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.     

Catalysis of ascorbic acid oxidation with peroxynitrite by biomimetic Cu -complexes

Different mononuclear and dinuclear Cu complexes show high catalytic activity at concentrations 1-10 mM in the oxidation of ascorbic acid by peroxynitrite. Their activity is similar to the activity of Mn-porphyrin complexes and weakly depends on ligand environment, provided at least one free coordination site is available. The proposed reaction mechanism involves the intermediate formation of a copper-peroxynitrito complex, which reacts directly with ascorbic acid.     

The geometry of thermodynamic potentials

In this paper, the performance of a diagrammatic method based on geometric and algebraic considerations is illustrated. This method, based on the particular symmetry of a thermodynamic diagram, allows to obtain the most important thermodynamic expressions of a simple system. In fact, these thermodynamic expressions can be developed with the application of various geometric patterns to the proposed diagram. The particular symmetry of the thermodynamic diagram allows to develop a matrix formulation of the different geometric patterns. This matrix formalism requires that the thermodynamic parameters of the diagram be recast in a vectorial form.On sabbatical leave from November 1995 until October 1996. Address during this period: Centro de Quimica Fisica Molecular, Univerdade Técnica de Lisboa, IST, Av. Rovisco Pais, 1096 Lisboa-Codex, Portugal.     

Photoactive Eu(III) and Tb(III) complexes of calix[4]arenes with pyridine-N-oxide pendant groups

Two calix[4]arenes with four 2-pyridyhnethyl-l-oxide pendant groups at the lower rim have been synthesized, and their Tb(III) and Eu(III) complexes are fluorescent upon UV light excitation at 312 nm. The complexes are not stable in aqueous solution, completely losing their luminescent properties.