GivenS|R a finite Galois extension of finite chain rings andB anS-linear code we define twoGalois operators, the closure operator and the interior operator. We proof that a linear code is Galois invariant if and only if the row standard form of its generator matrix has all entries in the fixed ring by the Galois group and show a Galois correspondence in the class of S-linear codes. As applicati...

A necessary and sufficient condition on the support of a generic unmixed bivariate polynomial system is identified such that for polynomial systems with such support, the Dixon resultant formulation produces their resultants. It is shown that Sylvester-type matrices can also be obtained for such polynomial systems. These results are shown to be a generalization of related results recently repor...

The construction of accurate generalized impedance boundary conditions for the three-dimensional acoustic scattering problem by a homogeneous dissipative medium is analyzed. The technique relies on an explicit computation of the symbolic asymptotic expansion of the exact impedance operator in the interior domain. An efficient pseudolocalization of this operator based on Padé approximants is the...

One component in Additive Schwarz Method (ASM) Domain Decomposition (DD) preconditioners BPS89, SBG96] using inexact subdomain solvers Boe89, HLM91] consists of an operator extending the boundary data into the interior of each subdomain, i.e., a homogeneous extension with respect to the diierential operator given in that subdomain. This paper is concerned with the construction of cheap extensio...

A necessary and sufficient condition on the support of a generic unmixed bivariate polynomial system is identified such that for polynomial systems with such support, the Dixon resultant formulation produces their resultants. It is shown that Sylvester-type matrices can also be obtained for such polynomial systems. These results are shown to be a generalization of related results recently repor...

This paper aims to enhance the practical applicability of relational grammars, which have been devised for the semantic analysis of natural language. We focus on their application in knowledge representation. In particular, we address how the representation problem for kl-one-based knowledge representation systems can be automatically solved with the help of relational grammars. New rules are p...

Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Topology, one of the most important subjects in mathematics, provides mathematical tools and interesting topics in studying information systems and rough sets. In this paper, we present the topological characterizations to three types of covering approximation operators. F...

We consider arbitrarily large networks of pulse-coupled oscillators with nonzero delay where the coupling is given by the Mirollo–Strogatz function. We prove that such systems have unstable attractors (saddle periodic orbits whose stable set has non-empty interior) in an open parameter region for three or more oscillators. The evolution operator of the system can be discontinuous and we propose...

We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The adaptivity is driven by the residual error estimator. We prove convergence even with optimal algebraic convergence rates. In particular, our analysis covers gene...

One component in Additive Schwarz Method (ASM) Domain Decomposition (DD) preconditioners BPS89, SBG96] using inexact subdomain solvers Boe89, HLM91] consists in an operator extending the boundary data into the interior of each subdomain, i.e. a homogeneous extension with respect to the diierential operator given in that subdomain. This paper is concerned with the construction of cheap extension...