Say that a cone is a commutative monoid that is in addition conical, i.e., satisfies x+y=0 ⇒ x=y=0. We show that cones (resp. simple cones) of many kinds order-embed or even embed unitarily into refinement cones (resp. simple refinement cones) of the same kind, satisfying in addition various divisibility conditions. We do this in particular for all cones, or for all separative cones, or for all...

in this paper, using clarke’s generalized directional derivative and di-invexity we introduce new concepts of nonsmooth k-α-di-invex and generalized type i univex functions over cones for a nonsmooth vector optimization problem with cone constraints. we obtain some sufficient optimality conditions and mond-weir type duality results under the foresaid generalized invexity and type i cone-univexi...

This study investigates the capacity of neuronal growth cones to synthesize protein locally and independently of their cell body. Isolated growth cones were prepared from cultures of neurons from the snail Helisoma by transecting neurites proximal to the growth cone. The capacity for protein synthesis was tested by radiolabeling cultures with 3H-leucine and analyzing the resultant autoradiogram...

We study the boundary structure of closed convex cones, with a focus on facially dual complete (nice) cones. These cones form a proper subset of facially exposed convex cones, and they behave well in the context of duality theory for convex optimization. Using the wellknown and very commonly used concept of tangent cones in nonlinear optimization, we introduce some new notions for exposure of f...

Relatively few animal species extract seeds from closed conifer cones because of the forces required to spread apart or penetrate the woody scales. Those species that forage on seeds in closed cones tend to forage selectively, and therefore act as selective agents on cone structure. However, little is known about the foraging preferences and thus phenotypic selection that is exerted on conifers...