关于模糊值凸函数的共轭问题的研究

在Goetschel-Voxman所引进的序关系下,首先给出了模糊值凸函数的共轭函数的概念,并证明了模糊值凸函数的共轭函数是模糊值凸函数等相关性质;其次给出了模糊值凸函数的二次共轭函数的概念,并证明了相关性质;最后讨论了模糊值凸函数的共轭与下卷积之间的关系,证明了两个模糊值凸函数的共轭函数与其下卷积的共轭函数之间的等式关系.     

Alternative proofs for inequalities of some trigonometric functions

By using an identity relating to Bernoulli's numbers and power series expansions of cotangent function and logarithms of functions involving sine function, cosine function and tangent function, four inequalities involving cotangent function, sine function, secant function and tangent function are established.     

Multifunctional assessment and zoning of crop production system based on set pair analysis-A comparative study of 31 provincial regions in mainland China

In this study, we present a multifunctional indicator system for the performance evaluation of crop production system by set pair analysis method. Five functions were summarized to represent the multifunctionality of crop production system, including production function, supply function, ecological function, security function and economic function. Setting a case study of 31 provincial regions in mainland China, this paper conducted a comparison of each function in different regions, divided into 9 groups by cluster analysis. The results show that: the levels of multifunction in most regions are under a low degree balance; the production function has a high coordination with the economic function and security function in China; the supply function is lowly correlated with the other functions, especially the economic function has negative correlation with the supply function to some extent; some relevant policies and suggestions are deduced for multifunctional improvement. It is concluded that the multifunctional indicators and the set pair analysis method can serve as an effective method for the assessment of crop production system.     

加权正则函数的一些性质

正则函数是Clifford分析中的一类重要函数,加权正则函数是正则函数的进一步发展,也是一类重要的函数,因此具有一定的研究意义.在正则函数的研究基础上,并利用加权正则函数自身的性质,讨论了加权正则函数的平均值定理,最大模原理,Weierstrass定理以及一些其它推论.     

关于P-凸函数的积分型Jensen不等式

基于P-凸函数的函数凸性,研究了P-凸函数的Jensen型不等式的积分形式,通过定积分的定义计算,得到了P-凸函数的积分型Jensen不等式;利用P-凸函数的一个充要条件,建立了P-凸函数的积分型Jensen不等式的加权形式.     

基于不同核函数的非参数与参数利率模型的国债定价

以上海证券交易所的国债回购利率数据为样本,本文采用两种不同核函数:高斯核和抛物线核对非参数利率期限结构模型进行估计.结果显示:短期利率的密度函数是非正态的,扩散过程的漂移函数和扩散函数都是非线性的,高斯核比抛物线核对扩散函数拟合更平滑.然后,给出了基于非参数和参数利率模型的国债定价的方法,并对非参数利率模型、Vasicek模型、CIR模型、多项式样条静态模型进行国债定价预测比较与分析.     

一类函数增量的局部渐近性质

文章研究了一类函数增量的局部渐近性质,发现这类函数增量的局部渐近性对于一元实函数,二元及多元实函数,向量值函数和复函数在一定条件下都会保持不变,进而提出了两个相关的猜想:此类函数增量的渐近性是关于函数变换的拓扑不变量。     

ALGEBROIDAL FUNCTION AND ITS DERIVED FUNCTION IN UNIT CIRCULAR DISC

In this article,the authors define the derived function of an algeboidal function in the unit disc,prove it is an algabriodal function,and study the order of algebroidal function and that of its derived function in unit circular disc.     

An Algorithm for Finding Global Minimum of Nonlinear Integer Programming

A filled function is proposed by R.Ge[2] for finding a global minimizer of a function of several continuous variables. In [4], an approach for finding a global integer minimizer of nonlinear function using the above filled function is given. Meanwhile a major obstacle is met: if $ρ > 0$ is small, and $||x_I-\overset{*}{x}_I||$ is large, where $x_I$ - an integer point, $\overset{*}{x}_I$ - a current local integer minimizer, then the value of the filled function almost equals zero. Thus it is difficult to recognize the size of the value of the filled function and can not find the global integer minimizer of nonlinear function. In this paper, two new filled functions are proposed for finding global integer minimizer of nonlinear function, and the new filled function improves some properties of the filled function proposed by R. Ge [2].Some numerical results are given, which indicate the new filled function (4.1) to find global integer minimizer of nonlinear function is efficient.     

New filled functions for nonsmooth global optimization

The filled function method is an effective approach to find a global minimizer for a general class of nonsmooth programming problems with a closed bounded domain. This paper gives a new definition for the filled function, which overcomes some drawbacks of the previous definition. It proposes a two-parameter filled function and a one-parameter filled function to improve the efficiency of numerical computation. Based on these analyses, two corresponding filled function algorithms are presented. They are global optimization methods which modify the objective function as a filled function, and which find a better local minimizer gradually by optimizing the filled function constructed on the minimizer previously found. Numerical results obtained indicate the efficiency and reliability of the proposed filled function methods.     

