MathOverflow

Given a Brownian motion $W$ on the real line starting at the origin, our goal is to apply a forcing that keeps the Brownian motion in $[-1, 1]$ up to a fixed time $T$ with minimal effort.
Formally, we choose a control process $K$ on $[0, T]$ adapted to $W$, which we require to be of bounded variation almost surely. The controlled particle $X$ satisfies...

Daniel Shanks introduced the "simplest cubic fields" in a 1974 paper [1]. These have cyclic Galois group of order 3, all roots are real, and a straightforward parameterization:
$$f = x^3 - tx^2 - (t+3)x - 1$$
for $t \in \mathbb{Z}$ and discriminant is $D = (t^2+3t+9)^2$. These polynomials are interesting because the fields they define contains all the roots of the polynomial, and the roots are units (not necessarily fundamental). As a consequence, the constant...

Let $n \geq 3$ and let $u \in C^\infty(\mathbb{R}^n)$ be a strictly positive, non-radial function (i.e., $u$ cannot be written as $f(|x|)$). Consider the conformal metric $g = u^{\frac{4}{n-2}}\delta$ on $\mathbb{R}^n$, where $\delta$ is the standard...

A cardinal $\kappa$ is real-valued measurable (rvm) if there is a $\kappa$-additive probabilistic measure on $\kappa$ which vanishes on singletons and is moreover atomless, i.e., any positive set can be split into two positive sets. There exists a rvm...