Some results on vector bundle monomorphisms

In this paper we use the singularity method of Koschorke [2] to study the question of how many different nonstable homotopy classes of monomorphisms of vector bundles lie in a stable class and the percentage of stable monomorphisms which are not homotopic to stabilized nonstable monomorphisms. Particular attention is paid to tangent vector fields. This work complements some results of Koschorke [3; 4], Libardi-Rossini [7] and Libardi-do Nascimento-Rossini [6].

Procedimiento de refutación para un conjunto de restricciones sobre documentos XML

We present a prototype that implements a set of logical rules to prove the satis ability for a class of speci cations on XML documents. Speci cations are given by means of constraints built on Boolean XPath patterns. The main goal of this tool is to test if a given speci cation is satis able or not, showing the history of the execution. It can also be used to test if a given document is a model of a given speci cation and, as a subproduct, it allows to look for all the relations (monomorphisms) between two patterns or the result of doing some operations by combining patterns in di erent ways. The results of these operations are visually shown and therefore the tool makes these operations more understandable. The implementation of the algorithm has been written in Prolog but the prototype has a Java interface for an easy and friendly use.

The first group (co)homology of a group G with coefficients in some G-modules

Let G be a group. We give some formulas for the first group homology and cohomology of a group G with coefficients in an arbitrary G-module (Z) over tilde. More explicit calculations are done in the special cases of free groups, abelian groups and nilpotent groups. We also perform calculations for certain G-module M, by reducing it to the case where the coefficient is a G-module (Z) over tilde. As a result of the well known equalities H-1(X, M) = H-1(pi(1)(X), M) and H-1(X, M) = H-1(pi(1) (X), M), for any G-module M, we are able to calculate the first homology and cohomology groups of topological spaces with certain local system of coefficients.

Characterization of esterases in a Brazilian population of Zaprionus indianus (Diptera : Drosophilidae)

The aim of this study was to characterize esterases in Zaprionus indianus, a drosophilid recently introduced into Brazil. A further aim was study the variation of activity of esterases in the presence of inhibitors and their expression according to sex, sexual activity and age of individual flies. Polymorphisms were detected in two esterase loci (Est-2 and Est-3) and monomorphisms in four others (Est-1, Est-4, Est-5 and Est-6). Biochemical tests using alpha- and beta-naphthyl acetate and the inhibitors malathion, eserine sulphate and PMSF allowed us to classify EST-2 and EST-5 as beta-esterases, both carboxyl-esterases, and EST-1, EST-3, EST-4 and EST-6 as alpha-esterases. EST-1 and EST-3 were classified as carboxyl-esterases and EST-4 and EST-6 as cholinesterases. EST-5 activity was more pronounced in males and EST-2 was restricted to them or to recently copulated females. EST-4, rarely detected, was not characterized. Based on their biochemical characteristics possible roles for these enzymes are suggested.