时变线性系统特征根判稳的推广

本文研究了二维时变线性系统零解的稳定性，给出了一些允许系数矩阵主对角元变号，系数矩阵特征根变号的判定稳定性的充分条件。     

模糊对向传播网络数据融合目标识别方法

重点研究了模糊对向传播网络 (FCPN)模型。针对数据融合和目标识别的特点 ,提出了基于模糊对向传播网络的融合目标识别方法和改进的模糊对向传播网络 (MFCPN)融合结构。利用仿真数据对网络的训练算法和融合结构进行了实验研究。结果表明 ,模糊对向传播网络较误差后向传播网络 (BPN)能够有效地实现融合识别 ;改进的模糊对向传播网络融合结构是可行的。同时还对FCPN和MFCPN应用于前视红外 (FLIR)和可见光摄像机目标跟踪系统进行了应用研究。     

Interference of probabilities and number field structure of quantum models

We study the probabilistic consequences of the choice of the basic number field in the quantum formalism. We demonstrate that by choosing a number field for a linear space representation of quantum model it is possible to describe various interference phenomena. We analyse interference of probabilistic alternatives induced by real, complex, hyperbolic (Clifford) and p‐adic representations.     

从立方抛物线谈起(1)--余弦型振动,椭圆余弦型振动与双曲线型非周期运动

从立方抛物线的特性谈起 ,用较初浅的方法 ,借助于雅可比椭圆函数求椭圆方程的解来说明一大类一维保守系统的余弦振动、椭圆余弦型振动与双曲线型非周期运动 .并以杜芬振子、单摆、倒摆、转动圆环上的小环运动为典型实例作了详细讨论     

Restrictions of Quadratic Forms to Lagrangian Planes,Quadratic Matrix Equations,and Gyroscopic Stabilization

We discuss the symplectic geometry of linear Hamiltonian systems with nondegenerate Hamiltonians. These systems can be reduced to linear second-order differential equations characteristic of linear oscillation theory. This reduction is related to the problem on the signatures of restrictions of quadratic forms to Lagrangian planes. We study vortex symplectic planes invariant with respect to linear Hamiltonian systems. These planes are determined by the solutions of quadratic matrix equations of a special form. New conditions for gyroscopic stabilization are found.     

从诺贝尔经济学奖看数学对经济学的作用

本文在分析2003年诺贝尔经济学奖学术贡献的基础上，阐述了数学思维方式和数学方法对经济问题的解决、经济理论的发展等方面的作用．     

Free probability and the von Neumann algebrasof free groups

This short note summarizes the circumstances of the birth of free probability theory andsome of the recent achievements.     

Controlling an oscillating Jackson-type network having state-dependent service rates

We consider a Jackson-type network comprised of two queues having state-dependent service rates, in which the queue lengths evolve periodically, exhibiting noisy cycles. To reduce this noise a certain heuristic, utilizing regions in the phase space in which the system behaves almost deterministically, is applied. Using this heuristic, we show that in order to decrease the probability of a customers overflow in one of the queues in the network, the server in that same queue – contrary to intuition – should be shut down for a short period of time. Further noise reduction is obtained if the server in the second queue is briefly shut down as well, when certain conditions hold.     

Enhancing the Bolzon–Schrefler–Zienkiewicz Constitutive Model for Partially Saturated Soil

This paper presents an enhanced version of the elasto-plastic model for partially saturated soil first proposed by Bolzon, Schrefler and Zienkiewicz in 1996, “BSZ” model, which uses the effective stress tensor and suction as independent stress variables. It is recalled that the effective stress tensor proposed by Lewis and Schrefler in 1982 is thermodynamically consistent and, compared with other choices of stress tensors, results particularly suitable for partially saturated soil mechanics. A hydraulic constitutive relationship and a hydraulic hysteresis are introduced in the model, to take into account the irreversible deformation during cyclic drying and wetting until structural collapse. For this reason the plastic rate of strain is split into the sum of two components: one depending on the effective stress tensor and the other one on suction. This is the new feature of the BSZ model. This enhanced model is then cast into a thermodynamical framework at macroscopic level and it is shown that it is possible to derive the constitutive law from the Helmholtz free energy and a dissipation function, both for associative and non- associative plasticity. Finally the model predictions have been compared with experimental data for Sion slime, with particular emphasis on the deviatoric part, and model predictions of hysteretic behaviour have been investigated in case of a wetting and drying cycle on compacted betonite–kaolin.     

An Algebraic Method for the Exact Solution of the Partition Function of the Canonical Ensemble in Nuclear Multifragmentation

We propose a unified method for deducing recursive relations for the canonical partition function of a system of noninteracting particles with charge conservation if the particles follow the Bose–Einstein, Fermi–Dirac, or Maxwell–Boltzmann statistics or parastatistics. For all these types of statistics, we find recursive relations for the partition function of a new statistical model of nuclear multifragmentation with electric charge and baryon number conservation, accounting for the internal degrees of freedom of the nuclear fragments.