具孤立奇点的完全交叉的上同调(三)

本文证明了不可约超曲面孤立奇点的无穷小邻域的全微分形式的上同调是有限维线性空间,并证明了它们与通常微分形式上同调之间的关系.     

高斯曲率估计与常数平均曲率超曲面的稳定性

本文利用活动标架法及Ｌａｐｌａｃｉａｎ特征值方法研究了常数平均曲率超曲面的稳定性．给出了三维拟常曲率流形中具有常数平均曲率超曲面的共形度量的高斯曲率之上界估计．证明了三维拟常曲率流形中具有常数平均曲率超曲面上一个单连通有界区域为稳定的充分条件．     

論黎曼測度V_m在常曲率空間S_(m+1)中的變形

<正> 在歐氏空間E_(m+1)中的安裝及變形問題在近一世紀的幾何學者的工作中得到了解决,而所確定的V_m E_(m+1)一般是不能變形的。就是說,能够變形的只是狹窄的一類超曲面.運用了外微分形式的方法,很詳細地綜合了這些工作,並且完全地給出     

四维时空中两个不同主曲率类时共形齐性超曲面的分类

如果对任意两点p,q∈M_1~3,都存在R_1~4中的一个共形变换σ,使得σ(x(p))=x(q),并且σ(x(M_1~3)=x(M_1~3),则称x(M_1~3)为共形齐性超曲面.在本文中我们主要研究类时共形齐性超曲面x:M_1~3→R_1~4,并假设其形状算子可对角化且有两个不同主曲率.首先通过定义共形不变度量g_c,典则提升Y,共形切标架{E_i}和典则法标架ζ,我们给出了这类超曲面的一个完备共形不变量系统{E_1,E_2,E_3}.接下来通过可积条件,我们构造出了一系列非杜邦超曲面的例子以及对应的共形变换子群,并完成了对这类超曲面的分类.     

复二维空间形式中曲率椭圆是圆的辛临界曲面（英文）

本文研究了复二维空间形式中曲率椭圆是圆的辛临界曲面.利用活动标架法,获得了这类曲面是极小曲面的结果,丰富了辛临界曲面的内容.     

局部对称仿射超曲面

本文用活动标架法证明了：仿射空间Ａｎ＋１中维数ｎ大于２的非退化超曲面Ｍｎ，相对于诱导的仿射连络局部对称，当且仅当Ｍ是虚（ｉｍｐｒｏｐｅｒ）仿射球或者是非退化的二次超曲面．     

四维洛伦兹空间中形状算子不可对角化且有两个不同主曲率类时共形齐性超曲面的分类

如果对任意两点p,q∈M₁³,都存在洛伦兹空间R₁⁴中的一个共形变换σ,使得σ(x(p))=x(q),并且σ(x(M₁³))=x(M₁³),则称x(M₁³)为共形齐性超曲面.在本文中我们主要研究形状算子不可对角化且具有2个不同主曲率的类时共形齐性超曲面x:M₁³→R₁⁴.通过定义共形不变度量g_c,典则提升Y,共形切标架{E_i}和典则法标架ξ,我们给出了这类超曲面的一个完备共形不变量系统{E₁,E₂,E₃}.接下来利用可积性条件构造出了这类超曲面的显式表达式及相应的共形变换子群,从而得到了对这类超曲面的分类定理.     

一类初等微分几何定理机器证明的算法与实现

空间曲面上的曲线论是初等微分几何的重要部分．作者提出了一种以外微分运算和向量计算为主要工具,可以进行有关曲面上曲线局部性质的定理机器证明的算法．该算法结合了曲面上的活动标架,曲面上曲线的测地标架和曲线自身的Frenet标架,在Maple 9下得到实现．对20个例子进行的测试表明,由该算法生成的自动证明简短可读．     

双曲空间Hn+1(-1)中完备超曲面

本文研究了双曲空间Hn+1(-1)中具有常数量曲率的完备超曲面.利用活动标架的方法,得到此类超曲面的两个刚性定理.     

S~3中等参曲面的两个特征

本文研究了三维球空间S~3中等参曲面.利用活动标架法,获得了S~3中关于等参曲面特征的两个结果.推广了三维欧氏空间R~3和三维双曲空间中等参曲面的相关结果.     

完全与不完全的随机网

本文证明了鞍点连线网在小扰动下可以产生完全随机网和不完全随机网两种情况,并按照动力系统理论讨论了两类随机网的结构.     

蜂群算法求解支持模糊QoS约束的电子采购模型

基于Web的电子物流采购是电子商务的热点.通过将模糊量化的QoS约束加入到Web电子物流采购模型,构造一种带有QoS约束的Web电子物流采购模型,并设计一种改进的人工蜂群算法进行求解.模型基于现有Web采购系统的采购模式,融合了非功能性Web服务评价理论,着重将带QoS约束的电子物流采购选择过程与人工蜂群算法求解过程相结合,从而能快速准确地获得使整体利益最大的解.经仿真计算,验证了模型的有效性.     

