维数

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。

The purpose is to provide a general comprehension for the relationship between soil physical properties and fractal dimension affected by soil alkalinization ,and to present a new heuristic idea to regional-level ma.

运用土壤颗粒质量分形模型计算松嫩平原低平地安达试区植被分布区和碱斑区样点土壤颗粒的分形维数，并建立分形维数与土壤颗粒不同粒级间的回归关系，以探讨土地碱化后土壤粒径分布的分形特征及其与土壤物理性状的关系。

The ann-injective rings start at the angle of annihilator,at the same time,the CT-injective rings start at the angle of cycle tortionless modules.

在第三章，我们引入了CT -内射维数的概念，从维数的角度来更进一步地认识CT -内射。

But under limited training sample size, increased dimension of remote sensing data means decreased samples/dimension ratio, which can lead to low classification accuracy if common statistic based pattern classification methods were used.

但在有限训练样本条件下，遥感数据维数的增高使样本/维数比率大大降低，采用常规的统计模式识别方法反而无法得到较好的分类结果。

The experimental results have shown that the common logarithm values of transverse rupture strength lgσ〓 increase with the increase of fractal dimension D〓, and has a linear equation relationship. The microfracture fractal model of cermets has been founded and the estimated fractal dimension formula of fracture surfaces proposed.

建立了颗粒型复合材料金属陶瓷断裂的微观fractal模型，提出了计算断口表面分形维数的公式，指出断口分形维数依赖于测量码尺的选择，对金属陶瓷来说其临界测量码尺为0.07μm。

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。

The correlation coefficient between the fractal dimension of soil water-stable aggregates in Beibei Karst mountains and organic matter, total N, total K, total P, available N and P and K, total exchangeable base and pH are:-0.617,-0.532, 0.798〓, 0.450,-0.550, 0.724〓, 0.652〓,-0.489, 0.781 (〓: correlation is significant at the 0.01 level,〓: correlation is significant at the 0.05 level) respectively.

北碚岩溶山地表层土壤的水稳性团聚体分形维数与有机质、全N、全K、全P、速效N、速效K、速效P、交换性盐基总量、pH的相关系数分别为-0.617、-0.532、0.798〓、0.450、-0.550、0.724〓、0.652〓、-0.489、0.781（**：α=0.01水平显著；*：α=0.05水平显著）：对26个样地60个样品的水稳性团聚体分形维数与养分指标的相关分析表明，分维值与有机质、速效N、全N的相关系数分别为-0.410、-0.452、-0.522，达到显著水平。

It is assumed here that ∑ is the same n-dimensional state space at all t ∈T .

如果状态空间的维数发生变化需要使用符号表示，对于 t ∈ T 系统的维数都是 n 维。

The results show that a the variation of annual mean runoff of Huayuankou section exist an intrinsic dynamic mechanism, which is the results of joint action of affecting factor of periodicity and non-periodicity, having obvious chaos characteristic; b the correlation dimension of attractor of phase space is 5.09 and saturation inserted dimension is 14. It shows that to establish a mathematical model of the annual mean runoff system of Huayuankou at least requires 6 independent variables and the required saturation inserted dimension for rebuilding phase space is 14; c the steady estimate of Kolmogorov entropy is 0.14, showing the average predictable time of the annual mean runoff variation of Huayuankou is about 7 years and; d using nonlinear deterministic chaos model is more suitable to describe the variation of annual mean runoff of Huayuankou.

结果表明：①花园口年平均径流量变化存在着内在动力学机制，是由周期性和非周期性影响因子共同作用的结果，具有明显的混沌特性；②相空间吸引子的关联维为5.09，饱和嵌入维数为14，这说明要建立花园口年平均径流系统的数学模型，至少需要6个独立变量，重构相空间所需要的饱和嵌入维数为14；③Kolmogorov熵的稳定估计为0.14，说明花园口年平均径流量变化的平均可预报时间大约为7年；④用非线性确定性的混沌模型比完全的随机模型更适于描述黄河花园口年平均径流量的变化。

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。

What are your goals and strategies for growth?

你的成长目标和策略是什么？

And unto the angel of the church in Sardis write; These things saith he that hath the seven irits of God, and the seven star I know thy works, that thou hast a name that thou livest, and art dead.

3：1 你要写信给撒狄教会的使者，说，那有神的七灵和七星的，说，我知道你的行为，按名你是活的，其实是死的。