Fertilization cones

Indecomposable Cones

We study some relations between a reproducing cone K in a linear space V over a fully ordered field F and the cone I(K) in Hom( V, V) consisting of all operators A such that AK G K. In particular, indecomposable cones are considered.

Algebraic Cones

A characterization of algebraic cones in terms of actions of the onedimensional multiplicative algebraic monoid Mm and the algebraic group Gm are given. This note answers a question of K. Adjamagbo asked in [A]. Below all algebraic varieties are taken over an algebraically closed field k. An irreducible algebraic variety X is called a cone if X is affine and its coordinate algebra k[X ] admits ...

Fertilization.

Rough convex cones and rough convex fuzzy cones

Based on the equivalence relation on a linear space, in this paper we introduce the definition of rough convex cones and rough convex fuzzy cones and discuss some of the fundamental properties of such rough convex cones.

Relating Homogeneous Cones and Positive Definite Cones via T-Algebras

T -algebras are nonassociative algebras defined by Vinberg in the early 1960s for the purpose of studying homogeneous cones. Vinberg defined a cone K(A) for each T -algebra A and proved that every homogeneous cone is isomorphic to one such K(A). We relate each T -algebra A with a space of linear operators in such a way that K(A) is isomorphic to the cone of positive definite self-adjoint operat...