维数理论

In the four section, from the interpolationdimension of an algebraic curve and an algebraic surface,using theoryand method of algebraic geometry, we get some interpolation of analgebraic curve and an algebraic surface, and we prove the reasonableof the interpolation dimension of an algebraic curve and an algebraicsurface.

第四章我们从沿代数曲线曲面空间的插值维数出发，利用代数几何理论与方法，给出了代数曲线曲面上的基本插值结构，并证明了我们长期应用的其上的插值维数公式的合理性。

Based on the research work of basic theories including phase space reconstruction,embedding theorem,correlation dimension,local dynamics,Lyapunov exponents,surrogate data etc,based on the research work of general methods such as principal component analysis,correlation dimension GP algorithm,false neighbors method,nonlinear time series prediction,local prediction, adaptive prediction,neural network model,support vector machines regression model, prediction power,nonlinear detection,coarse-graining methodology,conditional entropy and so on,the framework of nonlinear time series analysis are constructed.

在对包括相空间重构、嵌入定理、关联维数、局部动力学、Lyapunov指数、替代数据(来源：A97BC论文网www.abclunwen.com)、等基本理论与其物理意义的研究和讨论基础上；在对包括主分量分析、关联维数GP算法、伪邻近点法、非线性时间序列预测、局域预测、自适应预测、神经网络模型、支持向量回归模型、预测效果、非线性检测、粗粒化方法、条件熵等非线性时间序列一般分析方法的原理和算法研究基础上；构建了新的非线性时间序列分析的理论体系，归纳总结了非线性时间序列分析的基本问题和主要研究方面。2。

So using fractal theory box dimension and information dimension can be extracted from signal as the classification feature.

因此利用分形理论从信号中提取盒维数和信息维数作为分类特征，这种特征可包含信号幅度、频率和相位的变化规律，并集中了不同调制信号之间的差异信息。

Fractional integral is an essential branch of fractal theory. In this paper, the authors adopted fractional integral in the evaluation of time series dimension, which has a higher accuracy than other methods such as box dimension, gauge method and so on.

分数阶积分是分形理论的一个重要分支，应用分数阶积分进行时间序列维数估计，其精度比box维数、量规法等方法高。

Based on the methods of Hausdorff fractal dimension and space relation fractal dimension ,the paper advances calculation models on the fractal dimension and the arriving degree of network of Liaoning s highway network.

分析了辽宁省公路交通网络的基本现状，根据分形理论，利用Hausdorff维数简化算法和空间关联维数的计算方法，测算了以省内国道干线为基础的辽宁省公路交通网络的分维数和网络直通度。

Fractal and wavelet process inherently multiple-scale property and scale invariant that can be competent for roughness features in textural representation of texture image.

本文主要讨论分形维数理论在纹理图像特征提取方面的应用，首先我们系统地分析了图像处理中分形维数估计的一般计算方法，然后在此基础上做了改进。

However,for the large dimensional data.the sample covariance matrix is not a good estimator of the population counterpart.Many methods of parametric estimations and tests for multivariate statistical problems can not be simply used to deal with large dimensional data.

但是由于经典的大样本理论都是假定维数很小是固定的，故而经典极限理论并不适宜解决大维随机数据问题，很多多元问题的模型参数估计、模型检验的统计量已有的结果对大维海量数据并不能平凡推广。

The research about the subject largely developed and extended the classical results about homological algebra.The theory of relative homological dimensions of modules and rings are the main research field in the subject.

关于这门学科的理论研究，极大的丰富和发展了同调代数的经典结果，而环与模的相对同调维数理论是相对同调代数这一门学科的重要研究领域。

The partial least-squares regression model is built up to forecast crop leaf water potential of estival maize.Thirdly, atmosphere aspect, the low water age has been forecasting by R/S method of fractal theory in Si Chuan middle region. The chaotic behavior of agriculture meteorologic factors (average temperature, max temperature, min temperature, temperature of the earths surface, evaporators, precipitation, relative humidity, sunlight time) time series is investigated using the phase-space reconstruction technique, and the delay time and relation dimension and min embedding dimension and Lyapunov exponent and Kolmogrov entropy is calculated. The atmosphere water potential is calculated by surveyed data, and the day change law of atmosphere water potential and the relation between it and sun radiation has been discussed.

第三，关于大气方面，利用分形理论中R/S分析法对川中丘陵区的枯水年进行了预测；利用混沌理论的重构相空间技术，确定了农业气象因子(旬平均气温、最高气温、最低气温、地表温度、蒸发量、降水量、相对湿度、日照时数)的延时、关联维数、最小嵌入维数、Lyapunov指数、Kolmogrov熵，从而证明了以上各农业气象因子的时间序列具有混沌特性，为利用混沌理论预测各气象因子提供了科学依据；利用田间自动气象站的数据计算了大气水势并探讨了大气水势的日变化规律以及大气水势与太阳辐射的关系。

Using tools from dynamical system theory, such as phase space diagrams, Frequency analysis, Poincare sections and the calculation of statistical quantity of chaos: the correlation dimension, Reni entropy, Laypunov exponent and so on, the different solutions to the Navier-Stokes equations at different values of the Reynolds number have been identified and characterized through reconstructing the phase space of velocity time series by means of time delay and dimension embeding.

通过时间延迟和维数的嵌入对速度时间序列重构相空间，利用非线性动力系统理论方法诸如相空间分析，频谱分析，Poincare映射，以及通过对混沌统计量：关联维数，Reni熵，Laypunov指数等计算，对不同雷诺数N-S方程解的特征作了分辨。

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。