/sci/ - Science & Math

>>14629605
I associate all the porn of yukari that I see now with that disgusting brown canadian faggot.

>>14629605
I'm getting a drawing tablet to do math on my desktop PC but I don't know which drawing program to use yet? Anyone got any recommendations? I don't wanna use Onenote because I don't have a microsoft account.

>>14629605
Stupid question, but for an undergraduate student, is it possible to get a job in machine learning? Will publishing a paper help with my chances of landing a job? Thanks.

>>14629925
Don’t know where you’re studying but it shouldn’t be too hard to get something. No companies get presented to students at any point? They’ll want decent grades

>>14629748
He is a blight upon humanity

>>14629790
xournalpp

>>14629999
Is 3.4 bad? Do you think I should focus on my grade instead of trying to push for a paper? I really want to push for something in my senior year because I will be away from academic for a while.

>>14629605
given
[math]
V, W \in \mathbb{R}^n
[/math]


Is this true?
I think it is.. I am doing some trickery around with the kernels and I always get correct results
but i don't know how to formalize this
[math]
U = V\cap W\\
U = Ker(Ker(V)\cup Ker(W))
[/math]

>>14630450
forgot to add picrel

>>14630037
Thanks. Now which drawing tablet to get? I'm fine with spending a little more money. Probably some wacom one but which?

When do you actually use calculus once you learn it?

>>14630487
why are you fucking learning it if you dont know what you're using it for?
calc is crucial to every STEM subject, anything that has to do with rates of change, volume, fields, probability, or more esoteric stuff like signal decomposition are all underpinned by calc.

>>14630504
>why are you fucking learning it if you dont know what you're using it for?
Calm down anon, xe was just asking a question

>>14630522
I thought my answer was satisfactory. Dont u agree?

>>14630522
Did you just assume his Xender?

>>14630545
It was okay. Pretty much on the same level as just linking a wikipedia page, which is what I would do

>>14630450
Are you using calling a subspace's orthogonal complement [math]Ker[/math]? Because your question doesn't really make any sense.

Unanswered questions:

Maths questions:
>>14609132
>>14610175
>>14612015
>>14615471
>>14616753
>>14619857
>>14622960
>>14625203 [I really didn't expect this one to go unanswered but I suppose everyone's a bit tired.]
>>14626052
>>14628630

Physics questions:
>>14619656
>>14626623
>>14629290 [Just about any qm book has a relatively clean, understandable derivation of basic qm from Stern-Gerlach experiments and the like.]

Biology questions:
>>14607990
>>14619199
>>14622328
>>14622438
>>14628012

Chemistry questions:
>>14610542
>>14627658

Engineering questions:
>>14621034
>>14623333
>>14627206

/g/ questions:
>>14624960

Stupid questions:
>>14607995
>>14609034
>>14612149 [Depends on the library but instantiating should be near instantaneous most of the time.]
>>14616896
>>14619838
>>14624264
>>14627167
>>14627271
>>14627812
>>14628287

>>14630688
>Are you using calling a subspace's orthogonal complement Ker?
yes
isn't that called kernel?

>>14630708
I'm used to just calling it the orthogonal complement.
Anyhow, prove they're each a subset of the other.
If [math]u \in U[/math] then if [math]v \in Ker(V)[/math] clearly since [math]u \in V[/math] clearly [math]u \cdot v = 0[/math], and similarly for [math]W[/math].
Do the other one by yourself.

>>14630043
It’s great. Don’t sweat it. You have to ask around about a job now. There’s no way your school can’t connect you to a company.

How do you solve Hackerrank Updates Median in Python?

>>14630910
thank you!

>>14630937
Maybe you can use two heaps, one keeping the top half of all inserts, the other one keeping the bottom half of all inserts, with opposite sorting order. Inserting new elements and recomputing the median should be very fast.

>>14630992
Wait you need to allow for removals, never mind.

>>14629605
What is the difference between number theory and discreet mathematics? Which one should I study first?

>>14630996
Yeah I went through the same realization as you :/

>>14631010
You could just use some other priority queue implementation like https://en.wikipedia.org/wiki/Van_Emde_Boas_tree

I missed the response from anon last time i asked but i dont understand his response can someone help me with:

>>14628599

and anon responded >>14628639

sorry anon i missed your response

>>14631106
oh wow nevermind i got it just now.

the first sum also has a (n-1) that doesnt cancel out either so its:
2Sn = ((n-1) +n) + ((n-1)*(n) -1)
and then
2Sn = n^2 +n -2
Sn = (n^2+n)/2 - 1

What the hell is dark matter? So its invisible, does that mean if I had a bunch of dark matter in front of me I could simply walk through it? If dark matter is most of the matter in the universe then what does that make us? And how does this relate to dark energy?

I can't help but feel like this is all a bunch of shit we made up because we don't know the real answer.

>>14631160
Are you aware of the reason why you cant walk thru a wall?

>>14631160
>I can't help but feel like this is all a bunch of shit we made up because we don't know the real answer.
I will forward your opinion to the highest authorities in the field.
Thank you for your contribution.

>if an event has an x probability of happening with every attempt, how many attempts must you make to be y% sure it will happen?
Can someone remind me what's the formula for that? I'm too retarded to figure out what to google.

>>14631217
https://en.wikipedia.org/wiki/Binomial_distribution

>>14631226
thanks

>>14631217
The probability of at least one success within [math]n[/math] attempts is [math]1-(1-x)^n[/math].
The minimum number of attempts required is the [math]n[/math] that verifies [math]y \leq 1-(1-x)^n[/math], i.e. [math]n \geq \frac{\log_2(1-y)}{\log_2(1-x)}[/math]

>>14631020
How would I go about coding that from start to finish? I am pretty new to coding and got thrown into a DSA course where the (1st-year Ph.D. student) professor only goes over pseudocode straight from my online textbook.

>>14630688
dilate tranny

>>14631285
I'd import the priority queue from some library I found on google.
Then I'd initialize both priority queues (in the python global scope)
I'd declare a function for computing the median.
I'd declare a function for inserting a value that does the appropriate juggle of ensuring both queues have just about the same number of elements.
I'd declare a function for removing a value.
Then I would, in the main loop, read a line from the console, and parse it to a number.
I'd then do a for loop going from 1 to the number parsed and, for each time, read a line from the console. parse the line and insert/delete the value and print the median.

>>14629605
How effective is Plan B? Let's say you cum in a chick and she takes it right after. How effective is it?

>>14630923
Thank you anon.

>>14629605
Say we need to get to an expressin (1 + x - 1)/ y and we have x/y. Am I allowed to just add +1-1? Since it evaluates to 0 anyways. So:
x/y = (x(+ 1- 1))/y = (1 + x - 1)/y.
Pls help bros, I want to sleep, pulled an allnighter and some more.

Can someone verify my proof? Let [math]E/F[/math] be finite Galois. I claim that [math]E[/math] is the splitting field of some separable [math]f \in F[x][/math].

Proof: Write [math]E = F(\alpha_1 ... \alpha_n)[/math] and let [math]m_{\alpha_i}^F \in F[x][/math] denote the minimal polynomials. Note that if [math]\beta \in \text{Roots}_E (m_{\alpha_i}^F) \cap \text{Roots}_E (m_{\alpha_j}^F)[/math] then [math]m_{\alpha_i}^F = m_{\beta}^F = m_{\alpha_j}^F[/math]. Hence we may assume [math]\text{Roots}_E (m_{\alpha_i}^F) \cap \text{Roots}_E (m_{\alpha_j}^F) = \emptyset[/math] whenever [math]i \ne j[/math]. Now let [math]f = \prod_i m_{\alpha_i}^F[/math]. Since [math]E/F[/math] is normal, [math]f[/math] splits in [math]E[/math], and clearly [math]f[/math] does not split in any proper subfield of [math]E[/math] as [math]\text{Roots}_E (f) = \bigcup_i \text{Roots}_E (m_{\alpha_i}^F)[/math]. Since [math]E/F[/math] is separable, each [math]m_{\alpha_i}^F[/math] is separable, and by the disjointness of roots for [math]i \ne j[/math] we conclude that [math]f[/math] is separable.

