/sci/ - Science & Math

you bastard, i was gonna make the op konata.
at least its not another frog

>>14607949
Y u no like phrog?

>>14607941
How do I cope with being a late bloomer?
Had good grades in HS, and people thought I was going places. Became a shut-in after high school. Going back to uni at 24. All my friends have degrees and jobs while I'm just going back to uni. Does it ever get better? I'll be 27 - 28 when I graduate with no experience vs others 28 yo with 6 years experience. Kind of demoralized.

How many times am I allowed to post my question in these threads if it isn't being answered?

>>14607983
until you get bored and give up, or until it actually gets answered, but i warn you that if you question isnt physics or math it probably wont get answered.
also, please refrain from directly reposting your question in the immediate next thread, let the unanswered questions post get it.

If a patient were to take a prescribed dose of medication a day before a urine drug test without taking it months prior, would it read as normal or would it be known that the patient has only taken it recently?

why are magnets cool?

>>14607988
Thanks

Unanswered questions:

Maths questions:
>>14593425
>>14593443
>>14600677
>>14601310
>>14607673

Physics questions:
>>14590262 (Geometric algebra is such a tremendous meme term. Differential forms are useful because they retroactively replace all of vector calculus in a tight, intuitive fashion, like in electrodynamics. Clifford algebras are used for constructing spin groups and spinors, so they're essential all throughout qft. Also Witten received the Fields medal for his work on the Positive energy theorem using spinors, and that's a result in general relativity.)
>>14601276
>>14602493
>>14602901
>>14602988
>>14605033
>>14607583

Chemistry questions:
>>14599082
>>14600172
>>14603749
>>14603901
>>14604029

Stupid questions:
>>14593867
>>14595999
>>14600382
>>14600609
>>14602818
>>14605668
>>14606006
>>14607278
>>14607675

>>14599082
>Are there any ferromagnetic alloys of non-ferromagnetic metals?
Apparently there's a stoichiometric ferromagnetic alloy [math]\textrm{Ag}_5\textrm{MnAl}[/math]. Sadly every reference I could find about it is hidden behind the paywall.

>>14599082
>Are there any ferromagnetic alloys of non-ferromagnetic metals?
Apparently there's a stoichiometric ferromagnetic alloy [math]Ag_5MnAl[/math]. Sadly every reference I could find about it is hidden behind the paywall.

>>14608541
Just noticed the last three chemistry questions are supposed to be in stupid, my bad.

Are AoPS books any good?

>>14607941
Please answer my matrix question ;_;

>>14606225

Why is 28 February 2000 is still 28 February thirteen years later? Shouldnt the leap years between it changed the date of the day?

>>14609134
because 28 February is 28 February. if 28 February wasnt 28 February then 28 February wouldnt be 28 February, it would be a different day.

How do we get that b = -a from that?

It's not a joke, I'm that dumb.

>>14607941
here's a stupid question. When does programming click?

>>14609950
because [math]a+b=0[/math]

>>14609951
When you build your first thing. It's why building before learning, but still learning later, is the best way.

>>14609950
On one hand, -a + a + b = -a.
On the other hand, -a + a + b = b.
Equality is transitive ( if x=y and x=z, then y=z), so b = -a.

>>14609992
>>14610028
OHHHHH

I want to read on dual spaces, because I'm trying to learn about tensors.
Dual spaces never appeared in my Linear Algebra course. Any resources recommendations?
If you have any good resources about learning about tensors, I'd appreciate those too.

What are the principles of understanding, synthesizing and memorizing information in order to transform it into knowlegde? As far as I know, active recall and spaced repetition are considered the two pillars of learning. Is this true? Are there more?

To answer these, would I just plot each one and order them by order of growth?

>>14610188
> As far as I know, active recall and spaced repetition are considered the two pillars of learning. Is this true? Are there more?
That's more for memorization imo, but still applies to 'learning'. e.g, you wouldn't really practice spaced repetition or active recall in pure math class, instead you'd just do proofs until you understand the mechanics and derive stuff yourself.

Why does my book give #1 as the formula for finding the sum of a geometric series?

When i google it i find #2, but then neither of them actually work.

Only #3 works for me, and a has to be the first term of the series.

What's going on?

>>14610231
OK, I have the following:

constant: 6
logarithmic: logn
linear:
superlinear:
quadratic:
cubic:
exponential: 2^n
factorial: n!

but I'm not sure to deal with more complicated cases like log(logn), n/log(n), ln(m) etc.

if [math]\phi[/math] is a parametrized curve [math]\phi=(x(u,v),y(u,v),z(u,v))[/math], why is that
[eqn]\partial_u\phi \times \partial_v\phi = \left(\frac{\partial (y,z)}{\partial (u,v)},\frac{\partial (z,x)}{\partial (u,v)},\frac{\partial (x,y)}{\partial (u,v)}\right)[/eqn]
?

>>14610245
#3 is identical to #2. (-x)/(-y)=x/y. If you're getting different answers, you're evaluating one of them incorrectly.

#1 starts counting at k=0, so the last term is ar^n, for n+1 terms in total. #2 and #3 start counting at 1 so the last term is ar^(n-1) for n terms in total.

>>14610231
are k and m supposed to be constants?
to see how a function grows compared to another, evaluate [math] \displaystyle \lim_{x \to \infty} \frac{f(x)}{g(x)}[/math]. if its infinity, f grows faster, if its zero, g grows faster, and if its finite, they grow at the same rate.

>>14610304
ty anon

>#3 is identical to #2. (-x)/(-y)=x/y. If you're getting different answers, you're evaluating one of them incorrectly.

I found this information here online in pic, how is it you are allowed to pick and choose which one to use? shouldn't both work for everything if they are identical?

>#1 starts counting at k=0, so the last term is ar^n, for n+1 terms in total. #2 and #3 start counting at 1 so the last term is ar^(n-1) for n terms in total.

i'm confused how that's supposed to work. how do you evaluate S(n) if one of them potentially means ar^(n+1) and the other means ar^n? And is a actually a1 (the initial term) in all cases even when it doesnt have the subscript?

the question im looking at is the series:
1/3, 1/9, 1/27, 1/81, 1/243

only formula #3 from >>14610245 seems to work

>>14610351
sorry the sequence
1/3, 1/9, 1/27, 1/81, 1/243, ... and then you determine its (1/3)^n as the last term

and then you determine its sum

>>14610351
>how is it you are allowed to pick and choose which one to use?
You are not picking and choosing. They are the same. I don't know where you got that image, but it doesn't matter (and "numerical value" is an incorrect way of saying "absolute value" or "magnitude" there). To help elaborate on why they're the same:
>(x/y) = 1 * (x/y)
Good so far?
>1 = (-1)/(-1)
Okay, now for the magic trick:
>(x/y) = [(-1)/(-1)] * (x/y) = [(-1) * x]/[(-1) * y] = (-x)/(-y)
You literally multiply by 1.

>>14610368
ty anon, i will try and write out what im doing, i must just be doing something wrong

>>14610347
>are k and m supposed to be constants?
I honestly have no idea, it wasn't specified. And thanks about the limit logic.

So for example if I want to compare logn to loglogn, I'd do lim (loglogn / logn), and it's zero then it'd be bounded by logn, and thus is the same growth order, but if it were infinity it'd be in a different growth order? and if so, I'd continue on to the next growth order, which is linear (i.e, 'n'), and see if lim (loglogn / n) = 0?

but i imagine k is a constant, that's pretty standard IME, but m? no idea. i feel like it might imply a 2d array/matrix input or something but idk

>>14610347
shit wait, if it's zero it says nothing other than that it's bounded above. it has to be a constant, and so what I'm looking for is a function g(n) s.t the limit of f(n) / g(n) is a constant? if it's infinity it means I have to move g(n) up by and order of growth or complexity class, if it's 0 it means I have to move down?

i imagine after a couple runs you could just tell by glancing it at though, but i could use a mechanical and bulletproof approach to ensure i do well on this

>>14610373
See this: https://www.desmos.com/calculator/68xqj8lc6k
You can adjust the sliders manually or hit the play button and watch it move around.

>>14610394
tyvm anon, i dont get what im doing wrong, why dont they just say what a is?

i know im doing something wrong, i just dont know what when the 3rd formula works effortlessly

Are bricks combustible? How do buildings catch fire?

>>14610402
If your sequence is defined by (1/3)^n then a=1 and r=1/3. Think anon, think.
Your sum would be written as r^0 + r^1 + r^2 + ... + r^n. Since there are n+1 terms there, your closed formula is (r^(n+1)-1)/(r-1). I've adjusted your graph to demonstrate this: https://www.desmos.com/calculator/zmaieursro

>>14610402
I think i found the problem anon, I think it was my brain.

