A Bound for the Temperature in the Thermistor Problem

With a suitable transformation an upper bound for the temperatureis given in the thermistor problem when the electrical conductivityis bounded. Using a fixed-point argument the new formulationleads to the proof of a theorem that at least one solution exists.     

Three formulas for eigenfunctions of integrable Schrödinger operators

We give three formulas for meromorphic eigenfunctions (scatteringstates) of Sutherlandsintegrable N-body Schrödinger operators and their generalizations.The first is an explicit computation of the Etingof–Kirillov tracesof intertwining operators, the second an integral representationof hypergeometric type, and the third is a formula of Bethe ansatz type.The last two formulas are degenerations of elliptic formulasobtained previously in connection with theKnizhnik–Zamolodchikov–Bernardequation. The Bethe ansatz formulas in the elliptic case are reviewed and discussed in more detail here: Eigenfunctionsare parametrized by a Hermite–Bethe variety, a generalizationof the spectral variety of the Lamé operator.We also give the q-deformed version of ourfirst formula. In the scalar slN case, this gives common eigenfunctionsof the commuting Macdonald–Rujsenaars difference operators.     

INTERNATIONAL ENVIRONMENTAL AGREEMENTS WITH DEVELOPED AND DEVELOPING COUNTRIES IN A DYNAMIC APPROACH

This paper is devoted to study the stability of international environmental agreements (IEAs) in a pollution abatement model. We focus our attention on two asymmetric agents: developed countries characterized by a strong measure of environmental awareness and developing ones characterized by less attention to environmental preservation. We model a differential game in order to determine both the optimal path of the abatement levels and stock pollutant as results of open‐loop and feedback Nash equilibria. By means of the concepts of internal and external stability, we explain how the environmental awareness of two types of countries and the number of cooperators and defectors influence the size of stable coalitions. The results establish that the asymmetry assumption does not have consequences for the stability of the grand coalition, which can be obtained only with transfers.     

A Global Method for Relaxation in W1,p and in SBVp

 An integral representation formula for a class of functionals defined on and in (the space of special functions of bounded variation) is obtained without requiring the regularity conditions usually imposed in the literature. The approach is based on the general results of [10] and on a Poincaré-Wirtinger type inequality introduced by DE GIORGI, CARRIERO & LEACI [25]. Applications to relaxation problems and dimension-reduction problems in brittle thin films are presented. (Accepted May 8, 2002) Published online October 18, 2002 Communicated by L. Ambrosio     

Computation of the acetone ultraviolet spectrum in gas phase and in aqueous solution by a mixed discrete/continuum model

The ultraviolet spectrum of acetone in vacuum and in aqueous solution has been computed by different quantum mechanical methods coupled to the polarizable continuum model (PCM) for describing bulk solvent effects. The results in vacuo show that the time-dependent density functional theory (TDDFT) approach using the PBEO functional reproduces quite well the result obtained at the CASPT2 level. Supermolecule computations confirm that water molecules belonging to the first shell of polar groups (here the carbonyl oxygen) must be explicitly included in the quantum mechanical treatment, whereas the effect of other solvent molecules (which is far from being negligible) can be reliably described by the PCM. Moreover, statistical averaging effects have been taken into account by performing canonical molecular dynamics (MD) simulations followed by TDDFT quantum mechanical computations on representative clusters of increasing dimensions immersed in a polarizable continuum. The results show that the combined MD/DFT/PCM approach is reliable and effective, although the performances of the force field used in the MD simulations must be further investigated.     

Brownian dynamics with constraints

Systems possessing degrees of freedom operating on widely separated timescales, where the effects of those operating on the smaller timescales are relatively unimportant, may be modelled by the use of the Langevin equation. In order to study such systems containing complex polyatomic particles, holonomic constraints may be used. Though there is no lack of published algorithms for the numerical solution of the Langevin equation, few of them have been developed with sufficient rigour to ensure their precision, nor to demonstrate their compatibility with constraints. This study recapitulates an approach based upon Runge-Kutta equations which has the advantage of being perfectible to any desired order in the time-step, and shows how it may be combined with the SHAKE method in order to perform constrained Brownian dynamics simulations. Results are presented for some simple systems with a third order algorithm, and it is found that the correct dynamic and statistical behaviour is recovered.     

Existence of Weak Solutions for the Space-Charge Problem

A system of partial differential equations modelling a steady-statespace-charge problem is studied. The existence of a weak solutionis proved using an elliptic regularization under quite generalboundary conditions.     

Uniqueness for a problem of mixing in electrohydrodynamics

A uniqueness result for the initial-boundary value problem modellingthe mixing of fluids with different electric conductivitiesis proved. The equations are those of electrohydrodynamics andthe related approximations are assumed.     

EQUILIBRIUM AMONG HEMATOPORPHYRIN-DERIVATIVE COMPONENTS: INFLUENCE OF THE INTERACTION WITH CELLULAR STRUCTURES

Abstract— Hematoporphyrin-derivative (HpD) is a complex mixture of porphyrins in different aggregation states. The spectral analysis of HpD in aqueous solution shows the presence of monomeric species through the fluorescence emission spectrum and of both monomeric and aggregated species through the absorption spectrum.
The interaction with biopolymers and cellular components results in the appearance of new emission bands at 630 nm and in the640–670 nm spectral region which can be evidenced under suitable excitation conditions. Correspondingly, two new decay times (∼ 0.6 ns, and ∼ 3 ns), are observable. The new fluorescent species detected can be considered as the result of the hydrophobic effect induced by cellular structures on porphyrin aggregates.