/sci/ - Science & Math

Today is a great day
It's a day of learning math
In this happy place

/sci/bros, rec me a good book for thermo I.

Unanswered questions from the previous thread:

Math questions, exact subject in brackets (most of the time):
>>11121253 [Stochastic processes.]
>>11124498 followed by >>11135354 [Statistics.]
>>11133059
>>11135296 [Graphs.]
>>11135732 [Calculus.]
>>11135898 [High school algebra, ennumeration problem.]
>>11136817
>>11144287
>>11145316 [Combinatorics.]
>>11145332 [Bolzano-Weierstrass theory.]
>>11146319 [Linear algebra.]
>>11145317 [Asymptotics or limits.] [Also answered, but I'm pretty sure it was answered incorrectly.]

Physics questions:
>>11121120
>>11121790
>>11128162
>>11135738
>>11142711 [At least I think it's physics.]

Engineering questions:
>>11120997

Chemistry questions:
>>11127484
>>11136018
>>11137410

Alchemy questions:
>>11145472

Biology questions:
>>11123397
>>11126065
>>11127002
>>11127139
>>11127399
>>11139152
>>11143246
>>11145513

/g/ questions:
>>11128371
>>11142078 followed by >>11142098 [Technically answered, but anon has specifically replied to the answer with a thanks for bumping, so I'll make an exception and put it here.]

Stupid questions:
>>11126032
>>11127993
>>11128442
>>11133845
>>11139769
>>11146195

>>11146481
I recall that I didn't put a subject in the curve shortening flow one since the subject is "curve shortening flow", but I have absolutely no idea why I didn't add "module theory" to the other one.

Can sound waves transform into or run along magnetic waves?

>>11135738
No. Even assuming perfectly reversible processes, the maximum efficiency of a cycle is η=1-TL/TH (which is strictly less than 1) where TH is the thermodynamic temperature of your hot reservoir, and TL the temp of your cold resv. See Carnot's theorem.
If you aren't talking about a thermodyanmic cycle, then yes, a particle can move through a potential field without losing energy. This is the definition of a conservative field.

>>11120997
check valves

>>11145472
acquire philosopher's stone

>>11146536
Yes. That's how a microphone works.

My teacher calls Mn2O7 manganese(VII) oxide, but she also calls P2O5 diphosphorus pentoxide.

Is it correct to write manganese heptoxide and phosphorus(V) oxide as well?

>>11146587
Not a chemist, but I don't think that's acceptable simply because mangnese is a transition metal and phosphorus is not.

>>11146587

Metal means you simply list oxidation state, non-metal you list structure. Check with the IUPAC nomenclature for exact definitions.

Asked this in a previous thread, but it didn't get answered because it was on the verge of dying.

Is there any way to turn lead into a more useful element in an energy-efficient manner?

I'm not a chemist of any sort, but I do know there's at least a decent amount of lead on Earth that we get as a byproduct of mining operations, and that there aren't a lot of good uses for it given how toxic it is to humans. It does have a high atomic weight though, so maybe if there were a way to either fission it or turn it into something fissionable, we could end up with a bunch of not-lead that we could use for something else.

How do we know the universe is infinite?

What particles are we 100% sure exist?

What was before the big bang?

>>11146904
You don't need to repost, see >>11146481
>>11147039
We don't and it probably isn't.
>>11147040
None, go read Hume or Descartes.
If you mean "what's the general experimentally verified consensus", go look up the standard model page in wikipedia.
>>11147074
Last I checked, general consensus is that there was no before the Big Bang.

do chads carry genes for butch mannish women?
do skinny incels carry genes for cute petite girls?

What's going to happen when we collide with Andromeda?

>>11147099
>go look up the standard model page in wikipedia.
Doesn't say

why do matter and antimatter go boom when they touch each other?

>>11147110
A new, bigger galaxy will form over the course of millennia
Probably nothing will happen to the solar system because galaxies are mostly empty space so the chance of anything crashing into us is essentially zero
If there are any humans left when that happens they won't even notice the merge is happening, except for the few scientists actively studying it

>>11147137
>low chance of colliding with anything
>low chance of any extraterrestrial life visiting us
>low chance of anything
Fuck the space it's so big for no reason and we gain nothing for studying it

>>11147141
Space is unimaginably big and the speed limit is so relatively minuscule, the harsh truth is that even if there IS anything or anyone interesting out there chances are we'll never ever find it or get to do anything with it. But I wouldn't say there's nothing to gain by studying it, knowledge for knowledge's sake is not a bad thing

Would humans have come to be if the asteroid didn't kill the dinosaurs?

>>11146383

>>11147099

>there was no before the Big Bang
Wouldn't that suggest the existence of a God then? Something has to be the eternal, and I would assume that would be the universe itself, but...

>>11147160
Maybe, maybe not. How the fuck could anyone answer that when we're talking timescales of hundreds of millions of years

>>11147167
>Something has to be the eternal
why?

The derivative of |2x-2| would be [math]\frac{4x-4}{|2x-2|}[/math] right? Or do I not understand how to derive absolute functions?

>>11147168
Through thought exercises you retarded empiricist

>>11147127
also is there an antimatter equivalent of light? if we had a big enough chunk of antimatter that we could somehow contain in a vacuum so it wouldn't explode, would "normal" light do anything to it or does annihilation only happen with particles that have mass?

>>11147181
the anti-particle of a photon is a photon

If you have an interval and a function is not differentiable at a certain point in that interval, is it true to say "the function is not differentiable on the interval" or should you say "the function is not differentiable at a point in the interval" or something else?

It's for a question about the mean value theorem.

>>11147178
Not science and not math

>>11147173
Strictly speaking it doesn't have a derivative, since the function isn't derivable at 2x-2=0 (so x=1) which is part of the maximal domain of the absolute value. That said, if you define the function just on the intervals (-inf,1) and then (1,inf), you could define the derivative without issues. But for x<1, 2x-2 is negative, so the absolute value just becomes 2-2x, and for x>1, the absolute value remains the same so you have 2x-2. And you can probably find the derivative of either of those very easily.

From you solution, you have if x<1 then the derivative would be (4x-4)/-(2x-2)=-2, and (4x-4)/(2x-2)=2, if x>0. Which matches up almost perfectly with the results above, however you still need to get rid of the case x=1, since then the fraction becomes undefined and in general the derivative isn't defined.

>>11147206
Differentiability is a local property, saying a function is differentiable is just a short way of saying that it is differentiable at each point in it's domain. If a function is not differentiable at a point (even just a single one), then the proper thing to say is that the function as a whole isn't differentiable, or it is not differentiable in its domain. Of course you can change the domain by adding certain restrictions, but at that point you are technically working with a different function.

>>11147207
Science can be used to simulate a model to approximate a result using assumptions and confidence intervals. Don't be upset you're a brainlet and can't approach questions that are not solved in your textbook.

>>11147222
there is no model anywhere in all of biology that comes close to modeling evolution over thousands and thousands of generations, retard.

>>11147219
Thanks very much.

How the FUCK do I determine a sequence's convergence? As in how do I execute it? I know the definitions, |xn - limit| < ε for n>=N, etc., but I just can't ever really move forward from that whenever I have to do an actual exercise. How do I approach these exercises, what's the actual process to doing them? Please provide examples. 4th time I'm in some sort of basic Maths course in Uni and every time I get hung up on this shit and there goes the whole semester ;_;

is it a rule that if you have a=b/c you have c=b/a

>>11147268

a=b/c
ac=b
c=b/a

Checks out for the most part, except for cases where division by 0. If b=0, the whole thing blows up because...

a=0/c, therefore a=0
c=0/0 <- this isn't acceptable.

>>11147268
yes, this is always true so long as a=/=0

Doing the improper integral of xSinx/(x^2+2x+2) from -infinity to infinity through the complex plane, using the Cauchy theorem. However, I end up with a complex number result from the integral of the full semicircle in the complex plane, when the result should be entirely real, given that the curve part of the integral should go to 0. Am I fucking up my calculations or am I missing something?
Thanks for the help

What type of math describes the stuff you'd expect to see in a "Satisfying mechanisms compilation"?

>>11147488
engineering mathematics ;3

What do i do if i wanna learn college level stuff but dont wanna interact with others or spend money or take tests but im also not self motivated enough to study onmyown

>>11147626
Depends where you live. If you're in a first world country, there's probably some university around that doesn't have entry checks, which means you could just go and sneak into a class.

>>11147643
im too paranoid to do that consistently, and the one time i did do that it was just a lecturer with a thick hindi accent proving theorems. if i wanna read proofs i can easily do that alone, thats hardly a lesson lol

>>11147488
In all honesty, the two single smoothest and most immediately beautiful things in maths are complex analysis and symplectic geometry (in particular applied to mechanics).
Some other subjects are more attractive than either, such as contact geometry or sheaf theory, but those take time.
>>11147626
>I don't wanna interact with others
>I don't wanna study on my own
You'll need to either settle for studying with other people or without other people, there is no third option.

