Recently, the general topology has become the appropriated frame for every collection related to relations because topology is required not only for mathematics and physics but also for biology, rough set theory, biochemistry, and dynamics. In this paper, we have introduced another concept of the closure operator. In so doing, the idempotent condition, which has never been realized, is achieved...

The Fresnel equation governing the propagation of electromagnetic waves for the most general linear constitutive law is derived. The wave normals are found to lie, in general, on a fourth order surface. When the constitutive coefficients satisfy the so-called reciprocity or closure relation, one can define a duality operator on the space of the two-forms. We prove that the closure relation is a...

After a brief review of hidden algebra, we give behavioral speci cations for set theory and closure operators, and then use these to give a behavioral speci cation of an abstract protocol to support distributed cooperative work structured by dependencies in such a way as to form what we call a weak closure operator. We give some correctness proofs for this protocol, and then describe a concrete...

Improved inclusion-exclusion identities via closure operators Klaus Dohmen Department of Computer Science, Humboldt-University Berlin, Unter den Linden 6, D-10099 Berlin, Germany E-mail: [email protected] received March 24, 1999, revised September 6, 1999, accepted April 15, 2000. Let be a finite family of sets. We establish an improved inclusion-exclusion identity for each closure...

The paper describes an algebraic framework for representing and reasoning about 2D spatial regions. The framework consists of a Closure Algebra (CA) of half-planes (Boolean Algebra augmented with the closure operator). Terms of the Boolean part of the CA are Boolean combinations of half-planes. The paper also describes an implemented algorithm determining which of the RCC-8 (Region Connection C...

The main purpose of this article is to give a relationship between Fredholm multivalued linear operators and the demicompact relation; we provide some sufficient conditions on inputs closable block operator matrix ensure generalized demicompactness its closure. Our results generalize many known ones in literature.

We consider the dual of Theorem 1 from [33], relating closure conditions on subcategories with projectivity classes for collections of discrete cocones. We extend these results by adding a new operator for closure under domains of epis and show that this corresponds to taking projectivity classes for cocones with vertex a subobject of the terminal object. We show that these theorems apply to ca...

JSON Schema is an evolving standard for describing families of documents. It a logical language, based on set assertions that describe features the value under analysis and or structural combinators these assertions, including negation operator. Most languages with enjoy closure: every operator, they have negation-dual allows to be pushed through We show this not case Schema, study how changed ...

Abstract In this work, we analyze Gabor frames for the Weyl--Heisenberg group and wavelet extended affine group. Firstly, give necessary sufficient conditions existence of nonstationary translates. Using these conditions, prove from We present a representation functions in closure linear span frame sequence terms Fourier transform window functions. show that canonical dual translates has same s...

In this paper we show that nondeterministic space s n is closed under com plementation for s n greater than or equal to log n It immediately follows that the context sensitive languages are closed under complementation thus settling a question raised by Kuroda in See Hartmanis and Hunt for a discussion of the history and importance of this problem and Hopcroft and Ullman for all relevant backgr...