Modeled on the Gauss measure, the authors introduce the locally doubling measure metric space X, d, μ ρ, which means that the set X is endowed with a metric d and a locally doubling regular Borel measure μ satisfying doubling and reverse doubling conditions on admissible balls defined via the metric d and certain admissible function ρ. The authors then construct an approximation of the identity...

The main result of the present article is a (practically optimal) criterium for the pseudoeffectivity of the twisted relative canonical bundles of surjective projective maps. Our theorem has several applications in algebraic geometry; to start with, we obtain the natural analytic generalization of some semipositivity results due to E. Viehweg and F. Campana. As a byproduct, we give a simple and...

Based on a set of case studies in eight European countries a method of software evaluation has been designed within ESPRIT Project SCOPE (Software evaluation and certification programme Europe). This method deals with several types of information: software characteristics and metrics, product and process information, and evaluation techniques. In order to be applicable the method is supported b...

In this work a complete problem for an unambiguous logspace class is presented. This is surprising since unambiguity is a `promise' or`semantic' concept. These usually lead to classes apparently without complete problems.

We d escribe new methods for the e s t imation of the b o u nds of the coeecients of proper divisors of integer polynomials in one v ariable. There exist classes of poly-nomials for which our estimates are better than those obtained using t he polynomial measure or the 2-weighted norm.

We consider the problem of derandomizing random walks in the Euclidean space R. We show that for k = 2, and in some cases in higher dimensions, such walks can be simulated in Logspace using only poly-logarithmically many truly random bits. As a corollary, we show that the random walk can be deterministically simulated in space O(logn √ log log n), where 1/n is the desired precision of the simul...

In 1957 W.M. Hirsch conjectured that every d-polytope with n facets has edge-diameter at most n ? d. Recently Holt and Klee constructed polytopes which meet this bound for a number of (d; n) pairs with d 13 and for all pairs (14; n). These constructions involve a judicious use of truncation, wedging, and blending on polytopes which already meet the Hirsch bound. In this paper we extend these te...

In this paper we discuss the problem of determining a meeting point of a set of scattered robots R = {r1, r2, . . . , rs} in a weighted terrain P which has n > s triangular faces. Our algorithmic approach is to produce a discretization of P by producing a graph G = {V , E} which lies on the surface of P . For a chosen vertex p ∈ V , we define ‖Π(ri, p)‖ as the minimum weight cost of traveling f...