Positive Schatten(-Herz) Class Toeplitz Operators on the Half-space

On the harmonic Bergman space of the half-space, we give characterizations for an arbitrary positive Toeplitz operator to be a Schatten (or Schatten-Herz) class operator in terms of averaging functions and Berezin transforms. Examples are provided to show that various results are sharp. This research was supported by KOSEF(R01-2003-000-10243-0).     

The application of spectral distribution of product of two random matrices in the factor analysis

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.     

Some Decidability and Undecidability Results on Green's Relations for Automatic Monoids

We consider the problem of deciding Green's relations for various types of finitely presented automatic monoids. We establish some decidability as well as some undecidability results.     

Factorisation des polynômes de Poncelet

La condition pour qu’il existe des n-gones de Poncelet, inscrits dans un cercle, et circonscrits à un autre cercle, est polynomiale en les paramètres définissant ces deux cercles. Nous décomposons ces polynômes “de Poncelet” en facteurs irréductibles que nous interprétons géométriquement.     

Nash Equilibria in Noncooperative Predator-Prey Games

A noncooperative game governed by a distributed-parameter predator-prey system is considered, assuming that two players control initial conditions for predator and prey, respectively. Existence of a Nash equilibrium is shown under the condition that the desired population profiles and the environmental carrying capacity for the prey are sufficiently small. A conceptual approximation algorithm is proposed and analyzed. Finally, numerical simulations are performed, too.     

Case study: problem formulation and solution for a real-world sports scheduling problem

This case study paper describes a problem faced every year by the Devon Cricket League in England. Every league match requires two officiating umpires. There are various preferences relating to the deployment of umpires that fall short of being definite constraints. The requirement was to produce a computer system that would allocate umpires in a satisfactory manner without the need for human interaction, since the users of the system will be unqualified amateurs. This necessitated the construction of a very complex objective function, using imprecise and ill-defined information. The biggest challenge was thus one of problem formulation; the solution technique was relatively straightforward. The system has been put into successful use and it is expected that its use will continue indefinitely. The work raises ethical issues regarding work done for customers who are inexperienced amateurs.     

Zero-cycles on self-product of modular curves

We use the elements in K-cohomology groups which are constructed by Flach and Mildenhall to obtain a finiteness result for the torsion part of the Chow group of a self-product of a modular curve.     

Three classes of smooth Banach submanifolds in B(E,F)

Let E, F be two Banach spaces, and B(E, F), Φ(E, F), SΦ(E, F) and R(E,F) be the bounded linear, Fredholm, semi-Frdholm and finite rank operators from E into F, respectively. In this paper, using the continuity characteristics of generalized inverses of operators under small perturbations, we prove the following result Let ∑ be any one of the following sets {T ∈ Φ(E, F) IndexT =const, and dim N(T) = const.}, {T ∈ SΦ(E, F) either dim N(T) = const. ＜ ∞ or codim R(T) = const.＜ ∞} and {T ∈ R(E, F) RankT =const.＜∞}. Then ∑ is a smooth submanifold of B(E, F) with the tangent space TA∑ = {B ∈ B(E,F) BN(A) (∪) R(A)} for any A ∈ ∑. The result is available for the further application to Thom's famous results on the transversility and the study of the infinite dimensional geometry.     

Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries

This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries.By using super-and sub-solution techniques,we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively,and then give the necessary and sufficient conditions that two components u and v blow up simultaneously.Finally,the uniform blow-up profiles in the interior are presented.     

Perturbed recurrence relations II the general case

In this paper, we give some new explicit relations between two families of polynomials defined by recurrence relations of all order. These relations allow us to analyze, even in the Sobolev case, how some properties of a family of orthogonal polynomials are affected when the coefficients of the recurrence relation and the order are perturbed. In a paper we have already given a method which allows us to study the polynomials defined by a three-term recurrence relation. Also here some generalizations are given.