>>11147074
Time didn't exist until the big bang so how can there be a before

Is there a term for a type of hypothetical particle that exists at multiple points in time simultaneously? That is, if you emit there particles through a room, they will cast a shadow on the wall with the outlines of future things that would pass through that room, because they get blocked by future objects as well as present objects.

Pretty sure this doesn't describe tachyons and is instead something else. Also, does anything in physics hard disallow this? Because I feel this is a pretty tame way to "time travel".

>>11147680
well, id like to study with guidance and Human, i just meant i dont want to be around tons of shitty normies in a Uni setting

>>11147735
Sounds like you have a problem with your ego. Stop that.

>>11147735
How much money do you have?

>>11147741
a little bit yeah, but thats not the relevant cause. i just have social issues (ones not mainly stemming from ego)

>>11147749
not that much

>>11147764
>i just have social issues (ones not mainly stemming from ego)
Well, those can be fixed. And the best way is to interact socially. There's nothing wrong with normal people, anon. Good luck~

>>11147771
i dont wanna interact socially and yes normally people are cruel and i dont have money or mental stability for uni anyway

so how do i learn me some differential geometry?

>>11147774
>yes normally people are cruel
Most people are not cruel. I promise.
>so how do i learn me some differential geometry?
Years and years of study. You have to know the easy stuff before you know the hard stuff.

>>11147488
Is that device more complicated than it needs to be?

>>11147731
>multiple points in time
>simultaneously

simultaneity is a concept referring to occurence of events at the same time

>>11147916
doesnt look like it

>>11147919
But you understand what I mean. A particle that has a chance to collide with barriers that will block its path in the future, jumping forward in time as it does so.

>>11147983
if it collides with those barriers now then those barriers block it now rather than in the future

>>11147170

Nothing -> Something doesn't make logical sense.

>>11148151
based on logical first principles, explain why

What's the tern that describes the condition where one point continuously approaches another stationary point for infinity? Such as in the case of repeatedly halving a number forever with respect to zero.

>>11148180
A limit.

How do the brain worbk

>>11148180
Convergence?

what exactly are the specs of a 75ohm attenuation and where can i find out more info on the subject, possibly equations to help me attenuate video and sync signals

Can someone tell me if I understood addressing in x86 correctly?
Let's say we have address of something in ebx, ebx equals that address and [ebx] equals to whatever is stored in that address
ebx[esi] is the same thing as [ebx + esi]
Now the thing that confuses me:
if there's mem1 declared in .data, both mem1 and [mem1]
afaik mem1 and ebx are the same thing as offset mem1 and offset ebx, because assembler just assumes that it's what we meant, because having real address doesn't have sense

>>11148151
bruh, think one step back. If you cant have something from nothing what came before God?

>>11148781
That's the point, God is literally defined as the something that stops the infinite regress. This doesn't imply that God has any particular properties like being the Biblical God or whatever, it just literally identifies the concept of the necessary, non-contingent being with that word.

>>11148784
I mean you still have to prove the necessity of a 'God' and Occram's razor would suggest you don't need it.

>>11148786
Is logical necessity not sufficient? Reminder, you have an emotional reaction to the word "God". Pick another term if you like, but if you accept that all contingent things have causes, denying that there is some non-contingent thing at the beginning actually makes things much hairier and harder to justify. You don't automatically become a Christian fundamentalist if you accept this argument.

>>11148793
I don't believe a 'prime cause' or whatever the terminology is is a logical necessity. Especially when it could probably never be proven and therefore void/ indistinguishable from no cause. Also its 2am and I'v had too many beers.

While making an erotic text game I came across this problem:

I have some variable [math]F[/math] which changes as a function of [math]w[/math].
For any given starting value [math]w_0[/math] and a change in [math]w[/math] of [math]\Delta w[/math], the relationship is thus:
[eqn]F(w_0+\Delta w)=\dfrac{w_0f(w_0)+D\Delta w}{w_0+\Delta w}[/eqn]
Where:
[math]D[/math] is a parameter [math]0\leq D\leq 1[/math] that changes according the player's actions in the game.
[math]f(w_0)[/math] is some other function. Right now it is defined as [math]f(w_0)=\dfrac{w_0}{71.6h^2}[/math] ([math]h[/math] is some constant), but it could change in the future to [math]f(w_0)=\dfrac{w_0}{64.1h^2}-0.176[/math].
So to put it another way:
[eqn]F(w_0+\Delta w)=\dfrac{\dfrac{w_0^2}{71.6h^2}+D\Delta w}{w_0+\Delta w}[/eqn]

Is there a way to make this into a nice little [math]F(w)[/math] expression?
I COULD just program the entire thing as-is directly into the game code, but I need to determine the exact values of [math]D[/math] to plug in there. I don't want to manually test out values between [math]0[/math] and [math]1[/math].


Is such a function even possible..?
Someone please help me out, I've never been good at calculus

>>11148906
oh and in case anyone's wondering,

[math]F[/math] is the bodyfat percentage of the player.
[math]w[/math] is the player's weight
[math]h[/math] is the player's height
This function is basically to calculate the bodyfat % as the player gains/loses weight.
The two [math]f(w)[/math] functions are linear regressions of data I found on fat% vs. BMI (body mass index) for men and for women.
[math]D[/math] is some parameter that should change according to how much exercise the player has accomplished.

If anyone has a better idea of how to go about this, I'd be happy to hear it.

>>11148906
>>11148919
>simplify the function
Can't see any way of doing it and doubt there is one.
>linear regressions on fat% vs. BMI
That makes absolutely no sense. You do know that BMI is only a function of height and weight, right? It can't differentiate muscle and fat, so it false positives when you give it athletic people. Did you test your linear regression for validity?
My recommendation is simple. Set w=e+f+m, where w is weight, e is "essential weight" given by organs, bones and the like, f is fat and m is muscle.
E is constant, the variation of f is calories consumed minus calories burned times a constant, and variation of m is a function of exercise (a logarithm might work, but it all depends on how exercise is measured in game).

should i apply for a masters or straight to the phd if im in the US?

>>11149011
>You do know that BMI is only a function of height and weight, right? It can't differentiate muscle and fat, so it false positives when you give it athletic people. Did you test your linear regression for validity?
BMI is defined as [math]w/h^2[/math]. You're right, it can't differentiate muscle and fat, but there is a statistical correlation between BMI and bodyfat, which is where I got that linear regression from.

>Set w=e+f+m, where w is weight, e is "essential weight" given by organs, bones and the like, f is fat and m is muscle
The problem is that I'm trying to keep it very grounded and realistic. While I could just arbitrarily set the player to gain +X muscle mass when they exercise and +Y fat when they overeat, that's not how real bodies work. You don't just magically gain muscle when you work out, and you don't magically gain fat with no muscle when you get fat. These things go together, and I'm trying to figure out a reasonably accurate relation between them.
So if the player wants to gain muscle, they will need to both exercise AND have enough food.

In a roundabout way, that's what I've done. I've combined what you call "essential weight" with muscle mass under Lean Body Mass (LBM). This way I only have two real variable: Total body weight, and bodyfat %. LBM is then [math]LBM=(1-f)w[/math]


Looking back at >>11148906, I realize it probably wouldn't work out. What I should do is look at some sort of a function that looks like
[eqn]F(w+\Delta w)=a\dfrac{w+D\Delta w}{w+b \Delta w}+c[/eqn]
and find [math]a, b, c, D[/math] values that make it similar enough to the [math]f(w)[/math] in an appropriate range of value (basically, use the linear regression as a benchmark for my new function).

I still have no idea how to do it, or how fucking simplify that motherfucker. It looks like a college-level Calculus 1 problem but I'm a fucking dropout so wtf

>>11149134
That's a fractional linear transformation, it doesn't admit simplification.
>it doesn't work like that
It doesn't, but it's still better than assuming constant muscle proportional to height (which is quite literally what the regression does).

Can someone explain in Layman's term what's an adjoint representation and one of the simplest real world example?

why do these stupid chemist niggas say 2,2 dimethyl propene instead of 2 dimethyl propene

>>11149167
jk that doesn't exist hehe

>>11146481
wow, that's very nice of you to type that up, fren. are you a "based janny"?

what's the healthiest way to ingest nicotine?

>>11149315
gum

why the FUCK is this called 1,2-Cyclopropanediol instead of cyclopropanediol? Why does the 1,2 matter? what other forms could cyclopropanediol have?

>>11149336
it's a rooster

>>11147259
bls respond...

how can I ensure my vaping is minimally harmful? I don't have a vape yet but I'm running some prefunctory analysis before really considering budgetting for a vape

>>11149377
>>11147259
>tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx

>>11149382
also, i wanted to ask if people notie a difference in the high between vaping and pipe smoking

does this help?

