This remarkable little theorem and related phenomena have been the concern of many authors. Apart from the mysterious appearance of the number 14, the attraction of this theorem is that it is simple to state and can be examined and proved using concepts available after any first encounter with topology. The goal of this article is both to provide an original investigation into variations of the...

A new class of harmonic multivalent functions defined by an integral operator is introduced. Coefficient inequalities, extreme points, distortion bounds, inclusion results and closure under an integral operator for this class are obtained .

In this paper‎, ‎we consider a general integral operator $G_n(z).$ The main object of the present paper is to study some properties of this integral operator on the classes $mathcal{S}^{*}(alpha),$ $mathcal{K}(alpha),$ $mathcal{M}(beta),$ $mathcal{N}(beta)$ and $mathcal{KD}(mu,beta).$‎

We extend Kozen’s theory KA of Kleene Algebra to axiomatize parts of the equational theory of context-free languages, using a least fixed-point operator μ instead of Kleene’s iteration operator ∗. Although the equational theory of context-free languages is not recursively axiomatizable, there are natural axioms for subtheories KAF ⊆ KAR ⊆ KAG: respectively, these make μ a least fixed point oper...

This paper deals with some operator representations Φ of a weak*-Dirichlet algebra A, which can be extended to the Hardy spaces H(m), associated to A and to a representing measure m of A, for 1 ≤ p ≤ ∞. A characterization for the existence of an extension Φp of Φ to L(m) is given in the terms of a semispectral measure FΦ of Φ. For the case when the closure in L(m) of the kernel in A of m is a s...

In a former paper, the algorithm NextClosures for computing the set of all formal concepts as well as the canonical base for a given formal context has been introduced. Here, this algorithm shall be generalized to a setting where the data-set is described by means of a closure operator in a complete lattice, and furthermore it shall be extended with the possibility to handle constraints that ar...

We define the notion of rational closure in the context of Description Logics extended with a tipicality operator. We start from ALC +T, an extension of ALC with a typicality operator T : intuitively allowing to express concepts of the form T(C), meant to select the “most normal” instances of a concept C. The semantics we consider is based on rational model. But we further restrict the semantic...

Gap-deenability and the gap-closure operator were deened in FFK91]. Few complexity classes were known at that time to be gap-deenable. In this paper, we give simple characterizations of both gap-deenability and the gap-closure operator, and we show that many complexity classes are gap-deenable, including P #P , P #P1] , PSPACE, EXP, NEXP, MP, and BP P. If a class is closed under union, intersec...

In this note, we study the lattice structure on the class of all weak hyper K-ideals of a hyper K-algebra. We first introduce the notion of (left,right) scalar in a hyper K-algebra which help us to characterize the weak hyper K-ideals generated by a subset. In the sequel, using the notion of a closure operator, we study the lattice of all weak hyper K-ideals of ahyper K-algebra, and we prove a ...

Triadic Formal Concept Analysis (3FCA) was introduced by Lehman and Wille almost two decades ago. And many researchers work in Data Mining and Formal Concept Analysis using the notions of closed sets, Galois and closure operators, closure systems, but up-to-date even though that different researchers actively work on mining triadic and n-ary relations, a proper closure operator for enumeration ...