Want to stay in touch with the latest updates from Recent Questions - MathOverflow? That's easy! Just subscribe clicking the Follow button below, choose topics or keywords for filtering if you want to, and we send the news to your inbox, to your phone via push notifications or we put them on your personal page here on follow.it.
Reading your RSS feed has never been easier!
Website title: MathOverflow
Is this your feed? Claim it!
Prove that $$f(x, y) \equiv \arccos\left(\frac{x-y}{K}\right) - \arccos\left(\frac{x-y}{K}+y\right) - \frac{y}{x}\arccos(1-y^2) \ge 0$$
with the constraints:
$K\ge 2$ is an integer, $g(x, y) = (K-1)y^2+x^2-K=0$, $1\le x\le \sqrt{K}$, $0\le y\le 1$.Furthermore, $f(x, y) = 0$ if and only if $x=y=1$ or $x=\sqrt{K}$ and $y=0$.
Numerically it seems ...
Question. Let $n \in \mathbb{N}$. Is the truncated simplex category $\Delta^{\leq n}$ (consisting of $[0],\dotsc,[n]$) a generalized variety?
A category is a generalized variety if it has sifted colimits and there is a small set $G$ of strong...
Let $A$ be a finite set of statements and $R$ is the set of all implications between them. Let $K$ be the complete relation of all arrows between elements of $A$. If there are no equivalent statements in $A$, then $A$ is partially ordered by implication. To prove that only implications from $R$ hold, we need to refute some arrows from the complement $K \setminus R$. Call this...
It is somewhat well-known that countably generated torsion modules over a local PID are classified by their Ulm invariants.
I'm interested in homological properties of rings of the form $R_ := \mathrm{End}_k(T)$ for such modules over $k[[t]]$, or, equivalently, over $k[t]_{(t)}$, and how to express those properties in terms of Ulm sequence.
Main question...
Given a cardinal $\kappa > 2$, is there a triangle-free vertex-transitive graph $G=(V,E)$ with $\chi(G) = \kappa$?