lie bracket and all that jazz from here, just wanna make sure I'm doing things right so far.

is there work for chemE's outside of plant work? I'm finishing my degree and i hate working with industrial machines. Should've done physics lmao.

Any engineer got into consulting? how's the job like? EE looking to join a consulting firm because I heard the job is comfy

>>11467112
Looks good to me.

>>11466294
Remember that [math]a^\dagger[/math] is a sum of both [math]\hat{x}[/math] and [math]\hat{p}[/math], and the Fourier kernel [math]\exp(-ipx) = \langle p,x\rangle[/math] is a braket of the eigenstates of both. In other words it is an eigenstate of [math]a^\dagger[/math].

>>11459891
Both: [math]x+iy=re^{i \theta} =r cos(\theta) + i r sen(\theta)[/math] where [math]r=x^2+y^2[/math] and [math]\theta = arg(x+iy)[/math]

>>11467828
[math]r^{2}=x^2+y^2[/math]

>>11464174
I guess I really am a newfag

HELP ME I'M MENTALLY RETARDED (INBRED AND HAD MANY BRAIN ACCIDENTS) WHAT TO DO TO GET BACK NORMAL AGAIN OR CAN I DEVELOP THE SAVANT SYNDROME SOMEHOW?

>>11454375
libgen.is link broke

So is it called COVID-19 or Corona virus?
I'm assuming the latter is a general name and the former is a strain.

How far does a virus have to mutate to be considered a new strain?

Ok, lads. So, I'm given an SU(5) invariant potential:
[math] V(\Sigma) = -\frac{\mu^2}{2} Tr(\Sigma^2) + frac{a}{4} [Tr(\Sigma^2)]^2 [/math]

where [math]\Sigma = \Sigma_a T_a [/math] where [math] a = 1,...,24 [/math]. [math] T_a [/math] are the SU(5) generators and [math] \Sigma_a[/math] are the fields of my theory.

I was thinking that the kinetic term should be [math] Tr(\partial_{\mu} \Sigma \partial^\mu \Sigma) [/math], but I'm not sure.

Also if I wanted to make the theory Gauge invariant, I would only have to change the derivatives for the covariant derivatives, right?

[math] D_{\mu} = \partial_{\mu} - i g_a T_a A^a_{\mu} [/math]

>>11468579
The last term in the potential should be [math] \frac{a}{4} [Tr(\Sigma^2)]^2[/math]

What are some textbooks that are good for self-study? Any subject.

I'm working on some path counting problems where the width of the grid is M units and height is N units. The most common version of the problem is the one where start/end points are diagonal (i.e. start bottom-left, end upper-right, and can only move up or right). That one is easy and the number of possible paths between the points can be calculated as (M+N)!/(M!*N!). However, how would I approach a similar problem where paths start at lets say bottom-left corner and end at upper-left corner with the added requirement that some predetermined number of right-steps (and the same number of left-steps) must be used for each path (so going straight up is not a valid path)

>>11468482
COVID-19 is the disease

>>11466284
I still have literally no idea what you're asking. Is [math]p[/math] a polynomial and you're doing babby functional calculus on matrices?
Is [math]p[/math] continuous and you're doing autistic functional calculus on spectral measures?
Also, for the counterexample, try the [math]J[/math] operator of multiplication by [math]i[/math] in [math]\mathbb{C}^n = \mathbb{R}^2[/math] and notice that is squares to the negative identity.
>>11466355
>what are multiplicities
>>11466521
>Do they mean supplying a predicate p such that ∀y(p⟺y∈x)?
No, they mean explicitly giving the object desired.
As in, I want to demonstrate that [math]f(x)[/math] is integrable. A constructive proof would be literally writing down its integral, or giving an approximation procedure and showing its well defined. A non-constructive proof would be assuming it doesn't exist and deriving a contradiction.
>>11468450
Works for me.
Try https://libgen.is/
>>11468603
Melnikov's Exercises in Graph Theory.
>>11468666
We split up the path into two components: the vertical path (which is trivial, since it's up up up) and the horizontal path (which I think was actually a classical problem of moving back and forth in one direction, but I don't know the name).
So, you compute the number of possible horizontal paths, and then find the number of ways you can "embed" them into a full path (so you can think of any "full" path as a word made of the letters "h" for horizontal and "v" for vertical).

