/sci/ - Science & Math

Where are we right now with genetic modification, where is it legal, and how does it work? When and if I ever want to have a wife I'm considering doing some tweaking because why not? I'm thinking about having twins, a girl and a boy, then calling it quits because I want both at the same time so that they don't have to deal with the older/younger sibling BS. A better IQ would be cool as well but let me know what other positive traits I could give them. Also, can I just grow them in a tube so that my hypothetical wife can skip the pregnancy? And finally, I have SMA type 2. Can I just take that out for them?

~UNRESOLVED~

Math:
>>11300354

Physics:
>>11286876
>>11296408
>>11300717
>>11300736 (it is real. and no, it is not possible. ever seen a staircase from M. C. Escher?)

Chemistry:
>>11285751
>>11298508

Biology and physiology:
>>11287943
>>11288760 (curious about this one)
>>11294305
>>11295300

Economics and social science:
>>11290772
>>11295464 (reversing supreme court decisions does not change the law. goddamn was FDR a court-packing pinko)
>>11296622

Stupid:
>>11286634 (being tenured is extremely cushy)
>>11292057
>>11296886
>>11296972
>>11298621
>>11300539

>>11299667 (10/10, funny and creative use of names)

I missed one or two, didn't I? Find them.

Will I make it?

So this falls under psychology(I know I know)
but I've had multiple people independently tell me that whenever I'm in a room, everyone else in the room also feels the emotions that I do. Depressed, Excited, Humorous, etc. People seem to experience a sort of projection of emotion from me and I'm not some extroverted life of the party kinda person. Is there a name for this phenomenon? I've been referring to it as reverse-empathy.

>>11300354
It wants you to construct an explicit bijection.
Hint: euclidean division algorithm.
>>11290772
War on terror.
>>11300755
>reversing a court case doesn't change the law
The issue is essentially precedent on interpretation of the law during other related court cases.

>
>>11300354
>>11301043

>>11300936
social status. Extroversion/life-of-the-party appearance not required

>explain to a friend of mine an applied maths subject I studied
>he later tells me the wikipedia page is different
>open it up
>it's literally machine learning and bayesian statistics
>there's a classical result and method here and there, but the intuition is nonsensical bayesianism about "muh occam's dagger"
>the references and the bibliography are a complete fucking joke, a bunch of machine learning bullshit and one 30 pages long survey article about the topic, when the topic has dozens of books
What the fuck, do any of you know what's happening?

>>11300734
Is the universe all a cycle?
are we all related to the universe in some way?
are fractals the truth?

>>11300936
Expressiveness?

>>11301257
Yes. It means that hastily browsing shallow summaries of a subject gives you shallow insight on it.

Has anyone proved pic related from Hubbard's "Vector Calculus, Linear Algebra, and Differential Forms - A Unified Approach"?

The last equality of the so-called proof they give is clearly NOT correct, someone pls halp I've been stuck on this for hours

>>11301276
>Is the universe all a cycle?
>are we all related to the universe in some way?
Yes and yes. The cyclicity of life and existence is expressed by the path the Fool (0) has to take to reach self-realization and his place in the World (XXI), which is the same path everyone faces and thus an expression of the eternal return of this spiral of delusion and awareness only interrupted by reaching Moksha and thus freedom from reincarnation--which is the very spirality that keeps the world and the universe spinning, so to speak. To reach self-realization and Moksha, one has to get mastery over the spheres of desire (Kama, I-VII), life (Athra, VIII-XVI) and spirituality (Dharma, XVII-XXI). Notice how the first arcana are all symbols of various parts of sex life: the Fool (0) representing innocence and naiveness, as opposed to the Wizard (I) representing virginity with awareness of the possibility of sex; arcana from II to V represent the various sex organs, the High Priestess (II) seated in front of the temple's door represents the outer female body in general and the exterior female organ in particular (the columns represent the labia, the priestess herself the clitoris, and the crescent moon is a metaphor for the upcoming orgasm), the Empress (III) has always been know as a symbol of maternity and thus represents the womb, the Emperor (IV) looking towards the Empress from his own card is the penis, and the Hierophant (V) being a symbol of literature, wisdom and potentiality in general represents testicles; the Lovers' card (VI) is a symbols of duplicity and choice and it represents the possibility of sex; while the Chariot (VII) represents victory, a temporary one as opposed to the metaphorical one going on, a temporary mastery over one's one body and thus the temporary satisfaction after sex. ...

>>11301359 (cont)
The Athra sphere starts by gaining control over one's own impulses (Force, VIII) and culminates with another temporary victory represented by the Devil (XV) soon followed by the inevitable perspective of failure and the humbling experience of returning to square one (The Tower, XVI). Facing this perspective, one either chooses to get back to the world of matter and the Devil, or eventually learns to catch the interior glimpse of faith and hope (The Star, XVII) that hints the path of the Dharma (path only started after overcoming the subconscious threat of illusion (The Moon, XVIII)).

tl;dr >>>/x/sqt

>are fractals the truth?
Fractals are a mathematical construct. But yes, mastering each arcana requires a spiritual path of its own which can be divided into several parts reflecting the structure of the greater path of self-realization, and the yet greater path of capital L Life. To further explore this subject, read Differential Qabalah by Custardson and Miller (Oxford university press, 1969) as well as A Survey of Statistical Methods for Stochastic Gender Studies by Navidson and Cook (Sydney University press, 2018).

>>11301244
I've never seen myself as highly regarded so maybe, but I'm not sure.
>>11301292
I'm pretty blank though, so it's weird.

>>11301342
The last equality is correct, tho.
Essentially, you need to fiddle around with the [math][ ~ ]_R[/math] operator and use things like [math]\displaystyle \sup _R f(R) = \sup _{aR} f(aR)[/math].
Join everything up into one [math][ ~ ]_R[/math] and throw in the definition.

>>11301443
I was doing some wild guessing with the suggestions, but after taking a few minutes to actually solve it, you're supposed to use [math][f]_R + [g]_r \geq [f+g]_R[/math], which is trivial, and [math][f]_R+[g]_R \leq [f+g]_{2R}[/math], which works because we're assuming f and g are nonnegative.
Then you fiddle around with suprema.

>>11300734
>>11290772
USA declared war to Iraq and Afghanistan which at the time were major suppliers of oil.
In fear of oil shortage and increased demand for it during war times plus speculative economy the price sky rocketed.
Once USA won the corporations that took over the business of oil decided the price was fine as it was.
Its really that simple.

>>11300777
>anime poster
probably not even if you are ironic poster

*Artha

>>11301436
Radiance then

>>11301443
>>11301461
thanks a lot for your replies, I can see this would work but you assume [math][f+g]_R[/math] are integrable, how can you show this?

Why is it that the row space is orthogonal to the kernel of a matrix? Please no hard explanations, I'd like an intuitive one

>>11301569
>why is [math][f+g]_R[/math] is integrable
For [math]f, g[/math] nonnegative, we have [math][f+g]_R=[[f]_R+[g]_R]_R[/math].
If you have that [math][f]_R[/math] is integrable when [math]f[/math] is, the rest should be immediate.
>>11301575
[math]Au=v[/math]. We write out [math]A[/math] as the sequence of rows [math]A_i[/math].
Then, the i-th term of [math]v[/math] is [math]\langle A_i ^T, u \rangle[/math]. Thus, if [math]v[/math] is everywhere zero, [math]\langle A_ i ^T, u \rangle = 0[/math].

is it better to define a B field using a vector field approach, or will a long solenoid approximation work just as fine for calculating a Lorentz force?

Why are there no drones designed with the same principle as dyson's """bladeless""" fan?
I checked online and there are several artists (with no engineering knowledge, I presume) who have done concept visions of that, but no drone like that have been produced. Is it just not possible? Inefficient?

>>11301642
based
I showed that [math] [[f]_R + [g]_R]_R [/math] is continuous whenever [math] [f]_R + [g]_R [/math] is continuous, so the former is continuous except on a set with no measure.
Did you have an easier method in mind? I wouldn't say this was immediate for me

>>11301856
[math][f]_R[/math] and [math][g]_R[/math] are proper Riemann-integrable by definition, and thus [math][f]_R+[g]_R[/math] is proper Riemann-integrable.

>>11301889
Oh, you meant the [math]f[/math] Riemann-integrable implies [math][f]_R[/math] is Riemann-integrable.
It's a classical result in analysis you can probably find in Spivak. If [math]f[/math] and [math]g[/math] are Riemann-integrable, [math]h(x)= \min (f(x), g(x))[/math] is also Riemann-integrable. Same for max.

>>11301907

I know this will sound like the "How to learn python" of math but what is the best roadmap ?
Is pic related any good ?
Or should I go full khan academy ?

My order : algebra basics > algebra I > algebra II > Trigonometry > Precalculus > Differential calculus > Integral calculus > Multivariable calculus > differential equations.
Where should I put linear algebra inbetween ?