>>11149382
dont vape anything that claims to have added vitamins, esp vitamin C

If you guys had two years to read whatever you wanted to make yourself as employable as possible what would you read?

>>11149382
>running analysis to consider budget before vaping
What, lmao?

Why do nurses make me expose my entire hairy ass and then, inject me above the belt line?

Why is symmetry used so much?

remi's 5 century unwashed feet!

>>11149439
what do you not get? I'm trying to see how much vaping would cost (upfront cost and monthly upkeep), what the negative effects are, how to avoid them, and if the high is the same as cigarettes/pipe tobacco.

>>11149429
"employable as possibe" is a broad goal. better to narrow it down to something more specific; that's the frist thing I'd do. and I'd probably aim for software developer work.

Wikipedia, in the "Quadratic Equation" article, says:
[math](x + \frac{b}{2a})^2 = \frac{b^2 - 4ac}{4a^2}[/math]

But clearly this isn't the case, right? The `x` is completely absent. Expanding the left hand side yields, obviously:
[math]x^2 + \frac{xb}{a} + (\frac{b}{2a})^2[/math].

wtf?

>https://en.wikipedia.org/wiki/Quadratic_equation#Quadratic_formula_and_its_derivation

>>11149568
Ok, I see:
[math]a(x + \frac{b}{2a})^2 - \frac{4ac - b^2}{4a^2} = 0 [/math]
[math]a(x + \frac{b}{2a})^2 = \frac{4ac - b^2}{4a^2} [/math]

But this is still very different from Wikipedia's entry.

>>11149456
Simplifies calculations a lot.
>>11149514
No. Bad anon. Bad.

>>11149588
I imagine the Remi's feet, after a long century of being a vampire, must be absolutely disgusting from marinating in sweat, grease and bacteria. When she removes her shoes at the end of the day, she probably gets flustered at just how smelly and toxic her bare feet are; her own body betraying all standards of decency by producing an unbelievably lewd and slimy, biohazardous zone of filth within her own footwear. Shoes designed to look pretty and appealing, now soiled and turned into unusable, smelly, ruined trash by her own festering feet. It's almost amazing how an odor so potent and foul can come from a girl so cute. What a contrast!

The contrast would be captivating. On one side, you've got her beautiful, pale, shapely, happy feet. They're works of art, and can arouse anyone with their perfection. On the other hand, you've got endless of amounts of a stink so foul it can make plants wilt and birds fall from the sky just by spreading her toes! Imagine seeing the Remi dip her feet in the ocean and turning it into a bubbling, stinky green mess with her odor and killing all the fish, or having her grab your nose with them and make you take deep breaths!

Remi's cute, pale, smelly, vampire feet!

>>11149535
I think you are putting way too much thought into vaping. It makes no sense. Just fucking do it if you want and don't do it if you don't want. Smoking is a vice regardless.

>>11149568
x is being solved for. x is the square root expression at the end

>>11149597
i don't currently smoke or vape, and it's not like I'm going crazy about it - i.e if the little cartridges are going to cost $100 per month for casual use, that's ridiculous and i won't indulge the habit. similar logic applies if they make my lungs moldy or burnt, or if the high sucks compared to cigarettes/pipe tobacco (I don't want to spend $200 on equipment that doesn't even work for me). to me, all of this seems reasonable

>>11149598
is the notation being used wrong? wikpedia is not saying "x =" (which I would understand), they are saying "(x + b/2a)^2 =", and to me it currently seems incorrect, which i'm sure is my fault but i don't see how

>>11149606
>it currently seems incorrect
it isn't. there wikipedia article is fine.

>>11149568
>It can easily be seen, by polynomial expansion, that the following equation is equivalent to the quadratic equation:
[math]ax^2+bx+c=0[/math]
[math]x^2+\frac{b}{a}x+\frac{c}{a}=0[/math]
[math](x^2+\frac{b}{a}x+(\frac{b}{2a})^2)-(\frac{b}{2a})^2+\frac{c}{a}=0[/math]
[math](x+\frac{b}{2a})^{2}-\frac{b^2}{4a^2}+\frac{4ac}{4a^2}=0[/math]
[math](x+\frac{b}{2a})^{2}=\frac{b^2-4ac}{4a^2}[/math]

>>11149606
It's an intermediate step in the solution.
ax^2+bx+c = 0
=> x^2+(b/a)x+c/a = 0 (divide by a)
=> (x+b/2a)^2-(b/2a)^2+c/a = 0 (complete the square)
=> (x+b/2a)^2 = (b/2a)^2-c/a (move terms other than the square to the RHS)
=> (x+b/2a)^2 = b^2/4a^2-c/a (expand (b/2a)^2)
=> (x+b/2a)^2 = b^2/4a^2-4ac/4a^2 (multiply c/a by 4a/4a so the RHS can be factored)
=> (x+b/2a)^2 = (b^2-4ac)/4a^2 (factor RHS)
=> x+b/2a = ±√(b^2-4ac)/2a (square root both sides)
=> x = -b/2a±√(b^2-4ac)/2a (subtract b/2a)
=> x = (-b±√(b^2-4ac))/2a (factor RHS)

The key trick is noting that (x+b/2a)^2=x+(b/a)x+(b/2a)^2, which has two out of three terms in common with the equation in standard form (after dividing by a so the leading coefficient is 1). Thus the equation can be rewritten so that x only appears once. Then it's just a matter of basic algebra to get it to a x=... form.

>>11149660
> noting that (x+b/2a)^2=x+(b/a)x+(b/2a)^2,
(x+b/2a)^2=x^2+(b/a)x+(b/2a)^2
(missing ^2 in the first term on the RHS).

can I use DFT optimized structures as geometries for coupled-cluster calculations?

>>11149660
>>11149636
>>11149652
Ok, I realized I didn't distribute the negative after brought the "terms other than the square" to the RHS. Thanks! I kept getting 4ac-b^2 for the RHS numerator and it was buggin me. I probably should've stepped away from my work for a couple minutes and then re-evaluated before posting, lol.

Is there a word for the sum of something when you divide 1 by it?

>>11149986
multiplicative inverse

What's the difference between magnitude and amplitude?

>>11150201
google it? amplitude is a slippery concept sometimes, often used to denote many similar things

why there no solution quintic

Is there a definitive guide to algebra simplification? How do you know what the best form will be when finishing a problem? My textbook will leave something like e^-1/x in the denominator, but other negative rational exponents it will simplify to the denominator. Wouldn't it be easiest to always have a 1 in the numerator?

>>11149588
I was thinking of mass quantization, and what that S(2) means.

Turning a field into a group?

The kinetic theory of gasses, inelastic container vs. ideally elastic particles?

My thought on symmetry:

1. An object can only go as fast as c before it's two separate objects (1 object and EM)
2. If so, I can view it like a film strip at frequency c
3. No difference between symmetrical rotating and staying still

>>11146481
>>11120997

It's a picture of two check valves in series, also known as a double-check backflow preventer

>>11146481
>>11126065

Look up glycemic index

>>11149537
And if you're aiming for software development work you really want to do things instead of just reading about them. Having something to show is extremely important, especially if you don't have any formal qualifications.

>>11149336
1,1-Cyclopropanediol

Really stupid question

>>11150201

Magnitude is typically used when speaking of the raw quantity of something.

Amplitude is typically used when speaking of the maximum reoccurring value that occurs in some kind of sinusoidal or otherwise cyclic system.

They are related because the amplitude of something is equal to the magnitude at it's maximum value.

What happens if you boil clorox bleach? Does it release chlorine gas or anything harmful?

>>11150748
Hm, so that means the magnitude is the current value of something (that could be oscillating), while the amplitude is the coefficient basically, or the maximum magnitude attainable?
Thank you!

How do I take the limit of this? It's supposed to be 0, but I tried using a radical conjugate and I got infinity. Aren't limits at infinity supposed to be simplified first so there is no ambiguity? If I divide all terms by x (x^2 in the radical) the limit comes to 0, but I don't think you are allowed to do it that way. All the problems from the limit section make you turn these into fractions by using a radical conjugate.

>>11151322
I meant to say the limit comes to b/a if you divide everything by x, not 0.

>>11150442
Galois theory.
>>11151322
>0
Divide both by b/a, because linearity.
Basic sign analysis will tell you that, when [math]x^2 > a[/math] and [math]x < 0[/math], both terms are positive and strictly increasing as x gets smaller.
That's a typo.

Are you telling me that when I knock on a SOLID WALL the sound it makes is cause the wall "vibrates"?