Need some latex help please.
How do I get the numbers aligned better?
See how the division, addition, and subtraction are all aligned while the multiplication is off? I want it all aligned. Here's what I was using:
\begin{align}
40 &\div 10 &= \nonumber \\
72 &\div 18 &= \nonumber \\
25 &\cdot 19 &= \nonumber \\
1460 &- 591 &= \nonumber \\
3 &\cdot 29 &= \nonumber \\
2 &\cdot 26 &= \nonumber \\
497 &+ 252 &= \nonumber \\
565 &+ 115 &= \nonumber \\
\end{align}

Is every convex subset of [math] \mathbb{R}^n [/math] Lebesgue-measurable?
It feels like it should be true but I couldn't find a proof.

>>14632424
Yes.
>>14633225
Your google-fu sucks.
https://math.stackexchange.com/questions/207609/the-measurability-of-convex-sets

https://www.lexico.com/definition/rebunk
Has the word "rebunk" actually existed since the 1930s or am I misinterpreting this website?

>>14633141
There are unrelated problems with your code that needs to be addressed first.
1. If you do not want numbers in your equations, use an asterisk after the environment name, instead of repeating \nonumber in every line. This will hold true for every equation environment offered by amsmath package.
2. If you want to align multiple characters, you use alignat environment offered by amsmath. The second & in align environment is used to separate equations into columns.

The solution is to redefine \cdot to have the same width as any of the other symbols. This can be done by making a box of the required width, aligning by center. Moreover, the \mathbin command needs to be used on the box to make the spacing around it behave like a binary operator and not just any other symbol. Since \makebox does not work in math environment, \mathmakebox needs to be used from mathtools package.

Now, the code:

\documentclass{article}
\usepackage{amsmath,amssymb,mathtools}
\newlength\minuslength
\settowidth\minuslength{$\displaystyle-$}
\newcommand{\newcdot}{\mathbin{\mathmakebox[\minuslength][c]{\cdot}}}

\begin{document}
\begin{alignat*}{2}
40 &\div 10 &= \\
72 &\div 18 &= \\
25 &\newcdot 19 &= \\
1460 &- 591 &= \\
3 &\newcdot 29 &= \\
2 &\newcdot 26 &= \\
497 &+ 252 &{}= \\
565 &+ 115 & = \\
\end{alignat*}
\end{document}

Note:
The {} after the & is to preserve the relation spacing of =, otherwise, it acts as if there is no character behind the =. Only the line with 252, was chosen since that is the one with widest width.

More solutions are available here: https://tex.stackexchange.com/questions/499883/align-by-center-of-symbol

Is Hard Water a real thing and how do I create it?

Starting a mechanical engineering degree this fall, didn't touch math or physics since high school and that's been a couple of years ago, anyone can recommend me some books that can carry my ass ?

Say I am given a finite sequence of size k of n random integers with k > n.
Is there a way to search for copies of integers other than combing through the entire collection for every single integer?

The triangle is heavy. What is the term for the red bar if it can support a lot of weight? Like high tensile strength but I know tensile isn't the word.

>>14634001
It should be resistant to shear stress. I don't know if there is a more descriptive word for it.

>>14634001
Bending moment?

>>14633987
>Is there a way to search for copies of integers
Yeah.
This is a classic problem, /g/sqt can sort you out.

>>14634057
I am actually trying to (most likely erroneously) model a problem involving a shelf full of unsorted books.
I am not confident sorting algorithms would work in this case but I appreciate the help nonetheless.

Book for an introduction to category theory? (there's none in the book recs above)

>>14634081
>I am actually trying to (most likely erroneously) model a problem involving a shelf full of unsorted books.
It doesn't really matter, you just make a HashMap or a HashSet and go along checking for dupes.

>>14634093
Thanks.

basic economy recommendations?
inflation has been shitting up my poor eastern european country and of course my parent's didn't give enough fucks to teach me anything about economics/finance. I just want to have a rough idea what is happening around me/in my region, etc and how to save/invest my money with relative safety on the long run.

tl;dr
basic but "well established" personal finance and economics books recommendations

>>14634109
Buy bitcoins

>>14633487
Thanks man. I appreciate you taking the time to go through so much detail and improve my general code.
This helped me alot

This is a data sheet for a transistor.

They don't mention collector power dissipation for Ta, only Tc. Is there an equation to ball park it?

What happens if I put detergent powder in the drum with the clothes instead of in the drawer? Does it get washed out too early and I'm basically doing the wash with hardly any powder?

>>14634090
Mac Lane is fine.

>>14634109
Inflation=expanding money supply
Book recs for econ are mankiw and hazlitt

Can anyone explain tensors?

What's an organic structure?

I have a really basic homework assignment, find something around the house that has an organic compound in it (I was going to do paraffin wax in a candle) and show the organic structure of the compound. I've dug through all of the lecture videos and the textbook and the internet and haven't heard that specific term- I have a guess of what it might be but I'm not sure.

>>14635387
Inflation is increasing prices, not money supply, though the latter is a factor

>>14634109
Learning economics won’t help you unless you work in the Central Bank of your country, and that is to say, real Economics, not the mathematical bullshit they teach you in academia. Finance won’t help you either unless you are rich enough to actually trade and invest in financial instruments. Just read newspapers and look up words you don’t understand.

>>14635591
What causes higher prices other than increase in the money supply?

Can someone elaborate why strong induction has to be proven? Isn't it an obvious result from the basic induction?

>>14635715
A decrease in productivity, i.e. less valuable money

>>14635785
What causes a decrease in productivity?

How can a black hole achieve infinite density?

>>14635788
niggers

>>14630688
>>14610542
you'd use a dean-stark trap, in-flask dessicants (sieves, salts, excess strong base), or simply let the water boil off, depending on reaction conditions

>>14635715
Look up cost push inflation, demand pull inflation, stagflation

If a and b are two rational numbers such that square root of ab is rational, does it imply square root of a/b is also rational?

>>14627658
"Like dissolves like" refers to polar/nonpolar, not to acidic/basic.
A protonated acidic organic compound (e.g. a carboxylic acid) has usually neutral charge, i.e. it's relatively nonpolar and doesn't dissolve very well in a polar solvent like water.
A protonated basic organic compound (e.g. an amine) has usually positive charge, i.e. it's polar and dissolves well in water.
So in the first place, a pH=3 aqueous extract contains mostly basic compounds. When basified, those compounds are deprotonated to their free base form, which has neutral charge and is less soluble in water, i.e. it precipitates.
Any acid still present is deprotonated, i.e. negatively charged and more water soluble than before, so it remains dissolved.

>>14634109
>basic but "well established" basic economics books recommendations?
Blanchard's Macroeconomics.
>personal finance
Can't help you there.
>>14635975
[math]\sqrt{a/b} = a / \sqrt{ab}[/math]

Can you guys help me with this question?
It's asking me to say if it is an equivalence relation
[math]R = {(x;y) ∈ ℕ2/ x-y is divisible by 3}[/math]
Here's what I got so far:
We know that for a relation to be considered equivalent it has to attend three basic properties - reflexiveness, symmetry and transitivity, I concluded that they're both reflexive and transitive, but I can't see how it is symmetric, since this is the natural set, there's no way that both x-y and y-x pertain to the relation because that y-x implies a negative number and there aren't any in the natural's set, can we conclude that this is a vacuous truth and thus the relation is equivalent? Answer key says it its, but I'm not sure.

>>14636283
When we say "[math]n[/math] is divisible by [math]k[/math]" we allow for negative multiples.
So [math]3[/math] is divisible by [math]3[/math] and [math]-3[/math] is divisible by [math]3[/math].

>>14636342
Indeed, but that is a relation on the natural set, NxN, so there are no negative numbers. If it was on the integers or real set it'd make sense.

