/sci/ - Science & Math

I need to evaluate the given integral.
So I converted it into cylindrical coordinates.
Did I do it correctly? It still feels kinda hard to evaluate.

>>10125209
Hey guys, my self worth is determined by my intelligence right? Like if I have a high iq or if I can do math that makes me better than everyone else, right?

>>10125214
>sin^2
2sin, innit?

>>10125230
How is it 2sin? isn't (rsin)^2 = r^2sin^2

>moment about the planar lamina about the x-axis
This isn't inertia, but the first moment?
So the double integral about a region y*density?

>>10125244
Sorry, I was thinking in complex numbers for a second.

stupid question about specific heat capacity formula, q = C x m x T

C stands for specific heat. What does it mean the C has a subscript? I typically see P as a subscript of C but I've seen other letters also.

>>10125214
Switch order of integration. Integrate x first, then y. Doing so will introduce another y so you can u sub when you get to dy. Learned that on my Calc 3 final some time ago.

>>10125349
c_p means specific heart at constant pressure. Similarly, c_v means at constant volume. Please never use x again for multiplication unless it's a cross product between vectors.

>>10125375
Wow that was so easy. thanks

I have to questions, both stem from inconsistencies in what I "know" about physics / astrophysics.
1. How is the universe expanding at the speed of light if the universe is already infinite? How can something expand into nothing / infinity. I have a potential answer for this that I thought of but I'm probably wrong.
2. How do solar sails work? How do light waves/particles impart energy into something if they have no mass. Ek = 1/2mv^2 P=mv ect. require a mass to have energy / momentum.
Cheers for any answers

>>10125459
OP still. My potential answer for Q1 is that the center of the universe is a point of low entropy so things expand outwards to increase entropy. But this raises more questions such as is there even a center of an infinite thing like the universe?

Why are the limits of integration for the convolution integral sometimes defined from -inf to inf and other from 0 to t? I get tossing away (-inf, 0) to deal with positive time but I don't get why the upper limit just goes to t

Not a stupid question but an important one, I dropped out in 9th grade due to things in my life and would like to learn what I missed out on. Where do I start?

>>10125508
Probably from 9th grade

Next question

>>10125508
Community college or online courses? Im only 18 so take my advice with a healthy pinch of salt

i have a list of numbers, and a time stamp associated with each number. i want to graph the numbers, with x being the time stamp, and y being the number. if i plot each point, it looks sloppy. is there a way to get a better slop? some formula or integral to get the average number in the list at any particular second?

the list i have is about 400 pairs long, look like; [{0:00:01, 1234},{0:00:04, 1238}, ...{0:00:08,1198}]

>>10125508
night classes to get GED

>>10125566
Moving median.
Essentially, pick n and for each number i you calculate the median from i to i+n.

>>10125592
thats what i was thinking too. thought there would be something more elegant but works for visualizing the data. thanks!

>volume of the solid in the first octant bounded below by the surface z = x^2, z = 2-x, y = 3
How the fuck do I draw this? This is so hard. If I can draw this properly, I could easily create a triple integral. Can someone draw this?

What does it mean to extend a function? Specifically in the context of this question:

Let S be a subset of a metric space E. Suppose S is dense in E; that is, every point in the compliment of S is a limit point of S. H is a complete metric space, and f from S to H is a uniformly continuous function. Prove that f can be uniquely extended to a function from E to H, and that the extension is also uniformly continuous.

>>10125624
>z = x^2, z = 2-x
Is that a typo, or is that correct?

>>10125760
it's correct

>>10125749
>What does it mean to extend a function?
Probably this:
If f: S -> H and S is subset of E, then we say f can be extended to a function g: E -> H if there exists a function g: E -> H such that g(s)=f(s) whenever s is in S.

>>10125459
For question 2 waves transfer energy using a different formula that doesn't rely on mass. Im out here solving my own Qs

>>10125480
>and other from 0 to t?
It only simplifies to this when you assume the support of f and g is [math][0,\infty)[/math].

>>10125624
> z = x^2
This is a parabola in the X-Z plane
> z = 2-x
This is a straight line in the X-Z plane, from (0,2) to (2,0). It intersects z=x^2 at (1,1).
> y = 3
This is a plane parallel to the X-Z plane.

The fact that it asks for the first octant means it's also bounded by x=0, y=0 and z=0 (the last one is redundant, as z=x^2 is always above this).

So you basically have a 2D shape in the X-Z plane starting at (0,0), following z=x^2 to (1,1), a straight line to (0,2), then back to (0,0). This is extruded from y=0 to y=3 to form a volume.

The triple integral will be
0<=y<=3, 0<=x<=1, x^2<=z<=2-x

>>10125209
How do you motivate yourself to study?

What happens when the immune system suddenly wakes up to the presence of a massive tumor and starts attacking it? Does it slowly get absorbed by the body or does it quickly die then start necrotizing inside the body?

Are neural networks ever "mixed" with each other to improve performance?

>>10126334
Also, I'm not talking about adversarial networks, I'm talking actually splicing the "genes" of two networks together.

>>10126336
well yeah. Say you have a given neural network architecture with some parameters (number of layers for example). You can start with a few networks and score them with a metric you like. Then you can follow a process similar to a genetic algorithm to evolve the neural networks and find a locally optimal set of parameters

just look up genetic algorithm neural network

https://blog.coast.ai/lets-evolve-a-neural-network-with-a-genetic-algorithm-code-included-8809bece164

why havent we found a way to communicate with alternate realities yet

>>10125459
1. It's perfectly possible for an infinite thing to expand. Just imagine multiplying the real number line by 2 - it expands into itself. If you don't like the idea of the universe expanding, an equivalent view is that the spacetime metric is time dependent in such a way that the distance between two distant objects grows with time. The expansion (we think) is caused by space possessing a constant energy density - either dark energy or the cosmological constant.
Infinite things need not have a centre. The universe (which we don't know is infinite by the way) doesn't seem to have a centre. This doesn't mean it's infinite, it could be like the surface of a ball for example.
2. Those formulas are for slow moving massive bodies. For photons, which are fast and massless, their energy is E=hf where h is Planck's constant and f is the frequency of the light. Similarly their momentum is p=h/wavelength.

can someone explain (ii) step-by-step for a retard

>>10126476
If λ is an eigenvalue of A, there exists v s.t. A.v=λv
Put u=B^-1.v => v=B.u
=> A.(B.u)=λ(B.u)
=> B^-1.A.B.u = B^-1.(B.u)
= λ(B^-1.B.u)
= λu
Thus u is an eigenvector of B^-1.A.B with eigenvalue λ.

>>10126509
> => B^-1.A.B.u = B^-1.(B.u)
Typo; should be
=> B^-1.A.B.u = B^-1.(λB.u)

>Prove that, among all rectangles that have the same area A, the square has the smallest perimeter. Let (x,y) be the sides of the rectangles and p = x + y their half-perimeter and P their perimeter.
This is what I've done so far:
Given that both x and y are strictly superior to 0, we have y = A/x and P = x + A/x.
For the square in particular, x = y so x = A/x <=> x = sqrt(A).
So we want to show that 2sqrt(A) is the smallest possible value for P, meaning that if x =/= y, then 2sqrt(A) < x + A/x.
x + A/x - 2sqrt(A) = (A + x^2 - 2x(sqrt(A)) / x, so I figured I should prove that A + x^2 - 2x(sqrt(A)) is negative.
But I don't know what to do. Could I get some help?

I am reading Logic: the law of truth. I struggle to understand truth trees. Is there some easy material to understand them?

Is there a numerical system based only on prime numbers? What i mean with this is that the number system would ONLY have primes in it and it would go {1,2,3,5,7,...} instead of {1,2,3,4,5,...}.

Which question makes more sense: "why do composite numbers exist?" or "why do primes exist?"

>>10126622
What numerical operation would you even do in it? Next element of the sequence?

>>10126600
Put D=y-x, P/2=x+y, express x,y and then A in terms of P and D. Express P in terms of A and D, and it should be clear that P is minimised when D=0 => x=y.

>>10126600
Be careful mixing up P and p. You've correctly identified that you need to show p can't be less than 2sqrt(A). One way to do this is to rearrange your first equation to get x^2 + px + A = 0, and you can use the quadratic equation to find x (the two roots will actually give you x and y). In this you'll have the term sqrt(p^2 - 4A). The term in the sqrt needs to be >= 0 for the side lengths to be real, which means p^2 is at least 4A, or p is at least 2sqrt(A).