>>11146370
Stupid question here.
I am doing binomial theorem problems, but I'm a little confused now.
Some of the questions are asking to "state the range of values of x for which the series is convergent" or "state the limits of x for which the expression is valid". I have no idea what's it's asking for and my book doesn't explain it.

Anyone know what this is? A mate found it, belonged to his dad apparently? Dad was German, I think the words translate to Caution Radioactive. It's in a lead-lined box, kinda worried it might be dangerous, but we really want to find out what it is.

>>11151712
Probably cesium or some shit

I'm supposed to find the convergence/divergence of
[eqn]\sum _{n=1}^{\infty }\:\frac{2^{n-1}3^{n+1}}{n^n}[/eqn]
I think I'm supposed to use the root test, but I'm not sure how to manipulate the numerator so that the 2 and 3 are both just to powers of k.
Or does that not matter, and I just take the k out anyway and leave them as 2^0 and 3^2?

>>11152187
>k
meant to say n. It's k on my paper.

>>11149595
i didn't know you shitposted out of jp too.

>>11152187
Pull out the constants to get:
[eqn] \frac{3}{2} \sum_{n=1}^\infty \left( \frac{6}{n} \right)^2[/eqn]
And note that for sufficiently large* n, the n-th term is dominated by** the geometric series [math](1/2)^n[/math], which converges. So your series converges as well.

* I.e. by throwing away finitely many of the initial terms, which has no effect on the convergence/divergence of the sum
** I.e. [math] | (6/n)^n | \leq |(1/2)^n|[/math].

>>11152231
>squared
Power is n, actually.
Unless you were already skipping to the step of taking n>6 and bounding with ^2.

>>11152249
based

>>11152249
>Power is n, actually.
Whoops you're right, thanks.
The correct version (6/n)^n is in the footnote, though it's probably better to err on the side of pedantry for /sqt/.

What academic subject teaches you about stuff like exosphere, different types of metals, natural resources, and stuff like this?

Is it just "earth science"? How do I learn this?

>>11152337
To be entirely honest, I corrected you because I was typing up a reply and kept putting ^2 instead of ^n for no comprehensible reason, so I found it weird you did the same.
I was going to use the Basel series as a bound, tho.

>>11151710
bump.
I reall don't get why the limit for binomial expressions, (a+x)^n, where a=1 is always -1 < x < 1.

>>11146370
Brainlet here. I need to close the sides of a roof of a barn. The sides are two isosceles triangles, and the only data I have from them is their height and base length. See pic related of what I mean. My question is: is the midsegment theorem applied if I only know the height and base? (I know I can apply Pythagora's theorem, but I still don't know the distance of EB or FA) I've always thought yes, but never tested it in real situations, but now since this barn is nowhere near me I can't check if my result for the midsegment is correct.

Is there a term related to the idea of "this technology will never exist in this form because something better will come about before it can be created"? Or put another way "why would you do X if being able to do X meant you could do Y, and Y is better than X."

>>11152601
differential rates of development among potentially substituted future technologies. preemptive obsolescence maybe

>>11152532
And then you use the cosine rule.

>>11152621
180-theta*

>>11152646
Thanks, I'm going blind as a bat.

we’re doing Laplace transforms in dif eq, did i do this part right? specifically the right side

What are the best books I can get in order to learn how a transorbital lobotomy is performed? Hopefully something a non-physician/surgeon could understand.
I don't see how an icepick could be inserted without damaging the extraocular muscles.

>>11151562
I see that the x^2 would be -inf*-inf = sqrt(infinity squared), but would it be an acceptable answer if I put down inf - inf = 0? Isn't that sort of like an indeterminate form them?

>>11152991
The only thing that's wrong is you seem to have y0=-1 and y0=1 simultaneously

>>11153221
its supposed to be 1, where do you see the mistake?

>>11153233
Never mind, i misread. You look good.

>>11153253
ty anon
this is what i have now. any ideas? its supposed to become the terms in the top right. this is mostly an algebra question

>>11153263
Split up the numerator so that you have a sum of rational functions and then use partial fraction decomposition

>>11153314
how do you do partial fractions with a denominator you cant factor?

>>11153332
You dont factor the exponential, you factor the rational function that multiplies it. Then you look at a table of LTs and apply a shifting theorem.
>>11151632
Walls make sounds because they are not absolutely solid. Only a vibrating wall will move the air around it and make sound.
>>11150847
Bleach is a solution of NaClO. When you heat the water, the Na ions and ClO ions decompose to something like units of NaCl and NaClO3 according to wikipedia.
t. not a chemist
>>11152462
b/h = AB/(h-CD)
>>11149595
Gross!

>>11151710
nice questiom, how into binomial theorem for algebra (just use induction or is here something else?) and more important in calculus? binomial theorem for complex variable?

>>11153463
>You dont factor the exponential, you factor the rational function that multiplies it.
i legitimately do not know what you mean by this

>>11153528
>binomial theorem for complex variable
>about to tell anon the binomial theorem works for any commutative ring, even if some of the terms end up vanishing
>open wikipedia just in case
What the hell, I didn't even know this existed.
https://en.wikipedia.org/wiki/Binomial_theorem#Newton's_generalized_binomial_theorem

>>11153531
You manipulate the RHS of the equation to get a sum of rational functions. One of these terms, however, will have an exponential in the numerator (so it isnt really a rational function, but you know what I mean). You find the inverse LT of that function and use a shifting function (i.e. [math]\mathcal{L}^{-1}\big(\exp{-as}F(s)\big)=f(t-a)\cdot u(t-a)[/math]

>>11153553
fucked up the TeX, its obviously supposed to be exp(-as)F(s) inside the inverse LT

>>11153553
>>11153557
i cant inverse Laplace any of these
do i have to use partial fractions? i feel like a retard, but i understand how to solve the problem, i just do know how to move the numbers around in the correct way

>>11153572
>do i have to use partial fractions
Yes. It can be tedious, but usually not too bad. Just google how to do PFDs

>>11153583
>Just google how to do PFDs
from what im reading, if i cant factor the denominator then my options are limited

>>11153600
>I can't solve a second degree polynomial by hand

>>11153603
how would you do it?

>>11153607
With Baskara.

>>11153600
You dont understand PDF if you think this is a problem

>>11153615
thanks for the input

>>11153615
PFD***

>>11153618
Hunny, I've held your hand and done everything I can to help you with your HW problem save literally doing it myself. It is time for you to read the text, practice your algebra, and do it yourself. Good luck~!

>>11153633
its spelt "honey"
i asked for help with one step of a very long problem and you certainly tried to help me with it, and i appreciate that, but you really didnt have to dedicate an entire post to telling me i didnt understand something as soon as you decided that you wouldnt/couldnt help me

>>11153655
>wouldnt
Im just fucking with you.

>>11153655
Alright, Im feeling nice. Specifically which term are you having trouble decomposing?

Is cocohomology the same as homology?
I.e. I have a chain complex so I get homology. I dualize, so I get cohomology. I dualize again, what do I get?

>>11153675
>dualize
>dual
>what happens when I do it twice
>dualize

>>11153670
any of the ones with the second degree polynomial 2x^2+x+2 in the denominator (all of them)
my (tenuous) understand of PFD is that if the term in the denominator has no factors then you cant do anything. do i have to complete the square or something?

>>11147127
Antimatter are [math]CT[/math]-partners of matter, where [math]C[/math] and [math]T[/math] are charge conjugation and time reversal operators, respectively. The reason that [math]u + u^\dagger \rightarrow 2\gamma[/math] vertoces are allowed is because you have the the term [math]\psi^\dagger \not A \psi[/math] in the QED Lagrangian.
Remember, bosons have integer spin, and the Abelian [math]U(1)[/math] gauge boson (photon) has spin 0. This means that they transform under trivial representations of [math]\mathfrak{so}(1,3)[/math] for which [math]C[/math] and [math]T[/math] are both the identity.
>>11147731
In terms of plain relativistic QM, the Heisenberg algebra and its representation Fock space gives the proper setting for us to talk about "particles". For a particle to exist at different times, it must be an excitation of a non-local second-quantized field operator [math]\psi[/math] for which [math]\langle \psi^\dagger(t)\psi(t')\rangle \sim \text{const}[/math]. If this particle is not part of the vacuum (namely if [math]\psi \not\in P_0[/math] where [math]P_0[/math] is the orthogonal projection onto [math]\operatorname{ker}H[/math] with [math]H[/math] some Hamiltonian involving [math]\psi[/math]), then it necessarily violates the Lieb-Robinson bound [math]\langle[\tau^H_t(\psi),\psi]\rangle \sim \text{const}[/math], where [math]\tau_t^H(A) = e^{-iHt}Ae^{iHt}[/math] is the Heisenberg dynamics generated by [math]H[/math]. Unless the time direction is compactified to [math]S^1[/math] and [math]t = t' \mod 2\pi[/math] like in a time crystal, you best have a good reason for violating the Lieb-Robinson bound.
>>11149157
The adjoint representation is the natural action [math]h\mapsto ghg^{-1}[/math] of [math]G[/math] on [math]\mathfrak{g}[/math]. Think of this as the conjugation action on [math]G[/math] near the identity; naively it "rotates" the tangent space.

