The aim of this paper is to give a survey of some basic theory of semi-infinite programming. In particular, we discuss various approaches to derivations of duality, discretization, and first and second order optimality conditions. Some of the surveyed results are well known while others seem to be less noticed in that area of research.

In recent years a number of conditions has been established that a monoid must necessarily satisfy if it is to have a presentation through some nite convergent string-rewriting system. Here we give a survey on this development, explaining these necessary conditions in detail and describing the relationships between them.

Evaluation of Top-k Queries over Structured and Semi-structured Data

It is shown that the following classes have measure 0 in E: the class of P-selective sets, the class of P-multiselective sets, the class of cheatable sets, the class of easily countable sets, the class of easily approximable sets, the class of near-testable sets, the class of nearly near-testable sets, the class of sets that are not P-bi-immune. These are corollaries of a more general result st...

We establish a general weak* lower semicontinuity result in the space BD(Ω) of functions of bounded deformation for functionals of the form

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.

In this paper, we concern with SLLN for sums of independent random upper-semicontinuous fuzzy sets. We first give a generalization of SLLN for sums of independent and level-wise identically distributed random fuzzy sets, and establish a SLLN for sums of random fuzzy sets which is independent and compactly uniformly integrable in the strong sense. As a result, a SLLN for sums of independent and ...

In this paper we study a metric Hopf-Lax formula looking in particular at the Carnot-Carathéodory case. We generalize many properties of the classical euclidean Hopf-Lax formula and we use it in order to get existence results for Hamilton-Jacobi-Cauchy problems satisfying a suitable Hörmander condition.

A lower semicontinuity result is proved in the space of special functions of bounded deformation for a fracture energetic model ∫ Ju Ψ([u], νu)dH , [u] · νu ≥ 0 H − a. e. on Ju. A characterization of the energy density Ψ, which ensures lower semicontinuity, is also given.