The finite-temperature photoluminescence correlation function in semiconductor heterostructures

We report the inclusion of temperature effects on the Mahan-Nozières-De Dominicis framework to study both many-body and temperature effects in photoluminescence spectra of doped semiconductors. The electronic part of the correlation function characterizes the photoluminescence spectra. We have treated the optical valence hole as a localized scattering potential center and studied effects of the electron-hole interaction enhancement on the photoluminescence spectra leading to the appearance of shake-up structures. We also have identified a term in the correlation function which represents the finite-temperature contribution to the intensities of the shake-up structures. The method is used to study the magnetophotoluminescence of modulation-doped quantum wells with a weak periodic lateral potential. Received 20 November 1998 and Received in final form 5 March 1999     

Reduction of an invariant submodel of gas dynamics to canonical form

A method for reducing an invariant submodel to canonical form is considered. Translated fromMatematicheskie Zametki, Vol. 66, No. 3, pp. 439–444, September, 1999.     

Group classification of the generalized Emden–Fowler-type equation

We perform the Lie group classification of the Emden–Fowler-type equation xu^″+nu^′+x^νF(u)=0, which arises in several applications. These include the theory of stellar structure, the thermal behaviour of a spherical cloud of gas, isothermal gas spheres and the theory of thermionic currents. Seven cases arise for the possible extension of the principal Lie algebra, which in this case is trivial. Three new cases occur for which we have non-trivial Lie point symmetry algebra. We compare these cases with the Noether symmetry cases. Moreover, we also make comparisons with the partial Noether operators. Finally for three cases we reduce the Emden–Fowler-type equation to quadratures.     

Nonparametric estimation of the purity of a quantum state in quantum homodyne tomography with noisy data

The aim of this paper is to answer an important issue in quantum mechanics, namely to estimate the purity of a quantum state of a light beam. Estimation of the purity is based on the results of quantum homodyne measurements performed on independent identically prepared quantum systems. The quantum state of the light is entirely characterized by the Wigner function, which can take negative values and must satisfy certain constraints of positivity imposed by quantum physics. We estimate the integrated squared Wigner function by a kernel-based second order U — statistic. This quadratic functional is a physical measure of the purity of the state. We also give an adaptive estimator, which does not depend on the smoothness parameters. We establish upper bounds of the minimax risk over a class of infinitely differentiable functions.      

It was 30 years ago today when Laurens de Haan went the multivariate way

Since the publication of his masterpiece on regular variation and its application to the weak convergence of (univariate) sample extremes in 1970, Laurens de Haan (Thesis, Mathematical Centre Tract vol. 32, University of Amsterdam, 1970) is among the leading mathematicians in the world, with a particular focus on extreme value theory (EVT). On the occasion of his 70th birthday it is a great pleasure and a privilege to follow his route through multivariate EVT, which started only seven years later in 1977, when Laurens de Haan published his first paper on multivariate EVT, jointly with Sid Resnick.      

Lie symmetries for the orbital linearization of smooth planar vector fields around singular points

This work is a generalization of the method proposed in [I.A. García, S. Maza, Linearization of analytic isochronous centers from a given commutator, J. Math. Anal. Appl. 339 (1) (2008) 740-745] of linearization of analytic isochronous centers from a given commutator. In this paper we propose a constructive procedure to get the change of variables that orbitally linearizes a smooth planar vector field on C² around an elementary singular point (i.e., a singular point with associated eigenvalues λ,μ∈C satisfying λ≠0) or a nilpotent singular point from a given infinitesimal generator of a Lie symmetry.     

Implicit Iteration Scheme with Perturbed Mapping for Equilibrium Problems and Fixed Point Problems of Finitely Many Nonexpansive Mappings

We introduce an implicit iteration scheme with a perturbed mapping for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of finitely many nonexpansive mappings in a Hilbert space. Then, we establish some convergence theorems for this implicit iteration scheme which are connected with results by Xu and Ori (Numer. Funct. Analysis Optim. 22:767–772, 2001), Zeng and Yao (Nonlinear Analysis, Theory, Methods Appl. 64:2507–2515, 2006) and Takahashi and Takahashi (J. Math. Analysis Appl. 331:506–515, 2007). In particular, necessary and sufficient conditions for strong convergence of this implicit iteration scheme are obtained. In this research, the first author was partially supported by the National Science Foundation China (10771141), Ph.D. Program Foundation of Ministry of Education of China (20070270004), and Science and Technology Commision of Shanghai Municipality Grant (075105118).     

Linearization of analytic isochronous centers from a given commutator

In this paper we propose an algorithmic way to get the change of variables that linearizes an analytic isochronous center from a given commutator. Moreover, we use this method in order to obtain the linearization of some isochronous centers of the existent literature.     

A note on the stability of the many-queue head-of-the-line processor-sharing system with permanent customers

We consider a single server system consisting of n queues with different types of customers and k permanent customers. The permanent customers and those at the head of the queues are served in processor-sharing by the service facility (head-of-the-line processor-sharing). By means of Loynes’ monotonicity method a stationary work load process is constructed and using sample path analysis general stability conditions are derived. They allow to decide which queues are stable and, moreover, to compute the fraction of processor capacity devoted to the permanent customers. In case of a stable system the constructed stationary state process is the only one and for any initial state the system converges pathwise to the steady state. This revised version was published online in June 2006 with corrections to the Cover Date.     

An infinite set of conservation laws for infinite symmetries

We consider partial differential equations of a variational problem admitting infinite-dimensional Lie symmetry algebras parameterized by arbitrary functions of dependent variables and their derivatives. We show that unlike differential systems with symmetry algebras parameterized by arbitrary functions of independent variables, these equations have infinite sets of essential conservation laws. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 518–528, June, 2007.