It turns out 4/9 is the right answer of the sum and i was fixated on trying to get 1/9 because that was the second term

I spent a good 5 hours on this singular problem

i dont know if i should be happy or worried, maybe i have some kind of degenerative brain disease

ty for all your help anon, hopefully i will understand sums and sequences a bit better from now on after this

>>14610392
>so what I'm looking for is a function g(n) s.t the limit of f(n) / g(n) is a constant?
that'll tell you the growth, yeah. but since you only need to put those functions in a list, you dont have to pull a g(x) out of your ass or anything, you can just pit the functions against each other and figure out the list order like that. and yeah, eventually youll just be able to tell at a glance the higher/lower growth of two functions, as long as they arent too complicated. for example, the best known classical algorithm for factoring numbers larger than [math]10^{100}[/math] is of the order of
[math] \displaystyle
\exp \left( \left( \sqrt[3]{\frac{64}{9}}+o(1) \right) (\ln n)^{\frac{1}{3}} (\ln \ln n)^{\frac{2}{3}} \right)
[/math]
btw, there arent exactly "discrete levels" to growth order: for any two functions f(x) and g(x) of different growths, theres always a function h(x) with a growth order between them.

>>14610045
read this in renge's voice

>>14610417
so does one formula use a to mean the constant infront of r, and the other formula use a to mean the first term of the sequence?

thats diabolical

and sorry i mean to reply this >>14610420 to you

>>14610420
Well, we've all been there with something equally stupid. Here comes the fun part that people rarely do: think about your problem-solving strategy at a high, abstract level. What went wrong? Did you not revisit the premises? Make a note to do that every hour or so next time. Did you need to take a break? Make a note to do that. It's not enough to just sink time into these problems. Work on finding a smarter problem-solving approach. You should never be redoing the same thing over and over again, or just staring at it until you "get it."

>>14610424
> It's not enough to just sink time into these problems. Work on finding a smarter problem-solving approach. You should never be redoing the same thing over and over again, or just staring at it until you "get it."

I will take this to heart anon, i've been very inefficient with my time, trying to just brute force through it.

Also actually anon im looking at it again and its not technically right. i'm looking at a solution of it using the Sn = a1(1-r^n)/(1-r) formula. And that solution shows S2 = 4/9.

I have S1 = 4/9. But how does Sn even work from 0 to n+1 (rather than 1 to n)? The first term is 1/3, does that mean its [1/3 * (1/3)^n] as the last term instead of (1/3)^n?

>>14610423
Some people like to start their indices at 0. Others like to start their indices at 1. This small difference creates small differences in formulas, which can lead to wild differences in answers. I'll try to explain what probably went on.
If you write your sum as
>S(n) = sum_{k=0}^n a*r^k
then your closed formula is
>S(n) = a*(r^{n+1}-1)/(r-1)
If you write your sum as
>S(n) = sum_{k=1}^n a*r^{k-1}
then your closed formula is
>S(n) = a*(r^n-1)/(r-1)
In the course of your studying, you'll find that people will use wildly different letters/notation for the same thing, and you need to understand the concept well enough to create the right mapping. Now, let's look back at >>14610245.
#1 and #2 are not the same formula in that the exponent is different. Recall what I said above: this means that they derived from summations with different indices; the context is different. They ultimately say the same thing, but you're missing what the sum looks like.
#3 is weird, they probably should not have a subscript there. Nonetheless, I can imagine a scenario in which they do. Let's suppose we define a series by a_i = c*r^{i-1}. In this case, a sum we might like to find is a_1 + a_2 + ... + a_n. The formula there then works even though it would be more "correct" to replace a_1 with c.

>tl;dr
You can Google around for shit but at least give found formulas the dignity of reading the short article they're probably a part of.

[math]-\frac{27 \sqrt3-24\sqrt2}{15}[/math]
Can this be simplified more? The math program for my class says that it's equivalent to the right answer but isn't in the right format. The directions just say "simplify".

>>14610413
There are some theorized “dark buildings” which are made out of some unknown, non-brick substance.
But imo it’s just physicists making up new building materials because the data (occurrences of fires) isn’t adding up

>>14610433
What is a common factor for 27, 24, and 15?

>>14610435
I'm so fucking dumb
the shit I can't see is always the most obvious

>>14610430
It's more confusion with indices. Earlier I said:
>If your sequence is defined by (1/3)^n then a=1 and r=1/3.
There, I made the assumption that first term in the sequence is 1. Looking at your image, that's not the case. If the first term in the sequence is 1/3, set a=1/3 and r=1/3. Alternatively, if you want to be tricky, use a=1 and r=1/3, and then just subtract 1 from the result.

>>14610392
also, i didnt mention, but before you start doing derivatives, see if a little bit of common sense and algebra can bail you out, for example
[math] \displaystyle
\frac{ \left( \frac{1}{3} \right) ^n }{ \left( \frac{3}{2} \right) ^n } = \frac{ \left( \frac{1^n}{3^n} \right) }{ \left( \frac{3^n}{2^n} \right) } = \frac{2^n}{3^{2n}} = \left( \frac{2}{9} \right) ^n \to 0
[/math]

>>14610441
>It's more confusion with indices
I think it must be a big part of it, ty, i will try again tomorrow also the website you linked is very cool

ty again anon i appreciate all your help very much

>>14610419
>you can just pit the functions against each other and figure out the list order like that
you mean like seeing if it's quadratic order by finding lim f(n) / g(n), where g(n) is quadratic (where it'd be quadratic if constant)?

if so, my strategy for tomorrow will be just to do the following:
>choose function to find order of
>take a guess as to which order it's in using some template function g(n), e.g n^2 being quadratic order
>if lim f(n)/g(n) = constant, done, I've found the order
>else
>if lim f(n)/g(n) = inf, drop to a lower order and try again, e.g nlogn, superlinear
>if lim f(n)/g(n) = 0, go up an order and try again, e.g n^3, cubic

if that's all it is, I can handle that tomorrow no problem. got a big pile of shit outside to clean tonight lol, reorganizing things while it's nice out

>>14610441
I was playing around with the website anon and the indexing is definitely my problem.

in the video the guy has S2 = 4/9, but this website and the calculation i did here >>14610402 have S1 = 4/9.

But the formula he uses still works. And is it because his last term in the sequence is (1/3)^n, but if he started at S0 instead of S1, it would have been (1/3)^(n+1)?

>>14610444
checked and the fact it's zero would imply it's an order lower than 2^n? given that 1/3 < 1, then 1/3^n is of course decreasing, so it's obviously not exponentially increasing.. but since it's decreasing wouldn't it approach 0 and be less than constant order? i must be mistaken

>>14610531
>the fact it's zero would imply it's an order lower than 2^n?
the fact that its zero implies that the order of [math]\left( \frac{1}{3} \right)^n[/math] (the numerator) is less than that of [math]\left( \frac{3}{2} \right)^n[/math] (the denominator)

>>14610534
and if the order of the numerator is less than the demonator, that implies it's not in the demonators complexity class, right? implying i should run the limit again against the next lowest order? if so, since it's a decreasing function this would continue until it's less than constant order, no?

so with chemical reactions which produce water, like for example the dehydration of ethanol to make ethylene,
how do they get rid of the water so the reaction doesn't go backwards?
like, you couldn't just distill off the water because the ethanol boils before water does.

>>14610539
>and if the order of the numerator is less than the demonator, that implies it's not in the demonators complexity class, right?
i dont know the exact definition of complexity classes (whether theyre inclusive going up, or down, or neither, if that makes sense) but yeah, they have different complexities.
>implying i should run the limit again against the next lowest order?
there is no "next" order. this is what i was trying to say in >>14610419:
>btw, there arent exactly "discrete levels" to growth order: for any two functions f(x) and g(x) of different growths, theres always a function h(x) with a growth order between them.
the next function that you should compare to is whichever one in your list you think its next to.
if youre trying to find the "exact" order that it belongs to, then thats easy: [math] f(x) \in O(f(x)) [/math]. for example, [math] k^2 + \log k \in O(k^2 + \log k) [/math]. of course, this isnt really "simplified" because [math]O(k^2 + \log k) \in O(k^2)[/math], so it might be more "correct" to say [math] k^2 + \log k \in O(k^2) [/math], but both are technically right. i mentioned that limit thing because your original question asked you to "sort" those functions, and the limit thing would help you do that. i believe that your strategy for the question was to organize each function into the "buckets" you listed in >>14610247, but thats the wrong way of thinking about it because 1) you dont have to "find" the complexity of a function, it wears it on its sleeve like the example above, and 2) there are infinitely many buckets, even between any two buckets.
>since it's a decreasing function this would continue until it's less than constant order
splitting hairs here but to be exact, its not enough that the function decreases, it has to go to zero.

>>14610558
I'm getting confused at how I should be answering the question then (originally here: >>14610231), I guess rather than sorting into discrete classes I should be sorting them by infinite buckets? So a brute force method would be to say, compare the complexity / growth order (I thought these terms were synonymous?) until I find a lower one, by taking limits. Take this new lower one, if any, and repeat the process. By continuing this long enough, I'll have found the lowest growth order function, and I can start over but exclude that entry. Is that a viable way to solve the problem?

Of course in reality I'd do it a bit faster but if that method works than I've got this figured out.

