具有奇点的Laplace方程边值问题的原始能量-有限元结合法

在用变分原理离散数理方程时,可取函数在部分求解区域内,取成解析函数或奇异函数类;而在其余求解区域内取成分片低阶插值多项式.在两区域交界的结点上,可取函数连续.我们称此法为原始能量一有限元结合法.[3,p135]中提到过这种方法,但缺少理论分析.[4]曾给出初步的分析.本文与[5,6]就此方法给出较严格的理论分析.     

Newton-Type Methods for Quasidifferentiable Equations

In this paper, we present two Newton-type methods for solving quasidifferentiable equations in the sense of Demyanov and Rubinov (Ref. 1). Method I is well defined and is a natural extension of the classical Newton method, based on a generalized Kakutani fixed-point theorem. Method II is a simplified version and requires less computation than Method I. Under some mild assumptions, we establish a locally quadratic convergent theorem for Method I and prove a semilocal convergence theorem for Method II.     

The Multiplier Method for optimal control problems of parabolic systems

In this paper the application of the Multiplier Method (also known as Augmented Lagrangian Method or Penalty Shifting Method) to quadratic optimal control problems for linear parabolic distributed systems is studied and the convergence of the method on appropriate Hilbert spaces is proved. Numerical examples are reported.This work was partially supported by the Consiglio Nazionale delle Ricerche.     

A matrix formulation of the Tau Method for Fredholm and Volterra linear integro-differential equations

In this paper we obtain the matrix Tau Method representation of a general boundary value problem for Fredholm and Volterra integro-differential equations of orderv. Some theoretical results are given that simplify the application of the Tau Method. The application of the Tau Method to the numerical solution of such problems is shown. Numerical results and details of the algorithm confirm the high accuracy and userfriendly structure of this numerical approach.     

吴消元法与四元术

在解多项式方程组的过程中,吴消元法的核心是用对多项式约化求余式的方法消元.研究中发现,清代沈钦裴四元消法的三条法则均系互乘对消,都可以写成除法变换的形式.从而找到吴消元法与四元术的内在联系.得出吴消元法是四元术的直接继承,吴消元法是四元术现代化发展的结论.     

动态资产份额定价理论模型

运用倒向随机微分方程数学方法 ,建立了动态资产份额定价理论模型 .这一模型是资产份额定价法的改进 .求解模型得到动态资产份额定价理论公式 ,并得出结论 :资产份额定价公式完全可以作为特例 ,以离散时间意义和在不考虑动态投资的情况下 ,由动态资产份额定价理论公式得到 .     

A tale of three eras: The discovery and rediscovery of the Hungarian Method

In the Fall of 1953, a translation of a paper of Jen? Egerváry from Hungarian into English combined with a result of Dénes K?nig provided the basis of a good algorithm for the Linear Assignment Problem. To honor the Hungarian mathematicians whose ideas had been used, it was called the Hungarian Method. In 2005, Francois Ollivier discovered that the posthumous papers of Jacobi contain an algorithm that, when examined carefully, is essentially identical to the Hungarian Method. Since Jacobi died in 1851, this work was done over a hundred years prior to the publication of the Hungarian Method in 1955. This paper will provide an account for the mathematical, academic, social and political worlds of Jacobi, K?nig, Egerváry, and Kuhn. As sharply different as they were (Prussian monarchy, Hungary under the Nazis and the Communists, and the post-war USA), they produced the same mathematical result. The paper is self-contained, assuming little beyond the duality theory of linear programing. The Hungarian Method and Jacobi’s algorithm will be explained at an elementary level and will be illustrated by an example, solved both by the Hungarian Method and by Jacobi’s Method.     

C_0复杂度的改进及其在证券市场中的应用

系统地分析了Lemple-Ziv复杂性度量方法的应用过程中,将实际信号(时间序列)转变成符号序列的诸多方法中存在的一些问题,提出了更合理兼容法.该方法可以有效地刻划各种时间序列的复杂度.文章最后动态地分析了中国证券市场的复杂性.     

模拟随机数统计性质比较

本文总结了几种历史上有影响的模拟随机数发生方法 ,并对线性同余法和取小数法进行了统计比较 ,从而肯定了取小数法的优良性能     

Approximate traveling wave solution for shallow water wave equation

Reconstruction of Variational Iteration Method (RVIM) is used for computing the coupled Whitham-Broer-Kaup shallow water. Then RVIM solution is verified against exact one and is compared with powerful approximate solutions, the Homotopy Perturbation Method (HPM) and Homotopy Analysis Method (HAM). The existent error of the methods is computed and convergence of the RVIM solution has been presented. Results obtained expose effectiveness and capability of this method to solve the nonlinear systems in mechanics, analytically.     

