离散事件动态系统的关键路径与扰动分析

具有存储器的串行生产线是一典型离故事件动态系统．本文在其极大代数上线性状态方程的基础上，定义了关键路径，并研究了关键路径的特性．通过关键路径，给出了其扰动分析方法．     

带风险指数的金融均衡的存在性定理及其结构特征（上）

本文主要论证了在不完全市场条件下带风险指数的金融均衡的存在性，并揭示其均衡结构的特征．本文中建立的模型是一、二期货币投入产出金融经济且具有可微的资产结构，这一模型包括了许多具有特殊资产结构的均衡模型，如实资产结构、应资产结构、恒秩资产结构的均衡模型．因此本文的这一模型具有广泛的应用前景和实用价值．接着给出了本文的金融均衡的存在性定理，再借助微分拓扑给出它的证明过程，这一证明过程较之以前证明均衡存在性的经典方法（如Ｄｕｆｆｉｅ，Ｄ＆Ｗ．Ｓｈｆｅｒ（１９８５）的方法）要简便得多．同时也应注意到本文的这一结论既适用于资产市场下含随机风险因素的情形，也适用于商品空间为无限维的情形．除此之外，还给出了怎样判别资产结构是否属于Ｔ类的判别法，为检验均衡存在性提供了更为便利的途径．最后，本文论证了在金融市场里，尽管由于稀缺性的存在，从而导致均衡分配的多样化，然而均衡分配集却形成了一光滑子流，但该流形的维数与稀缺性有关．换句话说，尽管市场是不完全的，但均衡分配不确定性的度却是可比的．如此使得人们对均衡资产结构的认识更进一步．     

层状多孔介质中渗流湿峰的不稳定分析

在部分饱和与部分干的层状多孔介质中，建立了一维渗流问题的数学模型．在自然的条件下，证明了一类退化抛物方程弱解的存在唯一性．揭示了一个重要性质，即当下层介质的孔隙比上层更粗时，层状交界面具有隔水作用．这一作用将会在展状交界面不均匀时导致指状湿峰的出现．同时也说明，较粗孔隙的上层具有防止水分蒸发的作用．     

带风险指数的金融均衡的存在性定理及其结构特征(下)

本文主要论证了在不完全市场条件下带风险指数的金融均衡的存在性，并揭示其均衡结构的特征．本文中建立的模型是一、二期货币投入产出金融经济且具有可微的资产结构，这一模型包括了许多具有特殊资产结构的均衡模型，如实资产结构、虚资产结构、恒秩资产结构的均衡模型．因此本文的这一模型具有广泛的应用前景和实用价值．接着给出了本文的金融均衡的存在性定理，再借助微分拓扑给出它的证明过程，这一证明过程较之以前证明均衡存在性的经典方法（如Duffie，D＆W．Shfer（1985）的方法）要简便得多．同时也应注意到本文的这一结论既适用于资产市场下会随机风险因素的情形，也适用于商品空间为无限维的情形，除此之外，还给出了怎样判别资产结构是否属于T类的判别法，为检验均衡存在性提供了更为便利的途径．最后，本文论证了在金融市场里，尽管由于稀缺性的存在，从而导致均衡分配的多样化，然而均衡分配集却形成了一光滑子流，但该流形的维数与稀缺性有关．换句话说，尽管市场是不完全的，但均市分配不确定性的反却是可比的．如此使得人们对均衡资产结构的认识更进一步．     

一类EPD－方程的不完全惠更斯现象和离散现象

在本文中，通过引入含两个参数的Ｒｉｅｓｚ分布，我们给出了ＥＰＤ一方程。Ｕｔｔ＋α／ｔｕ＿ｔ－ｕ＿（ｘｘ）＋β／ｔｕ＿ｘ＝０的一类Ｃａｕｃｈｙ问题的解．当α，β取某些离散值时，解具有不完全惠更斯现象．对这些离散值，波具有单向传播的性质．利用此现象，可解释一些具有重特征方程的定解问题的离散现象．     

Lax表示的变形与Hamilton方程族的Lax表示

本文首先给出了构造演化方程族的Ｌａｘ表示的马文秀方法的一种变形，后对这一方法作了改进，使之适用于Ｈａｍｉｌｔｏｎ形式的方程族．作为应用，得到了具有非等谱Ｌａｘ表示的杨方程族．     

一个可供选择的敏感问题调查技术

为了估计一个人群总体中具有敏感属性个体的未知比例，本文提出了一种简便易行的随机化回答技术．提出的方法不需要对样本个体直接询问敏感问题．每个响应者要求根据抽自两个卡片包的两张卡片的颜色和响应者是否具有敏感属性作出一个序对的回答．通过设计参数的适当选择，说明提出的方案比已有的一些随机化策略具有更高的效率．另外，这一策略对个体隐私具有很好的保护性且容易实施．     

