维数理论

The first 10 chapters study cohomolgy of open set in Euclidean space,treat smooth manifolds and their cohomology and end with integration on manifolds.

全书分四章：范畴与函子及其在模论中的应用；特殊模与相应的维数；环模复形的同调理论；谱序列。

This method requires only the dimensions of systems and the expansion coefficient of density matrix which can be easily got, and the computation is easy, so it has its application value.

此判据仅依赖于系统的维数和密度矩阵的展开系数，而这些数据是易于求得的，使得量子纠缠态的判断简单易行且易于操作，在实际运用中具有理论价值。

As the basis of the thesis, measure theory and dimension concept including several technical lemmas are presented in the second chapter.

第二章概述了拓扑空间中的测度理论和维数概念，包括一些技术性引理，是全文的基础。

Fault diagnosis; chaos theory; correlation dimension; wavelet analysis; virtual instrument; hydraulic pump

故障诊断；混沌理论；关联维数；小波分析；虚拟仪器；液压泵

A tensile facture fractal model of grain filled polymer composites on the base of the fractal theory was established,and an equitation of the tensile fracture fractal dimension was proposed.

梁基照，吴成宝，颗粒填充高分子复合材料拉伸断口的分形模型基于分形理论构建了颗粒填充高分子复合材料拉伸断口的分形模型，进而提出了分形维数计算公式。

Keywords: molecular dynamics simulation; fractal theory; fractional Brown function; vapor-liquid interface.

中文关键词：分子动力学模拟；分形理论；分数布朗函数；分数维数；汽液界面

Based on fractal theory, the density, the temperature, the pressure tensor, the local surface tension and fractional dimension number of liquid-vapor interface at equilibrium are obtained by the help of molecular dynamics simulation.

本文在分形理论基础上，采用分子动力学模拟方法研究了在平衡状态下的汽液界面参数，得了界面区内的密度、温度、压力张量、表面张力和分维数的分布。

This fact is in conformity with the idea of physiology and What reported by other authors, so we think that the analysis of the dimension hassome theoretical meoretical in the representation of brain function.

这一事实和生理概念及其他作者所报道的结果相一致，故我们考虑维数分析在表示脑功能状态上有一定的理论意义。

In this paper, some fractal characters of colony and hypha were introduced and the possible mechanism of these phenomena were discussed.

分形理论是以局部的某些特征来解释整体，微生物的生长形态可以用分形维数来定量描述。

Characteristics of the Internet traffic data flow are studied based on the chaos theory. A phase space that is isometric with the network dynamic system is reconstructed by using the single variable time series of a network flow. Some parameters, such as the correlative dimension and the Lyapunov exponent are calculated,and the chaos characteristic is proved to exist in Internet traffic data flows. A neural network model is constructed based on radial basis function to forecast actual Internet traffic data flow.

摘 要：应用混沌理论，分析了网络流量，用单变量的网络流量时间序列重构与网络动力系统等距同构的相空间，进而计算了实际网络的关维数和Lyapunov指数，并证实了网络流量存在混沌特性；据此建立了基于径向基函数神经网络的模型，并对实际网络数据流进行了预测。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。