This paper introduces a new idea in the unital involutive Banach algebras and its closed subset. aims to study cohomology theory of operator algebra. We will algebra as an applied example algebra, be denoted by . The definitions cyclic, simplicial, dihedral group src=image/13426521_01.gif> introduced. presented definition src=image/13426521_14.gif>-relative that i...

vet C ˜e — ™onvex set in — f—n—™h sp—™e —nd r ˜e — ril˜ert sp—™eF por —n oper—torE v—lued smooth fun™tion—l © X C 3 B@rAD we dene the Bregman divergence of x; y P C —s D © @x; yA Xa ©@xA ©@yA lim t3CH t I ©@y C t@x yAA ©@yA : ‚e™—ll th—t origin—lly vev fregm—n introdu™ed this ™on™ept for re—lEv—lued ™onvex fun™E tions © ‘P“F yn the selfE—djoint oper—torsD there is — st—nd—rd p—rti—l orderingD A...

In this paper, we present a generalization of Tsallis relative operator entropy defined for positive operators and investigate some related properties. Some inequalities involving the generalized are pointed out as well.

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...

Let X be a Spin manifold with boundary, such that the Spin structure is defined near the boundary by an almost complex structure, which is either strictly pseudoconvex or pseudoconcave (and hence contact). Using generalized Szego projectors, we define modified partial differential-Neumann boundary conditions, Reo, for spinors, which lead to subelliptic Fredholm boundary value problems for the S...

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−...

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...

We introduce the branching transitive closure operator on weighted monadic second-order logic formulas where the branching corresponds in a natural way to the branching inherent in trees. For arbitrary commutative semirings, we prove that weighted monadic second order logics on trees is equivalent to the definability by formulas which start with one of the following operators: (i) a branching t...