>>11300753
hhi anons
sooo, this question has been pressing me. what ways do mathematicians know that one formulation is the 'right' one or the 'best' one? furthermore, how do you know that one is more 'natural' or not? ive been researching this for a while already but id like to ask anons here what they think

>>11296408
Solutions [math]A[/math] to the strong EL equation [math]d\ast F = j[/math] of the [math]U(1)[/math]-Yang-Mills action [math]S[A] = \int (F\ast \wedge F - j\ast A)[/math], coupled to a current [math]j[/math], determines the radiative pattern. Relativity postulates that [math]S[/math] is Poincare invariant, but shifting into non-inertial reference frames is manifestly [math]not[/math] part of the Poincare group. The difference [math]\delta S= S_\text{inertial}-S_\text{non-inertial}[/math], or classically its EL term [math]\partial_{dA} \delta S[/math], contributes to radiation amplitudes due to acceleration. Now [math]\delta S_\text{lin}[/math] for a linearly accelerating particle is still Poincare invariant in the plane perpendicular to the motion, while [math]\delta S_\text{rot}[/math] for a circularly accelerating particle is only Poincare invariant along the axis, hence they [math]must[/math] take different forms; in fact, assuming no quantum phase transition occurs in the system, this symmetry argument extend to the solutions [math]A[/math] and hence to the radiation pattern.
>>11301737
General it is more straightforward to define the fields via the curvature 2-form [math]F[/math] of a principal [math]U(1)[/math] bundle (or an associated vector bundle thereof), at least geometrically speaking. However if your base manifold [math]M[/math] is not simply connected, then the relation [math]F = dA[/math] need not necessarily hold. In the case of a magnetic monopole, for instance, [math]F=dA[/math] holds only on separate patches of the sphere (together with gauge equivalence/patch transition conditions on overlappnig regions). Physically, a monopole can be considered as one end of a semi-infinite solenoid, in which [math]A[/math] is not well-defined. In this case [math]M = \mathbb{R}^3 \setminus \mathbb{R}[/math] and your fields [math]A,E,B[/math] are [math]multiply[/math]-valued. In this case it may be more straightforward to consider a solenoid.

>>11301947
differential and integral calculus aren’t separate subjects really, linear algebra can be done as soon as you’ve finished calc. multi should be learned simultaneous to lin alg, diff eq after you’ve finished both. use vol ii of courant or apostol for multi

Do computer scientists know anything about hardware? Do they actually understand how a computer works?

>>11301947
>My order : algebra basics > algebra I > algebra II Do you really not know these subjects?

>>11301505
Oh

>>11300734
I need Paul Siple's original apparent temperature equation but I can't find It anywhere. Any one? And I mean the ORIGINAL not modern one.

>>11301937
excellente I will sleep well tonight

>>11302035
From Matthew 7:
>17 In the same way, every good tree bears good fruit, but the bad tree bears bad fruit. 18 A good tree cannot bear bad fruit, nor can a bad tree bear good fruit. 19 Every tree that does not bear good fruit is cut down and thrown into the fire. 20 Thus you will know them by their fruits.
>>11301947
>pic related any good
Pic related isn't humanly possible.
>full Khan academy
That's probably the most doable and reasonable option.
>Where should I put linear algebra inbetween ?
Either after precalc or after integral calculus.
>>11302340
Good night.

>>11301947
>algebra basics > algebra I > algebra II
Euler's Elements of Algebra
>algebra II > Trigonometry > Precalculus
Lang's Basic Mathematics
>[proofs]
Hammack's Book of Proof or similar
>Differential calculus > Integral calculus
Lang's A First Course in Calculus
>Multivariable calculus & [linear algebra]
Hubbard's Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach
>differential equations
Simmons' Differential Equations with Applications and Historical Notes

What are the physiological effects on a brain after several suicide attempts, as well as with suicidal ideation?

How do chemists estimate which carbon some group will bond to and/or with which probability during a reaction? This seems like a huge field of chemistry for obvious reasons, but it doesn't seem to have a name. Is there some database for this?

>>11301359
>>11301362
breddy interesting actually

>arcana from II to V represent the various sex organs
There's a joke in there somewhere about Tumblr invented genders.

>>11301805
If I had to hazard a guess, it's simply that a Dyson design, which is to essentially hide the fan, doesn't make much sense because flying objects are already designed to be as light and small as possible. There's no more volume to remove, so to speak, and hiding the blades would actually add unnecessary load. The one design you posted, for example, doesn't seem to have any space where the blades could be.

>>11290772
Capitalism.

>>11302591
It makes the brain more red.

>>11300936
vibes bro
u vibin?

Is eating food that fell on the floor really so dangerous?

My position is that we have immune systems for a reason...

>>11302899
Everything except for the speed of light is a game of chances, anon. The longer it stays on the floor, the higher the chances of infection. It starts out slow, but grows exponentially with each second. Altho it's a known fact that food which stays on the floor for up to 3 seconds is virtually as safe as it was before it hit the floor, it's hypothesized that food which stays on the floor for longer than 11 seconds becomes more poisonous than arsenic.

No bullshit, is renouncing your US citizenship but remaining in the country illegally a smart loophole to college admission & financial aid?

I mean the odds of getting deported from a blue state or sanctuary college town have got to be, like, zero, right?

>>11300755
I'll take a crack at a couple.

>>11296408
So in all three pics the axis of the torus IS parallel to the acceleration (the "oscillation" of the dipole), and that's correct. How the dipoles get warped is due the particle's velocity, which is relativistic in the bottom and top-right pics. What you're seeing is evidence of relativistic beaming and aberration. Any radiation that isn't pointed away from the particles velocity will appear to be enhanced and focused towards its direction of motion by an outside observer. It's like how snow, even if falling straight down, appears to be coming at you if go through it fast enough.

The top-left pic is a charge at non-relativistic speeds with a dipole whose axis is perpendicular to its motion. Top-right is that same charge going near the speed of light. Since one of the poles is pointed away from the particle's velocity its radiation appears greatly diminished to an outside observer. The other pole gets boosted and focused in the charge's direction of motion, appearing much brighter to anyone facing the particle head-on. In bottom pic the dipole axis is now parallel to the charge's velocity. Since neither dipole is facing away from the direction of motion they both appear focused in that direction.


>>11294305
Believe it or not, Cytosine's tendency to deaminate into Uracil is actually used in mRNA. Look up the ABOPEC protein family. These are a group of enzymes designed to actively deaminate Cytosine into Uracil. They're not fully understood, but they seem to play a role in fighting viral infections and managing cholesterol.

Electrical-anons: in Utility/grid systems, why does an imbalance between the power being generated and the load of the grid/power demand affect the frequency? I know that generation > demand = higher frequency and generation < demand = lower frequency, but I cannot recall the actual principles why.
From my rough understanding, it is due to the electrical load creating an opposing magnetic field in the stator, meaning if it is a large load (high demand/low generation) it will create a strong magnetic field and slow down the physical rotation of the generator assuming the input is not changed because the opposing magnetic field is stronger. Then the opposite occurs when there is less load (less demand/more generation). Is that correct or hilariously wrong?

>>11302955
But what's so special about the floor as far as infection goes? I mean unless I step in literal shit or something and then walk around in my kitchen with shoes on (which I don't) I don't think much is gonna get me... If anything I'd worry more about letting food touch the countertops since there's more possibility of cross contamination from raw meats or something.

>>11302973
Can you even renounce your citizenship if you don't have citizenship somewhere else already? I don't think you're allowed to be a citizen of nowhere.

But to answer your question I think it would be a pretty dumb decision. I doubt getting your citizenship back would be easy if you wanted it later and there's plenty of easier ways to get financial aid. Hell, there'd probably be less risk just lying and saying you're an illegal compared to actually becoming one and risking getting thrown out.

When is it that given a matrix nxn, its eigenvectors form a basis for R^n? Is it when the matrix is diagonalizable?

>>11300755
armchair physician here
>>11288760
1) the electric saw used to cut bone would leave debris in the form of dust rather than chips. Either way they shouldn't cause any harm if left in your body.
2) that being said, they probably suction excess debris up along with fluids and blood while working to keep the area clean and visible. Like a dentist's saliva vacuum.

>>11300734
How do I access this paper when my university library doesn't have access?
>https://ieeexplore.ieee.org/abstract/document/1170828

>>11302461
>From Matthew 7:
>>17 In the same way, every good tree bears good fruit, but the bad tree bears bad fruit. 18 A good tree cannot bear bad fruit, nor can a bad tree bear good fruit. 19 Every tree that does not bear good fruit is cut down and thrown into the fire. 20 Thus you will know them by their fruits.
I don't know. Ezra Pound wrote some interesting poetry.

astatine

Can I hug the touhouposter? S/He makes this place 230% less depressing, 430% more mathematically accurate, and 666% cuter.

>>11302461
o thanks remu. ive heard about the fruitfulness explanation before, but im guessing at this point we reach a roadblock as i dont think there is a consistent way of predicting how fruitful a field or framework will be. i point to grothendieck as an ironic example of this being the case. he claimed that topological vector spaces were 'dead'. the best grip you can have for this is by observing proofs using particular line of reasoning your framework supports. this can be seen by serre's usage of generic points and the advent of category theory making it more clear that the scheme concept could prove fruitful. at the same time, even then i doubt grothendieck would've foresaw how far the applications of some of his foundational work could yield. a foucauldian quote should suffice to express this: 'people know what they do; frequently they know why they do what they do; but what they do not know is what they do does'. i did post here in case there would be a few other ideas because i still feel as though i haven't exhausted all considerations. maybe im just procrastinating or something

>>11303668
there's like 2

>>11285751
I have never seen an amidation with NaOH before, logically that should kill the reaction. Usually you'd use a tertiary, non-nucleophlic amine base to mop up the HCl byproduct.
A quick look at wiki's Schotten-Baumann page claims the original reaction was two-phase, with the base being added slowly over the course of the reaction so as not to destroy the acid chloride. But I see no indication of that in your image.

Another sign that chemists need to have actually run these things before they try teaching them.

>>11302626
>How do chemists estimate which carbon some group will bond to and/or with which probability during a reaction?...doesn't seem to have a name.
Chemoselectivity

>>11303120
Basically, yes. Power=efficiency*2pi*frequency*torque.When the generator is online, there isn't going to be any clutch along the transmission from turbine to generator, so torque is more or less constant. So it is the frequency that changes with demand.
>>11302955
> it's hypothesized that food which stays on the floor for longer than 11 seconds becomes more poisonous than arsenic
"No"
>>11303486
That would be a necessary and sufficient condition, yes
>>11303504
Both of those make sense.
>>11303666
Lucifer digits checked
>>11303667
Yes, the halogens are based.

