带框形约束的线性规划问题的鞍点法

根据作者最近提出的求解线性规划问题的鞍点法[3],本文对带框形约束的问题 min c~Tx, s,t A_x=b, l≤x≤h,给出简单的迭代公式.该法的主要优点是它的强收敛性和它的迭代公式非常容易实现.     

非线性约束条件下的梯度投影方法

§1.引言 考虑问题:其中R={x∈E~n|h_i(x)≤0,i=1,…,m},并且满足 (H1)h_i(x),i=1,…,m为一阶连续可微的凸函数;f(x)为一阶连续可微函数。 (H2)对A_x∈R:{△h_i(x)|i∈J_0(x)}为线性无关的向量组,其中J_0(x)={i|h_i(x)=0}。 对这类非线性约束的极值问题,以往的梯度投影方法是先对切面做梯度的投影,然后拉回到可行区域,原因是梯度在切面上的投影往往已不是可行方向。本文改变了以往     

s型加性算子与a型加性算子

设有定义于某线性空间而取值于规定了乘法的另一线性空间的映象A,满足 A(x+y)=B_1(y)A_x+B_2(x)AY+C(x,y), 则A称为泛义加性算子。本文所研究的s型加性算子与α型加性算子是泛义加性算子的特例。它们分别是通常加性算子与E.Hill等关于指数函数(算子)概念的拓广。但引入方式与结论不同。     

“旋转数列”简论(续完)

四、旅转数列周期性的讨论有些无穷数列具有周期现象,即{A_n}满足条件:A_(x T)=A_x,(x∈N,常数T≠0),例如常数列{A_n}:A_1,A_2,…的周期T=1,正k次圆周型旋转数列[A_n,(P_0,θ)]的周期T=k(k>1)等。 (1)旋转数列通项计算公式     

一类由生成函数构成的可行方向算法

设非线性规划问题(P):min{f(x)|x∈R}。其中f:E~n→E~1,f(x)∈C~1,x∈E~n,R={x|A_x=b,x≥0},A为m×n阶矩阵,rankA=m,b∈E~m。 利用既约梯度建立可行方向算法目前在国内外已有不少,它们的特点在于:(1)将高维问题降为低维问题处理。此时的问题已近似于一个无约束的问题;(2)在计算的每一步上都是显式迭代,而不必去解一个复杂的线性的或二次的规划。这些特点使得算法变     

原始遞歸函數的定義

<正> 符號說明 本文中除以α表示常數外均以小寫拉丁字母表示自變數,以大寫字母表示函數關係,而一元函數A(x)常省寫為A_x. 在本文中只討論數論函數,自口自變數与函數所取之值均限於正整數或0(常     

点到直线距离公式的几种证明

新编初中《数学》第六册及其《教学参考书》分别给予了点到直线距离公式的证明,下面介绍几种别的证明方法,供教学参考或练习之用。命题已知直线l: A_x B_y C=O(A、B不同时为零)和点P(x_o,y_o),求证点P到直线l的距离     

浅谈导数学定义在导数计算的中地位与作用

不少学生学习了求导公式后 ,往往对导数定义不太重视。其实 ,导数的定义不仅是导数的原始基本概念 ,而且它在求极限、求导数的计算及证明中都有着重要的、甚至是不可替代的作用。本文仅就导数定义在导数计算中的地位与作用问题谈点粗浅的认识 ,以期学生对此问题引起重视。一、在分段函数求导计算中的情形对分段函数分段点的导数的计算 ,必须按定义求 ,不能套公式。例 1　设 f ( x) =e|x|,求 f′( x)。[错解 ]　因为 f ( x) =ex,　　 x≥ 0e- x,　 x <0 ,所以 ,f′( x) =ex,　　 x≥ 0-e- x,　 x <0[辨析 ]　 x=0是分段点 ,而对分段点的导数 …     

解非线性方程的一个非线性迭代法

1 引 言 用常微分方程及其数值解的理论和方法(简称ODE方法)来构造解非线性方程组的方法见Branin.F.H.等,但未能讨论收敛性。其后对线性方程组A_x=b和非线性方程f(x)=0都有专门的论述且论证了方法的大范围收敛性,对于求非线性方程f(x)=0在[a,b]内的根x~·的不使用导数的大范围收敛的算法使我们容易想到两分法和试位法,是否有其它更为有效的不使用导数的大范围收敛的方法,下面我们来讨论基于ODE方法原理的非线性迭代方法。     

关于正定可对称化线性代数方程组的预对称正则化算法

1引言考虑线性代数方程组A_x=b,A∈R~(n×n)非奇异,x,b∈R~n(1)的求解．当系数矩阵是大型稀疏的正定可对称化矩阵,文[1,2]讨论了一类预对称共轭梯度算法(LRSCG算法是其中之一),这类算法的实质是利用非对称的系数矩阵可对称化的性质,并结合共轭梯度法而构造的一种预处理的共轭梯度法[12,16,17]．但非对称的系数     

凝聚映象的不动点及算子方程Ax+Bx+Cx=x的可解性

按文[1]中方法得到几个对凝聚映象的不动点定理,还扩充文[2]中对于算子方程Ax B x=x到Ax B x Cx=x可解性的某些结论.主要结果是定理2、定理3与定理5.     

