This is the first time I write in this forum so hope I get everything right! I'm trying to resolve this double integral but I'm having trouble w...

I want to prove the Holder's inequality for sums: Let $p\ge1$ be a real number. Let $(x_{k})\in l_{p}$ and $(y_{k})\in l_{q}$ . Then, $$\overset{\inf...

Let $C$ be a convex set in $\mathbb{R}^d$ and $\overline{x}\in C$. We define the normal cone of $C$ at $\overline{x}$ by \begin{equation} N_C(\overline{x}...

Wikipedia give sheaf property using equalizer diagram by saying sheaf property means for any open cover $\{U_i\}$ of $U$ $$F(U) \rightarrow \prod_{i} F(U_...

The magnitude of a vector in Cartesian coordinates is just the length of the vector. But what about a vector in spherical coordinates and cylindrical coor...

What topological properties uniquely characterize the local topology of $\mathbb{R}^n$? I know $\mathbb{R}$ is the unique complete ordered field, but that...

I try to distribute beams on an horizontal array, with increasing spacings according to this series. 1+1=2 2+2=4 4+3=7 7+4=11 11+5=16 16+6=22 I'd lik...

I did the following proof which seems correct to me but does not match the approach of the answer provided by my professor, and seems pretty different fro...

A function $f : (a,b) \to \Bbb R$ is said to be convex if $$f(\lambda x+(1-\lambda)y)\le \lambda f(x)+(1-\lambda)f(y)$$ whenever $a < x, y < b$ and ...

Is there a proof for $\Bbb Z$ being an integral domain? Or is it an axiom that if $a*b=0$ then $a=0$ or $b=0$ where $a$, $b$ belong to $\Bbb Z$. Is it so ...