/sci/ - Science & Math

I have a data set where the means of the replicates of each variable are plotted on a bar graph.
Should I calculate the sample SD or population SD for the error bars on each bar?

Does appending the constant infinity function give you the one-point compactification of the space of holomorphic functions on a (simply?) connected region, with respect to the topology of compact convergence using the spherical metric?
Please help me I'm crying auuuuuu

This reminds me of this song:
https://www.youtube.com/watch?v=_ccoZhuNlls

Following up from >>16060345

I have tried learning the mnemonics that a handful of Anons suggested and showed to me. I am still struggling to understand. I repeatedly get questions wrong during class and on my homework. I literally cannot articulate what I do not know that I do not know. Memorization has not been working, because like I predicted, something, specific to trigonometry, is compromising this ability and my memory does not seem to have been significantly impaired in any other area of my life.

Since my last post, I have tried:
>Creating flash cards of each of the trigonometric functions
>Several hundred problems' worth of trivial trigonometric function problems (i.e., given Sinθ = 3/2, find [all other trig functions])
>Consulting two professors and a half-dozen tutors on all of the above
>Borrowing 45mg of Adderall from a family member for studying (I will not be doing this again, regardless of the dose)

To seemingly no avail.

I want to learn this subject. I believe in its value, and I understand that it is an essential branch of mathematics, but I am at a complete loss as to how I can go about identifying my misunderstandings and shortcomings. I am truly beginning to believe that I have a legitimate learning disorder of this subject, artificially induced or otherwise. I hope maybe one of you might be able to intuit something.

>>16085973
I'm replying to myself but I think it is the case. Let [math]H(U)[/math] denote the collection of holomorphic functions on our region [math]U[/math]. Not really worth proving fully but you can embed [math]\mathbb{C}[/math] as a closed subset of [math]H(U)[/math] w.r.t. the topology I specified, and you can imagine how the one-point compactification of [math]H(U)[/math] restricted to this embedding would look a lot like [math]\hat{\mathbb{C}}[/math]. Pointwise projections from the compactification should force our one-point to take the value of infinity on all of [math]U[/math]... or something...
For those of you not in the know, when I say the topology of compact convergence I mean the one where a sequence of functions converges to whatever when it converges uniformly (w.r.t. the metric of whatever space these functions are mapping into) on all compact subsets of the region you're working on. Also generated by sets of the form [math]B(f,K,\varepsilon ):=\{ g:X\to Y \, | \, \sup_{x\in K} d_Y (f(x),g(x))<\varepsilon \} [/math] over all functions [math]f:X\to Y[/math], compact [math]K[/math], and all [math]\varepsilon >0[/math].
...But whatever, this is turbo-autism. Riddle me this /sqt/: should I bother attending my diffy geo class in the morning?

>>16085973
Nope. ax as a->infinity converges to infinity everywhere except at 0, where it converges to 0. So it can't converge uniformly to infinity on any compact set containing 0.

>>16086159
Lol, I see. I think the issue might be that the function space is not locally compact to begin with, hence no one-point compactification.

>>16085923
I'm getting into chemistry and I'm trying to grasp the basics. There's plenty of material out there, but it usually ommits some crucial details that would explain why things are the way they are and because of this I can't really 'understand the thing' instead of just memorizing random rules. And I can't grasp the prediction of reactions.

There's few things I wanted to ask about;
>Fe + CuCl2 -> FeCl2 + Cu
Why does iron bond with chlorine instead of copper? Is it because both Fe and Cu are metals and they replace themselves in the bond? Is this because Fe-Cl electronegativity difference is lower than Fe-Cl?
Same deal goes with
>Cl2 + NaBr -> NaCl + Br
Here halogens replace each other. I often find these rules about things 'usually replacing each other' but it's never explained why. Electronegativity? Valence similiarity? Or something else?

>AgNO3 + MgCl2 -> AgCl + Mg(NO3)2
Why exactly NO3 doesn't break here? Is it because it's bond is stronger than potentially anything else in this equation?

There's a lot of specific affinities like that of various compounds to act in a certain way. I've seen special remarks concerning acids, salts, oxides and metals in reactions. I'm sure they're valid, but I'd like to know where they come from instead of trying to memorize what compound is a salt and how it reacts with other compounds because at this stage I don't even know the reason for this classification, so it has virtually no meaning to me. Could you point to some good resources on learning reactions?

What do I read to recognize when I can apply integrals to questions I'm curious about? Is there like a compendium of estimation questions à la "Street-Fighting Mathematics" or "Guesstimation" or "The Art of Insight in Science and Engineering" but about integration specifically, in biology, chemistry, and so on? Like, I don't want to find antiderivatives, I just want to be able to recognize when I can shove a function or probability density into Python and get an answer back, i.e. when this tool is available to me as an option to answer a numerical question.

>>16086190
>Fe + CuCl2 -> FeCl2 + Cu
Ionic states. Fe ion is Fe2+/3+
Cu ion is Cu2+
like magnets + and + repels.
Cl ion is Cl- so it attracts to Fe2+ ans Cu2+
They replace themselves because of electrochemical potential
electronegativity has to do with that but is only an indicator, it doesn't have strong predictive value
>Cl2 + NaBr -> NaCl + Br
*Cl2 +2 NaBr -> 2 NaCl + Br2
Cl has much stronger electronegativity. It makes more sense. The sense behind it is quantum mechanics and too hard for humans to grasp. Like I cannot explain WHY Cl binds better than Br but we know that Cl has higher electronegativity. There's rules to this with exceptions but if you can see the patterns then you can understand quite a few reactions.
>AgNO3 + MgCl2 -> AgCl + Mg(NO3)2
NO3 has no reason to break. It can bind to Mg very well. There's nothing preventing it or. forcing it to break to NO2. NO3 is much more stable anyways because the electron cloud can be spread over more elements (this doesn't always apply. huge proteins are less stable than smaller molecules)
Don't bother learning affinities. Learn the reactions and see how and why.
Learn the easy stuff first so acid base, electrochemistry, buffers. Then you've got a decent background and see the patterns (again many exceptions)
like i didn't know that br gets replaced in that reaction but i know Cl is a smaller. molecule and binds stronger than a big molecule than Br. In a salt Na would love to bind with the strongest possible ion so it'll go with Cl- over Br-
But I honestly don't know if the reaction as you describe it will work
it seems to make sense but that doesn't mean it will work like that
chemistry isn't math, especially organic chemistry. That's basically magic pretending to be science.

What stains carpet the worst? Like incurably bad? Something worse than coffee or wine?

>>16086284
4000 yearer
Catherine

Let [math]v,\, w \in V[/math] be linearly independent vectors. I want to know, if [eqn]v \otimes v + w \otimes w[/eqn]is an elementary tensor. I'd say yes, because you can write[eqn]v \otimes v = \sum_{i,\, j \in I} (v)_{b_i} (v)_{b_j}e_{i,\, j}[/eqn]and similarly for [math]w \otimes w[/math]. So when you define[eqn](u)_{b_i} = (v)_{b_i}(w)_{b_i}[/eqn]for [math]i \in I[/math], you should get a vector [math]u \in U[/math] with[eqn]u \otimes u = v \otimes v + w \otimes w.[/eqn]Hence, [math]u \otimes u + w \otimes w[/math] should be an elementary tensor.

Is it correct? If not, were's the mistake?

v = shitted
w∈V = shitted and farted
v⊗v=∑i,j∈I(v)bi(v)bjei,j = you shitted and you farted

>>16085923
WARNING: I am retarded and never did any math past high school other than some stats for biomed

I have been filtered hard by redditors on 0.99 recurring being EXACTLY 1

I've had this shape in my head ever since
If 359.99...° is exactly 360° then does this form a circle?
If lines A and B are of infinite length with an infinitesimal angle between them then is the area between them infinity or zero?

Please explain as simply as possible and be gentle I'm a dumbass

>>16086340
Consider how it looks in [math]\mathbb{R}^2[/math]. Let
[eqn]v = \begin{pmatrix} a \\ b \end{pmatrix} \\
w = \begin{pmatrix} c \\ d \end{pmatrix}
[/eqn]
then
[eqn]v \otimes v + w \otimes w = \begin{pmatrix} a^2 + c^2 & ab + cd \\ ab + cd & b^2 + d^2 \end{pmatrix} [/eqn]

There is not always a [math] u \in \mathbb{R}^2[/math] with [math] u \otimes u = \begin{pmatrix} a^2 + c^2 & ab + cd \\ ab + cd & b^2 + d^2 \end{pmatrix} [/math] as [math] \sqrt{a^2 + b^2} \sqrt{c^2 + d^2} \neq ab + cd[/math] in general.

>>16086364
Oh great, I understand. Thanks a lot.

>>16086348
You are mixing up many topics here which leads to confusion. Infinitesimals are related to calculus and differential equations. In your question you have an area that is infinity times an infinitesimal. You can't do that, neither are numbers. The answer is undefined. You would need to learn more math to know how to handle each correctly, and you would never mix them like that.

As for [math]0.\dot{9}[/math], ask your self what number exists between it and one. It should be clear that no such number exists, they have no difference so they must be the same. Alternatively, one of the usual proof for beginners runs like this:
[eqn]\begin{align}
x &= 0.999... \\ 10x &= 9.999... \\ 10x - x &= 9.999... - 0.999... \\ 9x &= 9 \\ x &= 1
\end{align}[/eqn]

>>16086348
The area of the sector is undefined as the other anon says. You can consider the limit
[math]A = \lim_{\theta\rightarrow0}\lim_{r\rightarrow\infty} \frac{\theta r^2}{2}[/math]
The value of this limit can be 0, infinity or any number in between depending on how you fix the relation between [math]\theta[/math] and [math]r[/math]
For example if [math]\theta(r) = 1/r[/math], then A goes to infinity, if [math]\theta(r) = 1/r^3[/math], A goes to zero, if [math]\theta(r) = 2a/r^2[/math], A goes to a which can be any positive number

>>16086348
the easy explanation is math doesn't allow you to do what you set up.

what you basically have is (inf)*(inf small) and our counting system doesn't allow that.

uhhh. i'll try to be clear without using calculus.

you can calculate things that approach an infinite using limits. that is, what does the equation aproach as a number gets infinitely large or small.

the limit as 1/x aproaches infinity is zero. the denominator gets infinitely large, so it gets closer and closer to zero. "it's approaching zero"

this doesn't work with uncoupled variables. the radians (circle angle) you are measuring is not coupled to the radius of the circle. the circle can be infinitely large, and the radians can be infinitely close to zero. but they could also either be one, ten, 400 without affecting the other.

if you separate it into two equations you can solve them independently and compare answers and see how you feel about them.

the limit of the area of a slice of circle aproaches zero as the number of radians aproaches zero. the closer the other slice gets to 100% the closer the smaller slice gets to 0%.

the limit of the area of a slice of circle as the radius aproaches infinity is infinity.

both of your premises for the test you set up work as you think. somewhat intuitively you cannot combine the two and get a meaningful answer.

