一个体现新课程理念的教学内容设计——“圆锥曲线第二定义”的教学体会

正新课程实验教材已完成了一轮教学.由于新课程的理念变了,编写意图也发生了变化,新教材相对于与原教材而言,内容变了、体系改了、要求不同了、方法更新了.因此,在教学中新     

分层教学的Bayes分析

对学校分层教学进行了初步探索 ,提出了分层分班的 Bayes决策 ,介绍了分层分班方法 ,获得了一些结论 ,并完成了对这些结论的证明 ,从理论上论述了分层教学是实施“因材施教”教育原则和素质教育的有效途径 ,给出了应用实例 .     

绿色食品需求函数的一种求解方法

本分析了影响绿色食品消费的因素，建立了消费消费绿色食品及同类一般食品的效用最大化数学规划模型，给出了Kuhn-Tucker条件；引入了绿色食品置信度参数并建立了一个可计算的二次效用函数，导出了该二次效用函数对应的需求函数，并详细地表述了求解过程和方法，讨论了绿色食品需求函数的性质。     

标准体系的使用期的模型与分析

本文提出了关于标准体系使用期的两个模型。首先定义了标准使用期,然后讨论了模型的合理性。通过模型讨论了标准使用期的性质,给出了数值示例。提出了需进一步研究的问题。     

数学是……

数学是一首悠扬的歌
　　直线成了五线谱
　　圆连成了音符
　　唱出了奇妙的快乐
　　数学是一幅清新的画
　　曲线成了浪花
　　线性规划调出了最佳
　　绘出了斑斓的色彩     

基于粗糙集的患者满意度评价模型及其实证分析

在文献阅读及实地调研的基础上,本文提出了患者满意度的定义,建立了影响患者满意度的指标体系,介绍了粗糙集的相关概念及利用粗糙集进行评价的步骤,提出了新的约简方法,构建了基于粗糙集的患者满意度评价模型并进行了实证分析,得出了影响患者满意度的关键指标,并计算了关键指标权重,对江西省十个医院进行了综合评价值的计算.     

网络安全产品研究

本文在研究了网络安全的国内外有关情况后对网络安全技术进行了探讨 ,介绍了一种简单而实用的网络安全产品 ,添补了这方面的空白 ,而且本文介绍的产品已经应用到了许多部门 ,为网络安全做出了贡献     

数学小报，我来也

数学小报好处多
　　1.开阔了视野,开发了思维。
　　2.给学习增添了新鲜感,激发了学习数学的积极性。
　　3.能够复习、梳理已学知识点,锻炼了整理知识的能力。
　　4.培养了动手、动脑的习惯,培养了想象力和创造力。     

分数阶抛物方程控制系统最优控制的稳定性（英文）

本文研究了一类分数阶抛物方程的最优控制问题,主要讨论了其最优控制与最优值的稳定性.利用了凸方法获得了获得了这类问题最优控制的稳定性结果,并且推广了在参考文献[3]中的最优控制稳定性结论.     

分数阶抛物方程控制系统最优控制的稳定性

本文研究了一类分数阶抛物方程的最优控制问题,主要讨论了其最优控制与最优值的稳定性.利用了凸方法获得了获得了这类问题最优控制的稳定性结果,并且推广了在参考文献[3]中的最优控制稳定性结论.     

Coupled-expanding maps and one-sided symbolic dynamical systems

This paper studies relationships between coupled-expanding maps and one-sided symbolic dynamical systems. The concept of coupled-expanding map is extended to a more general one: coupled-expansion for a transitive matrix. It is found that the subshift for a transitive matrix is strictly coupled-expanding for the matrix in certain disjoint compact subsets; the topological conjugacy of a continuous map in its compact invariant set of a metric space to a subshift for a transitive matrix has a close relationship with that the map is strictly coupled-expanding for the matrix in some disjoint compact subsets. A certain relationship between strictly coupled-expanding maps for a transitive matrix in disjoint bounded and closed subsets of a complete metric space and their topological conjugacy to the subshift for the matrix is also obtained. Dynamical behaviors of subshifts for irreducible matrices are then studied and several equivalent statements to chaos are obtained; especially, chaos in the sense of Li–Yorke is equivalent to chaos in the sense of Devaney for the subshift, and is also equivalent to that the domain of the subshift is infinite. Based on these results, several new criteria of chaos for maps are finally established via strict coupled-expansions for irreducible transitive matrices in compact subsets of metric spaces and in bounded and closed subsets of complete metric spaces, respectively, where their conditions are weaker than those existing in the literature.     

Representations for the conductivity functions of multicomponent composites

The effective conductivity σ* of a multicomponent composite material is considered. Integral representations for σ* treated as a holomorphic function on a polydisk with values in a half-plane are analyzed. A representation for σ* is introduced which is symmetric in the component conductivities and for which the moments of the positive measure in the integral are directly related to the coefficients in a perturbation expansion of σ* around a homogeneous medium. This second feature, which is important for obtaining bounds on σ*, was previously available only in the two-component case. In addition, a bound valid for any holomorphic function of the above type is proven.     

