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．     

A KIND OF DOUBLY-PERIODIC PROBLEM IN PLANE ELASTICITY WITH CRACKS

In this paper, some kind of doubly-periodic problems in plane elasticity with cracks is discussed with complex variable method. Without loss of generality, it is assumed there is only one sufficiently smooth arc (crack) in the fundamental cell. The correct formulation of the problem is given. The problem is reduced to some singular integral equation with undetermined constants, which is proved to be uniquely solvable with the suitably chosen constants.     

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。     

ON THE SUSTAINABLE GROWTH IN AN ECONOMY WITH PERFECTLY SUBSTITUTABLE EXHAUSTIBLE RESOURCES

Abstract A model of sustainable economic growth in an economy with two types of exhaustible resources is analyzed. The resources are assumed to be perfect substitutes with marginal rate of substitution varying over time. The optimal control framework is used to characterize the optimal paths under the maximin criterion. It is shown that the resource with increasing productivity is not used before the constant productivity resource is depleted. Afterwards the resource with an increasing productivity is asymptotically depleted as well. The results are based on an assumption that transversality conditions hold. A new sufficient condition for the transversality conditions is derived. Finally, an analogue of Hartwick’s rule for this non‐autonomous case is established.     

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.     

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．     

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。     

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。     

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.     

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.     

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.     

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.     

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     

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.     

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.     

GENERALIZED FUZZY FILTERS OF BL-ALGEBRAS

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered.In fact,this is a generalization of quasi-coincidence of a fuzzy point With a fuzzy set.By using this new idea,the notion of interval valued(∈,∈∨q)-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras,is defined,and related properties are investigated.In particular,the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-algebras.     

Further results on adaptive full-order and reduced-order observers for Lur’e differential inclusions

This paper is concerned with the adaptive observer design of Lur’e differential inclusions with unknown parameters. Under a relaxed assumption on nonlinear perturbation functions, a sufficient condition for the existence of an adaptive full-order observer is established. Comparing with results in the literature, the present conditions are complemented with a numerically reliable computational approach, which can be checked by means of linear matrix inequalities. Furthermore, it is shown that, under the sufficient condition, the existence of a reduced-order observer is guaranteed. Also, the reduced-order observer is designed. The effectiveness of the proposed design is illustrated via a simulation example.     

A projection method of estimation for a subfamily of exponential families

Summary This paper is concerned with estimation for a subfamily of exponential-type, which is a parametric model with sufficient statistics. The family is associated with a surface in the domain of a sufficient statistic. A new estimator, termed a projection estimator, is introduced. The key idea of its derivation is to look for a one-to-one transformation of the sufficient statistic so that the subfamily can be associated with a flat subset in the transformed domain. The estimator is defined by the orthogonal projection of the transformed statistic onto the flat surface. Here the orthogonality is introduced by the inverse of the estimated variance matrix of the statistic on the analogy of Mahalanobis's notion (1936,Proc. Nat. Inst. Sci. Ind.,2, 49–55). Thus the projection estimator has an explicit representation with no iterations. On the other hand, the MLE and classical estimators have to be sought as numerical solutions by some algorithm with a choice of an initial value and a stopping rule. It is shown that the projection estimator is first-order efficient. The second-order property is also discussed. Some examples are presented to show the utility of the estimator.     

具有学习效应的排序对策

建立了具有学习效应的排序对策模型,在这类排序对策中,工件的实际加工时间不再是常数,而是关于工件位置的递减幂函数。当所有工件的正常加工时间相等时,松弛可行顺序的条件,相应的排序对策是均衡的,但不一定是凸对策。