Mathematics

Stupid question about Jacobians: is it true that $ \left|\frac{\partial g^{-1}}{\partial y} \circ g(x)\right|^{-1} = \left| \frac{\partial g}{\partial x} \right| $?

ah, of course

Chris's sister

10:28 AM

Hi all.

(sister here)

user19161

@Chris'ssister Hi! I will assume it is the sister as the brother never comes to chat.

Chris's sister

Hi @JasperLoy! :-)

I was looking at the question here and I wondered if there is any mean to avoid Dominated convergence theorem.

sperners lemma

11:37 AM

I've asked a great question

I tried to adapt four squares proof but I couldn't

@Chris'ssister, that is a fearsome integral

I like that use of DCT, but I can see why you'd want a non DCT one

what's the smallest even number that needs to be written as four squares?

28 = 8^2 - 6^2

the next even number that needs 4 squares is 60 = 8^2 - 2^2

next is 92 = 24^2 - 22^2

I guess the key is to half them: 14 = 2^2 - 2*3^2, 30 = 2*4^2 - 2*1^2, 46 = 6^2 - 2*11^2

Chris's sister

12:02 PM

@spernerslemma: fearsome, but beautiful at the same time. :)

sperners lemma

46 = 2*12^2 - 2*11^2

Gustavo Bandeira

12:14 PM

Anyone know the book From Calculus to Chaos?

sperners lemma

I don't know it

I wonder if anyone knows Hasse-Minkowski, I'm curious if it's applicable to a problem I have

sperners lemma

12:41 PM

hello

how many signed squares do you need to sum every to integer?

it's either 2 or 3, but I'm not sure which

odd numbers you can write as a^2 - b^2, even numbers as 1^2 + a^2 - b^2

so I was looking for an even number that can't be written as a sum or difference of two squares

anyone know an example?

6?

so really it proves S+S-S=N

strange that that's so much easier to prove than S+S+S+S=N

Juan

Please anybody Can tell me Whats mean $C_0^\infty$?

sperners lemma

I think that's continuous functions on [0,\infty)

Juan

i think that not

Gustavo Bandeira

1:18 PM

@spernerslemma You need to use LaTeX, for the sake of beautiful exposition of mathematics. :p

sperners lemma

I still don't understand how rm + sn + rx^{m+n}R + sx^{m+n}R = rm + sn + x^{mn}R for R modules

Juan

What is a smaller space that contains a zero function ?

Gustavo Bandeira

@Juan Perhaps it's better to ask on the stack.

You can obtain answers fastly.

Since it's exposed to a bigger audience.

Matt N.

Exhibit A + Exhibit B => contradiction. Ex falso quodlibet therefore Asaf is a pony.

user19161

1:41 PM

@MattN. Er, what you said is beyond my paygrade!

user19161

@Juan Check the book for the definition of the notation.

Gustavo Bandeira

@JasperLoy I'm almost finishing a chapter on limits. =)

sperners lemma

cool

what's up

user19161

You know what I am going to say.

sperners lemma

2:13 PM

1

A: When is $1^5 + 2^5 + \ldots + n^5$ a square?

The general solution to $$m^2 = \frac{1}{12}(2n^6+6n^5+5n^4−n^2)$$ is $$m = \frac{n(n+1)}{2} y, \quad n = (x-1)/2$$ where $$x+\sqrt{6} y = (3+\sqrt{6}) (5+2 \sqrt{6})^k$$ for some integer $n$. Here are the first few values $$\begin{array}{|r|l|l|l|l|} \hline k& x & y & n & m\\ \hl...

so that pell equation is really effective

Nimza

Good evening!

hi @JonasTeuwen, do you know a PsDO for which $x \mapsto e^{-(x_1 y_1 + \ldots + x_n y_n)^{\alpha}}$ is en eigenfunction? Something that generalizes differentiation by direction

sperners lemma

good evening

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$Mathematics$ Mathematics