Estimation of the measure of the image of the ball

Under study is the class of ring Q-homeomorphisms with respect to the p-module. We establish a criterion for a function to belong to the class and solve a problem that stems from M. A. Lavrentiev [1] on the estimation of the measure of the image of the ball under these mappings. We also address the asymptotic behavior of these mappings at a point.     

From the neutrino to the edge of the universe

Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously.     

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed.     

森林救火中消防队员增援人数的确定

消防部门在接到森林火情后,由于无法精确得知森林火场的风速、气温、湿度、火势蔓延程度等相关信息,加之时差现象,致使消防部门派出的救援人数有可能过少,此时就必须进行增援.本文在无风、有风的情况下,建立森林损失费用与救援费用最小的优化模型,确定了最佳增援人数.     

On the local semiconcavity of the solutions of the eikonal equation

We show that if the Hamiltonian is locally semiconvex with respect to the state variables and strictly convex with respect to the gradient then every viscosity solution of the eikonal equation is locally semiconcave. Furthermore, in the 1D case, we show that every viscosity solution of the eikonal equation is semiconcave if and only if the Hamiltonian is Lipschitz continuous with respect to the state variable.     

用常微分方程模型分析预防和隔离措施对SARS发病率的影响

通过建立常微分方程模型 ,分析了预防和隔离措施对 SARS发病率的影响 ,并把计算结果与实际统计数据进行了比较 ,结果表明 ,及时高效的预防和隔离措施能够有效地控制 SARS的传播 .     

Hume, the Occult, and the Substance of the School

I have not been able to locate any critique of Hume on substance by a Schoolman, at least in English, dating from Hume's period or shortly thereafter. I have, therefore, constructed my own critique as an exercise in ??post facto history??. This is what a late eighteenth-century/early nineteenth-century Scholastic could, would, and should have said in response to Hume's attack on substance should they have been minded to do so. That no one did is somewhat mysterious. My critique is precisely in the language of the period, using solely the conceptual resources available to a Schoolman at that time. The arguments, however, are as sound now as they were then, and in this sense the paper performs a dual role??contributing to the defence of substance contra Hume, and filling, albeit two hundred?years or so too late, a gap in the historical record.     

Algebra at the Turn of the Century

At the turn of the century it seems to be appropriate to pause and to try to envision future possibilities. We want to discuss the prospects of algebra. To look into the future requires an understanding of the past, the longstanding aims, but also the difficulties which have been encountered. We are going to review part of the history of algebra in order to outline its present state. It is important to notice the missed opportunities and to analyze the reasons. To recognize the present possibilities requires to be aware of the tools which now are available and which may not yet have been used in an optimal way. We urge the reader to focus attention to the need for algebraic considerations in all parts of mathematics but also outside of mathematics. Of course, a view back should also strengthen the interest in classical open problems which now may be feasible to attack.This is a the written version of a lecture presented at the National Conference on Algebra VII, held in Beijing Normal University, October 1999.     

On the determination of the control parameters of the optimal can-order policy

This paper considers the well-known class of can-order policies. This type of coordinated replenishment policies accounts for a joint set-up cost structure, where a major set-up cost is incurred for any order and an individual minor set-up cost is charged for each item in the replenishment. Recent comparative studies have pointed out that the performance of the optimal can-order policy is poor, compared to other coordinated replenishment strategies, when the major set-up cost is high. This paper shows that it is the approximate decomposition method to calculate the optimal canorder parameters which performs bad in such situations and not the policy itself. Attention is focused to a subclass of can-order policies, which is close to the optimal can-order policy for high major set-up costs. A solution procedure is developed to calculate the optimal control parameters of this policy. It is shown that a properly chosen combination of the solution procedures to calculate can-order parameters leads to a can-order strategy which performs as well as other coordinated replenishment policies.     

我国环境污染、对外贸易和工业发展的关系探究

使用Eviews6.0软件分析1983年至2011年的统计数据,研究环境污染、对外贸易和工业发展之间的关系.首先,使用熵值法构造环境污染综合评价指数.然后,使用Grange检验确定三个变量之间的因果关系,使用VAR模型求解三者之间的量化关系,研究了脉冲响应分析和方差分解.结果表明:对外贸易会影响工业发展,对外贸易的变动冲击在前期会促进工业发展,随着年数的增加,其作用逐渐减少;对外贸易对环境的冲击表现为先增加然后平稳的减少;工业发展对环境污染的冲击最大出现在第二期,最后,采用分位数回归研究变量关系在不同分位点的变化规律,结果表明:对外贸易在各个分位点上都是高度显著的促进工业发展;对外贸易仅在高分位点上是显著的带来环境污染.     

