不等式等号成立条件的探求及应用

纵观有关不等式的证明问题，大致可以分为两大类：如果不等式的条件(若有条件)和结论皆为对称表达式，我们称这样的不等式为对称不等式．如果不等式的条件(若有条件)和结论至少有一个为非对称表达式，我们称这样的不等式为非对称不等式．     

共轭Neumann-Bessel级数的收敛速度

给出共轭Neumann-Bessel级数的核函数的渐近表达式，它的精度达到O（），然后利用这个表达式，讨论了该级数的收敛速度．     

固定-固定型无阻尼弹簧质点系统的质量约束问题

本文讨论了系统总质量约束下的固定一固定型无阻尼弹簧质点系统的构造问题，得到了该问题的可解性条件，给出了解的表达式和数值算法，算例说明算法是有效的．     

多凸域型网格的Buffon问题

本文研究了以多个凸域的并为基本区域的网格的Buffon问题．利用包含测度的有关结论，获得了Buffon问题的普遍公式，并作为举例具体计算了一种三个凸域的情况的表达式和特殊化的数值．     

谱约束下对称正交对称矩阵束的最佳逼近

讨论了对称正交对称矩阵的广义逆特征值问题，得到了通解表达式和最佳解的表达式。     

复合广义齐次Poisson过程的多险种破产概率

本文推广了经典的复合泊松风险模型，建立了两类复合广义齐次poisson过程的多险种破产模型．对于新模型，我们得到了初始资本为u的破产概率φ(u)的精确表达式以及特殊情况下φ(0)的表达式，并且导出了调节系数方程和调节系数R的上下界．     

关于加权广义逆的上确界

设P为一类半正定实对称矩阵的集合，满足本文推导此上确界的若干等价性表达式，并具体讨论几种特殊情形．该问题在数学规划和约束最优化问题中具有重要意义     

函数概念的两个注记

函数概念的两个注记黄炳生（东南大学）ｌ问题的提出己知两个函数（１）定义域为。一０，１，２．表达式为９一ｆ（Ｘ）一Ｉ’一Ｚ’一Ｔ（２）定义域为。一０．１，２，表达式为９一／１）一ｈＴ一３ＩＳ问这两个函数是否相同。回答是；既可以说是不同的函数。又可以说是...     

线性流形上D对称矩阵反问题的最小二乘解

本研究了线性流形上D对称矩阵反问的最小二乘解及其逼近问题，给出了最小二乘解的一般表达式，并就该问题的特殊情况－矩阵反问题，获得了有解的充分必要条件，并在有解的条件下得到了解的一段表达式。     

一类E-Vandermonde矩阵的求逆及逆的迭代公式

本文给出一类E-Vandermonde矩阵和广义E-Vandermonde矩阵可逆的条件及逆的矩阵表达式，并给出了求逆的迭代公式．     

From searching text to querying XML streams

XML data is queried with a limited form of regular expressions, in a language called XPath. New XML stream processing applications, such as content-based routing or selective dissemination of information, require thousands or millions of XPath expressions to be evaluated simultaneously on the incoming XML stream at a high, sustained rate. In its simplest approximation, the XPath evaluation problem is analogous to the text search problem, in which one or several regular expressions need to be matched to a given text. At a finer level, it is related to the tree pattern matching problem. However, unlike the traditional setting, the number of regular expressions here is much larger, while the “text” is much shorter, since it corresponds to the depth of the XML stream. In this paper we examine techniques that have been proposed for XML stream processing and describe a few open problems.     

Local search for the probabilistic traveling salesman problem: Correction to the 2-p-opt and 1-shift algorithms

The probabilistic traveling salesman problem concerns the best way to visit a set of customers located in some metric space, where each customer requires a visit only with some known probability. A solution to this problem is an a priori tour which visits all customers, and the objective is to minimize the expected length of the a priori tour over all customer subsets, assuming that customers in any given subset must be visited in the same order as they appear in the a priori tour. This problem belongs to the class of stochastic vehicle routing problems, a class which has received increasing attention in recent years, and which is of major importance in real world applications.Several heuristics have been proposed and tested for the probabilistic traveling salesman problem, many of which are a straightforward adaptation of heuristics for the classical traveling salesman problem. In particular, two local search algorithms (2-p-opt and 1-shift) were introduced by Bertsimas.In a previous report we have shown that the expressions for the cost evaluation of 2-p-opt and 1-shift moves, as proposed by Bertsimas, are not correct. In this paper we derive the correct versions of these expressions, and we show that the local search algorithms based on these expressions perform significantly better than those exploiting the incorrect expressions.     

Cauchy-Riemann方程的Riemann-Hilbert边值问题

本文考虑多柱域上非齐次的Cauchy-Riemann方程的Riemann-Hilbert边值问题.讨论了上述边值问题可解的充分必要条件,并给出了边值问题解的积分表达式.     