>>10126600
If I have two sides x and y, I can express them in terms of x=a+b and y+a-b.
*winks* *winks again* *winks a third time in case you didn't get it*

>>10125209
Hey guys. Got a report to do and I seem to be the only one in the group actually doing it. We have to make our own way of reducing local waste and I went with sampling plastics to see which out of three are the most prevalent.

As I have no idea how to get the results other than to go out bin-raiding (which the lecturer laughed his ass off at me when I suggested doing so) I'm thinking of just making up the results and sticking a picture of a bin on so it looks legit. I know the dimensions of a bin and can make an estimate of how much is in one so does it seem a good idea?

>>10126698
Right, I got it backwards, you want to minimize the perimeter.
x=ab, y=a/b.

How do you solve d/dy=sqrt(2y) without using the product or chain rule? The set of specifically says not to and find the derivative using algebra to break it up.

What is the critical energy density of the universe?
As far as I understand, it is the value which separates an ever expending universe to one that eventually collapses.

When we measure the energy densities today we find that they sum up to exactly this value, when we say that

[math] \Omega_m + \Omega_{\Lambda} = 1 [/math]

But at the same time we have found that the universe is expending and this expansion is accelerating. Shouldn't this mean that the measured total energy density should be above or below this critical density?

>>10126704
>[math]d/dy ax^n=nax^n[/math]

>>10126745
I suck at using Latex.
>[math]Dax^n=anx{n-1}[/math]

>>10126748
Fucking hell. Third time's the charm.
[math]Dax^n=anx^{n-1}[/math]

Can it be proven that n(n+1)/2, with n being an arbitrary natural number, also be written as a sequence defined as Sn = S(n-1) + n?

>>10126771
Yup, induction.

>>10126779
The problem is that I'm not supposed to use n(n+1)/2 yet since it's proven later in the exercise. For now I need to show that for S1 = 1, S2 = 3, S3 = 6, etc, Sn can be expressed as S(n-1) + n, but I'm struggling.

>>10126751
That gives y^-1/2 which the sheet said was wrong. I thought the same. I think my algebra is just confused.

>>10126790
[math]D(2y)^{1/2}=2^{-1}2^{1/2}y^{-1/2}=2^{-1/2}y^{-1/2}[/math]

>>10125209
For Arithmetic mean with 84,91,72,68,87 and 68, is
>sum({84,91,72,68,87,68})/6
right?

>>10126806
Yeah.

>>10126808
I fucking knew it.

I'm going to kick my retarded professor teeth in

>>10126805
Ah, OK. I never would have figured that out because I didn't think of sqrt2/2 being 2^-1*2^1/2.

>Emailed directly by recruiter for highly competitive company asking me to apply for positions, tell her what positions I'm applying to and she'll make sure the reviewers give my application special consideration

Is this commonplace like colleges emailing asking you to apply or do I have a good shot? This hasn't happened to me before

>>10126806
>Prof doesn't know how to take a mean
???

how does this show that [math]\mathbb{Z}_{14}^{*} \cong \mathbb{Z}_{18}^{*}[/math] ?

This is based on real life, got into a minor argument with my friend because we couldn't agree on the chances

>Trainstation where only Trains A and B stop
>They can both go either South or North
>If Train A going South comes first, you get on and eat at a burger on the way home
>If Train B going South comes first you wait for the next train
>If either Train A or B going North comes first, you get on and go straight home
>All four outcomes are completely random and equally likely

My friend said the chance you'll get to eat a burger is 1/3, I think it is an infinite series with an irrational limit (but I couldn't calculate which)

>>10127076
>infinite series
The possibility that loops doesn't matter, so your friend is right.
>doesn't matter?
Doesn't matter. It doesn't count as a real possibility because it just repeats the exact unchanged scenario. Ignore it.

>>10127054
Both are cyclic of order 6

>>10127082
Guess you are right

>>10127076
> My friend said the chance you'll get to eat a burger is 1/3, I think it is an infinite series with an irrational limit (but I couldn't calculate which)
It's an infinite series with a rational limit = 1/3.
S = 1/4+1/4*(1/4+1/4*(1/4+...)))
4*S = 1+1/4+1/4*(1/4+...))
= 1+S
=>3*S=1
=>S=1/3

>>10127084
I don't follow.

>>10127094
It's nice when the math just adds up

>>10127098
There is a unique cyclic group of order n for any n. Both those are isomorphic to the cyclic group of order 6 so they are isomorphic to each other.

>>10127115
By unique I mean upto isomorphism

>>10127098
Every finite cyclic group of order n is isomorphic to [math]\mathbb{Z}_{n}[/math]. If both have the same order then both are isomorphic to the same group, so it follows immediately.

>>10127093
And so is your friend. Go suck his dick and record it.

>>10126789
Anyone?
I can't figure out how I'm supposed to use induction to show that Sn = S(n-1) + n considering that there's nothing to rely on.

>>10127186
You can rely on S_0 = 0, or S_1 = 1, depending on where you want to start from.

>>10127207
Yeah, I usually know how to do induction proofs but not this one.
What I don't understand is how to get from the inductive step to proving (n+1) since I have nothing else to work with than S(n-1) + n.

is there a way to get the integral of 1/x(lnx)^2 by using the u x v - integral (v x du) method?

>>10127217
Please say, exactly verbatim, what the assignment is.
You can't prove a definition; "S_{n} = S_{n-1} + n" is just a sequence. If you want to show that S_n = n(n+1)/2, you start with s_0 = 0*1/2 = 0, and continue on with s_n = n(n+1)/2 => s_{n+1} = n(n+1)/2 + n+1 and work on that until it reads like (n+1)(n+2)/2.

>>10127227
Yes (and the word for the method is "partial integration")
[math] \int \frac{1}{x}\ln^2{x} = \ln^3x - 2 \int \frac{1}{x}\ln^2{x} [/math]
so
[math] 3 \int \frac{1}{x}\ln^2{x} = \ln^3x [/math]

>>10127229
"Determine the inductive definition of the set Sn", with S1 = 1, S2 = 3, S3 = 6, etc. The set represents cubes stacked on top of each other so that Sn is the nth "floor". The first floor S1 has one cube, the second floor is one cube (like S1) + two other cubes stuck to two of its faces, forming an "L", the third floor is three cubes (like S2) + three cubes that are similarly stuck to the two forward-most cubes as to "fill" the gaps, and it goes on like that.
I know it's a shitty description, I'd take a pic but I don't have the exercise with me right now.
Basically what I have to do is formulate that sequence of cube-stacking rigorously. n(n+1)/2 comes after that, so I can't use it right away.

>>10127248
>Determine the inductive definition of the set Sn", with S1 = 1, S2 = 3, S3 = 6
Ok -- note that what you said here:
>>10127186
>use induction to show that Sn = S(n-1) + n
is not the same thing.

"Sn = S(n-1) + n" is a recursive definition. An inductive definition would be
[math]S_n := \sum_{i=1}^n i[/math]

That's it. Nothing more to do. Weird exercise if you ask me..

>>10127269
So there's no actual induction proof involved?
Yeah, it is a weird exercise. Thanks though.

>>10127227
>>10127238
seems like it would be much more straightforward to just use substitution.

>>10127272
Look I don't know what your assignment means by "determine". To me, there's not proof involved, no.
But on the topic of "n(n+1)/2 comes later": You can use absolutely anything if you prove it from first principles if it helps you. Don't feel chained to any order given to you.

>>10127288
Of course, but the question was pretty explicit about the method.

Correct this number to two decimal places 0.99342105263

Is the answer 1 or 0.99?

>>10127248
>>10127269
The problem is clearly to show that the sequence S(n) defined as the number of cubes on the nth floor as constructed by the given algorithm follows the recursion S(n)=S(n-1)+n.
Presumably the next part of the problem is the show how many cubes there are in the "tower" up to the nth floor.

>>10127328
0.99

>>10127376
Thank you, I thought as much. A lecturer at my uni thinks its 1 and marked me accordingly. The number don't lie..

>>10127382
Maybe someone confused "significant digits" with "decimal places".