>>11303120
Basically, yes. Power=efficiency*2pi*torque*frequency. If your demand goes up, you are going to need to up the torque if you wish to continue delivering the same frequency (which is what you want because all the magnetic circuits and transformers down the line are fixed). But this isn't an instantaneous process. Turbines take time to spool up, there is a gear train on the transmission from turbine to generator, and the shaft of a generator under larger load will be more difficult to twist.
>>11303486
That is a necessary and sufficient condition, yes.
>>11303667
Halogens are based
>>11303666
Lucifer digits checked

>>11303486
Yes, and viceversa. If a matrix is diagonalizable, then choose a basis wrt it's diagonal, and those turn out to be all eigenvectors. If you have a basis of eigenvector, that basis also diagonalizes the matrix.

>>11303715
>there's like 2
Where do I have to sign to sell my soul to the cool kids' sect?

>>11303666
Pound was great.
http://www.gutenberg.org/ebooks/40200
>>11303715
>2
Every star in the sky is a Touhou poster. No two posts were ever made by the same Touhou poster.
Within the depths of your heart is, too, a touhouposter.

>i dont think there is a consistent way of predicting how fruitful a field or framework will be
Was there supposed to be one?
>>11303789
You're in.

What's the point of studying computer science if electrical engineers can get jobs in software just fine?

>>11303952
some people arent smart enough for electrical engineering. they just go to uni because they dont want to work and CS is easy as fuck so they can just chill for a few years.

>>11303952
Studying maths got me enough background to adapt to cs jobs without the pain or shame of studying eng or cs

Is there a notion of the "difference" of (additive) functors?

Can someone explain what the part in blue means? I don't really understand how those three values together equal a four dimensional plane. I don't even really understand what a four dimensional plane is

>>11304198
>I don't really understand how those three values together equal a four dimensional plane
They don't. The term in blue spans a 2D cross-section of R4. For your intents and purposes, just think of R4 as the set of all four-tuples.

>>11304117
The way it seems to be is that Phys/Math niggers can if at all competent move into CS, Eng, Bio, Finance, Chem, Medicine with ease. CS can do Finance, Bio if they’re above average intelligence and not too autistic; Chem can do Bio, and Med can do Law but no other translation of skills seems present. I’ve never met an engineer who seemed like they would make it in physics for instance

Does there exist a function [math]f: \mathbb R^n \to \mathbb R[/math] for some [math]n>1[/math], such that [math]f[/math] is (total/Frechet) differentiable at a point [math]p \in \mathbb R^n[/math] but isn't differentiable at arbitrarily small neighborhoods of [math]p[/math]?

Does twice-differentiability at a point imply once-differentiablity in a neighborhood of the point?
Specifically, does there exist a function [math]f: \mathbb R^n \to \mathbb R[/math] which is twice (total/Frechet) differentiable at some [math]p\in\mathbb R^n[/math], but fails to be differentiable at arbitrarily small neighborhoods of [math]p[/math]?

>get a laser
>it says 1mW, wave: 532NM

Can my eyes be kill if I look at the reflection glow when it hits walls, furniture etc?
Should I only use it outdoors to point at long distances?

>>11304310
If a function is twice differentiable at a point, its first derivative is differentiable at the point. For a function to be differentiable at a point, it's necessary that the function be defined in a neighborhood of the point (at least in real analysis, not sure if there's some technicality in a more general setting). So the first derivative must exist in a neighborhood of the point.

>>11304326
That's fairly powerful. I definitely do not reccomend looking at its reflection. That shit isn't a toy.

>>11304341
I got it to take it in my grandpa's house up in the mountains in the countryside to mess about with stars and pointing at the mountain.
Do you think I can carry it in my baggage in a flight (not handbag)?
It says Class III. The chinese can sell you anything.

>> power(sinc(pi/2), 2)

ans =

0.0391

explain this shit to me, everything else says it's ~0.4, why the FUCK is matlab off by a factor of 10?

>>11304402
https://www.mathworks.com/help/signal/ref/sinc.html

>>11304418
it's supposed to be the entire fucking thing all squared, I even checked on my calc, by hand, wolfram alpha, and on desmos, and they all give 0.4.

>>11304402
>>11304418
pi/2 or pi^2/2?

>>11304425
https://en.wikipedia.org/wiki/Sinc_function

>>11304435
>>11304426
fuck it, I just put the function in manually, and it worked.

Plenty of computing pioneers were mathematicians. Can mathematicians still contribute to the field?

>>11303806
>Within the depths of your heart is, too, a touhouposter.
i used to 2hu post clownpiss when id talk about ithkuil, but i am not learning ithkuil anymore and i am not sure if a certain person is still stalking me to wait until i post w it to insult me
>Was there supposed to be one?
i was thinking of a way to study material so id really understand it as a coherent framework (as opposed to related facts to a particular mathematical object) such that id gather enough wisdom to judge between various candidate frameworks of new theories. tho perhaps its a fool's errand perhaps. maybe u cant really teach yourself wisdom other than having raw experience with enough research

Really basic fucking question here, I just don't know how to word it so I can google it:
I have a circle (x-2)^2+y^2=4 (so radius 2 with the centre in (2,0)) and a line y=x, and I'm trying to find the borders both ways, for a double integral.
So the area with the "easier" borders would be:
0<x<2
x<y<sqrt(4x-x^2)

And for the aea with the "harder" borders I'd need to find x as a function of y. So I solve the quadratic equation and I get x=2+/-sqrt(4-y^2). Now, which one do I take, + or -? Should be different parts of the circle right?
Also this seems extremely basic, how did I miss this so far, Jesus..

>>11304634
Polar coordinates.

>>11304651
Not sure how's that supposed to help ;_;

>>11304665
What anon is trying to tell you is to stop trying to integrate w.r.t. [math] \text{d}x\text{d}y [/math] and instead integrate w.r.t. [math] \text{d}r\text{d}\theta [/math], of course setting your limits of integrations the right way. What region are you trying to integrate? Draw a picture.

Why is the seaborne package abbreviated sns

>>11304680
Oh, I see. It's not about the easiest way of integration tho, I'm just starting to learn about multiple integrals so this is just practising.
I think this particular example is supposed to show me two ways of determining the borders (and to show me which route I should take in the future I guess), and I'm not stuck on the integral part, but on the simple geometry part about which I'm asking.
The circled part on the picture. How do I know do I take the + or -?

>>11304693
>How do I know do I take the + or -
Look at pic related and think for a moment. The blue portion is represented by - part of the quadratic root and the red portion is represented by the + part. Now, which part do we want?

>>11304728
Yeah, I just remembered desmos. Thanks man.
Wolframalpha was fucking with the axis, which fucked with my brain.
Again, thanks!

>>11304736
yw. keep it up~

What the FUCK should I get my masters in?

>>11304767
biomechanics

>>11304767
Quantum literature

>>11304767
Black lives matter studies

>>11304767
Brazillian Jiu Jitsu.

How likely is it that we will have the technology to make anime real in the next 20 years?

>>11305046
Anthros are coming first. ;]

>>11300734
From old thread...
If a stream of positrons strikes a metal plate floating in space, does the plate develop a positive charge from losing electrons?

>>11301498
>Afghanistan
> major suppliers of oil.

Citation needed. The only oil export from Afghanistan is black tar heroin.

Is it true that living with cats decreases your lifespan?

>>11303539
https://booksc.xyz/book/21367838/e83b9a

Has it as pdf

Is life really worth living?

>>11305275
I don’t know this one for sure but I do know that cats carry a parasite called toxoplasmosis. It makes you more friendly towards them and it rewires your brain to do so. There’s a whole /an/ meme that calls cat owners “toxofags”

Do you think it will ever be possible to revive a dead person?

Does anyone mind creating a poll in strawpoll.me real quick?
Don't turn on "improve spam prevention."

>>11304634
Neither way is any harder than the other. You can solve (x-2)^2+y^2=2^2 for either x or y.

Draw a diagram. Relative to the centre of the circle, the bounded area is in the upper-left quadrant: (x-2)<0, y>0. So if you solve the implicit equation for the circle to get y(x) you want the upper solution (the lower bound is y=x), if you solve to get x(y) you want the lower solution (with x=y the upper bound).

With x as the inner variable, you have 0<x<2, x<y<sqrt(4-(x-2)^2).
With y as the inner variable, you have 0<y<2, 2-sqrt(4-y^2)<x<y

And ignore the suggestions to use polar coordinates. That will probably be harder overall (unless the added factor of r in the integrand results in something which is easier to integrate). Remember that [math]\iint f(x,y)\,dx\,dy = \iint f(\rho,\theta)\,\rho\,d\rho\,d\theta[/math]

I have $76 left in giftcards for amazon, what's something cool I can buy? I just bought a book on lie algebra just now.

YO, what's the standard cryptography book. (something suitable for somebody that knows jack shit about the subject but is a 4th year math undergrad so can handle rigor and shit)

Name a function which is both odd and even

>>11305610
0

>>11304190
Please.

Let [math]A, B[/math] be operators on a finite dim. Hilbert space [math](\mathcal{H}, \langle \cdot, \cdot \rangle)[/math] which are self-inverse ([math]A^2 = B^2 = \mathrm{id}_{\mathcal{H}}[/math]) and anticommuting ([math]AB + BA = 0[/math]). I have the following conjecture: [eqn]\langle \psi, A \psi \rangle^2 + \langle \psi, B \psi \rangle^2 \leq 1[/eqn] for all normalized [math]\psi \in \mathcal{H}[/math], i.e. [math]||\psi|| := \sqrt{\langle \psi, \psi \rangle} = 1[/math]. (As one might imagine, this question is motivated by QM.) Does anyone know a way to go about showing whether this is true or not, or if it's not, is there a straightforward counterexample?

My progress so far:
>it's true for [math]\mathcal{H} = \mathbb{C}^2[/math]. I don't like doing brute force calculations, though, so I haven't checked for higher dimensions.
>Cauchy-Schwarz seems like a clear way forward, but getting nontrivial bounds on [math]||A\psi||[/math] and [math]||B\psi||[/math] is the part stumping me. You can bound them by the operator norms (which are 1 due to being self-inverse), but that's too naive a bound.
>in particular, since [math]A[/math] and [math]B[/math] do not commute, I'm fairly certain that [math]\psi[/math] cannot simultaneously be an eigenvector of both, thus the above naive bound can never be achieved. Hence my suspicion that there is a tighter inequality using the anticommuting condition that may prove my conjecture.

