两类带有确定潜伏期的SEIS传染病模型的分析

通过研究两类带有确定潜伏期的SEIS传染病模型,发现对种群的常数输入和指数输入会使疾病的传播过程产生本质的差异．对于带有常数输入的情形,找到了地方病平衡点存在及局部渐近稳定的阈值,证明了地方病平衡点存在时一定局部渐近稳定,并且疾病一致持续存在．对于带有指数输入的情形,发现地方病平衡点当潜伏期充分小时是局部渐近稳定的,当潜伏期充分大时是不稳定的．     

Variable electrical and thermal conductivity in the theory of generalized thermoelastic diffusion

This paper deals with the problem of a thermoelastic half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time and with variable electrical and thermal conductivity. The bounding surface of the half-space is taken to be traction free and subjected to a time dependent thermal shock. The solution is obtained in the Laplace transform domain by a direct approach. A numerical technique is employed to obtain the solution in the physical domain. It is found that there exist two coupled waves, one of which is elastic and the other is thermal, and a third wave affects diffusion mainly. A comparison is made with the results obtained in a thermoelastic medium with and without diffusion in the following cases : (a) the electrical and thermal conductivities have constant values, (b) the presence of magnetic field and (c) the generalized theory in thermoelasticity. Received: June 1, 2005     

一类共轭梯度法的全局收敛性

共轭梯度法是求解大规模元约束优化同题的一种有效方法，本文提出一种新的共轭梯度法，证明了在推广的Wolfe线搜索条件下方法具有全局收敛性。最后对算法进行了数值试验，试验结果表明该算法具有良好的收敛性和有效性。     

A simplified expression of the Shapley function for fuzzy game

In this paper, a simplified expression of the Shapley function for games with fuzzy coalition is proposed, which can be regarded as the generalization of Shapley functions defined in some particular games with fuzzy coalition. The simplified expression of the Shapley function is compared with two definitions established by Butnariu, Tsurumi et al. A conclusion is drawn that the simplified expression of the Shapley function is equivalent to Butnariu’s definition when characteristic function is a game with proportional values, and is equivalent to Tsurumi’s definition when characteristic function is a game with Choquet integral forms. Furthermore, from an angle of interaction between two participation levels, the properties of the two games defined by Butnariu and Tsurumi are respectively studied.     

Analysis of an optimal control problem for the three-dimensional coupled modified Navier-Stokes and Maxwell equations

The mathematical formulation and analysis of an optimal control problem associated with a viscous, incompressible, electrically conducting fluid in a bounded three-dimensional domain with fixed perfectly conducting boundaries is considered. The objective of control is the matching of the velocity and magnetic fields to given target fields; control is effected through distributed mechanical force and current controls. The existence of optimal solutions is shown, the Gâteaux differentiability for the magnetohydrodynamic system with respect to controls is proved, and the optimality system is obtained.     

考虑公平偏好的供应链最优信用期和定价策略研究

论文将公平偏好引入商业信用供应链的运作中,研究公平偏好如何影响供应链的商业信用和定价策略。论文在三种情况下,即仅供应商关注公平,仅零售商关注公平和双方均关注公平,运用Stackelberg博弈分析了供应商的最优商业信用期及零售商的最优零售价格。研究发现,当零售商具有公平偏好时,零售价格与其公平偏好程度无关;零售商的公平偏好程度越大,供应商提供的商业信用期限越长。当仅供应商具有公平偏好时,供应商的公平偏好程度越大,零售商的零售价格越大,供应商提供的商业信用期限越短;当双方都具有公平偏好时,零售商的零售价格关于双方偏好均为增函数;供应商的商业信用期限为自身偏好系数的增函数,为零售商偏好系数的减函数。供应链成员的效用为自身偏好系数的增函数,对方偏好系数的减函数;双方具有公平偏好时,供应链利润小于无公平偏好时的供应链利润。     

