Some algorithms for numerical quadrature using the derivatives of the integrand in the integration interval

Some quadrature formulae using the derivatives of the integrand are discussed. As special cases are obtained generalizations of both the ordinary and the modified Romberg algorithms. In all cases the error terms are expressed in terms of Bernoulli polynomials and functions.     

The elastostatic three-dimensional boundary element method: analytical integration for linear isoparametric triangular elements

In this paper an analytical integration scheme is described that is designed to reduce the errors resulting from the numerical evaluation of integrals with singular integrands. The analytical scheme can be applied to linear triangular elements for use in elastostatic problems and is particularly useful for predicting distortion, to high accuracy, close to surfaces. It is demonstrated that although the analytical scheme takes longer computationally than the usual quadrature approach it is quicker when element subdivision is required to achieve reasonable accuracy. Numerical tests are performed on a simple test problem to demonstrate the advantages of the analytical approach, which is shown to be orders of magnitude more accurate than standard quadrature techniques.     

Mixed symbolic–numerical computations with general DAEs II: An applications case study

A variety of theorems and properties of nonlinear DAEs were discussed in part I. This paper illustrates many of these ideas within the context of analyzing a specific nonlinear system that exhibits a variety of interesting features. This revised version was published online in June 2006 with corrections to the Cover Date.     

Nonlinear transformation methods for accelerating the convergence of Coulomb integrals over exponential type functions

It is well known that in any ab initio molecular orbital (MO) calculation, the major task involves the computation of molecular integrals, among which the computation of Coulomb integrals are the most frequently encountered. As the molecular system gets larger, computation of these integrals becomes one of the most laborious and time consuming steps in molecular systems calculation. Improvement of the computational methods of molecular integrals would be indispensable to a further development in computational studies of large molecular systems. The atomic orbital basis functions chosen in the present work are Slater type functions. These functions can be expressed as finite linear combinations of B functions which are suitable to apply the Fourier transform method. The difficulties of the numerical evaluation of the analytic expressions of the integrals of interest arise mainly from the presence of highly oscillatory semi-infinite integrals. In this work, we present a generalized algorithm based on the nonlinear transformation of Sidi, for a precise and fast numerical evaluation of molecular integrals over Slater type functions and over B functions. Numerical results obtained for the three-center two-electron Coulomb and hybrid integrals over B functions and over Slater type functions. Comparisons with numerical results obtained using alternatives approaches and an existing code are listed.     

Quasi-Monte Carlo for Highly Structured Generalised Response Models

Highly structured generalised response models, such as generalised linear mixed models and generalised linear models for time series regression, have become an indispensable vehicle for data analysis and inference in many areas of application. However, their use in practice is hindered by high-dimensional intractable integrals. Quasi-Monte Carlo (QMC) is a dynamic research area in the general problem of high-dimensional numerical integration, although its potential for statistical applications is yet to be fully explored. We survey recent research in QMC, particularly lattice rules, and report on its application to highly structured generalised response models. New challenges for QMC are identified and new methodologies are developed. QMC methods are seen to provide significant improvements compared with ordinary Monte Carlo methods.      

缩短单点作业时间影响因素的排序研究

提出国家电网公司在实施设备的检修作业时尽量减少停电时间,以实现电缆线路状态的有效监控的重要意义.分析缩短单点作业时间的末端影响因素.提出三角模糊集、指数模糊集用于权重设置的具体途径,应用OWA算子于因素排序评价数值的加权,并拓展其基本原理和方法,使其对极端评分值有所抑制对中间评分值有所提升.以上海市电力公司检修公司为研究背景,应用直觉模糊集及其IFHA集成方法于缩短单点作业时间的末端影响因素评价指标排序,并得出u_≥u_≥u_1u_4u_6≥u_2u_3的结论.     

武汉市在校大学生数与经济增长的协整分析

近二十年来,我国高等教育规模不断扩大,高校在校生数不断增加,其中武汉市位居全国前列．为了研究高校在校生数对当地经济发展的影响,本文利用武汉市1992—2012年在校大学生人数数据,通过建立合适的模型,来定量探讨武汉市在校大学生数与经济增长的内在关系．结果表明,武汉市经济增长与武汉在校大学生人数模型之间存在着长期均衡关系且互为格兰杰因果关系．     

Continuous local martingales and stochastic integration in UMD Banach spaces

Recently, van Neerven, Weis and the author, constructed a theory for stochastic integration of UMD Banach space valued processes. Here the authors use a (cylindrical) Brownian motion as an integrator. In this note we show how one can extend these results to the case where the integrator is an arbitrary real-valued continuous local martingale. We give several characterizations of integrability and prove a version of the Itô isometry, the Burkholder–Davis–Gundy inequality, the Itô formula and the martingale representation theorem.     

Numerical integration over polygons using an eight-node quadrilateral spline finite element

In this paper, a cubature formula over polygons is proposed and analysed. It is based on an eight-node quadrilateral spline finite element [C.-J. Li, R.-H. Wang, A new 8-node quadrilateral spline finite element, J. Comp. Appl. Math. 195 (2006) 54–65] and is exact for quadratic polynomials on arbitrary convex quadrangulations and for cubic polynomials on rectangular partitions. The convergence of sequences of the above cubatures is proved for continuous integrand functions and error bounds are derived. Some numerical examples are given, by comparisons with other known cubatures.     

基于城乡物流一体化的连锁经营配送网络优化研究

基于城乡物流一体化的目标设定和相应基础设施平台的支持,提出连锁经营配送网络的建设模式,依据对当前连锁经营网络发展的重点工作的分析,建立了关于配送中心和农产品收购中心选择的网络优化模型.并引入算例说明模型的可行性和适用性.