I would not be too surprised if my conjecture turned out to be wrong, but if that's the case, I'd also like a sense of under what conditions it doesn't hold.

Anyway, not asking someone to do my work for me. Mostly looking for reference recommendation in the math literature, because my physics knowledge has failed me. I've been searching for stuff related to the Rayleigh quotient and Clifford algebras, but to no avail.

>>11305559
Introduction to Modern Cryptography by Katz and Lindell

An Introduction to Mathematical Cryptography by Hoffstein, Pipher, and Silverman

Just starting maths here. I can't even into Latex yet. When differentiating f(x)= x+5√x over √x why can I not just cancel √x ?

>>11305547
>$76 left in giftcards for amazon,
A Stirling engine kit or painless dent removal tools.

>>11305957
>painless dent removal tools
w-why would ordinary dent removal be painful?

>>11305741
I don't have a solution, but I do have some intermediary results.
[math]A( \phi + A \phi )= A \phi + AA \phi = \phi + A \phi[/math]
[math]A( \phi - A \phi )= A \phi - AA \phi = A \phi - \phi [/math]
This lets us give any [math]\phi [/math] as a sum of two eigenvectors of [math]A[/math], specifically [math]\frac{ \phi + A \phi}{2} + \frac{\phi - A \phi}{2}[/math].
There are some conditions on eingenvectors which essentially implies that [math]A[/math] and [math]B[/math] just swap around eigenvectors.
Specifically, assuming [math]A \phi = \phi [/math] (which is, by the way, one of the only two possible cases for eigenvalues), then we have [math]0= (AB + BA) \phi = AB \phi + B \phi [/math]. Then,
[eqn] AB \phi = -B \phi[/eqn]
Setting [math]\psi = B \phi[/math], we reach
[eqn] A \psi = - \psi [/math].
>book recs
My bad, don't have anything in particular.

>>11306002
I forgot to type this out, but it might be useful for hunting down counterexamples.
Assume [math]|| \phi + A \phi ||= 1[/math]
Then [math] \langle \phi + A \phi , A( \phi + A \phi \rangle ^2 + \langle \phi + A \phi , B ( \phi + A \phi ) \rangle ^2 = 1 + \langle \phi + A \phi , B ( \phi + A \phi ) \rangle ^2[/math]

Am I doing this right?
>Aniline is obtained from 400g of nitrobenzene with a purity of 80% reacting with hydrogen. Calculate the used volume of hydrogen in normal conditions.

C6H5NO2 + 3H2 -> Aniline + H2O
80% = 320g of pure nitrobenzene
Molar mass of nitrobenzene is 123g/mol so there are 2.6 moles, which leaves us with
2,6/1 = x/3 => x = 7.8 moles of H2
7.8 * 22.4 = 174.72 litres

>>11306002
>>11306026
Better idea:
Set [math]F: \mathbb{C}^4 \rightarrow \mathcal{H}[/math] by [math]F(e_1)=\phi[/math], [math]F(e_2)= A \phi[/math], [math]F(e_3)= B \phi [/math] and [math]F(e_4) = AB \phi [/math] and extend by linearity.
Because [math]A^2=B^2=Id[/math] and [math]AB=-BA[/math], [math]im ~ F[/math] is closed under [math]A[/math] and [math]B[/math].
We can then pull back the operator and the inner product to show that if there is a counterexample, then it exists in [math]\mathbb{C}^4[/math].
Similarly, if it actually works in some case lke "A and B are self adjoint", the trick still works.

>>11304767
what have you tried?

>>11298508
yes, since it's 12*n+2*n+3*15

knowing e.g. the mass and the moles of a unknown substance whose general formula is known you can then determine the substance

>>11305741
If A is
1 0
0 -1
And B is
0 t
1/t 0
Then changing t, <v,Bv> can be arbitrarily high while <v,Av> remains constant.

I need help

A gas mixture of CO2 and H2 at a given temperature, pressure, and with a known mixing ratio, enters a turbine where it cools down to a known temperature and drops down to a lower, known pressure.

I also know the volumetric flow rate (m^3/s) of the output, and need to calculate the volumetric flow rate of the input.

The mixture does not undergo any reaction through this whole process.

Will the ratio of the 2 ingredients remain the same at the turbine exit?

>>11306164
Kek.
Does teach me not to trust anons when they say they've proved some special case.

The last math module I have ends where "Advanced Engineering Mathematics" (Kreyszig) finishes.

Is that really all the pure math I'll need to be an engineer? I'm somewhat underwhelmed

>>11300734
I'm trying to find the non-relativistic limit of the differential cross section in electron-muon scattering. I've done the calculations with the traces etc and i've got for the amplitude:

[eqn] \overline{\left| \mathcal{M} \right|} = \frac{e^4}{4q^4}L^{(e)\mu\nu} L^{(\mu)} _{\mu\nu}[/eqn]

where the L's are the electron and muon tensors,

[eqn]L^{(e)\mu\nu} = \frac{1}{m_e^2} \left( p_A ^{\mu}p_C^{\nu} + p_A^{\nu}p_C^{\mu} - p_a \cdot p_C + m_e^2 g^{\mu\nu} \right)[/eqn]

and respectively for the muon (A and B are the ingoing electron and muon and C and D are the outgoing ones) and [math]q:= (p_D-p_B)[/math]. My question is how i'm i suppose to compute the non-relativistic limit where [math] p\rightarrow 0 \Rightarrow E \approx m[/math]. If i try to express the four-momentums and the Mandelstam variables like this i get [math]q^4 = (p_D-p_B)^4 \approx (m_{\mu} - m_{\mu} )^4 = 0[/math] in the denominator. Any help appreciated.

>>11306255
correction*

[eqn]L^{(e)\mu\nu} = \frac{1}{m_e^2} \left( p_A ^{\mu}p_C^{\nu} + p_A^{\nu}p_C^{\mu} - p_a \cdot p_C g^{\mu\nu} + m_e^2 g^{\mu\nu} \right)[/eqn]

>>11306169
>Will the ratio of the 2 ingredients remain the same at the turbine exit?
Mass and molar ratios will be the same, but definitely not the volumetric. As always, to solve these kinds of problems use
>energy balance
>mass balance
>tables
>gas laws
and you will be fine
>>11306194
>Kreyszig
lol pretty advanced isn't it? If you are undergrad, that's pretty much where the "pure" math stops. I'm not sure if there is time for an engie undergrad with all the other core modules.

>>11306328
i can't find a decent resolution general gas compressibility factor to calculate the compressibility factor for the gas mixture that I am dealing with, will this work:

The mixture is 0.7 CO2 and 0.3 H2 (molar ratios)

To calculate the compressibility factor for this mixture, I first calculate the molar volume for the mixture at the given conditions by calculating the volume of 0.3 moles of H2 and 0.7 moles of CO2 using the van der waals equation.

After calculating the volumes of each one, I add them app, and then (presumably) I have the molar volume of the mixture for the given conditions. Then by using z=(p*Vm)/RT I calculate z.

>>11306338
>will this work
Usually you determine the reduced pressure (Pr=P/Pcr) of each species weighted by its molar fraction (this is called Kay's rule, I think). Then, you can refer directly to a compressibility chart/table to find Z. Look up Nelson-Obert generalized compressibilty chart, and also Kay's rule. If you are still having trouble, post the whole problem and I will walk you thru later today when I get home.

>>11306345
that's what I initially did, and that what this whole thing is trying to teach you, to use kay's rule and reduced temp/pressure, the only chart I could find that wasn't a shitty scan of a book was the one on wikipedia, but the best I could guess it would be from the reduced pressure/temp I had calculated was ~0.98-0.99.

calculating it from what I just posted comes out at 0.999173, so it should be good enough.

i really need to get that shitty textbook, it also has the chart that you mentioned.

>>11306353
I'm having trouble posting the link because I am on phone, but google "thermodynamics cengel property tables" and the very first link or so has a pdf with a hugh quality compressibility table. And yes, you should expect a little error. Kay's rule is an approximation.

>>11306374
holy fuck thats perfect

thanks

>>11306380
yw~

>>11306169
If you want to do this without any assumptions about ideality or Kay's rule, find the molar volume with the Peng-Robinson equation of state.

Can a single eigenvalue have more than one eigenvector. For example if x = y = 0 and z = 4, is it possible for z to generate more than one eigenvector?

>>11306426
No it isnt

>>11306426
>Can a single eigenvalue have more than one eigenvector.
Yeah, the eigenvalue 1 can have as many eigenvectors as it wants in identity matrices.
>For example if x = y = 0 and z = 4, is it possible for z to generate more than one eigenvector?
Not sure what that means.

>>11306426
An eigenvalue has at least a whole line of eigenvectors, because if Ax=cx then for all t A(tx)=ctx. Some matrices have independent pairs or triples or more of eigenvectors associated to a same eigenvalues, for example the identity matrix has a single eigenvalue 1 and all vectors are eigenvectors.

how does one 'ask the right questions' in math?

How come [math]4^{3/2} = 8[/math]?

>>11306442
>>11306443
So for instance if I have a 3x3 matrix, whose eigenvalues are x1,x2,x3. x1=x2=0 and x3= 4.
Can 4 generate two eigenvectors, while 0 only generate one?