A rate-dependent algebraic stress model for turbulence

Based on the stress transport model, a rate-dependent algebraic expression for the Reynolds stress tensor is developed. It is shown that the new model includes the normal stress effects and exhibits viscoelastic behavior. Furthermore, it is compatible with recently developed improved models of turbulence. The model is also consistent with the limiting behavior of turbulence in the inertial sublayer and is capable of predicting secondary flows in noncircular ducts. The TEACH code is modified according to the requirements of the rate-dependent model and is used to predict turbulent flow fields in a channel and behind a backward-facing step. The predicted results are compared with the available experimental data and those obtained from the standard k-ε and algebraic stress models. It is shown that the predictions of the new model are in better agreements with the experimental data.     

Gutman极值六角链猜想的证明

六角系统是理论化学中苯碳氢化合物的自然图表示．六角链是一个六角系统满足任意一个顶点至多属于两个六角形，并且每个六角形至多与两个六角形相邻．Gutman提出了两个猜想：1）含有相同六角形个数、具有点独立集总数（Hosoya指数）最小的六角链是唯一的，且为锯齿链；2）含有相同六角形个数、具有边独立集总数（Merrifield－Simmons指数）最大的六角链是唯一的且为锯齿链．本文证实了这两个猜想     

A Semi-Supervised Learning Algorithm for Growing Neural Gas in Face Recognition

In many classification applications and face recognition tasks, there exist unlabelled data available for training along with labelled samples. The use of unlabelled data can improve the performance of a classifier. In this paper, a semi-supervised growing neural gas is proposed for learning with such partly labelled datasets in face recognition applications. The classifier is first trained on the labelled data and then gradually unlabelled data is classified and added to the training data. The classifier is retrained; and so on. The proposed iterative algorithm conforms to the EM framework and is demonstrated, on both artificial and real datasets, to significantly boost the classification rate with the use of unlabelled data. The improvement is particularly great when the labelled dataset is small. Comparison with support vector machine classifiers is also given. The algorithm is computationally efficient and easy to implement.     

进位返加与逐位模2加及模2n加的相容程度分析

深入分析了进位返加运算与逐位模2加运算及模2^n加运算的相容程度,给出了它们的相容概率的计算公式．结论表明,进位返加运算与逐位模2加运算的相容概率尽管很小,但远大于理想值2^-n;进位返加运算与模2^n加运算的相容概率很大,近似为2／3．     

ALTERING CONNECTIVITY WITH LARGE DEFORMATION MESH FOR LAGRANGIAN METHOD AND ITS APPLICATION IN MULTIPLE MATERIAL SIMULATION

A new approach for treating the mesh with Lagrangian scheme of finite volume method is presented. It has been proved that classical Lagrangian method is difficult to cope with large deformation in tracking material particles due to severe distortion of cells, and the changing connectivity of the mesh seems especially attractive for solving such issues. The mesh with large deformation based on computational geometry is optimized by using new method. This paper develops a processing system for arbitrary polygonal unstructured grid, the intelligent variable grid neighborhood technologies is utilized to improve the quality of mesh in calculation process, and arbitrary polygonal mesh is used in the Lagrangian finite volume scheme. The performance of the new method is demonstrated through series of numerical examples, and the simulation capability is efficiently presented in coping with the systems with large deformations.     

Diagonalization of tensors with circulant structure

The concepts of tensors with diagonal and circulant structure are defined and a framework is developed for the analysis of such tensors. It is shown a tensor of arbitrary order, which is circulant with respect to two particular modes, can be diagonalized in those modes by discrete Fourier transforms. This property can be used in the efficient solution of linear systems involving contractive products of tensors with circulant structure. Tensors with circulant structure occur in models for image blurring with periodic boundary conditions. It is shown that the new framework can be applied to such problems.     