>>11153722
I meant [math]\psi\not\in \operatorname{im}P_0[/math], of course.

>>11153679
>do i have to complete the square or something
yeah, turns out you do.
[eqn]\frac{1}{2s^2+s+2}=\frac{1/2}{(s+\frac{1}{4})^2+\frac{15}{16}}[/eqn]
This is something you should know how to inverse LT.
[eqn]\frac{1}{s^2(2s^2+s+2)}=\frac{A}{s}+\frac{B}{s^2}+\frac{Cs+D}{2s^2+s+2}=\ ...\ =-\frac{1/4}{s}+\frac{1/2}{s^2}+\frac{s/2}{2s^2+s+2}-\frac{3/4}{2s^2+s+2}[/eqn]
All of this you know how to inverse LT. Think: how would you manipulate the last two terms to being something more similar to the form in the first equation? (Hint: you will end up using the other shifting theorem.)

>>11153679
>do i have to complete the square or something?
yes.

[eqn]\frac{1}{2s^2+s+2}=\frac{1/2}{(s+\frac{1}{4})^2+\frac{15}{16}}[/eqn]

This is something you should know how to inverse LT.

[eqn]\frac{1}{s^2(2s^2+s+2)}=\frac{A}{s}+\frac{B}{s^2}+\frac{Cs+D}{2s^2+s+2}=\ ...\ =-\frac{1/4}{s}+\frac{1/2}{s^2}+\frac{s/2}{2s^2+s+2}-\frac{3/4}{2s^2+s+2}[/eqn]

All of this you know how to inverse LT. Think: how would you manipulate the last two terms to being something more similar to the form in the first equation? (Hint: you will end up applying the other shifting theorem.)

>>11153743
fucking damn. ignore the TeX, all the important bits are readable.

>>11153743
ty, anon, and double thanks for taking the time to tex it

>>11153751
<3

>>11149595
Scientifically speaking, how stinky would Remilia's unwashed vampire feet be?

>>11153761
heres what i finally got, no clue if its right but i thought you might like to see the fruits of your help c:
ty
(btw i just assumed your second line of tex was correct without checking it, so i hope it was!)

>>11153892
im too drunk and can't be assed to go through all the algebra right now but it looks like you're on the right track. if your answer isn't correct, it's because my PFD was bad or because you made some dumb algebra mistake. grats, babe.

>>11153929
>you made some dumb algebra mistake
it would be a christmas miracle if i didnt desu

Reposting from previous thread

Is it correct to say that a projective module is a module P such that every morphism onto it from any module has a right inverse that is also a morphism?

I'm trying to understand what a projective module is and why it's useful or important. I know the "lifting" definition but I don't get what it's trying to say, and I'm trying to work with its characterizations instead. For example I've seen projective modules be referred to as locally free modules, but I also don't get what's that's supposed mean since having a basis locally doesn't really seem to make too much sense, and I haven't seen someone define that property instead of just mention it (any textbook I should read that has that definition, by the way?). I've also seen the short split sequence "definition" (which we learned as a theorem), that states that a module P is projective iff every short exact sequence [math] 0 \longrightarrow A \longrightarrow B \longrightarrow P \longrightarrow 0 [/math] is split. Now, among all the characterizations of short split sequences, I remember that a short sequence is split iff the morphism from B to P has an inverse morphism to the right, and since that's supposed to happen for any module B, that's where I get my "definition" in the first paragraph, where I try to drop the context of short exact sequences and just mention surjective morphisms in general. Is this idea good enough, then? I'm a bit confused cause it seems like a way simpler form to understand its properties but no one states it like that. Also anyone has a better way to understand the idea of projective modules?

>>11154126
>Is this idea good enough, then?
Not quite, you still need the data of [math]A[/math] to make the statement that "every morphism [math]B\rightarrow P[/math] has an inverse morphism". More precisely, [math]given[/math] the morphism [math]B\xrightarrow{\phi} P[/math] with [math]\operatorname{ker}\phi = A[/math], we have a section [math]\psi: P\rightarrow B[/math] such that [math]\phi\psi = \operatorname{id}_P[/math]. This implies that the section implicitly depends on what [math]A[/math] (and hence what [math]\phi[/math]) is, and the statement about projectivity of [math]P[/math] is for [math]every[/math] such possible [math]A[/math] if you hold [math]B[/math] fixed.

>>11153722
OK Yukarifag, I got a question. What's really going on with the Feynman slash notation? Please explain all the machinery behind [math]A_{\mu}\mapsto\gamma^{\mu}A_{\mu}[/math], desu.

>>11154162
If the morphism from A to B is [math] f: A \longrightarrow B [/math], then isn't it just required that [math] ker ( \phi) = im (f) [/math]? Or you just mean that the kernel is isomorphic to A?
Okay so I've been thinking about it for a bit longer, the problem with the property I stated at first is that the condition is way too strong, right? Cause not every epimorphism onto P needs a section, just the ones that have kernels that are images of monomorphisms from A. But at the same time I can't find a case where this wouldn't hold for every epimorphism. For example, if P is projective and the property had to hold for any A in a short exact sequence, then in particular it would have to hold for [math] 0 \longrightarrow ker( \phi) \longrightarrow B \longrightarrow P \longrightarrow 0 [/math], where [math] \phi : B \longrightarrow P[/math] could be any arbitrary epimorphism and f is just the identity (mono)morphism. Wouldn't then this exact sequence imply that the property should hold for any arbitrary epimorphism?

If you have a higher order even exponent polynomial, can you rewrite say, 5x^4 + 7x + 9 as (5x^2)^2 and then use the quadratic formula?

>>11146370
hi

>>11153848
They wouldn't, Sakuya cleans them every day.
>>11154126
Sort of, you need surjectivity of the morphism to P.
Your proof is highly convoluted, have a simple one: Set [math]id: P \rightarrow P[/math] and [math]f: N P[/math]. Because it's surjective, by the definition of projectivity there's a lift to a map [math]g: P \rightarrow N[/math] such that the diagram commutes.
>>11154323
Was that supposed to be 5x^4 +7x^2 + 9?
If so, yes. You set y=x^2 and solve the quadratic normally.
Otherwise no.
>>11154324
Hello.

>>11154442
I fucking knew the surjective arrow would show up wrong. I went to wikipedia and they just had the symbol copied and pasted instead of the Latex, so I thought I'd be cheeky.
Hopefully it works now:
f: N P

>>11154126
from wikipedia:
A basic motivation of the theory is that projective modules (at least over certain commutative rings) are analogues of vector bundles.

So was Einstein a fraud or not?

>>11155022
How could Einstein possibly be a fraud?

How does smell work? e.g. why does rotten food emanate molecules that smell and how do they have energy to travel? Or worn out shoes

Can electromagnetic radiation be explained without special relativity?

How can i calculate the logarithm of 2 by hand provided i know that lg 5 = 0,699 and lg 6 = 0,778

If we make progress in nuclear fusion, doesn't it mean we could theoretically create gold?

>>11155163
log ab = log a + log b
log 10 = log 2 + log 5
log 6 is there as bait.
>>11155167
Nah.

>>11155189
Why not

Anyone here who can help me with (what I'm assuming) is a differential equation?
I haven't solved any of these in 3 or so years and I don't know where to start.
P_n-1 is 100 if thats of any interest.

>>11154442
So it's necessary and sufficient to say that every epimorphism onto P has a section map then? That about just sums the whole concept of projective modules? Sorry if I'm repeating myself but just want to have that 100% certain.
And at any rate, how does the lifting property relate to this, then? Sure, I get how it is defined and how it is used to get to the previous statement (which you already showed is kinda trivial anyways), but what is the advantage of defining projective modules like that if the concept is simpler? Or is there a stronger condition that is being implied and I'm missing?

>>11155125
Yes. Classical electromagnetism is a thing.

Help, I am not able too figure out where this definition of q comes from (3)
The section that explains it says "let A be the set of all positive rationals p, such that p^2 < 2, likewise, let B be the set of all positive rationals p such that p^2 > 2.
It's easy to see that in A there is no number greater than every element of the set, and in B there is no number smaller than every element in the set "
Then they say that for each p we can associate a q such that : (3)
pls help

>>11155270
Yeah.
>why do we define it this way
Golden rule for picking canonical definitions in maths is "which one is it easiest to state and prove all the others from?"
I've given you a proof of one way, which is one line, but proving the way back is a bit worse, (essentially, pick a surjective map from a free module F onto P write out the original definition with the projective P, factor it out with F and do some compositions to find a map from P to N such that the diagram commutes. So essentially, you show by hand that a free module is projective and then you argue from diagrams.)