>>10125209
I’m a molecular biology undergrad looking to get some research experience. I’m thinking about joining my organic chemistry professor’s lab since I’m doing extremely well in his class and he’s doing research on nucleotide structure which really interests me.

My only concern is that it will look bad if I work in a primarily chemistry lab as a biology major. Will this be an issue or am I just overthinking things

>>10125749
In general an extension is a lift along the inclusion homomorphism [math]\iota: A\hookrightarrow B[/math]. Suppose [math]f:A \rightarrow C\in \operatorname{Hom}(A,C)[/math] as a morphism in a category then an extension is a morphism [math]g\in \operatorname{Hom}(B,C)[/math] such that [math]g = f \circ \iota[/math]. This doesn't just mean what this anon >>10125789 said, but [math]g[/math] must also inherit the same properties as [math]f[/math], such as continuity.
>>10126741
No. The energy density determines the overall curvature of spacetime via GR and nothing more. What a unit (i.e. critical) energy density means that the universe is globally flat, which means that it does not have any tendency towards expanding or contracting. This doesn't contradict the fact that the universe is locally expanding.

>>10125216
Yes

Is there a function whose Laplace transform is itself?

I'm trying to find the Maclaurin series for this function, but I can't. The derivatives quickly get ridiculous and I'm unable to discern a pattern at all. Can anyone help?

>>10128214
You can write f(x) as x - 1 + 1/(x + 1) (partial fraction decomposition), which is easy to differentiate. Or you can also multiply the Maclaurin series of 1/(x + 1) by x^2.

>>10127734
overthinking things, nucleotides are extremely pertinent to your major. If i had your opportunity (I'm too early into my degree), I would jump on it. Consider yourself lucky he's willing to extend that opportunity to you, be useful, and get a letter of recommendation when you're done with his class.
>>10128004
your mom
>>10125216
More beautiful than others => Better than them
More powerful than others => Better than them
More creative than others => better than them
More perceptive than others => better than them
More athletic than others => better than them

What do you think cuck?

are subgroups of [math]Z_{16}[/math] under addition [math]\left< 1 \right> [/math] , [math]\left< 2 \right> [/math] , [math]\left< 4 \right> [/math] , [math]\left< 8 \right> [/math] , [math]\left< 16 \right> [/math] ?

>>10128214
For n>=2, the nth derivative is
(-1)^n*n!/(x+1)^(n+1)
Inductive step:
d/dx n!*(x+1)^-(n+1)
= -(n+1)*n!*(x+1)^-(n+2)
= -(n+1)!*(x+1)^-((n+1)+1)

At x=0, it's just (-1)^n*n! (i.e. n! for even n, -n! for odd n).

from the elementary calculus pdf on the wiki.
how the hell do I answer 15?? the answer key says the answer is 4 delta x

This has to be a typo in my math book
>find the Fourier series
>a) f(x)=-x, -1<x<1; T=2

T implies period. There's no way the period can be only 2 here? It has to be twice that to make sense with that interval, right? I found a similar task as an example in a different book where it's k instead of -x, and there the period is 4 while L(half period) is 2

>>10128484
>function is defined in [-1, 1]
>T=2
I low-key don't see the problem.

>>10128489
because that's just the "period" for the pulse going up. A period is when a pulse has completed a full cycle, eg gone from 0 to 1 and back to 0. Here it implies the period is from when the function is -x from -1 to 1. Does this imply it's -x forever? This is a Fourier series, not transformation so there has to be a cycle

>>10128498
Are you completely retarded?

>>10128317
Yes. In general, for all cyclic groups of order n, they have exactly 1 unique subgroup of order d, where d is any divisor of n.

>>10125209
should i study baby rudin, stewart, or both?

>>10128528
Read normal Calculus and Linear Algebra then go for Analysis.

>>10128535
thanks!

>>10128516
okay smarty, look here. This is a rough visualization of a function where f(x)=a at -1<x<1. The length of one pulse is clearly stated to be 2 as |-1|+|1|=2. And from all the info that is given, f(x) is only "a" at -1 to 1, and 0 otherwise. But this is a Fourier transform, so whenever f(x) is not "a", it has to be 0. From all info I can gather, the interval where it's 0 has to be between 2 and 0

>>10128540
>it has to have a part where it's zero
It literally doesn't

>>10128469
What have you tried? This is really trivial

>>10128528
Courant and John

>>10128469
Ex: [math]f(x)=x^{2} \implies f(x+\Delta x) = (x+\Delta x)^{2}[/math]. Just plug it in the function bro.

>>10128498
A function [math]f[/math] having a period [math]T[/math] just means that [math]f(x+T)=f(x)[/math] for all [math]x[/math]. A function doesn't have to be continuous to be periodic.
You can define such periodic function by giving its values on some interval [math][\alpha,\alpha+T][/math], because its periodic nature tells you exactly what its value is for any [math]x[/math] from this.
Your function's graph looks like copies of the section on [math][-1,1][/math] placed next to each other forever(assuming the domain is all real numbers).

>>10128469
take the outputs of f(x) and add Δx to them then take the outputs from that shift and subtract the output from f(x) again.

so you will take 4x+1 and add Δx and then you will again subtract 4x+1

I'm losing my damn mind over this bullshit ass problem. I never seem to be able to cancel the derivative no matter what I try.

Can someone please explain me what I'm missing?

What's the name of that fake experiment where you remove a single electron from a human being and the resulting chemical reaction basically kills the person horribly?
Something like "Geneva scenario"?

>>10129010
Don't maximize the rectangle, minimize the triangle area.

>>10129010
You can write [math]y[/math] in terms of [math]x[/math]. Notice that for a given [math]x[/math] we have [math]y = 20 - x\frac{20}{12}[/math]. Differentiate this and find the zero of the derivative.

>>10129090
Sorry, I didn't specify properly.
If you look at the rest of the big triangle other than the rectangle, you have three smaller triangles. Try minimizing their areas.

>>10129092
Sorry, I meant to write 'differentiate the rectangle area which will only depend on x'.

Could someone please explain to me the difference between PEGylated polylysine nanoparticle and regular PEG like I was ten years old?
Thanks

Recommend me a textbook on classical mechanics, currently reading Goldstein, especially interested in chaos

>>10125209
test

>>10125209
okay so when they give this equation for simple pendulums what does the x, the A and the q stand for????? I know what they do in maths, but how could i get those in dinamics? My precollege class on this was shit i suppose.
x(t)=A.sen(w.t+q)
v(t)=A.cos(w.t+q)w
a(t)=A.-sen(w.t+q)w^2
My guess is the distance between the pendulum an the "y axis"?? or maybe the arch of curve?I am not sure
Anybody knows?

>>10129192
x is the displacement of the pendulum measured as the arc length. A is the amplitude, which is the maximum displacement. Here q is just a phase shift term which allows the pendulum to start from a position different from x=0 at t=0. And w is the angular frequency.

If F=ma
and E=mc^2
...
Force = [E/(c^2)]a ???

How in the fuck did Pearson manage to create as terrible of an educational tool as masteringphysics? I just can't wrap my mind around how something can be so awful

>>10129296
Yes.
>>10129298
I have pasta tangentially related to this.
Khan academy
>Let me tell you about my favorite videos on math.
>Khan.... let me just write that out here...Khan... I'll do this in Purple. Khan...Academy.... You know, let me write Academy in Green. Khan... Academy.
>And you know, let me give you an intuitive sense as to why Khan Academy is useful.
>*COUGH*
>Let me write out my reasons over here in red..
>No, you know, blue is better.
>One reason is that he makes it simple
>Let me tell you why it's simple
>*writes out simple very slowly* Simple... Simple... You know what, let me write this out with every letter having it's own color.
>Let me tell-
>Let me tell you why it's simple.
>**Sal wrote out simple in 6 different colors, he meant to do it in 7** dialogue box pops out
>And if you could donate to Khan Academy.. Let me spell that out for you.
>Khan.... This time I'll do it in pink...... Academy....
>If you could-
>If you could donate to Khan Academy, see I spelt it out here
>*circles the pink Khan Academy*
>If you could donate that'd be great.
>I hope you have an intuitive sense of why his videos are so great.