>>11468946
Yeah. i figured that counterexample for R2 as I was walking the library, basically a new eigenvector is generated upon repeated transformation for R, or is able to, meaning eigenvectors of p(t) can be not based on eigenvectors of t, for R

however the proof for C requires that eigenvectors of p(t) must be based on eigenvectors of T and that repeated transformation cant generate new eigenvectors. Intuition says its because potential new eigenvectors would be already included due to rotatey nature of complex eigenvalues but im not 100% sure

p is a polynomial of linear operators or numbers. im doing linear algebra

>>11469208
>Intuition says its because potential new eigenvectors would be already included due to rotatey nature of complex eigenvalues but im not 100% sure
Ah, so a counting argument, like this?
[math]Ax= \lambda x[/math] implies [math]p(A)x= p( \lambda ) x[/math]. If we have a basis of eigenvectors [math]x_i[/math] of [math]A[/math], we also have a basis of eigenvectors of [math]p(A)[/math], and then it follows trivially.

>>11468579
Ok lads, I found out how to do it in the end. It should be:

[math] Tr[(D_\mu \Sigma)^{\dagger} (D^\mu \Sigma)] [/math]

Where [math] D_\mu = \partial_\mu - ig A_\mu^a \hat{T}_a [/math]

[math] \hat{T}_a \Sigma [/math] is the leading term when you're doing a gauge transformation on [math] \Sigma [\math], i.e. [math] \hat{T}_a \Sigma = [T_a,\Sigma] [/math]

>>11454375
What's equation for Poisson distrubution, or where can I find a thing where I do just plug in values?

>>11468946
Ok sure, but I was thinking more about objects like non-principal ultrafilters.
The axiom of choice tells us such an object exists, but we can't "construct" it.
If we "literally write down" such an object, then how would that be different from specifying for all x whether x is in the ultrafilter or not?
I realize the axiom of choice implies the law of excluded middle, though.
Is it universally true that you can only prove the existence of an object whose elements are unknown to you by invoking excluded middle?

>>11469208
Try proving that [math]f(z)g(z)=h(z)[/math] implies [math]f(A)g(A)=h(A)[/math] and using that to factor the polynomial and induct on dimension.
>>11469373
Basically, consider the existence theorem for bases of vector spaces.
It doesn't produce "this specific, canonical" base, it produces "some" base, which can be thought of as "randomly chosen". In a sense, the axiom of choice "randomly chooses an infinite number of times", so it doesn't make sense to speak of an object "constructed" by the axiom of choice.
In comparison, the proof in the finite dimensional case requires randomly choosing some element of the vector space a couple of times, which "sounds" non-constructive, but if you construct a finite dimensional vector space for me, I can concretely apply the procedure to obtain a base.

>>11469432
>induct on dimension
Induct on the polynomial's order.

>>11469432
so first off im assuming by A you mean the n i was referring to. second of all, im really confused by what you mean in sum. what are f,g, and h, why does factoring help, and why is induction necessary, and what exactly would i be inducting?
>inb4 ur retarded
no

>>11468579
Yep. Geometrically your fields are sections of the principal adjoint bundle [math]P=\operatorname{ad}\mathfrak{g} \rightarrow M[/math] and the covariant derivative [math]D = d+A[/math] acts as [math]D=d+\operatorname{ad}_A[/math] on the associated vector bundle [math]P\times_G V [/math].
Or alternatively think of [math]\Sigma: M\rightarrow \mathfrak{su}(5)[/math] as a NLSM and pull-back the principal gauge [math]SU(5)[/math]-gauge bundle [math]P\rightarrow \mathfrak{su}(5)[/math] defined with the canonical adjoint representation to [math]\Sigma^* P\rightarrow M[/math].
>>11467112
[math]\Lambda \in SO(1,3)[/math] and [math]L\in\mathfrak{so}(1,3)[/math] right? Then [math][\eta,\Lambda] = [\eta,1+\epsilon L] = \epsilon[\eta,L] = 0[/math]. I don't know how you got [math]\{\eta,L\}=0[/math], unless I misunderstood what your [math]\epsilon[/math] means.