>>16085923
my cousin is extremely stupid
as in he's 19 and struggles with basic arithmetic. He can barely do + and -. He uses his calculator for that. He cannot for the live of him do multiplication and division. He just guesses. Literally he just doesn't know how he should break down a multiplication question.
Don't even get me started on 'story questions'. Those are just straight up too hard for him.
He wants me to help him with practicing arithmetic. But honestly I've been doing this for years now. At this point I've honestly given up hope.
I can't fix him. He refuses to put in any effort and his parents quite casually admitted that I'm not really there to teach him, I'm there because I need to push him to actually study. He just doesn't study on his own.
I've honestly got no response to that. Someone who's above high school age should just simply be able to motivate himself.
Hell I can google 'arithmetic practice' on Google right now and do 10 questions.
Fuck you could just make up your own questions and just start calculating

Dead honest it's depressing to even help him. It's genuinely emotionally draining because I'm not there to help him. I'm there to be a concentration device and tell him 'okay now let's work on the problem' when he inevitably loses interest after every single problem.

There's just no way to help this guy. What should I even do at this point? I'll go there and actually just straight up leave after an hour because the whole thing is just depressing. If he can't study on his own, then there's no way that he's ever going to learn.

>>16086631
who exactly is he practicing arithmetic for? if he's an adult and that incapable there can't be anyone pushing for gim to get a job that requires it.

>>16086632
he's in school (an education level after high school but I don't think it's comparable to college level). He needs to do an arithmetic test (it's a standard kind of test that everyone there needs to do).
He's doing something in hospitality but he's failing his classes. All of them from what I've heard.
The last time I've helped him, I just did the entire thing for him because he struggles with typing, and reading.
He's only good at 2 things really that's fitness and fucking girls..my current working theory is that those 2 traits combined are fundamentally enough to breed and make his genes survive.

>>16086640
he should drop out and become a welder or something like that. wasting his time, your time, parent's time, and the teacher's time.

people who don't want to learn but show up anyway are fools

>>16086585
>the limit as 1/x aproaches infinity is zero. the denominator gets infinitely large, so it gets closer and closer to zero. "it's approaching zero"
Why do we not say that [math]0.\dot{9}[/math] is "approaching 1"? or that [math]1 - 0.\dot{9}[/math] is "approaching zero"?

>>16086644
Fair maybe I'll just suggest that
idk I'm ranting a little because I know how hopeless it is to help him but I still gotta do it
I'd rather switch with sisyphus and watch him fall into my pit of despair. Let's see if that fucker would still be happy then.

>>16086645
Because 0.999... is defined as having infinitely many 9s, not just an amount approaching infinitely many.
In contrast, we would say that 0.9, 0.99, 0.999, 0.9999, etc., where there are infinitely many terms but each has a finite number of 9s, DOES approach 1 without ever actually achieving it

>>16086645
Why don't we say that 1 is approaching 1 or pi is approaching pi? Because they're not actually changing, and neither is 0.9... . Decimal expansions are useful as ways to represent numbers, not sequences - there's a lot of sequences converging to 1 but only two decimal expansions representing it. The sequence defined by x_n = 0.(n 9s) does approach 1 without equaling it, but 0.9... does not represent that sequence and for good reasons.

When we draw a cartesian coordinate system, have we created a map from Euclidean space to R^(n) or from Euclidean vector space to R^(n)? As in, does the origin represent the zero vector or an arbitrary point in Euclidean space that we've given the coordinates (0, ... ,0)? Do the points in the cartesian plane correspond to points in Euclidean space or the associated vector space? If the plane corresponds to vectors, why can vectors be 'moved', as in translating the arrow that represents the vector?

Is the vector [x, y] an arrow that goes x in the x-direction and y in the y-direction ~anywhere~ in the plane, or is it the arrow from the origin to the point (x, y). (The book I'm reading says parentheses correspond to thinking of elements of R^(n) as points and brackets correspond to increments - vectors).

What does this all have to do with equivalence classes of directed line segments?

>>16086656
> but I still gotta do it
no you don't. the amount of fucks you can give is finite. sounds like to me you have exhausted your quota. man up and tell his parents it is not your job to fix him anymore. you have tried and you can't help someone that doesn't want to be helped. they just have to accept their son is an idiot. the most important person in this scenario is you, not your cousin.

>>16086656
You don't "gotta" do it. you want to maintain good family relations. and if honestly telling them that their son has no desire to improve or learn leads to them being mad at you, well they can go fuck themselves.

When's a linear map "canonic". I keep hearing this word, but I don't understand what it means.

hey guys, looking for some advice. i'm schizophrenic and i really hate how the meds make me feel. when i’m obsessing over math my symptoms are pretty manageable. most of my delusions will switch to math based delusions and everything just revolves around math, im able to take care of myself too. is there any job i could get where i just work on math stuff from home? i considered teaching, and though i’ve never been violent i get flighty sometimes when im unmedicated so i fear id end up ditching my own classes. can anyone think of something that might work, if not i’ll probably just stay on meds and try to find something. also im no genius, but im about to finish a computer engineering degree with pretty good grades.

>>16086348
The "area" is [math]\rho\, d\phi\, d\rho[/math].

Bump >>16086695

>>16086816
This is a slow general, chill anon.

When a charged particle spins, does its electric field change ([math]\mu _0 \epsilon _0 \frac{\partial E}{\partial t}[/math])?
Or is the resulting B field purely a result of current ([math]\mu _0 J[/math])?

>>16086190
>Fe + CuCl2 -> FeCl2 + Cu
>Cl2 + NaBr -> NaCl + Br
These are not simple ion exchanges, both of these involve redox

>Why exactly NO3 doesn't break here? Is it because it's bond is stronger than potentially anything else in this equation?
Correct

>>16086837
Neither. Particles are assumed to be point-like, they do not physically spin. "Spin" is kind of a misleading term, it is an intrinsic property of the particle just like charge and mass.

If; a, b and c are real integers, show that y(t) = e^(r*t) is a solution to a*(y') + b = 0
Note: r is a root of a*r + b = 0

Im dumb, help

>>16086865
>doesn't include c at all
even before working through this I have to ask if you copied down the problem correctly

>>16086695
you'll have to define what you mean with euclidean space. Generally speaking, if we have a finite dimensional vector space V of dimension n, then choosing a coordinate system is setting up an isomorphism between V and [math]R^n[/math] so there are maps both ways. The process of assigning coordinates to a vector in v is a map [math]V \to R^n[/math], and the process of retrieving a vector v in V from its coordinates in [math]R^n[/math] is a map [math]R^n \to V[/math].

>does the origin represent the zero vector or an arbitrary point in Euclidean space that we've given the coordinates (0, ... ,0)
0 corresponds to 0 under linear maps, we can't assign a nonzero vector the zero coordinates in a linear way (that is, a way that respects the vector space structure)

>Do the points in the cartesian plane correspond to points in Euclidean space or the associated vector space?
this is something you have to clear up, is the euclidean space not just a finite dimensional space with inner product?

>Is the vector [x, y] an arrow..
I'm assuming you mean (x,y) in [math]R^2[/math]. You may interpret this as an arrow from the origin to the point (x,y), did you see how addition of vectors gives you a new arrow?

>What does this all have to do with equivalence classes of directed line segments?
well instead of interpreting the vector (x,y) as an arrow from the origin to (x,y), we may also interpret it as a line segment with the same length and direction as the aforementioned arrow, but one that does not need to start at the origin or end at (x,y). So we may translate our line segment anywhere in the plane as long as we keep its length and direction the same. Then we identify all the equivalent line segments and say the vector (x,y) is that equivalence class.

>>16086878
Well apparently a Euclidean space is an affine space whose associated vector space is an inner product space over the reals. The associated vector space is called a Euclidean vector space and it acts additively on points in Euclidean space to translate them to other points.

My confusion lies in the fact that the Euclidean vector space itself satisfies the conditions to be a Euclidean space as it is its own Euclidean vector space. Cartesian coordinates serves as a map between the Euclidean (vector) space and the set R^n. I'm confused though about what the coordinates actually represent. Do they represent vectors or points, or is there no distinction? Why do textbooks sometimes insist on drawing vectors as arrows rooted at the origin, and sometimes free to move about?

>>16086874
Yeah, C appear in other problem

>>16086880
Okay let's just talk about finite dimensional vector spaces (which includes euclidean spaces as a subset).

If V is some finite dimensional vector space of dimension 2, we may assign to elements of V coordinates in [math]R^2[/math] by choosing a basis, or equivalently, finding an isomorphism between V and R^2. What this does, is identify each vector in V with a unique point in [math]R^2[/math]. Now [math]R^2[/math] is a vector space in its own right, so the coordinates of a vector in V is then a vector in [math]R^2[/math], and we may perform the usual operations on the coordinates (addition and scalar multiplication).

>I'm confused though about what the coordinates actually represent
the coordinates is a vector in [math]R^2[/math] representing a vector in V. This gives us a way of interpreting vectors in V (abstract mathematical concept) graphically (because we can draw things in [math]R^2[/math]), and the arrows and freely moving directed line segments you see in textbooks are all equivalent graphical interpretations.

>>16086856
>it is an intrinsic property of the particle just like charge and mass.
you're an idiot if you believe this

https://www.luminaprobiotic.com/
is this real?

>>16086924
Then give us your explanation if you believe otherwise.

Hi, I'm an Earth Scientist and I was asking questions of Chat.gpt about Milankovitch Cycles and it kept derailing the conversation to tell me about man made climate change and I'm like, "yeah, I get it, but this is not at all the question I was asking, I don't need lessons about man made climate change that is unrelated to the topic at hand."

I had a fantastic conversation about neutrino spin and the antimatter asymmetry paradox and the ongoing research into the fundamentals of the early universe but when I ask it questions related to my field I get elementary school answers trying to teach me the importance of climate change.

I feel like AI chat programs are a valuable tool for study, is there one I can use which isn't going to go off tangent because it's creators are worried I'm an 11 year old who needs a moral lesson about a subject I already know?

I'm trying to think of a name for a parent company, where the sub companies deal with mycology and botany primarily, mostly selling cultures/starts and equipment. One sub business is a mushroom spawn lab, the other is a micropropagation business, and I'd like another channel that sells some brewing related stuff or maybe just yeast cultures. The shared theme between them is high tech indoor growing stuff, and sort sciency with the sterile lab and electronic controllers and everything. I'd like a cool vibey and sciency / naturey name, but have struggled to think of anything that's not taken. Node Labs was probably my favorite that was taken. I'd like the name to work on a site that offers a lot of kits and stuff under one roof, so it won't seem out of place for a site selling mushroom cultures / kits / equipment, in vitro plantlet starters and yeast cultures / homebrew gizmos. Some names I like are Stasis, Empirica, Botanica,

Botanica is probably my favorite, but buying brewing stuff or yeast from a company named botanica seems retarded. In the future I'd like to also offer DIY synth kits maybe too. Something that evokes an image of a healthy techy utopia like pic rel

>>16087339
I don't have one, but at least I don't cling to nonsense as if it was truth
there is no framework under which an infinitely small non-spinning point "spin" (that doesn't actually spin) makes sense

How do you calculate the value of this infinite sum? The answer is 7/12 but I have no idea how to get it.