>>10129321
Can energy accelerate if it is not in the form of mass? Can energy move? How does it do that?

where do child prodigies come from? i'm talking about the 6 year old kids who can speak four languages and play symphonies on the piano and hold physics degrees. are they born a certain way? do they have a compulsion to pursue stuff that autistically or do their parents make them do it? if a hyper intelligent toddler is made and not born then why are they one in a million?

>>10129422
It's both.
Hypertalented children are really rare, and tiger parents that are willing and able to drop their kid out of elementary school and have them tutored 14 hours a day are also rare.
You need both in order to make a prodigy.

>>10129359
Waves.

>>10129262
ok man thanks so A is measured in the length of the arc? and q is measured as the starting angule?

>>10129445
Can waves accelerate?

>>10129455
>A is measured in the length of the arc?
A in this context is the maximum displacement from the "y" axis, using the small angle approximation it is half the total length of the arc
>q is measured as the starting angle?
it is better to think of it as a phase shift, it's just some value chosen so that the math lines up if the initial velocity is not zero, while it is technically an angle, it is not to be confused with the angle of the pendulum.

>>10129601
>so that the math lines up if the initial velocity is not zero
actually now that I look at it, initial velocity shouldn't be zero at q = 0 in this case, otherwise it's a rather uninteresting pendulum, but we still don't want to confuse phase with initial angle of the pendulum, they are definitely relatable, just not equal

>>10125508
Same here. I've been getting along just fine. Read what interests you and be the best at what you do. You don't need to take classes to get a GED. Put 75 percent of every raise into index funds until you reach twenty five percent of your income. Live happily ever after.

>>10125508
read the sticky please
>>10125513
bee careful about advertising your age on 4chan nigger

>>10125209
Everyone prepare your anii, you're about to be BTFO. Against all logic and despite all odds, I [eqn]will[/eqn] reign supreme.

are Newtons per second squared every used in science?

>>10129601
thanks man i'll study tha topic later

>>10125508

does classical gravity work differently if the two objects attracting each other are spinning

Why exactly aren't Stirling engines used more often for extracting energy from waste heat? Was it really that hard to manufacture them efficiently until just recently? Is there some logistics issue for implementing them?

>>10125209
I know how to do the answers now though why do we add mass and/ or density into the relevant equations without putting the numbers in as x 10^3 given that the units are kilograms?

>>10130679
> without putting the numbers in as x 10^3 given that the units are kilograms?
Because 1 kg is 1 kg not 10^3 kg.

>>10130684
I get that, why don't we convert back to grams though? Do the units not cancel or something? I get kg is the S.I. base unit though I still see converting every now and then, can't really make out when to do it. Also what do you do here? Used mg though that didn't do anything, I know density factors in somehow and alters though not sure how.

>>10130687
density d=m/V
-> d_iron = 7872.9
delta_d = d_iron - d_solution = 6787.9
effective mass m_eff = delta_d*V = 8.0166
F = m_eff * g =78.643
What was the problem?

How get better at nath

what's arctan -2 in terms of pi?

>>10130698
Had no idea you had to work out change in density. Thanks for the help! I swear the whole point of these questions is to make answers that are wrist-cuttingly obvious in hindsight.

What is a sufficient condition for a differentiable function to have a continuous derivative?

>>10131041
Having a second derivative.

What is the fundamental difference between putting components in parallel or in series.
I am talking about resistor, coil or capacitor.

>>10131399
The difference is in how voltage is distributed across the components

>>10131399
Same current in series different voltages across resistors.
In parallel, same voltage across resistors and current takes the path of least resistance.

Could virtual particles be potentially used for F R E E energy?

>>10125209
What value of X maximizes the angle of A?

>>10131580

Set the function a = f (L, H) where L and H are the coordinates ie the length of the bicentric and the height of the floor.

Set up L = l (x) and H = h (x)

Then insert the respective function a = f (l (x, h (x))

Derivera f (x)

Easier said than done.

>>10131583
That's incorrect because of the intregral value...

>>10125209
I need help or I will kill myself because of this fucking thing

how do the fuck do you end up with the creation/annihilation operators on the right hand side of the equation

>>10130687
> why don't we convert back to grams though?
Why would you? The SI unit of mass is the kg. Converting to g makes no more sense than converting distance to mm or time to ms. The question asks for the force in N, which is just kg.m/s^2. If you were given measurements in grams, you'd end up having to convert (implicitly or explicitly) to kg to get a result in N.

You can work in whatever measurements you want, so long as you keep track of the units, and express the final answer in the requested units (i.e. N=kg.m/s^2, not g.m/s^2 or g.mm/hour^2 or whatever).

>>10131604
https://en.wikipedia.org/wiki/Creation_and_annihilation_operators

>>10131818
I know theyre creation/annihilation operators and I know about their physical interpretation (n+1/n-1), I'm just wondering mathematically, how did they end up there, I'm self-learning about vectors/matrices/bra-ket/etc because the teachers just gloss over the stuff during lectures

but yeah, thanks anon

>>10131838
You can always take linear combinations of existing operators and see what happens. Since the harmonic oscillator has a quadratic hamiltonian, which gives linear equations of motion, it's simple enough that solving it with clever tricks like this works well.

Mathlet here, I have a question relating to the order in which to solve an equation. If I have 3(1/3x^2-9)^2 I'm supposed to factor the square first before multiplying by the coefficient on the outside, right?

>>10132416
Nvm I figured it out

>>10132416
>factoring
Nah. The whole thing only gives a zero if the part inside the parentheses gives a zero. Work with that polynomial.

Question about series in the complex numbers:
Let [math]z=x+iy[/math], show that [math]\sum\limits^{\infty}_{n=1} \frac{cos^{n}(z)}{(2cosh(y))^{n}}[/math] is uniformly convergent in the complex plane.

As an advice, I'm told to use the Weierstrass criterion. Here's what I have done so far. Using the exponential definitions of cos and cosh, I got to:

[math]\sum\limits^{\infty}_{n=1} \frac{(e^{-y+ix}+e^{y-ix})^{n}}{2^{n}(e^{y}+e^{-y})^{n}}[/math]

Considering that [math]|e^{ix}|=|e^{-ix}|=1[/math], is it alright to state that [math]|e^{-y+ix}+e^{y-ix}| \leq |e^{-y+ix}| + |e^{y-ix}| = |e^{-y}||e^{ix}|+|e^{y}||e^{-ix}|=|e^{-y}|+|e^{y}|[/math]?

After doing that I think it becomes easier to bound the function. With the Weierstrass criterion, that should be enough to prove uniform convergence, right? I just want to have confirmation if that's a step in the right direction or if I'm fucking up somewhere.

>>10131399
Ever had a burnt out turn signal and the other blinks twice as fast. They are in parallel so they share half the current. When one goe out the current doubles through the remaining. R=V/C.

How am I supposed to solve a non homogenous equation
A(n) = A(n-1) + A(n-2) + 3n
a(0) = 1, a(1) = 2

I keep reading different stuff online. Some say you have to do " a(0) + summation 3n" while others say you have to apply this equation (a(1)n + a(0)) but I get confused here because some tables say if g(n) = n do (a(1)n + a(0)) but others say if g(n) = (n +1) do (a(1)n + a(0)). Which fucking is it?
Both lead to different solutions
The summation is A(n)''= 1 + 3 (n(n+1)/2)

The eqn is A(n)'' = 2n + 1

So which fucking is it? There is no decent source online explaining it besides youtube videos and most just give the equation (a(1)n + a(0)) without really explaining anything or showing how its done

>>10132719
You know how to solve homogeneous recursion relationships with matrices? Expand on that and solve for [A(n),A(n-1),n+1,1] as a matrix times [A(n-1),A(n-2),n,1]

>>10125230
nope
https://www.google.com/search?q=y%3D%28sin%28x%29%29%5E2%2C2*sin%28x%29&oq=y%3D%28sin%28x%29%29%5E2%2C2*sin%28x%29

>>10132620
Looks alright to me

>>10132753
Can't use matrixes.
I have to do it the way I was told in class by the table way provided in my notes which basically say

G(n) = cn +1 (a(1)n + a(0))
Hence my confusion as everything online says g(n)=cn so not sure if they mean the same thing and my notes only provide the table without any examples

Only online video I could find didn't mention the table and instead just did it by getting summation of n (which is n(n+1)/2)

Basically my notes don't say shit i think i need to solve it using (a(1)n + a(0)) but don't know if I plug stuff in or just ignore and do it by summation like the only person I saw doing one.

