构造单调数列证明一类不等式

文[1]介绍了证明与自然数有关的一类不等式的方法——构造数列证明不等式．经笔者研究，发现此类不等式可用构造单调数列，利用数列的单调性予以证明，此法简便，易于操作．     

一类非混合单调算子方程的耦合解定理及其非单调迭代算法

研究无穷维序Banach空间中一类非混合单调算子，它可以表示成T=T1 T2，其中T1是混合单调算子，T2是反向混合单调算子(T2≠0)，得到了其耦合解的存在性定理．当尸是正规极小锥时，通过构造一系列确界生成序列，建立了耦合解的非单调迭代算法．置后，推广了最大一最小解的概念，定义了极大一极小解并研究了其存在的条件．     

一些类型的数学规划问题的全局最优解

本文对严格单调函数给出了几个凸化和凹化的方法，利用这些方法可将一个严格单调的规划问题转化为一个等价的标准D．C．规划或凹极小问题．本文还对只有一个严格单调的约束的非单调规划问题给出了目标函数的一个凸化和凹化方法，利用这些方法可将只有一个严格单调约束的非单调规划问题转化为一个等价的凹极小问题．再利用已有的关于D．C．规划和凹极小的算法，可以求得原问题的全局最优解．     

一类随机生态系统的生态稳定性

本文引入了混合拟单调方法，并将其应用到Ito型随机生态系统中，得到了一些新的结果。     

非单调关联系统FTA定量分析的新方法

本文在利用不交化最小割集矩阵求解非单调关联系统ＦＴＡ的ＰＩＳ基础上，进一步提出了利用所救是的不交化最小割集矩阵进行非单调关联系统定量分析的新方法，这种方法简单，直观，尤其适用于带有重复事件的非单调关联系统。     

非线性单调型Neumann问题的有限元方法

本文讨论了一类非线性单调型Ｎｅｕｍａｎｎ问题的有限元方法。首先，给出这类问题解存在性的一个新证明。其次，基于这一新证明，构造了问题的一个有限逼近格式。最后，应用基于等价极小化问题的有限元数值分析法，得到了线性有限元逼近解的收敛性结果和误差估计。另外，顺便还指出：如果将这一有限元数值分析法类似地应用于非线性单调型Ｄｉｒ－ｉｃｈｌｅｔ问题，那么Ｇｌｏｗｉｎｓｋｉ和Ｍａｒｒｏｃｏ＾［３］的结果可以进一步     

非线性方程组的具有单边初值条件的分裂型单调迭代数

本文利用区间迭代法的思想，提出一种使用单边初值条件的分裂型单调迭代方法，证明了该方法的收敛性，并且具体化到常见的单调迭代法。     

非线性方程组的具有单边初值条件的分裂型单调迭代法

本文利用区间迭代法的思想，提出了一种使用单边初值条件的分裂型单调迭代方法，证明了该方法的收敛性，并且具体化到常见的单调迭代法。     

Orlicz序列空间的一致单调系数及应用

本文给出了Ｏｒｌｉｃｚ序列空间一致单调系数数值，同时给出了Ｏｒｌｉｃｚ序列空间具有一致单调性的条件，进而讨论具有一致单调性的Ｏｒｌｉｃｚ序列空间中的最佳逼近算子的一些特征。     

论导数的“功绩”

导数的出现,为传统函数问题的求解开辟了新的途径,下面就导数在函数问题中的应用举例分析.一、颠覆了函数单调性传统的判别方法函数单调性的判定传统的方法是利用定义,但遇见较复杂的函数,符号的判断确实异常的烦琐,导数的引入为函数单调性的判断,提供了程序     

增长网络的形成机理和度分布计算

关于增长网络的形成机理,着重介绍由线性增长与择优连接组成的BA模型, 以及加速增长模型.此外,我们提出了一个含反择优概率删除旧连线的模型,这个模型能自组织演化成scale-free(SF)网络.关于计算SF网络的度分布,简要介绍文献上常用的基于连续性理论的动力学方法(包括平均场和率方程)和基于概率理论的主方程方法.另外,我们基于马尔可夫链理论还首次尝试了数值计算方法.这一方法避免了复杂方程的求解困难,所以较有普适性,因此可用于研究更为复杂的网络模型.我们用这种数值计算方法研究了一个具有对数增长的加速增长模型,这个模型也能自组织演化成SF网络.     