>>11306426
An eigenvalue with algebraic multiplicity N can (but isn't required to) have an N-dimensional space of eigenvectors. To take the example from
https://en.wikipedia.org/wiki/Diagonalizable_matrix
the matrix
[eqn]\begin{bmatrix} -1 & 3 & -1 \\ -3 & 5 & -1 \\ -3 & 3 & 1 \end{bmatrix}[/eqn]
has eigenvalues 1,2,2 and the eigenvalue 2 has eigenvectors [1 1 0]^T and [-1 0 3]^T, so all vectors of the form
[eqn]u\begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}+v\begin{pmatrix} -1 \\ 0 \\ 3 \end{pmatrix}[/eqn]
satisfy Ax=2x.
Eigenvalues with algebraic multiplicity 1 have a 1-dimensional eigenspace, meaning that the eigenvector is unique up to a scale factor (if Ax=λx then A(kx)=λ(kx) for any scalar k).

>>11306448
(a^b)^c = a^(b*c)
So 4^(3/2)=4^(3*(1/2))=4^((1/2)*3)=(4^(1/2))^3=2^3=8

>>11306467
No, because that's not how multiplicities work.

>>11306481
based answer, thanks!

>>11306467
The geometric multiplicity of an eigenvalue (the dimension of the corresponding eigenspace) cannot exceed the algebraic multiplicity (the number of times the root is repeated in the characteristic polynomial). So a unique eigenvalue (algebraic multiplicity 1) only has a 1-dimensional eigenspace.

>>11306467
>x1=x2=0
If by this you mean that the charactheristic polynomial is [math]x^2(x-4)[/math], then it is 0 that has multiplicity 2, so 0 has a bidimensional eigenspace, and 4 has only a line. Notice that this is only possible if your matrix has all zeroes except a 4 on the diagonal.

>>11306448
Because [math]8^{2/3}=4[/math]

>>11306447
By struggling with the problems yourself instead of just reading proof on a book.

I'm doing a masters (Europe) in pure math. Next semester Im taking a subject on PDEs and one on manifolds (symplectic mflds, lie groups, ...). Is Hamiltonian systems a nice subject to take on top of the others? My interests are focused on analysis and PDes.

>>11306538

Linking in here for the obvious reason of not wanting to pollute my thread with trivial discussion and a secondary reason of allowing the intelligent anons for which discussion was actually desired of unminimizing the thread, and many among that group likely minimized the thread at first glance.

what do the critical points on a phase portrait actually represent? The stability of something, but... of what?

>>11305319
It already is, countless people have died in operating rooms for tens of seconds only to be resuscitated right after.
The problem is brain death sets in after a minute or so, so unless you can regrow a rotten brain, it'll never happen.

>>11305290
If you're healthy, yes. Nobody who's healthy has any room to complain about their life, even if they're homeless. If you don't believe me, go talk to people who will be suffering in ways you can't even imagine every day for the rest of their lives, like people with a traumatic brain injury.

>>11306626
Well my worry is that even if you do fix the brain, it will hit a point where once it's been "turned off" so to speak the vital data is lost and will not come back even if you fix the physical hardware, similar to volatile memory on your PC that will have its contents purged as soon as the power is lost. Or does consciousness not work in such a way?

>>11304767
Symplectic theology
Industrial Kummer Theory
Neolatinate Hydrogeology
Proctomammary Synesthesiology
Art Studies of North African Nomadic Tribes' Usage of Guttural Sound When Speaking of Sexual Intercourse
Atlantic Topology of Jazz
Dysphemistic Applications of Geoanthropological Cognicance of Gender to the Catalogation of Coprolites Dating From Between Planck's Era to the Eighties

is it possible schizophrenia is a sleep disorder? I've recently noticed an intense sensitivity to melatonin, even at low doses like 0.1mg I get intense dreams, I've read melatonin sensitivity is common among people who don't get a lot of rem sleep normally which is the dream state, but thanks to alcoholics we know that when rem is suppressed long enough your brain lets dreaming states happen when you're awake so is it possible that's what causes hallucinations? schizos just don't get enough rem so every now and again the brain causes dreaming rem states when awake, anti psychotics are basically tranqs so would probably have some effect on rem, the two most common ways schizos self medicate is with alcohol and weed which both suppress rem sleep when awake and asleep which would explain why people are successful in self medicating, most psychologists and schizos I've spoken to in hospitals have all emphasized at somepoint the importance of not just sleep but a regular sleep schedule, regular sleeping patterns increase REM which would mean the brain would have to "take" less rem when awake which would result in a reduction of symptoms

could I be onto something or should I take my meds?

>>11305741
Put Hermitian operators [math]a = A + A^*[/math] and [math]b = b + b^*[/math]. Let [math]c = a,b[/math] and [math]C=A,B[/math], then [math]c^2 = 2 + {C,C^*}[/math] whence [math]|c^2| = 2 (1 + |C|^2) [/math]. We now use two results:
1. the spectral theorem, which states that [math]\operatorname{im}C[/math] is dense in [math]\mathcal{H}[/math] for normal operators [math]C[/math], and
2. the spectral bound [math]|A| = \max |\operatorname{Spec}A|[/math], where the norm over the spectrum is taken with the essential Lebesuge measure.
Now we can bound [math]\langle \psi,c\psi\rangle \leq \sum_{\lambda_n \in\operatorname{Spec}c}|d_n|^2 \lambda_n \leq K (\operatorname{dim}\mathcal{H}) d_{n_\text{max}}\lambda_{n_\text{max}} = K (\operatorname{dim}\mathcal{H})|d_{n_\text{max}}|^2 |c|[/math], where [math]\psi = \sum_n d_n \psi_n[/math] is a decomposition into eigenfunctions of [math]c[/math], and [math]K[/math] counts the number of possible degeneracies in the maximal eigenspace.
Now since [math]\psi \in P\mathcal{H}^* [/math] is normalized, we have control over [math]\sum_n |d_n|^2 \leq 1[/math] hence [math]|d_{n_\text{max}}|^2 \leq 1[/math]; on the other hand, we can use Cauchy-Schwarz on the [math]Hilbert~space~of~operators[/math] whence [math]|(c,c)|^2 = |(c^2,I)|^2 \leq |c|^2[/math] where the inner product is defined as [math](A,B) = \operatorname{tr}_\mathcal{H}(A^*B)[/math]. Hence [eqn]\langle\psi,C\psi\rangle \leq \frac{1}{2}K(\operatorname{dim}\mathcal{H})\sqrt{2(1 + |C|)} \implies \langle\psi,A\psi\rangle + \langle\psi,B\psi\rangle \leq \frac{\sqrt{2}}{2}\operatorname{dim}\mathcal{H}\left(K_a\sqrt{1+|A|} + K_b\sqrt{1+|B|}\right).[/eqn]
You can already see the problem with your conjecture: you can't possibly get 1 on the RHS unless [math]A = B = 0[/math].
>>11306255
You need to take the non-relativistic limit before you evaluate the Feynman integral. Internal lines aren't on-shell.

This got marked wrong, does anyone know why?

>>11306828
Probably you got something wrong. It's hard to tell what you were trying to accomplish.

>Directional vectors
Numerical numbers

>>11306824
Based overkill bitch.

>>11306828
why are you taking the difference from (0,-6,-3)? The line crosses (0,6,3).

And you should be dividing out the magnitude of (3,-3,1) not the other vector

>>11306824
I laughed for five straight minutes at this retarded shit, absolutely excellent.
>>11306532
I haven't studied all that much Hamiltonian dynamics, but what I did was good.

>>11300734
Why the fuck does 9mod4 = 1

3*4 = 12 and 12-9 = 3 so 9mod4 should be 3

Reeeeeeeeee

>>11307149
Do you remember remainders from elementary school? 9 divided by 4 is 2 with a remainder of 1. The remainder is what 9 mod 4 is.

What you should with your little calculation is that -3 is the same thing as +1 in mod 4 arithmetic.

>>11307177
showed not should. I have brain cancer or something

>>11307149
2*4=8 and 9-8=1 so 9≡1 (mod 4).

Help me out here, /sqt/. I think my textbook is lying to me.
>a 1/10 Horsepower, 24-volt motor which is 75% efficient uses ____ watts.
My book says 9.5, but i have no idea why. Please help. My professor is confused too.

>>11307293
>watts
Are you sure it isnt asking for current, given that they told you voltage?

>>11307302
No, it's asking for an answer in watts. It seems like it should be as simple as finding 75% of .1 hp in watts, which is simple enough but not close to what they say the answer is.

>>11307304
1/10 hp = 74.57 watts would be the motor's output. If it is 75% efficient, then it consumes 74.57/75% = 99.4 watts. So idk.

>>11307324
Okay, so I'm not completely retarded. Thank you.
They also say to divide by efficiency to get total power I.e. 75% efficiency being "power÷.75", but that's obviously more than 100% efficient. That's gotta be wrong too, right? Is thia book just full of shit?

>>11307333
>That's gotta be wrong too, right
No, that's right. An electric motor is going to consume more power (electric) than it delivers (mechanical). If a 100 watt motor is 50% efficient, then it consumes 100/.50 = 200 watts. Your textbook is fine, looks like there's just a typo on that one problem.

can someone explain whats being asked of me in parts b and c? I don't understand the wording of the problems (as in I feel its poorly written, but maybe its just me) so I cant even begin to start working on them...

>>11307344
I was literally just typing that. I had misread that section. That one problem was bugging me for the last hour so i thought that may be how they arrived to that conclusion. Thanks again.

>>11307350
y=-1 is a function. What is its derivative? What do you get when you plug it into the RHS of the equation? If both sides match you've shown that this is a solution.

And if you can't get y=-1 by plugging in some value of C in that other expression, that means it is a solution that is not covered by that other expression.

That's all it is.