I've had the worst mathematics learning through my life and I feel really dumb now because of it. I'm writing a program to move a robotic arm while keeping it level. I know the length of the arms and want to know the angles they need to be in. What formulas do I use? Do I not have enough information?

Why doesn't breastfeeding prevent female humans from getting pregnant? Shouldn't it signal the body that it won't be able to take care of anymore offspring if it reproduces now or something?

>>10133049
Women have two breasts and don't have to feed one child 100% of the time.

>>10133030
draw a picture and post it

>>10133059
I could maybe keep track of a virtual distance and know the base length as well but that might be annoying.

How do I show this?

>>10133084
Remember that a matrix is a linear operator. If x is an eigenvector, if τ(x)=λx, then τ(ax)=λax. Just show that since x and y are associated to different eigenvalues they aren't scalar multiples of each other.

>>10133064
notice the opposite angles of A, C and A'
[eqn] \angle A + \angle C - \angle B = 180 ^\circ \\
\angle C = \angle B + 180 ^\circ - \angle A \\
\angle C = \angle B + \angle A' [/eqn]

I doubt I'm posting in the right thread, but I need to keep my drinks cool when watching anime.

I already have a freezable gel cooler type, would an insulatable soda can cooler be more suitable?

I also have some taller 33cl soda cans which do not fit exactly in the freezable drink coolers, the diameter is different from the shorter 33cl cans.
However, this space could be filled up easily with some neoprene.

Should I buy an insulator cooler for my 33cl normal cans?

I always get pissed by the fact I can't seem to develop good reasoning for STEM exercises with my current study method. I try first to make a quick review read , then I get to the exercises and , if happen to not understand any of the exes I go to the resolution and kind of repeat the process until I get it.

Is there something wrong with my methods or am I lacking in the analytical brains department ? Do you have any tips to improve on this ?

I know this isn't /g/ but could someone explain Polymorphism, one of Object-Oriented Programming/Paradigm fundamental concepts?
here's how I understood it so far: a message is sent to an object and this object will resort to an interface which will check for all classes that has a deal/responsability to implement all its matching methods then late binding will choose the correct method matching the message sent

Let [math]f, p: [a, b] \rightarrow \mathbb{R}[/math] such that f is continuous and p integrable on [a, b] with [math]p(x) > 0 \forall x \in [a, b][/math].

Then, show that:

[math]\int_a^b f(x)p(x)dx = f(a)\int_a^bp(x)dx \implies \exists c \in (a, b) : f(a) = f(c)[/math]

------

It looks very similar to the Mean Value Theorem for Integrals, but I can't visualize what's going on here. I tried separating into cases such as when f(a) is the max, min or none of them of f in (a, b), but still nothing.

Any hint would be extremely appreciated.
Thanks!

>>10133400
Assume f(x) is strictly larger than c. Then the integral on the right is larger than on the right. Assume f(x) is strictly smaller than c. Then the integral on the left is smaller than on the right.
Alternatively, apply integration by parts.

>>10133419
Right, I forgot to say that f(x) would have to be either strictly larger or smaller because of continuity.

>>10133419
Thanks.
But I don't see how that would show the existence of c.

I have a feeling this isn't right.

>>10131604
In general the ladder operators are generators of the Heisenberg algebra [math]H[/math], which is a (possibly infinitely-generated) free [math]*[/math]-algebra. A unitary representation [math]\rho: H \rightarrow \mathcal{U}(\mathcal{H})[/math] on a Hilbert space [math]\mathcal{H}[/math] is possible if the number operator [math]N = a_i^\dagger a_i[/math] is well-defined, and this is equivalent to the existence of a cyclic vacuum state [math]|0\rangle \in \mathcal{H}[/math] such that [math]a_i |0\rangle = 0[/math] for every [math]i[/math]. Hence for ever ladder operator problem you should think to yourself: what is this vacuum state? Can you make it from [math]\hat{x}_i[/math] or [math]\hat{p}_i[/math]? If the answer is yes then the ladder operators are well-defined.
>>10133084
Let [math]A \in \operatorname{Hom}(V,V)[/math] and suppose [math]\operatorname{Spec}A = \{\lambda,\mu\}[/math] with [math]\lambda \neq \mu[/math]. Define projectors [math]P_{x} = A - x I[/math] for [math]x = \lambda,\mu[/math], we have subspaces [math]W_{\lambda,\mu} = \operatorname{ker}P_{\lambda,\mu}[/math], then it suffices to show [math]W_\lambda \perp W_\mu[/math]. Suppose [math]{\bf a} \in W_\lambda \cap W_\mu[/math], then [math]P_{\lambda,\mu}{\bf a} = 0[/math] so [math]\lambda {\bf a} = \mu{\bf a}[/math]. But [math]\lambda \neq \mu[/math] so [math]{\bf a} = 0[/math], which implies [math]W_\lambda \cap W_\mu = 0[/math] and hence [math]W_\lambda \perp W_\mu[/math]. Since [math]{\bf x} \in W_\lambda[/math] and [math]{\bf y}\in W_\mu[/math], they must be linearly independent.

>>10131604
solve for x, clearly a plus a dagger is proportional to x, then divide by the proportionality constant.

>>10133770
E[X]=(1/2+1/8)-(1/4-1/8)=1/4
E[Y]=1/8+1/2+2*1/8=7/8
'S right.

using dice notation is AdB = BdA?

Need help shifting a sinusoidal wave.
V = cos(400pi*t + 60degrees)
I'm told to shift this function 5-6ms to the right.
I graphed this out and found the function to be 8.3ms to the left. Where do I go from here?

>>10134207
Say, f(x+6) moves x 6 to the right. So V(f(x)) should be six to the right compared to V(x), innit?

>>10134224
>f(x+6) moves x 6 to the right
that's a leftward shift

>>10134247
Right, sorry, thanks.

>>10134224
That's where I'm confused. How should I find what to add to the cosine argument to make this shift 5ms to the right? I've tried multiplying the angular frequency with the 5ms but I end up with 22pi. My book says it's 1/3 pi

Simple dumb question.
In telecommunications, if I have 2 signals, one of 10Gbps and other of 100Gbps, and they are both modulated using the same digital modulation (for instance QPSK), do they have the same BER?

I know that different modulations have different BER, but I'd also like to know how bit rate affects it.

>>10134264
you might notice that the period is 5 ms, so shifting it rightward or leftward by the period isn't going to do shit. the method of replacing t with t - 0.005 is valid and should net you with a total phase of
- 5 pi /3, they probably also want you to represent the phase as an angle between - pi and pi so add or subtract 2 pi as many times as needed

>>10134318
Sorry, got that wrong.
The question was same modulation, but different Bandwidth.

>>10133813
thank god.

>>10133929
No. For a start, the mean of AdB is A*(B+1)/2 while BdA is B*(A+1)/2. For sufficiently large A and B, those two will both tend to A*B/2, but more dice will produce a narrower distribution (a single die has a uniform distribution).

For a continuous random variable X the probability that X = x (a particular value) is 0. Can anyone provide some intuition for why this is the case?

I need some help clearing up some stuff from multivariable differential calc. Let's say I have a function [math]f: \Omega \subset \mathbb{R}^{n} \longrightarrow \mathbb{R}[/math].
From the definition in pic related, f is differentiable at a point [math]x_{0}[/math] iff there exists a linear map (T) that is dependent on [math]x_{0}[/math] but acts on h, and meets the equation in the pic.
What I understand, is that the generalization of the derivative operator (which I'll call D) we know from real-valued functions is a function [math]D: \Omega \subset \mathbb{R}^{n} \longrightarrow \cal{L}(\mathbb{R}^{n},\mathbb{R})[/math] that maps points from each value in the domain to a linear map between the domain and codomain.

What about the differential of a function, though? I think it is the function (or linear map, to be precise) that results from the function D defined earlier, right? So if I want the differential of f at the point x, do I just need to evaluate [math]D(x)[/math]? And then the differential is just the matrix of partial derivatives I get as a result? This is the concept I'm the most confused about. Is "differential" in this context just the same as what is also known as "total derivative"?

