In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of Type-2 Theory of Effectivity. This gives rise to a natural representation of the set M(X) of Borel probability measures on X. We compare this representation to a canonically constructed representation which encodes a Borel pro...

We deal with a family of functionals depending on curvatures and we prove for them compactness and semicontinuity properties in the class of closed and bounded sets which satisfy a uniform exterior and interior sphere condition. We apply the results to state an existence theorem for the Nitzberg and Mumford problem under this additional constraint. Ref. S.I.S.S.A. 85/99/M (July 99)

For every finite nonnegative measure ft we introduce the Sobolev spaces W^'(Q,K) and we study the lower semicontinuity of functionals of the form where the integrand / is quasiconvex.

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