>>16087529
Clearly you're an idiot. Nothing is spinning. The term spin is a misnomer. It's an intrinsic form of angular momentum and the property was named before scientists knew what they were measuring. A century later it is still confusing people.

>>16087539
Decompose it into partial fractions. You will have to do this a several times to obtain more manageable series.

What should I study if I want to understand Noether's theorem?

>>16087587
The calculus of variations and the Euler–Lagrange equation.

>>16087587
any classical mechanics textbook should build up to it

Questions about math.
1. Is math basically just reading books and papers, and then writing your own? Is that it? Is there anything else I'm missing?
2. If I just read a lot of books and papers, and solve most exercises in the books, and I think a lot about what I read, am I on the right path? What else should I be doing?
4. What resources aside from books and papers should I use? I only know proof wiki, wikipedia, encyclopedia of math and wolfram math world.
5. Is there an age limit/maximum age to get into a phd program, do a postsdoc or get tenure? Like 40 or 50 years old? Or does age not matter as long as you can can write nice things?

>>16088371
>What else should I be doing?
Learning what number comes after 2 and before 4.

>>16088431
[math]\pi[/math]

Why does every theorem differentiate between continuous at [a,b] and differenetiable at (a,b)?

>>16088498
Because they're not equivalent conditions. The latter is strictly stronger than the former.
[math]|x|[/math] is continuous over the entirety of the reals, but not differentiable on any interval containing [math]x=0[/math]. And for a more extreme example, there's the Weierstrass function, continuous everywhere but differentiable nowhere

>>16087539 following the other guy's advice, I omitted some steps like decomposing into partial fractions cuz I'm a bit in a hurry
also fuck this site why am I being banned

Could anyone help me see where I’m going wrong with this probability question? i keep getting an answer bigger than one

>>16088859
This is what I get, but 0.12/0.0625=1.96, which is obviously false

>>16088862
[eqn]P(1/10 < Y | X < 1/2) \\
= \frac{P(1/10 < Y , X < 1/2)}{P(X < 1/2)} \\
= \frac{\int_{-\infty}^{1/2} \int_{1/10}^\infty f(x,y) dy dx}{\int_{-\infty}^{1/2} \int_{-\infty}^\infty f(x,y) dy dx} \\
= \frac{\int_{1/10}^{1/2} \int_{1/10}^x (8xy) dy dx}{\int_{0}^{1/2} \int_{0}^x (8xy) dy dx} \\
= \frac{\int_{1/10}^{1/2} (4 x^3 - \frac{1}{25} x) dx}{\int_{0}^{1/2} 4 x^3 dx} \\
= \frac{\frac{36}{625}}{\frac{1}{16}} \\
= \frac{576}{625}
[/eqn]

>>16088879
You legend, thanks a lot! Sketching the problem made it a lot better to understand

This guy was smushed between two cars and thrown off his bike over the bridge railing. He lived without any life threatening injuries.
Am I just inventing broscience physics in my head or did getting tossed onto a downward slope that caused him to roll down into the bushes diffuse all of his kinetic energy and save him? as compared to just smacking straight into flat ground

Anyone else eat popped pimples?

>>16088927
The bush branches are elastic and he had a (relatively) even body distribution upon impact, which absorbed a tremendous amount of the energy involved. If he had landed on the asphalt and/or had landed head- or legs-first, then it would either have been less absorption or less distribution, resulting in more damage.

>>16088927
The rolling is secondary and does nothing, it's the impact with the slope that matters. The amount of force experienced is proportional to the deceleration [math]\Delta v / \Delta t[/math] and in a collision [math]\Delta t[/math] is proportional to the distance it takes to stop. So impacting hard concrete hurts because it does not compress, you stop in an instant over no distance producing a large negative g-force. In this collision he hit the bush first, reducing his speed, and then the hill soil was likely wet / soft - it squished when he landed. That made the difference between a few g's of deceleration and tens of g and serious injury. He also landed fairly flat, distributing that force over the entire body instead of a single limb.

What are the best things to do to increase baseline testosterone and IQ / executive function? My anecdotal evidence, which I trust above all, suggest that lots of math/problem solving, fasting, reading (and avoiding scrolling), adequate high quality sleep and exercise are totally yuge here. Also it's sort of nebulous but in general keeping a tidy environment and staying on top of basic things like cleaning my room etc are equally important.

>>16089075
Those all sound good. Zinc helps a bit too.

>>16085923
can crispr cas 9 manipulate the covid in bats to create covid19 because wuhan labs use a lot of crispr cas 9 on everything and found on web that crispr cas 9 block mutations of covid 19

If there is a line with an angle [math]\theta[/math] respective to the X axis, and this line is tangent to a circle, if I connect circle origin to where this line intersects the circle, will this connecting line always split the angle on the other side of the line i.e. [math]\phi = 180^\circ - \theta[/math] in half? If not how it will split [math]\phi[/math]?

>>16089317
your description is unclear please provide a drawing

>>16085923
is it true that [math]x^T A x = x^T A^T x[/math] where A is any nxn matrix and x is a vector considered as an nx1 matrix

it's funny how chuds are jsut porn addicts, you know democracy is safe when chuds can only coom in paper tissues kek

>>16089384
No. It would only be true if [math]A[/math] is symmetric ([math]A = A^T[/math]).

>>16089398
can you give me one counterexample?

>>16089384
it's true. write it out as a sum. in both cases you get [math]\sum_{ij} a_{ij}x_ix_j[/math]

>>16089384
Yes, because [math]x^T A x[/math] is a [math]1\times1[/math] matrix (just a real number) and so equals its transpose [math]x^TA^Tx[/math].

>>16089494
>>16089486
thanks

>>16088927
See how he landed. He landed on his ass. If it was concrete, he'd have broken his tailbone or hipbones or something. Humans generally only survive falls like these, even from a few metres, only by pure luck. Nothing else. No technique, no judo move can save you from landing on concrete. You can only diffuse kinetic energy up to some maximum.
The bushes saved him. Also the earth. It's a lot lot softer than concrete and it saved his brittle bones.

>stadium of 100,000 people screaming is louder than 1 person screaming
trying to intuitively understand why this is. first guess is since sound is a vibration, all the waves combine to create a higher amplitude that results in higher volume?

seeing how ocean waves sometimes collide and cancel each other out (sometimes combining to get bigger), is there theoretically a a possibility of 100,000 people screaming in a specific way that the waves cancel each other out into silence (incredibly unlikely fluke type thing but theoretically possible?). is this whole line of thought about amplitudes completely retarded?

>>16089209
Do I need more than a multivitamin would provide?

If an object is laying on a line that can be any angle with respect to the ground, how is gravitational force the object exerts on the line changed when the angle of the line is changed? The object touches the line in only one point.

Real analysis is hard. So many things to prove.

>>16089628
>could add a hastily drawn MS paint diagram to clarify their question
>chooses to add an irrelevant meme image for no reason

>>16089715
alright, i thought everyone would understand what i talk about
basically, on the image i want to find component forces of G and alpha = 45°

>>16089560
No you're thinking about it correctly
That's how noise canceling headphones work, they generate a wave that's the opposite of the noise
Another thing is that 100 people screaming will not be 100 times louder because human perception of sound is logarithmic

>>16089735
If you simply want to break G into components parallel and perpendicular to the ramp, you will have G sin alpha directed down the ramp, and G cos alpha directed into the ramp.

It looks like you drew two contact points, each of which may have a friction and normal force, so breaking G into components is just part of the problem

Why does this hold? I don't really get O notation , I thought it just meant that a = O(b) if b grows faster than a(for example when x->infty), but 3x^4 grows slower than the LHS?

>>16090047
>but 3x^4 grows slower than the LHS?
no it doesn't

>>16090047
read the definition of big O again carefully

>>16088498
because most proofs rely on an open neighborhood of points in the interval. If you have a closed interval, the extremities doesn't have an open neighborhood around them. But if you use an open interval, any point in it has open intervals that contain it

I want to get a microscope how do I keep an eye out for an okay cheap one
How do I get into this as hobby

>>16090047
>>16090047
f=O(g) (or f∈O(g)) means that f,g grow at the same rate. f(x)<ag(x) and g(x)<bf(x) for some constants a,b and all x greater than some lower bound (i.e. you can ignore the behaviour for "small" x). For a polynomial, you ignore all terms except the one with the largest exponent, as that will eventually dominate: x^(n+1) > kx^n for all x>k^(1/n) regardless of k.

How is the square root of 0.81 larger than 0.81?
I tried watching this but it didn't explain it well.
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:radicals/v/finding-square-root-of-decimal

>>16090629
If you take some positive number x and multiply it by a number between 0 and 1 (not including either of those), your output is smaller than x, right?
That still holds even if x itself is between 0 and 1. So if x is between 0 and 1 and you square it, it's reasonable that x will be larger than its square.

>>16085953
I'm trying to solve the 2D heat equation in cylindrical coordinates with initial condition of the form [math]1/r[/math]. The problem is as follows:

[math]
\begin{equation}
\begin{cases}
\frac{\partial u}{\partial t} = \left( \frac{\partial^2 u}{\partial r^2} + \frac{1}{r} \frac{\partial u}{\partial r} \right), & \text{for } r > 0, t > 0 \\
u(r, 0) = \frac{1}{r}, & \text{for } r > 0
\end{cases}
\end{equation}
[/math]
I separated variables and obtained the solution to the temporal part as well as the solution to the radial part which consists of a linear combination of Bessel functions.

[math]
u(r,t)=(C_1 J_0(\sqrt{\lambda}r)+C_2Y_0(\sqrt{\lambda}r))e^{-\lambda t}
[/math]


The problem that's left however is matching this solution to the initial condition. It seems impossible to do so, considering that the Bessel functions don't display this singular behaviour. Should I try approaching the problem in a different way? Any help is much appreciated.

By the way, as an alternative I thought of using the convolution:

[math]G(r)=A \int_0^\infty \ln|r-r'|\frac{1}{r'} dr'[/math]

But this doesn't seem to have an analytic solution.

>>16090881
[eqn]u(r,t) = \sqrt{\frac{\pi}{4 t}} e^{- \frac{r^2}{8 t}} I_0 \left( \frac{r^2}{8t} \right) [/eqn]

>>16090905
Thanks, I'm super dumb though and didn't realize I don't have a scalar function but a vector field in cylindrical coordinates, so the equation is actually:

[math] \begin{equation} \begin{cases} \frac{\partial u}{\partial t} = \left( \frac{\partial^2 u}{\partial r^2} + \frac{1}{r} \frac{\partial u}{\partial r} -\frac{u}{r^2}\right), & \text{for } r > 0, t > 0 \\ u(r, 0) = \frac{1}{r}, & \text{for } r > 0 \end{cases} \end{equation} [/math]

I can still solve it via separation of variables and get

[math] u(r,t)=(C_1 J_1(\sqrt{\lambda}r)+C_2Y_1(\sqrt{\lambda}r))e^{-\lambda t}[/math]

Is convolution still viable?

>>16090748
Thank you

Why is it force multiplied by distance and not force multiplied by time?

