SQT thread

as someone who has been on Veeky Forums for roughly 8 years now and whose life has gone downhill ever since i really cannot help you but i'd like to extend my most sincere condolences towards your current situation.

Companies use it whether you like it or not.

For complex function to be differentiable at some point "z" the Cauchy-Riemann equations must hold.
However, do the functions must be equal or their values at point "z" must be equal?

Because from proof it seems that the value must be equal but in practice we only check if functions are equal...

Differentiable at z if the partial derivatives are equal at z
Differentiable everywhere if the partial derivatives are equal everywhere

Say you have three variables, a,b,c
These variables can only have positive integer values (1 or bigger), and they have the constraints: 0 < a < b < (c-a), b ≠ 2a
Since c is bigger than b and a, you can sort the possible combinations by c, the biggest variable

like this:
a - b - c
1 - 3 - 5
1 - 3 - 6
2 - 3 - 6
1 - 4 - 6
1 - 3 - 7
2 - 3 - 7
1 - 4 - 7
1 - 5 - 7
1 - 3 - 8
etc

what is the growth rate of c? is there a function where x represents the xth place in the list, and y is the value of c?
all I know is that it's the inverse of a polynomial, does it have to be approximated, or can I figure out an exact formula by looking at the constraints?

I'd like to add that if the constraints were just a < b < c, then the function would be the inverse of the triangular number function, x(x+1)/2
so it's something similar, right? does b ≠ 2a fuck it up? what if you ignore that constraint and just focus on the 0 < a < b < (c-a) part?

I have this ecuation

x1+x2+x3=15
0=

I mean, for example if
du/dx=xy
dv/dy=x/y
and take point z=(x,y)=(1,1). Partial derivative functions are not equal but their values at z are equal.

Trial and error. You don't have that many options.

By bruteforcing it I got there's 40 possibilities I think.

I'm sure there's a way to do it with combinatronics but I'll be fucked if I know. I don't understand how to exclude upper limits or limits on both ends.

If x1=0 you have 8 possible combinations of x2 and x3 to get 15
If x1=1 you have 8 as well
etc.
If x1=5 you have 8 as well since at most x2=8 and 5=8=13

OP this is easy.
Let [math]{D_1} = \operatorname{Spec} \frac{{\mathbb{C}\left[ {x,y} \right]}}{{\left\langle {y - {x^4} + 2} \right\rangle }}[/math] and [math] {D_2} = \operatorname{Spec} \frac{{\mathbb{C}\left[ {x,y} \right]}}{{\left\langle {y - k{x^2}} \right\rangle }}[/math].

Then [math]{D_1} \cdot {D_2} = \sum\limits_{x \in {D_1} \cap {D_2}} {\dim \frac{{{\mathcal{O}_{\mathbb{A}_\mathbb{C}^2,x}}}}{{\left\langle {y - {x^4} + 2,y - k{x^2}} \right\rangle }}} [/math] is clearly nonzero for all k.

...

He literally answered your question already.
In that case, it's differentiable at z.

**Slight abuse of notation with x. The point x is different from the indeterminate x in the polynomial.

Actually I got it wrong, x1 can be 0, 1, 2, 3, 4, 5; so it would be 6*8=48.

I'm trying to get it into C(n, r) = [math]\frac{n!}{r!*(n-r)!}[/math] form.
My notes are making no sense since I only have an example with lower restrictions.

is there an unspoken rule against repeating unanswered questions from previous threads once they're archived? if not,

if i'm interpreting [math]\Delta S = \int \frac{\delta Q}T[/math] right, trying to cool an object to absolute zero would require an unbounded total change in entropy.

how does that tie in with the 3rd law stating that the entropy of an increasingly cold object approaches a constant value? does the 2nd law instead describe the entropy produced in trying to remove that thermal energy?

>Veeky Forums uses intersection theory of divsors in varieties to solve high school level math problem

How do I determine the current on the diodes and resistors? I know that I can use nodal analysis but the diodes up there are confusing me a lot

Can we have more of this shit actually? It's pretty funny lol.
I haven't studied much AG but I'd be interested in anyone breaking down how to solve easy problems with the big guns.
Assuming I know what a variety is, zariski topology, Spec of a ring, and some standard commutative algebra.

Well those curves can also be made into manifolds in the obvious way. This you means you go at the problem for the differential topology point of view. Where the intersection number would be the cup product (in the deRham cohomology) of the fundamental classes of the curves.

Can anybody just point me on which method to use to solve this?

I need to determine currents and voltages on resistors and diodes.