>>14610573
>complexity / growth order (I thought these terms were synonymous?)
ive been using them interchangeably
>I guess rather than sorting into discrete classes I should be sorting them by infinite buckets?
its easy to put the functions into buckets, like [math]k^2 + \log k \in O(k^2 + \log k) [/math], but the question is asking you to put the buckets in order of complexity, and also determine which buckets are equivalent (e.g. [math]O(k^2 + \log k) \in O(k^2)[/math], also these examples are assuming k isnt a constant). given two buckets, the limit thing will determine their relationship. the reason i said your original plan of categorizing the functions is the wrong way to think about it is because it doesnt really make sense to find the complexity of a single function, we only care about its growth order *compared to other functions*. im trying to hammer this in because you seem to be misunderstanding growth orders.
>By continuing this long enough, I'll have found the lowest growth order function
there is *only one* growth order for a function (i looked it up, its noninclusive), and you do not have to "find" the growth order of a function, all you have to do is look at the function and you will know its growth.

>>14607941
Scientifically speaking, why do people avatarfag as underage anime girls?

>>14610642
clownpiss is like a billion years old, nigger

>>14610658
clownpiss? I am unaware of this scientific phenomena, please explain

>>14610666
Clownpiece's piss is absolutely not for beginners—it's the most fearsome fairy pee currently known! Her strong, deep yellow madness-inducing piss is not to be trifled with, and it takes an experienced NEET, highly acclimatised to all other forms of fairy pee, to enjoy it safely. Others run the risk of hallucinations, dementia, death, or "Lunatic Time," the immediate transformation into lesser fairies of Hell. What's more, while any other fairy will be at least somewhat self conscious about peeing in company, Clownpiece will cram her cunt forcefully into her victim's face and piss straight into his mouth without mercy! Clownpiss is the absinthe of fairy pee.

>>14610351
> shouldn't both work for everything if they are identical?
They do. It's just convention. In particular, if 0<r<1, then 0<1-r<1 and 0<1-r^n<1.

> i'm confused how that's supposed to work. how do you evaluate S(n) if one of them potentially means ar^(n+1) and the other means ar^n?

Does S(n) mean the sum over 0≤k≤n (n+1 terms) or over 0≤k<n (n terms)? If it's the former, use #1, if it's the latter, use #2/#3. Note that in both cases, a is the first term (ar^k for k=0).

> And is a actually a1 (the initial term) in all cases even when it doesnt have the subscript?
Again, convention. Note that if you use ar^k and start at k=1, a_1 = ar (a would be the "zeroth" term, the one before the first).

>>14610261
>curve
>two parameters
[math]\frac{\partial (y, z)}{\partial (u, v)} = \frac{\partial y}{\partial u} \frac{\partial z}{\partial v} - \frac{\partial z}{\partial u} \frac{\partial y}{\partial v}[/math] innit? Because it's the jacobian? Just expand the left side out.

>>14607941
Ruri dragon is shit brong back 2hu.

>>14610861
thanks anon much appreciated

so it doesnt matter what S(n) formula i choose as long as i properly account for the indexing right?

like if i go from 0 to n (n+1 terms) then my last term in the sequence will be different than the last term in 0 to n-1 (n terms), which will change the equation in the S(n) formula so it ends up being the same,

so its up to me to choose the formula and indexing but i also have to account for it properly?

I think that's what i have been screwing up and not understanding the most

I have a really dumb question I can't figure out. Let [math]\alpha[/math] be a permutation of the n-set [math]\{1,2,\dots,n\}[/math]. I want to show that the sum of absolute values [math]|\alpha(1) - 1|+ |\alpha(2) - 2 | + \cdots + |\alpha(n) - n|[/math] is in fact even.

I can prove this by simply squaring the entire sum and expanding until I get an expression which is clearly even. However there's supposed to be a really easy observation to make that proves this. What am I missing?

>>14611297
prove that
[eqn]
|\alpha(n_1) - n_1| + |\alpha(n_2) - n_2| \equiv |\alpha(n_2) - n_1| + |\alpha(n_1) - n_2| \; \; \; \mod 2
[/eqn]
and then notice that for the "identity permutation" or however you would say that, the sum is clearly zero.

>>14611616
actually, this is more correct
[eqn]
|a - b| + |c - d| \equiv |c - b| + |a - d| \; \; \; \mod 2
[/eqn]

>>14611297
|a| = a mod 2 for integers, because -1 = 1 mod 2.
So mod 2 you get the sum is equal to
a(1) + ... + a(n) + 1 + ... + n = 2 * (n(n+1)/2) = 0 mod 2

>>14611297
>>14611616
>>14611624

>>14611645
they cant all be pretty

>>14611638
Correctamundo.

not sure if it goes here but: is there an accessible and reasonably modern intro to general relativity which does not, usually around page 10, goes like "we'll set c=1 because it simplifies the formulae"? like, man, you are about to dive deep into tensors and Christoffel symbols of all kinds, do you think a lone coefficient c will make any difference?
by accessible I mean not deeply entrenched in physical arcana like Noether symmetries and suchlike. advanced math is not a problem. but I cannot follow a discussion where c has been eliminated because there's nothing to carry the proper units of measure. I tried to read a couple of these books and always fail at trying to reintroduce c, figuring out where should it appear.

>>14611638
Arigato

>>14611665
>do you think a lone coefficient c will make any difference?
I don't think it's just that.
It's that our entire unit system is wrong because we shouldn't be using two different units for time and space at all, we should be using a single space-time unit, and velocity should be adimensional as a fraction of the speed of light. Having both time and space units means we need to mix them together in Lorentz transformations, which is beyond jarring and makes any discussion involving relativity a pain in the ass.
>but I cannot follow a discussion where c has been eliminated because there's nothing to carry the proper units of measure
You can just picture it's all metres. Half a metre long ruler, five metres long duration.

For coordinate transforms on integrals, is there any general formula/procedure to find the new limits of integration, or is the best we can do really sketching shit out?

Is the 'basic operation' here traversal through the array or comparison via subtraction?

>>14610231
Ok, please tell me if this is right. I compared the limits of each and ordered them accordingly. I also graphed all the functions to ensure it was correct.

Does instantating a ML take more time than training it?

model = SARIMAX(y, parameters)
results = model.fit()

Which line takes longer?

>>14612144
interesting that [math]n^{\frac{1}{3}}<\log n < \sqrt{n}[/math]

>>14612233
It’s wrong. Pic related

>>14612256

>>14612256
In fact I’ll generalize it for any integer root

>>14612256
>>14612271
this is a good example of why graphing the functions to check your work may or may not be a good idea: it may take a very very long time for a function to overtake another.

>>14612256
>>14612233
I didn't say n^1/3 < logn, I said n^1/3 + logn = logn, and of course logn < sqrtn. Is my answer correct?

>>14612286
>I said n^1/3 + logn = logn
unless [math]O(n^{\frac{1}{3}}) = O(\log n)[/math] then im pretty sure that implies that [math]n^{\frac{1}{3}}[/math] has a lower growth order.
>Is my answer correct?
iunno bro

>>14612286
No you’re wrong. The cubic root grows faster. Meaning the sum obviously grows faster. That’s what I proved there

>>14612290
again, i did not say n^1/3 = logn. I said n^1/3 + logn = logn.

>>14612309
oof, for some reason i was thinking it'd approach zero over time like a dummy, thx m8. so it should probably sit between the logns and the sqrt(n) right?

Hey anons, is this a typo in my book?

Its really messing with me. Or can you just change the index from 0 to 1?

>>14612320
>again, i did not say n^1/3 = logn
are you ESL or something?
[math]O(f(x)+g(x)) = O(f(x)) \; \; \to \; \; O(g(x)) \leq O(f(x))[/math]

>>14612332
i didn't read his sideways scribbles but i see now

>>14612341
try to read peoples post before replying to them next time

>>14612331
Typo, yeah.

How do i do a negative arithmetic sum from -1 to -(n-1)?

I know for 1 to n you do:

Sn = [1 + 2 + ... + (n-1) + n]
Sn = [n-(n-1) + n-(n-2) + ... + (n-2) + (n-1) + n]
2Sn = [n] + [n*n] = n^2 + n = n(n+1)
Sn = n(n+1)/2

But i cant get this method to work when i try it with negatives, and even worse is stopping at n-1 and not n.

Also in this line, is "+n" correct at the very end, or should i stop at (n-1)?
>Sn = [n-(n-1) + n-(n-2) + ... + (n-2) + (n-1) + n]

>>14612609
The formula is obviously very similar. But you need to change it to

Sn = -n(n-1)/2

You’ll see why when you repeat to proof you posted but for negatives.

And yes you keep that + n obviously. Go thru the proof again it seems like you haven’t quite grasped it.

>>14611275
It's simple enough to derive the formula:
S(n) = a + ar + ar^2 + ... + ar^(n-1)
=> rS(n) = ar + ar^2 + ar^3 + ... + ar^n
=> rS(n) = S(n) - a + ar^n
=> (r-1)S(n) = ar^n - a = a(r^n-1)
=> S(n) = = a(r^n-1)/(r-1)

The same approach will work (with a slightly different result) if the first term is ar^1=ar instead of ar^0=a and/or if the last term is ar^n instead of ar^(n-1).

