with respect to the Euclidian norm, where F :Rn →Rn is a nonlinear operator. Section 2 is devoted to a brief description of asynchronous parallel algorithm. In Section 3, we prove the main result concerning the convergence of the general algorithm in the synchronous case to a fixed point of a nonlinear operator fromRn to Rn. A particular case of this algorithm (algorithm of Jacobi) is applied i...

For n ∈ {2, 3} we prove minimax characterisations of eigenvalues in the gap of the n dimensional Dirac operator with an potential, which may have a Coulomb singularity with a coupling constant up to the critical value 1/(4 − n). This result implies a socalled Hardy-Dirac inequality, which can be used to define a distinguished self-adjoint extension of the Coulomb-Dirac operator defined on C0 (R...

It has been recognised that the expressivity of description logics benefits from the introduction of non-standard modal operators beyond existential and number restrictions. Such operators support notions such as uncertainty, defaults, agency, obligation, or evidence, whose semantics often lies outside the realm of relational structures. Coalgebraic hybrid logic serves as a unified setting for ...

in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...

Forthcoming in the Journal of Aritificial Intelligence We introduce mathematical programming and atomic decomposition as the basic modal (T-Box) inference techniques for a large class of modal and description logics. The class of description logics suitable for the proposed methods is strong on the arithmetical side. In particular there may be complex arithmetical conditions on sets of accessib...

We present a model-driven approach for adding extra-functional properties to component and connector (C&C) models. The approach is based on a tagging mechanism that allows non-invasive extensions of existing languages and their models, here C&C models, with attributes for extra-functional properties. Importantly, our language extension provides means for integrated formal analyses of the consis...

We continue our investigation on how to revise a Description Logic knowledge base when detecting exceptions. Our approach relies on the methodology for debugging a Description Logic terminology, addressing the problem of diagnosing inconsistent ontologies by identifying a minimal subset of axioms responsible for an inconsistency. In the approach we propose, once the source of the inconsistency ...

The value of a single dataset is increased when it is linked to combinations of datasets to provide users with more information. Linked Data is a style of publishing data on the Web by using a structured machine-readable format, RDF, and semantically typed relations to connect related data. Its structured representation opens up new possibilities in the way these data can be accessed and querie...

ð2Þ ~ T 1⁄4 T ; 8 2 V: We use HBðV;W Þ to denote the set of Hahn–Banach operators. The classical Hahn–Banach theorem states that every rank-1 operator from V into W is a Hahn–Banach operator. It can also be restated in the following way: if dimW 1⁄4 1, then HBðV;W Þ 1⁄4 LðV;W Þ. Observe that the two statements above are slightly different. In the first case we describe a property of an operator...

A consistent description of kinetics and hydrodynamics of systems of interacting particles by means of the nonequilibrium statistical operator method A statistical approach to a self-consistent description of kinetic and hydrody-namic processes in systems of interacting particles is formulated on the basis of the nonequilibrium statistical operator method by D.N.Zubarev. It is shown how to obta...