>>14636346
Either we assume that the question is incoherent and [math]x - y[/math] for [math]x, y \in \mathbb{N}[/math] isn't necessarily defined hence the relation isn't well defined or that the minus operator for [math]\mathbb{N}^2[/math] has integer image, which isn't really weird at all.

>>14636353
>that the minus operator for N2N2 has integer image, which isn't really weird at all.
Can you explain that a bit further, please?
I'm still confused that the question has "equivalent relation" in the asnwer key, maybe it's just incoherent?

>>14635971
Feel free to explain them
Stagflation wasn’t an increase in the money supply?

>>14636357
The plus operator has domain [math]\mathbb{N}^2[/math] and image [math]\mathbb{N}[/math], because the sum of two natural numbers is always a natural number.
It's not so for subtraction. Either we restrict subtraction's domain to [math]D = \{ (x, y) \in \mathbb{N}^2 : x \geq y \} [/math] or we expand the image to [math]\mathbb{Z}[/math]

I can only understand longitudinal waves, because, especially for sound waves, it's very intuitive to imagine particles being pushed in one direction, hitting nearby particles, those nearby particles hitting other particles and so on. But for transverse waves? What would compel particles to move like in this gif? Please explain without bringing in electromagnetism

>>14636381
I get it now, should I just dismiss the question because of how ill elabored it is? I've going mad over it for the last couple of days. Thank you!

>>14636383
Gravity waves, s waves are other examples.
The restoring force just points in a different direction.

is anyone aware what's the state of the art regarding text generation currently? is it all transformers or do GANs or maybe even RNNs still compete with them?
i struggle to find a SOTA review article and papers with code benchmarks regarding text generation are useless

thinking of switching to computer science
since it appears to involve more foundations of maths than actual maths does, like automata theory and formal languages and logic. Which I am interested in.
If anyone here has studied it, does it have much emphasis on these fields?

>>14636759
>since it appears to involve more foundations of maths than actual maths does
This is obviously not true, anon. Automata theory and formal languages are definitely beautiful subjects, but I don't think you'll see much of them in a typical CS curriculum. As far as I know, undergrad CS programs tend to put little emphasis on the "pure math" parts of the field; majoring in CS probably entails taking *lots* of programming courses, one or two courses in operating systems, data bases, etc.

If you're interested in logic, study logic (and major in math). If it's theoretical CS that has you hooked, I'd suggest that you major in math and acquire a solid background in algebra, combinatorics and logic.

if someone gets a testicle transplant and has a kid long after their body accepts the organ, the kid will be theirs right?

If a city of 1,737 people is 0.12% African American, how many black people is that?

>>14636932
A lot.

>>14636814
oh ok, maybe i'll stick to studying maths then

>>14636932
1,737 x 0.0012 x [math]\frac{3}{5} \approx[/math] 1 and a quarter black people

>>14636950
I saw a quarter black person yesterday.
It was a bit scary, but he was nice.

>>14636950
Alright, that looks legit, thank you. I guess the ones I saw were tourists.

>>14636389
>I get it now, should I just dismiss the question because of how ill elabored it is?
Sure, why not.
>>14636950
I'll bite, where did 3/5 come from?

>>14636962
a bit of american humor
https://en.wikipedia.org/wiki/Three-fifths_Compromise

>>14636932
>CITY of 1,737 people
that doesn't exist please take your medication immediately

>>14636970
sure it does, I live in a city of 1600 right now
you must be a brit, they always argue this on /int/ for some reason

>>14636979
>city of 1600
that is literally village tier

>>14636953
the ones in my town are so calm theyll smoke menthols right out of your palm

>>14636964
Lmao.

>>14636962
>Sure, why not.
For real? I'm not really sure on it, but to my beginner brain the question alongside its answer key don't make sense. I'm I greenlit to proceed, mathanon?

>>14637046
Yeah sure, reasonable confusion and you understand why the book says it's true.

>>14637067
Willco, thank you, anon!

not sure if I should ask here or tech, but I'll ask here
just a random thing, but I got an electric lighter recently for my candles, and just messing around while listening to something I decided to shock a penny (idk why)

when it arced across, the monitor that was near it (~8 inches away) would turn off momentarily.
what would be the cause of it? it doesn't happen when I just use the lighter by itself near it, just when shocking something else.
is it creating some electric field or something? and if so, how does it work in turning off the monitor?

Is there a symbol for "value approaches"? e.g. if i were to say A (approaches) B ∴ A/B (approaches) 1

>>14637123
[eqn]\lim_{A \to B} \frac{A}{B} = 1[/eqn]

>>14637129
thants.

How would you define "death" in a biological sense? Like is there one consistent definition that could apply for humans, sponges, trees, bacteria, etc.

>>14637306
chemical equilibrium

Why does it work that to check if a number is divisible by 3: add up all the digits and if the result is divisible by 3 then the actual number is too.

Is there a math reason or theorem or something for this?

>>14637390
Every natural number [math]x[/math] can be written as
[eqn]x = \sum_{k=0}^N a_k 10^k [/eqn]
with [math]a_i \in \{0,1,2,...,9\}[/math].
Now by the binomial theorem [math]10^k = (1 + 9)^k = 1 + \sum_{i=1}^k {k \choose i }9^i [/math] so [math]10^k \equiv 1 \qquad \text{(mod 3)}[/math]
So
[eqn]x = \sum_{k=0}^N a_0 10^k \equiv \sum_{k=0}^N a_0 \qquad \text{(mod 3)}[/eqn]

>>14637390
[eqn]
d_0 + 10d_1 + 100d_2 + 1000d_3 + \cdots \\
d_0 + (9+1)d_1 + (99+1)d_2 + (999+1)d_3 + \cdots \\
d_0 + 9d_1 + 1d_1 + 99d_2 + d_2 + 999d_3 + d_3 + \cdots \\
\underbrace { \left( 9d_1 + 99d_2 + 999d_3 + \cdots \right) }_{\text{definitely divisible by 3...}} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; + \underbrace { \left( d_0 + d_1 + d_2 + d_3 + \cdots \right) }_{\text{...so whether or not the entire number is divisble by 3 is decided by this}}
[/eqn]

it's been a while since I've taken calc 3 or had to do anything with partial derivatives

for something of the form
[math]\frac{\partial y}{\partial x}dx[\math]
what is the meaning/significance behind the partial derivative being multiplied by the total differential(?) of the value in the "denominator"?
I have a faint buzzing in my head about the chain rule but I can't remember enough to really say

>>14637568
>[math]\frac{\partial y}{\partial x}dx[\math]
[math]\frac{\partial y}{\partial x}dx[/math]
oops lol my latex is showing

>>14637526
>>14637460
wow that's clever

>>14637526
>>14637460
ty anons you guys always impress, i will try and take some time to understand this

>>14637526
>>14637460
does this mean eg for 7 i can do d0+ (7+3)d1 + (98+2)d2 + (994+6)d3?
d0 =7
d1 =5 (5*3=15)
d2 =1 (6*1=6)
7+15+6 is divisible by 7

hmm i guess its only good for 3?

>>14637758
It does work like that for 7.
1057 is divisible by 7 because 7 + 3*5 + 6*1 is divisible by 7.

>>14637793
its pretty cool! i made a thing to test it out

for (int i = 1; i <= 9; i++)
for (int j = 1; j <= 9; j++)
for (int k = 1; k <= 9; k++)
if ((i + 3 * j + 2 * k) % 7 == 0)
printf("%d ", i+10*j+100*k);

511 721 231 931 441 651 161 861 371 581 791 112 812 322 532 742 252 952 462 672 182 882 392 413 623 133 833 343 553 763 273 973 483 693 714 224 924 434 644 154 854 364 574 784 294 994 315 525 735 245 945 455 665 175 875 385 595 616 126 826 336 546 756 266 966 476 686 196 896 217 917 427 637 147 847 357 567 777 287 987 497 518 728 238 938 448 658 168 868 378 588 798 119 819 329 539 749 259 959 469 679 189 889 399

>>14637758
>does this mean eg for 7
It works for anything but you need to tabulate [math]10 ^n \mod k[/math] (it loops with period at most [math]k[/math])

what do i study to calculate higher dimensional interpolations?
e.g. to calculate the ideal position in a 4 dimensional graph like pic related. even 3 dimensional.
hell I don't even know how to do 2 dimensions i only studied to calc 2

>>14637568
Your i is a function of v, i=i(v)
Now, a small change in v, delta v, corresponds to a small change in i, delta i, by the derivative of i wrt v.

