Important progress in understanding the behavior of hadronic matter at high density has been achieved recently, by adapting the techniques of condensed matter theory. At asymptotic densities, the combination of asymptotic freedom and BCS theory make a rigorous analysis possible. New phases of matter with remarkable properties are predicted. They provide a theoretical laboratory within which chi...

We are interested in the homogenization of elastic-electric coupling equation, with rapidly oscillating coefficients, in periodically perforated piezoelectric body. We justify the two first terms in the usual asymptotic development of the problem solution. For the main convergence results of this paper, we use the notion of two-scale convergence. A two-scale homogenized system is obtained as th...

Abstract— The stability analysis problem is studied in this paper for a class of discrete-time switched time-delay systems described by delayed recurrence equations or a state matrix transformed after under the arrow form, by applying the comparison, the aggregations techniques and the M-matrix properties, new asymptotic stability conditions of such systems are derived under arbitrary switching...

The asymptotic behaviour of cubic field theories is investigated in the Regge limit using the techniques of environmentally friendly renormalization, environmentally friendly in the present context meaning asymmetric in its momentum dependence. In particular we consider the crossover between large and small energies at fixed momentum transfer for a model scalar theory of the type φ 2 ψ. The asy...

We derive high-order terms in the asymptotic expansions of the boundary perturbations of steady-state voltage potentials resulting from small perturbations of the shape of a conductivity inclusion with C2-boundary. Our derivation is rigorous and based on layer potential techniques. The asymptotic expansion in this paper is valid for C1-perturbations and inclusions with extreme conductivities. I...

We investigate the structure of spherical τ -designs by applying polynomial techniques for investigation of some inner products of such designs. Our approach can be used for large variety of parameters (dimension, cardinality, strength). We obtain new upper bounds for the largest inner product, lower bounds for the smallest inner product and some other bounds. Applications are shown for proving...

We devise a new-class of asymptotic-preserving Godunov-type numerical schemes for hyperbolic systems with stiff and non-stiff relaxation source terms governed by a relaxation time ε. As an alternative to classical operator-splitting techniques, the objectives of these schemes are twofold: first, to give accurate numerical solutions for large, small and in-between values of ε and second, to make...

Consider a branching random walk evolving in a macroscopic time-inhomogeneous environment, that scales with the length n of the process under study. We compute the first two terms of the asymptotic of the maximal displacement at time n. The coefficient of the first (ballistic) order is obtained as the solution of an optimization problem, while the second term, of order n, comes from time-inhomo...

Suppose we are given the free product V of a finite family of finite or countable sets. We consider a transient random walk on the free product arising naturally from a convex combination of random walks on the free factors. We prove the existence of the asymptotic entropy and present three different, equivalent formulas, which are derived by three different techniques. In particular, we will s...