Approximation of bandlimited functions

Many signals encountered in science and engineering are approximated well by bandlimited functions. We provide suitable error bounds for the approximation of bandlimited functions by linear combinations of certain special functions—the prolate spheroidal wave functions of order 0. The coefficients in the approximating linear combinations are given explicitly via appropriate quadrature formulae.     

Well-Posedness by Perturbations of Variational Problems

In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented.     

Bilateral generating functions and operational methods

Bilateral generating functions are those involving products of different types of polynomials. We show that operational methods offer a powerful tool to derive these families of generating functions. We study cases relevant to products of Hermite polynomials with Laguerre, Legendre and other polynomials. We also propose further extensions of the method which we develop here.     

Identity principles for commuting holomorphic self-maps of the unit disc

Let f,g be two commuting holomorphic self-maps of the unit disc. If f and g agree at the common Wolff point up to a certain order of derivatives (no more than 3 if the Wolff point is on the unit circle), then f≡g.     

物体内部三维位移场分析的数字图像相关方法

提出了物体内部三维位移场的数字图像相关分析方法，对物体变形前后，或连续变形的两个相邻状态的内部三维结构的数字图像，通过相关运算获得三维位移场.文中给出了三维相关法的体搜索窗口、相关函数及亚像素运算的相关系数拟合函数.数字模拟结果证明了三维相关法的正确性及可靠性.位移计算精度为0.02像素. 关键词： 数字图像相关 三维相关 亚像素     

一种新的奇偶非线性相干态的位相统计性质

根据Pegg-Barnett位相定义, 计算了一种新的奇偶非线性相干态的位相概率分布函数, 利用数值计算方法研究了它们的位相统计性质. 数值计算结果表明：新的奇偶非线性相干态的位相特性与通常奇偶相干态的位相特性截然不同.     

可重构制造系统重组过程中设备选择模型的研究

根据生产任务选择加工设备进行制造资源重组是实现可重构制造系统的关键问题之一，由于设备的选择涉及到多种因素，既有定量指标，又有定性指标，传统的依靠人工经验的方法显得力不从心。本文首先结合实际情况，提出了一套设备选择评价体系，通过对模糊判断矩阵采用最小对数二乘法确定各评价因素的权重系数，针对定性指标和定量指标采用不同的方法确定其性能指标值，通过模糊积分对评判指标进行综合评判，最后进行了实例研究。所提出的方法有效地简化了决策过程，为可重构制造系统设备选择提供了一套行之有效的方法。     

凸域内单叶函数的导数

设函数f（w）为凸区域D内的单叶解析函数,对于2≤n≤8和所有w∈D,本文得到估计式|f（n）（w）/f＇（w）|的精确上界.这个结果推广了一些已知的结论.     

On a class of new and practical performance indexes for approximation of fold bifurcations of nonlinear power flow equations

Efficient measurement of the performance index (the distance of a loading parameter from the voltage collapse point) is one of the key problems in power system operations and planning and such an index indicates the severity of a power system with regard to voltage collapse. There exist many interesting methods and ideas to compute this index. However, some successful methods are not yet mathematically justified while other mathematically sound methods are often proposed directly based on the bifurcation theory and they require the initial stationary state to be too close to the unknown turning point to make the underlying methods practical.This paper first gives a survey of several popular methods for estimating the fold bifurcation point including the continuation methods, bifurcation methods and the test function methods (Seydel's direct solution methods, the tangent vector methods and the reduced Jacobian method) and discuss their relative advantages and problems. Test functions are usually based on scaling of the determinant of the Jacobian matrix and it is generally not clear how to determine the behaviour of such functions. As the underlying nonlinear equations are of a particular type, this allows us to do a new analysis of the determinants of the Jacobian and its submatrices in this paper. Following the analysis, we demonstrate how to construct a class of test functions with a predictable analytical behaviour so that a suitable index can be produced. Finally, examples of two test functions from this class are proposed. For several standard IEEE test systems, promising numerical results have been achieved.     

On bent functions with some symmetric properties

This paper discusses a kind of bent functions that have some symmetric properties about some variables. Section 2 mainly discusses the bent functions symmetric about some two variables and gives the necessary and sufficient condition for these functions. Section 3 gives algebraic expressions of some bent functions.