What is the conductance of water?

>>14638270
Also why is Viktor schaumberger not talked About more

>>14638270
Like idk what waters conductance is but if voodoo is illegal on sci then You can consider its polarity, the phase change of river to cloud,and its minerality
Just 3 equations for mont Carlo so its ez

>>14637390
10 ≡ 1 (mod 3)
=> 10^n ≡ 1 (mod 3)
=> k·10^n ≡ k (mod 3)
=> x = Σ d[n]10^n ≡ Σ d[n] (mod 3)
where d[] are the decimal digits of x.

>>14638270
The resistivity of pure water is ~182 kΩm, which is a fairly good insulator. E.g. a 1 metre long pipe with a cross section of 1 cm^2 would have a resistance of 1.82 GΩ. Impure water is far more conductive, e.g. sea water is ~0.2 Ωm, roughly a million times less resistive / more conductive. The same pipe filled with sea water would have a resistance of 2kΩ.

I'm trying to show that:

[math]span\{e^{ip+\frac{2\pi}{a}m}\}=span\{e^{iq+\frac{2\pi}{a}n}\}\Leftrightarrow p-q=\frac{2\pi}{a}j[/math]

Where m,n and j are integers. My (evidently retarded) attempt was the following:

[math]e^{i(p+\frac{2\pi}{a}m)x}=e^{i(q+\frac{2\pi}{a}n)x}[/math]

[math]e^{i(p-q+\frac{2\pi}{a}(m-n))x}=1[/math]

[math]p-q+\frac{2\pi}{a}(m-n)=2\pi j[/math]

[math]p-q=2\pi (j-\frac{m-n}{a})[/math]

What am I doing wrong?

I'm trying to show that:

[math]span\{e^{i(p+\frac{2\pi}{a}m)x}\}=span\{e^{i(q+\frac{2\pi}{a}n)x}\}\Leftrightarrow p-q=\frac{2\pi}{a}j[/math]

Where m,n and j are integers. My (evidently retarded) attempt was the following:
[math]e^{i(p+\frac{2\pi}{a}m)x}=e^{i(q+\frac{2\pi}{a}n)x}[/math]

[math]e^{i(p-q+\frac{2\pi}{a}(m-n))x}=1[/math]

[math]p-q+\frac{2\pi}{a}(m-n)=2\pi j[/math]

[math]p-q=2\pi (j-\frac{m-n}{a})[/math]

why are solvable groups interesting?

one popular way to motivate the concept is through Galois theory. are there any other reasons to study group solvability?

is there any way to accelerate the convergence of an arbitrary Fourier series?
By analogy, we have Taylor series which approximates functions using sums of polynomials. However, some Taylor series are very slow to converge on their parent functions. As an alternative, there are Padé approximants which instead use rational functions to approximate a function. For some functions, they converge significantly faster and more accurately than the equivalent Taylor Series ever could.

Is there an equivalent for Fourier series?

Motivation: I'm making a hardware digital synthesizer. Right now, I have to pre-render the waveforms I want the thing to output. As in, I essentially supply the program running on the microcontroller a series of Fourier harmonic bins, and it just iterates and sums together the resulting sine waves. While this does work, I want to eventually make it real-time. I have yet to take any hardcore fourier analysis or DSP classes.

I would be willing to trade some accuracy if it means I can generate the waveforms faster in real time.

could you explain it to a retard why matter forms a disc around black holes?

>>14639221
its the state that results in the fewest collisions between particles. same reason that most star systems form a disc.

>>14639161
> As in, I essentially supply the program running on the microcontroller a series of Fourier harmonic bins, and it just iterates and sums together the resulting sine waves.
Use the FFT, as that's O(n.log2(n)) rather than O(n^2). If the output size differs from the input, truncate or zero-pad the input to the desired size. If the output is much larger than the input (specifically, if you have fewer than log2(n) harmonics), summing sinusoids may end up being faster.

>>14634001
Flexural strength or modulus of rupture

best way to develop my problem solving skills?

>>14629605
Question for a friend! I have 70% isopropyl alcohol
as long as I cut it with a healthy amount of beer for example is it drinkable? Is there a magic ratio that gets beer to like 30%?
How many ml of 70% alcohol vs 355ml of 5% beer? Or is just the inherit potency of it deadly?

>>14640166
solve problems

>>14640302
kek
you think solving problems from international math and physics olympiad would help me be a great problem solver?

>>14640315
if youre trying to solve math and physics problems, then yeah thats a good start

>>14637009
we got a wemi laugh

>>14640166
take psychedelics (maybe)

>>14638873
The if part is your job.
We break up [math]\exp \left( i \left( p + \dfrac{2 \pi}{a} m \right) x \right) = \exp (ipx) \exp \left( \dfrac{2 i \pi}{a} m x \right) [/math]. From this we notice that [math]span \left\{ \exp \left( i \left( p + \dfrac{2 \pi}{a} m \right) x \right) \right\}[/math] is, actually, basically any complex function with period [math]a[/math] times [math]e^{ipx}[/math].
So if [math]e^{ipx} = f(x) e^{iqx}[/math], where [math]f(x)[/math] is [math]a[/math]-periodic, we can do [math]e^{i(p-q)x} = f(x)[/math], hence [math]p-q = \frac{2 \pi j}{a}[/math]

I want to make a catgirl artificial intelligence, where do I start?

>>14641503
>basically any complex function with period [math]a[/math] times [math]e^{ipx}[/math].
My bad, the imprecision here can actually give you completely irrelevant issues filling in the gaps.
"Basically complex functions of the form [math]\displaystyle \sum \exp \left( \dfrac{2 i \pi m x}{a} \right)[/math], all of which have period [math]a[/math], times [math]e^{ipx}[/math]"

same anon as >>14633141
Running into another problem now. Wondering how I should fix this?
I want the operators and equal signs to be aligned and want them in nice aligned columns
Also how do I fix the issue of the alignat going off the page?
\begin{alignat*}{11}
1375&-409&{}= 966&& \hspace{5em} 28&\times22&{}= 616&& \hspace{5em} 928 &+ 613&{}=1541&& \hspace{5em} 210&\div10&{}= 21\\
650 &+ 991&{}=1641&& \hspace{5em} 25&\times16&{}= 400&& \hspace{5em} 500 &+ 427&{}=927&& \hspace{5em} 20&\times19&{}= 380\\
16&\times6&{}= 96&& \hspace{5em} 375&\div25&{}= 15&& \hspace{5em} 728&\div26&{}= 28&& \hspace{5em} 20&\times20&{}= 400\\
\end{alignat*}

This was from a friend's exam: The side of an octagon is 9.7 and they were asked to calculate the circumscribed circle's perimeter. It was a multiple choice exam and the right answer was written as [math] 7\pi \sqrt{4-2\sqrt{2}} + 14\pi \sqrt{2-\sqrt{2}} [/math].

I know how to solve it but, for the life of me, I haven't been able to figure out how they were supossed to get that answer. I've tried different approaches and got different forms of the answer, but I just can't get the one above.

Needless to say, you may not use a calculator to solve it.

>>14642033
>The side of an octagon is 9.7
I meant 7. lmao

>>14642033
>>14642040
Mark out the centre of the octagon. Choose a side, and draw lines connecting the centre with both vertices. That's an isosceles triangle, and the small angle is 45 degrees. You can then use the cosine or sine rule to compute the other two sides/the radius and multiply it by 2pi.
That's how I'd solve it today and how I'd probably have solved it when I was twelve.

