We complete a description of additive partition entropies. This time we do not assume I to be continous. In the process we solve a 2-cocycle functional equation for certain subsets of convex cones. 1. Introduction. We assume all definitions and results from [3]. In the current follow-up paper we drop the assumption of the continuity of the additve partition entropy. Our aim is to prove a theore...

In this paper we study the boundedness of Bergman projectors on weighted spaces homogeneous Siegel domains Type II. As it appeared to be a natural approach in special case tube over irreducible symmetric cones, such scale mixed-norm Lebesgue spaces. The sharp range for operators is essentially known only Lorentz cones. prove that equivalent variuos notions atomic decomposition, duality, and cha...

A real symmetric tensor is completely positive (CP) if it a sum of powers nonnegative vectors. We propose dehomogenization approach for studying CP tensors. This gives new Moment-SOS relaxations Detection tensors and the linear conic optimization with cones can be solved more efficiently by approach.

Cones with peak sensitivity to light at long (L), medium (M) and short (S) wavelengths are unequal in number on the human retina: S cones are rare (<10%) while increasing in fraction from center to periphery, and the L/M cone proportions are highly variable between individuals. What optical properties of the eye, and statistical properties of natural scenes, might drive this organization? We fo...

The Carathéodory number κ(K) of a pointed closed convex cone K is the minimum among all the κ for which every element of K can be written as a nonnegative linear combination of at most κ elements belonging to extreme rays. Carathéodory’s Theorem gives the bound κ(K) ≤ dimK. In this work we observe that this bound can be sharpened to κ(K) ≤ `K−1, where `K is the length of the longest chain of no...

SeDuMi is an add-on for MATLAB, that lets you solve optimization problems with linear, quadratic and semideeniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved eeciently, by exploiting sparsity. This paper describes how to work with this toolbox. SeDuMi stands for Self-Dual-Minimization: it implements t...