It seems a bit strange to me that {1} wouldn't be considered an element of {{1,2,3},4,5}. Is this part of the definition of sets, or is it a logical result of the definition?

The set {{1, 2, 3}, 4, 5} has three elements: The set {1, 2, 3}, and the numbers 4 and 5.

The set {1} (that is, the set containing the number 1) is not one of those elements, so it is not an element of the set. On the other hand, the set {1, 2, 3} is an element of that set.

When differentiating quotients, i got an answer [math]\frac{2x^{2}+2x}{(2x+1)^2} [/math] but the answer in the worksheet is [math]\frac{2x(x+1)}{(2x+1)^2} [/math]

Isnt the first more correct?

>more correct
No, they're both the same. The second one is arguably more elegant because you can easily see the factors, and you should get in the habit of factoring anyway, but ultimately they are both equally correct.

The limit of the integrand goes to zero according to the third law, so basically a unit decrease in heat causes a larger decrease in temperature at small temperatures.

That does make sense, so I guess I was just mistaken about what constitutes an element of a set. Thanks

i thought you always wanted to factor out brackets for answers as its more 'simple'

It really doesn't matter. In some problems, like in maximization and minimization problems, it's better to keep the factors like in the 2nd version because if you set that to 0, you can easily see that there are two solutions: x = 0 and x = -1. It's also generally just a pain in the ass to distribute a bunch of shit if you have a complicated expression, and that just isn't worth the time. Don't get too bogged down in the algebra.

Can someone explain Fundamental polygons to me? (Or tell me what I need to learn first) The idea of representing surfaces this way sounds really neat.
I'm an undergrad with only calculus (incl 3) and a vague understanding of group theory

is [math] \frac{1}{2}x^{\frac{-1}{2}}[/math]as a fractionn [math] \frac{1}{\sqrt{x}} [/math]?

Oh i see, thanks.

Circuit analysis typically involves using Kirchhoff's voltage and current laws to formulate a system of linear equations which are then solved.

However: a) that won't work for non-linear elements such as diodes, and b) it's overkill for something this simple.

Clearly D2 will be reverse-biased, so you can ignore it. D1 will be forward biased, so it's effectively a -650mV source. That gives you 9.35V and 2670 ohms for a loop current of ~3.5mA.

No need for the 1/2
x^-1/2 = 1/(x^1/2)

how do you prove that e^(z1+z2) (being z1 and z2 complex numbers) is equakl to e^z1·e^z2 ?

It's implicit in the definition of exponentiation. The argument being complex doesn't change anything.

could you explain this for a^(x1+x2) = a^x1·a^x2? lt's easy for me to see why that happens when they x1 and x2 are both integers

a·a·a..(x1+x2 times) = a·a·a..(x1 times)·a·a·a..(x2 times)

but when they're real l have no idea, how would you multiply "a" pi times by itself for example?

> lt's easy for me to see why that happens when they x1 and x2 are both integers
> but when they're real l have no idea
You missed the in-between case: rationals.

Given a^(b+c)=(a^b)*(a^c) and (a^b)^c=a^(b*c) where a,b,c are integers:

x=a^(b/c) x^c = (a^(b/c))^c = a^((b/c)*c) = a^b

x=a^((p/c)+(q/c)) = a^((p+q)/c) x^c=a^(p+q) = (a^p)*(a^q)
x=(a^(p/c))*(a^(q/c)) x^c = ((a^(p/c))^c)*((a^(q/c))^c) = (a^((p/c)*c)*(a^((q/c)*c) = (a^p)*(a^q)
=> a^((p/c)+(q/c)) = (a^(p/c))*(a^(q/c))

For the reals ... uh, I guess it basically follows from the construction of the reals, but I couldn't really give any more detail than that (my background is CS, so I tend to view the reals as more of a philosophical concept than something which actually exists).

find a 3x3 matrix with determinant 31, all of whose entries are negative.

Don't tell me what to do.

Complete and utter retard here trying to refresh myself on high school math.

>Truck rental agency A charges 49 dollars per day plus .20 cents per mile. A competing truck rental agency (B) charges 29 dollars per day plus .25 cents a mile. How many miles would somebody have to drive in a truck from agency to pay an amount equal to the amount they'd have to pay at agency B?

