The set of closed convex cones in R (d ≥ 3), with the operations of intersection and closed sum, is a lattice. We determine all endomorphisms of this lattice. As a consequence, we obtain a characterization of the duality of convex cones. MSC 2000: 52A20

Hyperbolicity cones are convex algebraic cones arising from hyperbolic polynomials. A well-understood subclass of hyperbolicity cones is that of spectrahedral cones and it is conjectured that every hyperbolicity cone is spectrahedral. In this paper we prove a weaker version of this conjecture by showing that every smooth hyperbolicity cone is the linear projection of a spectrahedral cone, that ...

assume that $mathbb{d}$ is the open unit disk. applying ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{g}(alpha)$ and $mathcal{f}(mu)$ as follows begin{equation*}  mathcal{g}(alpha):=left{fin mathcal{a}:mathfrak{re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right)

in this paper, a local approach to the concept of hudetz $g$-entropy is presented. the introduced concept is stated in terms of hudetz $g$-entropy. this representation is based on the concept of $g$-ergodic decomposition which is a result of the choquet's representation theorem for compact convex metrizable subsets of locally convex spaces.