In this paper,  fuzzy convergence theory in the framework of $L$-convex spaces is introduced. Firstly, the concept of $L$-convex remote-neighborhood spaces is introduced and it is shown that the  resulting category is isomorphic to that of $L$-convex spaces. Secondly, by means of $L$-convex ideals, the notion of $L$-convergence spaces is introduced and it is proved that the  category of $L$-con...

In this paper, we define a kind of lattice-valued convergence spaces based on the notion of $top$-filters, namely $top$-convergence spaces, and show the category of $top$-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete $MV$-algebra, a close relation between the category of$top$-convergence spaces and that of strong $L$-topological spaces is establish...

A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given. Afterwards, several applications are presented. First a global construction of monotonic and/or convex generalized splines interpolating monotonic and/or co...

Hybrid systems with memory refer to dynamical systems exhibiting both hybrid and delay phenomena. While systems of this type are frequently encountered in many physical and engineering systems, particularly in control applications, various issues centered around the robustness of hybrid delay systems have not been adequately dealt with. In this paper, we establish some basic results on a framew...

In this paper we present a Multi-Element generalized Polynomial Chaos (MEgPC) method to deal with stochastic inputs with arbitrary probability measures. Based on the decomposition of the random space of the stochastic inputs, we construct numerically a set of orthogonal polynomials with respect to a conditional probability density function (PDF) in each element and subsequently implement genera...

Let V be an l−dimensional real vector space. A subspace arrangement A is a finite collection of affine subspaces in V . There is no assumption on the dimension of the elements of A. Let M(A) = V −∪A∈AA be the complement of A. A method of calculating the additive structure of H(M(A)) was given in [G-MP] using stratified Morse theory, proving that H(M(A)) depends only on the set of all intersecti...

In this paper we present an adaptive multi-element generalized polynomial chaos (ME-gPC) method, which can achieve hp-convergence in random space. ME-gPC is based on the decomposition of random space and generalized polynomial chaos (gPC). Using proper numerical schemes to maintain the local orthogonality on-the-fly, we perform gPC locally and adaptively. The key idea is to combine the polynomi...

In this paper, we construct a new iterative scheme by hybrid projection method and prove strong convergence theorems for approximation of a common element of set of common fixed points of an infinite family of asymptotically quasi-φ-nonexpansive mappings, set of solutions to a variational inequality problem and set of common solutions to a system of generalized mixed equilibrium problems in a u...

We consider two-stage stochastic programming problems with integer recourse. The L-shaped method of stochastic linear programming is generalized to these problems by using generalized Benders decomposition. Nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques. Finite convergence of...

We consider stochastic processes fX(t; ) : t 2 Tg with continuous parameter t 2 T = [0;1[. These processes are so called generalized supermartingales, where the generalization comes from a modification of the right side of the supermartingale inequality. The assumptions on the process and the probability space are the same as for the classical convergence theorem of DOOB (see KOPP [2]). The aim...