维数

Only the last parameter of a method can be a parameter array, and the type of a parameter array must be a single-dimensional array type.

只有方法的最后一个参数可以为参数数组，并且参数数组的类型必须为一维数组。

The mathematical programming formulation and related solution procedure are established by the traditional BEM. Through the discretization of space and time, the elastoplastic stress simulation method and reduce-basis technique are adopted to construct the self-equilibrium stress field. The numbers of variables and constraint equations in the resulting mathematical programming formulation are reduced greatly and then the dimension obstacle of computation in 3-D limit and shakedown analysis is overcome.

采用常规边界元方法建立了三维结构极限与安定分析的数学规划格式，通过对时间和空间的离散化，并采用弹塑性模拟法构造自平衡应力场和引入减缩基技术，大大减少了所形成的数学规划格式中的未知变量和约束方程的数目，有效地克服了三维结构极限与安定分析中的维数障碍问题。

In the third chapter, at first the significance and basic idea of the phase space reconstruction is discussed.

第三章首先讨论了相空间重构的意义及基本思想，给出分形维的概念及分形维的计算方法，分析了关联维数的相关问题。

The interface is limited to 10x10 dimensions, but the solver itself can be used to calculate the Inverse of any Rectangular Matrix, provided the determinant of it is non-zero.

界面只允许计算10x10维，但程序本身可以计算任意维的矩阵，只要维数不为零。

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。

Based on them, we calculated precisely some enegy levels of P-wave and D-wave of a helium atom, presented and proved the general interdimensional degeneracies for a quantum N-body system, derived the general spherical spinor functions and the exact solution to the Dirac equation for the hydrogen atom, and proved uniformly the Levinson theorem for the Dirac equation in D-dimensions.

在此基础上，我们精确计算了氦原子P波和D波若干较低能级，建立和证明了量子N体系统不同维数状态间最普遍的简并，推导出任意 D 维空间广义球旋函数和Dirac方程氢原子的精确解，统一地提出和证明了任意 D维空间Dirac方程Levinson定理的一般形式。

Itshows that the dimension reduction algorithm based on the tangent bundle is an effectivemethod by dimensionality reduction experiments on handwritten data and breast cancer data.

通过对手写体数据的降维实验和Breast Cancer实验表明，基于切丛的维数约简方法是一种有效的降维算法。

So, the dimension constraints in 3D can be consilient with graphs in 2D.

协同了尺寸三维约束与二维图形在维数上的不一致。

The 3D topography of fractured surfaces was reconstructed and quantified by the means of SEM stereo pairs, image processing and analysis, and computer vision. It was shown that measured 3D roughness indexes Rs, Rq and Rmax have good positive relations to the crack propagation part of absorbed impact energy. Although fractal behavior had been checked out on the fractured surfaces, the fractal dimension was found nonsensitive to the fracture mode and mechanical properties. The geometric characteristics of fractal fractured surfaces should be quantified in fractal dimension together with absolute parameters.

利用扫描电镜立体对技术、图像处理与分析和计算机视觉方法对示波冲击断口形貌进行了三维重建和定量分析结果表明，断口三维粗糙度指数Rs，Rq和Rmax与示波冲击裂纹扩展功有很好的对应关系，显示了它们良好的应用前景断面虽然表现出分形行为，但分形维数是一个对断裂模式和性能不敏感参量对分形断口的几何特征描述应将分维和绝对尺度结合起来

Then, according to phase space reconstruct technique from one-dimensional and multi-dimensional time series, the quantitative criterion and rule of system chaos which combine neural network, analyses, computations and sort are conducted on EEG signals of five kinds of human consciousness activities. The author finds that statistic results of the determinism computation in time series indicate that chaos characteristic may lie in human consciousness activities, and central tendency measure is consistent with phase graph, so it may become one division way of attractor; approximate entropy of different subjects exists discrepancy; correlation dimension and Lyapunov exponent of different consciousness activities indicate that attractors of human activities are all fractional; nonlinear quantitative criterion and rule, which unites neural network, can distinguish different styles of consciousness activity in principle, and the result of sortation takes on that consciousness activity type of arithmetic is distinguished more easily than that of abstract.

采用一维与多维时间序列相空间重构技术和系统混沌的定量判据准则，结合神经网络，对五种思维作业方式的脑电信号进行了分析、计算与分类，发现确定性计算的统计结果表明人类的意识活动中可能蕴含混沌特性，中心趋向测量(Central Tendency Measure，CTM)与相图吻合较好，可作为EEG吸引子的区分方法之一；功率谱分析反映出单个受试者的各种意识形态的差异很小，但是不同意识活动谱中的活跃频段还是略有差异的；个体之间的近似熵存在差异，同种状态下近似熵大的人可能具有更好的创新性；关联维数和Lyapunov指数的计算结果表明大脑的运动落在具有分维的奇怪吸引子上；非线性量化方法与神经网络相结合，可对人脑思维活动进行较好的分类，并且从分类结果来看数理计算类思维活动较抽象类思维活动有着更好的区分度。

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。