>>16091171
Work has the same units as energy, not momentum

>>16089384
it's true
[math]
<x, Ax>=<Ax, x>
[/math]
[math]
x^tAx = (Ax)^tx
[/math]
[math]
x^tAx = x^tA^tx
[/math]

>>16089712
just use complex analysis to prove them,
[math] \int_0^\infty \frac{sin(x)}{x} \, dx [/math] is extremely easy in complex

What actually is a "shadow?"
So the light hits the object and leaves a dark shape on the other side?
How?
There is light literally everywhere, how can it not just fill the space where the shadow is being projected too?

>>16091274
Light travels in (for all practical purposes) a straight line until it hits an object, at which point some is absorbed and some is reflected (at least, if the object isn't transparent). You perceive brightness by how much light is coming from a given direction.
When an object blocks light, that obviously prevents the light in question from getting behind it, and since there's comparatively little light reflecting off of whatever's behind the object, you perceive this as a shadow. There's plenty of light in the space between an object and its shadow, yes, but the catch is that that for you to see a surface, light has to reflect off of it, which requires it to be travelling to the surface in a straight line to begin with, which it can't do if the path is blocked.

Shadows aren't usually pitch-black, though, and that's because it's possible for light to reflect off of multiple surfaces, so you might get it bouncing off of a wall or something, hitting the shadowed surface at an angle, and then being able to make it into your eyes. If, on the other hand, you're out in an empty field on a bright day, there's very little to reflect light onto the surface your shadow appears on, and so it will appear extremely dark (especially relative to how bright its surroundings are).

Is this correct?

>>16091356
Why would it be wrong? It's a definition, though kind of a non-standard way of writing it.

>>16091274
>>There is light literally everywhere, how can it not just fill the space where the shadow is being projected too?
It does. Shadows on a sunny day are 10x brighter than indoor lighting

>>16091395
I want to show that the two possible contractions of the tensor are 0 each. Can I calculate this on the LC symbol / standard basis representation of the LC tensor? Or is there something I'm missing?

>>16085923
>stupid questions
Wtf is a spinor?
Like i have a representation of some algebra's spin group and those elements rotate shit. That makes sense. Why don't we just leave it at that? What is the motivation behind taking minimal ideals and maximally isotropic subspaces etc? Why do we make these new spinor objects? How do these new objects relate to our original algebra? Are we just splitting the double cover of the rotation group into two equivalent copies?

I hate math when it's simultaneously abstract and has applications. It's always either written at such a high level of abstraction that I have no idea how to do computations, or it glosses over the abstractions so I have no idea wtf is going on in the bigger picture.

As someone who knows nothing about math research, what journals should I look through first?

what's the best place to practice big o notation coding problems?

>>16092012
Look at the publications and whether it fits your field of research

>>16091662
this is why you only talk to applied physicists, and shun mathfags with extreme prejudice

>>16092041
What does that mean? Learning how to calculate big O scaling of some algorithm?

>>16091662
> Why do we make these new spinor objects?
Because we need them to describe nature.

You can justify it by saying spinors are needed to encode basic information about the topology of the group of rotations because that group is not simply connected, but the simply connected spin group is its double cover. But that is kind of after the fact, we would have only done that after experimental observation.

>>16092052

yeah. there are coding challenge places, but i'm looking for ones that demonstrate algorithmic complexity?

does some of the water split into hydrogen and oxygen when you shoot it with a bullet? or is there nowhere near enough energy to do this

>>16092484
There is no molecular reaction during the collision. You will not split water shooting it with a bullet. It would take a lot more energy to do that.

How to calculate how much time has passed in a place light years away? Lets say there is a planet that is 3000 light years away from earth. Does that mean 3000 years have passed on that planet since the observation of it's light on earth?

>>16092653
To give an exact answer you would need to know the relative velocity of the planet to us. But assuming the planet is not zipping around space at some percentage of the speed of light then we can say that yes, 3000 years has passed give or take several seconds.

>>16091563
I think that's not necessarily true, if the basis is not orthogonal.

Are the spirals of the milky way gigantic gravitational waves which emanate from the high-mass center of the galaxy? Does this explain the shape of these spirals?

>>16092676
How spiral arms form and remain in existence is still an open question. It is believed various factors are involved and they may not be the same for every galaxy. Shearing (not all parts of the galaxy rotate at the same speed), density waves causing stars to clump, influence of neighbouring galaxies and so on.

>>16091662
>I hate math when it's simultaneously abstract and has applications

I don't think that understanding spinors in terms of "minimal ideals" has much of an application compared to the usual (theoretical physicist) way of thinking about them. Basically the generators of the spin group can be represented in terms of elements of a Clifford algebra (the gamma matrices) and the spinors are the vectors acted on by this representation.

I searched and found a video, because I never even heard of minimal ideals in a spinor context:
https://www.youtube.com/watch?v=tASmO3NE4IQ

It seems it just a way to fit the spinors (which are usually thought of as vectors in a representation of the spin group) into the Clifford algebra itself (which are objects of the same type as the gamma matrices). This isn't a necessary thing to do to understand spinors, even if you want to be mathematically rigorous.

>>16091662
Basically to make my above post extremely concrete:

>Usual way of thinking:
In 4D spacetime spinors are 4 component vectors and both generators of the spin group (the double cover of the Lorentz group) and the Clifford algebra are 4x4 matrices that act on the spinors. But in the construction you are learning, they are trying to make spinors be 4x4 matrices themselves by just having one column be filled with zeros. The "minimal ideal" language is just there to make the column vector construction be basis independent, but there is no reason to treat spinors as 4x4 matrices in the first place.

>>16085923
Going through Lang's Basic Mathematics, stuck on chapter 1, section 4's exercise.
>If a is odd and b is odd, then a + b is even.
Division hasn't been introduced, which I think implies that this can be proved without division. Does this make sense?
[math]a=2m+1,\; b=2n+1[/math]
Let [math]2a=1[/math]
[math]a+b = (2m+2a)+(2n+2a) = 2m+2a+2n+2a[/math]
[math]= 2(m+a+n+a) = 2(m+n+a+a)[/math]
[math]=\boxed{2(m+n+2a)}[/math]

>>16093466
I don't understand what the idea behind [math]2a=1[/math] is. (There's also the issue of it reusing variables within the same expression, but that's another matter altogether)
Just leave it as 1.
[math]a+b=2m+1+2n+1=2m+2n+2=2(m+n+1)[/math]

>>16093472
ah, kek. You're right. I was trying to factor out 2 from the 1s individually. Also yeah, messed up with the variable names. Thanks.

>>16092676
last I heard they were basically just sound waves with massive wavelengths

MS in Data Science or MS in Bioinformatics? I'm from the US

What if you accelerate a rocket out in space from a planet. You give it some speed and turn of the engines. Then it just goes by its kinetic energy further and further into space.

Does the rocket ever fall back down to the planet? Assumimg mathematically idealized situation, no other planets or variables.

Supposedly the gravity of that planet, although becoming weaker farther away, still extends infinitely into space. So no matter how far the rocket is, the gravitational field of the planet is always eating away the kinetic energy of the rocket. So my theory is that at some point given enough time the rocket slows down, starts moving to the opposite direction and goes back to the planet where it started.

Is this right and why or why not?

>>16085923
dont want to ask /g/ this cause they suck. But how can i become a competent programmer and pass entry level comp sci courses? Ive passed all my math classes with A so far so i will have no issues with that part. thanks

>>16086656
probably have his parents find another tutor. cuz when he gets some girl pregnant by mistake the fuck are too stupid to do arithmetic so they damn sure ain't takin care of no bastard child! Then guess whose responsibility that ends up being!? YOURS! Factoring in the fact that the mother dies while giving birth...

>>16094585
You shouldn't need to be a competent programmer to pass entry-level compsci courses. Those courses are there to teach you to be a programmer. If you're struggling already then either your classes/professors are garbage, you aren't actually practicing coding, or you have no logical and algorithmic thinking abilities.
The use of math in computer science is vastly overstated by people who don't actually code. There is some math used but for most programs you won't need anything more advanced than simple arithmetic. Programming is primarily about logic and problem solving. It's more like solving puzzles rather than solving math problems. If you're struggling with that but otherwise have no problem with math then maybe you should switch your major to something that has more math involved.

>>16094647
i havent taken any programming courses or any programming at all. I just want to get into a good mindset before taking these courses.

>>16094721
Oh, well then you shouldn't have much to worry about unless you literally don't know how to use a computer.
If you want to get a head start you can just install an IDE/compiler and then follow some basic coding tutorials, like how to print "Hello World", taking input from the user, if-else statements, and loops. Look at the documentation for your language of choice if you want to learn more.
I would recommend starting with Java. Some people will suggest Python for beginners but Python has vastly different syntax from a lot of other commonly used language and has some misleading aspects like calling what are technically lists as arrays which will trip you up when you move to a more complex language.
If you really want to dive in head-first to get a really good understanding of low-level computing, then you can start with C, just know that C's standard libraries can be a bit lacking and you'll spend time reinventing the wheel for shit that other languages can handle no issue. But if you do learn to code in C you'll get a very intimate understand of computing and can move on to more advanced things like assembly. C is just one level removed from assembly, and assembly is one level removed from binary.

What is this phenomenon called and/or how does it work? I could swear I remember it being likened to a Mach effect but trying to search it just produces garbage.

>>16094750
appreciate it. Will any book on java do?

>>16094756
Hydraulic jumps

>>16094758
Excellent, thank you. I was starting to think of it in relation to the heliopause and what do you fuckin' know: more garbage search results. There's a brand of sparkling water called Pause because of fucking course there can be absolute no websearch not crowded by random bullshit.

>>16094762
lmao i just use reverse image search and gave me the answer immediately

>>16094765
Well I got that image by doing an image search (it was below a bunch of garbage so I lucked out just a little) which declined to include the wikipedia citation of it in the related materials. So fuck me, I guess.

>>16094756
>>16094765
>>16094770
Oh, scratch that. It actually DID give me a wiki in the related. The HEBREW wiki. For fuck's sake.

>>16094757
You don't really need a book to learn programming, or at least to learn a specific language. Books will help with getting an understanding of the overarching and abstract fundamentals of computer science, i.e. things like implementing data structures and algorithmic thinking, but books aren't necessary for those either. Most of what you need can be found from online tutorials and documentation. https://dev.java/learn/getting-started/ - this website for example, but I would recommend using an IDE and clicking the "compile and run" button in it instead of compiling from the command line if you're a beginner. Although if you do learn to build programs with the command line then you're going to be way ahead of your peers.
If you do decide to go with the book route, make sure your book is for a relatively recent release of Java and doesn't expect you to download files from a now-defunct website. I tried to learn C++ with a book when I was in middle school and it taught me an outdated version of C++ and I couldn't even do everything in the book because it wanted me to download asset files from a dead website.

>>16094578
If the rocket was moving perpendicular to the planet and not at an angle (which would produce a curved trajectory or orbit) then yes, eventually it would fall back to the planets surface. The velocity of the craft would be given by [math]v = v_0 - (GM/r^2)t[/math] so at some point in time the velocity would be negative and it would return. However since [math]v = dr/dt[/math] and [math]r=r(t)[/math] this is a nasty ODE to solve so I can't tell you how long or how far it would take.