>>14612632
>>14612670
tyvm anons i will keep working at it

>>14612609
The sum of an arithmetic sequence is n(a+b)/2, where n is the number of elements, a is the first element, b is the last element (note the symmetry; swapping a,b doesn't change the result).

The mean is the sum divided by the number of elements, so the sum is the mean multiplied by the number of elements. For an arithmetic sequence, the mean of the first and last elements is equal to the mean of the sequence. Also, the mean of the second and second-to-last elements is equal to the mean of the sequence. And so on. If the sequence has an odd number of elements, the middle element is equal to the mean of the sequence.

Why is cos, sin and tan used so much? Is it just because sin and cos make up waves and tan makes up any slope on a circle.
And well then there's the real life application we're told about in school to find how far something is or the height of things in the distance.

>>14612697
ty anon i never thought about it like the mean

>>14612751
sin and cos solve the ODE [math]y'' + \alpha y = 0[/math], which occurs a lot in physics (for example, the force on a spring is proportional to its displacement).
tan is mostly used in geometric scenarios.

>>14608541
>Geometric algebra is such a tremendous meme term. Differential forms are useful because they retroactively replace all of vector calculus in a tight, intuitive fashion, like in electrodynamics. Clifford algebras are used for constructing spin groups and spinors, so they're essential all throughout qft. Also Witten received the Fields medal for his work on the Positive energy theorem using spinors, and that's a result in general relativity.
Thanks for your reply.
Does anyone happen to know of any readings that explain this further?

would learning knot theory help me to tie my shoes? I know a little bit of topology but I've been trying to learn to tie my shoes since kindergarden and I think maybe I need to take a more theoretical approach

>>14613855
Doesn't knot theory study only "closed" knots?

>>14613378
What part? Differential forms in electrodynamics, constructing spin groups from clifford algebras, qft or Witten's proof of the positive energy theorem using spinors?

Can somebody pls explain to me why magnetic forces do not do work without using equations

Trying to understand Character Tables. So, I get that on the rows are individual operators, and on the columns are what amounts to sets of top-conjugated elements. What are the elements that result of the intersection, then?
Let's say it's the row A, column B, and the elemnt there is a. Does that mean that elements of B are eigenvectors of A with eigenvalue a, or what?

>>14614984
Because the force produced is ALWAYS perpendicular to the speed, hence it's ALWAYS perpendicular to the direction where the particle moves in at every instant. Work is the result of a scalar product between Force and displacement, so in every instant Work is 0. Hence total work is always 0.
It's basically analog to how the Normal force never does any work in mechanics.

>>14615045
Thank you Anon

>>14615045
You’re correct but normal force can do work. Imagine standing in elevator. Floor does work on you. That’s the normal force

how do i find d/dr [ (dr/dx)^2 ] ?

>>14615416
Product rule.

>>14615448
the question says to use the chain rule and that the answer is just d2r/dx2. how would i use the product rule?

How do i find the actual formula for this recurrence relation? I know the answer is a(n) = 1 but i want to know the real formula before it becomes 1.

a(n) = 2[a(n-1)] -1, where a(0) = 1.
a(0) = 1
a(1) = 2(a(0)) -1 = 1
a(2) = 2(2(a(0)) -1) -1 = 1
a(3) = 2(2(2(a(0)) -1) -1) -1 = 1

So 2 gets multiplied by itself three times. So that should be 2^n for a(n).

But the problem is -1. I originally thought i could do -1 gets multiplied by 2 n-1 times, then subtract -1.

But its actually [2*(-1)]-1 so its multiplication and addition in one loop.

I think i need to end up with 2^n + -[2^(n-1) + 2^(n-2) + 2^(n-3) + ... + 2^2 + 2^1 + 2^0]

>>14615474
Use induction.

>>14615485
i havent learned that yet

i think i have it:
a(n) = 2^n + [(1-2^n)/(1-2)]

This took me 2+ hours to solve. Is it supposed to take this long?

>>14615416
Power rule and chain rule: [2(dr/dx)^2-1]dr/dx

>>14615506
oops
a(n) = 2^n - [(1-2^n)/(1-2)]

I'm doing some predictive modeling on a time series with temperature as the dependent variable. I get a mean squared error of 1.75 when comparing my forecast with the test set. Does that mean my model predicts the correct temperature (as far as we know/with the available data) to be within +/- 1.75 degrees C?

In other words, is the unit of mse just the unit of your dependent variable? And does a mse
of x mean your model predicts the right value within +/- x of the real value?

And actually now that I look at pic related I'm realizing the answer to my question is no. There are clearly times where the difference between the model predictions and the actual data are more than 1.75. Is mse the average of the squared residuals? Classification metrics make more sense to me. I might be too dumb for regression metrics. Maybe I should take a moment to look anything up before asking a question here. Oh well.

>>14615575
>Does that mean my model predicts the correct temperature (as far as we know/with the available data) to be within +/- 1.75 degrees C?
no.
it means that the average error, squared, is 1.75

I have a(n) = n*a(n-1) , where a(0) = 5. Which i think is factorial.

How do i write a(n) = 5*n! without the !

Is there a sum for this?

anyone know some apps that lets you organize research papers or articles nicely? or preferably a chrome extension
i want something with which i can save papers as read for later, mark some important ones (or leave a note), a list of papers i've already read and stuff like that, it'd be especially great if it worked between different repositories (so e.g. if i mark one paper on arxiv as read, if i open the same on on scienceDirect it'd show that i read it already)

>>14615740
The factorial is basically the gamma function, which is an integral.

>>14597844
Not sure if I'm oversimplifying, but can't you just take each open set from each dimension, and those are all unions of open balls, and then union them all together?

is there a textbook on differential geometry that covers the generalized stokes's theorem?
I bought do carmo but it doesn't cover it

>>14615926
Why did you buy it without reading the index?
Try Lee's Introduction to Smooth Manifolds or Tu's Introduction to Manifolds.

>>14615845
okay ty anon

>>14607941
I somehow got accepted into a decent uni in a cs bachelor's degree but it's been 4 years since I graduated high school and did any math and I forgot everything, my classes start in october, how fucked am I?

>>14616015
What math classes do you have right away? Just brush up on algebra and you should be fine

>>14616015
same program for me except shit university and probably 8 years math.

I have 95%+ average thanks to the help from anons here.

Get a book on pre-calculus algebra and brush up on the basics, or watch a youtube series that covers it.

Then get a book on discrete math eg the one by Kenneth Rosen and work through it chapter by chapter.

You could start learning a programming language now (ideally C since this is what the school will likely use as the first language) or when classes start.

It really doesnt matter so much, the programming is easy, the math will be hard. The programming parts that require math concepts (algorithms, recursion, and things like that) will be even harder if you haven't learned the math yet.

You have a few months to get a very good head start on the math, and by then the programming will also be easier to pick up.

>>14616273
>I have 95%+ average thanks to the help from anons here.
<3

What software can I use to symbolically simplify some differential equations with fuckton of constants?

>>14616015
You might struggle through calculus, but that's okay as long as you pass because you won't need it very often afterwards (some classes like statistics or machine learning may still use it), universities just use them as a way to weed out students. Focus on nailing discrete math and linear algebra, you'll need concepts from one or both these in almost every course you take after them.

>>14616283

Can Nuclear Power SAVE The Car Industry?

>>14614105
Sorry, I meant how all of those things are part of geometric algebra, in particular differential forms.

what would win, a sun of ice or a sun of fire?

While this place has its downsides, it really is leagues better than most of the other boards on this site.

Let's say the walls are thin and your adjacent roommate can hear quiet-moderate level sounds in your room. You want to reduce how loud he hears you, so you open the window? Does this decrease or increase the sound that travels to them? On the one hand, opening the window lets sound waves out but there could be other effects

Whats some deterministic way to measure a canvas and know intrinsicly how much clout it ll generate based on its content?

scientifically speaking, if you have an allergy to cats, would you also be allergic to catgirls?

>>14615844
Mendeley requires you to save as a PDF, but does mark read, not read, add notes, tags, etc. Free too

>>14617344
Yes.

>>14616294
WxMaxima has a Maple-like syntax and can do some simplifications. Takes a bit to get started to learn the syntax but pretty useful

>>14617263
You answered your question, it depends. Acoustics is very dependent on the room geometry and the types of sounds your trying to reduce.

>>14617332
Clout generated is not intrinsic, so no.

>>14617374
Ok so if not intrinsic how to best determine it on basic level

>>14617360
>Mendeley
seems very nice, do you know if it supports working across different computers?

>>14617344
if you do one in the butt youll get toxo

>>14617626
Is toxo as much of a rush as meth? If so, I'm all in.

>>14616673
Nuclear power will save humanity.

>>14617374
Hello

How to determine in straightforward systematic manner

>>14617471
Yes, that's where the pay can come in. You get x space free to sync your documents. Gets too large, you'll need to pay. Just for what its worth, I never hit the cap through my whole PhD

>>14617664
no, it turns you into a fag.
of course, passing up the opportunity to have ass sex with a catgirl also makes you a fag, so its a bit of a catch 22.