How would you go about setting up this equation? I figure that you'd be solving for y (where y = miles driven) in an equation like this

[math]49x + .2y = 29x + .25y[/math]
[math](49x - 29x) + .2y = .25y[/math] --> [math]20x + .2y = .25y[/math]
[math]20x = .5y[/math]
[math]20 / .5 = [/math] 40 miles

Which I believe is the correct answer but it just doesn't feel right logically speaking. Shouldn't you be dividing .5 by 20 in order to solve for y? I don't think that's correct because y would be equal to 0.025 in that instance, but I also don't understand the logic behind dividing 20 by .5 in order to figure out the value of y.

Fuck, I don't even know familias, I doubt anything I said even made sense. I think I might actually be retarded.

this is frank garret?

Is there any significant diference between gram-positive and gram-negative bacteria apart from the reactions to the Gram staining?

How come panda express asked for ID for my mom who was using debit, but did not ID any other person standing in line? Is it because we were Latino? The others were white. The cashier was a black women.

any help for these problems? they're on chegg if anyone is willing to screen cap that

I took physics like 2 semesters ago and I completely forgot this stuff. don't have the book atm either

Maybe they were paying with cash or credit

i used to work as a cashier. usually only credit required ID or verification of last 4 digits. maybe your mom had some weird debit card brand?
could just be a racist black cashier.

when do you add two derivatives like this? i thought you always multiplied them

A charges $20/day more but 5¢/mile less.

With A, you save $1 for every 20 miles driven. You'd need to drive 400 miles/day before the saving compensates for the extra $20/day hire fee.

> (49x - 29x) + .2y = .25y --> 20x + .2y = .25y
okay so far.
> 20x = .5y
You lost a decimal place. 0.25-0.20 = 0.05, not 0.5.

20x = 0.05y 400x = y y/x = 400

Product rule: d[f*g]/dx = f*dg/dx + g*df/dx
Chain rule: d[f(g(x))]/dx = (df/dg)*(dg/dx).

> I also don't understand the logic behind dividing 20 by .5 in order to figure out the value of y.
You're not after the value of y, you're after the value of y/x (miles driven per day hired).
a*x=b*y a=b*y/x a/b=y/x

ah i see, i just wasnt used to seeing it with fractions.

thanks kind user

how do i know when to use the product rule and the chain rule, as apposed to just the chain rule?

You use the product rule if you're differentiating a product.

It's saying you shouldn't count rotations as unique seating.

[math]
1 \\
4 = 1 + 3 \\
9= 4 + 5 \\
16 = 9 + 7 \\
25 = 16 + 9 \\
36 = 25 + 11
[/math]

why do square numbers = n - 1 square number + nth odd number like dat

nature crazy

go on user, this gets me high

Do you know algebra? If so, know that the nth square number can be represented by:

[math]n^2[/math]

and the (n-1)th square number is:

[math](n-1)^2[/math]

and the nth odd number (starting from 1)

[math]2n-1[/math]

Then, adding the (n-1)th square number and the nth odd number:

[math](n-1)^2 + 2n - 1 = n^2 - 2n + 1 + 2n - 1 = n^2 [/math]

--------

If you don't know algebra, see pic related, the green squares have area (n-1)^2, the entire grid has area n^2, and the entire grid is split into the green square, and the red boxes and the orange box.

There are 2 lots of the red box (for the 2 sides of the square), 2 * a number is always even, so 2 * (number of red boxes) is even, but then we have 1 orange box left, so 2 * (number of red boxes) + (orange box) = odd number.

So odd number + (green square area) = (entire square area).

A question about neural networks.
I get the benefits of normalizing or standartising input data when training a network.

But when I do so, I also have to normalize any actual data I then throw into the network for classification after training.
How can I normalize each of those 'single' inputs without the training data to calculate means and min-max stuff.

are the p-adic numbers algebraically closed? if not, what is its closure?

also, i keep hearing that the surreal numbers are "so big that they aren't a set, they're a proper class", but why are they so big? what do they contain that makes them so huge?

>are the p-adic numbers algebraically closed?
No, and there's no reason to expect them to be. Look into Hensel's lemma.

Is anyone familiar with how Chinese universities publish papers? I've thought about learning how to read (I don't care about speaking it) Chinese as an advantage for doing research. Any thoughts on this? My field would be math or computer science.

The important results get published in English. Don't bother.

OK, I should've figured as much. I think I'm just trying to justify learning it because I love symbols.

You can still learn it if you want, but the most common second languages in math are French, German and Russian. Every few schools still make math PhDs study a second language.

10c4 x ((4p4)/4)

She was using debit from Visa.

I don't see how it's infinite for n>2

oh... never mind, sign error..

you can show that the square root of 2 is not rational using the Fermat-Wiles theorem.

Can someone explain the central limit theorem?

