A vectorizable potential energy functional for reactive scattering

Critical steps in trajectory programs for vector restructuring are analysed. The crucial effect of potential energy routine design on the efficiency of trajectory calculations performed on supercomputers have been investigated using a test program for which time consumptions when different algorithms are implemented are compared. Comparisons have been extended to more realistic computational situations by inserting related routines in a trajectory program and calculating reactive properties of some systems of chemical interest.This paper was presented at the International Conference on The Impact of Supercomputers on Chemistry, held at the University of London, London, UK, 13–16 April 1987     

Polysingular integral operators

Summary We study a class of linear singular integral operators of the Cauchy type on the n-torus; an application is given to a boundary value problem for functions of several complex variables.     

Comparative molecular field analysis of CCK-A antagonists using field-fit as an alignment technique. A convenient guide to design new CCK-A ligands

Summary Comparative molecular field analysis (CoMFA) has been used as a three-dimensional quantitative structure-activity relationship (QSAR) method to correlate the affinities of several antagonists towards CCK-A receptors with their steric and electrostatic fields. In this publication, we describe, for the first time, a field-fit operation as an alignment technique. These results could serve as a guide for the design of new non-peptide antagonists.     

Weak differentiability of BV functions on stratified groups

We prove the almost everywhere approximate differentiability of functions with bounded variation in stratified groups and we study their approximate discontinuity set. We introduce functions of bounded higher order variation and obtain a weak version of Alexandroff differentiability theorem in this context. We present a nontrivial class of functions with second order bounded variation, arising from inf-convolution formula of a suitable ``cost' function.     

Multiple-coloured graphs and pseudocomplexes

Riassunto Nel presente lavoro si prova che ogni pseudocomplesso può essere rappresentato da un opportuno grafo con ricoprimento. La costruzione generalizza la rappresentazione di una particolare classe di pseudocomplessi per mezzo di grafi colorati sugli spigoli.

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Work performed under the auspices of the G.N.S.A.G.A. of the C.N.R. (National Research Council of Italy), and within the Project ?Geometria delle varietà differenziabili?, supported by M.P.I.     

The geometric structure of the expected/observed likelihood expansions

Stochastic expansions of likelihood quantities are a basic tool for asymptotic inference. The traditional derivation is through ordinary Taylor expansions, rearranging terms according to their asymptotic order. The resulting expansions are called hereexpected/observed, being expressed in terms of the score vector, the expected information matrix, log likelihood derivatives and their joint moments. Though very convenient for many statistical purposes, expected/observed expansions are not usually written in tensorial form. Recently, within a differential geometric approach to asymptotic statistical calculations, invariant Taylor expansions based on likelihood yokes have been introduced. The resulting formulae are invariant, but the quantities involved are in some respects less convenient for statistical purposes. The aim of this paper is to show that, through an invariant Taylor expansion of the coordinates related to the expected likelihood yoke, expected/observed expansions up to the fourth asymptotic order may be re-obtained from invariant Taylor expansions. This derivation producesinvariant expected/observed expansions.This research was partially supported by the Italian National Research Council grant n.93.00824.CT10.