周期函数和非平稳周期函数的小波变换

探讨了三角函数、周期函数以及一类非平稳周期函数小波变换的一些性质,发现周期函数的小波能谱的峰高和峰宽均正比于信号的周期.提出了一个新的只利用与信号周期有关的一个尺度小波变换系数的重构公式,它可准确地重构三角函数,对一般周期函数的重构结果优于其Fourier级数中的任何一项,对一类均值和振幅变化的非平稳周期函数的重构结果与信号非常吻合.     

全局最优化问题的一个无参数的填充函数算法

本文研究了全局最优化问题.利用构造填充函数的方法,提出了一个新的无参数填充函数,它是目标函数的一个明确表达式.得到了一个新的无参数填充函数算法,数值试验结果表明该填充函数算法是有效的,从而推广了填充函数算法在求解全局最优化问题方面的应用.     

Integrals of psi—function

To the author's knowledge, among the so—called special functions, the gamma function is a unique one which is defined by a linear difference equation and is a hyper—transcendental function. There exists an another well—known hyper—transcendental function called the psi function, which is merely the logarithmic derivative of the gamma function. In this paper the author consider an extension of the gamma function and then obtain a series of integrals of the psi function.     

齐次生产函数条件下长期成本函数的确定方法

文章研究一般性齐次生产函数条件下长期成本函数的确定方法，证明了长期成本函数是关于产量的幂函数，并指出了长期边际成本函数和长期平均成本函数之间的特殊关系。     

收入分布曲线的线性正态插值函数拟合方法

用样本数据的分组均值与总体方差为参数的正态函数作为插值基函数,构造出线性正态插值函数曲线以拟合中国城乡居民收入的概率分布函数曲线,并论证了这样构造的线性正态插值函数存在且唯一,此插值函数任意阶可微.利用拟合的正态插值函数曲线计算出拟合的函数面积估计值并与相应的样本数据直方图面积做比较,进而得出正态插值函数拟合曲线面积与样本数据直方图的面积误差比率.     

基于二次多项式的积极集光滑化max函数及其在无约束minimax问题中的应用

本文基于分段二次多项式方程,构造了一种积极集策略的光滑化max函数.通过给出与光滑化max函数相关的分量函数指标集的直接计算方法,将分段二次多项式方程转化为一般二次多项式方程.利用二次多项式方程根的性质,给出了该光滑化max函数的稳定计算策略,证明了其具有一阶光滑性,其梯度函数具有局部Lipschitz连续性和强半光滑性.该光滑化max函数仅与函数值较大的分量函数相关,适用于含分量函数较多且复杂的max函数的问题.为了验证其效率,本文基于该函数构造了一种解含多个复杂分量函数的无约束minimax问题的光滑化算法,数值实验表明了该光滑化max函数的可行性及有效性.     

基于功能不可加系统的系统优化

为了揭示系统的某一功能达到最优与其所有子系统为实现系统这一功能而提供的功能之间的关系,基于系统功能具有可加和不可加的特性,探讨了功能不可加系统的功能优化方法,以子系统功能的实现度为决策变量,以系统功能发挥最大效用为目标函数,以实现功能所需的资源为约束条件,建立了功能不可加系统优化的规划模型,最后辅以算例,并通过EXCEL Solver求解进行了分析.     

Algorithm of Barrier Objective Penalty Function

In this paper, an algorithm of barrier objective penalty function for inequality constrained optimization is studied and a conception–the stability of barrier objective penalty function is presented. It is proved that an approximate optimal solution may be obtained by solving a barrier objective penalty function for inequality constrained optimization problem when the barrier objective penalty function is stable. Under some conditions, the stability of barrier objective penalty function is proved for convex programming. Specially, the logarithmic barrier function of convex programming is stable. Based on the barrier objective penalty function, an algorithm is developed for finding an approximate optimal solution to an inequality constrained optimization problem and its convergence is also proved under some conditions. Finally, numerical experiments show that the barrier objective penalty function algorithm has better convergence than the classical barrier function algorithm.     

Unconstrained Optimization Reformulations of Variational Inequality Problems

Recently, Peng considered a merit function for the variational inequality problem (VIP), which constitutes an unconstrained differentiable optimization reformulation of VIP. In this paper, we generalize the merit function proposed by Peng and study various properties of the generalized function. We call this function the D-gap function. We give conditions under which any stationary point of the D-gap function is a solution of VIP and conditions under which it provides a global error bound for VIP. We also present a descent method for solving VIP based on the D-gap function.     

Components exponential scator holomorphic function

The components exponential scator function, succinctly labeled “cexp,” is a function of scator variable in 1+n dimensional elliptic scator algebra. This function is introduced here, and its elementary properties are studied. In 1+1 dimensions, the cexp function becomes the usual complex exponential function of complex variable. The cexp function is shown to be scator holomorphic in the entire scator set according to the differential quotient criterion. The scator derivative of the cexp function is the cexp function itself. The relationship between the Cartesian and polar forms of the cexp function can be seen as a higher-dimensional extension of Euler formula. The mappings of grids in 1+2 dimensional space exhibit ellipses and Lissajous-like figures in addition to circles and radial lines. A cusphere surface is generated for the isometric condition in the function's image. An interesting application of the cexp function as propagators regarding the quantum measurement problem is outlined.