τ选择及其在BCO理论中的应用

本文利用τ弱仿紧空间的概念证明了一种τ选择的存在性。作为选择理论的应用，我们说明了具有可数序基的τ弱仿紧空间存在点τ的可数序基。     

遗传覆盖性质和选择理论

通过引入局部下半连续集值映射的概念,建立了遗传覆盖性质与多种选择之间的一些重要联系,说明了选择构造本身与原象空间的分离性无关.     

p-仿紧空间

本文研究了p-仿紧空间和p-可数仿紧空间的相关问题.利用预开集和覆盖性质理论,得到了p-仿紧空间和p-可数仿紧空间的定义、等价刻画及αp-仿紧子集的性质,推广了一般拓扑学中仿紧空间的部分结果.     

n维Rayleigh方程周期解的存在性

本文主要讨论ｎ维Ｒａｙｌｅｉｇｈ方程周期解的存在性。利用Ｍａｗｈｉｎ的重合度（ｃｏｉｎｃｉｄｅｎｃｅｄｅｇｒｅｅ）理论，我们给出了其周期解存在的两个充分条件。对其特例ｎ锥Ｄｕｆｆｉｎｇ方程给出了周期解存在唯一的条件。     

遗传中紧空间与散射分解

本文证明了可数仿紧(中紧、亚紧)空间有类似Junnila的刻画，遗传中紧空间不具有类似Junnila的刻画，并给出了每个散射分解有紧有限的开膨胀的充要条件．     

抽象空间混合型微分-积分方程两点边值问题的解

本文利用混合单调算子理论及Ｍ?ｎｃｈ的一个结果，得到了一类微分方程两点边值问题的解．     

抽象空间混合型微分积分方程两点边值问题的解

本文利用混合单调算子理论及Ｍ¨ｏｎｃｈ的一个结果，得到了一类微分方程两点边值问题的解．     

迁移理论中一类具连续能量的参数方程的解

本文研究迁移理论中含参数δ的具连续能量的板几何中子迁移方程的解.用泛函分析的方法,讨论了使该方程有非零解的参数在复平面上的分布.     

关于S-Lindelf空间及其子空间(英文)

本文是在半开集理论中提出了S_Lindel f空间的概念。指出S_Lindel f空间是S_紧空间的一种推广 ,并对该空间及其子空间所具有的性质进行了一些有益的讨论。     

Browder－Hartman－Stampacchia变分不等式研究概况及问题

本文介绍了Ｂｒｏｗｄｅｒ－Ｈａｒｔｍａｎ－Ｓｔａｍｐａｃｃｈｉａ变分不等式理论及应用当前研究的概况及存在的某些问题。     

Damage and Failure of Metal/Fibre-Reinforced Polymer Tensile Specimens with Inelastic Interface

Hybrid specimens of metal and fibre-reinforced polymer are applied in automotive and aerospace industry. The simulation and analysis of damage of such engineering structures is the focus of this research. The investigation includes a computation of the extension of single lap tensile specimen, produced by ultrasonic metal welding. The specimen is manufactured from CF-PA66 - fibre-reinforced polymer and AlMg3 (AA5754), which is used as a metallic joining partner. The aluminium substrate is treated as an elastoplastic material. The polymer composite generally shows an orthotropic elastic behaviour. The interface material has been numerically modeled as an elastoplastic material with linear hardening, coupled with Lemaitre-type damage. The finite element method is used for the investigation of so-called interface elements. The geometry of the interface is a consequence of the welding sonotrode geometry. The behaviour of specimens with square and ring interface geometry are analysed. The influence of the interface geometry on the mechanical properties of the joint is shown. The increase of the damage parameter and the development of failure are described for both cases. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parallel multi-frontal solver for p adaptive finite element modeling of multi-physics computational problems

The paper presents a parallel direct solver for multi-physics problems. The solver is dedicated for solving problems resulting from adaptive finite element method computations. The concept of finite element is actually replaced by the concept of the node. The computational mesh consists of several nodes, related to element vertices, edges, faces and interiors. The ordering of unknowns in the solver is performed on the level of nodes. The concept of the node can be efficiently utilized in order to recognize unknowns that can be eliminated at a given node of the elimination tree. The solver is tested on the exemplary three-dimensional multi-physics problem involving the computations of the linear acoustics coupled with linear elasticity. The three-dimensional tetrahedral mesh generation and the solver algorithm are modeled by using graph grammar formalism. The execution time and the memory usage of the solver are compared with the MUMPS solver.     

