We introduce a new notion of *-product of two integrable series with coeficients in distinct Grothendieck rings of algebraic varieties, preserving the integrability and commuting with the limit of rational series. In the ...

The main purpose of this paper is to extend to a situation involving matrix valued orthogonal polynomials and spherical functions, a result that traces its origin and its importance to work of Claude Shannon in laying the ...

We present a novel, quantitative view on the human athletic performance of individuals. We obtain a predictor for athletic running performances, a parsimonious model, and a training state summary consisting of three numbers, ...

We consider Gillette's two-person zero-sum stochastic games with perfect information. For each $k \in \mathbb{Z}_+$ we introduce an effective reward function, called $k$-total. For $k = 0$ and $1$ this function is known ...

We suggest a new algorithm for two-person zero-sum undiscounted stochastic games focusing on stationary strategies. Given a positive real $\epsilon$, let us call a stochastic game $\epsilon$-ergodic, if its values from any ...

The aim of the paper is to attach a noncommutative cluster-like structure to each marked surface $\Sigma$. This is a noncommutative algebra $\mathcal{A}_\Sigma$ generated by “noncommutative geodesics” between marked points ...

We construct graph-valued analogues of the Kuperberg sl(3) and $G_2$ invariants for virtual knots. The restriction of the sl(3) and $G_2$ invariants for classical knots coincides with the usual Homflypt sl(3) invariant and ...

We study a class of symmetric critical points in a variational 2$D$ Landau - de Gennes model where the state of nematic liquid crystals is described by symmetric traceless $3 \times 3$ matrices. These critical points play ...

A set $\Lambda$ is called $p$-spectral if there is a function $g \in L^p (\mathbb{R})$ such that all $\Lambda$-translates $\{g(t-\lambda),\lambda \in \Lambda\}$ span $L^p(\mathbb{R})$. We prove that exponentially small ...

In this article we develop a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, we give a negative answer on an old question of Schreyer about surface singularities ...