>>14642033
>>14642040
Mark out the centre of the octagon. Choose a side, and draw lines connecting the centre with both vertices. That's an isosceles triangle and the small angle is 45 degrees. 45 being a common angle means you can then use the cosine or sine rule to compute the other two sides, both of which equal the radius, and multiply by 2pi for the circumference.
That's how I'd solve it today and how I'd probably have solved it when I was twelve.
But I'd need to look up the cosine rule from somewhere because I don't really remember it off the top of my head.

>>14642057
I case it wasn't clear, I don't care how you'd solve it; what I'm interested in is how whoever designed that exam solved it.

>>14642087
Gee anon, pay attention.
You use the cosine rule, you get [math]2 \pi R = 2 \pi \dfrac{7}{\sqrt{2 - \sqrt{2}}}[/math]
Attempt to rationalize the denominator by multiplying by [math]\dfrac{ \sqrt{2 - \sqrt{2}} }{ \sqrt{2 - \sqrt{2}} }[/math] for [math]2 \pi \dfrac{7 \sqrt{2 - \sqrt{2}} }{ 2 - \sqrt{2} }[/math]. Attempt to rationalize again by multiplying by [math]\dfrac{2 + \sqrt{2} }{ 2 + \sqrt{2} }[/math] and you'll get the thing you posted.

>>14629748
>>14630028
Wait what happened?

>>14629605
Hello. If singular integrals evaluate the area under a curve and double integrals the volume under a surface, then what do triple integrals calculate?

>>14642349
Also a volume.

>>14642353
But this time not under a curve but of an arbitrary shape that can be anywhere on the cartesian plane?

>>14642388
>Under a curve
I meant "under a surface".

How do I interpret this graph? The percents sum to more than 1. Only 15% of women included the 5'8 filter but 30% included 7'0? And more than 100% included multiple redundant filters between 6'0 and 7'0? What?

OK so I have a hypothetical physics question.
If the remains of something existed that would be impossible to develop if the strength of gravity were constant throughout time. How would you test it?
Lets say we found the remains of an animal or animals that were otherwise proportionally consistent but of an unbelievably huge size?

>>14642600
One woman can use all filters between 4'11 and 7'0 if they want. So you should view it as every individual woman filtering multiple things. Then every bar represents how many women of the total ammount filtered that height.

Anyone know about 2D random walk? Why does it return to the origin after N iterations?

>>14642600
>>14642657
Holy shit it's bad for us under 5'9".

>>14642657
That doesn't make any sense. Why turn on the filter for 6'0 if you filter out anything below 6'4? I'd understand if they meant that they include all the other filters automatically, but then no filters would have a lower % than 7'0 does.

Question in picture.

>>14642675
The proof(s) of that are rather long and technical. It essentially comes down to a limit question: you can show the probability that a random walk in [math]d[/math] dimensions intersects with itself approaches 1 as the number of steps approaches infinity and [math]d \le 2[/math]. Calculating the formula for the probability and then finding the limit, each is a non-trivial step.

a function is injective if and only if VxVy(f(x) = f(y) -> x = y)

why can't i say VxVy(x = y -> f(x) = f(y))?

Is there a time when x can equal y and f(x) doesnt equal f(y)?

>>14643105
also you can say VxVy( x != y -> f(x) != f(y)) so how is this different than VxVy(x = y -> f(x) = f(y))?

>>14643105
>VxVy(x = y -> f(x) = f(y))
because that's true for all functions, even the ones that are definitely not injective? think
>>14643107
these are equivalent statements

>>14642656
there's no evidence that the earth's gravity was very different a billion years ago

>>14634109
Economics is not science. Astrologers are more reliable than economists.

>>14642293
I don't think anything happened, anon is just randomly seething at Yukarifag.
>>14642349
The same.
But picturing it physically is easier than geometrically. Imagine the function you're integrating is "density" (not a probability density, but rather a physical density, except signed) and then the triple integral is the "mass" of the volume.

WTF is this example, it is a simple problem but didn't the author forget the last step to multiply the velocity by the cosine? The problem asks to find velocity. But the solution only gives the direction.

>>14643287
yeah, so you've got the direction. do you know how to get the magnitude?

>>14634001
the red bar experiences tensile, compressive and shear stresses. depending on the material, a different strength might be relevant.

So i finished college and tried to get into architecture, but ultimately failed cause i was too much of a coward to hand in my drawings for the entry (they weren't finished either). Now my question is whether i should even study a field and what field, when i even fail at that. Math skills are not good btw

Any good books on the history of chemistry?
Preferably a scholarly one written by a professional historian

>>14643116
But that isn't the question.

>>14643061
is it really that hard in dimension 2?
I just need to show that when I start from a random position (x,y) and do the brownian motion/Random walk, the average value (temperature) is 25 which is the temperature at the center of this grid

>>14643909
No, it's only hard in continuous time on R^2.
If you're on a discrete grid then each state can be representated with a vector and going from one state to the next is just a matrix-vector multiplication. So it's just a simple Linear Algebra problem. If you do infinite steps then you're just left with the Eigenspace to the Eigenvalue 1.

>>14643929
is there a proof of that somehere on the internet?

>>14643956
There's a proof on just about any Markov chains textbook.

>>14644037
This is only a thing because it's symmetric?

>>14629605
Shouldn't the requirement of the matrix be just the matrix on the LHS of the answer have a rank = 2? Because if they have a rank=1 then that means one of the lines is a multiple of the rest of them, but they're only suppose to meet at one point.

>>14642721
>>14642721
>>14642721
Pls help me understand, you guys

>>14644091
Yeah.
If a random walk had a greater chance of going in some direction it would, at infinity, go towards that direction.

>>14642600
I've never used Bumble (or any dating app for that matter but whatever) but I think that women who set advanced filters select a minimum and a maximum height. So the value 6'0 is within the filter values set by ~60% of women, 6'2 is within the filter values set by ~80% of women and so on and so forth.

>>14642349
>>14642353
I think this answer is misleading. A triple integral only finds a volume if the integrand is 1. 1dxdydz. Likewise a double integral could be used to calculate area if the integrand is 1: 1dxdy. In both cases you can lower the dimension so that your integrand is a function, not 1.
But in a general case a triple integral's integrand is some function. You can't visualize the whole thing since it is kinda 4D but it but it could be density for example. Then you integrate in 3 dimensions to get mass.

Could you help me with this?
Why do we use -1C / (Farad electrons) on that product and why also put minus before 3?
I read it is about the relation of Q with Farada and electron numbers but I don't get the equation.

>>14643111
but for the logic operations only
VxVy(f(x) = f(y) -> x = y)
and
VxVy( x != y -> f(x) != f(y))
are logically equivalent.

is it ok for VxVy(x = y -> f(x) = f(y)) to be equivalent as well even if with logic you cant do that?

Is there a formula or model for how much u should increase the quantity of trade each success when you're dealing with a new person? Assume you start with a very rough estimate of scam traders.
Intuitively there should be a way to optimize how much you want to increase volume. Would you or could you factor in the relative urgency of the target trade level? And how would you define or use the level of confidence?
For the confidence level you can just use the standard rating system probability starting at 0 initially right?

>>14644923
I forgot one part. For example: You have 1,000 of a rare cryptocurrency that you want to sell by the end of the month. However, it's so rare that there is only one available buyer, and he's never been traded with. So if you can make 1 trade per day, what is the optimal amount to start trading and increase?

So the same amount of force increasing the velocity by the same amount is a bigger amount of change of kinetic energy if the velocity is higher? I don't get it. What is the point or use of the "work" statistic instead of just change in velocity? What does kinetic energy indicate?

Scientifically speaking, how come Elden Ring is way less replayable than Dark Souls II and III?
I've beaten it once, I did a second playthrough up to Fire Giant and I'm exhausted of the game.