The Chebyshev–Shamanskii Method for Solving Systems of Nonlinear Equations

We present a method, based on the Chebyshev third-order algorithm and accelerated by a Shamanskii-like process, for solving nonlinear systems of equations. We show that this new method has a quintic convergence order. We will also focus on efficiency of high-order methods and more precisely on our new Chebyshev–Shamanskii method. We also identify the optimal use of the same Jacobian in the Shamanskii process applied to the Chebyshev method. Some numerical illustrations will confirm our theoretical analysis.     

Generalizing the modeling of fuzzy logic controllers by parameterized aggregation operators

We describe the type of reasoning used in the typical fuzzy logic controller, the Mamdani reasoning method. We point out the basic assumptions in this model. We discuss the S-OWA operators which provide families of parameterized “andlike” and “orlike” operators. We generalize the Mamdani model by introducing these operators. We introduce a method, which we call Direct Fuzzy Reasoning (DFR), which results from one choice of the parameters. We develop some learning algorithms for the new method. We show how the Takagi-Sugeno-Kang (TSK) method of reasoning is an example of this DFR method.     

On the limited memory BFGS method for large scale optimization

We study the numerical performance of a limited memory quasi-Newton method for large scale optimization, which we call the L-BFGS method. We compare its performance with that of the method developed by Buckley and LeNir (1985), which combines cycles of BFGS steps and conjugate direction steps. Our numerical tests indicate that the L-BFGS method is faster than the method of Buckley and LeNir, and is better able to use additional storage to accelerate convergence. We show that the L-BFGS method can be greatly accelerated by means of a simple scaling. We then compare the L-BFGS method with the partitioned quasi-Newton method of Griewank and Toint (1982a). The results show that, for some problems, the partitioned quasi-Newton method is clearly superior to the L-BFGS method. However we find that for other problems the L-BFGS method is very competitive due to its low iteration cost. We also study the convergence properties of the L-BFGS method, and prove global convergence on uniformly convex problems.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under contract DE-FG02-87ER25047, and by National Science Foundation Grant No. DCR-86-02071.     

On a numerical solution of the Cauchy problem for the Laplace equation by the fundamental solutions method

We discuss a numerical method to solve a Cauchy problem for the Laplace equation in the two-dimensional annular domain. We consider the case that the Cauchy data is given on an arc. We develop an approximation method based of the fundamental solutions method using the least squares method with Tikhonov regularization. The effectiveness of our method is examined by a numerical experiment. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The alpha interpolation method for the solution of an eigenvalue problem

We present a weighted residual finite element method for the solution of an eigenvalue problem. As a test function, we take a linear combination of two functions which belong to different spaces. We call this method the alpha interpolation method (AIM) for the eigenvalue problem. We compare the AIM with the Standard-Galerkin finite element method (SGFEM).     

A domain decomposition method based on the iterative operator splitting method

In this article a new approach is proposed for constructing a domain decomposition method based on the iterative operator splitting method. The convergence properties of such a method are studied. The main feature of the proposed idea is the decoupling of space and time. We present a multi-iterative operator splitting method that combines iteratively the space and time splitting. We confirm with numerical applications the effectiveness of the proposed iterative operator splitting method in comparison with the classical Schwarz waveform relaxation method as a standard method for domain decomposition. We provide improved results and convergence rates.     

A Generalized Univariate Newton Method Motivated by Proximal Regularization

We devise a new generalized univariate Newton method for solving nonlinear equations, motivated by Bregman distances and proximal regularization of optimization problems. We prove quadratic convergence of the new method, a special instance of which is the classical Newton method. We illustrate the possible benefits of the new method over the classical Newton method by means of test problems involving the Lambert W function, Kullback?CLeibler distance, and a polynomial. These test problems provide insight as to which instance of the generalized method could be chosen for a given nonlinear equation. Finally, we derive a closed-form expression for the asymptotic error constant of the generalized method and make further comparisons involving this constant.     

A generalized conditional gradient method and its connection to an iterative shrinkage method

This article combines techniques from two fields of applied mathematics: optimization theory and inverse problems. We investigate a generalized conditional gradient method and its connection to an iterative shrinkage method, which has been recently proposed for solving inverse problems. The iterative shrinkage method aims at the solution of non-quadratic minimization problems where the solution is expected to have a sparse representation in a known basis. We show that it can be interpreted as a generalized conditional gradient method. We prove the convergence of this generalized method for general class of functionals, which includes non-convex functionals. This also gives a deeper understanding of the iterative shrinkage method.     

The method of mechanical quadratures for integral equations with fixed singularity

We investigate the method of mechanical quadratures for integral equations with fixed singularity. We establish estimates of the error of this method based on a quadrature process, which is the best in the class of differentiable functions. We prove the convergence of the method in finite-dimensional and uniform metrics. We find that the investigated quadrature method is optimal by order on the Hölder class of functions.