>>16094757
Don't learn Java, at least not as your first language. If I was starting today then 100% it would be Python. There are tons of courses online, maybe the best one to start with would be the Google's own. It's thorough and completely free.

>>16094856
I wonder how bad Javascript with a strict linter, or even Typescript would be as first languages. They're at least curly brace based

>>16094860
Hmm, if you were focused on web-dev it wouldn't be a terrible idea. I guess there's also node-js too. But for a noob learning how to code for the first time you want a language that teaches you the core principles that can then be applied to other languages later on. Python perfectly fits that criteria.

>>16085923
>>attach an image (animal images are ideal, you can grab them from >>>/an/. Alternatively use anime from safebooru.donmai.us)
Please add maidposting to the next OP.

>>16095042

I only barely understand abstract algebra, so please help a guy out.
Consider the following: the additive group Q contains no maximal proper subgroups.
>If H is a proper additive subgroup of Q then [Q : H] = ∞; if the index were finite, say n, then H ⊃ nQ = Q, so H = Q, which isn't true.
>If we pick r ∈ Q−H then the subgroup H +Zr properly contains H with finite index (why?), so H + Zr != Q.

For the first line, I get why nQ = Q, but why would nQ be in H in the hypothetical? I dont really get the logic for second line at all. This ain't for school, im just trying to self learn stuff. Can anyone explain this to me?

Guys listen. I think i may have a concept in mind that will in principle allow us to build matter synthesis technology.

I am most likely an ignorant crazy person but the benefits are worth you wasting some time helping me work out details.

Can you explain to me details about how the exact size and shape of the two slit experiment gives rise to what interference pattern? What alterations to the space between them causes the pattern to disappear?

>>16095424
By the definition of index, H has n cosets, and for any q in Q, the bijection x |-> x+q maps one coset to another. In particular, if you start at 0 and apply this function n times, you end up cycling through the cosets and ending up back in the coset where you started, which is H. In other words, nq is in H.

>>16095542
The width of the slits is taken to be smaller than the distance between them (d) but their size does not affect the spacing between the maxima, only the contrast of the fringes; if they look blurred or not, smaller is clearer. Like any wave the interference pattern disappears if you block one slit or send the source wave through a single slit only.

One level of Tooling Workshops building requires an input of 30 units of wood and 20 units of iron, to produce an output of 60 units of tools. One level of Logging Camps building requires an input of 5 unit of tools to produce an output 60 units of wood. One level of Iron Mines building requires an input five units of wood to produce and output 20 units of iron.

i) To get a balanced economic equilibrium with no surplus or deficit of items of production of wood, units and tools, what factored form equation (if I can solve) must I solve?
ii) What factored form equation must I solve to get whole unit levels of buildings?

>>16096812
> To get a balanced economic equilibrium with no surplus or deficit of items of production of wood, units and tools
That doesn't make sense. You are always going to have an excess of tools. Follow the supply chain: 5 tools is used to produce 60 wood, 60 wood is used to produce 120 tools. There is no way to balance that.

Probability question:
Suppose I am assigned a number 1-5. If two random numbers are picked, I have a 40% chance of winning.
However, if one number is picked and then another number is picked, I have a higher chance of winning.
What gives?

>>16097104
>However, if one number is picked and then another number is picked, I have a higher chance of winning.
Explain your reasoning.

>>16096812

correction: i) To get a balanced economic equilibrium with no surplus or deficit of items of production of wood, iron and tools, given that I may construct additional levels of buildings, what factored form equation (if I can solve) must I solve?

>>16097146
>>16096812
correction ii:

One level of Tooling Workshops building requires an input of 30 units of wood and 20 units of iron, to produce an output of 60 units of tools. One level of Logging Camps building requires an input of 5 unit of tools to produce an output of 60 units of wood. One level of Iron Mines building requires an input of 5 units of tools to produce an output of 20 units of iron.

i) To get a balanced economic equilibrium with no surplus or deficit of items of production of wood, iron and tools, given that I may construct additional levels of buildings, what factored form equation (if I can solve) must I solve?

>>16097154
>input of 5 unit of tools to produce an output of 60 units of wood
>input of 5 units of tools to produce an output of 20 units of iron
>input of 30 units of wood and 20 units of iron, to produce an output of 60 units of tools
The other anon is right, one level of this setup lets you turn 10 tools into 60 tools with 30 extra wood left over.
To get a balanced economic equilibrium with no surplus or deficit, you need a MARKET PRICING MECHANISM

what are the row space, column space, null space, and the null space of the transpose

>>16097783
actually what i'm supposed to do is show the row space and null space are perpendicular to each other, and the same for the transpose but the book said the column space is a plane described by x1-x2=0 but i don't get how they did that

>>16097792
The row space is spanned by the vectors (3, 3, 4)^T and (-1,-1,5)^T. To write it in plane form you find a vector orthogonal to both for example the cross product which is (19, -19 , 0)^T.
The plane then all vectors which have a zero dot product with the normal vector above. This condition can be written as x1 - x2 = 0.

When I need to calculate the center of mass of a "circle" that is missing a quartercircle, is it correct to calculate the area and center of mass for the entire circle, then plug them into the formula for center of mass (total moments of all objects / total mass of all objects) along with negative area of the missing quartercircle and its center of mass?

I don't know very much about chemistry but I did get 94% on AP physics a decade ago. I set out to learn a little bit about the chemical processes that make diesel from crude oil and wound up learning about covalent bonding.
Now, I can roughly follow any Lewis dot explanation of bonding with only a couple difficulties just from having a brain but I've learned that:
>Lewis dot models are a bad approximation
>Molecular orbital theory is a good approximation
When I do a cursory search for molecular orbital theory the only visual models are some kind of energy level diagram like the attached image but the associated text in the places I find them implies that it is typical undergraduate homework to just create such a diagram for some given molecule from first principles with rules of thumb and no DE solving.
If MO theory is that easy, then I can learn the theory from scratch to the point of being able to do it myself before I get bored of this topic.
So
>Have I missed any intermediate approximation theories out?
>If I haven't, can you recommend me a good beginner textbook that has a chapter on the Lewis theory and then jumps to a full explanation of MO theory? I'm not afraid of calculus but I don't know any math beyond it.

>>16098134
Yes, but instead try framing it as the center of mass of three quartercircles. Easier that way.

>>16098134
X = (M1 X1 + M2 X2)/(M1+M2)
X1 = ((M1+M2)X - M2 X2)/M1

X1 is the center of mass you are trying to find X2 is the center of mass of the missing piece M1 and M2 are the corresponding masses (which are proportional to area)
X is the center of mass of the complete circle (and you may as well choose a coordinate system where this is zero)

>>16086733
When you can construct it without making arbitrary choices.
>>16095042
If you want to modify the OP pasta you should just make the new thread, change what you want changed and hope no one catches you.

Growing up my dad had a kind of spin on the stoned ape theory that he used to explain how humanity evolved. His theory was that monkeys who were too schizo to be accepted by monkey society in the trees, would be thrown down to the ground. Those plains monkeys would have to adapt and survive or else they'd be eaten. These are the animals that ended up evolving into humans. Basically sentience is a result of concentrated monkey schizophrenia.
Is there any real theory or study this is based upon? Or was my dad just feeding me his own schizo stories?

>>16098150
>Have I missed any intermediate approximation theories out?
Yes, in ochem they teach valence bond theory and orbital hybridization, which is a very useful (if not entirely accurate) off-the-cuff approximation for reactivity
>If I haven't, can you recommend me a good beginner textbook that ... jumps to a full explanation of MO theory?
[Anslyn, Dougherty] - Modern Organic Physical Chemistry

>>16098931
Your dad was either schizo or trolling you.

>>16098931
Theories like the Stoned Ape Theory and the idea of "schizo" monkeys evolving into humans lack scientific backing, other models like the cognitive niche theory and the EDSC model provide more plausible explanations for the development of human intelligence. The consensus in the scientific community is that human cognitive evolution is the result of a complex interplay of environmental, social, and biological factors .

What is meant by [math][\widetilde{V\otimes U}]_0 [/math]? Not familiar with that notation

>>16099304
well they tell u its spanned by elements of the form a, b, and c. Notice that in normal cases they all equal 0.
The tilde prob represents the free/general vector space generated by the addition and scalar multiplication rules, and nothing else. The subspace with _0 is a subspace of that free vector space from those two rules that now has extra rules for when something equals 0, so it adds a bunch of distributive properties.

So we can say something like 2v * u = v * 2u in the tensor product/quotient space V * U because they differ by 0 in the relation 2v * u - v * 2u = 0 for the subspace _0

If you consume things that kill gut bacteria are you damaging the genetic diversity of them by over culling?

>>16097135
If I have a 1 in 5 chance at winning and then a 1 in 4 opportunity, that must certainly be higher than 1 in 5 and then another 1 in 5 odds.

>>16099445
Thank you. I'm guessing it's common in algebra to give a certain structure a desirable property by considering these quotients?

>>16099524
>1/5 winning then a 1/4 winning
Bruh, u cant win both times, u can only win once. It's just 1/5 + (OR) 1/5

>>16099547
uh, idk, it's common to start with a general space then go specific by requiring specific properties. Associativity, distributivity, and commutivity aren't always true for every algebra, so it's important to say when an algebra is or isnt.
Equivalence classes is taught pretty early on in universities, and you learn about mod arithmetic (like 2 = 14 for mod 2) in HS. Quotient spaces just establish equivalences classes. Idk, use it when its needed. Understand it when its being used. *shrug*

>>16099577
That doesn't even make sense. Winning on the first draw means a 100% win and is an irrelevant statistic for the calculation.
>in the case where you have won (100%), then the chances on your odds decrease
What.

>>16099524
You have a 1/5 chance of winning the first draw, which means a 4/5 chance of losing.
In the event that this 4/5 event happens, you have a 1/4 chance of winning on the second draw.
So the odds that your second draw even happens are 4/5, and the odds that you win on it are 1/4.
Multiply those together... and you get a 1/5 chance that the second draw happens AND that you win on it.

There is no difference.

what's the theory or hypothesis or whatever which states that a person who is financially successful has the potential for exponential growth? I think I heard it in a JBPeterson lecture or his appearance on JRE. I thought it was the Pareto distribution, but I can't really find where he infers that a successful person will be more successful in the future.

White noise is stated as having equal energy across all frequencies. Some definitions I've seen state across the human audible spectrum.
What I'm wondering is if white noise contains decimal frequencies too.

For example, I know white noise would contain, among others, such frequencies as 207, 463, and 1159 Hz; but would a white noise signal also contain 207.2, 463.58, and 1159.672 Hz?

Also, what about in practice?
If white noise theoretically contains decimal frequencies, does software generators like Audacity and others typically generate white noise with decimal frequencies? Or is that too much to process and therefore only integer frequencies are generated?

>>16099764
> If white noise theoretically contains decimal frequencies
By definition white noise has the same spectral energy at every frequency.