On optimal control problems connected with eigenvalue variational inequalities

The eigenvalue optimization problem for a variational inequality over the convex cone is to be dealt with. The control variable appears in the operator of the unilateral problem. The existence theorem for the maximum first eigenvalue optimization problem is stated and verified. The necessary optimality condition is derived. The applications to the optimal design of unilaterally supported beams and plates are presented. The variable thickness of a construction plays the role of a design variable. The convergence of the finite elements approximation is proved. Copyright © 2001 John Wiley & Sons, Ltd.     

Stair Laguerre pseudospectral method for differential equations on the half line

A stair Laguerre pseudospectral method is proposed for numerical solutions of differential equations on the half line. Some approximation results are established. A stair Laguerre pseudospcetral scheme is constructed for a model problem. The convergence is proved. The numerical results show that this new method provides much more accurate numerical results than the standard Laguerre spectral method. Dedicated to Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 65N35, 41A10. Li-lian Wang: The work of this author is partially supported by The Shanghai Natural Science Foundation N. 00JC14057, The Shanghai Natural Science Foundation for Youth N. 01QN85 and The Special Funds for Major Specialities of Shanghai Education Committee. Ben-yu Guo: The work of this author is partially supported by The Special Funds for Major State Basic Research Projects of China G1999032804, The Shanghai Natural Science Foundation N. 00JC14057 and The Special Funds for Major Specialities of Shanghai Education Committee.     

A bayesian approach to the probability density estimation

Summary A Bayesian procedure for the probability density estimation is proposed. The procedure is based on the multinomial logit transformations of the parameters of a finely segmented histogram model. The smoothness of the estimated density is guaranteed by the introduction of a prior distribution of the parameters. The estimates of the parameters are defined as the mode of the posterior distribution. The prior distribution has several adjustable parameters (hyper-parameters), whose values are chosen so that ABIC (Akaike's Bayesian Information Criterion) is minimized. The basic procedure is developed under the assumption that the density is defined on a bounded interval. The handling of the general case where the support of the density function is not necessarily bounded is also discussed. The practical usefulness of the procedure is demonstrated by numerical examples. The Institute of Statistical Mathematics     

自由表面与粘性尾迹的相互作用

解析地研究了无限深不可压粘性流体中运动物体产生层流尾迹与自由表面波的相互作用．以定常的Oseen方程模拟受扰流动,对于小振幅自由表面波则采用线性化的运动学和动力学边界条件．在数学描述上,运动物体以Oseen极子模拟,受扰流场分解成表述粘性尾迹的无界奇异Oseen流和描述自由面效应的有界正则Oseen流之和．通过积分变换法,得到自由表面波的精确解．借助Lighthill的两步格式,导出了自由面波高带有附加校正项的渐近解．所得对称解显示了波动的振幅因粘性和潜深的存在而呈指数衰减．     

An optimal control problem for a pest, predator, and plant system

The paper is devoted to an optimal control problem for a system of three nonlinear parabolic equations from population dynamics. The equations model a trophic chain consisting of a predator, a pest and a plant species. The existence and uniqueness of the positive solution for the system are proved. The control variable is connected with the action of a pesticide. Our goal is to minimize the density of the pest and to maximize the plant density. The existence of the optimal solution is proved. The first and second order optimality conditions are established.     

Water waves diffraction by a circular plate

The interaction of water waves with circular plate within the framework of a linear theory is considered. The plate lies on the free surface in water of finite depth. The integral transform technique is used to solve this problem. The problem is reduced to a system of dual integral equations for a spectral function. The way to solve these equations consists in converting them into Fredholm integral equation of the second kind. The asymptotic solutions of this equation are obtained. Representations for diffraction field and for the forces on the plate are given.     

Supercomputer simulation of viscous noncompressible flow past bodies of complex shape

The article reports the results of numerical analysis of viscous thermally conducting noncompressible flow past bodies of complex shape. The effect of physico-chemical processes is ignored. Flow past bodies with various nose cone designs is examined. The process is described using a system of Navier–Stokes equations augmented with the energy equation. The continuity equation is used to control the numerical accuracy. The simulation results are reported in the form of vector fields and surface components of the velocity vector in various channel sections. The results are analyzed for various body configurations.     

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??Hidden Markov model is widely used in statistical modeling of time, space and state transition data. The definition of hidden Markov multivariate normal distribution is given. The principle of using cluster analysis to determine the hidden state of observed variables is introduced. The maximum likelihood estimator of the unknown parameters in the model is derived. The simulated observation data set is used to test the estimation effect and stability of the method. The characteristic is simple classical statistical inference such as cluster analysis and maximum likelihood estimation. The method solves the parameter estimation problem of complex statistical models.