I'm back.
>>11306824
Kind of whipped this up in 5 mins so there are a few typos.
1. it should be [math]c^2 = 2 + \{C,C^*\}[/math], not sure why the braces didn't show up.
2. The spectral bound holds only for ESA operators, or symmetric operators with a self-adjoint extension.
3. We actually don't need [math]\operatorname{dim}\mathcal{H}[/math] in our bound, [math]K[/math] suffices.
4. It should be [math]|C|^2[/math] under the square root, so the final bound should read
[eqn]\langle \psi, A\psi\rangle + \langle \psi,B\psi\rangle \leq \frac{\sqrt{2}}{2}\left(K_a\sqrt{1+|A|^2} + K_b\sqrt{1+|B|^2}\right).[/eqn]

>>11306164
Hmm, I suppose self-inverse is not sufficient then. I'm dealing with QM observables, so A and B have to self-adjoint, which I thought would be covered by being self-inverse, but I see that it's not. Thanks for pointing that out.
>>11306002
>>11306026
>>11306125
>>11306824
>>11307515
Does the restriction to self-adjoint A, B change anything? I admit I'm not fully following all the steps but I recognize that the spectral bound already implies this restriction. If I understand correctly, that would change those square root bounds to just be [math]\sqrt{4}[/math], correct? Though that still seems to be irreconcilable with a final bound of 1.

I'll need to think on this more and go through these posts more closely. Thanks for the help, anons.

>>11307350
By [math]y \equiv -1[/math] they mean the function [math]y : \mathbb{R} \to \mathbb{R}, \ x \mapsto y(x) = -1[/math]. I.e. the constant function at -1. What's the derivative of any constant function?

>>11307609
Do you ever read the other reply before you type yours?

>>11307598
>I'm dealing with QM observables, so A and B have to self-adjoint
Careful, fermion creation/annihilation operators [math]c,c^\dagger[/math] are [math]not[/math] themselves observable, if they're what you're studying. Gauge non-invariant quantities aren't typically observables, unless some quantum phase transition occurs (like in a superconductor).
>Does the restriction to self-adjoint A, B change anything
If [math]C=A,B[/math] are in addition self-adjoint (SA) then [math]\operatorname{Spec}C\subset \mathbb{R}[/math] and [math]C^2 = 1[/math] implies that [math]\operatorname{Spec}C \in \{\pm 1\}[/math]. Using the spectral theorem you can see that all matrix elements of [math]A+B[/math] are bounded by 2.
If on the other hand you mean to restrict [math]C[/math] to the domain on which it is SA, then
1. [math]\{A,B\} = 0[/math] may not make any sense as the domains of their SA restrictions may be disjoint; in particular, their domains may not even intersect [math]P\mathcal{H}^*[/math].
2. Since [math]A,B[/math] aren't necessarily SA, they do not form SA extensions of their SA restrictions, so the spectral theorem only holds on the SA domains, not all of [math]\mathcal{H}[/math].
By considering SA restrictions you are basically throwing away the "bad vectors" so of course you can find tighter bounds on the quantities. But then the question becomes "how much do you lose with this restriction?"

>>11306824
>>11307598
I forgot to mention, bounds for [math]\langle\psi,c\psi\rangle[/math] give rise to bounds for the real and imaginary parts of [math]\langle\psi,C\psi\rangle[/math] if [math]\langle\cdot,\cdot\rangle[/math] is sesquilinear. This is why I had [math]\frac{1}{2}[/math] in the bounds; the LHS should really say e.g. [math]\operatorname{Re}\langle\psi,C\psi\rangle[/math]

>>11307624
Nah, nothing so grand, just generalized Pauli operators (tensor products of Pauli matrices, possibly with some adjoint unitary rotation; could feasibly be generalized to prime-dimensional Paulis but I'm not even looking that far ahead). So while I appreciate the functional analysis perspective, I'm not worried about domain considerations.
>>11307633
Ah, I see.

>>11300734
i've been told the statement
∀P((0∈P∧∀i(i∈P-->i+1∈P))-->∀n(n∈P))
captures the principle of mathematical induction in second order logic.
why wouldn't the antecedent i∈P-->i+1∈P be sufficient, since we're using the universal quantifier on i? wouldn't that apply the condition to every element in P, including the base case?

>>11307708
>functional analysis
Those are general operator algebra theory considerations. If you're on an infinite lattice, your Hilbert space [math]\mathcal{H} = \bigotimes_n \mathcal{H}_n[/math] is still infinite dimensional, and the domain problems crop up as soon as non-local things start propagating, like correlations in the long-range entangled phase. Not to mention difficulties with the continuum limit if you want an effective field theory.
In any case, your problem has been sufficiently answered I hope? Good luck out there.

What's a good introductory book on Discrete Mathematics? Struggling to keep up with Knuth's work..

>>11303736
Well I'll be damned. It's amazing how knowing the right word can be the difference between day and night when researching stuff. Thanks.

>>11306791
underrated

>>11307775
Try Mathematics: A Discrete Introduction by Scheinerman
You can actually find a free pdf easily using Google

>>11307744
[I wish I worked on anything as interesting as that, heh.] Yeah, thanks again.

on /tv/ i saw alot of anons mention that it's actually mathematically improbable that there are or were aliens in the universe. i never though about it like that but i forget what was the mathematical reasoning

anyone on here that can support that?

why do you have to connect headphones as an antenna to listen to FM radio on your phone when the cellular data etc. is also transmitted using FM radio and you dont need any (large and external) antenna for that? isnt the cellular signal way more complex and carries more data? then it should be more difficult to pick up compared to "classic" FM radio.

do cellular towers just push a stronger signal? then why dont radio stations?

>>11308081
(((they))) want more radiation targeted at your brain.

>>11308092
never reply to me again, idiot

>>11308097
Ok. Oops, I just replied to you.

>>11308032
[math]
\mbox{Aliens} = \mbox{Yes}
[/math]
[math]
\mbox{Aliens} - \mbox{Yes} = 0
[/math]
[math]
(\mbox{Aliens} - \mbox{Yes})
(\mbox{Aliens} - \mbox{No}) = 0
[/math]
[math]
\mbox{Aliens} - \mbox{No} = 0
[/math]
[math]
\mbox{Aliens} = \mbox{No}
[/math]

>>11308097
if you don't think 5g can be weaponized then you're wrong and very ignorant about the nature of e/m radiation

>>11308295
>Dividing by zero
You see, this is why the aliens refuse to talk to us.

>>11308310
I literally do not care about that

How do I find the middle of a segment using determinants?
>Find M, the middle of the segment determined by the points A(2,-1) and B(0,3)

>>11308420
You must average each coordinate separately. Determinants have nothing to do with that.
(2+0)/2=1
(3-1)/2=1
=>(1,1)

>>11308313
Aliens won't talk to us because of your ugly butt.

>>11308354
Caring has no metaphorical meaning in that sentence.

>>11308446
>Determinants have nothing to do with that.
Don't they? The chapter is called "applications of determinants in geometry"

I got a question about physics.
I'm working on a game and I think I'm misunderstanding something about gravity.
Gravity pulls everything down at constant rate of 9.8 m/s^2 , right?

So to find the velocity of an object being pulled down by gravity I would take the amount of time thats passed and multiply it by gravity right?
So v = t * g?

>>11308589
If you are working with a flat, infinite earth, yes (almost). I will treat the "up" direction as positive.
v_final = v_initial - g*t

>>11308600
So if I did vFinal = vInitial - g*t constantly that would increased the speed constantly? Would that physically correct?

>>11308617
I don't think I understand your question. [math] v(t)=v_0-gt [/math]. v(t) is a function of time. You do not need to "do" anything.

>>11308617
while your method will work and is a perfectly valid solution, a better method might be to increment the velocity instead such as "velocity += gravity * deltaTime" where deltaTime would be the amount of time between frames or a fixed value of whatever you feel is appropriate. This way you only need to store one velocity value for each object as well as the initial velocity for each object created will be much more intuitive to understand regardless of when the object is added to the scene.

>>11308617
v(t) = v_i - gt

>>11308630
>>11308638
>>11308645
I think I'm getting it now

>>11307366
>>11307609
thanks

ignoring air resistance, would a car driving on a paved road on the moon stop faster or slower than on earth? Assuming the car has the same initial velocity (and etc.) on the earth and moon.

braking is a function of friction between the brake disks and rotors, but also of the redistribution of weight of the car onto the front tires which have rolling resistance with the ground.
Less gravity means less rolling resistance means most of the braking will be done by the disks, with less help from the wheels. The car still has the same mass, and thus momentum, even though it weighs less.
I'm leaning towards it would take longer to stop, am I thinking that through right?

How many hours of study do I need to place well (say, 75th%) on the GRE Math subject test if the last class I passed was university calc 1?

>>11309055
Much slower. Lower gravity = lower traction = lower deceleration (mass remains unchanged).

> braking is a function of friction between the brake disks and rotors, but also of the redistribution of weight of the car onto the front tires which have rolling resistance with the ground.
You don't understand braking. If the wheels are turning, braking is a function of friction between the pads and the discs/drums. If the wheels are locked, it's a function of friction between the wheels and the ground.

The maximum deceleration is determined by the lesser of the two. If the brakes are capable of locking the wheels (and if they aren't, either your brakes are fucked or the vehicle is overloaded), friction between the wheels and ground is the limiting factor. This is why stopping distances haven't gone down with improvements in braking; rubber hasn't changed and nor has tarmac.

As a first (and quite close) approximation, maximum deceleration = gravitational acceleration * coefficient of friction between wheel material and ground material. Downforce (from spoilers etc) helps a bit at speed, weight transfer not so much (brakes are applied to rear wheels as well as front unless you're on a motorcycle).

Is it possible to skip calculus and go straight on to real analysis and linear algebra after Basic Mathematics

Reply to >>11309346 for good health and excellent luck.
>>11308032
No.
>>11309180
All of them.
>>11309360
It is, but depending on what exactly you mean with analysis, it's either a bad idea (because you want to skip to topology and measure theory) or it's irrelevant (because you fell for the "analysis is rigorous calc" meme).
Basic Linear Algebra doesn't really require knowledge of calculus.

>>11309388
I want to skip calc on to something like Tao's analysis. I'd rather get on to real mathematics as soon as I can.

