We give explicit polynomial-sized (in n and k) semidefinite representations of the hyperbolicity cones associated with the elementary symmetric polynomials of degree k in n variables. These convex cones form a family of non-polyhedral outer approximations of the non-negative orthant that preserve low-dimensional faces while successively discarding high-dimensional faces. More generally we const...

In the present paper, a newly combined higher-order non-differentiable symmetric duality in scalar-objective programming over arbitrary cones is formulated. literature we have discussed primal-dual results with cones, while this article, derived result one model cones. The theorems of are for these problems under ?-pseudoinvexity/?-invexity/C-pseudoconvexity/C-convexity speculations

In many retinal diseases, the malfunction that results in photoreceptor loss occurs only in either rods or cones, but degeneration can progress from the affected cell type to its healthy neighbors. Specifically, in human and mouse models of Retinitis Pigmentosa the loss of rods results in the death of neighboring healthy cones. Significantly less is known about cone-initiated degenerations and ...

Several studies have indicated that the rainbow trout (Oncorhynchus mykiss) loses ultraviolet (UV) sensitivity and the associated UV-sensitive corner cones when the animal transforms from a small (parr) juvenile to a larger, silver-coloured, smolt. Similar changes supposedly take place when parr juveniles are treated with thyroid hormone (T(4)) or retinoic acid. In contrast to previous investig...

Background:Antioxidant effects of cypress cones extract have been previously demonstrated. In this study, the protective effect of cypress cones extract was investigated. Gentamicin, an aminoglycoside antibiotic administrated for the treatment of gram-negative bacteria infections, was used for nephrotoxicity induction. Methods: In this study, 60 wistar male ra...

Abstract For nonconvex set optimization problems based on the less order relation, this paper presents characterizations of optimal sets and gives necessary conditions for inequalities non-optimal using directional derivatives. specific cones, derivatives known functionals describing negative cones are also given.