> If white noise theoretically contains decimal frequencies
That isn't how audio is digitally encoded or produced. Raw audio data tends to be PCM, essentially a snapshot of the audio's waveform amplitude at a particular time-slice (i.e the sample rate). You would then have use a Fourier Transform to convert that into the frequency domain (or vice-versa). The frequency histogram of white noise in the ideal case would be a flat line. So your frequency histogram bucket size would have to set to produce the sample rate of the audio data you want to generate and over a range that humans can hear, ~20Hz - 20Khz

>>16099764
> If white noise theoretically contains decimal frequencies
By definition white noise has the same spectral energy at every frequency.

> does software generators like Audacity and others typically generate white noise with decimal frequencies?
That isn't how audio is digitally encoded or produced. Raw audio data tends to be PCM, essentially a snapshot of the audio's waveform amplitude at a particular time-slice (i.e the sample rate). You would then have use a Fourier Transform to convert that into the frequency domain (or vice-versa). The frequency histogram of white noise in the ideal case would be a flat line. So your frequency histogram bucket size would have to set to produce the sample rate of the audio data you want to generate and over a range that humans can hear, ~20Hz - 20Khz

In the context of time-independent perturbations, the Stark and Zeeman effect concern an external electric and magnetic (respectively) as the perturbing entities. However, in the Hamiltonian for both effects, the electric and magnetic fields are both treated classically. When looking at a specific time-dependent perturbation, namely the spontaneous emission and absorption of radiation, the Hamiltonian of the electromagnetic field is instead quantized and therefore treated in a fully quantum manner. Why is it the case that we can treat the electromagnetic field classically in the Stark and Zeeman effect, but not in the spontaneous emission and absorption of radiation?

>>16099940
> Why is it the case that we can treat the electromagnetic field classically in the Stark and Zeeman effect, but not in the spontaneous emission and absorption of radiation?
You are talking about two very different processes. Using your terminology the Hamiltonian in any Schroedinger equation is "classical". Solve the S.E for the hydrogen atom and the Hamiltonian used contains the classical Coulomb potential. What makes the answer "quantum" is placing boundary conditions on the wave function which restricts the allowed solutions. In this case it quantizes the atomic orbitals and it is the energy levels of those orbits that limits the emission and absorption of radiation.

In the case of Stark and Zeeman effect you are simply adding a "classical" perturbation to an already "classical" Hamiltonian.

>>16100059
I'm moreso wondering why physically we are able to treat the electromagnetic field classically in one case but not the other. Is it because, in the case of spontaneous emission/absorption, we are dealing with how individual photons cause excitations/are emitted, and in the Stark/Zeeman effect, we are dealing with an innumerable number of photons in the form of a electric/magnetic field that can be treated classically because we are in the classical regime?

>>16100096
There isn't any difference, it's the same kind of field in both cases. It's a field in the "classical limit" as you state. Also I'm not clear why you mean by "treat the electromagnetic field classically in one case but not the other." In the Stark + Zeeman effects you are perturbing the eigenvalues you got from earlier Q.M calculations. You can't get more "quantum" than that.

>>16099630
>what's the theory or hypothesis or whatever which states that a person who is financially successful has the potential for exponential growth?
Compound interest. Actually, "compounding investment" is probably a better name for it, but compound interest is how I've usually heard it described to the normies.

>>16085923
>Portable/directional EMP

When I think of an EMP, I think of the nuclear missile EMP from MW2. Are there smaller EMPs, perhaps even car portable or human portable?
There is so much surveillance-capable technology nowadays that you can't even walk down the street without being captured on 4k HD garage door security cameras and having your face recognized by the law enforcement face recognition databases. Unless you carry a faraday bag to hide your phone from GPS and wear a stupid coronavirus coofmask at the same time, it's almost as if you are automatically identifiable just by virtue of existing.

I was thinking of asking on /g/, but I figured you guys would be more knowledgeable. Does the technology or science exist to create a human portable device to emit electro magnetic pulses to disable/destroy security cameras and phones/computers in a short radius? Purely theoretical of course. I don't want to get you nerds in trouble.

>>16099630
retarded bullshit nvgmi

clean your room bucko

>>16100469
Forgot to mention the "partial plate recognition". I've met so many dudes in jail who got caught up just because a home security camera captured only part of their license plate.

>>16100469
Go look into explosively pumped flux compression generators, yes they are a real thing.

>>OP
is there such thing as an E2EE payment processor? I want to be able to send and receive money from someone's bank account while keeping as small a record as possible.
I know that cryptocurrency is typically used to such an end, but I don't like crypto because it's inherently speculative and counter productive. Fiat currency is a tool to facilitate transactions, and speculative cryptocurrencies are a regression to bartering.

>>16100521
I've heard of those before, but I can't find much beyond wikipedia. Do you have any sources?

>>16099940
Since things like position and momentum are treated as operators, but the scalar and vector potentials V and A arent for Stark and Zeeman effects, they're called semi-classical. For something like spontaneous decay, you can't assume like normal that A and its derivative equal 0; it would be like saying x=p=0, which violates uncertainty. When the field strength is too low, semi-classical approximations fail, so now the field needs to be quantitized to get the right answers. There's nothing wrong with trying to quantitize the field for the Stark and Zeeman effects - its just overkill. You already get good answers in practice.

It's like Rayleigh scattering; you dont need QM to describe why the sky is blue. Only classical mechanics is needed to get good results.

See Shankar 18.5 for detailed info.

>>16085923
Do animals with broader spectrum vision actually see additional colors? The way it's always presented is that IR and UV would have new incomprehensible by humans colors but could it also be the case that the same colors we see are just stretched across a wider spectrum? Take goldfish for example, easy one because they can see all three portions of the light spectrum. Would IR just be red to them, red to us maybe orange to them, and conversely UV to them just be our violet and so on?

Let V be an inner product space of dimension n and T: V -> V be linear. Is there a general formula for the orthogonal projection onto the subspace of T invariant vectors? (one that does not require choosing an o.n.b. for this subspace)

>>16100469
>>16100521
are EMPs from these explosively pumped flux compression generators directional? Can you aim them?

Also, wouldn't these be good for taking down drones? You would think that they would be using these in Ukraine, with all of the drone warfare going on.

How do I actually study?

I am pretty sure I have ADHD (no medication is imported for that in my country) I am studying medicine and until now I cruised through solely on my IQ, past exams and stuff like that.

I delayed taking the anatomy exam as long as possible. It's oral and you basically have to know everything + it's in Latin. I was never forced to sit and study like a drone over 600 pages.

Pls help

what are good whiteboard and marker brands?

>>16100583
I cant speak for the animals, but how would you imagine them seeing violet, if they see UV as violet already. Following this logic they would have to map some visible colors to "invisible" colors.

so yes, I think they see additional colors, and see UV light in the color "ultraviolet", not the color "violet"

but being able so see additional colors doesnt necessarily mean they can generally see more colors than us. most of the times their spectra are more limited than ours, but they are also often shifted into ranges humans cant see

>>16101054
find a reason to care

>>16101041
I don't think any EMP is directional. By its very nature the source will emit omni-directionally. Trying to then constrain the produced field would be *hard*. Best you could do is shielding with an open aperture.

The problem was to find the center of mass of a circle whose one quarter was replaced by a straight segment. I've found that the COM has moved further to the straight segment (I expected it would move away from it). Is my intuition correct or the COM really should move toward the straight segment? It has only moved negligably, btw (radius is 4 and the shift of COM is ~0.03).

>>16101124

I can't, I don't care about anything anymore, not even myself.

>>16101095
>ut how would you imagine them seeing violet, if they see UV as violet already
More violet and higher frequencies of indigo. I don't just mean the colors shift I mean the whole visible spectrum gets stretched outwards to IR and UV.

why are Hall voltages observed in metals? my reasoning for why they *shouldnt* be observed is that both electrons and holes carry current in a metal, roughly the same amount, and they both experience a Lorentz force in the same direction, so there shouldnt be an excess charge built up if theyre getting pushed in the same direction. this would theoretically also be true for intrinsic semiconductors. we should only observe the Hall effect in materials where one charge type dominates the current. is it the different mobilities?

>>16101350
>opposite charges
>they experience a lorentz force in the same direction
explain

My book writes electric fields in the complex notation (pic related), saying that the complex conjugate ensures the quantity is real. But it also says that [math]A(r,t)[/math] can be complex, and this doesn't make sense to me because I get:
[math]Ae^{i(kz-\omega t)}+A^*e^{-i(kz-\omega t)}=(A+A^*)\cos(kz-\omega t)[/math]
Which is not always real. What am I doing wrong?

>>16101593
A can be complex because it can contain the phase, call it delta or theta. Expand the e^i... of the LHS into sin and cos. They do not equal the right

>>16101455
well, if positive charges are moving in one direction, and negative charges are moving in the other, both of those represent the same direction of current.

What exactly is an electric charge? Physics books just state that like charges repel each other while unlike charges attract each other, but what exactly are they? Are they like atoms or something similar that’s present in all living beings?

How do I prove x+e^x is injective? I know that i need to show that x1=x2 from the equation x1+e^x1=x2+e^x2, but don't know how to. Or is it just that the derivative of it is 1+e^x and since it is always positive that means that it's strictly increasing therefore it's injective?

How can I estimate how much imbalance (in terms of radial force) a centrifuge can tolerate? The mfrs only say that I have to balance it exactly which is unreasonable

>>16101350
When u look at a (+) current through an infinitely long wire, the B field goes counter clockwise about the wire. If u look at it's (-) hole, it also goes counter clockwise. That doesn't mean the B field is twice as strong. It's use one model, OR the other, not AND.

>>16101733
trying to answer that is like trying to ask what exactly is magnetism. U go down a rabbithole. All we can really do is describe its properties. Eventually the question isnt what is electricity and what is magnetism, but how is QED described, which then goes to Electro-Weak, etc.

>>16101745
ask chat man. This is this generation's learn to google shit. It does depend on using the derivative

>>16085923
How many loud sound notifications per day get generated by Apple Watches due to the Apple Watch being near a hand dryer?

>>16101797
U need to describe a tolerance. You would also need to describe the centrifuge (a heavy centrifuge will move less than a light one). Technically all imbalance would lead to wobbling. You would also have to question things like stable or an unstable equilibrium.

I'm taking babby's first proofs, and cannot for the life of me figure out how to square this fibonacci induction.

[math][/math]
the proposition is
>Let [math]c[/math] be a given positive integer with [math]c \geq 2[/math]. Let [math]f_n[/math] be the sequence of Fibonacci numbers. Prove that for every integer [math]n \geq 1[/math], [math]f_{c+n} = f_cf_{n+1} + f_{c-1}f_n[/math].

We know [math]f_1 = f_2 = 1[/math], [math]f_r = f_{r-1} + f_{r-2}[/math] by the definition of the Fibonacci sequence, and so we can see that when [math]n = 1[/math] the proposition resolves as follows
[math]f_{c+1} = f_{c} + f{c-1}[/math]
[math]f= f_{c}f_{2} + f_{c-1}f_{1}[/math],
so the proposition is true when [math]n = 1[/math].

Then, we assume that the proposition is true for [math]n=k[/math], i.e. [math]f_{c+k} = f_cf_{k+1} + f_{c-1}f_k[/math].

Now, when trying to prove the [math]n = k+1[/math], I have to show [math]f_{c+(k+1)} = f_cf_{k+2} + f_{c-1}f_{k+1}[/math].

