函数问题疑难解析

函数是高中数学中的重要内容 ,学习函数时如果概念不清 ,性质理解不深刻 ,就会造成许多后遗症 ,影响后续知识的掌握 .下面提出有关的若干疑难问题进行剖析 .1　表达式相同的两个函数是否相同很多学生容易把具有相同表达式的两个函数看作同一个函数 .其实 ,由函数的表达式相同 ,只能知道它们的对应法则相同 ,但还有定义域是否相同的问题 .例如 ｆ(ｘ) =2ｘ + 1和 ｇ(ｘ) =2ｘ + 1　 (ｘ∈Ｒ+ ) ,尽管ｆ(ｘ) 和ｇ(ｘ)的表达式相同 ,但由于它们的定义域分别为Ｒ ,Ｒ+ ,故它们是不同的两个函数 .2　定义域和值域分别相同的两个函数是否是同一个…     

工件具有相同加工时间和相同窗口交货期的单机E/T调度问题

研究工件具有相同的加工时间和相同的窗口交货期,目标函数是总费用函数的单机调度问题.给出了求解该问题的一个简洁的数学公式.     

整代数体函数与其导函数的增长级

对整代数体函数与其导函数的增长性进行了研究,得到了整代数体函数与其导函数的特征函数之间关系式,并证明了它们具有相同的级和下级,从而将亚纯函数的相应结果推广到了整代数体函数.     

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．     

Stokes问题基于泡函数的简化的稳定化混合元格式的收敛性

利用泡函数导出Stokes问题的两种新的、简化的稳定化混合有限元格式.并证明这些格式与通常带泡函数的稳定化格式具有相同的收敛性,但是自由度可以大大减少.     

上方一致光滑逼近函数及其在绝对值方程中的应用

给出了绝对值函数的一些上方一致光滑逼近函数,分析了这些光滑逼近函数共同具有的性质,并通过图像展示了逼近效果;进而从中选取逼近程度较好的光滑函数应用于求解绝对值方程.通过和已有文献对比,采用的上方一致光滑函数的逼近程度优于已有文献,因此在相同条件下具有计算耗时较少等优点.     

例谈分段函数问题中的几种特殊图象

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．它不仅在初等数学乃至高等数学中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：把握住分段函数的图象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“分段函数”问题中的几种特殊图象展开例析．     

广义基插值的正交多尺度函数和多小波

给出一类具有广义插值的正交多尺度函数的构造方法, 并给出对应多小波的显示构造公式. 证明了该文构造的多小波拥有与多尺度函数相同的广义基插值性.从而建立了多小波子空间上的采样定理. 最后基于该文提供的算法构造出若干具有广义基插值的正交多尺度函数和多小波.     

基于点X=0的均值函数的性质及其应用

研究平均值函数φ（x）=1/x∫0^xf（t）dt,利用微积分学的有关概念,得到了它和被积函数具有相同或相似的奇偶性、周期性、单调性、连续性、可导性等性质,并配有应用实例．     

具有四个分担值的亚纯函数的唯一性

对给定的复数a,本文引入一个用来刻画两个亚纯函数的重数相同的公共a值点的比重的量τk,并把有关这一量与拟亏量或者权分担相结合的条件附加到两个具有四个分担值的亚纯函数上,得到了两个关于亚纯函数唯一性的定理.     

代数体函数的导函数的级

讨论了代数体函数的导函数,并首次证明了它也是代数体函数,证明了有限级整代数体函数的级等于其导函数级.     

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.     

A new constructing auxiliary function method for global optimization

A new auxiliary function method based on the idea which executes a two-stage deterministic search for global optimization is proposed. Specifically, a local minimum of the original function is first obtained, and then a stretching function technique is used to modify the objective function with respect to the obtained local minimum. The transformed function stretches the function values higher than the obtained minimum upward while it keeps the ones with lower values unchanged. Next, an auxiliary function is constructed on the stretched function, which always descends in the region where the function values are higher than the obtained minimum, and it has a stationary point in the lower area. We optimize the auxiliary function and use the found stationary point as the starting point to turn to the first step to restart the search. Repeat the procedure until termination. A theoretical analysis is also made. The main feature of the new method is that it relaxes significantly the requirements for the parameters. Numerical experiments on benchmark functions with different dimensions (up to 50) demonstrate that the new algorithm has a more rapid convergence and a higher success rate, and can find the solutions with higher quality, compared with some other existing similar algorithms, which is consistent with the analysis in theory.     

一类奇异积分算子的加权估计

假设A是一个Young函数,MD#为广义sharp极大函数.本文首先引进了LA-Hrmander条件,对于满足LA-Hrmander条件的算子T,得到了与T相关的广义sharp极大函数的估计.然后,再利用该估计得到了算子T的加权Lp范数被Hardy-Littlewood极大函数和与Aˉ相关的极大函数的加权Lp范数所控制(0相似文献   

Uniqueness of entire function sharing a small function with its derivative

This paper is devoted to studying the relationship between an entire function and its derivative when they share one small function. We generalize some previous results of Gundersen and Yang [G. Gundersen, L.Z. Yang, Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl. 223 (1998) 85–95], Chang and Zhu [J. Chang, Y. Zhu, Entire functions that share a small function with their derivatives, J. Math. Anal. Appl. 351 (2009) 491–496].     

CD生产函数与CES生产函数的几点比较

本文对ＣＤ生产函数与ＣＥＳ生产函数进行了几个方面的比较分析，以便于实际运用中的选择。     

Finding nonnormal bent functions

The question if there exist nonnormal bent functions was an open question for several years. A Boolean function in n variables is called normal if there exists an affine subspace of dimension n/2 on which the function is constant. In this paper we give the first nonnormal bent function and even an example for a nonweakly normal bent function. These examples belong to a class of bent functions found in [J.F. Dillon, H. Dobbertin, New cyclic difference sets with Singer parameters, in: Finite Fields and Applications, to appear], namely the Kasami functions. We furthermore give a construction which extends these examples to higher dimensions. Additionally, we present a very efficient algorithm that was used to verify the nonnormality of these functions.     

Differentiation identities for hypergeometric functions

It is well-known that differentiation of hypergeometric function multiplied by a certain power function yields another hypergeometric function with a different set of parameters. Such differentiation identities for hypergeometric functions have been used widely in various fields of applied mathematics and natural sciences. In this expository note, we provide a simple proof of the differentiation identities, which is based only on the definition of the coefficients for the power series expansion of the hypergeometric functions.     

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.     

ON ENTIRE FUNCTIONS, BLOCH AND NORMAL FUNCTIONS

New criteria for an analytic function to be Bloch and for a meromorphic function to benormal are given. These criteria generalize the recently introduced area integral conditionsinvolving a Green's function.