宏观因素影响下的系统中元件重要性研究

为研究复杂系统在工作环境中其组成元件对系统安全运行的重要性,将汪培庄先生的因素空间理论与笔者提出的空间事故树理论相结合,构造了一套元件重要性研究方法.构建系统T={U,C,D},将元件作为研究对象集合U,系统工作的宏观环境作为因素集C,元件重要性排序集作为D.对宏观环境中的工作时间a1和温度a_2进行划分形成不同的状态区域S_q,计算在S_q中元件xj的失效权重γ(AS_q(x_j))和在S_q中系统T的失效权重δ(AS_q(T))),从而得到x_j在S状态下的等效失效权重Z(AS_q(x_j)),研究状态S_q下的原件重要性排序D_η,及元件x_j失效性对a_1及a_2的敏感性.使用一个实际的电气系统维修情况统计资料,使用上述方法进行了研究,结果表明:不同工作环境下元件对系统的重要程度是不同的.元件对温度和使用时间是敏感的,并得到了在10³0°且5030°且50⁷5d环境下工作系统可靠性是最高的结论.在给定工作环境下,重要性大的元件多储备,重要性小的元件少储备,以满足系统维修需要,并指导实际工程.     

Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary.     

On choosing the location of the sources in the MFS

The satisfactory location for the sources outside the closure of the domain of the problem under consideration remains one of the major issues in the application of the method of fundamental solutions (MFS). In this work we investigate this issue by means of two algorithms, one based on the satisfaction of the boundary conditions and one based on the leave-one-out cross validation algorithm. By applying these algorithms to several numerical examples for the Laplace and biharmonic equations in a variety of geometries in two and three dimensions, we obtain locations of the sources which lead to highly accurate results, at a relatively low cost.     

基于数字化校园的校园一卡通平台设计

校园一卡通是“数字化校园”建设重要组成部分和基础工程，为“数字化校园”提供了全面的数据采集网络平台。本文从校园一卡通的功能模块、为其他管理系统提供平台、资金结算和系统安全四个方面论述了校园一卡通平台设计。     

Understanding the development of mathematical work in the context of the classroom

ZDM – Mathematics Education - According to our approach to mathematics education, the optimal aim of the teaching of mathematics is to assist students in achieving efficient mathematical...     

On the unicity of the Kato decomposition

The aim of this work is to study the unicity of the Kato decomposition associated to a pair of operators. We will prove that this decomposition is unique up to isomorphisms and we will give necessary and sufficient conditions to have unicity. This will generalize some results due to Mbekhta and Ouahab (Acta Sci. Math. (Szeged) 59 (1994) 525-543).     

Refinement of the asymptotics of the power of the quantile test

One investigates the asymptotic properties of the quantile test, similar to the properties of the Pearson's chi-square test of fit.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 153, pp. 5–15, 1986.The author is grateful to D. M. Chibisov for useful remarks.     

On the accuracy of the projection computation of the collision integral

The accuracy of the projection method as applied to the computation of the collision integral is analyzed. It is shown that the method has an error of the second order of smallness with respect to the mesh size. An optimal method for choosing additional nodes that minimizes the computational error is found. The theoretical conclusions and the optimality of the method are confirmed in a series of numerical experiments.     

On the determination of the coefficients in the viscoelasticity equations

For the integrodifferential viscoelasticity equations, we study the problem of determining the coefficients of the equations and the kernels occurring in the integral terms of the system of equations. The density of the medium is assumed to be given. We suppose that the inhomogeneity support of the sought functions is included in some compact domain B ₀. We consider a series of inverse problems in which an impulse source is concentrated at the points y of the boundary of B ₀. The point y is the parameter of the problem. The given information about the solution is the trace of the solution to the Cauchy problem with zero initial data. This trace is given on the boundary of B ₀ for all y ∈ ?B ₀ and for a finite time interval. The main result of the article consists in obtaining uniqueness theorems for a solution to the initial inverse problem.     

Tackling the Challenge of the Nineties

In this annual Blackett Lecture the experience of pursuing the challenge of rational planning and decision-making in London Transport is discussed. Secondly, some of the major challenges affecting all large business organizations in the 1990s are described. Thirdly, the characteristics which enable organizations to respond effectively to these challenges, and which help ensure their survival and success, are delineated.