>>10134618
You can try thinking of it in terms of measuring something roughly continuous, like a person's weight. You can ask for P(weight = 40kg), but suppose your scale is accurate to the nanogram. It will be vanishingly rare for you to find somebody that is EXACTLY 40kg and not 40.00001kg, or 39.999998 kg.
The higher you push up your measurement accuracy, the worse this situation gets. The idealized density model is just the limit of this when your accuracy becomes infinite, and the probability of finding an exact match becomes zero.

>>10134654
that helps, thanks

>>10134632
Let [math]f:M\rightarrow N[/math] be a smooth map between manifolds, the derivative [math]D_x(f)[/math] of [math]f[/math] at [math]x \in U[/math] is a [math]C^\infty(M)[/math]-linear map between tangent spaces [math]T_xM \rightarrow T_{f(x)}N[/math] satisfying the Leibniz rule. This reduces to your intuition on local charts [math](U,\alpha)[/math] at [math]x\in M[/math] and [math](V,\beta)[/math] at [math]f(x)\in N[/math].
In general, the derivative is a map [math]D: C^\infty(M) \times M \rightarrow T_xM\otimes T_{f(x)}N[/math]. Though it is [math]C^\infty(M)[/math]-linear, you can't make the identification [math]\operatorname{Hom}(A\times C^\infty(M),B)\cong \operatorname{Hom}(A,C^\infty(M)\otimes B)[/math] in an honest-to-god way unless
1. a countable basis exists for [math]C^\infty(M)[/math],
2. [math](C^\infty(M))^* \cong C^\infty(M)[/math], and
3. [math]A \times C^\infty(M) \cong A\otimes C^\infty(M)[/math].
Conditions 1 and 2 basically makes [math]C^\infty(M)[/math] into a Hilbert space, so you'd need a [math]L^2[/math]-structure: [math] f^*\sigma \in \Gamma(M,L)\cap L^2(M)[/math] for every [math]f \in C^\infty(M)[/math] and every section [math]\sigma: M \rightarrow L[/math] for an Euclidean (or Hermitian) line bundle [math]L\rightarrow M[/math].

>>10134726
The section should be [math]\sigma:N \rightarrow L[/math].

I have a linear algebra question. Say [math]W_1,W_2 \subset F^n[/math] subspaces and [math]B_1 = \{\alpha_1,\dots,\alpha_j\}, B_2 = \{\beta_1,\dots,\beta_k\}[/math] are respective bases with [math]j + k = n[/math]. How would you calculate [math]\dim[L(W_1) \cap L(W_2)][/math]?

The only method I've come up with so far is reasoning about the coefficient value choices you have for where [math]T \in L(W_1) \cap L(W_2)[/math] maps the basis vectors. This gives [math]\dim[L(W_1) \cap L(W_2)] = j^2 + k^2[/math]. Is there a nicer way with this setup considered?

For the biochemists:

Does calculating fold change in gene expression with end-point PCR (through band intensities) versus qPCR (Pfaffl method) yield the same results?

I calculated the fold increase for p21 in response to 5-FU in wildtype p53 and null p53 cell types and got something like 1.5 for wt & 1.0 for null using end point PCR and 150 for wt & 8 for null using qPCR. Since p21 is induced through the action of p53 the first results make more sense to me, despite them coming from the less accurate method.

Are my results fucked or am I interpreting the Pfaffl ratio wrong?

>>10134838
>[math]j^2 + k^2[/math]
That's wrong, unless you meant to compute [math]\operatorname{dim}(L(W_1) \oplus L(W_2))[/math]. In general the two bases can overlap and you'll need to compute [math]\operatorname{dim}\operatorname{ker}P_qP_2[/math] where [math]P_{1,2}[/math] are projectors onto [math]W_{1,2}[/math].

>>10133049
This is because prolactin which induces milk formation inhibits GNRH secretion which is necessary for ovulation. It's a hormone thing.

>>10133049
Read your question wrong. Breastfeeding is one of the oldest contraceptive methods. Idk why you say it isn't

>>10134891
Oops. I'm not familiar with [math]\oplus[/math] but it looks like that's what I meant. I guess also assume [math]W_1 \cap W_2 = 0[/math]. In the original problem I'm considering they are eigenspaces corresponding to a diagonalizable linear operator.

Why is nuclear waste stored and not used as a fuel? It is still radioactive and emitting energy. Why isn't that energy being captured?

>>10134891
How long does it take for you to type all that latex?

>>10133084

ax+by = 0 so A(ax+by)=A0 ==> alx+bmy = 0 where l is \lamba and m is \mu. Then,
ax+by = alx + bmy
since x not proportional to y, the two are linearly independent and the above says
a=al and b=bm which means l=m=1 or a=b=0. The first contradicts the assumption so a=b=0.

To see that x and y are linearly independent, suppose for sake of contradiction that x=ny for some scalar n. Then
Ax=A(ny) = mny = mx but also Ax=lx
So, mx = lx => m=l but this is again a contradiction

>>10125209
If someone stood in a near perfect vacuum chamber on earth would it RIP them apart and kill them or would the vacuum not be applying enough force.

Also can you show your math if so thanks

>>10135245
not that person but I am a research mathematician (re: postdoc) and I can write latex at 60wpm easily.

>>10135452
Vacuum doesnt apply any force. The supposed force that you see in movies is the difference in pressure: a fluid will move from an area of high pressure to an area of low, the speed at which it does so depending heavily on the temperature of that fluid, or in this case, air. However, don't make the mistake to think that this would create a massive current of air outside the whole in normal circumstances, you would feel at most a small current towards the hole, since there is no reason other than random chance that a particle might want to go through the hole. That is, there is no acceleration or force towards it.

If there was a massive (or a small, whatever) chamber with perfect vacuum, with a small hole in it that led to earth, then the air from Earth would slowly fill it up until both areas had equal pressure. If you put your hand over that hole and sealed it perfectly, it would feel no different than if you had your hand over a cup.

not strictly /sci/ related, but how do i get a bold fraktur math font in latex? im seriously on the cusp of killing myself right now

I want to get a microscope to see microorganisms from the channel nearby. I am a uni student, so I would prefer something that doesn't destroy my wallet. Should I buy a pocket microscope, a digital one, or a normal one? I live in Europe

>>10135867
Use google, there surely is an answer out there. Also, I think you need to define you own command.

You need to use something like in the pic.

>>10125209
How do I do these? I rearranged F = ma then divided velocity by acceleration on the first one given that it was decelerating. Don't see how I could have used SUVAT or anything else.

Again ball should be decelerating and effected by gravity so used F = ma to obtain force then w = Fs to obtain work done.

Don't see where I'm going wrong, the powerpoints don't appear to suggest an alternate method so what do?

>>10135916
6- Apply Torricelli.
7- Calculate the kynetic energy it has in the beginning, calculate the potential energy it has at the top. The difference is obviously what air resistance dissipated.
8-Do 7 again.
9-See: 8.

Here in Poland we are taught mathematics at school (elementary/junior high/high school) by having the theoryexplained and then doing numerous math problems. Textbooks are accompanied by math problem collections. When a teacher explains something to students, they then practice in the classroom (doing problems from the book) and they have a number of problems from the book assigned as homework.
From what I know, this is not how it's done in the US or UK.
How is mathematics taught in schools there? How do you practice new stuff?

>>10131604
it's literally just inverting a 2x2 matrix

>>10135989
It's the same in the US

>>10135989
Same in Brazil.

>>10135989
This is how its done in the US too and everywhere else on Earth

>>10135867
\mathbf \mathfrak doesn't work?

>>10136002
>>10135997
>>10136000

all right. I was under the impression that it's some former Soviet bloc relic. Are there any classic math problem collections in English I should know about if I'm an adult trying to master high school level mathematics?

I'm in my first year of uni and enjoying analysis (the workload is pretty painful), but I'm really understanding why some people don't like the real numbers, they really aren't as "nice" as the previous subsets (N, Z, Q).

How much can I do without completeness? Does extending the rationales into the complex plane make any sense? Anybody else feel the same way about reals?

While applying the Gram-Schmidt orthogonalization process of the basis {1, x, x2} with respect to the inner product given by the integral between 0 of 1 of the product of polynomials, we're going to get an orthogonal basis {1, p, q}.