遗传算法、差分演化和一个处理约束的映射

S.Koziel和Z.Michalewicz(1999年)提出了一个处理约束的映射,研究该映射与不同算法相结合后的不同的代数结构.从理论上证明了当其与遗传算法相结合时,该映射是同构映射,而在差分演化算法的变异操作下,该映射不是同态映射,更不是同构映射.进而表明,该映射更适宜于与遗传算法相结合,而并不太适宜于与差分演化算法(及其类似的算法)相结合。     

热方程非线性边界条件问题的有限差分方法

This article is concerned with the numerical solution to a parabolic equation with a kind of nonlinear boundary conditions. A difference scheme is constructed by the method of reduction of order on uniform mesh to solve the problem. It is proved that the difference scheme is uniquely solvable and uncon-ditionaUy convergent with the convergence order 2 in both space and time in an energy norm. An effective iterative algorithm is given and a numerical example is presented to demonstrate the theoretical results.     

The simulation of offshore turbulent dispersion using seeded eddies

A way of representing turbulence in a two-dimensional situation is introduced appropriate to depth-independent offshore fluid mechanics. The turbulence is simulated by a collection of eddies, each of which has an analytically simple form but whose size, strength and position is governed by stochastically assigned variables. The problem addressed here is how contaminant is dispersed in such an eddy field. A number of experiments are performed whereby the eddies are seeded with marked particles that move with the fluid. The variance of these particles is monitored as time varies, and the results are compared with an assumed power law distribution. Although not a perfect fit, the results are in general accord with a power law with index between 1.5 and 2.5, which is in agreement with the observed power law of 2.34 due to Okubo, and a marked improvement on random walk models which give a variance directly proportional to time. Some further applications of this technique are discussed, namely the simulation of turbulent boundary layers and the simulation of the cascade of energy up turbulent length scales.     

A FINITE DIFFERENCE METHOD FOR THE HEAT EQUATION WITH A NONLINEAR BOUNDARY CONDITION

This article is concerned with the numerical solution to a parabolic equation with a kind of nonlinear boundary conditions. A difference scheme is constructed by the method of reduction of order on uniform mesh to solve the problem. It is proved that the difference scheme is uniquely solvable and uncon-ditionaUy convergent with the convergence order 2 in both space and time in an energy norm. An effective iterative algorithm is given and a numerical example is presented to demonstrate the theoretical results.     

The existence and stability of traveling waves with transition layers for the S-K-T competition model with cross-diffusion

This paper is concerned with the existence and stability of traveling waves with transition layers for a quasi-linear competition system with cross diffusion,which was first proposed by Shegesada,Kawasaki and Teramoto.When one of the random diffusion rates is small and the cross-diffusion rate is not small,by the geometric singular perturbation method,the existence of traveling waves with transition layers is obtained.Further,by the detailed spectral analysis and topological index method,the traveling waves...     

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A Markov observation model with dividend is defined and the interpretation of the practical significance is given. We try to use an irreducible and homogeneous discrete-time Markov chain to modulate the inter-observation times and embed a dividend strategy. In the Markov observation model with dividend, a system of liner equations for the expected discounted value of dividends until ruin time is derived. Moreover, an explicit expression is obtained and proved. Finally, some interesting properties are illustrated by numerical analysis and by comparing with the complete compound binomial model with dividend.     

行政垄断对铁路多经物流业绩效水平的影响研究

通过结构方程理论模型,研究行政垄断对铁路多经物流业绩效水平的影响。其中行政垄断为外生自变量,用级别、企业性质和管理关系三个指标来衡量。铁路多经物流业绩效水平为内生因变量,分别用人力绩效和财务绩效来衡量。通过LISREL8.5进行了验证性因子分析和结构方程检验。结果表明,行政垄断对人力绩效和财务绩效的影响均是负的,且均是显著的,其中人力绩效是-0.15,财务绩效是-0.3。人力绩效对财务绩效的影响是-0.05,也是显著的。     

一维交替型脉冲微分系统

讨论一维空间中超前型与滞后型交替的脉冲微分系统.首先考虑具常系数的脉冲微分系统平凡解稳定的充分条件;其次研究了具变系数的脉冲微分系统的振动性,并给出了其解的表示式.