The main aim of this paper is to deal with a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the fuzzy linear programming and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. Keywords Farkas Lemma, Fuzzy Linear Programming, Duality, Ranking Functions.

In this paper, we establish weak and strong duality theorems for a pair of multiobjective symmetric dual problems. This removes several omissions in the paper "Symmetric and self duality in vector optimization problem, Applied Mathematics and Computation 183 (2006) 1121-1126".

in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

A new notion of higher-order weakly generalized adjacent epiderivative for a set-valued map is introduced. By virtue of the epiderivative and weak minimality, a higher-order Mond-Weir type dual problem and a higher-order Wolfe type dual problem are introduced for a constrained setvalued optimization problem, respectively. Then, corresponding weak duality, strong duality and converse duality the...

We shall address from a conceptual perspective the duality between algebra and geometry in framework of refoundation algebraic associated to Grothendieck’s theory schemes. To do so, we revisit scheme standpoint provided by problem recovering mathematical structure A its representations $$A \rightarrow B$$ into other similar structures B. This vantage point will allow us analyze relationship alg...

hairball in a urethral diverticulum has rarely been reported. these hairballs are usually formed in the diverticulum coated with a hair bearing epithelium and can lead to urinary obstruction or infection. using laser is a safe way to ablate such stones.

Gabriel Taubin Brown University Holly Rushmeier, who’s served as associate editor in chief (AEIC) for special issues since 2007, has recently been appointed co-editor in chief of Eurographics’ Computer Graphics Forum, effective May 2010. Owing to her increased responsibilities and numerous other commitments, Holly has decided she’ll be unable to continue serving effectively in her current CG&A ...

Unlike the uniform completion, the Dedekind completion of a vector lattice is not functorial. In order to repair the lack of functoriality of Dedekind completions, we enrich the signature of vector lattices with a proximity relation, thus arriving at the category pdv of proximity Dedekind vector lattices. We prove that the Dedekind completion induces a functor from the category bav of bounded a...

Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...