>>14640296
Why drink isopropanol? No its metabolites are not particularly toxic, but its potential for CNS depression is much higher. More than a few ounces can put you in a coma: https://doi.org/10.3109/15563650.2014.914527

does anyone see what I'm doing wrong with setting up this PNP small signal analysis problem?
I feel like all of my intermediate steps are valid, so the only thing I could be fucking up is the re-drawing of the diagram

>>14643909
>>14643929
>>14644210
The average value has nothing to do with that.
It's because of the linearity of the boundary conditions
There are 4 edges, 4 BC;

BC1+BC2+BC3+BC4 = 100 ( one is 100 the other 0)

So by linearity The average would be 25

>>14638221
Thank you, that makes sense breaking it down like that.

>>14647160
negating [math]V_{BB}[/math] also gives an incorrect answer so it can't be just that

>>14629605
How do I develop intuition for number theory? Thinking geometrically works fine in analysis, topology, algebra (to an extent) and geometry, but I'm a number theory brainlet.

i want to apologize for making that big uoohh tower, i didnt want people to start spamming it

>>14647160
hope this helps anon

>>14647423
typo: I forgot the [math]m[/math] in the last result for [math]g_m[/math] to indicate 'milisiemens

>>14647193
doesn't make sense to me

>>14647160
Shouldn't 1.145 - 0.7 = 50000I_B?
I_B ~ 9 uA
I_C ~810 uA
R_π ~ 2.89 kπ which is relatively close to the 2.92 kπ
Why did you draw V_cc not linked to R_c?

>>14643251
I just hate homosexual attention whore brownoids. That's all.

>>14647423
>>14647443
>>14647452
So instead of trying to convert it to a positive supply and re-drawing the circuit, I should just analyze it with the negative supply as is?

My professor made it seem like we had to convert the PNP transistor from a negative supply to a positive supply somehow, and analyze it from there. He never really showed us how though so that was me giving it my best shot.

>>14647488
>My professor made it seem like we had to convert the PNP transistor from a negative supply to a positive supply somehow, and analyze it from there.

Also valid but it need a few extra an unnecessary steps.

>>14647498
What are those steps, for future reference? I always try and blame myself for fucking up before blaming my professors, but he honestly sucks. He really didn't show us how to convert it to a positive supply.

>>14647511
give me a couple of minutes and I'll post it.
What book are you using btw?

>>14647514
Thank you.
Neamen's Microelectronics: Circuit Analysis and Design, 4th ed. (ISBN:978–0–07–338064–3)

>>14647527
np mate. Oh yeah, kind of good book, I already have it.
Here you go anon, as you can see is absolutely unnecesary because it doesn't give you any 'new' aditional information, it only helps to visualize how to set your equations.

>>14647527
>>14647554
oh, and [math]V_{CC}[/math] should be a positive supply for the complete 'changed' circuit. Analysis and all is the same in both cases.

Is the fine structure constant a computable real?

>>14647663
it's not a rational number, but it's close to one. what does it even mean for a physical constant to be "real"? it's computable, certainly.

>>14647730
Why is it certainly computable?

>>14647739
because the constant has been computed before

>>14647768
No it hasn't

>>14647774
wtf

>>14647782
That's not the full decimal expansion of the number. That's not the actual fine structure constant. The actual fine structure consant is a real number

>>14647804
>That's not the full decimal expansion of the number.
physical constants *do not* have "full decimal expansions."
get used to it you fucking nerd

>>14647804
>The actual fine structure consant is a real number
which one?

>>14647812
If the fine structure constant were different in a single digit of its infinite decimal expansion the universe would not exist as it does.
>>14647819
That's what I'm asking.

>>14647841
mumbo jumbo not math or science
>what if pi was...3.15 dude jorge luis borges lmao

>>14647850
How is it mumbo jumbo/not science or math?

>>14647730
>what does it even mean for a physical constant to be "real"?
The number is approximate-able to an endless level of precision using convergent Cauchy sequences. That's what [math] \mathbb{R} [/math] is: https://math.ucsd.edu/~tkemp/140A/Construction.of.R.pdf

>>14644184
You're misreading the question. There must exist some point which all lines pass through. Duplicate lines are fine.

Rank 1 means that all rows are scalar multiples of each other. For the LHS, that means that all lines are parallel, for the RHS, it means that all lines are the same line. So if the LHS has rank 1, the RHS must have rank 1 otherwise there is no point through which all lines pass.

If the LHS has rank 2 then no two lines are parallel. If the RHS has rank 2 then you can choose any 2 lines and all others are linear combinations of those, which means that they pass through the intersection point of the chosen 2.

The LHS can't have rank 3. If the RHS has rank 3 then there are three linearly-independent lines which form a simplex, i.e. three distinct intersection points.

If the RHS has rank 0 then all "lines" have the equation 0=0, which isn't a line.

>>14647460
According to my sources he wasn't brown, he was chinese.

>>14648110
it'll still burn out since the resistance isn't going to be uniform and heat dissipation is a lot slower than heat generation when it comes to [math]I^2R[/math] losses

>>14648110
check the rated current capacity for AWG wires, then calculate the current in each circuit, this should give you the answer.

What are the different ways to measure volatility?
Is there more than one?
>Is there a measure of volatility within a range that touches the upper and lower bound of the range x amount of times?
>Is there a measure of volatility that gives you how wide of the swings up and down are?

>>14647782
>>14647804
Neither of these are true. First note that the formula clearly states "recommended value". This is because the fine structure constant is not actually a constant. It varies depending on the energy scale. The value of ~ 1/137 is just the asymptotic value at zero energy.

>>14648155
My confusion comes from the fact that current capacity only seems to take into account the current, not the total power. Since the 10m wire introduces more total resistance in the circuit, less current will flow. But yet the power dissipation in the 10m wire is bigger than the others since it drops more voltage than in the others.

The only way current capacity working like that makes sense to me then is to assume that the longer wire must be better at dissipating heat because it's longer and the dissipation spreads out.

>>14648253
I see, I understand your confussion. But a longer wire will 'eat' more part of the power making the load to see less voltage. Then applies what the other anon said at >>14648153 specially the non uniformity thing. The wire will behave more and more as a dissipator than a wire and it will be critical at the narrower points and joints. Maybe without a lab experience to test this it's difficult to see, but indeed, wire heats up significantly and it needs one single spot to fail to make the whole circuit to break.

>>14648196
damn, we should've called derivatives "volatiles", thats a much cooler name

>>14648289
Method of fluxions says anything?

>>14648295
that was also a cool name

>>14648289
I prefer disintegrals

>>14629605
Why does this say "(just)" after Lagrange? Am I retarded?

>>14648274
Well then shouldn't the length of the wire be more of a factor in its ratings? Seems everywhere I look all that's considered is the thickness of wire vs the amps going through it.

>>14648421
Lagrange famously had his wife take everything in the divorce

>>14648430
I'm still thinking about it, anon. It's a good question.
So far I've think about, well, what would happen with an even longer wire, infinite wire maybe. Obviously it would not burn because it would require infinite current to heat the wire.
Actually we can prove that the power dissipated by the wire is
[eqn]P_w= V^2 \frac{\rho_w l}{(\rho_w l+R_L)^2}[/eqn]
where
[eqn]\rho_w = 0.169 \frac{\Omega}{m}[/eqn]
and [math]l[/math] is in meters.

On the other hand we have an ampacity given in amps [math]I_A[/math], and the resistance per unit length [math]\rho_w[/math]. This way the wire will 'not burn' while the power [math] P_w < I_A^2 \rho_w l[/math]

>It was about the same time, 1792, that the unaccountable sadness of his life and his timidity moved the compassion of 24-year-old Renée-Françoise-Adélaïde Le Monnier, daughter of his friend, the astronomer Pierre Charles Le Monnier. She insisted on marrying him, and proved a devoted wife to whom he became warmly attached.

>>14648472
Also in order for the wire to behave like a good distributed dissipator, the heat should propagate quickly along the whole wire.which is very unlikely to happen due to physical limitations such as the material and the environmental conditions. And the heat generated by the current [math]I[/math] through the wire will heat it up faster than the heat propagates, irradiating to the environment.