Criteria for Pointwise Growth and Their Role in Invasion Processes

This article is concerned with pointwise growth and spreading speeds in systems of parabolic partial differential equations. Several criteria exist for quantifying pointwise growth rates. These include the location in the complex plane of singularities of the pointwise Green’s function and pinched double roots of the dispersion relation. The primary aim of this work is to establish some rigorous properties related to these criteria and the relationships between them. In the process, we discover that these concepts are not equivalent and point to some interesting consequences for nonlinear front invasion problems. Among the more striking is the fact that pointwise growth does not depend continuously on system parameters. Other results include a determination of the circumstances under which pointwise growth on the real line implies pointwise growth on a semi-infinite interval. As a final application, we consider invasion fronts in an infinite cylinder and show that the linear prediction always favors the formation of stripes in the leading edge.     

格上点式一致结构的刻划与点式度量化定理

本文通过对格上远域映射,特别是△-映射和＊-映射的性质的研究,给出了格上点式一致结构的若干简明刻划,证明了几个重要的格上点式度量化定理,并提出了与格上点式度量理论相协调的若干分离性公理.     

格上点式仿紧性

本文在拓扑分子格（ＴＭＬ）上提出一种仿紧性，它以格上点式紧性［３］为特款，讨论了它在ＴＭＬ上的几种不同的表现形式以及它与正规性的关系．     

Pointwise estimates for the maximal multilinear singular integral operators

Two pointwise estimates relating the maximal multilinear singular integral operators and some classical maximal operators are established. These pointwise estimates imply the rearrangement estimate and the BLO(Rn) estimate for the maximal multilinear singular integral operators.     

逐点伪轨跟踪性质与混沌

本文研究了逐点伪轨跟踪性质与拓扑混合等混沌性态的关系,给出了$f$具有逐点伪轨跟踪性质时,$f$具有一致正熵和完全正熵的一些等价条件.     

Pointwise Well-Posedness of Perturbed Vector Optimization Problems in a Vector-Valued Variational Principle

In this note, we point out and correct some errors in Ref. 1. Another type of pointwise well-posedness and strong pointwise well-posedness of vector optimization problems is introduced. Sufficient conditions to guarantee this type of well-posedness are provided for perturbed vector optimization problems in connection with the vector-valued Ekeland variational principle.     

Improvement of Hartman''''s linearization theorem

Hartman's linearization theorem tells us that if matrix A has no zero real part and f(x) is bounded and satisfies Lipchitz condition with small Lipchitzian constant, then there exists a homeomorphism of Rn sending the solutions of nonlinear system x' = Ax + f(x) onto the solutions of linear system x = Ax. In this paper, some components of the nonlinear item f(x) are permitted to be unbounded and we prove the result of global topological linearization without any special limitation and adding any condition. Thus, Hartman's linearization theorem is improved essentially.     

Geometric classification of warped products isometrically immersed into Sasakian space forms

The main objective of this paper is to study the warped product pointwise semi‐slant submanifolds which are isometrically immersed into Sasakian manifolds. First, we prove some characterizations results in terms of the shape operator, under which influence a pointwise semi‐slant submanifold of a Sasakian manifold can be reduced to a warped product submanifold. Then, we determine a geometric inequality for the second fundamental form regarding to intrinsic invariant and extrinsic invariant using the Gauss equation instead of the Codazzi equation. Evenmore, we give some applications of this inequality into Sasakian space forms, and we will investigate the status of equalities in the inequality. As a particular case, we provide numerous applications of the Green lemma, the Laplacian of warped functions and some partial differential equations. Some triviality results for connected, compact warped product pointwise semi‐slant submanifolds of Sasakian space form by means of Hamiltonian and the kinetic energy of warped function involving boundary conditions are established.     

Hartman定理的推广

本文研究微分方程全局拓扑线性化,在某些弱条件下得到系统χ’=Aχ+f(χ)的 全局线性化,推广了Hartman的结果.