马氏环境中可数马氏链的Poisson极限率

研究了马氏环境中的可数马氏链,主要证明了过程于小柱集上的回返次数是渐近地服从Poisson分布。为此,引入熵函数h,首先给出了马氏环境中马氏链的Shannon-Mc Millan-Breiman定理,还给出了一个非马氏过程Posson逼近的例子。当环境过程退化为一常数序列时,便得到可数马氏链的Poisson极限定理。这是有限马氏链Pitskel相应结果的拓广。     

A sphere in a second degree polynomial creeping flow parallel to a wall

Comprehensive results are provided for the creeping flow arounda spherical particle in a viscous fluid close to a plane wall,when the external velocity is parallel to the wall and variesas a second degree polynomial in the coordinates. By linearityof Stokes equations, the solution is a sum of flows for typicalunperturbed flows: a pure shear flow, a ‘modulated shearflow’, for which the rate of shear varies linearly inthe direction normal to the wall, and a quadratic flow. Solutionsconsidered here use the bipolar coordinates technique. Theycomplement the accurate results of Chaoui and Feuillebois (2003)for the pure shear flow. The solution of Goren and O'Neill (1971)for the quadratic flow is reconsidered and a new analyticalsolution is derived for the ambient modulated shear flow. Theperturbed flow fields for these two cases are presented in detailand discussed. Results for the force and torque friction factorsare provided with a 5 x 10^–17 accuracy as a reference.For the quadratic flow, there is a force and a torque on a fixedsphere. A minimum value of the torque is found for a gap ofabout 0·18a, where a is the sphere radius. This minimumis interpreted in term of the corresponding flow structure.For the modulated shear flow, there is only a torque. The freemotion of a sphere in an ambient quadratic flow is also determined.     

A necessary and sufficient condition for Pareto-optimal security strategies in multicriteria matrix games

In this paper, a scalar game is derived from a zero-sum multicriteria matrix game, and it is proved that the solution of the new game with strictly positive scalarization is a necessary and sufficient condition for a strategy to be a Pareto-optimal security strategy (POSS) for one of the players in the original game. This is done by proving that a certain set, which is the extension of the set of security level vectors in the criterion function space, is convex and polyhedral. It is also established that only a finite number of scalarizations are necessary to obtain all the POSS for a player. An example is included to illustrate the main steps in the proof.This work was done while the author was a Research Associate in the Department of Electrical Engineering at the Indian Institute of Science and was financially supported by the Council of Scientific and Industrial Research, Delhi, India.The author wishes to express his gratefulness to Professor U. R. Prasad for helpful discussions and to two anonymous referees for suggestions which led to an improved presentation.     

Decision Networks

Decision Networks is a technique for solving problems which involve a sequence of decisions. It is similar in style to critical path analysis in that it consists of arrow diagrams which give a visual representation of the problem and are used as a basis for a simple calculation procedure. The technique can deal with deterministic and stochastic problems and in the latter case is more general than decision trees. The decision network approach meets the need for a method of solution for multi-stage decision problems which is easily understood, helps the user to visualize the nature of the problem and is routine in application.     

Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations

A variety of numerical methods are available for determining the stability of a given solution of a partial differential equation. However for a family of solutions, calculation of boundaries in parameter space between stable and unstable solutions remains a major challenge. This paper describes an algorithm for the calculation of such stability boundaries, for the case of periodic travelling wave solutions of spatially extended local dynamical systems. The algorithm is based on numerical continuation of the spectrum. It is implemented in a fully automated way by the software package wavetrain, and two examples of its use are presented. One example is the Klausmeier model for banded vegetation in semi-arid environments, for which the change in stability is of Eckhaus (sideband) type; the other is the two-component Oregonator model for the photosensitive Belousov–Zhabotinskii reaction, for which the change in stability is of Hopf type.     

A Robust Replacement Model with Applications to Medical Equipment

Perceived shortcomings in the applicability of capital equipment replacement modelling, identified in a 1987 survey within the UK are addressed and a robust replacement model formulated. First, however, a comparison between the 1987 survey and a similar 1988 survey undertaken within the USA is made and explanations for apparent differences in conclusions are presented. A replacement model is then developed in the context of medical equipment where factors such as service and risk play a role in replacement decision-making. A mechanism for quantitatively allowing for qualitative and for political type factors within a short time horizon replacement model is introduced by means of a penalty factor. A case example is presented for medical ventilator equipment.     

Approximate analytic solutions to Radulet equations for the analysis of electromagnetic transients in single-phase power transmission lines

In this work, an analytic development for a transmission line with a corona effect for simulating an electromagnetic transient is presented. The asymptotic solution for the Radulet equations in which a nonlinear term is presented is obtained. The study is carried out for a single-phase transmission line. The electrical parameters for an overhead line are defined and several formulations for their calculation are presented. The frequency dependence of the electrical parameters is considered. In the first part, the linear problem solution is found; the Fourier and Laplace transforms are applied with respect to distance and time respectively. After finding the solution in the Fourier–Laplace domain, which is expressed in terms of a Green’s function integral, an approximate analytical solution is obtained in the distance–time domain by means of asymptotic methods. Finally, the nonlinear solution is found using as a first approach the linear solution. The results obtained show an attenuation in the voltage wave due to the corona effect.