>>11309509
>Tao
>I download it to take a look
>starts with set theory
>literal 150 pages of stuff like construction of the reals until continuous functions
Sure thing, go right ahead.

Is fire an adhesive? When I smoke a cigarette and it burns and I tap it, the burnt stuff falls right off but the bit thats on fire stays stuck on. Is it some ionic attraction caused by the ionized gasses or do tobacco leaves just have a natural resin that keeps it together until heat destroys it?

>>11309526
ty rabbit anon

What's the music for the yukarispace section in that touhou super mario clone?

>>11309573
Super Marisa Land?
I dunno, but the entire OST seems to be on youtube.
(Also, ask this stuff in >>>/wsr/ )

>>11309055
Make it an easier problem. Assume the brakes lock up and the friction coefficient is that same for both road surfaces.

The loss to friction is then directly proportional to the gravitational attraction. It'll take a lot longer to stop on the moon.

>>11309837
In Kerbal Space Program this is fun to play with. On low gravity moons you have like no traction at all. Most of my mum rovers have RCS thrusters facing UP to add to the downforce and give more traction to get out of craters.

>>11309543
No. Cigarette tobacco is intentionally cut long and thin to allow for ashing without the cherry falling off, because the unburnt tobacco strands are interlinked. Once the tobacco is burned the cellulose is destroyed and the residual ash is fragile, so it breaks away with little force.

"Find the values of p for wich the improper integral converges and diverges."
I got no fucking idea on how to do this

>>11309837
>Assume the brakes lock up
No.

>>11306823
Make a thread. Nobody looks at this crap. I think you're on to something but I don't know shit.

Dear /sci/,

Why does the hydrostatic pressure exerted onto an object depend only on the depth of the object inside a body of water?

Also, imagine an aquarium 10m deep, and imagine an aquarium just 1m deep, but with a 9m pipe extending from the top. If both are full of water, an object at the bottom of either of those should feel the same pressure, right?

>>11310439
>right?
Yeah. Sides are contained, one way or another altitude of column is all that matters. Is this bothering you? Some call it the hydraulic paradox.

>>11310448
That was more of a follow up question to the first one, why is the altitude the only thing that matters, even if the column is much smaller than the main body of water?

>>11310473
Thats in my answer too. Maybe I'm too dumb to explain. The surface of the tank with the 9m pipe is holding the weight that the column is imposing. The further down, the more weight above. At any point, the pressure is equal to the wall of the container at a right angle. If it wasn't, you'd have flow.

A solution of sugar in water is to be concentrated from 5 % w/w to 18.1% w/w by a bubble column. The solution is fed at a rate of 1000 kg/h into the column.

Air at a temperature of 40 C with a dew point of 10 C is fed through the column and when it exits, it emerges saturated. No heat is exchanged during this process.

I need to calculate the absolute humidity (kg H2O/kg D.A.) of both air streams (in and out).

So far I've been able to calculate how much water is absorbed by the air stream (~724 kg/h).

How can I use the data given to calculate the AH? Which table do I have to use?

[math]5+\frac{7}{2}+\frac{49}{20}+\frac{343}{200}+... [/math]

[math]5+\frac{7}{2}+[\frac{49}{20}+\frac{343}{200}+... ][/math]

[math]\frac{17}{2}+[(\frac{7}{2})\frac{7}{10}+(\frac{7}{2})\frac{49}{100}+... ][/math]

[math]\frac{17}{2}+[\frac{7}{2}(\frac{7}{10})^1+\frac{7}{2}(\frac{7}{10})^2+... ][/math]

[math]\frac{17}{2}+[\frac{\frac{7}{2}}{1-\frac{7}{10}}][/math]

[math]\frac{17}{2}+\frac{\frac{7}{2}}{\frac{3}{10}}[/math]

[math]\frac{17}{2}+(\frac{10}{3})(\frac{7}{2})[/math]

[math]\frac{17}{2}+\frac{70}{6}[/math]

[math]\frac{121}{6}[/math]

Why am I wrong?

>>11310811
you didn't apply the formula for the geometric series properly, notice that your infinite sum starts with a power of 1, where the formula you used requires the first term to begin with a power of 0.

So you need to subtract 1 at that step.

>>11310424
Essentially:
>throw it into wolfram to see if there's an indefinite integral (there isn't)
>apply bullshit trickery (i.e. check if 1/(x log^p x) has an indefinite integral (it does, thanks wolfram)
>check where that one fails
>try to do some comparisons like setting u=x-1 and gouging out inequalities
If you can't get solutions from that, try comparing the integral with the series.

>>11310424
The integrand is [math] \frac{1}{x(ln(x) - 1)^p} dx[/math] which has a primitive function
[eqn]\frac{(ln(x) -1)^{1-p}{1-p}[/eqn]

>>11310894
>\frac{(ln(x)-1)^{1-p}{1-p}

I mean [eqn] \frac{(ln(x) -1)^{1-p}}{1-p}[/eqn]

>>11300753
>Also, can I just grow them in a tube so that my hypothetical wife can skip the pregnancy?
No, you retard.

Maybe you are right

Should I take a masters degree in visual computing or just teach myself what I can and throw myself into some job in the area?

I'm currently a CS undergrad. The biggest problem that I face in taking a masters in the area is that it would require me to go abroad and that could mean learning the spoken language of the country that I go to and spend a lot more money, however I might be able to mitigate money issues since I have family living in some of the cities that I'm thinking off and might get free rent.

>>11309571
you’re literally not going to know why anything is motivated or what it applies to, Tao doesn’t even thoroughly discuss differentiation, and linear algebra intertwines with analysis precisely when calc begins to merge into the abstract background. just read a fucking hard calculus book there are many of them available

>>11310439
>>11310483
Okay, so imagine you have a large, still body of water, like a lake. Now, select a differential element in the middle of the lake, some depth down. Choose this element to be a cube with its edges aligned with the Cartesian axes to make analysis simple (z dir. points up, and x and y are horizontal directions). Now, we know for an experimental fact that pressure changes with depth, we just don't know how. We also know there are some forces on this differential cube and that the cube is in equilibrium. (Forces in the horizontal directions balance obviously by symmetry, nothing interesting to look at.) As far as forces along the z dir. go, there is a pressure on the bottom face, [math]
P [/math], pressure on the top face [math] P+\text{d}P [/math], and the body force of gravity [math] W=\gamma\text{ d}V [/math] where gamma is specific weight and dV is the volume of the cube. Now, since we have equilibrium, we are ready to apply Newton's laws.
[eqn] \sum F_z=P\text{ d}A-(P+\text{d}P)\text{d}A-\gamma\text{ d}V=0 \implies \text{d}P\text{ d}A=-\gamma\text{ d}V [/eqn]
But, since [math] \text{d}A=\text{d}x\text{d}y [/math] and [math] \text{d}V=\text{d}x\text{d}y\text{d}z [/math], we get
[eqn]\text{d}P=-\gamma\text{ d}z\implies\frac{\partial P}{\partial z}=-\gamma [/eqn]
which says that the hydrostatic pressure at a depth is proportional to that depth and to the density of the fluid, and nothing else. That's the symbolic "proof" that comes from Newton's laws, but you are also welcome to confirm this with experiment. It is counter-intuitive, but nature doesn't care.
>>11310705
Use a psychrometric chart. https://www.ashrae.org/File%20Library/Technical%20Resources/Bookstore/UP3/SI-1.pdf If the process is adiabatic, you will be following that straight, diagonal line of constant enthalpy.
>>11309543
>do tobacco leaves just have a natural resin
that's called "tar," darling. isn't smoking fun?

>>11311162
thanks, I found http://www.flycarpet.net/en/PsyOnline in the meantime.

the "saturated" part means that the relative humidity in that specific air stream is 100%, correct?

>>11311178
>the "saturated" part means that the relative humidity in that specific air stream is 100%, correct?
Yes, that is correct.

>>11311180
so i calculated everything else, but the final question has me stumped

it reads:

Calculate the volumetric flow in m^3/h of (wet) air in both air streams (in & out).

What does this even mean? Is it related to the psychometric diagram again?

Do I just have to find how much volume 1kg of air takes up and then multiply by whatever number I have?

>>11311162
>Forces in the horizontal directions balance obviously by symmetry, nothing interesting.

Not obvious to some as you say yourself.

>It is counter-intuitive,

I never misunderstood this. Even without your education but, I see full grown engineers playing with x and Y as if they could change something. Sometimes with dangerous results. I'll have to trust you on the symbolic representation. A cigarette has a grain. If you switch warp and weft, it falls apart. Are you one of those so smart, you are dumb types?

Can the universe or evolution consider intelligence as a obstacle in front of survival?and how?

Wasn't there a paper or some kind of analysis done that said bones could be many times stronger if there was a straightforward substitution of calcium for titanium? Or some other too-rare-for-evolution-to-handle element.

>>11311069
>applications
why is this important?

>>11311680
You said you knew the mass flow rate, right? Well, you can determine the specific volume of the air directly from the psychometric chart
Volume flow rate = mass flow rate × specific volume
(specific volume is literally just 1/density)

>>11311744
>not obvious
It's just an argument from symmetry, anon. If you don't agree with my (admittedly) hand-wavey derivation of the principle of hydrostatic pressure, that's fine, I'm just sketching the proof. It does't matter anyway because the result I got to in >>11311162 has been known and tested and utilized since the fuckin 17th century. If it was wrong, we'd probably know by now.
>something something cigarettes
Genuinely don't know what you are taking about. I am a "legitimately kinda stupid" dumb person.
>>11311825
Applications are more interesting to some people

>>11311883
***psychrometric

>>11310435
>make a thread about this schizo shit
Please have mercy on this poor board.
>>11311069
>you’re literally not going to know why anything is motivated or what it applies to
Anon, he said
>real maths
I'm sure he's aware of all that.
>>11311744
He's the cute-smart-dumb type.
>>11311803
Yeah, look up Baki the Grappler.
>>11311825
They're fun.
>>11311883
I think he was replying about the cigar thing.

