We characterise equality cases in matrix H¨older’s inequality and develop a divergence formulation of optimal transport vector measures. As an application, we reprove the representation formula for measures polar cone to monotone maps. generalise last result wide class of cones, including cones tangent unit ball space differentiable functions Sobolev spaces.

The nonadiabatic photodynamics of the all-trans-2,4-pentadiene-iminium cation (protonated Schiff base 3, PSB3) and the all-trans-3-methyl-2,4-pentadiene-iminium cation (MePSB3) were investigated in the gas phase and in polar (aqueous) and nonpolar (n-hexane) solutions by means of surface hopping using a multireference configuration-interaction (MRCI) quantum mechanical/molecular mechanics (QM/M...

We present two different descriptions of positive partially transposed (PPT) states. One is based on the theory of positive maps while the second description provides a characterization of PPT states in terms of Hilbert space vectors. Our note is based on our previous results presented in [22], [18], and [20]. 1 Definitions and notations In Quantum Computing a characterization of states with po...

For a smooth projective variety, Kleiman’s criterion for ample divisors states that the closed ample cone (i.e., the nef cone) is dual to the closed cone of effective curves. Since the work of Mori, it has been clear that extremal rays of the cone of effective curves play a special role in birational geometry. These correspond to certain distinguished supporting hyperplanes of the nef cone whic...

We devise a method for proving inequalities on submodular functions, with a term rewriting flavour. Our method comprises of the following steps: (1) start with a linear combination X of the values of the function; (2) define a set of simplification rules; (3) conclude that X ≥ Y , where Y is a linear combination of a small number of terms which cannot be simplified further; (4) calculate the co...

Algorithms are presented for evaluating gradients and Hessians of logarithmic barrier functions for two types of convex cones: the cone of positive semidefinite matrices with a given sparsity pattern, and its dual cone, the cone of sparse matrices with the same pattern that have a positive semidefinite completion. Efficient large-scale algorithms for evaluating these barriers and their derivati...

Almost a century ago Voronoi [1908] formulated his fundamental algorithm to find the perfect (real positive definite quadratic) forms in n variables. Among these one finds the forms representing the locally extreme lattice packings of spheres. The subject was taken up by M. Koecher [1960], who gave an axiomatic treatment of self-dual cones and a corresponding Voronoi algorithm in this situation...

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 correspon...

A sectorial matrix is an n×n whose numerical range contained in open half-plane, and such matrices have many nice properties. In particular, the subset of strictly accretive a convex cone space matrices, results related to positive definite recently been generalized this cone. Moreover, used define phases matrix, these can be angularly bound eigenvalues by majorization-type inequalities similar...

In this paper we introduce a primal-dual affine scaling method. The method uses a search-direction obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions (Jansen et al., 1993; Monteiro et al., 1990), nor does it fit in the generic primal-dual method (Kojima et al., 1989). The new method ...