But the norms of p and q are going to be zero, since the elements of that basis are orthogonal to each other (in particular, <1, p> = <1, q> = 0) and because of the nature of the inner product. Regular orthonormalization would give me the basis {1, p/||p||, q/||q||} but in this case the norms of p and q are zero, so I can't get an orthonormal basis out of this procedure.

Where's my mistake?

>>10136269
I think your sentiment is pretty common. R is a pretty gross field in a lot of ways, it just happens to be by far the most common one that shows up in actual problems so we live with it.

For some of your questions:

The issue with extending the rationals into C is that there are two ways of doing this.
For R, you can think of R->C either as adding on i to make R[i], or you can think of it as the algebraic closure of R (basically, make it big enough that every equation has a root).
For R, these two coincide, but for Q they are different. You'll see these kinds of ideas of extending fields when you take Galois theory.

As for what you can do without completeness, unfortunately not much. You can develop differentiation fine, and you can develop a very primitive integration theory (primitive; without transcendentals, you can't even integrate 1/x), but not much else. For example, you're in a place where e and ln don't exist, and neither do trig functions. It sucks.
Analysis is fundamentally about limits; it makes no sense to work in a field where limits don't work. Completeness is a totally natural assumption.

>>10136316
Thanks for this.
I just really didn't like how in our first lecture for a module we were going over the usual stuff of defining basic things:
N={0, 1, 2,...}
Z={...,-2,-1,0,1,2,...}
Q={p/q : p, q (in symbol) Z, q=/=0}
R={fuck if I know}
C={a+bi : a, b (in symbol) R, i^2 =-1}

From this it seems like C is less of an assumption than R desu

>>10136332
>R={fuck if I know}
R is just Q with enough points added that you don't have any holes where your limits should be, i.e. any limit that converges actually converges _to_ something.
Algebraically you're correct, the actual construction of R is very convoluted. But once you get balls-deep into the course you'll see that literally everything in analysis is a limit, so it's important to set up your field so that limits actually work.

>>10136332
I know three derivations of the reals, and there probably are more out there.
It's just a huge pain of a set.

https://en.wikipedia.org/wiki/Evan_O%27Dorney

how do you deal with the fact that there's always someone better out there and you'll probably never make any meaningful contribution

>>10136386
The kid you posted hasn't made any meaningful contributions either. He won a bunch of competitions and fast-tracked through undergrad. He won't even have a PhD for a couple years.

>>10136289
The GS orthog process GIVES you the p and q, but you are somehow starting with the p and q?

GS goes like this:
>normalize 1 (gives you 1, the first "orthogonal" vector in your new basis)
>compute p* = x - <1,x>
>normalize p* to get p
>compute q* = x^2 - <1,x^2> - <x,x^2>x
>normalize q* to get q
WA LAH

>>10136332
Just think of R as Q but such that all sequences converge

https://www.wolframalpha.com/input/?i=gradient+of+(magnitude(v))%5E2

Wolfram Alpha says gradient of the magnitude of a vector is the 0 vector. Is this right? Why? I don't know how to visualize this.

>>10136402
>normalize p*, normalize q*
That's the problem. The norm of p* = x - <1,x> = x - 1/2 is zero! So I can't "normalize it"

>>10136386
because no matter what there will always be someone better than you in any circumstance.

Also, imagine for a moment you're the best there is. Now realize that nobody really gives a shit anyway and only 0.01% of the population actually knows who you are.

You do it because you love it, not because you enjoy penis measuring.

>>10126213
Inspire yourself and set the mood

>>10136413
well that's because {1,x,x^2} is not a basis for your space. If such an orthogonal vector gives you zero, then the GSO procedure tells you find a random vector that is non-zero, and the theory tells you it must exist. Therefore, you must generate new vectors until you get one that just werks

for example, try something like x+1 instead of x, or x^2+x, etc

>>10136393
>https://en.wikipedia.org/wiki/Evan_O%27Dorney
this gu has some great music https://www.youtube.com/watch?v=xo3YER2d7EU

>>10125209
Please recommend me a good book on advanced statistics

All I know about is the basics of probability, discrete distributions, and calculating sample std dev

>>10136451
But {1, x, x^2} is obviously a basis for the space of polynomials of degree less or equal than 2.

So, the GSO procedure doesn't work for any given basis? Fuck

>>10136472
They're completely different spaces since they have a different norm, so there is no guarantee that one basis will be the basis of the other

>>10136483
Let a, b, c be real numbers such that ax2 + bx + c = 0 for every real number x. We obviously end up with a = b = c = 0. Therefore {1, x, x2} is a linearly independent list.

Now since every polynomial of degree less or equal than 2 can be written in the form ax2 + bx + c, and this is a linear combination of the set {1, x, x2}, we conclude that {1, x, x2} is a basis for the polynomials of degree less or equal than 2.

You don't need to define a norm to find a basis of a vector space.

>>10136511
I never said you needed one, but if you have a normed vector space, you're obviously gonna have different bases depending on the norm. And by the way, your reasoning is wrong for finite fields.

>>10134931
In that case you'd be correct. If [math]W_1 \cap W_2 = 0[/math] then their bases don't intersect (trivial exercise), and [math]L(W_1)\oplus L(W_2)[/math] are just block diagonal matrices [math]W_1^* \otimes W_1 \oplus W_2^* \otimes W_2[/math]. Not much to prove here really.
>>10135245
5000 hours in MS paint.

>>10136517
>finite fields
You mean fields with characteristic k=2?
> you're obviously gonna have different bases depending on the norm
Normal bases, yeah. An orthogonal base is orthogonal for every norm.

>>10136522
Right, not orthogonal, a base is a base for every norm.
An orthogonal base can't work with just a norm, it needs an inner product.

Is there a site or software I can use that would convert my verilog code to a circuit?
I'm having trouble drawing what this code should look like:

module code1( input clk, a, b, c,
output reg y);
reg x;
always@(posedge clk) begin
x <= a & b;
y <= x|c ;
end
endmodule

What's the ring strain numbers represent? kcal/mol is represented in a different column so I'm not sure what they're getting at here.

I'd just like to thank the anons on here who help people out with their studies. Thanks to you guys I got a near perfect score on my Real Analysis exam. Thanks for answering my stupid questions lads, and I'm sure I'll have plenty more to come.

Is this the right place to ask questions on combintatorial logic?
What is A+B if
A = D9_16
B = 1B_16 ?

>>10136407
bls respond

>>10136764
I'm wondering if I should just leave my answer as A + B.
The question asks what the output would be for a mux at S0 = 0 S1 = 1. At 01, it is an OR gate with inputs A and B.

>>10136771
Wolfram Alpha doesn't know what you mean by v. Try calculating it yourself and see what happens.

if a sequence has a constant rate of change [0,1] does it always converge? consider the sequence of 1/2n (1/2,1/4,1/8/,1/16) The rate of change from one entry to the next is .5

>>10136796
Yes. For x=1 and x=0 you have of course a constant sequence so it is immediately convergent. For any value in between you only need to consider the sequence of powers of the rate of change (so for ex. for 2/3 you consider (2/3,4/9,8/27,...)), since the value that gets affected by the rate of change is just a constant, and if a sequence is convergent then the same sequence times a constant is also convergent.

You have a sequence that is strictly decreasing, and is bounded above by the initial value (the initial rate of change) and bounded below by zero, because the sequence can't ever become negative since the rate of change is a constant positive real number. And the monotone convergence theorem for real number sequences guarantees that it will be convergent.

I administered an saline enema 20min ago to no success. Didn’t get very much of the liquid inside. After a couple minutes I had the urge to drop shit but all I’ve gotten is some of solution back out with a burning sensation. Now I just feel the need to shit but still have the same constipation as before only now coupled with some pain. Why do people think god is real? Also the point is me asking for tips here, what do?

Why is this statement incorrect? Is it because x isnt a vector, but an equation describing a line?

>>10136848
The keyword here is "[math]some[/math]".

>>10136852
is the "for some" the existential quantifier, which makes sense when describing a line?

This is the definition from my slides btw

>>10136863
Well, there's that, and there's also that it has to be a set of vectors. The incorrect statement says the line is expressed as A VECTOR for SOME t. The correct statement would be A SET of such vectors for ALL t.

>>10125209
>TEX
?

