Regularity results for positive solutions of a semilinear elliptic system

Let , N≧3 be an open set. In this paper we study weak positive solutions of the following semilinear system where p≧1, q≧1, with pq>1, and u∈L^q(Ω), v∈L^p(Ω), and we give in particular some regularity results. Furthermore, we give some applications to the biharmonic equation. Entrata in Redazione il 25 febbraio 1999.     

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.     

Bessel functions of third order and the distribution of cyclic planar motions with three directions

The exact distribution of a cyclic planar motion with three directions is explicitly derived in terms of Bessel functions of order three (suitably combined). The absolutely continuous part of the distribution is proved to satisfy suitable boundary conditions and some of its properties are analyzed. The transformations converting the governing equations of order three is presented and its solutions (used here) derived by applying the Frobenius method.     

Formula di Cauchy (n+1)-dimensionale per le funzioni analitiche din variabili complesse

Ad Andreas Speiser nel suo 60^o compleanno. Anmerkung der Redaktion. Die vorliegende Arbeit war für die Festschrift Andreas Speiser, Orell Füssli, 1945, berechnet. Wegen versp?tetem Eintreffen konnte sie leider nicht mehr in diese aufgenommen werden.     

Reactivity of lithium 2,3-dihydro-1-benzothiophene-1-oxide toward aldehydes and imines and DFT calculations

The sulfinyl carbanion derived from 2,3-dihydro-1-benzothiophene-1-oxide and its lithium salt has been investigated by DFT calculations. The lithium carbanion was treated with aldehydes and imines to give chiral hydroxy and amino derivatives, with high stereoselectivity at the carbon α to the sulfoxide group (trans diastereoisomers), but with low diastereoselectivity at the hydroxyl or amine group. DFT calculations were used to rationalize the different stereochemical behavior of cyclic and acyclic lithiated sulfoxides in the reaction with aldehydes and azomethines.     

Formation of cerium titanate,CeTi<Subscript>2</Subscript>O<Subscript>6</Subscript>, in sol–gel films studied by XRD and FAR infrared spectroscopy

The process of formation of cerium titanate films as a function of annealing temperature and composition has been studied by combining X-ray diffraction analysis and far infrared spectroscopy. The films have been prepared by a sol–gel synthesis using metal chlorides as precursors; the synthesis allows obtaining cerium titanate films upon annealing in air. A brannerite type, CeTi₂O₆, phase has been identified by X-ray diffraction and Rietveld analysis on thin films. CeTi₂O₆ is formed upon annealing at 700 °C and in a limited range of ceria-titania mixed compositions. The far infrared spectra are useful to observe the formation of crystalline phases at the beginning of the crystallization process at lower firing temperatures, when the XRD analysis is not enough sensitive.     

The Influence of Accelerator Science on Physics Research

We evaluate accelerator science in the context of its contributions to the physics community. We address the problem of quantifying these contributions and present a scheme for a numerical evaluation of them. We show by using a statistical sample of important developments in modern physics that accelerator science has influenced 28% of post-1938 physicists and also 28% of post-1938 physics research. We also examine how the influence of accelerator science has evolved over time, and show that on average it has contributed to a physics Nobel Prize-winning research every 2.9 years.     

Polymers with spatial or topological constraints: Theoretical and computational results

In this review, we provide an organized summary of the theoretical and computational results that are available for polymers subject to spatial or topological constraints. Because of the interdisciplinary character of the topic, we provide an accessible, non-specialist introduction to the main topological concepts, polymer models, and theoretical/computational methods used to investigate dense and entangled polymer systems. The main body of our review deals with (i) the effect that spatial confinement has on the equilibrium topological entanglement of one or more polymer chains and (ii) the metric and entropic properties of polymer chains with fixed topological states. These problems have important technological applications and implications for life sciences. Both aspects, especially the latter, are amply covered. A number of selected open problems are finally highlighted.