im retarded when it comes to math but what formula would i need to figure out how many days a storage device would last if i wrote 100 gbs a day up until i hit its tbw rating, just want to know so i can compare it to other ones

Can somebody explain this basic shit to me?

shouldn't this be a(sub)1+a(sub)2+a(sub)3+a(sub)4 ?

if a(sub)j are just variables how can you sum them?

>>11470367
Just sum them lmao

>>11470379
isn't a(sub)j just the notation to say that there are four variables? i don't get it

>>11470410
[math]\sum_{j=1}^4 a_j[/math] is short-hand for [math]a_1 + a_2 + a_3 + a_4[/math]. That's all there is to it.

>>11470226
[math]A[/math] is a matrix.
[math]f[/math], [math]g[/math] and [math]h[/math] are polynomials.
Factoring helps because induction.
Induction isn't necessary, it's just a proof strategy.
You'd be inducting on the degree of the polynomial.

>>11470523
So that's the answer?

>>11470526
honestly i do not udnerstand

for the first time i have to skip a problem in this book, oh well so sad

Is it possible that momentum secretly behaves similarly to electrical charge? That is, there is a weak attractive force between two objects based on the difference in their momentum.

what are the chances i can get into a chinese professors lab and get him to be my advisor if all his phd students are chinese as well except one visiting student from poland?

>>11470529
Yes? I'm not sure what you're looking for. You're asking why people can write x + y when x and y are "just variables". Of course you can sum variables.

>>11470635
Intrinsically? No. However the (screened) Coulomb potential reads [math]-\sum_k \frac{\lambda}{k^2+q^2}[/math] so coupling between particles with different momenta is possible through Coulomb.

>>11470862
Does that mean that a particle that is somehow moving in a direction opposite to its own momentum would have a tendency to "stick" to other particles that lacked this anomalous property?

>>11470867
Just through Coulomb? No. However with electron-phonon coupling, [math]q \sim \omega[/math] where [math]\omega[/math] is the effective phonon frequency, and this can be tuned such that the Coulomb potential becomes attractive in a certain region. These then allow electrons to form Cooper pairs [math]c_k^\dagger c_{-k}^\dagger[/math] at which point superconductivity occurs.

>>11470877
I just looked up what a phonon is. It sounds like superconductivity occurs due to the material having an extremely low elasticity and thus an extremely fast speed of sound. Is there more to the story than that?

>>11470940
Read Tinkham or de Gennes hun.

riddle me this /sci/

pseudocode for Jacobi method and Guass-Seidel method is the same everywhere I look, but the methods are supposed to do something else (on wikipedia, for example)

tell me in what way am I retarded please

>>11470836
Because the exercise says that the only answer is one if the following:

a(sub)j = 2 ;
a(sub)j = j ;
a(sub)j = 2 - j ;
a(sub)j = j^2 ;
a(sub)j = 2/j ;
a(sub)j = sin(j(pi symbol))

>>11471553

>>11471553
>>11471574
I understand now, thanks /sci/. I always seem to figure shit out after posting it here.

What's the deal with antibiotic-resistant bacteria?
How come there isn't way more of it given how much antibiotics are used (in cattle and humans)?

>>11471628
bonus:
Are antibiotics a "stopgap" measure?

I've seen news of computers making new antibiotics (combinations) capable of killing previously resistant strains, but won't the bacteria eventually become resistant to that too?

>>11470352
>literally one minute googling what the fuck you're asking later
First, convert the TBW rating to GBW by GBW=1000TBW.
Then it's GBW/(GB/D), in words, the gigabites written rating divided by the number of gigabites written per day.
>>11471561
Give context.