>>10136875
but there is no vector where the equation would be true for all t

given 3 stocks of different prices, how can I find the optimal distribution between the three such that I maximize shares owned while maintaining as close to equal a distribution as possible, while not exceeding $5000?

what method would I use to solve such a problem?

>>10136892
There's no vector for all t, but for all t, there are corresponding vectors.

>>10136894
im assuming you cant own fractions of stocks, so it would be an integer programming problem

If I was driving towards my house at 50% the speed of light, and my friend was also driving towards my house at 50% the speed of light from the other direction, would I be travelling at 100% the speed of light relative to my friend?

>>10136931
no

Let [math]f: \mathbb{R}^{n} \longrightarrow \mathbb{R}[/math] be differentiable, such that [math]f( \frac{x}{2} ) = \frac{f(x)}{2}[/math], for every x in the domain. Show that f is linear.

I have only been able to prove that the directional derivatives at 0 meet the condition [math] \frac{ \partial f(0)}{ \partial v} = f(v)[/math]. But I don't know how to deduce the conditions for linearity from that.

>>10136902
I must be fucking something up here

>>10137013
You didn't put anything in there about being a close to equal distribution.

>>10137018
I wouldn't even know how to specify that in wolfram language

>>10137020
Well, what metric do you want for closeness?

I'm having trouble defining the governing differential equation for this beam-column case. Any help here?

>>10137021
I sort of figured it out, but I can't broaden my tolerance as then it'll just tend towards the first result (x=0, y=109.457, z=0)
but if I narrow the tolerance then it'll stray further than the actual maximum

I'm just not sure why a metric needs to be specified considering there should really be only one solution where all three are maximized if I understand correctly

>>10137046
You say you want to maximize money while keeping them as close as possible. So obviously you need a metric for closeness.

>>10137080
I guess it makes more sense when I frame "metric" as "constraint"

by the way, I found a near optimal solution

given three stocks, valued at $44.01, $30.75, and $45.68, a near-optimal distribution would be 42 shares of the first stock, 43 shares of the second stock, and 40 shares of the third stock, for a total of $4997.97

If torque = force * distance from axis of rotation, then why is first gear the most powerful gear if it's the smallest? Why isn't fifth gear the most powerful?
t. dumb engineering 102 student who doesn't get it

>>10136386
get so specialized that you can make at least contribution that no one else can

>>10137089
> If torque = force * distance from axis of rotation, then why is first gear the most powerful gear if it's the smallest?
At the point where the gears make contact, the forces are equal. So t1/r1=F=t2/r2 => t1/t2=r1/r2 => t2=t1*r2/r1. If r2>r1, t2>t1, i.e. a smaller gear driving a larger gear results in an increase in torque.

how to get rid of rotten sewage ass smell?
i shower every day, clean myself thoroughly in and around my asshole
still, the smell comes back soon
in the past i have tried eating musli but it did not help
i drink plenty of water
what do?

>>10137503
Did you try antitranspirants?

>>10137035
Help

Let V be a vectorspace, W linear subspace of V, while H is a hyperplane of V with W⊈H
how do i show that dim(H intersec W) = dim(W)-1

>>10137616
Show H intersect W is a hyper plane in W.

>>10137650
yea well thats the definition for a hyperplane, to have n-1 dimensions, so its just the same meaning, or isnt it?

>>10137616
>linear subspace
Never seen that expression before.
Anyhow, let W' be the orthogonal space to W. Since H is not contained in W, and H is a subspace, H contains W'. Further, H-W' is the intersection between H and W, and had dim(H)-1.

>>10137660
The problem says H is a hyperplane in V. You need to show H intersect W is a hyperplane in W. These are different statements; notice how I used different words to convey them.

Is it just me or is the proof given in https://en.wikipedia.org/wiki/Ostrowski%27s_theorem flawed?
in particular, they claim that for some integers [math]a,b\gt 1[/math] and some norm, which I will just label
[math]\left|\cdot\right|_\mathcal{A}[/math] on [math]\mathbb{Q}[/math] we get the following if expanding [math]b^n[/math] in base a:
[eqn]\left|b^n\right|_\mathcal{A} = \left|\sum_{j\lt m} c_j a^j\right|_\mathcal{A}\le a m \max(1,\left|a\right|_\mathcal{A}^{m-1})[/eqn]
however, the way i see it:
[eqn]\left|b^n\right|_\mathcal{A} = \left|\sum_{j\lt m} c_j a^j\right|_\mathcal{A}\le \sum_{j\lt m}\left| c_j \right|_\mathcal{A}\left|a\right|_\mathcal{A}^j\le m\left| a-1 \right|_\mathcal{A}\max(\left|a\right|_\mathcal{A}^{m-1},1)[/eqn]
because [math]c_j \lt a[/math] ! You can then continue [math]\left| a-1 \right|_\mathcal{A}\le a-1[/math]
Of course, that error does not change much of the proof because while you would have to correctly state
[eqn]\left|b\right|_\mathcal{A} \lt \sqrt[n]{ ma\max(\left|a\right|_\mathcal{A}^{m-1},1)}[/eqn]
Which, given [math] m\le n\log_a{(b)}+1[/math], would continue to yield for [math]n\rightarrow\infty[/math]
[eqn]\left|b\right|_\mathcal{A} \le\lim_{n\rightarrow\infty} \sqrt[n]{ (n\log_a{(b)}+1)a\max(\left|a\right|_\mathcal{A}^{m-1},1)} = \max(\left|a\right|_\mathcal{A}^{m-1},1)[/eqn]
But still, isn't it an error?

I need to make a 1 hour presentation about a topic related to the continuum hypthesis, large cardinals, well founded cardinals or some other set theory topic.
Can you recommend me a subject that doesn't require much mathematical background besides Set theory (I'm a CS major).

>>10138062
Continuum hypothesis is easy. Just waste some time on Cantor's previous work and then waste more time on Godel's other stuff.

Why does the orbital 4s have less energy than 3d?

>>10138091
god made it that way

>>10137928
Why do you think that [math]|c_j|_{\mathcal{A}} \leq |a-1|_{\mathcal{A}}[/math]? p-adic norms are not monotonic.

>>10138126
it doesn't need to be, be just know that
[math]c_j \le a-1 [/math] and
[eqn] \forall n\in\mathbb{N}^* : \left| n \right|_\mathcal{A} =
\left| \sum_{k=1}^n 1\right|_\mathcal{A} \le
\sum_{k=1}^n \left| 1\right|_\mathcal{A} = n[/eqn]

In game theory, I understand why mixed strategies are represented like {(a, b);(c;d)] but how come pure strategy Nash equilibria also have to be represented in the same way? Can't they just be given as the initial value? I don't get why they're always like (1, 0) or (0, 1) either since the lecturer never explains anything, what's the deal with this? Thanks

>>10138165
new
>>10138165

>>10138139
>it doesn't need to be
it does if you want the equation you wrote directly beneath "however, the way i see it" to not be wrong.

Regardless, it is not true that [math]|b^n|_{\mathcal{A}} \leq m(a-1)max(|a|^{m-1}_{\mathcal{A}},1)[/math]. You may consider b^n = a with standard absolute value for a counterexample.

it holds for that example, because [math]m=2[/math] (notice the summation over all j=0 o m-1), given that this proof assumes [math]a>1[/math].
[eqn]\left|b^n\right| = \left|a\right| = \left|\sum_{j<2}c_j a^j\right| \le 2(a-1)a[/eqn]
And the equation does not assume monotony because it only provides an upper bound.
For [math]p[/math]-adic norms the statement [math]\left|n\right|_p \le n [/math] holds trivially for all nonnegative integers. The proof i gave in the second post holds because of the triangle inequality,
hence all valid absolute values on [math]\mathbb{Q} [/math] have this property, as well as [math]\left|\pm1\right|_\mathcal{A} = 1[/math].

>>10138173
>>10138300

>>10138167
>Thread hasn't reached 500 replies yet
Fuck off retard

>>10125209
ok i am starting the university physics with modern physics text book. should i just do the challenge problems? i know unis usually give out like 6 problems a week, so that is my general goal i guess

Should I go for math master or theoretical physics master?
I want to work with physics but I also want to learn lots of maths that can be used in physics. (including group theory)

>>10138326

>>10138326
>bump limit is 500
try again

>>10138646
>>10139270
>Falling for obvious bait

>>10139384