Critical Point Theorems and Applications to Differential Equations

This paper contains a generalization of the well-known Palais-Smale and Cerami compactness conditions. The compactness condition introduced is used to prove some general existence theorems for critical points. Some applications are given to differential equations.     

Influence of oxidation time on semiconductive behaviour of thermally grown oxide films on AISI 304L

The oxide films formed on AISI 304L stainless steel at 300 °C in the oxidation time range between 2 and 4 h have been studied by photoelectrochemistry. Photocurrents were investigated as a function of the wavelength of the incident light and the electrode potential. The investigation allowed the determination of the semiconductive properties of the oxides. The oxide films showed n-type behaviour. A duplex structure of the oxide films has been suggested on the basis of the photocurrent spectra, with an internal oxide layer having an optical gap (E_g2 = 2.16-2.3 eV) depending on the applied potential and oxidation time, higher to that of the external oxide layer (E_g1 ≈ 1.9 eV). Significant variations in the amplitude of the photocurrent were detected as a function of the applied potential and the oxidation time.     

Diagramme polythermique du systeme ternaire H2O—Al(NO3)3—Mg(NO3)2

The solid—liquid equilibria of the ternary system H₂O—Al(NO₃)₃—Mg(NO₃)₂ were studied at –30, –20, –10 and 0°C by using a synthetic method which allows to detemine all the characteristic points of isothermal sections. The stable solid phases which appear are respectively: ice, Al(NO₃)₃·9H₂O, Mg(NO₃)₂·9H₂O and Mg(NO₃)₂·6H₂O. Neither double salts nor mixed crystals are observed in the temperature and composition field studied. Polytherm diagram layout show two invariant transformations correspond with an eutectic point and a peritectic point.This revised version was published online in November 2005 with corrections to the Cover Date.     

Synthesis of a new class of uridine phosphorylase inhibitors

A new series of potent uridine phosphorylase inhibitors have been prepared from barbituric acid. Among them, 1-[(2-hydroxyethoxy)methyl]-5-)(m--benzyloxy)benzylbarbituric acid ( 37 , BBBA) is the most promising having a K_i value of 1.1 ± 0.2 nM with uridine phosphorylase from human liver. The new inhibitors are easily synthesized and are better inhibitors of human uridine phosphorylase than their uracil counterparts.     

The Problem of Capacity Addition in Multi-user Elastic Demand Communication Networks

In this paper we consider some properties on prices under flow control in a network that is to be shared by noncooperative users. Each user is faced with an optimization problem which is formulated as the minimization of its own criterion subject to constraint on the flows of the other users. The operating points of the network are the Nash equilibria of the underlying routing game. Our objective is to study the behavior of prices of all users when the network designer needs to allocate capacities to network links. For parallel links topologies, we show that degradation of the performances such as prices will not take place, as well as the users may find it beneficial to improve their requests     

Approximating Clarke’s subgradients of semismooth functions by divided differences

We show that the algorithm presented in an earlier paper by Studniarski (Numer. Math., 55:685–693, 1989) can be applied, after only a small modification, to approximate numerically Clarke’s subgradients of semismooth functions of two variables. Results of computational testing of this modified algorithm are also reported.