>>11471628
>antibiotic-resistant bacteria
antibiotic-resistant bacteria isn't resistant to the human immune system. the problem is when bacteria that the body already struggles/can't defeat becomes a super bug.
even worse is if this bacteria is very infectious, lethal and can't be dealt with by the immune system alone. if this happen then this might actually be the end of humans or at least most of them.

>>11471641
see >>11470367

>>11454375
Does my proof work? Picrel, seems too simple.

>>11471890
It works, yeah.
>too short
It's set theory, of course it's short.

>>11471903
Glad it works, yeah this us for an analysis class and were coming from rudins chapter into topology were every proof is long as shit (if you iron out the details at least) so 2-3 line proofs are very suspicious to me.

why is Anthraquinone illegal? is it toxic?

>>11472007
I mean, you could be extremely formal, but it doesn't really matter.
For a), you'd have something like [math]f(f^{-1}(E)) = \{ f(x) \in \mathbb{Y} : x \in f^{-1} (E) \} = \{ f(x) \in \mathbb{Y} : x \in \mathbb{X} \wedge f(x) \in E \} \subset E[/math].

>>11472117
Yeah I dont see the need to be annoyingly formal, as long as the argument and well presented my prof is happy and so im I.
Thanks for the help bros.

>>11470775
bump

>>11454375
SQT is a fucking farce. I posted a simple conjecture I had here a few months back, and all I got was shit for asking it and obtuse half-answers (that didn't actually solve anything) from the 2hu avatarfags because they love to blow every math/physics question out of proportion with their oh-so-sophisticated mathematical machinery, regardless of the context of the problem.
Well anyway I found 2 papers that present 2 different proofs of it as throwaway lemmas (because it was a stupid question after all, and yes I am the brainlet too for not being able to solve it myself), 1 very recently and the other about 2 decades back. Both proofs fairly short and straightforward, no need to invoke 50 different techniques from some obscure yellow book.

Neurogenesis

Do the newly generated neurons in the Dentate Gyrus express Cholecystokinin?

>>11472326
you arent white lmao

>>11472419
nevermind, people, I found it
https://www.frontiersin.org/articles/10.3389/fncel.2013.00013/full

>>11472448
Rofl

>>11464350
that happens to me at least once a week

>>11469432
>>11468946
i get what ur saying about that proof of f(z)=f(A), i dont really know where to go from there. i'll give u some background though, im reading sheldon axlers book and he has this whole bit where he does this:

to show eigenvalues of a complex space, he writes a spanning list of V with v, Tv, T^2v, etc, so uts not linear independent

then 0 = av+a2Tv+a3T^2v, etc where as arent 0, thus factorable into a complex polynomial, where the roots make the polynomial not injective thus being eigenvalues. Now, my idea is somehow showing that when you replace T with p(T) and then create some polynomial out of p(T), the a's will change in such a way to make the roots equal to p(lambda), contrasted against p(T) as in q(p(t)) = (p(t)-lam1)(p(t)-lam2)... etc. but i suck at algebra and am adhd fogbrain , can you help? im gonna check the solutions too, for the first time in the book, ill post what i find

how do i make a cleaner burning fire? its cozy and helpful to my mental health to watch a fire at night, so i filled my cup with 1/10 cup olive oil and dunked some paper towels into it. it burned for about an hour and made me very cozy but it set off the smoke alarm twice. also, i bet it will cause brain damage to inhale smoke every night. how do i make a clean burning lamp?

does any enclosed piece of metal constitute a faraday cage? can i wrap aluminum foil around an object and walk through a detector and not trip off the barcode thing? i want to steal a book from the library cause i dont have a library card

>>11472947
eye found it

>>11472956
wow algebra is so funny. such triviality yet it passed me by for days. how does one parse the intuition of these ages and depths of simple equivalences?

why am i allowed to have a gf if im retarded? isnt this immoral because men should lead the woman and i cant lead if im retarded? how do i become smart so i can lead her properly

>>11471890
Fing

>>11454375
okay, there are a lot of zoonotic diseases, viruses that originate in animals, that end up in humans and then it's very bad.
Are there any viruses that originate in humans, that get passed over to animals and then fuck them up?

