Su un legame tra metriche di un dominio fattoriale e del suo campo delle frazioni

We introduce in a U. F. D.,A, and in its quotient fieldK two metricsd and \(\bar d\) connected to the (p)-adic topology onA and its extension toK; we prove that: \(\bar d\left( {\frac{x}{y},\frac{{x'}}{{y'}}} \right) = \inf \left( {\frac{{d(xy',yx')}}{{2d(yy',0)}},1} \right)\) .     

Vanishing and cocentralizing generalized derivations on Lie ideals

Let R be a prime ring of characteristic different from 2, U its right Utumi quotient ring, C its extended centroid and L a not central Lie ideal of R. Suppose that F, G and H are generalized derivations of R, with F≠0, such that F(G(x)x?xH(x)) = 0, for any x∈L. In this paper we describe all possible forms of F, G and H.     

Differential Inclusions and Monotonicity Conditions for Nonsmooth Lyapunov Functions

In this paper we address the problem of characterizing the infinitesimal properties of functions which are nonincreasing along all the trajectories of a differential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous differential inclusions. Moreover, we show that the same criterion applies also in the case of Lipschitz continuous functions and continuous differential inclusions.     

On the capacity of boolean graph formulæ

In a recent paper we have solved several well-known combinatorial problems treating them as special cases of our generalization of Shannon's notion of graph capacity. We present a new simple formalism to deal with all such problems in a unified manner, considering graphs or families of graphs as special formulæ the variables of which are pairs of vertices of their common vertex sets. In all of these problems, the maximum size of a set ofn-length sequences from a fixed alphabet is to be determined under various restrictions on the element pairs present in the same coordinate of any two sequences from the set. For sufficiently homogeneous formulæ capacity becomes computable.New applications include generalizations of our result on the maximum number of pairwise qualitatively independentk-partitions of ann-set from independence to various forms of qualitative dependence.Work partially supported by the Italian Ministry of the University and Scientific Research, Project: Algoritmi, Modelli di Calcolo e Strutture Informative.     

Gaussian Limiting Behavior of the Rescaled Solution to the Linear Korteweg–de Vries Equation with Random Initial Conditions

We analyze the asymptotic behavior of the rescaled solution to the linear Korteweg–de Vries equation when the initial conditions are supposed to be random and weakly dependent. By means of the method of moments we prove the Gaussianity of the limiting process and we present its correlation function. The same technique is applied to the analysis of another third-order heat-type equation.     

Reduced data acquisition time in multi-dimensional NMR spectroscopy using multiple-coil probes

A new hardware-based approach is presented to reduce data acquisition times in multi-dimensional NMR spectroscopy using a multiple-coil probe. Using a four-coil setup, two-dimensional COSY and TOCSY spectra were acquired in one-quarter the time of conventional spectra by simultaneous acquisition of different effective t1 evolution times for each coil. Data processing consists of simple phase-shifting and intensity normalization of the individual data sets, and results in spectra almost identical to those acquired in a conventional manner. This method can potentially be integrated with other new data acquisition and processing schemes for further increases in data acquisition speed.     

Tuning iridium(III) phenylpyridine complexes in the "almost blue" region

We report on the synthesis and photophysical properties of blue emitting iridium(iii) complexes. The use of a negatively charged ligand, such as a triazolyl pyridine, allows a facile preparation, maintaining the high energy emission (blue region) of heteroleptic complexes. We discuss the role played by electron withdrawing substituents of a different nature and also how the substitution position of the same group influences the spectroscopical behaviour.