>>11311883
I know that there's ~1700 kg/h of 16% RH fed into the bubble column, and while passing through it, it absorbs ~700 kg of water to 100% RH.

So in the input side I'd have 1700 and on the output side 2400?

and on the specific volume thing, so for the airflow going in, I have ~0.007 specific humidity and a Tdb of 40C, so it's the blue point on the chart, which equates to 0.9m^3/kg of air, correct?

What about the air going out of the bubbler? It's specific humidity is ~0.05 which is off the charts, literally.

>>11306823
https://www.ncbi.nlm.nih.gov/pubmed/?term=rem+schizophrenia
>Cognition in schizophrenia improves with treatment of severe obstructive sleep apnoea
>EEG 40 Hz Coherence Decreases in REM Sleep and Ketamine Model of Psychosis.
>Disturbances of sleep quality, timing and structure and their relationship with...Alzheimer's disease and schizophrenia
>This review provides a critical evaluation of clinical and animal literature describing sleep and circadian disturbances in two distinct conditions and animal models thereof: Alzheimer's disease (AD) and schizophrenia
i.e., ̶G̶o̶o̶g̶l̶e̶ ̶i̶t̶ search PubMed for the state of the art, then Sci-Hub for the papers.

>>11306547
Come to think of it, it may actually be possible to form an economic proof that trickle down systems imply trickle up more often than any other kind of trickle.

>>11311923
It's leverage and mobility. "Trickle down" really means "trickle everywhere," and concentrates in the hands of those with the most leverage/economic mobility.
The net movement, therefore, becomes "trickle up"

>>11311903
>>11311883
come to think of it, is the assumption that since no heat exchange takes place between the air flow and the rest of the system the temperature on the output will be the same as the input correct?

>>11311903
>and on the specific volume thing, so for the airflow going in, I have ~0.007 specific humidity and a Tdb of 40C, so it's the blue point on the chart, which equates to 0.9m^3/kg of air, correct?
Yes.
>What about the air going out of the bubbler? It's specific humidity is ~0.05
Huh? Yeah, I wouldnt be able to tell you without going through the whole problem. Maybe check the units? Sometimes specific humidity is in g/kg instead if kg/kg
>>11311894
>He's the cute-smart-dumb type.
impossibly kind~

>>11311944
>is the assumption that since no heat exchange takes place between the air flow and the rest of the system the temperature on the output will be the same as the input correct
No, bad assumption. Twb should be the same, I think.

>>11311964
so I basically I assumed something stupid on the output side hence why everything's gone to shit.

There's 1747 kg/h of air at Tdb=40C and Tdp=10.

It absorbs 724 kg/h of water from the mixture, which makes it fully saturated with moisture.

how do I calculate the absolute moisture knowing that the relative moisture of the airflow going out is 100%?

>>11311977
>how do I calculate the absolute moisture knowing that the relative moisture of the airflow going out is 100%?
Once again, psychrometric chart. At a given pressure (usually atmospheric), the following variables are dependent and satisfy the thermodynamic state postulate: Tdb, Twb, h, ν, absolute humidity, rel humidity. This means if you know two properties, you automatically know all the rest

what would happen if we had negative pressure?

>>11312099
It's nothing exotic. It's the same thing as tension, like an elastic band. That's what dark energy is by the way, some kind of (positive) energy density that has negative pressure

>>11312099
Negative absolute pressure is physically meaningless. We can have negative gage pressure easily, though. Just imagine a vacuum chamber that is in the process of being evacuated. It will have negative gage pressure. The atmosphere is trying to crush the chamber only to be resisted by the stress in its walls. Negative stress is also a thing.

>>11312107
>Negative absolute pressure is physically meaningless
wrong

>>11312112
Then explain

Is our universe discrete? Otherwise whats the meaning of the Planck constant.

>>11312116
There's no evidence the universe is discrete. Planck's length is a derived quantity.

ah better ask it here.
what is the mathematical abstraction of time? i mean time is oftern used as an argument of a fuction. what if time is a function itself??

>>11312115
I just did. It is like tension of a stretched string, but for a volume rather than just one dimension. In ordinary pressure you lose internal energy as the volume expands, with negative pressure you gain internal energy. You can think of this like potential energy gained due to the work needed to stretch the volume.

>>11312137
That isnt absolute pressure, anon.

What is a practical example of a quadruple integral, similar to density being a triple integral?

>>11312142
Do you know what a stress-energy tensor is? That is how the big boys talk about pressure

>>11312099
Can you give an example? Human blood is under less than 2psig. Our differential is relatively negative in an airplane. You get itchy at 1/3 atmospheric and may pop if you didn't flash freeze in space. What do you mean? I'm with >>11312107
So far.

>>11312146
i mean mass (density being the function under dxdydz)

why are computers so useless in making discoveries. all the important shit was discovered long time ago.

>>11312147
>do you know what [not pressure] is?
Pressure is absolutely not a tensor.

>>11312161
It is the trace of the spatial part of the tensor. It can also be defined in a thermodynamic context as the variable conjugate to volume. Both of these two definitions agree. Nothing I have said is non-standard, but if you are using terms like "absolute pressure" I think you are talking about introductory physics, so maybe it's not relevant to you

>>11312161
You say tomato, Anon says tomato.

can someone please explain how I can find the length of the new BE (in red)?
I was going to use the law of cosines to find the distance between B and the B and the distance between E and the new E and add/subtract them from the original BE but I can't figure out the distances A -> new B and F -> new E in order to use the law of cosines
please help

what if the earth was obliterated but millions of people survived including some high IQ people. but no technologies to copy, no textbooks, not scientific articles, no internet. nothing. we are back to hunting and gathering. and all the neets and zoomers learned hunting and agriculture. early marriages became the norm again. everyone is back at the bottom of the maslow pyramid. but some people still remember how it was pre-apocalypse. how quickly would the humanity get back to the original levels of both scientific advancement and social degeneracy?

>>11312095
nevermind, I figured it out

all I need to do now is to multiply the mass flow rate with the specific volume in the input and output side to get the two volumetric flow rates?

what are the physical boundaries of the spacetime universe? and what is beyond that?

Do real flower petals have an order to them like a trig function on a polar graph?

>>11312218
I don't think this thread is intended to be for literal stupid questions

Which field of math is the memiest? Is it chaos theory?

How does 12/-6 = -2 ?

How can we take a positive number and then divide it by a negative number, how can there be -2 of -6 in 12? How does this make any logical sense?

>>11312255
because 12/-6 is equivalent to -1(12/6) which is equivalent to -1(2), or -2

>>11312146
There are quite a few integrals over spacetime in physics.
I don't have any "do at home" examples, tho.
>>11312211
>deformation not a parallelogram
Rough.
I'd probably just use analytic geometry. This is genuinely the kind of shit you should use it for.
>>11312244
Would you rather anon made a new thread?
>>11312245
Applied category theory.

>>11311883
I do agree dummy. You need to put down the calculator and work on your communication skills. I was trying to help you with that part and figured you could teach me some of that fancy math stuff, at another time.

>>11306823
You’re on to something but most schizos chain smoke cigs and smoke weed, i haven’t met many who drink.
>>11311825
Calculus was developed to be applied to problems in the sciences, not knowing how to solve a related rates problem or compute a basic volume integral is idiotic.

>>11312278
>i haven’t met many who drink.
Let me introduce myself. But yeah, he ain't whistling dixie.

>>11312213
Yes! lol you are so close

>>11312211
NEVERMIND

>>11312146
Multivariate probability distributions

Guys how do I find the line perpendicular to say a point on a circle?
I'm made a picture it's the green line

>>11312971
Draw a line from the center of the circle to that point.

>>11313053
That is quite big brained, thank you sir

But now what if the shape is an irregular polygon,,,

>>11313113
If a side has slope m, the perpendicular has slope -1/m
C'mon, anon

>>11313113
Calculus.

Why does semen bleach textile dyes?

Can anyone help >>>/wsr/759974 ?

Let a be a positive number. Then there exists exactly one natural number b such that b++ = a.

b++ is the Successor of b. Tao defined a positive number is a natural number that is not equal to 0. Btw this is the Peano Axioms from Tao's Analysis I.

I've tried applying induction on a, but it's only a vacuous truth on the base case(since if we let a = 0, this will be false by definition). On b, I was stucked in the inductive step, I tried where b will become b++, that is ((b++)++) = a.

>>11313894
Axiom 2.4 gives uniqueness immediately.
For the existence, we consider the property [math]P(n)[/math] which is true either if [math]n=0[/math] or n is the successor of some number.
P(0) is trivial.
For any n, n++ is the successor of n, and thus [math]P(n) \rightarrow P(n++)[/math].
Induction applies immediately.

https://www.youtube.com/watch?v=Lg-blZScZJ0
Is this bullshit, can you get that much motion from such a setup?

>>11314365
I find it a bit suspicious that it only seems to move more when the camera is away from it

>>11300936
Infj: the post

>>11314365
>perpetual motion
As always, it is bullshit

>>11301436
Youre infj

>>11314381
He even admits in the video it's not, but I'm wondering if you can even get that much motion

>>11314365
Unless I'm missing something, it doesnt look like it picked up very much motion at all. it's just a simple homoplanar motor. Also, never give ken wheeler views.

>>11314445
>homoplanar motor
Isn't it just a magnet?
>ken wheeler
is he well known here?

according to this video https://www.youtube.com/watch?v=8H0l1u_xQ5o
[math]\sqrt[3]{1819} = 19[/math]
but my math textbook shows that [math]\sqrt[3]{1819} = 12,21[/math]

i don't know how to calculate [math]\sqrt[3]{something}[/math]

>>11315754
Where does that video say that? I didn't watch it but I skipped frames and they showed that the cube root of 2197 is 13. Clearly since 1819 is smaller than 2197 it's cube root can't be 19 and they would never make a mistake so basic if they're going through all the trouble of making a video.