函数振幅的性质与应用

函数振幅是微积分中最基本的概念之一，它的性态决定了函数许多解析性质．本文中扩充了函数振幅的定义．并利用它定义了函数振动性强弱的概念．作为这一概念的应用，建立起判定函数连续性、一致连续性、可积性、有界变差性的比较判别法，并给出了一些应用实例．     

D.C.隶属函数模糊集及其应用(Ⅱ)--D.C.隶属函数模糊集的万能逼近性

本文是D．C．隶属函数模糊集及其应用系列研究的第二部分。指出在实际问题中普遍选用的三角形、半三角形、梯形、半梯形、高斯型、柯西型、S形、Z形、π形隶属函数模糊集等均为D．C．隶属函数模糊集，建立了D．C．隶属函数模糊集对模糊集的万有逼近性。探讨了D．C．隶属函数模糊集与模糊数之间的关系，给出了用D．C．隶属函数模糊集逼近模糊数的e-Cellina逼近形式，得到模糊数与D．C．函数之间的一个对应算子，指出了用模糊数表示D．C．函数的问题。     

一道函数关系建立习题的复习课教学设计及反思

函数是中学数学的核心内容，函数关系的建立是函数的“灵魂”，具有实际背景的函数关系的建立是一个难点，如何破解这个难点是一个无法回避的问题．在今年的高三复习中，笔者试从必修1教材一道习题出发，通过该题的横向变式和纵向类比来突破，是否妥当，求教于各位专家和同行．     

用初等函数表示一类分段函数的方法

用初等函数表示一类分段函数的方法郑州粮食学院龙洪波，伍毅分段函数作为特珠的函数是建立数学模型时经常遇到的一类函数．在一定的条件下，如果能将分段函数化成初等函数，将有利于研究它们的各种性态．本文将给出只有一个分段点，且在两区间段上的表达式均为多项式函数...     

一类min-max-min问题的区间算法

讨论了一类由一阶连续可微函数构成的无约束min-max-min问题．通过构造目标函数的区间扩张、无解区域删除原则，建立了求解min-max-min问题的区间算法，证明了算法的收敛性，给出了数值算例．理论证明和数值结果表明方法是可靠和有效的．     

危险拒绝函数估计的两个定理

对于未知分布律的生存发展函数和危险拒绝函数作出了新的非参数估计，建立并证明了两个定理，得出了二次均方差最小化的最佳参数值．     

线性l1模极小化问题的熵函数延拓法

本文通过利用极大熵函数构造同伦映射，建立了求解无约束线性l1模问题的熵函数延拓算法，证明了方法的收敛性，并给出了数值算例．     

非线性规划中凝聚函数法的稳定性

本文引入"非退化点"的概念，在很弱的条件下对一类广泛的函数类建立了凝聚函数法的稳定性定理．     

广义函数框架下的小波变换及其性质

本文将L^2空间的小波变换推广到广义函数空间上，建立了广义函数框架下的小波变换，证明了广义函数的小波变换及其有关性质，使小波变换这一信号分析的数学工具有了更大的应用范围．     

指数有界的C余弦算子函数

本文引入了指数有界的Ｃ余弦算子函数的生成元，讨论了生成元的基本性质，建立了相应的生成定理、逼近定理及扰动定理．最后给出了指数有界的Ｃ余弦算子函数与指数有界的Ｃ半群的基本联系．     

On the convexity of the multiplicative version of Karmarkar's potential function

Karmarkar's potential function is quasi-convex, but not convex. This note investigates the multiplicative version of the potential function, and shows that it is not necessarily convex in general, but is strictly convex when the corresponding feasible region is bounded. This implies that the multiplicative version of the potential function in Karmarkar's algorithm is convex, since it works on a simplex.     

An Iterative Global Optimization Algorithm for Potential Energy Minimization

In this paper we propose an algorithm for the minimization of potential energy functions. The new algorithm is based on the differential evolution algorithm of Storn and Price (Journal of Global Optimization, vol. 11, pp. 341–359, 1997). The algorithm is tested on two different potential energy functions. The first function is the Lennard Jones energy function and the second function is the many-body potential energy function of Tersoff (Physics Review B, vol. 37, pp. 6991–7000, 1988; vol. 38, pp. 9902–9905, 1988). The first problem is a pair potential and the second problem is a semi-empirical many-body potential energy function considered for silicon-silicon atomic interactions. The minimum binding energies of up to 30 atoms are reported.Visitor at the Institute for Mathematics and its Applications, University of Minnesota, USA.     

