Low-temperature photoluminescence spectra of highly excited quantum wires

Optical spectra of highly excited quantum wires at low temperatures have been studied within the dynamical screening approximation. We found a strong Fermi-edge singularity (FES) in the photoluminescence spectra. The spectral shape and FES intensity strongly depend on temperature in agreement with recent experimental results.     

Numerical solution of Navier–Stokes equations using multiquadric radial basis function networks

A numerical method based on radial basis function networks (RBFNs) for solving steady incompressible viscous flow problems (including Boussinesq materials) is presented in this paper. The method uses a ‘universal approximator’ based on neural network methodology to represent the solutions. The method is easy to implement and does not require any kind of ‘finite element‐type’ discretization of the domain and its boundary. Instead, two sets of random points distributed throughout the domain and on the boundary are required. The first set defines the centres of the RBFNs and the second defines the collocation points. The two sets of points can be different; however, experience shows that if the two sets are the same better results are obtained. In this work the two sets are identical and hence commonly referred to as the set of centres. Planar Poiseuille, driven cavity and natural convection flows are simulated to verify the method. The numerical solutions obtained using only relatively low densities of centres are in good agreement with analytical and benchmark solutions available in the literature. With uniformly distributed centres, the method achieves Reynolds number Re = 100 000 for the Poiseuille flow (assuming that laminar flow can be maintained) using the density of , Re = 400 for the driven cavity flow with a density of and Rayleigh number Ra = 1 000 000 for the natural convection flow with a density of . Copyright © 2001 John Wiley & Sons, Ltd.     

Radical Formation in the Gas‐Phase Ozonolysis of Deprotonated Cysteine

Although the deleterious effects of ozone on the human respiratory system are well‐known, many of the precise chemical mechanisms that both cause damage and afford protection in the pulmonary epithelial lining fluid are poorly understood. As a key first step to elucidating the intrinsic reactivity of ozone with proteins, its reactions with deprotonated cysteine [Cys?H]^? are examined in the gas phase. Reaction proceeds at near the collision limit to give a rich set of products including 1) sequential oxygen atom abstraction reactions to yield cysteine sulfenate, sulfinate and sulfonate anions, and significantly 2) sulfenate radical anions formed by ejection of a hydroperoxy radical. The free‐radical pathway occurs only when both thiol and carboxylate moieties are available, implicating electron‐transfer as a key step in this reaction. This novel and facile reaction is also observed in small cys‐containing peptides indicating a possible role for this chemistry in protein ozonolysis.     

3D Study of the Morphology and Dynamics of Zeolite Nucleation

The principle aspects and constraints of the dynamics and kinetics of zeolite nucleation in hydrogel systems are analyzed on the basis of a model Na‐rich aluminosilicate system. A detailed time‐series EMT‐type zeolite crystallization study in the model hydrogel system was performed to elucidate the topological and temporal aspects of zeolite nucleation. A comprehensive set of analytical tools and methods was employed to analyze the gel evolution and complement the primary methods of transmission electron microscopy (TEM) and nuclear magnetic resonance (NMR) spectroscopy. TEM tomography reveals that the initial gel particles exhibit a core–shell structure. Zeolite nucleation is topologically limited to this shell structure and the kinetics of nucleation is controlled by the shell integrity. The induction period extends to the moment when the shell is consumed and the bulk solution can react with the core of the gel particles. These new findings, in particular the importance of the gel particle shell in zeolite nucleation, can be used to control the growth process and properties of zeolites formed in hydrogels.     

Value sharing problems for differential and difference polynomials of meromorphic functions in a non-Archimedean field

In this paper we discuss the uniqueness problem for differential and difference polynomials of the form (f ^nm (z)f ^nd (qz + c))^(k) for meromorphic functions in a non-Archimedean field.     

Splitting extragradient-like algorithms for strongly pseudomonotone equilibrium problems

In this paper, two splitting extragradient-like algorithms for solving strongly pseudomonotone equilibrium problems given by a sum of two bifunctions are proposed. The convergence of the proposed methods is analyzed and the R-linear rate of convergence under suitable assumptions on bifunctions is established. Moreover, a noisy data case, when a part of the bifunction is contaminated by errors, is studied. Finally, some numerical experiments are given to demonstrate the efficiency of our algorithms.     

On functional equations for meromorphic functions and applications

Donovan’s conjecture states that there exist only finitely many Morita equivalence classes of p-blocks with a given defect. This conjecture was shown by Radha Kessar to be equivalent to two other conjectures, one of which is that the basic algebras of p-blocks with a given defect can all be defined over a single finite field. We shall show that this latter conjecture is equivalent to the seemingly stronger statement that all p-blocks with a given defect can be defined over a single finite field.     

On the No-Gap Second-Order Optimality Conditions for a Discrete Optimal Control Problem with Mixed Constraints

Motivated by our recent works on optimality conditions in discrete optimal control problems under a nonconvex cost function, in this paper, we study second-order necessary and sufficient optimality conditions for a discrete optimal control problem with a nonconvex cost function and state-control constraints. By establishing an abstract result on second-order optimality conditions for a mathematical programming problem, we derive second-order necessary and sufficient optimality conditions for a discrete optimal control problem. Using a common critical cone for both the second-order necessary and sufficient optimality conditions, we obtain “no-gap” between second-order optimality conditions.     

Existence and Exponential Decay of Solutions for a Wave Equation with Integral Nonlocal Boundary Conditions of Memory Type

In this paper, we consider a wave equation with integral nonlocal boundary conditions of memory type. First, we establish two local existence theorems by using Faedo–Galerkin method and standard arguments of density. Next, we give a su?cient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results.