[math]f_{c+(k+1)} = f_{c+k} + f_{c+k-1}[/math]
[math]f_{c+(k+1)} = f_cf_{k+1} + f_{c-1}f_k + f_{c+k-1}[/math]

Is what I figured were natural first steps, but after this I'm basically stuck. [math] f_{c+k-1}[/math] can be split into [math]f_{c+k} - f_{c+k-2}[/math], but expanding further that either loops you back or leads you nowhere that seems to alter the associated terms in the correct direction.

Am I going about it all wrong, or is there some Fibonacci property I'm missing that would help me massage this? Thanks.

>>16101816
>It's use one model, OR the other, not AND.
well that's just straight up not true.

How do I know when to use direct proof, proof by contradiction or proof by contraposition?

>>16101920
There's no fixed rule for that. Often they all work. Just try them in order and find the first one that does.

>>16101892
Thats for semiconductors. Those holes are "real". For >>16101350, those holes aren't real. Ur two cases refer to different things objects.

Please explain Algebraic Geometry to me using maids

>>16101624
You are right I made a mistake, but I still don't get how E is always real. I get:
[eqn]Ae^{i(kz-\omega t)}+c.c.=Ae^{i(kz-\omega t)}+\left[Ae^{i(kz-\omega t)}\right]^*=
Ae^{i(kz-\omega t)}+A^*e^{-i(kz-\omega t)}=
A[\cos(kz-\omega t)+i\sin(kz-\omega t)] + A^*[\cos(-(kz-\omega t))+i\sin(-(kz-\omega t))]=
A[\cos(kz-\omega t)+i\sin(kz-\omega t)] + A^*[\cos(kz-\omega t)-i\sin(kz-\omega t))]=
(A+A^*)\cos(kz-\omega t)+i(A-A^*)\sin(kz-\omega t)[/eqn]
Which could still be complex

>>16102116
then why do some metals exhibit positive Hall voltages?

>>16102167
Expand out A in terms real and complex components.
[math]A=x+iy[/math]
[math]A*=x-iy[/math]
[math](A+A*)\cos=x\cos+iy\cos+x\cos-iy\cos=2x\cos[/math]
[math](A-A*)i\sin=xi\sin-y\sin-xi\sin-y\sin=-2y\sin[/math]

>>16102218
Thank you, finally I got [math]2 \Re(A) \cos(kz-\omega t)[/math], which makes sense.

>>16101889
i know nobody replied and probably nobody cares about this baby shit but my solution was assuming the proposition was true for [math]n=k-1[/math] as well, then doing
[math]f_{c+k+1} = f_{c+k} + f_{c+k-1}[/math]
[math]= (f_cf_{k+1} + f_{c-1}f_k) + ((f_cf_{k} + f_{c-1}f_{k-1}))[/math], using our fancy new assumption
[math]= f_c(f_{k+1} + f_k) + f_{c-1}(f_k + f_{k-1})[/math]
[math]= f_c(f_{k+2}) + f_{c-1}(f_{k+1})[/math],
so if it's true for [math]n = k, n = k-1[/math] then it's true for [math]n = k+1[/math].

when [math]n=2[/math] the propo says we should get [math]f_{c+2} = f_cf_3 + f_{c-1}f_2 = 2f_c + f_{c-1}[/math], which we arrive at via [math]f_{c+2} = f_{c+1} + f_c = (f_c + f_{c-1} + f_c = 2f_c + f_{c-1}[/math], so it's true for [math]n = 2[/math].

it's true for [math]n=2[/math] and [math]n=2-1=1[/math], so it must be true for [math]n=3[/math], and therefore [math]n=5, 6, ...[/math] for all positive [math]\mathbb{Z}[/math] Q-E-mothafuckin-D.

i didn't intuit that you could do induction using two assumptions if you satisfied the larger base case until just now!
[math][/math]

How do I go about to calculate
[eqn]
\sum_{j=0}^{n}\xi_j^2
[/eqn]
where each [math]\xi_j[/math] is a distinct root of [math]X^n-1[/math] over [math]\mathbb{C}[/math]?

>how can we measure the rate of time if we live in time?

thought back to how i felt that something i did just this afternoon already felt like it was done days ago, and that now i get bored so easily. it made me wonder if time itself was getting faster, such that there was legitimately more time in between each second, thus making a day longer. and yet, how could we ever prove that? we live in seconds, and if their rate changed, our experience within them would change accordingly, and yet still i personally feel as though time is just longer. twelve hours should not feel like a day or two ago, and yet it does, so has time changed, and if it did could we ever measure it?

>>16102708
[eqn]\xi_j^2 = e^{\left(\frac{2i\pi j}{n}\right)^2} = e^{\left(\frac{4i\pi j}{n}\right)} = e^{\left(\frac{4i\pi }{n}\right)^j}[/eqn]
you can recognize a sum of the terms of a geometrical sequence
[eqn]\sum_{j=0}^{n-1} q^j = \frac{1-q^n}{1-q}[/eqn]
which amounts to 0 in this case

>>16102945
You are talking about the difference between physical (chronological) time and subjective time. The human perception of time is something that has been studied but it has nothing to do with how fast experimentally measured time passes.

How to solve
[eqn]
\begin{cases}
\alpha+\beta+\gamma = -1\\
\alpha\beta+\alpha\gamma+\gamma\beta=-3\\
\alpha\beta\gamma = -2
\end{cases}
[/eqn]
I know these are Vieta's formulas, but I can't find a general way of solving them

>>16103292
[eqn]0 = (x - \alpha)(x - \beta)(x - \gamma) = x^3 + x^2 - 3x + 2[/eqn]
Let [math]x = y - \frac{1}{3} [/math]
[eqn]y^3 - \frac{10}{3} y + \frac{83}{27} [/eqn]
Plug it into the cubic formula
[eqn] y_1 = -\sqrt[3]{ \frac{83}{54} + \sqrt{ \left( \frac{83}{54} \right)^2 - \left( \frac{10}{9} \right)^3}} - \sqrt[3]{ \frac{83}{54} - \sqrt{ \left( \frac{83}{54} \right)^2 - \left( \frac{10}{9} \right)^3}} \\
y_2 = -\frac{-1 + i \sqrt{3}}{2} \sqrt[3]{ \frac{83}{54} + \sqrt{ \left( \frac{83}{54} \right)^2 - \left( \frac{10}{9} \right)^3}} - \frac{-1 - i \sqrt{3}}{2} \sqrt[3]{ \frac{83}{54} - \sqrt{ \left( \frac{83}{54} \right)^2 - \left( \frac{10}{9} \right)^3}} \\
y_3 = - \frac{-1 - i \sqrt{3}}{2} \sqrt[3]{ \frac{83}{54} + \sqrt{ \left( \frac{83}{54} \right)^2 - \left( \frac{10}{9} \right)^3}} - \frac{-1 + i \sqrt{3}}{2} \sqrt[3]{ \frac{83}{54} - \sqrt{ \left( \frac{83}{54} \right)^2 - \left( \frac{10}{9} \right)^3}}
[/eqn]
The solution of the orginal system are just those [math]-\frac{1}{3} [/math].

>>16103292
Since they're Vieta's formulas, they define a monic cubic [math]x^3-x^2-3x-2[/math] whose roots are [math]\{\alpha,\beta,\gamma\}[/math]
This cubic has no rational roots so you have to use the cubic formula (the poster above me) or a numeric method like Newton's method
There is no general way to exactly solve Vieta's formulas of arbitrary degree because of the Abel-Ruffini theorem

Why aren't cross products defined in terms of being an operation that gives you an orthogonal vector? That's their main use.

So a cross product in 2 dimensions would be a unary operation, say x, such that x e1 = e2.

>>16103399
Problem 1: Determining the magnitude of the output vector.
Problem 2: Your definition doesn't work outside of a 2-dimensional space. Even in 3 dimensions, for a given axis, there are infinitely many orthogonal axes (corresponding to all possible bases of the remaining plane)

>>16103399
Ignoring the unpleasantness of an operator with variable arity, how do you determine the magnitude and orientation of the resulting vector?

>>16103399
Have can a vector be orthogonal to two other vectors in 2d space?

>... incidence per admission
>... occurrence per admission
What is the difference? I cannot find any explanation of the difference between occurrence and difference.

>>16103378
>>16103388
I see, so there's no analytic solution without the cubic formula. Thanks guys

>>16103415
For 2D vectors, you can just do v = a e1, then X a e1 = a e2, which has the implicit choice of X e1 = e2 instead of X e1 = -e2.

>>16103416
For a 2D case it would be a unary operation, it only operates on a single vector.

>>16103439
And what of vectors beyond 2D? How, for example, would I compute the product of (1,0,0,0), (0,2,0,0), and (0,0,1,4)?

>>16103439
> it would be a unary operation
Then it wouldn't be a product would it. That requires at least two terms.

>>16103417
check this paper under the heading "Statistical analyses", they define incidence, prevalence and occurrence:
https://systematicreviewsjournal.biomedcentral.com/articles/10.1186/2046-4053-2-68

>>16103489
Nice, thanks. It makes sense now.

>>16103462
That's kinda what I'm asking. The only axioms I thought is why the generalization of the cross product isn't in the lines of prioritizing having an operation f such that for some [math]V = \{v_1,...,v_n\}[/math], then for all [math] v_i \in V, \langle v_i, f(V) \rangle = 0[/math] and we probably want [math] ||f(V)|| = \prod_{i=1}^n ||v_i||[/math] when the vectors of V are orthogonal, which is their main properties instead of trying to preserve other properties like arity or whatnot else you might have to give up.
Ideally you'd want something that reduces to the cross product in 3D.

I guess naively we could just do something like, consider the matrix [math]M[/math] formed by the vectors of [math]V[/math], and like just do [math]\displaystyle \frac{\text{ker(M)}}{||\text{ker(M)}||}\prod_{i=1}^n ||v_i||[/math] or something like that.

Which would give (0,0,-8,2).


>>16103476
You can just call it an artifact of nomenclature.

>>16103399
use bivectors

>>16103658
Do you mean [math]v \times u = \star(v \wedge u)[/math]? If so, I'm aware of it, and I do think it's a better generalization than the one that just gives a cross product in a few dimensions. Still, I kinda want to know why nobody went with the obvious of just having an operation that gives an orthogonal vector since it's the main thing.

>>16103706
iirc heaviside was part of the group that shilled for it. Big respect for the guy usually, but it was a dumb move.

ive taken a break from school and now im coming back in the fall. What can i do to prepare for diff eq?

What is the BNF/EBNF form for the english language?

Just need someone to check this for me.

>>16103749
read a simple book about it. I took a proficiency test for a diff eq class, and only studied 1 week before and still passed. It was dumb of me, but still, read the book or find oen

>>16104253
Gotcha, I'll just review my basic calc one and 2 derivatives and integrals

What are the prerequisites for David Morin: Classical mechanics ?
I am already done till calc 3 and linear algebra (also done with physics classical mechanics Taylor book)

>>16104041
context-free grammar is inadequate to express natural language
>>16104557
that's enough to start

Is there a component like a negative transistor where it's on my default but a small charge across a control pin switches it off?

