非线性微分方程的多步修正和修正的渐近Adomian分解法（英文）

Adomian分解方法是解微分方程的一种分析方法.基于Adomian分解方法和修正的渐近Adomian分解方法,给出了多步修正的渐近Adomian分解方法.指出修正的渐近Adomian分解方法可以给出非线性微分方程的精确解.多步修正的渐近Adomian分解方法也可以给出精确解且最小化计算量.一些数值例子表明多步修正的渐近Adomian分解方法的有效性.对于一些问题,多步修正的渐近Adomian分解方法是优于Adomian分解方法和修正的渐近Adomian分解方法.     

关于结构分解技术中两种分解方法的比较研究

投入产出技术中的结构分解技术被广泛的应用于经济系统的各个领域,但随着不同的经济分析的需要,发现传统的结构分解方法——算术分解法在分析效率、强度等指数型指标时存在一定的分解困难。因此,本文提出了广义指数分解方法的基本概念和一般解,通过模型建立、以及我国生产能源消耗量的实证分析,对两种分解方法进行比较。研究表明,两种分解方法适用不同的指标形式,广义指数分解法在分析指数型指标时,更具优势。     

几类可升分解的图

Ａｌａｖｉ等人在文献［１］中定义了图的一种新分解，即“升分解”，并且猜想：任意有正数条边的图都可升分解。本文证明了下面三类图可升分解，并得到了一些有意义的推论。１设Ｒｎ是一个至多含有ｎ个顶点和至多含有ｎ条边的图，Ｋｎ－Ｒｎ可升分解（ｎ≥５）；２对称图可升分解；３对称图Ｇ的混合积（Ｇ；ｋ）可升分解。     

矩阵的满秩正交分解

旨在给出矩阵一种新分解(满秩正交分解).分解简单易求,且与矩阵的奇异值分解有类似的性质和应用.     

时间序列的经验模态频率分解EMFD

在经验模态分解的基础上,提出了经验模态频率分解.经验模态频率分解是正交分解,有很好的性质和频率意义.     

完全二分图的升分解

Ａｌａｖｉ等人定义了一种关于图的新分解，即“升分解”并且猜想，任何有正条边的简单图可升分解。Ｈｕｎｇ－ＬｉｎＦｕ曾证明恰有（ｎ＋１／２）条边的完全二分图可升分解。本文得到了一个中的结论，证明了具有任何条边的完全二分图都可升分解。     

唯一分解整环上的矩阵分解问题

主要讨论唯一分解整环上矩阵的子式素分解和因子素分解问题,得到该环上判别任意矩阵是否具有子式素分解的充分必要条件,并对行满秩矩阵给出其关于其正则因子是否存在因子素分解的判定条件.     

数学形态学中结构元素的分解

本文讨论了数学形态学中结构元素的分解问题(B=B_1⊕…⊕B_n)并给出了一系列结果。本文的重点是二维结构元素的1-D分解和点对分解。且相应的可分解必要条件和分解算法被提出。我们的算法是高效的,它们的时间复杂度均为o(n~2),这里n是被分解结构元素中点的个数。     

O-对称矩阵的奇异值分解及其算法

本文研究了具有轴对称结构矩阵的奇异值分解,找出了这类矩阵奇异值分解与其子阵奇异值分解之间的定量关系.利用这些定量关系给出这类矩阵奇异值分解和Moore-Penrose逆的算法,据此可极大地节省求该类矩阵奇异值分解和Moore-Penrose逆时的计算量和存储量.     

一般的正项几何规划的一种分解方法

关于几何规划的分解方法，［１３］均给出特殊类型的几何规划的分解方法，本文则对一般的正项几何规划给出一种直接分解方法。     

一类群的幂半群的半格分解

讨论了一类群的幂半群的半格分解,得到了最大半格分解的刻划,及有关滤子,完全素理想等一系列结果,作为特例,得到了Putcha.M.S.关于有限群的幂半群的最大半格分解的结论。     

A Geometric Study of the Split Decomposition

This paper sheds new light on split decomposition theory and T-theory from the viewpoint of convex analysis and polyhedral geometry. By regarding finite metrics as discrete concave functions, Bandelt-Dress' split decomposition can be derived as a special case of more general decomposition of polyhedral/discrete concave functions introduced in this paper. It is shown that the combinatorics of splits discussed in connection with the split decomposition corresponds to the geometric properties of a hyperplane arrangement and a point configuration. Using our approach, the split decomposition of metrics can be naturally extended to distance functions, which may violate the triangle inequality, using partial split distances.     

On the convergence of cross decomposition

Cross decomposition is a recent method for mixed integer programming problems, exploiting simultaneously both the primal and the dual structure of the problem, thus combining the advantages of Dantzig—Wolfe decomposition and Benders decomposition. Finite convergence of the algorithm equipped with some simple convergence tests has been proved. Stronger convergence tests have been proposed, but not shown to yield finite convergence.In this paper cross decomposition is generalized and applied to linear programming problems, mixed integer programming problems and nonlinear programming problems (with and without linear parts). Using the stronger convergence tests finite exact convergence is shown in the first cases. Unbounded cases are discussed and also included in the convergence tests. The behaviour of the algorithm when parts of the constraint matrix are zero is also discussed. The cross decomposition procedure is generalized (by using generalized Benders decomposition) in order to enable the solution of nonlinear programming problems.     

On the Canonical Decomposition of Quiver Representations

Kac introduced the notion of the canonical decomposition for a dimension vector of a quiver. Here we will give an efficient algorithm to compute the canonical decomposition. Our study of the canonical decomposition for quivers with three vertices gives us fractal-like pictures.     

李超三系的分解唯一性

该文首先研究了李超三系的中心、导子超代数和内导子超代数的分解问题, 给出了具有平凡中心的李超三系的分解唯一性定理, 同时讨论了李超三系的自同构的扩张.     

ON THE ASCENDING SUBGRAPH DECOMPOSITIONS OF REGULAR GRAPHS

The definition of the ascending suhgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition.     

On the Convergence Rate of a Space Decomposition Method

Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which can be applied to some nonuniformly elliptic problems.     

Operator Decomposition of Graphs and the Reconstruction Conjecture

We present a new type of decomposition of graphs – the operator decomposition connected with the classical notion of homogeneous set (or module). Using this decomposition we prove that Kelly-Ulam reconstruction conjecture is true for graphs having homogeneous set with prescribed properties, as well as for non-p-connected graphs.     

A remark on the canonical decomposition of a connection at an irregular singular point

We give a remark on the proof of the theorem of existence and uniqueness of the slope decomposition and the Turritin-Levelt decomposition of a connection in several variables. Using a lemma from [2], we show that the slope decomposition and the Turritin-Levelt decomposition of the relative connection in one variable is stabilized by the absolute connection.     

The Kullback-Leibler risk of the Stein estimator and the conditional MLE

The decomposition of the Kullback-Leibler risk of the maximum likelihood estimator (MLE) is discussed in relation to the Stein estimator and the conditional MLE. A notable correspondence between the decomposition in terms of the Stein estimator and that in terms of the conditional MLE is observed. This decomposition reflects that of the expected log-likelihood ratio. Accordingly, it is concluded that these modified estimators reduce the risk by reducing the expected log-likelihood ratio. The empirical Bayes method is discussed from this point of view.