Does it mean that we can always approximate distributions by a normal distriubtion if there are a large enough number of points? Or, are there conditions where it doesn't hold? How do you know? I'm just really confused as to when we are allowed to invoke it.

I have a question about gene cloning

When you insert a gene of interest into a cloning vector via a restriction site that's within a resistance gene on the vector, you end up inactivating the resistance gene upon insertion, right?

So when the plasmid is introduced into a cell, does RNAP still attach to the now inactive resistance gene's promoter region and try to transcribe it until it reaches the inserted gene? Does it keep transcribing RNA that is eventually degraded, or is there a way to prevent the cell from initiating transcription on the broken gene in the first place? Also, how does RNAP know when to stop transcribing the broken gene? Do they add an in-frame terminator region to the start of the gene to be inserted into the vector or something

If
[math] w_1,\dots,w_n[/math] are complex numbers with norm 1, how do I show that [math] a_N=w_1^N+\dots+w_n^N[/math] doesn't converge to zero.

>Fermat-Wiles theorem

In the oracle formulation of the polynomial hierarchy, are the power towers associative?

e.g. does NP^(NP^(NP^NP)) = (NP^NP)^(NP^NP)?

It seems so because it just boils down to quantifiers in the end.

Could you be any more wrong?

Really stupid question here
What's the name of this experiment?
youtube.com/watch?v=zifQYUG8Iiw

0 0 -1
0 -1 0
-31 0 0

It means you can approximate sample means of distributions with a normal, if your sample size is large enough.

If it did, at some point the sum would always be within 1/4 of zero. But then you couldn't add another point on the circle and stay in that 1/4-radius circle.

sorry, this doesn't quite work... N exponent changes with the a's...

>For the reals ... uh, I guess it basically follows from the construction of the reals, but I couldn't really give any more detail than that (my background is CS, so I tend to view the reals as more of a philosophical concept than something which actually exists).

It really is just a matter of definition. We extend the notion of exponentiation to arbitrary complex arguments with a well-behaved power series that agrees with the informal notion on the rationals.
en.wikipedia.org/wiki/Exponential_function#Formal_definition

Certain things, like e^(i*x)=cos(x)+i*sin(x), are entirely consequences of this definition.

More generally, en.wikipedia.org/wiki/Analytic_continuation

It's differentiable only over the space where those are valid

not that guy but this was a really nice explanation. i wouldnt have thought of expressing it geometrically.

thanks user, it's nice how a lot of neat things like that in elementary number theory can be expressed geometrically, like with triangular numbers, and the more general figurate numbers:

mathworld.wolfram.com/FigurateNumber.html

What's a better or more interesting elective for applied math, PDEs or Complex Variables?

This is probably an easy question but I'm not sure how to go about it.

Can I just pick M to be integers and then should I just try and guess some relations that fit the questions? Seems like there's a better way but I'm not sure

I picked M = {0, 1, 2} and given that R1 is a subset of M x M, then one can construct something that can satisfy the properties given pretty easily.

[math]$For some relation:$ \ R [/math]

[math](\forall x) R(x,x) : $reflexivity$ [/math]

[math](\forall x)(\forall y) R(x,y) \Rightarrow R(y,x) : $symmetry$ [/math]

[math](\forall x)(\forall y)(\forall z) R(x,y) \land R(y,z) \Rightarrow R(x,z) : $transitivity$ [/math]

One just needs to look at the finite set M x M = {(0,0), (0,1), (0, 2), (1, 0) , (1, 1), (1,2), (2,0), (2,1), (2,2)}, and pick an appropriate subset for each of R1, R2 and R3, such that the appropriate definition fails.

You may find that easier (since you can construct what you need), or perhaps look for natural examples within the integers.

Yeah that's what I ended up doing, but with M = {1,2,3,4}. I don't know why but before I was thinking I needed to think up a kind of equation kind of relation that fits the criteria rather than just listing the actual relations. Thanks your post helped me clarify that I ended up doing it right in the end

Dunno what you mean by 'better', but in tems of applicability to the real-world (e.g. some high-level engineering, or 'applied maths-type position' in some big company), a PDE course seems more appropriate to me.

However, given that 1) a bit of complex analysis is not superfluous in PDEs 2) complex analysis also has its use in engineering (if you ever hear about poles, Laplace transforms, Z-transforms and stuff, you'll know what I mean), I would suggest that you take bot of them, if possible. If not, PDEs first.

Disclaimer : PDE theorist here. :)

do you think there are any electromagnetic waves we can't detect yet or is there a limit to the frequencies?