>>14617762
i see, thanks

What's they best way to get cheap physical textbooks? I don't like reading from screens.

>>14618434
The library.

>>14618467
kek

>suppose [math](v_1,...,v_m)[/math] is linearly dependent in V and [math]v_1\neq 0[/math].
>then not all [math]a_2,...,a_m[/math] can be 0
why? the a's are coefficients such that [math]a_1v_1+...+a_mv_m=0[/math]

>>14618575
not zero + 0 + 0 + 0 + ... + 0 = not zero

>>14618630
makes sense. I feel stupid. thanks anon

>>14618575
Since [math](v_1, ..., v_n)[/math] is linearly dependent, there exists a non-trivial linear combination [math]a_1v_1 + ... + a_mv_m = 0[/math] such that at least one [math]a \in \{a_1, ..., a_m\}[/math] is not zero. If [math]a \in \{a_2 ..., a_m\}[/math] then they're not all zero. If [math]a = a_1[/math] then [math]a_1v_1 \neq 0[/math] because [math]v_1 \neq 0[/math] and thus there is some non-zero [math]a' \in \{a_2, ..., a_m\}[/math] as the other anon noted.

What is the mathematical term for this mistake i keep making? I am not accounting for compounding multiplications in a series or sequence or whatever.

I keep doing things like this:
3(3(3 + 1)+1)+1 = 3*3*3 + 3(1+1+1) when it should be 3*3*3 + 3*3 + 3 + 1.

eg for the recurrence relation:
a[n] = 2*n*a[n-1]. a[0] = 3.

I wrote this as a[n] = 2*n!*3 when it should be (2n)!*3.

and for:
a[n] = 2a[n-1] -1, where a[0] = 1.

I wrote it as 2^n*a[0] + (-1)*2^(n-1) -n, because i tried to separate each term like:
a[5] = 2*2*2*2*2*a[0] + (-1)*2*2*2*2 + (-1 -1 -1 -1)

I keep doing this and i know im susceptible to it but i dont know what its called (besides being a brainlet), and it just keeps happening, and i dont realise what ive done until ive spent a bunch of time trying to figure it out.

Pls help, i must be violating some common law thing

>>14618434
Dover textbooks on amazon

What books do you think one should read before writing a sci-fi novel?

>>14618770
why the fuck do people try to make their sci-fi "realistic"? its science FICTION, retard, its supposed to be all made-up.

How do i solve this sum?

I know how to do the arithmetic and geometric ones, but i've never done one where two things both depend on J are inside the same sum.

It cant be separated into two sums right?

Why do most of the plasmids I look at have two origins of replication? Can’t you just make one big one?

>>14619178
>It cant be separated into two sums right?
Sure it can.
Break it up on [math]j \mod 2[/math].
And then break it up again on [math]n - j[/math]

>>14619178
The sum of any two adjacent terms (starting at an odd term) will be:
(n-k) - (n-(k+1)) = 1
So each pair simplifies to 1. Just sum up all the 1s and what do you get?
The funky stuff in the equation is just to handle the awkward case where n is odd

>>14619178
[eqn]
\sum_{j=1}^n (-1)^{j-1}(n-j) \\
\sum_{j \in \{ 1,3,5,\cdots,n \} } (n-j) \; \; - \sum_{j \in \{ 2,4,6,\cdots,n-1 \} } (n-j) \\
\left( (n-1) + (n-3) + (n-5) + \cdots + (n-n) \right) - \left( (n-2) + (n-4) + (n-6) + \cdots + (n - (n-1)) \right) \\
\left( \frac{n(n+1)}{2} - \left( \frac{n+1}{2} \right)^2 \right) - \left( \frac{n(n-1)}{2} - \frac{(n+1)(n-1)}{4} \right) \\
\frac{2n^2 + 2n}{4} - \frac{n^2+2n+1}{4} - \frac{2n^2-2n}{4} + \frac{n^2-1}{4} \\
\frac{1}{4}(2n-2) \\ \\
\sum_{j \in \{ 1,3,5,\cdots,n-1 \} } (n-j) \; \; - \sum_{j \in \{ 2,4,6,\cdots,n \} } (n-j) \\
\left( (n-1) + (n-3) + (n-5) + \cdots + (n-(n-1)) \right) - \left( (n-2) + (n-4) + (n-6) + \cdots + (n - n) \right) \\
\left( \frac{n^2}{2} - \left( \frac{n}{2} \right)^2 \right) - \left( \frac{n^2}{2} - \frac{n(n+2)}{4} \right) \\
- \frac{n^2}{4} + \frac{n^2+2n}{4} \\
\frac{1}{4}(2n)
[/eqn]
i feel like i need to apologize to jesus for this one

The Fourier transform is defined on -inf to +inf, but sin and cos are only orthogonal on a certain interval such as -pi to pi which is the foundation of the Fourier series.
It also seems like the FT integral shouldn't even converge since the integral of cos^2(x) on -inf to inf is infinity.
What gives? Some trickery as usual?

None of the books on the Fourier transform explains this.

So mathematicians are just as unemployed ....

Do physics generally scale at any size?
Like, would the shape, size, diameter of the splash, etc be comparable between a raindrop into a puddle and a ball of water 10000x as large as a raindrop falling onto the ocean?

>>14619280
I think you're confusing the Fourier transform with the Fourier series. If a function is periodic, or has a periodic component, then the integral on which the Fourier transform is based is divergent for any frequency which is a multiple of the periodic component's fundamental frequency (the reciprocal of its period). The Fourier transform is well-defined for functions which are either zero outside of a finite interval or which converge to zero at ±∞ (e.g. square-integrable functions such as e^-(x^2), sinc(x), etc).

The Fourier series is only applicable to periodic functions; the Fourier transform of a periodic function is essentially the product of its Fourier series and a Dirac comb (i.e. the transform is everywhere either 0 or infinite).

>>14607964
Would you like to be 28 with a degree or just 28?
It sucks but at least you are on the right path now(in your mind). Noone can say you wouldnt have dropped out of college at 21.

>>14608772
Have you tried scihub?

is the reality we are in even possible in a deterministic universe? could we really just be observers?

does that even make sense intuitively? that we have order from total chaos? or is there some force that we cant measure ala chaos theory?

it boggles my mind that there could even exist free will but the fact that reality is as it is, is it truly deterministic?

>>14613855
Fantastic meme post

Being a bit of a tard in regards to statistics.
I have a multiclass-classification problem with a confusion matrix.
Does it make sense to calculate a single F1 score for the whole matrix like
[math]F_1 = \frac{2TP}{2TP+FP+FN}[/math]
(https://en.wikipedia.org/wiki/Confusion_matrix))
With the sum of the diagonal as true positive, everything below the diagonal as false positive and everything above as false negative?
Intuitively I'd say no, but I am pretty sure I read somewhere that you can calculate one F! score for the whole thing and I'm not sure if I'm misremembering or just too much of a retard to figure it out (or both)

How do I find strength to open my email and read through my supervisor's comments and a list of corrections on my thesis when all I can think of is killing myself?

>>14619859
Remember this quote

What's the deal with this newfag trying to make chemistry and physics generals and why are jannies deleting his threads?
>inb4 they're not just sliding out of the catalog?
No, they're being deleted.

>>14619790
>I think you're confusing the Fourier transform with the Fourier series
No, I know that the Fourier series is over a period such as -pi to pi, and the FT generalizes that and extends the period to infinity.

>The Fourier transform is well-defined for functions which are either zero outside of a finite interval
Which essentially makes it a Fourier series, right? Since if it is zero outside of an interval, it is the same as evaluating it on that interval which sounds like the Fourier series.
> or which converge to zero at ±∞
Yes, that's the part I missed.

>square-integrable functions
That confuses me too, since the Hilbert space is L^2 and its bases are sin and cos on -pi to pi. Sounds like they are square-integrable on a specific interval. Then perhaps there is also a different class of square-integrable functions that converge on -inf to +inf?

>>14607673
>i don´t understand what is the dx of the integral
I might be wrong but nowadays it means nothing; is just notation and we have Leibniz to blame for causing so much confusion.

>>>14607673
Informally, it is the width of the "rectangle" whose area you are measuring. f(x) is the height.

>>14620097
If you make a general for chemistry and physics, you might as well make a general for every other field. And then you don't have enough space for the /pol/ and /x/ threads.

>>14620520
>Informally
>Reimann sums are informal
ur cruisin 4 a bruisin m8

>>14619242
>>14619203
>>14619236
thanks anons

>>14619242
holy smokes that is powerful anon thank you, that looks so hard to learn

how come it repeats twice? are those two terms at the end of each sum added together to produce the RHS?

the 1/4(2n-2) and 1/4(2n)? i am in awe anon

Let [math]G[/math] be a finite non abelian group and [math]A \le G[/math] an abelian subgroup of index 2. I need to show there exists a complex irrep [math]U[/math] of [math]H[/math] such that the induced representation [math]U \uparrow G[/math] is an irrep of [math]G[/math].