Why is /sci/ such a shithole full of retards? I'm sure 80% of the people here are below 90 IQ

Ignoring social stigma, are there any inherent dangers to cannibalism in humans?
What about wide-spread cannibalism, like say multiple tribes where it occurs frequently?
Is cannibalism amongst humans more risky (to the eater) than cannibalism between other animals?

>>11473606
>are there any inherent dangers to cannibalism in humans?
You can contract (serious) diseases through cannibalism. Most viral stuff like HIV will die in cooking (it goes without saying that eating raw people is _extremely_ dangerous) but not everything will.
The prototypical example of this is Kuru, a prion disease (basically mad cow but for people) that was rampant in tribal Papua New Guinea because their funeral practices involved eating their dead tribesmember, from whom they would then catch the disease.

Can someone please explain how to design digital filters?
Say I wanna filter the frequency [math]\frac{3 \pi}{16}[/math] out of a signal, as in eliminate that frequency, how would I do so?

>>11473617
I thought Kuru only affected those who ate the brain tissue (In regards to the PNG case, the oldest son/male relative of the deceased), and not in general the others who ate other cuts?

I've read accounts of Holodomor (1932-33) no cannibalism-related diseases popped up even though it was rampant (though it may be that the conditions they lived in masked it)

>>11470285
>Λ∈SO(1,3) and L∈so(1,3) right?
yea
I got to L⊺η+ηL=0 just by substitution, mspaint because i can't be arsed to latex rn

https://youtu.be/UulqkJzpSaA

Gonna try a science themed tea & chill session in 5 hours here, if you're quarantine and bored.
Currently thinking of broad topics, ideas?

>>11454375
Help a retard out.
What is:
f([math]\pmatrix{a& b\\ c& d} [\math]) = (a + d) + (b + d)x

With respect to the standard basis for degree 2 polynomials and the standard 2x2 basis?

>>11474580
Can't even into type setting.

How long do you think it will take until the first attempt at building a space station with artificial gravity happens?

>>11473939
You're out of luck, that's the one frequency that cannot be removed from any signal

Did i do this right

I want to prove that [math]\lim_{(x,y)\rightarrow (0,0)}xy\log(x^2+y^2)=0[/math] (I don't even know if this is true yet).

My work:
[math]
\forall \epsilon>0 \ \exists \delta=\epsilon^{1/4}>0 \text{ such that,}\\
0<|x|,|y|<\sqrt{(x-0)^2+(y-0)^2}<\delta \\
\implies |xy\log(x^2+y^2)-0| \leq|x||y||x^2+y^2|<\delta^4=\epsilon\\
\mathbb{Q}.\mathbb{E}.\mathbb{D}.?
[/math]

>>11472963
It happens every now and then.
>>11474681
Am I reading it wrong or did you bound [math]|log(x)| < |x|[/math]?
Because that doesn't work.
I'd probably solve it like this: set [math]a(t) = min_{||(x, y)|| = t^2} xy[/math], [math]b(t) = max_{||(x, y)||= t^2} xy[/math].
These are two classical, easy to solve maximization/minimization problems (I recall that maximization occured with (c, c) and minimization with (c, -c) ), and you'll get a somewhat clean function of t.
Then, [math]\lim _{t \rightarrow 0} a(t)log(t^2) \leq \lim _{(x, y) \rightarrow 0} xy ~ \log(x^2+y^2) \leq \lim _{t \rightarrow 0} b(t)log(t^2)[/math].
Then I'd just throw L'Hospital at it like a faggot.

>>11474824
Buncha fucking typos, Jesus Christ.

