Dually normal relations on sets

In this paper, the concept of dual normal relations on sets is introduced and generalized. Intrinsic characterizations of them are obtained.     

On Quasi-Hyperideals in Semihypergroups

In this article, we introduce the notion of quasi-hyperideal in semihypergroups, and moreover, we introduce the notions of an (m, n)-quasi-hyper-ideal, n-right hyperideal, and m-left hyperideal in semihypergroups, and relations between them are studied. We obtain different characterizations concerning different properties of (m, n)-quasi-hyperideals, minimal (m, n)-quasi-hyperideals, minimal m-left hyperideals, and minimal n-right hyperideals, and relations between them are investigated. Also, some intersection properties and characterizations of (m, n)-quasi-hyperideals of semihyperideals and regular semihyperideals have been studied. In the sequel, m-left simple, n-right simple, and (m, n)-quasi-simple semihypergroups are defined, and some properties of them are investigated.     

Projection representable relations on Menger (2, n)-semigroups

Abstract characterizations of relations of nonempty intersection, inclusion end equality of domains for partial n-place functions are presented. Representations of Menger (2, n)-semigroups by partial n-place functions closed with respect to these relations are investigated.     

关于L_p球的几个新不等式和性质(英文)

本文研究了L_p球的相关问题.利用对偶混合体积、球面Radon变换和Fourier变换的方法,获得了关于L_p球的几个新不等式和性质,其中一个不等式与著名的最大切片猜想有关.     

Characterizations of set order relations and constrained set optimization problems via oriented distance function

Set-valued optimization problems are important and fascinating field of optimization theory and widely applied to image processing, viability theory, optimal control and mathematical economics. There are two types of criteria of solutions for the set-valued optimization problems: the vector criterion and the set criterion. In this paper, we adopt the set criterion to study the optimality conditions of constrained set-valued optimization problems. We first present some characterizations of various set order relations using the classical oriented distance function without involving the nonempty interior assumption on the ordered cones. Then using the characterizations of set order relations, necessary and sufficient conditions are derived for four types of optimal solutions of constrained set optimization problem with respect to the set order relations. Finally, the image space analysis is employed to study the c-optimal solution of constrained set optimization problems, and then optimality conditions and an alternative result for the constrained set optimization problem are established by the classical oriented distance function.     

On Inner Characterizations of Aõ-Algebras and some Applications to Calkin Algebras and Symmetric Tensor-Algebras

Spacefree characterizations of Aõ-algebras are discussed, and their applications to (unbounded) Calkin algebras and symmetric tensor-algebras are considered. For Calkin algebras, a sufficient condition for being an Aõ-algebra is provided. On symmetric tensor-algebras, Õ-lopologies are constructed and their relations to the well-known topologies are examined.     

Book review of Israel Gohberg,Seymour Goldberg,Marinus A. Kaashoek,Basic Classes of Linear Operators,Birkhäuser Verlag,Basel–Boston–Berlin 2003, 423 p. ISBN 3-7643-6930-2

In projective space three notions of convexity (weak convexity, strong convexity, p-convexity) are regarded systematically. Since these notions are defined only by incidence relations, there can be introduced dual notions. We consider relations.between the introduced notions and the most essential properties of convex sets. To all assertions. can be formulated dual assertions, too. The most important theorems given by Fenchel can be generalised. The property of a point set (a set of hyperplanes) to be strongly convex or p-convex, respectively, is invariant with respect to correlations.     

Terms which are Mal’cev modulo some functions

We derive consequences from the existence of a term which satisfies Mal’cev identities (characterizing permutability) modulo two functions F and G from admissible relations to admissible relations. We also provide characterizations of varieties having a Mal’cev term modulo F and G. Received September 21, 2006; accepted in final form March 20, 2007.     

Comparison between different duals in multiobjective fractional programming

The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.      

Divided-difference equation and three-term recurrence relations of some systems of bivariate q-orthogonal polynomials

Partial divided-difference equations and three-term recurrence relations satisfied by the bivariate Askey–Wilson and the bivariate q-Racah polynomials are computed in this work. By using limiting processes, partial divided (or q)-difference equations and three-term recurrence relations are also provided for each of the following families of orthogonal polynomials: the bivariate continuous dual q-Hahn, the bivariate Al-Salam-Chihara, the bivariate continuous q-Hahn, the bivariate q-Hahn, the bivariate dual q-Hahn, the bivariate q-Krawtchouk, the bivariate q-Meixner, and the bivariate q-Charlier polynomials.