I had several ideas and they all failed, so I'd appreciate any guidance.

>>14620416
> Which essentially makes it a Fourier series, right?
Well, a Fourier series is a function Z->C, a Fourier transform is R->C. Also, the series is defined for periodic functions, the transform for aperiodic functions. AFAIK, a periodic function can't be square-integrable (unless it's the constant-zero function).

The series is an integral over [t,t+T] where T is the period and t is unspecified. For a periodic function, t doesn't matter. For an aperiodic function, you're essentially turning it into one by repeating the interval [t,t+T] and ignoring everything outside that interval. But then different values of t would give you different functions with different transforms.

>>14620613
Not him, but he obviously meant the width of an "infinitely narrow" rectangle. Now that's informal.

I can't see why, for every initial segment there should exist a ordinal number isomorphic to it (so that F(x) is correctly defined), I have been thinking about the least x for such an ordinal number doesn't exist (just as the text recommends), but I cannot see any contradiction.

This is from Jech, Set Theory, the definition for ordinal number are the transitive sets well-ordered by the membership relation.

I would appreciate a hint, rather than the direct argument

>>14620705
Imagine for a second you have [math]a \in A[/math] and [math]g \in G[/math] such that [math]ag \neq ga[/math].
If you can find a one-dimensional rep of [math]A[/math] which has one value on [math]a[/math] and a different one on [math]gag^{-1}[/math] then the image of the induced rep cannot possibly be abelian, and hence needs at least two dimensions, and hence is irreducible.

>>14620856
Assume there is such a least [math]x[/math].
Then [math]\alpha + 1[/math] is isomorphic to [math]x + 1[/math], a contradiction.

I think.

>>14607941
>black holes are black because huge gravity prevents light from coming out
>gravity force works with mass
>light has no mass
??

>>14620948
After general relativity, mass and energy aren’t completely distinct. Light has “mass” in the sense that gravity effects it

>>14620694
>how come it repeats twice?
first one assumes n is odd, bottom on assumes n is even. i highly recommend not trying to follow it, its extremely unreadable and frankly i just posted it because i spent like 15 minutes typing up the tex and wasnt ready to throw it away.

>>14620888
Oh wait, this is backwards.
I think you might need to do a transfinite induction-link argument.

>>14620948
>>gravity force works with mass
no, energy warps spacetime such that the straight line that light travels in curves into the black hole. this is why gravity isnt described as a "force" once you get to higher physics.

lads, i work with my hands and use rock drill oil at work. i'm trying to understand what exactly rock drill oil is. looked for charts that show crude oil distillation into methane, petrol etc but can't find anything for rock drill oil

is it even from crude oil?

>>14620741
>Well, a Fourier series is a function Z->C, a Fourier transform is R->C.
This is really confusing since the kernel is a function of two variables. The Fourier series is a function of n and x (or t). n takes discrete values while x is continuous:

[math]c_n = \dfrac{1}{\pi}\int_{-\pi}^{\pi}f(x)e^{-inx}dx[/math]

So how is it Z->C? What is Z here? n in c_n? I would think it is R->C, since x ∈ R, right? And since n takes discrete values isn't n ∈ Z? Shouldn't we consider x as the range, along with n, since we integrate with respect to x?

Because the reverse Fourie series is a discrete summation of n=-inf to +inf which would be Z->C, right?

And the Fourier transform is
[math]F(i\omega) = \int_{-\infty}^{\infty}f(x)e^{-i\omega x} dx[/math], so it can be considered either R->C or R->R depending on how you interpret the left side, since it is sometimes defined as F(w) or F(jw). And the reverse FT is also an integral, unlike the Fourie series, so it is probably C->R or R->R.

>>14621070
The Fourier series is the (countably-infinite) list of coefficients. F(n) is the coefficient of the sinusoid with frequency 2πn/T. For the transform, F(ξ) is the coefficient of the sinusoid with frequency ξ. n∈Z, ξ∈R.

> so it can be considered either R->C or R->R depending on how you interpret the left side, since it is sometimes defined as F(w) or F(jw)
It's R->C. The Laplace transform is C->C, and the Fourier transform is the (two-sided) Laplace transform with s=jω, ω∈R.

>>14620975
I don't understand

>>14607941
Should I watch garden of sinners after hunter x hunter 1999?

>>14621794
you should watch the original tsukihime anime first because that's what garden of sinners is based on

>>14621783
you know how light mostly travels in a straight line? well, a straight line through space is called a geodesic. energy (matter) warps spacetime such that the geodesic that light travels on looks curved. so you understand why light doesnt need to has mass in order to be affected by gravity.

>>14621964

>>14621964
>>14622042

>>14620868
Thank you. I can see why such [math]a,g[/math] exist, but I don't follow the rest at all - can you expand a bit more please?

Can you distill a microbial solution without killing it?

Are telomeres and random mutations the only things that cause cells to die? I'm talking in the absence of toxic waste buildup, astrocytes fucking up etc.

>>14622048
Imagine you've found a rep [math]f: A \to GL( \mathbb{C} , 1)[/math] such that [math]f(a) \ neq f(g^{ -1 } a g)[/math].
A splitting of the induced rep [math]h \to GL( \mathbb{C} , 2)[/math] into a sum of reps is a factoring of [math]h[/math] through [math]GL( \mathbb{C}, 1) \oplus GL( \mathbb{C}, 1)[/math], which is an abelian group. But [math]h[/math] cannot possibly factor through an abelian group because [math]h(ga) \ neq h(ag)[/math]

>>14610434
It's because the houses are made of weakly interacting bricks, which cannot be bound with mortar or seen. You pass through such houses many times a day, yet you don't even realize it.

>>14620761
>Not him
But I am a transwoman.

>>14610434
yawn

>>14611665
Eliminating c is the proper units of measure. That's why they do it. Keeping c around would be like if we measured height and horizontal distances in different units of length and then kept the conversion factor around in all rotationally symmetric formulas.

>>14622466
Thanks!

Is a polyhedral angle equal to the sum of the (plane) angles of its faces?

>>14607941
>tfw getting filtered by AC circuit analysis
Am I a brainlet? Though I've only been working on it for 2 days.

The rangeban is off.
You lads can keep making the threads, I'm just mentioning it so I don't feel like I'm lying by omission if satokofag asks me what image I want him to use on a new thread.

>>14623531
Are you leaving forever anon? Then I will feel sad, you're my favorite fed.

>>14623545
I'm just not immediately taking over the thread-making.

>>14623575
Understood anon, you can datamine plenty from us. We could outdo many of your research departments.

Is this picture wrong?
Isn't the tangent actually the length of the hypotenuse of the large triangle? Not the adjacent.

Where does the idea that "acid is green" come from? Why do cartoons, and educational videos depict acid as green?

Every acid I have ever worked with has been clear before it reacts with something else. Green is not a common color in chemistry labs. What gives?

>>14623755
> Is this picture wrong?
No.
> Isn't the tangent actually the length of the hypotenuse of the large triangle? Not the adjacent.
"sohcahtoa".
sine = opposite / hypotenuse
cosine = adjacent / hypotenuse
tangent = opposite / adjacent
The blue triangle has hypotenuse=1, so sin and cos are the opposite and adjacent respectively. The red triangle has adjacent=1, so the opposite is the tangent and the hypotenuse is the reciprocal of the cosine, i.e. the secant.

>>14618700
>besides being a brainlet
No no it's just that. Try to do more problems now that you recognize it, if it doesnt get better IT IS OVER for you I'm sorry.

I'm generating a PDF with matplotlib for later printing. Turns out that figsize determines the page size, and not the size of the actual figure inside.
Anyone know how I can control the size of the figure itself, so that when I print it on an actual paper, the sizes inside will be the exact ones I want?

Took a break from college due to health reasons and now I'm going back in the fall. What topics should i review for calc 3?

>>14624742
Then why do I also always see this? There it's the hypotenuse of the opposite triangle which will grow larger.

>>14625742
You're reading the triangle similarity incorrectly in that one.
1 is to cosine as tangent is to sine.

I'm autistic and may possibly develop schizophrenia later in my life. Given I know nothing above high-school-level chemistry, how would I feasibly be able to extract the supposed bufotenin from my piss? If it's tiny trace amounts, how many "rounds" of pissing (assuming I piss an average of 400mL, with the average chemical ratios) would I have to process to get an amount of bufotenin that could actually affect me when ingested?

>>14625812
You aren’t autistic.

>>14625821
What gives you the reason to say that?

>>14625790
oh, so I assumed wrong thinking the blue and green, or large projected vs opposite triangle were the same triangle? I should really get myself a ruler and protractor lol

>>14625862
>>14625790
or oh wait, maybe they are the same, but the hypotenuse of the green is the same as the adjacent of the blue. But they are just mirrored so I was getting confused.

>>14625879
>>14625862
or wait, the green + black make up the blue?

>>14625885
definitely not this one after thinking about it more. I just got confused since I was so sure the blue and the green were the same in my head.

