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.     

Inclusion compounds of N,N,N′,N′-tetraisopropylfumaride with isomers of methyl phenol and water

The crystal structures and thermal analyses of the host compound, N,N,N,N-tetraisopropylfumaride, witho-cresol,m-cresol and water are reported and compared to that of thep-cresol complex previously reported in an attempt to elucidate the reasons for host selectivity.     

Conditional functional equations and orthogonal additivity

Summary Some examples of classes of conditional equations coming from information theory, geometry and from the social and behavioral sciences are presented. Then the classical case of the Cauchy equation on a restricted domain is extensively discussed. Some results concerning the extension of local homomorphisms and the implication -additivity implies global additivity are illustrated. Problems concerning the equations[cf(x + y) – af(x) – bf(y) – d][f(x + y) – f(x – f(y)] = 0[g(x + y) – g(x) – g(y)][f(x + y) – f(x) – f(y)] = 0f(x + y) – f(x) – f(y) V (a suitable subset of the range) are presented.The consideration of the conditional Cauchy equation is subsequently focused on the case when it makes sense to interpret as a binary relation (orthogonality):f: (X, +, ) (Y, +);f(x + z) = f(x) + f(z) (x, z Z; x z). A brief sketch on solutions under regularity conditions is given. It is then shown that all regularity conditions can be removed. Finally, several applications (also to physics and to the actuarial sciences) are discussed. In all these cases the attention is focused on open problems and possible extensions of previous results.