Quaestiones Mathematicae 

Abstract: A graph G is well-covered (or w-c) if every maximal independent set of points in G is also maximum. Clearly, this is equivalent to the property that the greedy algorithm for constructing a maximal independent set always results in a maximum independent set. Although the problem of independence number is well-known to be NP-complete, it is trivially polynomial for well-covered graphs. The concept of well-coveredness was introduced by the author in [P1] and was first discussed therein with respect to its relationship to a number of other properties involving the independence number. Since then, a number of results about well-covered graphs have been obtained. It is our purpose in this paper to survey these results for the first time. As the reader will see, many of the results we will discuss are quite recent and have not as yet appeared in print.

Abstract: In this paper we take convergence of stratified L-filters as primitive notion and construct in this way a cartesian closed category, which contains the category of stratified L-topological spaces as reflective subcategory. The class of spaces with non-idempotent stratified fuzzy interior operator is characterized as subclass of the class of our stratified L-fuzzy convergence spaces and a first characterization, which fuzzy convergences stem from stratified L-topologies is established.

Abstract: In this paper, we have used the homotopy analysis method (HAM) to obtain approximate solution of fractional integro-differential equations (FIDEs). Convergence of HAM is considered for this kind of equations. Also some examples are given to illustrate the high efficiency and precision of HAM. Keywords: Fractional integro-differential equation, homotopy analysis method, convergence control parameter Quaestiones Mathematicae 36(2013), 93–105

Abstract: A new set of orthogonal polynomials is found that are solutions to a sixth order formally self adjoint differential equation. These polynomials are shown to generalize the Legendre and Legendre type polynomials. We also show that these polynomials satisfy many properties shared by the classical orthogonal polynomials of Jacobi, Laguerre and Hermite.

Abstract: This paper sets forth in detail point-set lattice-theoretic or poslat foundations of all mathematical and fuzzy set disciplines in which the operations of taking the image and pre-image of (fuzzy) subsets play a fundamental role; such disciplines include algebra, measure and probability theory, and topology. In particular, those aspects of fuzzy sets, hinging around (crisp) powersets of fuzzy subsets and around powerset operators between such powersets lifted from ordinary functions between the underlying base sets, are examined and characterized using point-set and lattice-theoretic methods. The basic goal is to uniquely derive the powerset operators and not simply stipulate them, and in doing this we explicitly distinguish between the “fixed-basis” case (where the underlying lattice of membership values is fixed for the sets in question) and the “variable-basis” case (where the underlying lattice of membership values is allowed to change). Applications to fuzzy sets/logic include: development a...