>>14648472
Also, if [math]l[/math] tends to [math]\infty[/math], [math]P_w[/math] tends to 0, so the wire dissipates all the power applied to it, and it will never burn.

>>14648472
and now, Applying Thevenin's theorem to the wire, the max power dissipated will occur when [math]\rho_w l = R_L[/math]. In such case
[eqn]P_w = \frac{V^2}{4\rho_w l} [/eqn]

Then
[eqn] \frac{V^2}{4\rho_w l} < I_A^2 \rho_w l [/eqn]
Thus
[eqn] \frac{V}{I_A} < 2 \rho_w l[/eqn] to not burn the wire.

>>14648520
But [math]\rho_w l = R_L[/math], then the wire should be fine if
[eqn]\frac{V}{2I_A} < R_L[/eqn]

>>14648430
No. Power dissipation per unit length is I^2×ρ where I is current and ρ is resistance per unit length. Provided that the current remains unchanged, doubling the length doubles the power dissipation so dissipation per unit length remains unchanged.

The longer wire has less current, 10/11.69 = 0.855A versus 10/10.0169 = 0.998A, but you'd normally spec the wire so that wire resistance is negligible compared to load resistance.

>>14648220
in any case, are the numbers irrational or rational? I'm pretty sure the values are all irrational and not in Q

Question for medical people.

My first shot of the vaccine lead to me developing myocarditis and for 2-23 days after initial vaccination my heart would go into atrial fibrillation sporadically. I was in hospital for 11 days and during that time they captured over 100 episodes of atrial fibrillation. The constant inflammation of my heart lead to the thickening of my hearts walls and I was dianogsed with cardiomyopathy. We know this was caused by the myocarditis because a year prior we did full screening of my heart and there was no thickening.

I was advised to stop taking my ADHD medication which is dextroamphetamine because of the recurring inflammation and chest pain. However I started taking small doses anyway. I've found that while on dextro my heart does not hurt at all. There's no pain and it prevents ectopic beats.

Is there a medical explanation for this?

>>14643287
you literally have the velocity as a solution in the form of a vector, you don't need much else except calculate the magnitude with euclidean metric but why be so autistic to do that is my question?

I'm reading up on modular forms and started with Diamond's "A First Course in Modular Forms". It's been years since I actually touched series and analysis in general. I'm being very retarded and can't seem to prove that Eisenstein series are bounded as [math]\text{Im}(\tau)\rightarrow\infty[/math].

>>14651500
Forgot pic

>>14648921
So my initial assumption here was correct? >>14648253

Any Sobolev chads here?

Let [math]\Omega \subset \mathbb{R}^d[/math] be open with smooth boundary, [math]u \in H_0^1 (\Omega)[/math] an eigenfunction of the Laplacian (say [math]\Delta u = \lambda u[/math]). Is there any bound of the form [math]|u|_{H^k} \le C(|u|_{L^2} + |\Delta u|_{H^{k-2}})[/math] for some constant [math]C[/math] independent of [math]u[/math]?

When genomes are cataloged in databases, how do biologists determine what sequence represents a species? Do they take multiple samples to account for mutations? For animals like dogs and humans, is there a specific breed that gets chosen as the model sequence?

>>14643312
>>14651040
yeah the magnitude is the pythagorean but i am not sure it's what is being asked. for example if the plane flies away from the observer (90 degree) the perceived speed from the observer's perspective would be zero, right? so it is a projection problem and we have to multiply the magnitude by the cos of the angle relative to the observer?

>why be so autistic
let's say you stand on the ground and measure a plane's speed with a radar of a plane moving along the horizon but not along the horizon but at some angle (towards or away from you).

this is a bird's view picture. you see a plane flying away from you. and you are standing at the ground measuring its speed with a radar. isn't this cosine?

>>14651729
forgot pic

For my conclusion in an inductive proof, can i say:

"Therefore, since P(0) is true and by induction P(n+1) is true given P(n), it must be the case that P(n) is true."

Is this how i word it?

>>14651508
A wire's ampacity (current-carrying capacity) is dictated by power dissipation per unit length. The total length doesn't matter, other than to the extent that it affects the current, which it might not. Heaters and incandescent lamps tend to be quite close to constant-current loads; if the voltage drops due to wire resistance, the element/filament will run colder which decreases its resistance. Similarly, DC power supplies with linear regulators tend to have a current draw which is largely independent of small changes in supply voltage.

Temperature is dictated by the ratio of power dissipation to surface area, and both of these increase in proportion to length. A thicker wire has lower power dissipation (due to lower resistance) and greater surface area. An increase in temperature results in an increase in resistance, and above a certain threshold this turns into a positive feedback loop: more current -> more power dissipation -> higher temperature -> higher resistance -> more power dissipation -> and so on until the wire vaporises.

>>14651894
> and by induction P(n+1) is true given P(n)
that is worded incorrectly. proving P(n+1), and possibly P(n), are true is not induction but part of the entire process.

anyways, all you need to say is something like "this completes the induction" as long as you have proven the earlier steps.

>>14651544
Man I'm in NT/AG now but I absolutely LOVED distributions.

>>14651544
How on earth did compactly supported eigenfunctions of the Laplacian work again?
IIRC [math]u \in \mathbb{ H } ^1 _0 ( \Omega )[/math] needs to zero on some compact subset of [math]\Omega[/math], which implies it's zero on an open subset of any connected component of [math]\Omega[/math], which implies it's analytic by elliptic regularity (see https://en.wikipedia.org/wiki/Elliptic_operator)), so it's zero everywhere.
What's my mistake?

>>14651894
What the other anon said. It also really depends on how explicit you actually need to be to correctly convey the essential part of the induction.

>>14652553
>zero on some compact subset
Outside of some compact subset, that is.

>>14647313
What are you looking for exactly? For instance, simple examples of arithmetico-geometric correspondences directly come from the Spec functor applied to a field/integer ring diagram. Check out Mumford’s treasure map. You can "see" the ramification of prime ideals as geometrical ramification in a covering space.

>>14652553
>>14652565
Oh right, [math]_0[/math] isn't compactly supported, it's closure of the thingy, thanks wikipedia.

>>14632812
This looks fine. I would just use the primitive element theorem though.

>>14652615
I even struggle with fairly simple concepts tho, without even going into category theory or even applications of analysis to number theory.

>>14644551
Bump for electrical engineering.

Electronics:
I have a design in mind that would require opto-isolation of a ~13MHz digital signal. Actually 3 signals, in sync with each other (bit clock, word clock, data).
It seems that such isolators exist, but are uncommon and require special design considerations (I was hoping to get away with breadboard prototyping and a basic amateur pcb design for the final version).

I have full control over the sender and receiver, so if the need for 3 signals is an issue I could conceivably use a self clocking signal instead (manchester/8b10b), but would love to avoid that and keep it simple.
It's for a university project so while I don't mind tinkering somewhat, this is only a small part of the overall setup and I can't spend too much time and energy on it. If it's impractical or iffy/borderline, I'll need to think of something else (like wireless or IP).
Any thoughts appreciated. Mostly looking for a general sense of whether this is practical with basic electronics skill on a student budget.

Can anyone explain covectors?

I don't have a Kill A Watt with me and can't get one soon enough, so I might as well ask here.
How much power would a i3-5500 Laptop use with the lid closed (but with the laptop still on and running stuff)?

>>14653488
Are you talking about linear forms? In that case it's nothing but a linear map from a [math]k[/math]-vector space to [math]k[/math].

>>14653446 (Me)
I think I'm a dumbass and fixated on chips marketed as optocouplers, when I actually just need a "digital isolator". Those are way faster and should work just fine for my purposes.

Can someone please explain about withdrawing groups in organic compounds? Especially the effects on amine basicity

I understand that light travels at a certain speed, but why does the James Webb telescope specifically see 13.5 billion years ago and what would it take to see further back in time?

>>14654343
What are they used for?

