与高一同学谈抽象函数问题

抽象函数问题,是指没有给出函数的解析式,只给出函数具有的某些特征,求此函数应具有的其它特征的问题．由于高一同学只熟悉一些具体函数,如：正比例函数、指数函数、对数函数等,对抽象函数不够了解,没有具体的函数模型和解题方法可供参考．因此,许多同学对求解抽象函数问题感到很困难,     

与高一同学谈抽象函数问题求解策略

抽象函数问题,是指没有给出函数的解析式,只给出函数具有的某些特征,求此函数应具有的其它特征的问题．由于高一学生只熟悉一些具体函数,如一次函数、二次函数、正比例函数、指数函数、对数函数等,对抽象函数不够了解,没有具体的函数模型和解题方法可供参考。因此,学生对求解抽象函数问题感到很困难,不知如何下手,导致解题失败．     

等效均衡函数的性质及均衡函数的构造

从均衡函数的等效性出发研究均衡函数的性质,证明了等效的均衡函数之和、积以及数乘仍为均衡函数,并且得到的新均衡函数与原均衡函数等效,这些性质表明等效的均衡函数关于加法和乘法运算均具有半群的代数结构。另外,进一步讨论了构造均衡函数的方法,给出了两个构造均衡函数的定理,该方法具有一般性,现有文献中的均衡函数几乎都能由其构造得到。     

解决高斯函数的函数值问题的策略初探

对于每一个实数x,我们用[x]来表示不大于x的最大整数,并将函数f(x)=[x]称为高斯函数.高斯函数首先是由德国数学家高斯于十九世纪所提出,而后广泛应用于生产生活的各个方面.高斯函数作为一种重要的初等函数,不仅具有简洁的结构和通俗的意义,而且还具有其他初等函数所没有的特性———连续的定义域和离散的函数值域,再加     

有限偏差函数与调和函数

分别借助解析函数与调和函数两类函数的Dirichlet积分,利用相关文献给定边界值的拟共形映射极值伸缩商的估计方法,通过有限偏差函数和拟共形映射的关系估计了具有给定边界值的有限偏差函数的极值伸缩商.得到了解析函数的Dirichlet积分在有限偏差函数下具有拟不变性,同时给出有限偏差函数极值伸缩商的下界估计.     

基于Sendograph度量的连续逼近

证明En中的模糊数关于Sendograph度量可以用具有连续截集函数的模糊数任意逼近,并给出连续映射下由扩张原理导出的函数关于Sendograph度量也是连续的.特别地,具有连续的截集函数的模糊数在严格单调的连续函数之下的象也具有连续的截集函数.     

分担四个或五个小函数的亚纯函数

本文证明了两个非常数亚约函数在具有五个ＩＭ分担小函数的前提下附加一定条件,则这两个函数必恒等,并研究了两个具有四个ＣＭ分担小函数的非常数亚纯函数之间的关系,推广了Ｎｅｖａｎｌｉｎｎａ四值定理．     

例谈分段函数问题的构图解法

分段函数是一类特殊表达形式的函数,指的是自变量在不同的取值范围内,其对应法则不相同的函数．它在初等数学及至高等数学中不仅具有重要的理论价值,而且具有较广泛的应用价值．笔者经过研究发现：把握分段函数的图像特征对于解决此类问题而言具有至关重要的作用,下文将就此展开例析．     

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.     

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.     

Basis function-based adaptive critic learning and its learning parameters selection

An adaptive critic learning (ACL) structure consists of two modules: the action and the critic ones. Learning occurs in both modules. The critic module learns to evaluate the system status. It transforms occasionally occurred failure signals into useful evaluation information. Utilizing such information, the action module can learn the control technique. In this paper, we investigate the technique of using basis functions (BFs) in ACL. One difficulty in the scheme is on selection of learning parameters. Without a guideline, the best set of learning parameters must be obtained from a large number of test simulations. This study investigated the effects of parameters through analysis and verified the analytical results by simulations. In addition to the problem of parameter selection, effects of measurement errors on the CMAC-based (one basis function technique) ACL have been also examined and reported.     

A new class of exact penalty functions and penalty algorithms

For nonlinear programming problems, we propose a new class of smooth exact penalty functions, which includes both barrier-type and exterior-type penalty functions as special cases. We develop necessary and sufficient conditions for exact penalty property and inverse proposition of exact penalization, respectively. Furthermore, we establish the equivalent relationship between these penalty functions and classical simple exact penalty functions in the sense of exactness property. In addition, a feasible penalty function algorithm is proposed. The convergence analysis of the algorithm is presented, including the global convergence property and finite termination property. Finally, numerical results are reported.     

Nonlinear Chebyshev approximation to set-valued functions

In this paper, we give a characterization of best Chebyshev approximation to set-valued functions from a family of continuous functions with the weak betweeness property. As a consequence, we obtain a characterization of Kolmogorov type for best simultaneous approximation to an infinity set of functions. We introduce the concept of a set-sun and give a characterization of it. In addition, we prove a property of Amir–Ziegler type for a family of real functions and we get a characterization of best simultaneous approximation to two functions     

Acceptable Numerations of Morphisms and Myhill-Shepherdson Property

Myhill-Shepherdson property in recursive function theory states that extensional effective program transformations determine continuous operations on partial functions. Case showed that this property fails to characterize acceptability of numberings of partial recursive functions. In this note we present a higher type analogue to Myhill-Shepherdson property. Our purpose is to show that higher type Myhill-Shepherdson property characterizes weak acceptability under a natural condition.     

A note on the engulfing property and the -regularity of convex functions in Carnot groups

We study the engulfing property for convex functions in Carnot groups. As an application we show that the horizontal gradient of functions with this property is Hölder continuous.

     

滴状性质与局部滴状性质的序列流特征

利用Rolewicz所提出的序列流的概念和局部完备性理论,我们给出了局部凸空间中滴状性质和局部滴状性质的序列流特征．应用所获结果,研究了滴状性质(分别地,局部:商状性质)与泛函数取极值问题之间的联系．     

On Lipschitz behaviour of some generalized derivatives

The aim of the present paper is to compare various forms of stable properties of nonsmooth functions at some points. By stable property we mean the Lipschitz property of some generalized derivatives related only to the reference point. Namely we compare Lipschitz behaviour of lower Clarke derivative, lower Dini derivative and calmness of Clarke subdifferential. In this way, we continue our study of λ-stable functions.     

Algebras of almost periodic functions with Bohr-Fourier spectrum in a semigroup: Hermite property and its applications

It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener-Hopf type of rectangular matrix functions and the Toeplitz corona problem in the context of almost periodic functions of several variables.     

拓扑线性空间中的Drop定理与Drop性质

给出了拓扑线性空间中的一个Drop定理.利用此Drop定理,证明了拓扑线性空间中的每个序列紧凸集具有Drop性质;每个可数紧闭凸集具有拟Drop性质.而且结出了拓扑线性空间中Drop性质和拟Drop性质的序列流特征.也讨论了Drop性质和拟Drop性质与泛函取极值之间的联系.