>>14625742
>>14623755
these two pics are so fucking confusing to me. why do some people make everything so complicated? like, in the first picture tanQ is simple CB/OB, the blue label "cosQ" is actually hypothenuse * cosQ, and "sinQ" is hypothenuse * sinQ.

>>14625956
You are supposed to understand that the radius of the circle is 1. It is a good picture for demonstrating the relationship between tan and sec, I have never seen it before.

>>14625812
>bufotenine synthesis from piss with no chemistry background or materials
Not happening, sorry anon. If you want access to certain drugs or testing, join clinical trials. At clinicaltrials.gov.

If I'm trading stocks of different sizes relative to my bankroll and closing the winning and losing trades at different gain and loss percentages and I figure my expected win rate is 60%...
>how high does an individual trade get for it to be at / above my expected 60% win rate?

I thought this would be simple to figure out but it is fogging my brain. Please help, bros.

>>14607941
If I stuck an MRI machine in a faraday cage, would it block out the magnetic effects on the outside, or would it pull in and destroy the cage like an inverse of neodymium magnets in ur stomach

If something could squeeze a star what would it feel like?
Are they squishy?

>>14625862
After thinking more about it I realised they are not the same triangles because the bottom of the blue triangle stays the same at 1. Now I just need to intuitively understand why tan is on both triangles.

>>14626203
basically what I had in mind was that the bottom also changed in relation to the sin of the black triangle.

>>14626101
probably kinda powdery

>>14625985
Ok, forget the lack of expertise, then; let's make this speculative. Given our (as a society's) understanding of biochemistry, what would be the most possible way of isolating the bufotenine? The same question form earlier applies about how much piss would be needed to contain an amount large enough to give any noticeable effects.

what is the best textbook on thermodynamics?

>>14625742
>There it's the hypotenuse
No it isn't, it's the opposite. The hypotenuse is horizontal (extend the yellow line until it reaches the red line). The radius becomes the adjacent.

>>14626085
A Faraday cage blocks electromagnetic radiation, not magnetism. If you want to block static magnetic fields, you'd use something with high magnetic permeability such as mu metal or permalloy.

>>14626708
the hypotenuse isn't the side facing the 90 degrees? The red line

>>14607941
What are numbers and why do we use them?

Someone recommend me a graduate or postgrad level book on the structural-physical and aerodynamic shape design of aircraft. I've gone through many books and they all cover the same freshman shit

What matters more for grad school, GPA or publications?

>>14627121
The hypotenuse is the sign facing the right angle, which is at the apex of the triangle, marked with a red square, right next to where it says (cos θ, sin θ).

There are two distinct triangles in that picture. One has the adjacent in yellow labelled cos θ, the opposite in green labelled sin θ, and the hypotenuse in teal/cyan labelled 1. The other has the adjacent in teal/cyan labelled 1, the opposite in red labelled tan θ, and the hypotenuse unmarked and unlabelled (it's the portion of the X axis between the centre of the circle and the red line).

>>14627480
>The hypotenuse is the sign
*side

>>14607941
This is the kind of shit that ruins /sci/. Little annoying girls should not be in a board for scientists.

Does anyone else here only use the index, middle and ring fingers to hold glasses and the like? My pinky doesn't actually stretch out or anything, it just hovers off to the side and I have no idea why do I do this or if it's normal.

Can someone explain this? It's either true or false.

"In a process of precipitation by change of pH, when treating an aqueous extract of pH=3 with a solution of NaOH until reaching a pH=14, the acidic organic compounds will precipitate."

One of my friends thinks it's false and that the base would precipitate. I'm confused and don't understand why; I thought that similar substances dissolve in similar substances, so the precipitate would be acidic because it wouldn't be able to dissolve in a base.

Why can't you have computers and programs that use light instead of electrons so there are more temporal probabilities than 0 and 1 and therefore its easier to compress data because you can have any range of wavelength

Is it true that statistically people are more likely to choose the left path when confronted with a new place? Learned this in hxh 1999

>>14627750
You can in theory (we already have optic fiber for very high speed data transmission). We use electricity because electronics are much cheaper and easier to manipulate than optics.

>>14627551
just report the weeb for avatar use

>>14627581
if i ever see some faggot hold a glass like this i will beat him up with a fluorescent lamp in hopes it's you

>>14627816
If I ever see a man walking around with a fluorescent lamp for no reason I will preemptively beat him up in self-defense.

>>14627847
https://youtu.be/STJVeeo2gOE?t=94

>>14627750
> so there are more temporal probabilities than 0 and 1
you don't have to use light for that, you could just use electrons. either way there's no point. it's orders of more magnitude in difficulty and cost to engineer some new transistor that could do that but there is zero benefit. you can do exactly the same with a bunch of 0's and 1's, and it would be much, much easier.

>>14627904
Yeah but instead of 1s and 0s you can have wavelength. Thats cool

>>14607941
How would you guys go about solving this AC circuit, it's starting to fuck with me. None of my peers have the answer and I have no one to compare it with. Changed the values so I won't get doxxed.

>>14627937
It's a run of the mill RLC, what are you struggling with?

>>14627964
I found the book and it only lists the solutions. Mine are different, but I suspect the books to have errors. Sec, I'll post how I'd solve it.

>>14627581
yeah i do that instinctively too. i think its where homo sapiens evolved to hold their cigar.
>>14627847
wumia <3

>>14627937
take all the elements and convert them to the frequency domain, then just solve the problem normally.

could some kind of fungus grow in fairly concentrated aquaous copper acetate solution (it's most likely contaminated with decent amounts sodium and other things)?
I've got 2 sites with either VERY fine white needle crystalisations or it's some kind of underwater mold

>>14627992
I've just found a stock photo of a man doing it.
I think that the distance between the palm and the glass makes it harder for the pinky to grip things properly, so it just relaxes.

>>14627937
>>14627964
So this is how I would solve this circuit.

Firstly, our phase angle would be:
[math] \omega = 2 \pi f = 2 \pi \cdot 1\text{kHz} = 2000 \pi \text{ Rad/s} [/math]
and from that we gather the following for our impedances:
[math] \text{Resistor: }X_R = R = 20 \,\Omega \, ,[/math]
[math] \text{Coil: }X_L = j \omega L = 2000 \cdot \pi \cdot 1 \cdot 10^{-3} \, \Omega = 2 \pi \, \Omega \, ,[/math]
[math] \text{Capacitor: }X_C = \dfrac{1}{j \omega C} = \dfrac{1}{2000 \cdot 100 \cdot 10^{-6} \cdot \pi \cdot j \, \Omega} = \dfrac{1}{(\frac{1}{5}) \pi j \, \Omega} = -5j \, \Omega. [/math]

With this we can calculate the total impedance in this circuit:
[math] X = X_R + X_L + X_C = 20 \, \Omega + 2 \pi j \, \Omega -5 \pi j \, \Omega = 20 \, \Omega \, - 3 \pi j \, \Omega = sqrt\left(20^2+(-3)^2\right)e^{(tan^{-1}(\frac{-3}{20})j)} \approx 20,22e^{-0,14\overline{88}j}[/math]
Thus, for the current we gather:
[math]U_{rms} = IX \Leftrightarrow I = \dfrac{U_{rms}}{X} = \dfrac{5 \, \text{V}}{X} \approx \dfrac{5e^{0j}}{20,22e^{-0,14\overline{88}j}} \, \text{A} \approx 0.25e^{-0,1488j} \, \text{A}[/math]

So now I'm a little confused on what to do. Our book would just say 0.25 Amperes and calculate for the resistance: 0.25 * 20 V = 5V for the voltage drop there, disregarding the phase angle. In reality it should be 0.25A with a phase angle of tan^(-1)(-3/20) = -8.53 degrees right? No fucking clue, I might be making mistakes. I'm supposed to calculate the voltage drops across all components in the circuit.

>>14628082
Also, I get:
U_C = 0.25 * -5j V = -1.25j V for the voltage across the capacitor. What brainlet mistake am I making, there shouldn't be a complex number there right?

The Russians have been adding estrogen to my water again or something.
Why am I feeling so weak these days, /sqt/?

>>14628101
It looks mostly good to me. Nothing wrong with a complex voltage in the frequency domain; however, remember that the current is also complex as you calculated in >>14628082, so U_C = I*X_C should include one more phase factor.
However, you seem to be confusing RMS values with the complex phasor voltage/current -- iirc we always use peak voltage/current for magnitudes, not RMS.
[math]U = \sqrt2 U_{rms}, \quad I = \frac{U}{X} = \sqrt2 \frac{U}{X}[/math].

>>14628328
Yeah, I'm confusing a few things, thanks anon. I'll just read through the topic a bit more and solve some problems. Have to submit an assigment sheet tommorow anyways, worst case I'll fuck it up and get corrected. Have a good one.

what is it about pseudoscience that makes it so fun

>>14628395
escapism. its why fiction is more popular than non-fiction

I got a question for any biochem or chem anons.
What generally does the process to develop chemicals/drugs look like?
Obviously not something a retard (myself) could do in a garage but I have been going down various rabbitholes dealing with research in drugs for cancer and scarless-post op healing and reading about these drugs but there's no information on what these drugs are made out of or what steps are taken to make them.