>>11474681
It is poorly written. Your assumption should be [math] |(x,y)| < \delta [/math], and you are supposed to derive other stuff from that in steps. Instead you omit your actual assumption and instead you mix on some of the steps into a derived and somewhat malformed assumption.

how does one "think outside of the box"? i try to solve equations for like 30 minutes straight with no clue how to go about it. i don't think spending more time on it is the solution. i'm not even talking about unsolved by modern math sort of equations, just simple integrals

>>11474824
This is the way I learned it from Kenneth A. Ross, the derivation you talk about you'll write in a discussion not in your formal proof.

why can't anything go faster than the speed of light?

>>11474824
Oh damn, yeah you read that correctly I made an error in that inequality. I will look at it again.

>>11474955
This comes from the fact that the speed of light is the same in all reference frames, this is just a fact of nature.

Is there any reliable information about benefits or side-effects of noopept?
When I looked around it was hard to figure out if it's risky or not.

>>11475156
I wouldn't mess around with stuff that is meant for mentally retarded people, unless of course you are...

>>11471890
Termina el ejercicio. ¿Qué condiciones hacen falta, separadamente, para que se cumpla la igualdad en a) y en b)?

>>11475283
Of the top of my head, In both cases f would need to be a 1-1 mapping.

I dont think that was part of the exercise tho

>>11474969
some things could be slower, some things could be faster
I don't see how that prohibits from something moving faster than light

which is better, EE or ChemE?

>>11475335
>better
What do you want to do? They're both good disciplines

>>11475335
EE no doubt

I coughed onto a sterile petri dish, in a sterile setting. How do I check it for COVID-19?

>>11475305
>Of the top of my head, In both cases f would need to be a 1-1 mapping.
Nope.
Assuming anon means "for all E", you can get a pretty nice necessary and sufficient condition.

>>11464350
fucking hate this. especially when i go through a much much longer method when all i need is something very simple.

>>11475466
Theres no such thing as virus cultures you fucking idiot

>>11472016
anyone? i want to add that it's found in yerba mate and many other herbs.
the official statement bans it because they say it has laxative properties that could be potentially cause problems after a long time but other studies online said it is highly radioactive and carcinogenic while others said its shown to lower the chance of getting cancer, autoimmune and diabetes and to be overall healthy and very good for the body.
so which one is it? cancer, diarrhea or good

i'm a first year, if seeing a question like this makes me reevaluate my degree choice then what are my chances

>>11475516
Yes there is, it's what you call a culture of bacteria that has the virus.

>>11475516
>http://simulab.ltt.com.au/4/laboratory/personalstudy/psVirusCulture.htm
>https://en.wikipedia.org/wiki/Viral_culture

>>11475308
Essentially the Gallileian-Newtonian way you are thinking implies the speed of light relative to any reference frame could be reduced to zero, or reduced at all. All observations indicate however that this is simply not the case. Light propagates through space with definite speed independent from the source or observer. I could explain why this implies the speed of light is the limit but I'm not a science communicator so it would involve some maths. Actually all you need is Pythagoras

>>11475591
Literally use the definitions they offer you write them down and write them down with the information you are given

>>11475609
i meant more in the "i hate this stuff" category. calculus and stuff is great but discrete math or whatever it's called is just dull

>>11475626
Why do you hate algebra desu?

>>11475626
Just suck it up for now

When you reach further into your undergrad you usually have more freedom to choose the subject areas you enjoy. Meaning you can avoid algebra if you wished.

>>11475466
Depends how much money do you have?

>>11475636
i think i just get no satisfaction from answering it

>>11475651
0 dollars but I do have an at home industrial strength sterile lab and some equipment.

>>11475677
I'd suggest looking if there are any antibodies that bind with with some antigen COVID produces and see if you can somehow observe the binding process, discoloring or something. the nice thing about antibodies is they only work specifically to one molecule (a rather large molecule though) so you dont have to worry about it reacting to the other macromolecules in your coogh

>>11475371
I'm not sure. I like maths and physics but I think i'm too low IQ to pursue a degree in either of those. I'm not too excited to work with my hands though, like soldiering and stuff, which I heard there is a lot of in EE.