>>14629605
for an arbitrary real-valued impulse response [math]h[/math], consider the (discrete time) LTI system with impulse response [math]h*h_\sigma[/math], convolving [math]h[/math] with [math]h_\sigma[k]=h[-k][/math]. Compute the frequency response of this system and deduce that it applies a zero-phase lag to any input frequency.

why am i too dense to get this ;_;

>>14629605
Wolfgang Smith, what's your take on his quantum interpretation?

>>14655924
It's impossible to look too far back in time because the Universe went through a period called the Dark Ages in which it had absolutely zero light-emitting objects as a result of its radiation being red-shifted by its expansion. The Dark Ages are followed up by the era of reionization which is when the first stars and galaxies were born. This era is when the furthest objects we can possibly observe appeared. Current telescopes allow us to look into this era and the JWST is precisely tailored to observe objects from the very beginning of reionization thanks to its bigger mirror and increased sensitivity in near-IR wavelengths.

>>14629605
How do I deal with the fact there is always a non-zero chance someone is masturbating thinking about me right now?

"Which of these relations A -> R, A= [-1; 2] , represents a function?"
Answer key says a & d.
Now, it's quite obvious to me that b) is not a function since it doesn't pass the vertical line test, but
why is d) considered a function if the graph extends a bit further from the domain? And
why is c) not a function?

>>14647984
Thankyou that explaines it well

>>14656703
>why is c) not a function?
Not defined at 1.
>why is d) considered a function if the graph extends a bit further from the domain?
Answer key is wrong.

What does the [math] / \equiv [/math] means? This is an analysis book.

>>14656814
How does having a discontinuity disqualify it from being a function?

>>14656924
He just defined it right there.. it probably covers equivalence relations in the appendix. It’s basically a similar but new concept for equality.

Does anyone know how to read two summations in this context?

The equation will give me the x1 coordinate, there is a similar equation for the y1 coordinate. The (x,y) in the equations are just the values of the 9x9 array so (0,0) is 600.

I think it's saying that starting at x=0, (the first row), look at the values under it including itself, so 600, 553, 561... 550 and apply the 50(600..550). Then repeat it for the next column where x=1. Same for the denominator. Afterwards I'll get like 9x9 numbers where I then add them all up and I'll get the x1 coordinate?

>>14629605
How do I show [math]\mathbb{R}^{\infty}[/math] is paracompact as a subspace of [math]\mathbb{R}^{\omega}[/math] in the box topology. Where [math]\mathbb{R}^{\omega}[/math] is the set of real sequences and [math]\mathbb{R}^{\infty}[/math] the set of sequences that are eventually zero.

>>14657142
It's not a discontinuity it just isn't defined at that point. You cant have a function and say the domain is A if the domain isn't actually all of A

>>14656723
Actually, I made a mistake:
>>14647984
>If the LHS has rank 2 then no two lines are parallel.
If the LHS has rank 2 then at least one pair of lines is non-parallel.
So basically there are two cases which satisfy the condition:
1. Both are rank 1 => all lines are the same line => there are infinitely many points that all lines pass through.
2. Both are rank 2 => there is exactly one point which all lines pass through.

>>14629605
So im an engineering student and im wondering if taking a proof based math would be beneficial to me in any way? (i love math btw but i feel the engineering track might make me more of an efficient problem solving monkey rather than someone who can reason out things)

Thats not my homework, i swear!
There are two same-sized arrays, first one is filled with unique elements.
Every attempt i pick x random elements from array 1, throw away ones array 2 already has and copy them.
How can i calculate chance if array 2 would fill up at t-nth attempt?

>>14656924
https://en.wikipedia.org/wiki/Quotient_space_(topology)

>>14629605
>14629605
When you have a function:
[math]F(x)[/math]
is the gradient: grad(F(x)) = dF(x)/dx ?

>>14659167
Say F(x) = 2x.

>>14658165
It's metrizable innit?
The [math]l^1[/math] metric fails on [math]\mathbb{R}^{\omega}[/math] because it explodes, but it should work on [math]\mathbb{R}^{\infty}[/math]

non newtonain fluids dont obey newtonian laws how do they get affected by gravity?

>>14629605
Why does every book define [math] \gcd[/math] as the common divisior that is divisible by all common divisors. Why not just call it, the common divisor that is the greatest? That's just putting cart before the horse. It should be treated as a theorem that the [math] \gcd[/math] is divisble by all other divisors, but of course every book leaves that out because that's just in muh definition, it cannot be proven. What is a good intuitive reasoning behind the [math] \gcd[/math] being divisible by all common divisors?

I don't get boats. Sure, I can read about all that displacement and buoyancy crap but I just don't get it. If I took a boat and wadded it up into a ball why does the boat float and the ball sink? They weigh the same, why don't they displace the same?

>>14659406

>>14659406
Because you can define the gcd for more than just integers. The definition is chosen like that as it will allow you to extend it to all communtative rings. If you don't have some kind of euclidian function to compare the size of objects then it's not obvious what "greatest divisior" is supposed to mean.

>>14659575
Because the boat has sufficient volume to displace its own mass without becoming submerged, the ball doesn't. The displaced volume of water cannot exceed the volume of the object. The displaced mass of water cannot exceed the mass of the object. If the mass limit is reached before the volume limit (i.e. net density is less than that of water), the object floats. If the volume limit is reached before the mass limit (i.e. net density exceeds that of water), the object sinks.

>>14659328
The first line of the wikipedia entry for "Non-Newtonian fluid" is:
> A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, i.e., constant viscosity independent of stress.
Newton's other laws (motion, gravity) are unrelated to the definition.

>>14656814
Thanks, anon

how much seed does sneed need to feed all his steed?

>>14659666
>Why, all this stuff you don't understand

>>14644551
the C on the left and the C on the right are different, the left one is capacitance and the right is Columbs, the SI unit of charge.
the factor [math]\frac{-1 \; \text{C}}{6.241 \times 10^{18} \; \text{electrons}}[/math] is equal to 1 and is used to convert the electrons in the left factor into Columbs.
im not entirely sure where the minus 3 comes from, maybe its the fact that the electrons are "leaving" the plate. it doesnt really matter anyway, sign errors dont count.

Having a hard time with this, I don't get where the cyclic tower in G' comes from or what it means to induce it. I guess my understanding of cyclic factor groups is failing me, can you always find a subgroup of a group that makes their factor group cyclic? Super frustrated because I don't even really know where to start or where I'm wrong.

i-is there a way to "round" a rational number into the closest one with a desired prime factorization? (such as [math]2^{n} \times 5^{n}[/math])

I started taking only cold showers, but afterwards I notice small hives on my face, especially on the nose and brow. Today I took a bath and my arms and legs were very itchy and patchy, a worse reaction than usual. Will it get worse if I keep exposing myself to cold?

>>14660428
i-i mean [math]\forall x \in \mathbb{Q}, f(x)=2^{n} \times 5^{m}, (n,m) \in \mathbb{Z}^{2}[/math]

>>14660495
I don't get it

>>14660538
l-looking for a fast algorithm to "snap" rational numbers into ones following a desired prime factorization
e.g.
[eqn]x = 0.0000354 = 2^{-6} \times 3 \times 5^{-7} \times 59 \\
f(0.0000354) = 0.00002 = 2^{-4} \times 5^{-5}[/eqn]
prime factorization algorithms are too slow

is there a python Trie thingymabob that I can just get from like "Import Trie"

All the guides are saying I have to create the class and define the add and remove functions.

I'm just trying to do the 'Contacts' Hackerrank problem. Any ideas?

>>14660583
maybe there is this heuristic for two primes [math](p_{0},p_{1})[/math] where [x] is rounding
[math]
b = p_{0} p_{1}, a = b^{[log_{b}(x)]}
[/math]
scan values [math]a * p_{i}^{n}[/math] and return closest
(although fast is relative, logarithm is cheaper than loops in smart-contract env im using)

>>14660879
https://pypi.org/search/?q=trie