An Inexact Newton Method Derived from Efficiency Analysis

We consider solving an unconstrained optimization problem by Newton-PCG like methods in which the preconditioned conjugate gradient method is applied to solve the Newton equations. The main question to be investigated is how efficient Newton-PCG like methods can be from theoretical point of view. An algorithmic model with several parameters is established. Furthermore, a lower bound of the efficiency measure of the algorithmic model is derived as a function of the parameters. By maximizing this lower bound function, the parameters are specified and therefore an implementable algorithm is obtained. The efficiency of the implementable algorithm is compared with Newtons method by theoretical analysis and numerical experiments. The results show that this algorithm is competitive.Mathematics Subject Classification: 90C30, 65K05.This work was supported by the National Science Foundation of China Grant No. 10371131, and Hong Kong Competitive Earmarked Research Grant CityU 1066/00P from Hong Kong University Grant Council     

复指数系的完备性

对直线上的非负凸函数α,设Cα是由直线R上所有满足当t趋向无穷大时,f(t)exp(-α(t))趋向零的复连续函数f全体,在一致范数下,Cα是Banach空间.文中得到了复指数系在Cα中完备的充要条件.     

一类多偏差变元的n种群Lotka-Volterra模型的周期正解

本文研究了一类多偏差变元Lotka-Volterra种群模型的间期正解问题,利用重合度拓展定理和一些分析技巧,得到了周期正解存在性的新结果.与已有文献相比,本文所讨论的模型更具一般性,它包含了以前人们所研究的竞争-种群模型、捕食-种群模型等,而且估计先验界的方法也是全新的.     

初-边值问题驻波解的渐近稳定性

本文考虑一带有人工粘性的二维定常等熵无旋平面流方程组的初-边值问题. 在一定的假设下,我们证明其驻波解是渐近稳定的.     

弱双曲流形的逼近

弱双曲流形是一类包含中心流形作为其特例的不变流形.本文讨论了它的逼近问题,不仅给出了计算其逼近的方法,还估计了使得这一逼近有效的它的局部性半径. 同时给出了一个具体实例来展示这些计算和估计.     

On the finite sum representations of the Lauricella functions <Emphasis Type="Italic">F</Emphasis><Subscript>D</Subscript>

By using divided differences, we derive two different ways of representing the Lauricella function of n variables F_D⁽ⁿ⁾(a,b₁,b₂,...,b_n;c;x₁,x₂,...,x_n) as a finite sum, for b₁,b₂,...,b_n positive integers, and a,c both positive integers or both positive rational numbers with c–a a positive integer. AMS subject classification 33D45, 40B05, 40C99Jieqing Tan: Research supported by the National Natural Science Foundation of China under Grant No. 10171026 and Anhui Provincial Natural Science Foundation under Grant No. 03046102.Ping Zhou: Corresponding author. Research supported by NSERC of Canada.     

Minimax inequalities and fixed points of expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces

Some minimax inequalities involving two bifunctions with noncompact and nonconvex domains are first proved in finite continuous topological spaces (in short, FC$FC$-spaces) without convexity structure. As applications some new Fan–Browder type fixed point theorems for expansive set-valued maps with noncompact and nonconvex domains and ranges are obtained in general topological spaces. These results generalize some known results in the recent literature.     

左联合谱的一个刻划及其应用

In this paper we characterize the left joint spectrum of an n-tuple T =(T1,... ,Tn) of dominant bounded linear operators on a complex Hilbert space H and the unital C^*-algebra C^*(T) generated by T1,… , Tn and I; moreover, we give an application of this characterization.     

POSITIVE SOLUTIONS OF NONLOCAL BOUNDARY VALUE PROBLEM FOR NONLINEAR RETARDED DIFFERENTIAL EQUATION

§1　IntroductionAt present,boundary value problems (BVPs) are widely investigated with variousmethods and techniques. BVPs with integral boundary conditions constitute a veryinteresting class of problems such as multipoint,three-point,four-point and nonlocalboundary value problems which are considered by many authors.And the existence ofpositive solutions for these problems becomes the subjectof many papers[1—6] .In a recentpaper[7] ,the authors have studied the existence of positive solut…     

An Arc as the Inverse Limit of a Single Bonding Map of Type N on [0,1]

Let I = [0, 1], c ₁, c ₂ ∈ (0, 1) with c ₁ < c ₂ and f : I⊸I be a continuous map satisfying: are both strictly increasing and is strictly decreasing. Let A = {x ∈ [0, c ₁]∣f(x) = x}, a=max A, a ₁ =max(A\{a}), and B = {x ∈ [c ₂, 1]∣f(x) = x}, b=minB, b ₁ =min(B\{b}). Then the inverse limit (I, f) is an arc if and only if one of the following three conditions holds: (1) If c ₁ < f (c ₁) ≤ c ₂ (resp. c ₁ ≤ f (c ₂) < c ₂), then f has a single fixed point, a period two orbit, but no points of period greater than two or f has more than one fixed point but no points of other periods, furthermore, if A≠φ and B≠φ, then f (c ₂) > a (resp. f (c ₁) < b). (2) If f (c ₁) ≤ c ₁ (resp. f (c ₂) ≥ c ₂), then f has more than one fixed point, furthermore, if B≠φ and A\ {a} ≠φ, f (c ₂) ≥ a or if a ₁ < f (c ₂) < a, f ² (c ₂) > f (c ₂), (resp. f has more than one fixed point, furthermore, if A≠φ and B\{b}≠φ, f (c ₁) ≤ b or if b < f (c ₂) < b ₁, f ² (c ₁) < f (c ₁)). (3) If f (c ₁) > c ₂ and f (c ₂) < c ₁, then f has a single fixed point, a single period two orbit lying in I\(u, v) but no points of period greater than two, where u, v ∈ [c ₁, c ₂] such that f (u) = c ₂ and f (v) = c ₁. Supported by the National Natural Science Foundation of China (No. 19961001, No. 60334020) and Outstanding Young Scientist Research Fund. (No. 60125310)