>>11154442
>They wouldn't, Sakuya cleans them every day.
This is simply not true. Remilia's feet have gone 5 centuries without a single wash.

Can virtual particles be oscillated to a >=1 energy level?

http://tutorial.math.lamar.edu/Solutions/CalcII/TrigSubstitutions/Prob9.aspx

on step 3 how does he get 4secX/(4tanX)^4? sorry can't do the math notation thingy

>>11154170
In general slashed quantities appear in observable scattering amplitudes like [math]\operatorname{tr}\not p[/math]. Note that the gamma matrices furnishes a spinor representation of [math]\mathfrak{sp}(1,3)= \operatorname{Isom}\mathbb{M}[/math], this means that the map [math]\operatorname{Tr}^\text{Spin} = \operatorname{tr}\gamma \cdot[/math] is a map that, intuitively, averages over the spin degree of freedom. You can think of [math]\operatorname{Tr}^\text{Spin}[/math] as a "supertrace" of sorts.
>>11154271
>Or you just mean that the kernel is isomorphic to A?
Yep. In fact, projective modules are exactly those that enter as a semidirect product factor in a module [math]B[/math], at least locally in terms of its generators. As a direct analogy, fibre bundles fit into the exact sequence [math]0\rightarrow F\rightarrow E\xrightarrow{\pi} B\rightarrow 0[/math] with [math]F[/math] the fibre space, and vector bundles are always locally trivializable with [math]\pi^{-1}U \cong F \times B[/math] for [math]U \subset B[/math].

Let [math] R = \mathbb{Z} / n \mathbb{Z} [/math] be a ring. Show that if and only if the nilradical [math] R_N = (0) [/math], no squared prime number will divide n.

I don't know how I show either direction, can't find the connection.

>>11155506
nvm I got it after doing the next example which was cleaner

>>11155303
It's just a convenient construction, it doesn't come from a particular formula or theorem you should know by that point, just from some clever dude's creativity. It's a common construction used for that particular proof (which you'll find basically everywhere else), so they just throw it out.
Or rather I guess you can technically obtain that particular construction using some tricks, for example the secant method or some more advanced stuff, but that is not expected for you to know or prove, and you could also construct it from intuition, trial and error, if you wanted to prove that for other values. You may even find another expression that leads to the same conclusion

>>11155568
Nilradical is the intersection of prime ideals.
If no squared prime number divides n, n = p1..pn. Chinese remainder thoerem: Z/nZ = Z/p1Z x ... x Z/pnZ. Prime ideals are of the form (1)x..x(1)x(0)x(1)x...(1). The intersection is 0.
Alternatively do it directly. If a^k = 0, Each pi divide a^k, hence each pi divide a, since pi are prime, hence a=0. So nilradical is 0.
If a square of a prime p divides n, say p^2 = 0 mod n. Then p is in the nilradical and is nonzero.

>11155511
>fibre bundles fit into the exact sequence
>fibre bundles
>topological spaces
>exact sequence
>exact sequence of topological spaces
Please don't confuse him further.

>>11155701
The quotation broke for whatever reason, meant for >>11155511

>>11155705
The reason it broke is because you used two usenet quotes instead of one.

>>11155671
we haven't had the fact that the "Nilradical is the intersection of prime ideals" yet, so thanks for a direct proof. cheers

btw bless the touhou poster(s) for making this thread every time, i don't know why you (singular or plural) put up with this shit every week or so cheers

>>11155701
How is it confusing? Exact sequences (fibration, homotopy, relative, Meyer-Vietoris, Gysin, etc.) appear everywhere in algebraic topology. I just used a very elementary example.

Could climate change be a alien terraforming program?

Questions about getting into grad school and changing major to statistics

>undergrad was in finance
>got a decent job and discovered statistics was far more interesting

How does getting into graduate school work when you want to change majors like this? Do you have to take undergrad classes or can you potentially skip or test out of them?

>>11155914

>>11153675
can anybody answer this?

>>11153675
CW's in [math]h{\bf Spec}[/math] are dualizable so using Brown representability all cohomology theories [math]E^n(X) = [X,\Sigma^n E][/math] with [math]X[/math] weakly-CW are dualizable. Given a weakly CW-fold, you can use Poincare duality to move between homology and cohomologies.

>>11155870
Because it's a homology exact sequence, not a topological space exact sequence.
Exact sequences of pointed spaces are honestly the absolute stupidest shit.

>>11155986
It helps to visualize what's going on in a fibration.
>absolute stupidest shit
Thank you for your opinion.

>>11155997
>It helps to visualize what's going on
It does, but don't call it an exact sequence, call it an intuition or an analogy.

>>11155883
could you be a retard?

Say you had something that let you sit in the air without moving. A floating chair or something. Would the earth eventually move without you? If not, why not? Wouldn’t be suspended in the air mean you’ll always fall at a different spot due to Earth’s rotation?

>>11156074
Define "not moving." Your velocity is zero with respect to what point in space, exactly?

>>11156081
Like keeping the thrusters of a jet pack going to keep you up, but not going towards any other direction.

>>11156125
Then you would hover over the same spot on the earth because you have the same initial angular velocitu about the center of mass of the earth as the earth does.

>>11156128
Where does the angular velocity come from?

>>11156138
the rotation of the earth

>>11146370
What is a good introductory book into real analysis for self learning and where can I find a pdf?

>>11155627
Thank you

can someone check if it's correct?
"There is a real number a, so for every integer b the result of the amount of a - b is a rational number."
>answer, pic related

Is this a good introductory AI course?
https://artint.info/2e/html/ArtInt2e.html
I feel like reading about AI since we didnt have a course about it in university and I dont wanna miss out

>>11156403
i got confused and put Z instead of Q, i thought Z was rational numbers not Q

>>11156403
I would turn the colon into a comma. Also you need to say that b is an element of Z.

>>11156428
thanks

So I need to take a mapping modulo p here and show that this has infinitely many a that works. I cannot use any other method, i.e. eisenstein. Completely lost how to do this.

>>11156428
can you check if this is correct?
"Each complex number is of the form z = w + i · v with two real numbers w, v."

i've done the negation, idk it's correct but i also have to do the simplification which i can't

>>11156447
Why can't you use Eisenstein criterion? Let [math] a = 3p [/math] where [math] p [/math] is a prime bigger than 5. Then 3 divides 15, 3 divides -30 and 3 divides 3p, but 9 does not divide 3p. Ergo infinite solutions.

What are the fluid-dynamic differences between a converging-end and open-end swirl injector?

>>11156459
What you wrote there would most likely be read by most people as "For all complex z=w+vi, where w,v are real numbers" (also you should probably drop the paranthesis, it looks like you are writing them as an ordered pair in which case they are in [math] \mathbb{R}^{2} [/math] and not the real line)
From what I understand you are more intfor every z, whereas in your statement it just sounds as if you're picking the complex z's that can have that form, but not stating that that is precisely every complex number z. I could rephrase that statement as "For each complex number z there exist real values of v,w such that z = w+iv", in which case you'd write it as [math] \forall z \in \mathbb{C} , \exists w,v \in \mathbb{R} : z = w+iv [/math].

>>11156507
Also I'm a bit confused about your usage of [math] \ni [/math]. It is supposed to represent set inclusion but just written in the opposite direction, so something like [math] \mathbb{R} \ni \forall b \in \mathbb{Z} [/math] is hard to read, let alone find a meaning for. Or what did you intend to write? I assume that you meant to say that since b is an integer then it is also a real number, but that is not necessary to mention and even if you wanted to do so you could just write [math] \forall b \in \mathbb{Z} \subset \mathbb{R} [/math] (ignoring the details about the construction of both sets and other formal stuff).

For the negation, it's just a matter of negating the quantifiers first (so basically "exists" becomes "for all" and viceversa), and then negating the predicates, which isn't too hard since if you talk about inclusion then the negation is just not being included, and if you talk about equality then the negation is just an inequality.

>>11156625
>From what I understand you are more intfor every z
Accidentally deleted something when trying to rephrase it. I meant "From what I understand you are more interested in the existence of w and v for every z"

>>11154442
Can you explain the quadratic formula thing more? So if you have an equation that has an even root and could be rewritten as say (x^3)^2, do you then have to have the next term as a x^2 and then a constant to make the typical ax^2+bx+c. I don't quite understand why the second term can be squared other than what you said about defining y as x^2....so I guess instead of solving for x you do everything the same way, but the answer is x^2. Is this correct?

