二重数值积分公式的高精度对偶公式及其应用

给出了计算二重积分的Simpson公式与两点高斯公式的对偶公式的构造过程,得到与之对应的高精度对偶修正解,提高了二重数值积分公式的计算精度,同时给出了二重积分的一种估值方法.最后,应用于几个典型的数值算例,计算结果表明：对偶修正解比对应的数值积分公式及其对偶公式的解有更高的计算精度和更快的收敛速度.     

折叠波导行波管切断匹配的设计

 利用电磁模拟软件,计算得到了H面渐变与E面渐变的楔形衰减器匹配效果,指出在相同渐变长度下,E面渐变匹配效果优于H面渐变。H面渐变衰减器反射主要来源于电场集中处,而E面渐变衰减器主要来源于渐变前部尖端处。在此基础上设计出了一种变形的匹配衰减器,即在E面渐变衰减器渐变开始处向前延伸一块薄片。计算结果与测试结果表明:与H面渐变和E面渐变的楔形衰减器相比,所设计衰减器在近截止频率处的匹配效果得到了明显的改善。     

Computing economies of vertical integration,economies of scope and economies of scale using partial frontier nonparametric methods

So far, in the nonparametric literature only full frontier nonparametric methods have been applied to search for economies of scope and scale, particularly the data envelopment analysis method (DEA). However, these methods present some drawbacks that might lead to biased results. This paper proposes a methodology based on more robust partial frontier nonparametric methods to look for scope and scale economies. Through this methodology it is possible to assess the robustness of these economies, and in particular to assess the influence that extreme data or outliers might have on them. The influence of the imposition of convexity on the production set of firms was also investigated. This methodology was applied to the water utilities that operated in Portugal between 2002 and 2008. There is evidence of economies of vertical integration and economies of scale in drinking water supply utilities and in water and wastewater utilities operating mainly in the retail segment. Economies of scale were found in water and wastewater utilities operating exclusively in the wholesale, and in some of these utilities diseconomies of scope were also found. The proposed methodology also allowed us to conclude that the existence of some smaller utilities makes the minimum optimal scales go down.     

城乡一体化的供排水系统规划初探

从城乡一体化角度,阐述城乡供排水系统统筹建设、协调发展的规划原则和措施对策.主要包括是否与城市联网供水、集中供水和分散供水模式的选择、不同地区排水系统的确定、水源保护以及适合农村地区的污水处理方式等几个方面,并提出实施的具体对策,以期逐步实现城乡一体化的区域协调供排水系统建设.     

基于Shannon-Cosine小波精细积分法的壁画降噪修复方法

为修复受破损且噪声点众多的壁画图像,提出了用偏微分方程（partial differential equation,PDE）扩散的方法对图像进行降噪修复。针对PDE法求解精度较低的问题,提出了一种Shannon-Cosine小波精细积分法,运用小波数值方法对偏微分方程进行离散处理,降低其方程组规模,并采用精细积分法求解,有效提高了计算速度。试验结果表明,采用该算法对受损壁画降噪处理后,视觉上,图像边界更清晰,且噪声点得到有效减少,达到了保边降噪的效果,更符合人眼的视觉效果;客观上,与中值滤波、均值滤波和维纳滤波方法相比,采用本算法处理后的图像其PSNR值和SSIM值均最大。因此,运用Shannon-Cosine小波精细积分法求解图像的PDE模型是可行的,取得了较好的图像降噪效果。     

矩形校正公式的误差分析

This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively.It also displays an analysis on convergence order of compound corrector formulas for rectangular rule.Examples of numerical calculation have validated theoretical analysis.     

Analysis of discrete techniques for image transformation

Let an image be distorted by a nonlinear transformationT, and then be restored back to its original by the inverse transformationT ^–1. Such a cycle conversion,T ^–1 T, of digital images can be facilitated by the combination (CSIM) given in [6] using the splitting-shooting method and the splitting-integrating method forT andT ^–1 respectively. Since there is no need to solve nonlinear equations, CSIM has been widely applied to specific areas of image processing and pattern recognition, even those with complicated transformations, e.g., the harmonic transformation [12]; however, no strict error analysis has been provided so far. In this paper, a priori error estimates and convergence rates are derived for pixel greyness obtained from CSIM; also the analytical results are extended to the harmonic transformation. Numerical and graphical experiments are provided to support the theoretical analysis.Some preliminary results of this paper were presented at the 40th anniversary meeting of SIAM, Los Angeles, July 20–24, 1992. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada, the Fonds pour la Formation de Chercheurs et l'Aide à la Recherche of Quebec by the Ministère de l'Enseignement Supérieur et de la Science (Action Structurante), and the Science Council of Republic of China under Grant No. NSC-85-2121-M-008.     

Response probability density functions of strongly non-linear systems by the path integration method

The paper discusses challenges in numerical analysis and numerical/analytical results for strongly non-linear systems—systems with “signum”-type non-linearities. Such non-linearities are implemented for instantaneous variations of the systems’ parameters, to reduce their mean energy response when subjected to random excitations. Numerical results for displacement and velocity response probability density functions (PDFs), energy response PDFs and various order moments are obtained by the path integration technique. Attention is also given to evaluation of mean upcrossing rate, related to the system's half period, via Rice's formula informally applied to discontinuous response PDFs.     

Effect of numerical integration in the DGFEM for nonlinear convection‐diffusion problems

This paper is concerned with the effect of numerical integration applied to the discontinuous Galerkin finite element discretization of nonlinear convection‐diffusion problems in 2D. In the space semidiscretization the volume and line integrals are evaluated by numerical quadratures. Our goal is to estimate the error caused by the numerical integration and to show what numerical quadratures guarantee that the accuracy of the method with exact integration is preserved. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

On the regularization of an equation of the first kind with a multiple integration operator

The zero-order Tikhonov regularization method as applied to an equation of the first kind with a multiple differentiation operator is considered for the case when the solution belongs to a class from the domain of the adjoint operator. An estimate of the error of the approximate solution in the uniform metric is obtained, which is sharp with respect to the order, and the order is established. It is proved that the proposed method is optimal with respect to the order. Unimprovable estimates of the order of the modulus of continuity of the inverse operator are obtained.