If T is a bounded linear mapping (briefly, operator) in a Hilbert space 3C, the numerical range of T is the set WiT) = {(Tx, x): |[x|| = l}; thus WiT) is convex [8, p. 131], and its closure clfW^r)] is compact and convex. Roughly speaking, in this note we observe that cl[TF(T)] can be uniquely defined for an element T of an abstract C*-algebra, while WiT) cannot. The C*-algebra setting yields a...

Link-based data may be studied formally by means of unordered trees. On a dataset formed by such link-based data, a natural notion of support-based closure can be immediately defined. Abstracting information from subsets of such data requires, first, a formal notion of intersection; second, deeper understanding of the notion of closure; and, third, efficient algorithms for computing intersectio...

Concurrent games as event structures form a partial order model of concurrency where concurrent behaviour is captured by nondeterministic concurrent strategies—a class of maps of event structures. Extended with winning conditions, the model is also able to give semantics to logics of various kinds. An interesting subclass of this game model is the one considering deterministic strategies only, ...

A new modal logic D is introduced. It describes properties of provability by interpreting modality as a deductive closure operator on sets of formulas. Logic D is proven to be decidable and complete with respect to this semantics.

This paper deals with the relationships between two classes of infinite matroids–the classes of matroids of arbitrary cardinality and of independence spaces primarily with the help of hyperplane set approach and sometimes of closure operator approach.

This research aims to present a linear operator Lp,q?,?,?f utilizing the q-Mittag–Leffler function. Then, we introduce subclass of harmonic (p,q)-convex functions HTp,q(?,W,V) related Janowski For p-valent f class, investigate geometric properties, such as coefficient estimates, convex combination, extreme points, and Hadamard product. Finally, closure property is derived using under q-Bernardi...

We continue Mizar formalization of General Topology according to the book [19] by Engelking. In the article the formalization of Section 1.2 is almost completed. Namely, we formalize theorems on introduction of topologies by bases, neighborhood systems, closed sets, closure operator, and interior operator. The Sorgenfrey line is defined by a basis. It is proved that the weight of it is continuu...

We construct a universal tangle invariant on a quantum algebra. We show that the invariant maps tangle to commutants of the algebra; every (1, 1)-tangle is mapped to a Casimir operator of the algebra; the eigenvalue of the Casimir operator in an irreducible representation of the algebra is a link polynomial for the closure of the tangle. This result is applied to a discussion of the Alexander–C...

In this paper, we study the desingularization problem in the first qWeyl algebra. We give an order bound for desingularized operators, and thus derive an algorithm for computing desingularized operators in the first q-Weyl algebra. Moreover, an algorithm is presented for computing a generating set of the first q-Weyl closure of a given q-difference operator. As an application, we certify that s...

The notion of pseudo-annulets is introduced in Stone lattices and characterized in terms of prime filters. Two operator α and β are introduced and obtained that their composition β ◦α is a closure operator on the class of all filters of a Stone lattice. A congruence θ is introduced on a Stone lattice L and proved that the quotient lattice L/θ is a Boolean algebra.