离散模型两个不变闭曲线的分支存在性研究

主要研究的是二维离散模型,基于余维1的N-S分支理论,探讨了离散模型产生两个不变闭曲线的余维2的分支问题.给出了定理及其证明的详细过程,主要用复正规形的方法简化方程,消掉全部的二次,四次项和部分一次,三次项,利用极坐标使方程化为最简形式.分析产生两个不变闭曲线的条件,通过计算相关系数k_1(α)和k_2(α),进而计算出关键系数L_2(0),给出了不变闭曲线的存在性和稳定性.当L_2(0)0(L_2(0)0)时,参数满足一定条件会出现两个不变闭曲线,此时里面的不变闭曲线稳定(不稳定),外边的不稳定(稳定).在分析过程中,不仅给出相关系数k_1(0),k_2(0)的计算公式,而且给出了特定情形下k_2(0)的简化计算公式,使得运用更加方便.还通过举例展示了方法的应用过程,也通过数值模拟显示了方法的正确性.     

关于曲线f(x)=(x-a_1)~(k_1)(x-a_2)~(k_2)…(x-a_n)~(k_n)拐点的探讨

通过分析多项式函数的实重根及其导数的性质,结合罗尔定理和泰勒公式,给出了分析曲线f(x)=(x-a_1)~(k_1)(x-a_2)~(k_2)…(x-a_n)~(k_n)拐点的一般方法 ,指出了在实数域内可以分解的多项式函数全部拐点的分布范围.     

于改进UGF算法的线性拓扑WSN系统可靠性评估

提出了面向感知数据融合的通用发生函数(UGF)改进算法,并使用该算法对线性拓扑结构的无线传感网络(WSN)可靠性进行了评估。首先对PEGASIS协议下WSN的线性拓扑结构及数据传输过程进行抽象,建立了双向连续k/n:F系统模型。然后根据WSN感知数据传输及融合方式,在改进算法中重新定义了传感节点的UGF表达式和组合算子。最后对双向连续k/n:F模型进行单向化分解,根据得到的单向模型可靠性推导出双向模型的可靠性表达式。通过具体实例对提出的改进算法进行了验证,计算结果显示改进的算法可有效解决传感网络线性拓扑结构可靠性评估问题。     

基于不确定理论的原油海运网络连通可靠性研究

原油海运网络是原油进口国的海上生命线,为科学衡量网络中节点受到突发事件影响后的原油海运网络的连通可靠性,本文采用不确定变量来描述突发事件发生后各节点的连通性,引入不确定理论对原油海运网络连通可靠性进行评估,并建立了不确定原油海运网络的最可靠路径选择模型。本文不确定变量的引入不再依赖较多的历史数据去描绘节点失效的概率分布,而且提出的最可靠路径选择模型可以确保突发事件发生后原油的及时运输。本文还提出了α-最可靠路径和最大测度最可靠路径选择问题,给出不确定原油海运网络最可靠路径风险值的不确定分布,为突发事件发生后决策者的路径选择提供依据。本文以中国进口原油海运网络为例作案例分析。     

关于平面格图圈的计数

<正> 平面格图中初级回路称为圈.对 m×n 格图圈的计数,文[1]用点阵分析方法研究了 m=1,2的情形.本文用直接递归法得到 m=2时的递归式、生成函数及显式表达,并推广到 m=3,4的情形,得到3×n,4×n 格图圈个数的递归式.     

弧k/n(G)与节点k/n(G)网络模型可靠性估计的对偶变量蒙特罗洛方法

针对弧k/n(G)网络无法刻画网络节点对上游节点输入需求的问题,提出了节点k/n(G)网络模型.在节点k/n(G)网络中,通过设定网络节点工作条件为接收工作输入点集中n个节点里的至少k个输入,节点k/n(G)性质被进一步延伸至对上游任意节点.为采用蒙特卡洛方法对弧与节点k/n(G)网络的可靠性进行估计,分别对两类k/n(G)网络设计了基于随机邻接矩阵的网络连通性算法.并结合k/n(G)网络结构函数的单调性,将对偶变量方差缩减技术应用于两类k/n(G)网络的蒙特卡洛方法,仿真实验表明:所设计的仿真方案能够有效地对两类k/n(G)网络的可靠性进行估计,对偶变量方法提高了蒙特卡洛方法的计算精度并减少了计算时间.     

另一类广义Euler数

本文由函数φ_r(x)=1+x~(-1)+x~(-2)+…+x~(-r)出发,使用对数运算及算子θ=xD得出了与[1]中不同的男一类广义Euler数,并对其主要性质进行了描述,列出了其生成函数、递归关系等。     

任意k紧优双环网络无限族的构造

在L形瓦理论的基础上,结合中国剩余定理和数论中的素数理论,通过讨论A+z-2j≠0的一般情况,证明可以构造任意k_0紧优双环网络无限族:{N(t)=3t~2+(2i-1)t+B;B=k_0~2-nk_0+m,t=f~2-if-nk_0+m,f=(2i-i~2+4B)p_1~2p_2~2…p_(k_0~2)~2e+c,其中i=1,3,e≥0,m,n均为整数}.结点数N(t)为e的4次多项式,也可以为e的2次多项式且系数含有参数.     

书本图与齿轮图的子树计数及渐进密度特性分析

图的子树数拓扑指标对指导可靠性网络设计和分析化合物的物理与化学性质均具有重要意义.本文基于生成函数、结构分析及矩阵映射的方法给出书本图B_(n,2)(n≥2)和齿轮图G_(n,1)(n≥3)的子树数生成函数,并分析了B_(n,2)(n≥2)和G_(n,1)(n≥3)的子树密度的渐进特性,本研究为探索复杂圈图和分子的结构新特性提供了新的视角和方法.     

无线传感器网络传输可靠性计算

无线传感器网络是由传感器节点和汇聚节点组成的以数据为中心的无线网络.汇聚节点根据一个或多个源节点传送的采集数据对事件进行监测和判断,而数据传输的可靠性直接影响到监测和判断的准确性.在无线传感器网络中,一方面,网络拓扑结构是动态变化的,数据传输的可靠性与网络拓扑结构有关;另一方面,网络中的传感器节点是能最受限的,因此传输的可靠性还与节点的能昔密切相关-针对无线传感器网络的特点,给出了无线传感器网络的传输可靠性概念,提出一种传输可靠性度量,分别在有数据融合和无数据融合两种情况下,对网络节点的能耗情况进行了分析,获得r网络节点正常工作的概率随时间的变化关系,并导出数学表达式,用于计算节点所产生的数据包成功传输给汇聚节点的概率,从而获得了求整个网络传输可靠性的计算方法.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in