>>11156571
I know very little about this desu but "Theory and Practice of Swirl Atomizers" by Yuriy Khavkin seems to be a source for pretty much everything you need to know
https://books.google.com/books?id=3tqWpzXLVzAC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false
good luck on finding a full copy online

>pg 22
>for "very open" atomizers with short nozzles, the transition of Fr<1 to Fr>1 takes place without hydraulic jump
>nozzle => hydraulic jump

>>11156782
remilia-anon is saying that for any polynomial [math]ax^{2n}+bx^{n}+c=0[/math] you can find the roots by simply letting [math]y=x^n[/math] and applying the quadratic formula for y. I kinda don't understand specifically what you are asking lmao.

>>11155919
>attach some image to bring attention to the post

>>11155322
Thanks, this helped a lot since at least I kinda know what I'm doing now with the formal definition

>>11156782
>I don't quite understand why the second term can be squared
It usually can't, but when it's of the form ax^2n+bx^n+c it can, you set y=x^n, as bunnyposter pointed out.
>you do everything the same way, but the answer is x^2
Yeah, if you've swapped y=x^2 and you solve for the roots of y, you then need to take the square roots of those roots to find the solutions to the original problem. Same thing for n-th roots.
>>11156808
>I kinda don't understand specifically what you are asking lmao.
Me neither, I've been wildly guessing since the first reply.

In Latex, is there a way to disable all floating / remove glue stretch+shrink from the entire document?

In word documents, I have everything exactly where I want it to be. Latex however tries to be fancy and stretch every page without break into full size. But some pages due to large figures that follow are half empty. Then Latex stretches this half page onto the full page and it looks awful.

I just want Latex to act normally without this stupid floaty shit causing different spacing for every single page. Google was useless.

>>11156625
>Also I'm a bit confused about your usage of ∋
It means "such that" in this case

Let's say you've got a ring homomorphism from the ring of all complex polynomials in x to the ring of 3x3 matrices with complex coefficients. It is defined by h(x) = A, where A is some matrix in the codomain.

How do you know that you can define the homomorphism by just this one mapping? I thought you could only do that if x generates the entire ring (if I remember right, that was true for groups), but I don't see how that could be the case here. I haven't read about ideals yet so if that is essential to understanding the situation please let me know. Thank you anons.

>>11157419
It's true that x alone doesn't generate the whole ring by itself, but x together with 1 does, and 1 is locked onto the identity matrix.

>>11157419
>ring homomorphism
Are you sure it isn't an algebra homomorphism, or a linear ring homomorphism?
>>11157425
I don't think that works for ring homomorphisms, since you can just lift complex conjugation to an automorphism of C[x] (pointwise conjugation) and obtain a second homomorphism that still maps x to A.
I think, might be wrong. Conjugation was an automorphism of C[x] , wasn't it?

>>11157446
There's nothing to "work". Many authors (who choose to work with unital rings) take as part of their definition that the multiplicative identity is preserved:
https://en.wikipedia.org/wiki/Ring_homomorphism

Admittedly I'm assuming that this is what anon's book is doing, but that's the only way this question makes any sense, since otherwise there are of course multiple homomorphisms that send x to the same matrix.

>>11157456
>identity to the identity
That's not what I'm talking about, I'm saying that I recalls conjugation of coefficients fixing x and being a ring automorphism (which fixes the identity, obviously) of C[x] to itself, which would mean we have at least two ring homomorphisms which satisfy what anon said, that is, mapping h(x)=A.

>>11156507
I see three problems in your negation of (a). First, negations are evaluated before subtraction and set inclusion, so you need to have parentheses around a - b ∈ R. You do want to negate the entire expression, right? In fact, ~a doesn't even have a well defined meaning, because a is a number, not a proposition.

Second, recall that when you're negating a logical statement you should change ALL the quantifiers, not just the first one. Lastly (and this is a more subtle point but it's still very important), you should switch ∋ and the comma. Why? Think about what you'd be saying if you don't:

"For all a in R such that there exists b in Z, a - b is not in Q."

This is complete nonsense. How the hell does the existence of some element in Z depend on an an element in R? I don't even know what that question is asking, and you shouldn't either. Now consider this sentence:

"For all a in R, there exists b in Z such that a - b is not in Q."

Spend as much time as you need until you grasp intuitively why is this is the negation you're looking for.

You don't seem to have much intuition for how to phrase statements in logical notation. I highly recommend (for the time being) that you write out the negations in English first, then translate from there, because right now you seem to be blindly following formalistic rules (and not particularly well-formed rules, either); try to keep in mind the sense of what you're ultimately aiming to say. It may also be helpful to examine actual numerical examples: literally try to find a real number such that blah blah blah... it should help you get a clearer idea of what the proposition means.

Your original statement of (b) is all screwed up so I'm not even going to comment on the negation.

>>11157425
>>11157446
>>11157456
Here is the actual statement of the problem. We haven't discussed algebra or linear ring homomorphisms, as far as I'm aware, but then again I usually can't tell what's going on in class. I believe we defined our rings so that they always have an identity element.

Could I hear more about how x and 1 generate the ring? For some reason I can't even locate a section about ring generators in Artin or D&F (we don't have an official textbook). Right now it looks to me like they would generate all polynomials with integer coefficients, but not complex.

>>11157504
Ok I think I will go learn about ideals now.

>all polynomials with integer coefficients
Rational coefficients, actually.

>>11156546
because we haven't "learned" it yet, so we cannot use it for our HW

>>11146463
Read the sticky!

>>11156808
>I know very little about this desu but "Theory and Practice of Swirl Atomizers" by Yuriy Khavkin seems to be a source for pretty much everything you need to know
Thanks!

so I'm doing calc 2 for computer science prerequisites at my university
can someone just explain to me what the FUCK is the point of finding the integral of some random gay ass function

like I look at the graph of these things and I don't think anything in the real world can be represented by these so what's the fucking point?

>>11157607
To be able solve differential equations later on.

>>11157607
>can someone just explain to me what the FUCK is the point of finding the integral of some random gay ass function
There unironically isn't. Sometimes it is useful to find anti-derivatives when deriving formula from first principles, but basically never is it something more than integrating a sinusoidal function or an exponential.
Being very very good at solving arbitrary rational functions is essentially a useless skill. They make you do it in calc II to weed out the super brainlets.

I have been working on a model similar to the newton cradle and other "kinetic art" that has an interesting science/physics attraction and because it has science/physics involved I thought /sci/ might be the place to post about it

The version I have now is made of drinking straws, small ball bearings, and neodymium magnets from ebay and some from old hard drives. I was planning on building a larger model using PVC pipe, larger ball bearings, and either large neodymium or just stacking them together. The way the small model works is similar to how I hope the large model will work except just bigger. With the small model the steel balls role around the track from start to finish about 5 or 6 times with the max being the occasional 8 or 9. The larger bearings I already have seem to travel smoother in PVC pipe than the drinking straws I am using on the smaller model

My question is do you think a single larger neodymium magnet and many smaller neodymium magnets would have a similar magnetic field? If multiple magnets would have a similar magnetic field maybe have the ability to adjust magnetic fields by swapping around magnets could allow for finer adjustment

>copy and paste "Thanks in advance." to the end of the post
"Thanks in advance."

>>11157607
PID control. Think of a thermostat. To turn the furnace on or off, you could:

Proportion: Apply some proportion to the current signal
Integral: Evaluate all the past signals
Derivation: Try to predict to the future by focusing into the current signal's highest resolution possible.

Also derivation of laws. You have
- integral formation: Different equation for a range of inputs
- regular equation: all inputs, some inputs may output infinities
- derivative formulation: works for all inputs, no sharp corners

>>11157634
Im not sure if magnets are a good way to get the bearing up that incline.

>>11146370
Where the hell does the 1 come from?

>>11157607
Integrals are mostly used to solve PDE's and ODE's once you graduate, and you will need to know how to solve ODE's and PDE's if you have any hope of a career in Science. Pretty sure CS will need to know these as well, especially if you plan to work with programming engines.

I have graduate friends and they say PDE's and ODE's are the biggest chunk of their work.

>>11157640
It works on the smaller model. The distance between the bottom and top of the ramp decreases and the bearings travel upward to the top of the ramp. On the small model the bearings overshoot the ramp enough that with molded plastic ridge and a part where the bearing hits the to of the straw is enough to knock the bearing free of the magnets pull and continues rolling

Rollin upwards is not the problem but finding the exact point where the magnetic force is enough to pull upwards but also just right to let go is key. I used a piece of steel to finely tune the magnetic attraction and that was the key on the smaller version. If or when I build the larger version is whether or not a single large magnet or multiple smaller magnets will work

Put a steel bearing in a plastic pipe next to a strong neodymium style magnet and the ball will travel vertical in an attempt to get closer to the magnet and it does it with speed

>>11157652
Any number divided by itself (except for zero) is 1.

>>11157652
Wait why is the original expression supposed to equal zero? Otherwise the solution doesn't make sense.