关于调和级数的部分和的推导及证明

中世纪后期,数学家Oresme证明了所有调和级数都是发散的,但是调和级数的拉马努金和存在,且为Euler常数.Euler在1734年利用Newton的成果,首先给出了调和级数的部分和的表达式.通过分析Ross,S.M.对经典概率论问题"优惠券收集问题"的解决方法,得到了调和级数的部分和的不同表达式,并运用数学归纳法,变量代换证明了表达式的正确性.     

圆形界面刚性线夹杂的平面问题

研究了圆弧形界面刚性线夹杂的平面弹性问题．集中力作用于夹杂或基体中的任意点,并且无穷远处受均匀载荷作用．利用复变函数方法,得到了该问题的一般解答．当只含一条界面刚性线夹杂时,获得了分区复势函数和应力场的封闭形式解答,并给出刚性线端部奇异应力场的解析表达式．结果表明,在平面荷载下界面圆弧形刚性线夹杂尖端应力场和裂纹尖端相似具有奇异应力振荡性．对无穷远加载的情况,讨论了刚性线几何条件、加载条件和材料失配对端部场的影响．     

Boundary value problems for second-order differential operator equations

It is proved that the resolution problem of an operator boundary-value problem for a second-order differential operator equation with constant coefficients is solved in terms of solutions of certain algebraic operator equations. Explicit expressions of solutions are given.     

Integral formulae in the coupled problem of the thermoelasticity of an inhomogeneous body. Application in the mechanics of composite materials

A coupled unsteady problem of thermoelasticity for an inhomogeneous body, described by a system of four second-order partial differential equations with coefficients that vary depending on the coordinates, is considered, and the same problem for a homogeneous body of the same shape (the concomitant problem) is examined together with this original problem. Integral formulae are obtained that allow one to express the displacements and temperature in the original problem in terms of the displacements and temperature in the concomitant problem. Integral formulae are used to represent the solution of the original problem in the form of series over all possible derivatives of the solution of the concomitant problem. A system of recurrence problems is written for the coefficients of these series. Expressions are found for the coefficients of the concomitant problem (effective coefficients) and special boundary value problems are formulated, from the solution of which specific expressions are found for the effective thermoelasticity coefficients. A theorem concerning the fact that the effective coefficients satisfy the physicomechanical constraints imposed on the thermoelastic constants of real bodies is proved. The case of a layer that is inhomogeneous in its thickness is considered and explicit analytical expressions for all the thermoelasticity coefficients are obtained for it. The case when the thermoelasticity coefficients depend periodically on the coordinates is examined in detail.     

动态 Stackelberg 诱导对策问题

Stackelberg 诱导(Incentive)对策,以简单的二人对策来说,是讨论对一个具有递阶决策结构的系统,处于领导地位的决策者,如何通过选择和宣布适当的策略,来诱导处于随从地位的决策者采取对领导最为有利行动的问题.自从文[1]从控制理论的观点讨论了 Incentive 的概念后,Stackelberg 诱导对策的研究受到了较多的关注,发现了不少研究成果.然而从到迄今所出现的文献来看,对概念性问题的研究较多,而较缺乏有效的,特     

均值-方差准则下的多期最优保险投资(英文)

近年来,最优保险投资问题吸引了越来越多的注意。一般这个问题是在连续时间框架下来研究的。本文针对这一问题建立离散时间的最优控制模型。应用动态规划原理求解模型对应的近似问题,得到了最优投资策略和投资有效边界的解析表达形式。本文得到的最优投资策略和投资有效边界均依赖于承保参数。通过数值例子分析了承保参数对最优投资策略和有效边界的影响。     

The generation of beams of three-dimensional periodic internal waves in an exponentially stratified fluid

The spectral method is used to construct an exact solution of the linearized problem of the generation of disturbances by localized sources that execute arbitrary periodic motions in a viscous exponentially stratified fluid. The expressions obtained do not contain any adjusting parameters and describe conical beams of three-dimensional periodic internal waves and two types of boundary layers, the spatial scale of which is given by the kinematic viscosity and the buoyancy frequency of the medium. The thickness of one of them, which is analogous to Stokes periodic flow in a homogeneous viscous fluid, is specified by the kinematic viscosity and the wave frequency, that is, it additionally depends on a ratio of the wave and buoyancy frequencies. The thickness of the specific internal boundary layer also depends on the geometry of the problem. In the approximation of weak stratification and low viscosity, asymptotic estimates of the expressions obtained are presented for two types of generators, namely, in the form of a plane inclined rectangle that vibrates along its surface (a frictional source) and along the normal to it (a piston source) in the non-degenerate case when the wave cone does not touch the radiating plane. In limiting cases the analytical expressions obtained agree with known exact solutions of the problem of generating axially symmetric and two-dimensional periodic internal waves.