Slepian半小波基函数及其在无线通讯信号概率密度估计中的应用

文[20]引进了Slepian半小波基函数并讨论了这组基在概率度估计核方法中的应用[21]，Slepian半小波基函数具有极好的性质．包括多重尺度结构和局部非负性．更值得指出的是．与Gauss核不同，Slepian函数是与无线信号类似的具有平滑谱的有限带宽函数．在所有相同带宽的函数中．Slepian函数在特定的时同区域上具有最大能量．在逼近具有平滑谱的无线信号中．这些特性使得Slepian半小波核与Gauss核以及其他小波基相比具有潜在的优越性．美中不足的是．和其他核密度估计一样．Slepian核密度估计的算法设计具有一定的挑战性．幸运的是．我们注意到Slepian核可以被表示成卷积形式．这一观察具有重要的计算意义．本文主要讨论Slephn核密度估计的应用及其计算．我们首先设计了基于离散卷积的算法并讨论了这一算法的有效性．在文章的结尾，以Slepian核密度估计作为具有平滑谱的远程信号的衰减包络的模型为例．我们考查了Slepian核及其算法的性质．为了尝试数学理论与应用的紧密联系，本文的数值试验不仅采用了模拟数据而且包括了从无线通讯用户的硬件直接采集的实际数据．     

广义精确可微罚函数

本文利用凝聚函数，构造了一个新的广义精确可微罚函数，并设计了一类具有全局收敛的算法．该算法允许任意初始点，并自动调整罚因子，调整步骤是有限的．新的广义精确可微罚函数不会有“零，一阶病态”发生．     

立足基础 挖掘“缺失”——也谈试卷讲评课

试卷讲评是目前高三后阶段教学中的一个重头戏．试卷该如何讲评，是一个具有争议性的话题．最近新昌县举行了一次高三试卷讲评优质课活动．笔者有幸听了几位教师的讲评课，现对在这个活动中产生的一些看法和感悟进行阐述．     

Numerical experiments on a hybrid WENO5 filter for shock‐capturing

In the present paper, a hybrid filter is introduced for high accurate numerical simulation of shock‐containing flows. The fourth‐order compact finite difference scheme is used for the spatial discretization and the third‐order Runge–Kutta scheme is used for the time integration. After each time‐step, the hybrid filter is applied on the results. The filter is composed of a linear sixth‐order filter and the dissipative part of a fifth‐order weighted essentially nonoscillatory scheme (WENO5). The classic WENO5 scheme and the WENO5 scheme with adaptive order (WENO5‐AO) are used to form the hybrid filter. Using a shock‐detecting sensor, the hybrid filter reduces to the linear sixth‐order filter in smooth regions for damping high frequency waves and reduces to the WENO5 filter at shocks in order to eliminate unwanted oscillations produced by the nondissipative spatial discretization method. The filter performance and accuracy of the results are examined through several test cases including the advection, Euler and Navier–Stokes equations. The results are compared with that of a hybrid second‐order filter and also that of the WENO5 and WENO5‐AO schemes.     

AN EXAMPLE OF THE NON-UNIQUENESS OF THE L_5(10) ASSOCIATION SCHEME

It is known from Bose and Shimamoto that the existence of a Latin square typeL_5(10)association scheme with parameters v=100,n_1=45,p_(11)~1=20,and p_(11)~2=20 presupposesthe existence of a set of three mutually orthogonal Latin squares of order 10.But as yet wehave not known whether such a set of orthogonal Latin squares exists.In this note the author gives an association scheme with the above parameters which isnot an L_5(10)association scheme.     

Analysis of a 6-point binary subdivision scheme

In this paper, a linear 6-point binary approximating subdivision scheme with support [−6, 5] is fully investigated. It is shown that the scheme is simple and has elegant properties. We prove that the scheme can have high order continuity, polynomial reproduction and convexity preserving properties simultaneously. Furthermore, we explore the trade-offs among these properties. Examples are given to demonstrate the efficiency and flexibility of the scheme.     

