强链回归集与强跟踪性

为了研究强跟踪性，本文给出了强链回归集的定义．证明了：若度量空间上的一个连续自映射有强跟踪性，则其强链回归集与极限集相同．     

Rate of Convergence of a Stochastic Particle System for the Smoluchowski Coagulation Equation

By continuing the probabilistic approach of Deaconu et al. (2001), we derive a stochastic particle approximation for the Smoluchowski coagulation equations. A convergence result for this model is obtained. Under quite stringent hypothesis we obtain a central limit theorem associated with our convergence. In spite of these restrictive technical assumptions, the rate of convergence result is interesting because it is the first obtained in this direction and seems to hold numerically under weaker hypothesis. This result answers a question closely connected to the Open Problem 16 formulated by Aldous (1999).     

基于"纵横向拉开档次法"的上市公司经营业绩评价

鉴于目前已具有较全面、完整、连续的有关上市公司各项指标的纵横向数据，为充分利用数据所蕴涵的信息，本文提出运用“纵横向拉开档次”的综合评价方法，其特点是使指标权重的确定能尽量将被评价对象在纵横向拉开档次。将该法运用于安徽地方板块的18家上市公司业绩评价，获得了各公司在1999～2001年间动态发展的分析结果。     

Limit Regimes of Braking of Disc-Type Composite Flywheels Made by Filament Winding

A set of invariants describing the limit regimes of braking disk-type wound composite flywheels is suggested. The limit regime is determined by using a linear failure criterion. It is shown that, for generating short-time impulses of very high power, a set of small identical flywheels is more effective than one large flywheel with an equivalent mass. Particular examples illustrating the theory considered are discussed.     

A Law of Large Numbers for the Zeroes of Heine–Stieltjes Polynomials

We determine the limiting density of the zeroes of Heine–Stieltjes polynomials (or of any set of points satisfying the conclusion of Heine–Stieltjes Theorem) in the thermodynamic limit and use this to prove a strong law of large numbers for the zeroes.     

Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers

We give asymptotic formulas for the multiplicities of weights and irreducible summands in high-tensor powers V_λ^⊗N of an irreducible representation V_λ of a compact connected Lie group G. The weights are allowed to depend on N, and we obtain several regimes of pointwise asymptotics, ranging from a central limit region to a large deviations region. We use a complex steepest descent method that applies to general asymptotic counting problems for lattice paths with steps in a convex polytope.     

HILBERTIAN INVARIANCE PRINCIPLE FOR EMPIRICAL PROCESS ASSOCIATED WITH A MARKOV PROCESS

The authors establish the Hilbertian invariance principle for the empirical process of a stationary Markov process, by extending the forward-backward martingale decomposition of Lyons-Meyer-Zheng to the Hilbert space valued additive functionals associated with general non-reversible Markov processes.     

关于无界无限维商品空间上的生产经济均衡

本文研究了无界无限维商品空间上的生产经济均衡的存在性．虽然我们把商品空间看成是Ｒｉｅｓｚ空间，但并没有在它的正锥上作任何内部假设．同时我们的结果也为现代企业或公司从事经济预测、制订生产计划、改善经营管理、提高劳动生产率以及优化经济机制提供了理论依据．     

Breathers in ferrimagnetic systems

Breathers in discrete nonlinear ferrimagnetic spin lattices are investigated for both easy-axis and easy-plane configurations. The region in frequency space of the formation of breathers is determined and the anticontinuum limit discussed. The monochromatic and the coloured breathers are found out numerically for different parameters and different conditions of excitations.     

RELAXATION TIME LIMITS PROBLEM FOR HYDRODYNAMIC MODELS IN SEMICONDUCTOR SCIENCE

In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.