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.     

Graphs with prescribed mean curvature on hyperbolic spaces

We study a quasilinear elliptic equation in the unit ball ofℝ ^m . Using this result we get the existence of graphs with prescribed curvature on hyperbolic spacesℍ ^m inℍ ^m ×ℝ.     

Numerical approximation for a Baer-Nunziato model of two-phase flows

We present a well-balanced numerical scheme for approximating the solution of the Baer-Nunziato model of two-phase flows by balancing the source terms and discretizing the compaction dynamics equation. First, the system is transformed into a new one of three subsystems: the first subsystem consists of the balance laws in the gas phase, the second subsystem consists of the conservation law of the mass in the solid phase and the conservation law of the momentum of the mixture, and the compaction dynamic equation is considered as the third subsystem. In the first subsystem, stationary waves are used to build up a well-balanced scheme which can capture equilibrium states. The second subsystem is of conservative form and thus can be numerically treated in a standard way. For the third subsystem, the fact that the solid velocity is constant across the solid contact suggests us to compose the technique of the Engquist-Osher scheme. We show that our scheme is capable of capturing exactly equilibrium states. Moreover, numerical tests show the convergence of approximate solutions to the exact solution.     

On the stability of gradient polynomial systems at infinity

We first define the notion of the infimum at infinity of a polynomial function and the notion of stability at infinity near the fiber of the gradient descent system. Then we prove that the gradient descent system is stable at infinity near the fiber of the infimum value at infinity.     

Dynamic Picone's identity and its applications

We prove some Picone-type identities and inequalities for a class of first-order nonlinear dynamic systems and derive various weighted inequalities of Wirtinger type and Hardy type on time scales. As applications we study oscillatory and related properties of these systems including Reid's roundabout theorem on disconjugacy, Sturm's separation and comparison theorems, as well as a variational method in the oscillation theory.     

Morse-Palais lemma for nonsmooth functionals on normed spaces

Using elementary differential calculus we get a version of the Morse-Palais lemma. Since we do not use powerful tools in functional analysis such as the implicit theorem or flows and deformations in Banach spaces, our result does not require the -smoothness of functions nor the completeness of spaces. Therefore it is stronger than the classical one but its proof is very simple.

     

On the simpleness of zeros of Stokes multipliers

The aim of this paper is to discuss the simpleness of zeros of Stokes multipliers associated with the differential equation -Φ^″(X)+W(X)Φ(X)=0, where W(X)=X^m+a₁X^m-1+?+a_m is a real monic polynomial. We show that, under a suitable hypothesis on the coefficients a_k, all the zeros of the Stokes multipliers are simple.     

Experimental investigation of liquid chromatography columns by means of computed tomography

The efficiency of packed chromatographic columns was investigated experimentally by means of computed tomography (CT) techniques. The measurements were carried out by monitoring tracer fronts in situ inside the chromatographic columns. The experimental results were fitted using the equilibrium dispersive model (EDM) and varying the so called apparent axial dispersion coefficient. The additivity of the first and second central moments was exploited to estimate column efficiency in different regions of the column. The results showed that the columns under investigation offered a higher column efficiency in the centre compared to the wall region. Furthermore the void fraction in the vicinity of the walls was lower than that in the column core. For this reason the bands were conveyed faster in the central region of the column where the permeability was higher. This result is in good agreement with earlier findings.     

Pseudodifferential operators with real analytic symbols and approximation methods for pseudodifferential equations

This paper introduces some methods (including an approximation method) for investigating pseudodifferential equations and related problems (Cauchy problems, boundary value problems,…) based on the technique of pseudodifferential operators with real analytic symbols.     

An efficient catalytic system for cyclocarbonylation of terpenes into lactones

Three different kinds of representative monoterpenic alcohol are involved in the palladium‐catalysed cyclocarbonylation reaction. Lactone formation is shown to occur when cyclic ( 1 ), tertiary ( 3 ) and primary allylic alcohol ( 7 ) functions are reacted, in the presence of CO with [HPd(SnCl₃)L₂] as the active catalytic species. Good yields and selectivities can easily be reached for isopulegol ( 1 ), and dihydromyrcenol ( 3 ). However, more modest results are obtained for the functionalization of geraniol into the original lactone ( 9 ). This lactone can be largely favoured by using a basic chelating diphosphine ligand such as 1,4‐bis(diphenylphosphino)butane. Copyright © 2005 John Wiley & Sons, Ltd.