>>11475371
Not the anon that asked the question, but suppousing I wanted to get into bio/pharma/genetics, which would provide a better path.

>>11475693
how bout you do all that stuff and then just tell me what to do

pls

Explain to me the difference between chaotic and periodic phenomena, why does math make a distinction between periodic and chaotic systems? Isn't every "chaotic" system just a highly complex periodic system?

chaotic systems don't necessarily have a sequences of values that exactly repeat themselves actually they tend not to

if I have the starting center coord and radius for two circles, how do i find the intersection of two spheres if I know they only intersect once?

like in my pic, if I know circle 1 on the left starts at x,y,z coords (1, 1, 0) with r=1 and circle 2 starts at (3, 1, 0) with r=1, how can i find the intersection point

>>11475734
Nigga, chaotic systems are periodic since they can be replicated through systems. They’ve gotta do with that valued of dS = dH/dT for thermo.

>>11475789
There's a unique line [math]l[/math] that goes through both circle's centers, and also through the point of tangency.
So you just write down the formula for the line and solve for the point in it at the right distance from one of the centers.
Hint: try using vector bullshit.

>>11475801
I think there was also a neat formula that you could use to compute it as a convex combination, but I forgot it.

>>11475801
I found how to get the line that goes through both points, for my image example its:
0x-2y=-2

so the point of tangenency is in this line, so next is "solve for the point in it at the right distance from one of the centers."

how do i find out which point to solve for?

my two circles wont always be right next to each other, they might intersect on the bottom/top or other sides too (but always only one intersection)

>>11475870
Let [math]a[/math] be the center of the first circle, [math]b[/math] the second's, and [math]r[/math] the first sphere's radius.
Then, we have [math]a+ r \frac{(b-a)}{||b-a||}[/math] is the midpoint.
I'm one hundred percent sure there was a convenient convex combination formula I just can't remember tho.

>>11475883
thank you for spoonfeeding my dumb ass i really appreciate it.

so if a = (1,1) [the center of the first circle on the left] with radius =ra = 1
and b = (3,1) [center of second circle on right) with radius = rb = 1

but how do i add the coords together in the >>11475883 midpoint equation? wouldnt it be like

[math]\left(1,\:1\right)+1\left(\frac{\left(\left(3,\:1\right)-\left(1,\:1\right)\right)}{\left|\left(\left(3,\:1\right)-\left(1,\:1\right)\right)\right|}\right)[/math]

>>11475991
You haven't learned linear algebra?
Shit.
[math](3, 1)-(1, 1) = (2, 0)[/math]. This is how you subtract vectors, pointwise.
[math]||(x, y)||[/math] equals [math]\sqrt{x^2 + y^2}[/math]. In this case, [math]||(2, 0)||=2[/math].
Multiplication is done pointwise, so [math]\frac{1}{2} (2, 0) = ( \frac{2}{2} , \frac{0}{2} ) = (1, 0)[/math]. Then, [math]r (1, 0) = (r1, r0) = (r, 0) = (1, 0)[/math]
The final computatyion then reads [math](1, 1) + (1, 0) = (1+1, 1+0)= (2, 1)[/math], which is what you'd expect.

>>11476051
thanks i get it now, i had a question about how to do pointwise multiplication but i put the problem in on symbollab and can follow the steps there.

bruh i havent used linear algebra for the past 3 years, now im doing a coding challenge that uses it and it was a brain fuck at first but i feel better now. just goes to show i need to practice maths more.

thx

Would a black box that converts all matter placed inside of it into iron and heat, violate any known laws of physics?

>>11475789
Interpolate the centres in the inverse ratio of the radii. I.e. (p1*r2+p2*r1)/(r1+r2).

Let [math]G[/math], [math]H[/math] be groups and let [math]R[/math] be a ring. Is the group ring [math]R ( G \times H )[/math] isomorphic to the direct product of the group rings [math]RG[/math] and [math]RH[/math]?