This work deals with the numerical simulation of wave propagation on unbounded domains with localized heterogeneities. To do so, we propose to combine a discretization based on a discontinuous Galerkin method in space and explicit finite differences in time on the regions containing heterogeneities with the retarded potential method to account the unbounded nature of the computational domain. T...

In this paper, we are concerned with a non-overlapping domain decomposition method for solving the low-frequency time-harmonic Maxwell’s equations in unbounded domains. This method can be viewed as a coupling of the finite element and the boundary element in unbounded domains, which are decomposed into two sub-domains with a spherical artificial boundary. We first introduce a discretization for...

In this paper, we prove a version of weighted inequalities of exponential type for fractional integrals with sharp constants in any domain of finite measure in R. Using this we prove a sharp singular Adams inequality in high order Sobolev spaces in bounded domain at critical case. Then we prove sharp singular Adams inequalities for high order derivatives on unbounded domains. Our results extend...

This work is devoted to the analysis of elasto-plasticity models arising in soil mechanics. Contrary to the typical models mainly used for metals, it is required here to take into account plastic dilatancy due to the sensitivity of granular materials to hydrostatic pressure. The yield criterion thus depends on the mean stress and the elasticity domain is unbounded and not invariant in the direc...

This paper is concerned with the electromagnetic theory of microstretch elasticity. First, the initial boundary value problem is formulated in the framework of the linear dynamic theory of microstretch magnetoelectroelastic solids. Then, the spatial behavior of solutions is studied in both bounded and unbounded regions. The obtained result gives an exact idea of the domain of influence, in the ...

The design and verification of cryptographic protocols is a notoriously difficulttask, even in symbolic models which take an abstract view of cryptography. This is mainlydue to the fact that protocols may interact with an arbitrary attacker which yields averification problem that has several sources of unboundedness (size of messages, numberof sessions, etc.).In this paper, ...

The applications of software benchmarks place an obvious demand on the precision of the benchmark results. An intu­ itive and frequently employed approach to obtaining precise enough benchmark results is having the benchmark collect a large number of samples that are simply averaged or other­ wise statistically processed. We show that this approach ignores an inherent and unavoidable nondetermi...

A functional model for nondissipative unbounded perturbations of an unbounded self-adjoint operator on a Hilbert space X is constructed. This model is analogous to the Nagy– Foias model of dissipative operators, but it is linearly similar and not unitarily equivalent to the operator. It is attached to a domain of parabolic type, instead of a half-plane. The transformation map from X to the mode...

A functional model for nondissipative unbounded perturbations of an unbounded self-adjoint operator on a Hilbert space X is constructed. This model is analogous to the Nagy– Foias model of dissipative operators, but it is linearly similar and not unitarily equivalent to the operator. It is attached to a domain of parabolic type, instead of a half-plane. The transformation map from X to the mode...

We present a method based on abstract interpretation for verifying secrecy properties of cryptographic protocols. Our method allows to verify secrecy properties in a general model allowing an unbounded number of sessions, an unbounded number of principals and an unbounded size of messages. As abstract domain we use sets of so-called super terms. Super terms are obtained by allowing an interpret...