We fully describe the doubly stochastic orbit of a self-adjoint element in noncommutative $$L_1$$ -space affiliated with semifinite von Neumann algebra, which answers problem posed by Alberti and Uhlmann (Stochasticity partial order: maps unitary mixing. VEB Deutscher Verlag der Wissenschaften, Berlin, 1982) 1980s, extending several results literature. It follows further from our methods that, ...

In this paper, we study three types of rotational surfaces in Galilean 3-spaces. We classify satisfying $$L_1G=F(G+C)$$ for some constant vector $C\in \mathbb{G}^3$ and smooth function $F$, where $L_1$ denotes the Cheng-Yau operator.

We present an Alternating Direction Method of Multipliers (ADMM) algorithm for solving optimization problems with an `1 regularized least-squares cost function subject to recursive equality constraints. The considered optimization problem has applications in control, for example in `1 regularized MPC. The ADMM algorithm is easy to implement, converges fast to a solution of moderate accuracy, an...

Let $X/\mathbb {F}_{q}$ be a smooth, geometrically connected, quasi-projective scheme. $\mathcal {E}$ semi-simple overconvergent $F$ -isocrystal on $X$ . Suppose that irreducible summands {E}_i$ of have rank 2, determinant $\bar {\mathbb {Q}}_p(-1)$ , and infinite monodromy at $\infty$ further for each closed point $x$ the characteristic polynomial is in $\mathbb {Q}[t]\subset \mathbb {Q}_p[t]$...