>>11157607
if your function is a rate you can integrate it to find a value

examples:
function is velocity (distance/unit time) -> integrate to find the total distance between two times
function is a probability density (probability/unit something) -> integrate it to find the total probability
function is a physical density (mass per unit space or number of things per unit space or whatever) -> integrate it to find the total mass or number of things

for cs you can probably get away with
- knowing it's sort of the inverse of differentiating
- knowing you're basically summing the area under the curve
- knowing about newton's method and some extensions to it as that's the building blocks of numerical integration methods
- knowing what differential equations are because modelling them is a huge part of what high performance computing actually gets done

you need the rest of it to pass the course though lmao

idk if im retarded or what, i didnt touch graph theory for a long time, but shouldn't K 1,1,1 be just a triangle? unless K doesn't mean a complete partite graph as i remember
this is what the book im reading now shows K 1,1,1 as

>>11157543
So what gives? Is this not a properly defined homomorphism then?

I'm confused with magnetic torque.
For (a) and (b), the magnetic moment would be pointing towards me/away from me. For (a), using the right hand rule, my thumb representing the magnetic moment, is pointing towards me. My index finger (B-field) points to my left, so the rest of my fingers point straight down. Since the torque would be perpendicular to the axis of rotation, there would be no net torque, right? Same with (b)?

But then, looking at (c), the B-field and the magnetic moment would be in the same direction, making their cross product be 0... meaning no net torque. Obviously one of these is wrong.

can somebody who studied their respective field tell me what is the most difficult branch of mathematics, physics, biology and chemistry?

>>11158378
For (a), the magnetic moment points into the page, meaning the torque points up within the plane of the page

>>11146370
Am I retarded or should the answer here be 4.981... x 10^-5

>>11158569
That's what I thought (just opposite signs) so I'm confused as to how the thing can even rotate

>>11152462
similar triangles. DE is half the base. GD is given. GC is 2.5-0.6. Now you can find CB by setting up the proportions. Then multiply it by 2 to get AB

>>11158672
Magnetic moments aside, you know that in (a) the current in the loop makes a magnetic FIELD that goes into the page by RHR. Magnetic fields want to align with each other, so the torque is CCW. (b) is obviously CW by same logic. For (c) the field made by the current is parallel to external field, so no torque.
>>11158450
[My field]

>>11158367
Yeah, I think so.
Either way, they probably want the map that sends constant a to matrix aI.
I think the answer is something like the ideal generated by the matrix's characteristic polynomial.
>>11158450
>maths
Probably PDEs, to be entirely honest.
I think just about half of the problems in differential geometry and topology can be turned into existence and smoothness of PDEs, but that just makes shit harder to solve.

Are "brain trainer" apps a meme? I'm just looking for nice puzzle games on Android that aren't completely brain-dead like Candy Crush or something.

>>11158697
sudoku

>>11158695
>PDEs
Differential equations in general is a fucking mess of a field. Also, external flow theory in fluid mech.
t. ME

>>11158722
>Differential equations in general is a fucking mess of a field.
mind going into more detail? What makes that so, from your point of view?

>>11158787
There is no general theory to solve arbitrary PDEs.
At some point, a lot of PDEs need their own methods and theory to tackle. The entire subject just feels a bit disconnected and unorganised

>>11158787
This guy >>11158889 isnt me, but basically what he said. Differential equations is disgusting as compared to, say, algebra or complex analysis.

>>11158787
>>11158889
>>11158897
don’t worry fellas, i just looked up the Navier-Stokes problem and it doesn’t look so bad. expect a revolution in the field by 2025.

>>11146370
Mathematically speaking, if 88 < 100 why are blacks still considered human?

>>11159147
because IQs are only comparable between members of the same species.

>>11159152
But that one ape had an IQ of 66. Comparable to the IQ of an African child.

>>11159147
because 10>5.5

white boi

>>11159158
yeah apes are close enough
now that i think about it blacks may be the missing link after all

>>11159160
>muh dick
typical

>>11159147
>>11159152
>>11159158
>>11159160
>>11159168
>>11159170
not the thread for this. please leave.

>>11159172
Sorry, please direct me to the nearest appropriate thread.

>>11159177
/pol/.

>>11158897
>>11158889
I've been aware that they're difficult/well-nigh impossible to solve, but trying to google "why is it difficult to a the solution to a differential equation" only brings up people looking for homework help

I wish I could find actual literature on this kind of stuff so I could learn about it more

>>11159189
it's literally not. Don't fall for the autistic mathematician circlejerkers meme. You literally just treat dx/dy as a fraction and rearrange. Problem solved. It's only hard if you have extreme autism like all the mathematicians. Adopt an engineering mindset and it will set you free.

>>11159197
I don't mean for random well-behaved cut-and-dry ODE/PDEs they give in textbooks that are guaranteed to have solutions, I mean for the gnarly ones that you find working in the wild that don't have any pretty algorithm found in a textbook to solve

Why are those difficult? How did the progenitors of calculus go about solving them by hand long before we had numerical methods, or even computers? Shit like that

>>11159197
>You literally just treat dx/dy as a fraction and rearrange
this doesn't work if you are working with partials or an order higher than 1

>>11159219
Source?

So, I'm really bad with statistics. Can't remember how to do real easy shit, and can't figure out how to Google what I need. My problem is something like this:

20% of the components for a project are capacitors.
I have a shitty supplier, so the capacitors are twice as likely to fail as the other components. Assume the other components are equally likely to fail.
What percentage of my failed components are failed capacitors?

Can I do this?
Given that they are twice as likely to fail, can I just double their number and divide by the new total: that is, as 20 of 100 components are capacitors, so 40 of 120 components are failed capacitors, so 1/3 of my components are failed capacitors?

>>11159258
solve [math]\frac{\text{d}^2x}{\text{d}t}+x=0[/math] while treating the second derivative as a fraction.

>>11159258
solve [math]\frac{\text{d}^2x}{\text{d}t^2}+x=0[/math] while treating the second derivative as a fraction

>>11158378
>perpendicular to the axis of rotation
you _just_ said the torque is up or down in the same damn sentence do you know what perpendicular means?

Work out the percentage for everything and then work out what the question is asking. Statistics is honestly so easy. You're asking what percentage of failed components are capacitors so you need to know the ratio of capacitors and ratio of fail rate which you know. 2:8 * 2:1 = 4:8 = 1/3

Can someone help me intuitively understand this "Mean Value Proposition"?
Its statement is as follows:

[math]

Let \textbf{x} be a point in \mathbb{R}^n and let \mathit{r} be a positive numer. Suppose that the function \mathit{f}: B_r(\textbf{x}) \to \mathbb{R} has first-order partial derivatives. Then if the point \textbf{x} + \textbf{h} belongs to B_r(\textbf{x}), there are points \textbf{z}_1, \textbf{z}_2, ... , \textbf{z}_n in B_r(\textbf{x}) such that:

\mathit{f}(\textbf{x} + \textbf{h}) - \mathit{f}(\textbf{x}) = \sum_{i=1}^{n} h_i \frac{\partial f}{\partial x_i}(\textbf{z}_i)

and

||\textbf{x} - \textbf{z}_i|| < ||\textbf{h}|| for each index \mathit{i} with 1 <= \mathit{i} <= n

[/math]

I grok what it means but I can't really visualize it not reason through it.
Thank you!

>>11159332
Same content but reformatted (new to LaTeX)


Let \textbf{x} be a point in \mathbb{R}^n and let \mathit{r} be a positive numer. Suppose that the function \mathit{f}: B_r(\textbf{x}) \to \mathbb{R} has first-order partial derivatives. Then if the point \textbf{x} + \textbf{h} belongs to B_r(\textbf{x}), there are points \textbf{z}_1, \textbf{z}_2, ... , \textbf{z}_n in B_r(\textbf{x}) such that:

[math]
\mathit{f}(\textbf{x} + \textbf{h}) - \mathit{f}(\textbf{x}) = \sum_{i=1}^{n} h_i \frac{\partial f}{\partial x_i}(\textbf{z}_i)
[/math]
and

||\textbf{x} - \textbf{z}_i|| < ||\textbf{h}|| for each index \mathit{i} with 1 <= \mathit{i} <= n

>>11159305
It looks like it comes to the same results. Given the math, that makes sense. Thanks anon.

>>11159346
Fucking dammit, here it is

Is it true that if p(x) | q(x), then any root of p should also be a root of q?

>>11159872
You can write q(x) as p(x)*r(x) for some polynomial r(x). When is this equal to zero?

>>11159269
I mean even

y' = y + x

cannot be solved by "literally just treat dx/dy as a fraction and rearrange"

if we square adjacency matrix Gi,j shows how many paths of length 2 are there, right?
does it work the same way for cubed and paths of length 3? if yes, does it go indefinitely?