浅析大M法与两阶段法的一致性

分析了大M法与两阶段法在思想方法、辅助线性规划问题的构造、初始可行基、初始单纯形表、最优性检验和算法步骤等方面的一致性.     

Assembly and Solution of the High-Fidelity Generalized Method of Cells with Interface Damage

The assembly of the system of equations and its solution are presented for the High-Fidelity Generalized Method of Cells (HFGMC) with interface damage. The direct stiffness assembly, which is used in the Finite Element Method with its unknown nodal displacements, is applied to the HGFMC. The nonlinear set of equations due to damage is solved with Newton's Method for the microscopic surface-averaged displacements, which are the unknowns in the efficient version of the HFGMC. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

ON BLOCK MATRICES ASSOCIATED WITH DISCRETE TRIGONOMETRIC TRANSFORMS AND THEIR USE IN THE THEORY OF WAVE PROPAGATION

Block matrices associated with discrete Trigonometric transforms （DTT＇s） arise in the mathematical modelling of several applications of wave propagation theory including discretizations of scatterers and radiators with the Method of Moments, the Boundary Element Method, and the Method of Auxiliary Sources. The DTT＇s are represented by the Fourier, Hartley, Cosine, and Sine matrices, which are unitary and offer simultaneous diagonalizations of specific matrix algebras. The main tool for the investigation of the aforementioned wave applications is the efficient inversion of such types of block matrices. To this direction, in this paper we develop an efficient algorithm for the inversion of matrices with U-diagonalizable blocks （U a fixed unitary matrix） by utilizing the U- diagonalization of each block and subsequently a similarity transformation procedure. We determine the developed method＇s computational complexity and point out its high efficiency compared to standard inversion techniques. An implementation of the algorithm in Matlab is given. Several numerical results are presented demonstrating the CPU-time efficiency and accuracy for ill-conditioned matrices of the method. The investigated matrices stem from real-world wave propagation applications.     

Multi-Product Inventory Situations with One Restriction

The problem of maintaining inventories for a number of products when there is a restriction on the maximum inventory investment, or on maximum warehouse space, is considered. A method of adjusting the order intervals of the products, the Equal Order Interval Method, is shown in general often to produce significantly better cost solutions to these problems than the well known Lagrangian Multiplier Method. Examples are given which demonstrate how the Equal Order Interval Method can be applied effectively and efficiently by heuristics.     

非重复析因试验数据分析的两个方法

本文介绍了非重复析因试验数据分析的两个比较实用的方法 :Lenth方法和Dong方法 ,并对这两个方法进行了比较全面的比较     

The Buchstab’s function and the operational Tau Method

In this article we discuss some aspects of operational Tau Method on delay differential equations and then we apply this method on the differential delay equation defined byw(u) = 1/u for 1 ≤u ≤ 2 and(uw(u))′ = w(u-1) foru ≥ 2, which was introduced by Buchstab. As Khajah et al.[l] applied the Recursive Tau Method on this problem, they had to apply that Method under theMathematica software to get reasonable accuracy. We present very good results obtained just by applying the Operational Tau Method using a Fortran code. The results show that we can obtain as much accuracy as is allowed by the Fortran compiler and the machine-limitations. The easy applications and reported results concerning the Operational Tau are again confirming the numerical capabilities of this Method to handle problems in different applications.     

Three analytical methods applied to Jeffery–Hamel flow

Three new analytical approximate techniques for addressing nonlinear problems are applied to Jeffery–Hamel flow. Homotopy Analysis Method (HAM), Homotopy Perturbation Method (HPM) and Differential Transformation Method (DTM) are proposed and used in this research. These methods are very useful and applicable for solving nonlinear problems. Then, the results are compared with numerical results and the validity of these methods is shown. Comparison between obtained results showed that HAM is more acceptable and accurate than two other methods. Ultimately, the effects of Reynolds number and divergent and convergent model of the channel on features of the flow are discussed.     

一类PerMIA的识别方法

PerMIA是对信噪比的重要推广。本文将针对一类较常见的PerMIA ,用Gamma 图方法以及标准Gamma 图方法来判定调节因子并估计PerMIA。     

Analysis of a damped nonlinear multilevel method

Summary In this paper, we present a new algorithm that is obtained by introducing a damping parameter in the classical Nonlinear Multilevel Method. We analyse this Damped Nonlinear Multilevel Method. In particular, we prove global convergence and local efficiency for a suitable class of problems.     

一种基于最小二乘的群组AHP方法

本文以层次分析法中解决群组决策问题的判断矩阵算术加权平均法为基础 ,提出了一种基于最小二乘的群组 AHP方法 ,大量数值模拟计算表明 :该方法较之现有方法在获取排序向量方面更加有效和可靠