>>14628485
It’s… complicated. Depends very much on the product.

Read Derek Lowe’s in the pipeline articles to get a real impression of what’s going on. He’s got a gift for writing and a legendary sense of humor

how can I prove that work is an inexact differential using the formal definition of an inexact differential? this definition being that [math]A[/math] is an inexact differential if [math] \frac{\partial M}{\partial y} \neq \frac{\partial N}{\partial x} [/math] in [math] A = M(x,y)dx+N(x,y)dy [/math].

Also, my textbook says that one way to enunciate the 1st law of thermodynamics is
>the work done to bring a thermally isolated system from a initial state to a final state is independent of the path taken
but that not only would mean that work is an exact differential as it doesn't make sense, because in pic related the area under each isothermal is different. what am I missing here?

>>14628549
Take dW=PdV. Do the integral in PV space. Show that different paths result in different values. QED.

As for second question, for a path to be different from other paths would imply heat enters/leaves the system. You can see this from the first law written out in equation

>>14628549
>because in pic related the area under each isothermal is different
That's where the heat transfer in the engine comes into play. So the integral from a-f and i-b.

>>14628571
>for a path to be different from other paths would imply heat enters/leaves the system
it does not answer my question.
the quote
>>the work done to bring a thermally isolated system from a initial state to a final state is independent of the path taken
assumes that in an adiabatic system, work does not depend on the path taken. my question is, how can it be if work does depend on the path taken?
>>14628584
comment above

Hi Anons, how do i derive the formula for the sum of 2 to n?

I realise you can just do n(n+1)/2 - 1 so you are subtracting the sum of 1 to n by the first term.

But i want to do it the way i do for the sum of 1 to n like:
Sn = 1 + 2 + 3 + ... + (n-2) + (n-1) + n
Sn = (n-(n-1)) + (n-(n-2)) + (n-(n-3)) + ... + n-3 + n-2 + n-1 + n-0
Add them together so -(n-1) and n-1 cancel, and the -3 in n-3 cancels with +3 etc.
2Sn = (n) + (n + n + n + ... + n)
2Sn = n + n(n)
Sn = n(n+1)/2

But when i try this from 2 to n i get
Sn = 2 + 3 + 4 + ... + (n-2) + (n-1) + n
Sn = n-(n-2) + n-(n-3) + ... + n-4 + n-3 + n-2 + n-1 + n-0
Adding them together (the second Sn is n-1 terms of n and an additional -1 that never cancelled out from n-1)
2Sn = (n) + (n-1)(n) -1
Sn = (n^2 -1)/2

What am i doing wrong?

>>14628587
Are you trying to understand me or not? For paths to have different values MUST imply that heat is being exchanged. If heat is not being exchanged, work becomes an exact differential (equation of state). This is evident from the first law as stated mathematically.

I highly recommend looking at a higher level thermodynamics/statistical mechanics course. It seems you’re missing some fundamental basic info which is leading to your confusion

>>14628587
When you consider an isolated gas, your state space is made up of coordinates P and V. When you consider a gas that exchanges heat with it's environment tthe state of the system is no longer defined just by its pressure and volume, hence what consitutes a path returning to the same point also changes.

>>14628587
>my question is, how can it be if work does depend on the path taken?
You mean how [math]dU = \delta W[/math] can be true?
No idea

Has any mathematician ever asked (or answered) the question as to why certain theorems are so "hard" to prove? And I don't mean that in an intellectual way, but more in the sense of number of logical steps required. I find it remarkable that something like the Four-Colour Theorem or De Rham's Theorem requires dozens of pages, as it were, full of derivations to prove them. I would think that such fundamental mathematical truths would emerge quite readily as a result of some profound symmetry. Could it be are overlooking such a symmetry, like how Galois theory simplified our understanding of algebra?

>>14628599
What's n^2/2 + 1/2 -1?

>>14628622
>>14628627
I'm still confused, but I can understand a little better now.
I think I'll try reaching out to a professor at my uni, but thanks for the explanations

>>14607941
Re(ab) = Re(a)Re(b) where a, b are complex numbers.

Is this true?

>>14628750
Let a = c + di and b = e + fi
Re(ab) = Re(ce - df + (cf + de)i) = ce - df
Re(a)Re(b) = ce
So no.

>>14628485
It's vastly different depending on the drug you're trying to develop. Lots of different ways to pick a molecule too. Lipinski rules can give you a good idea of if a molecule will be a good drug candidate, more or less. Computers can synthesize tons. Then it's about testing. Pharmaceutical technology and pharmaceutical chemistry then marry along with biopharmacy and pharmacokinetics, lots of tears and clinical trials, and after a decade or two you have a drug.

"Quantum states you generally think of as very delicate, and if there’s any kind of external interaction, you kind of destroy that state"

How the fuck do you even figure this shit out? Are they literally "blackbox" testing the universe itself?

Are most of the explanations of the Twin Paradox just wrong? It doesn't have anything to do with acceleration right?

What if you have two objects that are both constantly accelerating with respect to one another, like if they were moving in huge circles next to each other at near light speed? You'd still get these asymmetries.

Or what if you had triplets or quadruplets traveling next to each other, splitting up etc.

I read the wikipedia article on it and apparently Einstein et al. just thought it was immediately obvious that there was no paradox from the math.

Can someone explain this shit?

>>14629561
>Can someone explain this shit?
There's no lorentz transformation from one system to the other. The math checks out, it's just hard to explain in words.

>>14629561
>It doesn't have anything to do with acceleration right?
It does.

You literally just can't transform away acceleration.
If object [math]A[/math] is accelerating away from object [math]B[/math] at [math]x[/math] kilometers per hour you cannot transform away the acceleration so [math]B[/math] is accelerating away from [math]A[/math] at [math]-x[/math] kilometers per hour.
This isn't anything new since even classical mechanics doesn't let you transform away acceleration, it's just more glaring.

I'm trying to learn basic electricity so I can build a solar system. I have bought four 100 watt 12 volt solar panels and one Victron 100/30 solar charge regulator.
I'm completely stuck at this video: https://www.youtube.com/watch?v=cX4s-bxn4fs after 15:34 he appears say that you need a solar charge controller able to handle at least 33 amps to utilize 4 100 watt solar panels. What does he mean by 33 amps? My solar panels are 5.4 amps each. Doesn't this mean that in series they would produce 5.4 amps and in parallel 21.6 amps? Can someone please what my misunderstanding is?

>>14629620
12V @ 5.4A = 64.8W. If they can only supply 5.4A, they aren't 100W panels. 100W @ 12V = 8.33A, and 4 of them in parallel would be 33.3A (4 in series is 48V @ 8.33A).

>>14629735
Thanks but that's another thing I don't get. 12 volts? Where does 12 volts come from? The label on the back of the solar panel has a billion different metrics but it doesn't mention 12 volts anywhere. Only the Amazon product page title says 12 volts. ???????????????

As for amperage: I must have arbitrarily picked one of the many amperage metrics on the solar panel sticker and product page instead of using my brain and keeping in mind that v*a must add up to 100 watt if it's a 100 watt panel. If I divide 100 watt by 12 I get 8.33 amp indeed. Great. But the product page doesn't mention 8.33 amp anywhere for some reason. Probably for the same reason that it doesn't say 12 volts anywhere. Anyway...

In this video https://www.youtube.com/watch?v=TJBGbufexEM at 4:17 he says that your solar charge regulator should be 60 amps to handle the 50 amp load from 600 watts of solar panels / 12 volt. Okay, but doesn't this assume that the solar panel array is being run in parallel? If that's the case, why doesn't he mention straight serial setups or 2 serial pairs of 2 panels being run in parallel? 2 serial pairs run in parallel would mean twice the voltage and half the amperage, wouldn't it? In other words, 24 volts and 25 amps, right?

Putting aside my butthurt drunken rambling above, can someone please tell me if my 4 100 watt panels will fit my Victron 100/30? Again, even if the amperage is too high in all parallel I should still be fine if I run the panels as 2 series in parallel, right?

>>14629794
A photovoltaic cell typically puts out 0.55-0.65 V (varies with temperature) at no load. A panel will have multiple cells wired in series to produce a more useful voltage, and multiple "strands" wired in parallel to make up the area (this also means that a single cell failing results in a proportionate decrease in output rather than the entire panel failing).

The output voltage has to match the converter. If the converter is designed for 12V, you can't wire the panels in series and feed it 24V. Having panels which put out roughly 12V means that you can run 12V equipment (e.g. anything that can connect to an automotive 12V supply) from them directly without the need for a converter, so that's fairly popular for consumer-grade panels.

The actual output voltage varies with panel temperature, load, and illumination. At no load, illumination doesn't matter much, but the lower the illumination the less current you can draw before the output voltage starts to drop significantly. Any decent converter uses maximum power point tracking (MPPT) to control the current draw to maximise power (less current -> less power, more current -> lower output voltage -> less power).

>>14629605
>>14629605
>>14629605
New