An application of optimization theory to the study of equilibria for games: a survey

This contribution is a survey about potential games and their applications. In a potential game the information that is sufficient to determine Nash equilibria can be summarized in a single function on the strategy space: the potential function. We show that the potential function enable the application of optimization theory to the study of equilibria. Potential games and their generalizations are presented. Two special classes of games, namely team games and separable games, turn out to be potential games. Several properties satisfied by potential games are discussed and examples from concrete situations as congestion games, global emission games and facility location games are illustrated.     

Generation of Delaunay meshes in implicit domains with edge sharpening

A variational algorithm for the construction of 3D Delaunay meshes in implicit domains with a nonsmooth boundary is proposed. The algorithm is based on the self-organization of an elastic network in which each Delaunay edge is interpreted as an elastic strut. The elastic potential is constructed as a combination of the repulsion potential and the sharpening potential. The sharpening potential is applied only on the boundary and is used to minimize the deviation of the outward normals to the boundary faces from the direction of the gradient of the implicit function. Numerical experiments showed that in the case when the implicit function specifying the domain is considerably different from the signed distance function, the use of the sharpening potential proposed by Belyaev and Ohtake in 2002 leads to the mesh instability. A stable version of the sharpening potential is proposed. The numerical experiments showed that acceptable Delaunay meshes for complex shaped domains with sharp curved boundary edges can be constructed.     

环面上具有间断梯度的势函数的模拟退火

本文证明了环面上具有间断梯度的势函数的模拟退火过程：dXt=-VU(Xt)dt √2dWt概率收敛到势函数的全局极小集附近。     

Estimation of interaction potentials of spatial point patterns through the maximum likelihood procedure

Summary A homogeneous spatial point pattern is regarded as one of thermal equilibrium configurations whose points interact on each other through a certain pairwise potential. Parameterizing the potential function, the likelihood is then defined by the Gibbs canonical ensemble. A Monte Carlo simulation method is reviewed to obtain equilibrium point patterns which correspond to a given potential function. An approximate log likelihood function for gas-like patterns is derived in order to compute the maximum likelihood estimates efficiently. Some parametric potential functions are suggested, and the Akaike Information Criterion is used for model selection. The feasibility of our procedure is demonstrated by some computer experiments. Using the procedure, some real data are investigated. The Institute of Statistical Mathematics     

Application in Aerohydrodynamics of the Solution of an Inverse Boundary Value Problem for Analytic Functions

We consider a modified inverse boundary value problem of aerohydrodynamics in which it is required to find the shape of an airfoil streamlined by a potential flow of an incompressible nonviscous fluid, when the distribution of the velocity potential on one section of the airfoil is given as a function of the abscissa, while, on other sections of the airfoil, as a function of the ordinate of the point. The velocity of the undisturbed flow streamlining the sought-for airfoil is determined in the process of solving the problem. It is shown that, under rather general conditions on the initially set functions, the sought-for contour is closed unlike the inverse problem in the case when, on the unknown contour, the velocity distribution is given as a function of the arc abscissa of the contour point. We also consider the case when, on the entire desired contour, the distribution of the velocity potential is given as a function of one and the same Cartesian coordinate of the contour point.     

Interactive decisions and potential games

The aim of this contribution is an overview on Potential Games. This class of games is special, in fact we can investigate their properties by a unique function: the potential function. We consider several types of potential games: exact, ordinal, bayesian and hierarchical. Some results are generalized to multicriteria decisions.      

Solving inverse boundary-value problem of aerohydrodynamics in a new statement

We consider a modified inverse boundary-value problem of aerohydrodynamics, in which it is required to find the shape of a wing profile, streamlined by a potential flow of incompressible inviscid fluid, when the distribution of the velocity potential on one section of the profile is given as a function of abscissa, and on the rest of the profile as a function of the ordinate of the profile point.     

A Sub-Density Theorem of Sturm-Liouville Eigenvalue Problem with Finitely Many Singularities

We study the distribution of the Sturm-Liouville eigenvalues of a potential with finitely many singularities. There is an asymptotically periodical structure on this class of eigenvalues as described by the entire function theory. We describe the singularities of its potential function explicitly in its eigenvalue asymptotics.