Given two convex lower semicontinuous extended real valued functions F and h de…ned on locally convex spaces, we provide a dual transcription of the relation

If K is a nonempty compact subset of X and f : X → [−∞,∞] is lower semicontinuous, there is some x0 ∈ K such that f(x0) = infx∈K f(x). A rate function is a function I : X → [0,∞] such that (i) there is some x ∈ X with I(x) <∞ and (ii) for any c ∈ [0,∞], f−1([0, c]) is compact (namely, the sublevel sets of I are compact). Condition (ii) implies that a rate function is lower semicontinuous. For S...

We introduce the concept of optical control of the fluorescence yield of CdSe quantum dots through plasmon-induced structural changes in random semicontinuous nanostructured gold films. We demonstrate that the wavelength- and polarization dependent coupling between quantum dots and the semicontinuous films, and thus the fluorescent emission spectrum, can be controlled and significantly increase...

Two-boundary problems for a random walk with negative geometric jumps are considered, and the corresponding results for a usual semicontinuous random walk are generalized for them. The following results are obtained: the probability distribution of ruin is found and expressed in terms of the lower and upper boundaries; formulas are given for the joint distribution of the infimum, supremum, and ...

This paper is a continuation of [5]. We apply the upper envelope representation method (or the quasilinearization method) in vector lattices developed in [4, 5] to the homogeneous functional calculus of linear and bilinear operators. Explicit formulae for computing φ̂(T1, . . . , TN ) for any finite sequence of regular linear or bilinear operators T1, . . . , TN are derived. For the theory of ve...

We use Green-Riefel machinary to induce representations from a closed subgroupoid crossed product to the groupoid crossed product with a lower semicontinuous bundle of C∗-algebras .

In this paper, we will give a new fixed point theorem for lower semicontinuous multimaps in a Hausdorff topological vector space.

Given a compact topological dynamical system $(X, f)$ with positive entropy and upper semicontinuous map, any closed invariant subset $Y \subset X$ entropy, we show that there exists continuous roof function such the set o

We prove a theorem on the existence of solutions of a second order differential inclusion governed by a class of nonconvex sweeping process with a mixed semicontinuous perturbation.