the big eye kilka, clupeonella grimmi, is a marine fish living in depth of 20 to 200 meter of the caspian sea. its eye and retina were processed for histological and sem studies. paraffin embedded retina was cut radially and tangentially in 5 ?m thickness and stained with hematoxylin and eosin method. the unstained sections were manipulated for sem image observations. tangential retinal section...

For a closed cone C in Rn, the completely positive cone of C is the convex cone K in Sn generated by {uuT : u ∈ C}. Completely positive cones arise, for example, in the conic LP reformulation of a nonconvex quadratic minimization problem over an arbitrary set with linear and binary constraints. Motivated by the useful and desirable properties of the nonnegative orthant and the positive semidefi...

We describe a Jordan-algebraic version of results related to convexity of images of quadratic mappings as well as related results on exactness of symmetric relaxations of certain classes of nonconvex optimization problems. The exactness of relaxations is proved based on rank estimates. Our approach provides a unifying viewpoint on a large number of classical results related to cones of Hermitia...

In this paper we construct two approximation hierarchies for the completely positive cone based on symmetric tensors. We show that one hierarchy corresponds to dual cones of a known polyhedral approximation hierarchy for the copositive cone, and the other hierarchy corresponds to dual cones of a known semidefinite approximation hierarchy for the copositive cone. As an application, we consider a...