For a small quantaloid Q, a Q-closure space is a small category enriched in Q equipped with a closure operator on its presheaf category. We investigate Q-closure spaces systematically with specific attention paid to their morphisms and, as preordered fuzzy sets are a special kind of quantaloid-enriched categories, in particular fuzzy closure spaces on fuzzy sets are introduced as an example. By...

We propose a solution to a problem that is encountered in defining a notion of full meet base revision, ensuring that the output can always be re-used as an input. For this purpose, we introduce the concept of a separable belief base and show that separable bases are exactly those for which the full meet revision closure operator satisfies the extended set of A. G. M. postulates. We then define...

One of the major questions in the theory of Toeplitz operators on the Bergman space over the unit disk D in the complex plane C is a complete description of the commutant of a given Toeplitz operator, that is the set of all Toeplitz operators that commute with it. In [4], the first author obtained a complete description of the commutant of Toeplitz operator T with any quasihomogeneous symbol φ(...

We prove an extension theorem for a small perturbation of the Ornstein-Uhlenbeck operator (L,D(L)) in the space of all uniformly continuous and bounded functions f : H → R, where H is a separable Hilbert space. We consider a perturbation of the form N0φ = Lφ + 〈Dφ,F 〉 where F : H → H is bounded and Fréchet differentiable with uniformly continuous and bounded differential. Hence, we prove that N...

We demonstrate a one-to-one correspondence between idempotent closure operators and the so-called saturated quasi-uniform structures on category C. Not only this result allows to obtain categorical counterpart P of Császár-Pervin quasi-uniformity P, that we characterize as transitive compatible with an interior operator, but also permits describe those topogenous orders are induced by The P⁎ P−...

In this paper, we introduce and discuss the passage to hydrodynamic equations for kinetic models of conservative economies, in which the density of wealth depends on additional parameters, like the propensity to invest. As in kinetic theory of rarefied gases, the closure depends on the knowledge of the homogeneous steady wealth distribution (the Maxwellian) of the underlying kinetic model. The ...

in this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{t}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. we use a strong convolution technique and derive inclusion results. a radius problem and some other interesting properties of these classes are discussed.

By defining a closure operator on effective equivalence relations in a regular category C, it is possible to establish a bijective correspondence between these closure operators and the regular epireflective subcategories of C, on the model of the closure operators on kernels in homological categories [5]. When C is an exact Goursat category [6], this correspondence restricts to a bijection bet...

In this paper, by presenting some notions and theorems, we obtaindifferent types of fuzzy topologies. In fact, we obtain someLowen-type  and Chang-type fuzzy topologies on general fuzzyautomata. To this end, first we define a Kuratowski fuzzy interioroperator which induces a  Lowen-type  fuzzy topology on the  set ofstates of a max- min general   fuzzy automaton. Also by  provingsome theorems, ...

We consider linear time temporal logic enriched with semiextended regular expressions through various operators that have been proposed in the literature, in particular in Accelera’s Property Specification Language. We obtain results about the expressive power of fragments of this logic when restricted to certain operators only: basically, all operators alone suffice for expressive completeness...