Existence and stability of stationary profiles of the lw scheme

In this paper we study the behavior of difference schemes approximating solutions with shocks of scalar conservation laws When a difference scheme introduces artificial numerical diffusion, for example the Lax-Friedrichs scheme, we experience smearing of the shocks, whereas when a scheme introduces numerical dispersion, for example the Lax-Wendroff scheme, we experience oscillations which decay exponentially fast on both sides of the shock. In his dissertation. Gray Jennings studied approximation by monotone schemes. These contain artificial viscosity and are first-order accurate; they are known to be contractive in the sense of any l^p norm. Jennings showed existence and l¹ stability of traveling discrete smeared shocks for such schemes. Here we study similar questions for the Lax-Wendroff scheme without artificial viscosity; this is a nonmonotone, second-order accurate scheme. We prove existence of a one-parameter family of stationary profiles. We also prove stability of these profiles for small perturbations in the sense of a suitably weighted l² norm. The proof relies on studying the linearized Lax-Wendroff scheme.     

Generic attacks on the Lai–Massey scheme

In this paper we present generic attacks on the Lai–Massey scheme inspired by Patarin’s attacks on the Feistel scheme. For bijective round functions, the attacking results are better than non-bijective round functions for the 3, 4-round Lai–Massey scheme. Our results show that there are some security differences of these two schemes against known attacks. The generic attacks on the 4-round and 5-round Lai–Massey scheme require more complexity than the 4-round and 5-round Feistel scheme respectively. Through the analysis we believe the Lai–Massey scheme has some advantage than the Feistel scheme within 5 rounds.     

Numerical schemes for Hamilton-Jacobi equations on unstructured meshes

Summary.  In this paper, a numerical scheme is presented by applying the finite element method to the viscosity equations of the Hamilton-Jacobi equations on unstructured meshes. By improving the finite element scheme, another numerical scheme is constructed. Under certain limitations, the numerical solutions of the two schemes converge to the viscosity solutions of the Hamilton-Jacobi equations. The latter numerical scheme has weaker restrictions than the former scheme for convergence. Numerical examples are provided to test the stability, convergence and sensitivity to different meshes. Received November 5, 2001 / Revised version received March 5, 2002 / Published online October 29, 2002 RID="*" ID="*" Current address: Department of Applied Mathematics, University of Petroleum, Dongying 257062, Shandong, P.R.China; e-mail: xianggui_li@sina.com Mathematics Subject Classification (1991): 65M60     

Compact finite difference scheme for the solution of a time fractional partial integro‐differential equation with a weakly singular kernel

In this paper, we develop a high‐order finite difference scheme for the solution of a time fractional partial integro‐differential equation with a weakly singular kernel. The fractional derivative is used in the Riemann‐Liouville sense. We prove the unconditional stability and convergence of scheme using energy method and show that the convergence order is . We provide some numerical experiments to confirm the efficiency of suggested scheme. The results of numerical experiments are compared with analytical solutions to show the efficiency of proposed scheme. It is illustrated that the numerical results are in good agreement with theoretical ones.     

Non-Expansive Hashing

non-expansive hashing scheme, similar inputs are stored in memory locations which are close. We develop a non-expansive hashing scheme wherein any set of size from a large universe may be stored in a memory of size (any , and ), and where retrieval takes operations. We explain how to use non-expansive hashing schemes for efficient storage and retrieval of noisy data. A dynamic version of this hashing scheme is presented as well. Received: February 5, 1996     

A FIFTH-ORDER ACCURATE WEIGHTED ENN DIFFERENCE SCHEME AND ITS APPLICATIONS

1. IntroductionIn the paPer [1], where Zhang Hed et al. preseated the nonoocUlatory 3rdorder ENNWence scheme. The idea of ENN scheme is to compare the 1st-order dmerence and 2ndorderWence to attain 3rdorder accurate scheme and to avod spurious oscillatious neax shocks.However the ENN stwe has certain drawbaCks. One Problem is ouly 3rdords accuracyeven in the very smooth regions. AIlOther is to use a 1ot of logical statemeats which dst theconvergence rate and the efficiency Of parallel…     

HIGH ORDER FINITE DIFFERENCE/SPECTRAL METHODS TO A WATER WAVE MODEL WITH NONLOCAL VISCOSITY

In this paper, efficient numerical schemes are proposed for solving the water wave model with nonlocal viscous term that describe the propagation of surface water wave. By using the Caputo fractional derivative definition to approximate the nonlocal fractional operator, finite difference method in time and spectral method in space are constructed for the considered model. The proposed method employs known 5/2 order scheme for fractional derivative and a mixed linearization for the nonlinear term. The analysis shows that the proposed numerical scheme is unconditionally stable and error estimates are provided to predict that the second order backward differentiation plus 5/2 order scheme converges with order 2 in time, and spectral accuracy in space. Several numerical results are provided to verify the efficiency and accuracy of our theoretical claims. Finally, the decay rate of solutions is investigated.