The concept of antipodality relative to a closed convex cone K ⊂ Rd has been explored in detail in a recent work of ours. The antipodality problem consists of finding a pair of unit vectors in K achieving the maximal angle of the cone. Our attention now is focused not just in the maximal angle, but in the angular spectrum of the cone. By definition, the angular spectrum of a cone is the set of ...

A closed convex cone K is called nice, if the set K∗ + F⊥ is closed for all F faces of K, where K∗ is the dual cone of K, and F⊥ is the orthogonal complement of the linear span of F. The niceness property plays a role in the facial reduction algorithm of Borwein and Wolkowicz, and the question whether the linear image of a nice cone is closed also has a simple answer. We prove several character...

This paper develops inferential theory for hypothesis testing under general convex cone alternatives for correlated data. Often, interest lies in detecting order among treatment effects, while simultaneously modeling relationships with regression parameters. Incorporating shape or order restrictions in the modeling framework improves the efficiency of statistical methods. While there exists ext...

A symmetric matrix S is copositive if yT S y≥0 for all y≥0, and the set of all copositive matrices, denoted C∗, is a closed, pointed, convex cone; see [25] for a recent survey. Researchers have realized how to model many NP-hard optimization problems as copositive programs, that is, programs over C∗ for which the objective and all other constraints are linear [7, 9, 13, 16, 32–34]. This makes c...

In this paper we consider a partial overdetermined mixed boundary value problem in domains inside cone as [18]. We show that, cones having an isoperimetric property, the only which admit solution and minimize torsional energy functional are spherical sectors centered at vertex of cone. also that close C1,1 -metric to one isoperimetric, generalizing so result [1]. This is achieved by using chara...

Absact This paper deals with the study of test sets of the knapsack problem and simultaneous diophantine approximation. The Graver test set of the knapsack problem can be derived from minimal integral solutions of linear diophantine equations. We present best possible inequalities that must be satisfied by all minimal integral solutions of a linear diophantine equation and prove that for the co...

Let B1, B2 be balls in finite-dimensional real vector spaces E1, E2, centered around unit length vectors v1, v2 and not containing zero. An element in the tensor product space E1 ⊗ E2 is called B1 ⊗B2-separable if it is contained in the convex conic hull of elements of the form w1 ⊗w2, where w1 ∈ B1, w2 ∈ B2. We study the cone formed by the separable elements in E1⊗E2. We determine the largest ...

The cone of lower semicontinuous traces is studied with a view to its use as an invariant. Its properties include compactness, Hausdorffness, and continuity with respect to inductive limits. A suitable notion of dual cone is given. The cone of lower semicontinuous 2-quasitraces on a (non-exact) C*-algebra is considered as well. These results are applied to the study of the Cuntz semigroup. It i...

The convex cone of n × n completely positive (CPP) matrices and its dual cone of copositive matrices arise in several areas of applied mathematics, including optimization. Every CPP matrix is doubly nonnegative (DNN), i.e., positive semidefinite and component-wise nonnegative, and it is known that, for n ≤ 4 only, every DNN matrix is CPP. In this paper, we investigate the difference between 5×5...