Equivalence of difference equations within the web theory

Elementary version of moving frame method is applied to the symmetries and equivalences of second-order difference equations. Close links to the web theory and Riemannian geometry are established.     

���ڳ�����α�������������ĺ�ѡ�����ݿ����������ƶ��о�

??How to solve the inference problem of candidate database web surveys is an urgent problem to be solved in the development of web survey. In order to solve this problem, the inference method of non-probability sampling based on superpopulation pseudo design and the combined sample is proposed. A superpopulation model is firstly built up to construct pseudo weights for a survey sample of the web candidate database. The estimator of the population mean is then computed according to the combined sample composed of the survey sample of the web candidate database and a probability sample. The variance estimator of the population mean estimator is lastly derived according to the variance estimation theory of the superpopulation model. The Bootstrap and Jackknife methods are also used to compute the variance estimator. And all these variance estimation methods are compared. The research results show that the population mean estimator based on superpopulation pseudo design and the combined sample is better, and has higher efficiency than the estimator only using the probability sample and the weighted estimator only using the survey sample of the web candidate database. The variance estimator computed by using the VM1, VM2 and VM3 method are relatively better.     

Research on Inference of Candidate Database Web Surveys Based on Superpopulation Pseudo Design and the Combined Sample

How to solve the inference problem of candidate database web surveys is an urgent problem to be solved in the development of web survey. In order to solve this problem, the inference method of non-probability sampling based on superpopulation pseudo design and the combined sample is proposed. A superpopulation model is firstly built up to construct pseudo weights for a survey sample of the web candidate database. The estimator of the population mean is then computed according to the combined sample composed of the survey sample of the web candidate database and a probability sample. The variance estimator of the population mean estimator is lastly derived according to the variance estimation theory of the superpopulation model. The Bootstrap and Jackknife methods are also used to compute the variance estimator. And all these variance estimation methods are compared. The research results show that the population mean estimator based on superpopulation pseudo design and the combined sample is better, and has higher efficiency than the estimator only using the probability sample and the weighted estimator only using the survey sample of the web candidate database. The variance estimator computed by using the VM1, VM2 and VM3 method are relatively better.     

Dynamical foundation and limitations of statistical reaction theory

We study the foundation and limitations of the statistical reaction theory. In particular, we focus our attention to the question of whether the rate constant can be defined for nonergodic systems. Based on the analysis of the Arnold web in the reactant well, we show that the survival probability exhibits two types of behavior: one where it depends on the residential time as the power-law decay and the other where it decays exponentially. The power-law decay casts a doubt on definability of the rate constant for nonergodic systems. We indicate that existence of the two types of behavior comes from sub-diffusive motions in remote regions from resonance overlap. Moreover, based on analysis of nonstationary features of trajectories, we can understand how the normally hyperbolic invariant manifold (NHIM) is connected with the Arnold web. We propose that the following two features play a key role in understanding the reactions where ergodicity is broken, i.e., whether the Arnold web is nonuniform and how the NHIM is connected with the Arnold web.     

一类未搅拌恒化器中食物网的共存态

本文讨论了一类在单种营养物输入的未搅拌恒化器中的简单食物网模型,该模型除了营养物以外,还包含有一个捕食者种群和两个竞争的食饵种群.应用Dancer不动点指数和度理论的知识,给出了该系统共存态存在的充分必要条件.     

搜索引擎综合评价模型研究

首先给出了搜索引擎评价指标体系及计算公式 ,然后讨论了各指标权重的确定方法 ,在此基础上 ,利用多目标决策理论建立起搜索引擎综合评价数学模型 ,并通过具体实例说明了模型的使用     

Observability and observers in a food web

The problem of the possibility of recovering the time-dependent state of a whole population system from the observation of certain components has been studied in earlier publications, in terms of the observability concept of mathematical systems theory. In the present note a method is proposed for effectively calculating the state process. For an illustration an observer system for a simple food web is numerically constructed.     

A theory for nonlinear soft webs

In this paper, a fundamental theory for deformable webs not resisting any compressive membrane forces is developed through a direct derivation on the deformed configuration. In order to better describe the deformable webs, the classification of deformable webs is presented. A theory for the non-continuum elastic network webs consisting of many deformable cables is presented from the deformable cable theory, and then a theory for fabric deformable webs without relative sliding is developed as well. Finally, a nonlinear theory for continuous deformable webs is presented on the deformed configuration. The local criteria for the existence of such deformable webs are presented through the definitions, and such criteria are very significant for the wrinkling stability of the deformable webs. A deformable web possessing the local wrinkling is an unsolved problem in numerical computations. The theory for fabric webs with relative motions needs to be further developed. Herein the fundamental theory for deformable webs is presented only, and numerical examples will be presented in sequel. Such a theory of deformable webs can be applied to textile or other soft materials and bio-membranes.