Knowledge reduction of dynamic covering information systems involves with the time in practical situations. In this paper, we provide incremental approaches to computing the type-1 and type-2 characteristic matrices of dynamic coverings because of varying attribute values. Then we present incremental algorithms of constructing the second and sixth approximations of sets by using characteristic ...

For the kind of coverings codes called multiple coverings of the farthestoff points (MCF) we define μ-density as a characteristic of quality. A concept of multiple saturating sets ((ρ, μ)-saturating sets) in projective spaces PG(N, q) is introduced. A fundamental relationship of these sets with MCF codes is showed. Lower and upper bounds for the smallest possible cardinality of (1, μ)-saturatin...

We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of Denef,Loeser, Cluckers. The method depends on an analysis of definable sets up to definable bijections. We obtain a precise description of the Grothendieck ...

This paper is devoted to the study of a discrepancy-type characteristic -- fixed volume discrepancy Korobov point sets in unit cube. It was observed recently that this new allows us obtain optimal rate dispersion from numerical integration results. observation motivates thoroughly version discrepancy, which seems be interesting by itself. extends recent results V. Temlyakov and M. Ullrich on Fi...

In this paper, we study the ε-lemniscate of the characteristic polynomial in relation to the pseudospectrum of the associated matrix. It is natural to investigate this question because these two sets can be seen as generalizations of eigenvalues. The question of numerical determination of the ε-lemniscate raises the problem of computing the characteristic polynomial p. We can express the coeffi...

Let R be a recursive noetherian integral domain of characteristic zero with fraction field K. Assume that K is finitely generated (as a field) over Q. Equivalently, assume that K is the function field of a variety over a number field. We show that recursively enumerable sets are diophantine for the polynomial ring R[Z]. 2000 MSC: 11D99 (primary), 03D25, 12L12, 11R58, 12E10 (secondary).

There are many real-life problems that, because of the need to involve a wide domain of knowledge, are beyond a single expert. This is especially true for complex problems. Therefore, it is usually necessary to allocate more than one expert to a decision process. In such situations, we can observe an increasing importance of uncertainty. In this paper, the Multi-Criteria Decision-Making (MCDM) ...

For X a separable metric space define p(X) to be the smallest cardinality of a subset Z of X which is not a relative γset in X, i.e., there exists an ω-cover of X with no γ-subcover of Z. We give a characterization of p(2) and p(ω) in terms of definable free filters on ω which is related to the psuedointersection number p. We show that for every uncountable standard analytic space X that either...

In order to generate complex virtual cities, models of buildings have to be defined in advance. A common approach describes individual components of these buildings, which are in turn restricted by geometric constraints such as orthogonality, parallelity or symmetry of building parts. A major challenge is to ensure consistency and avoid redundancy. Tools are needed which support geometric reaso...