MathOverflow

It is known that
$$\int_0^{\pi/2} \theta^2 \ln(2 \sin(\theta))d\theta=-\frac{\pi}{4}\sum_{k=1}^{+\infty}\frac{(-1)^k}{k^3}$$
Also $\sum_{k=1}^{+\infty}\frac{(-1)^k}{k^3}=-\eta(3)=-\frac{3}{4}\zeta(3)$. Therefore

Given a $C^\ast$-algebra $A$, let $\kappa(M)$ be$$\sup\{|B| : B~\text{is a m.a.s.a. of}~A\}$$(where a m.a.s.a. is a maximal abelian subalgebra).
For monotone complete $A$, let $\lambda(A)$ be the least cardinal such that for any norm-bounded directed family $F$ of self-adjoint elements of $M$, there is a subfamily $F_0 \subseteq F$ with $|F_0| \leq \lambda(M)$ such that $\sup F_0 = \sup F$....

This question is motivated by the observation that finding an optimal tour through a set of points in the Euclidean plane is especially simple, if the points are in convex configuration and, that the relative order of the points on the convex hull is...

Suppose $f:(0,1)\rightarrow \mathbb R$ has a stationary point at 1/2 and higher derivatives that blow up towards 1 (I can be more precise, but I think I need first a general idea).Suppose $\lambda >Y>0$ are both large with $Y$ a small fixed power...