>>16104612
Yes. there are a couple options.
- You can chain two transistor amplifiers together (they act like inverters in Common Emitter mode), so when you turn the first one "on" it pulls low and turns the second one "off"
- You can configure your amplifier as Common Collector (this class has its own issues)
- If you're working with MOSFETs, there are Depletion-types that conduct when low, and Enhancement-type FETs that conduct when the gate is high

If I need to show that there's no loss in generality by assuming a certain statement, do I essentially have to show that the assumed stuff implies that statement?

>>16103462
watch this
https://www.youtube.com/watch?v=60z_hpEAtD8
and ignore the stupidity of anything involving cross products (start at 13:41 or 14:36)

TL;DW: write each vector as a sum of their basis vectors, and simply multiply them using the distributive property. The dot product, "cross product", and any other higher dimensional product relations fall out naturally

Also, cross products are essentially rotations, so by definition they can only be 2D

>>16104658
that was quite helpful

"Construct a bounded set of real numbers with exactly three limit points."

Can I get a hint on this? It can't be continuous because there would be infinitely many limit points between any two, it can't be discrete because there would always be a smaller distance between the three points that you could make a neighborhood with a radius of, what could it be?

>>16105114
You can literally put your question into google and get multiple answers. Filtered.

>>16105123
She asked for a hint, not a solution.
>>16105114
Can you think of a bounded set with exactly one limit point? Can you then 'copy and paste' this set twice?

>>16085923
How do I determine convergence of the series [math] \sum_{n=1}^{\infty} \ln(1 + 1/n^2) [/math] ?

[math]F[X,Y]\cong F[X]\otimes F[Y][/math] for any field F. When is this ever useful?

>>16105114
What is the definition of "limit point" you're using?

Can "excessively"(like a lot) repeating formulas and equations in your brain make your memorization sweak ? Like ADHD or something?

>>16105246
Bound it with [math]\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}[/math].

>>16105139
Ah, like a set [eqn]A_n = c + \frac{1}{n}[/eqn] for some real [eqn]c[/eqn] and all real [eqn]n[/eqn], three different c?

>>16105321
[math]n \neq 0[/math], of course.

>>16105246
set the series equal to x. Exponentiate both sides to get e^x. Expand the RHS using binomial theorem, and let n go to infinity. Then natural log both sides to get back to x. This is a simple enough trick u should know

>>16105248
It's like the fact that 1+1=2. It's obvious, and it may or may not show up in whatever problem you're solving.

>>16105294
I see, that makes sense; since ln(1+u) ≤u , therefore ln(1+1/n^2) ≤1/n^2 . Thanks anon

>>16105342
Thanks for reminding me of this trick;
but if we use your approach we get [math] e^x = \prod_{n=1}^{\infty} (1 + 1/n^2) [/math] ; how does the binomial theorem come into it?

can use this book as a beginner comp sci student?

https://www.amazon.com/Structure-Interpretation-Computer-Programs-Engineering/dp/0262510871#customerReviews

or should i wait until i have more programming knowledge?

What are the pre requisite for data structures and algorithms for competitive programming ?


>t.1st year CSE major

>>16105989
This book is legally available online for free:
https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/6515/sicp.zip/index.html
It was traditionally used at MIT as a freshman course, so you can use it, but be aware it is difficult. You will also need to learn on your own how to apply functional programming concepts in non-functional languages. You can try it now and if you find it really difficult you can come back to it later

>>16090937
you can use the J0 as an orthogonal base to make a Fourier-Bessel serie of the initial condition. btw, if in your domain r goes to 0, the initial condition diverges. the Ozisik book about heat conduction is an excellent resource for these problems. gl hf.

>>16105321
Assuming you mean (for example) the set [math]\{c+\frac1n: n \geq 1, c\in\{1,4,8\}\}[/math], sure.
You should probably explicitly prove that there are only three limit points.

>>16103067
That sounds wrong.
If n is say, 1, the result of the sum should be just 1, not 0, no?

Using the power sum sounds good tho.

>>16106286
Oh, I think I see the issue.
The way anon wrote it he sums over [math]n + 1[/math] roots of [math]X^n - 1[/math]. Common indexing mistake.

>>16106286
>>16106291
if n=1 the sum is just [math]q^0[/math] which equals to 1, it should be correct regardless for other values of n but feel free to correct me, haven't done this in a while
but yes you are right, the original post summed over more roots than there are so I just corrected the indexing

Wich methods are the best to divide something(with big and small numbers)? I always forget how to make a simple division, I can do 10/2 easy, but 10/3 I quite didn't grasp the rules yet how to calc it correctly, somehow is easier to understand the Σ than a simple 264,28÷0,3, and Idk also how to use irrational numbers in math operations(maybe that's the main problem that makes me unable to do division correctly, also, I can calc √4(2) but not √5(2.23606798?? O_O))

im trying to figure out where quantum numbers come from. so far, as i understand it, solving the schrodinger equation for an atom (hydrogen maybe) involves a Hamiltonian that looks like
[math] \displaystyle
H=-\frac{h}{2 \mu} \nabla ^2 - \frac{e^2}{4 \pi \epsilon_0 r}
[/math]
where the right term is the Coulomb potential and the right side is angular momentum. since the angular momentum operator doesnt depend on r, we can separate the wave function like
[math] \displaystyle
\psi(r, \theta, \phi) = R(r)Y(\theta, \phi)
[/math]
then the eigenfunctions of the angular momentum operator are spherical harmonic functions, and the eigenvalues are l and m.
is this correct?
where does n come from?

>>16106490
The radial component. Though it's a bit more complex that a 1:1 mapping. R depends on n and l. Y depends on l and m.

>>16106497
you wouldnt happen to have a general form of R and Y would you?

>>16106504
jesus wept, just google it you tard.

>>16106298
1^2+(-1)^2 = 2
From the start:
[math]\displaystyle \sum_{k = 0}^{n - 1} e^{4 \pi k/n} = \sum_{k = 0}^{n - 1} \exp(4 \pi / n)^k = \dfrac{1 - \exp(4 \pi / n)^2}{1 - \exp(4 \pi / n)}[/math].
So for the cases [math]n = 1, 2[/math] we have a division by zero and need to calculate the value the old way.

>>16106602
Numerator should be up to the power of n.

>>16085923
What can i do to better my persistence and will power ? Im a fucking idiot and i want to be more intelligent - i hate not knowing things and getting dunked on by everyone in life.

What can i do ?

>>16106638
Just do it, stop comparing. Don't focus too much on the future and focus on what can be done in the present

What notation am I supposed to use for the inverse of a derivative of some function vs the derivative of the inverse of the same function.

>>16106840
What's wrong with:
[eqn]\left( \frac{df}{dx} \right)^{-1}, \frac{d}{dx} f^{-1}(x)[/eqn]

Question if i use Stormfront to find a wife , would you say that would be a bad or good idea?

>>16106856
I was just trying to write a composition of the inverse of the derivative of a function with another function, could I do that with the left notation?

>>16107191
You could define a function that is a derivative of the first, and take the inverse of that.

>>16097783
10. The Four Fundamental Subspaces
https://www.youtube.com/watch?v=nHlE7EgJFds&list=PL49CF3715CB9EF31D&index=10

What are some official free papers to read? I never really got into research when I was in uni, but now I miss having massive library access. Might be too vanilla, but I'm not looking for libgen or such, official is what I want.

>>16107456
It would be nice to have a compilation of "MUST READ papers x <specific area>" with a "recomended order of reading".

>>16107456
is there any particular (non-moral) reason you'd prefer to read officially?

>>16085923
What is the cheapest microscope that I can buy? I've been enountering these gnats lately that are very small and almost imperceptible. Only when I can smush one when it makes impact with my skin can I feel between my fingers that there's actually something there. I would take a photo of the miniscule object but my phone sucks. I want to buy a microscope so I can capture an image. Are there microscopes that can take pictures?

>>16086348
0.999... repeating endlessly means that the "missing value" is just an infinite string of zeros, with no 1 at the end. This makes 0.999... have an identical value to 1. Also 1/3 equals 0.333... which multiplied by 3 would appear to equal 0.999..., except we started off with 1, ergo 0.999... = 1.
If this is confusing to you, you have less IQ than a heavily sleep deprived man who smokes weed twice a week, so try to plan your life around that limitation.

>>16088927
He lived because he landed ass first on turf. Turf absorbs impacts by deforming, and the ass is much more impact tolerant than the skull or neck. If he landed on that same hill the same way dyring a drought he'd have a broken pelvis/leg/legs, and if he landed head first he'd likely be dead.

Is there a quick way to show [math]\operatorname{dim}_\mathbb{Q}\mathbb{R}\geq\aleph_0[/math] by contradiction?

Hey, probably dumb question but what is it called when you do little work and then immedeatly decide to take a break? Like some sort of procrastination?

>>16107843
Lazy?

>>16085923
So how long is the longest possible wavelength of a particle? What's the longest one we've measured?
Is it theoretically infinite, or what?

>>16108010
Theoretically infinite though there is likely a physical limit on the longest you could detect. Probably the length of the visible universe.

>studying circuits
>realize that it's literally programming but with physical objects instead of virtual ones
what the fuck. is this all electrical engineering is? physical programming?

>>16108549
That's all of science anon. Breaking things down into discrete logical components.

>>16108549
i find it hard to believe you had to solve a differential equation at some point in your Java adventures.

where does the [math]\Phi(\phi)=\Phi(\phi + 2 \pi)[/math] condition come from? is it a physical argument? i dont see how the math implies it.

>>16108613
[math]e^{ix} = \cos{x}+ i\sin{x}[/math] (as can be verified by expanding both sides as power series, or differentiating both sides, etc.), which are obviously periodic with period 2π

>>16108613
Euler's formula: [math]e^{ix} = \cos{x}+ i\sin{x}[/math]. sin and cos are both periodic over 2 pi.

>>16108623
>>16108626
obviously [math]e^{ix}[/math] is periodic in 2pi, but the general solution is [math]e^{im\phi}[/math], which is *not* periodic in 2pi for non-integer choice of m, but is otherwise still a solution to the dif eq.

>>16108613
OP here.
after thinking about it for a bit, i think it probably is a physical argument: when calculating the shape of an electron orbital, it would be weird if it wasn't periodic in one full rotation. not rigorous, but intuitive and likely backed up experimentally.

>>16108638
Correct, it is a boundary condition. The wavefunction has to be identical after a full rotation.

[eqn] .25x + .35y + .55z = .3
.35x + .25y + .40z = .3
.40x + .45y + .05z = .4
[/eqn]
Solve this without using linear algebra techniques, showing work. I spent hours on it and am unexplicably retarded.

>>16108651
>Solve this without using linear algebra techniques
What does that even mean? Don't use math at all?

>>16108657
As in the middle-schooler "multiply equation 3 by 8 and subtract from equation 2" style(the request is just as pointless as it sounds).

>>16108713
Well you would start by multiply everything by 100 to get rid of the decimals and they divide by the common factor of 5. After that is just a set of 3 standard integer linear equations.

>>16108645
thanks <3