It is well known that the quantum mutual information and its conditional version do not increase under local channels. I this paper we show recently established lower semicontinuity of implies (in fact, equivalent to) loss (conditional) channels considered as a function on Cartesian product set all states composite system sets (equipped with strong convergence). Some applications property are c...

This paper is concerned with solvability and solution stability of parametric generalized equations governed by set-valued mappings. By a degree-theoretic approach for multifunctions, some new results on lower semicontinuity of the solution map to a parametric generalized equation are established.

We propose a very weak type of generalized distance called weak τ -function and use it to weaken the assumptions about lower semicontinuity in existing formulations of Ekeland’s variational principle for a kind of minimizers of a set-valued mapping, which is different from the Pareto minimizer, and in recent results which are equivalent to Ekeland’s variational principle.

We derive sharp necessary conditions for weak sequential lower semicontinuity of integral functionals on Sobolev spaces, with an integrand which only depends on the gradient of a scalar eld over a domain in R . An emphasis is put on domains with in nite measure, and the integrand is allowed to assume the value +∞.

We examine the validity of the zero duality gap properties for two important dual schemes: a generalized augmented Lagrangian dual scheme and a nonlinear Lagrangetype dual scheme. The necessary and sufficient conditions for the zero duality gap property to hold are established in terms of the lower semicontinuity of the perturbation functions.

Multi-objective (vector) combinatorial problem of finding the Pareto set with four kinds of non-linear partial criteria is considered. Necessary and sufficient conditions of that kind of stability of the problem (quasi-stability) are obtained. The problem is a discrete analogue of the lower semicontinuity by Hausdorff of the optimal mapping. Mathematics Subject Classification 2000: 90C10, 90C05...

We show that the limit f of a weakly convergent sequence of W 1,1 homeomorphisms fj with finite distortion has finite distortion as well, provided that it is a homeomorphism. Moreover, the lower semicontinuity of the distortions is deduced both in case of outer and inner distortion.