维数

The study investigates time fractal properties of time series of spontaneous discharge of auditory nerve, we bring to light the shortcoming of the algorithm of capacity dimension and correlation dimension applied to time series of spontaneous discharge of auditory nerve, and offer basis to further study.

本研究从多角度考察了听神经自发放电时间序列的时间分形特性，指出了标度变换法和关联维G-P算法应用于听神经自发放电时间序列分维值计算的不足之处，分析了听神经自发放电序列赫斯特指数的意义，为进一步开展相关的研究提供了基础。

In chapter 2 we use harmonic 1-forms and discuss the relationship between an almost nonnegatively Ricci curved n-manifold with the first Betti number equal to n and a flat n-torus.

在第二章中我们利用调和1-形式研究了第一贝蒂数等于n且Ricci曲率几乎非负的n维黎曼流形和n维平坦环面之间的关系。

In this research a new mathematical model - cubic polynom with two given derivatives at end points - was proposed which can good match the S-shpae curve.This model has a number of analytical features:describing the geographic phinomena prosesses in three hierarchies (textural fractal,structural fractal and state fractal); the boundary values of the structural fractal can be considered as the boundary values of interval of scaleless.

在研究中提出了扩展分维表达函数：带导数三次多项式，它能很好地表达反S形分布曲线，具有一系列解析特征：可从三个层次（纹理分形、结构分形和态势分形）上描述地理现象或过程；其中结构分形的边界可近似地看作是非扩展分维无标度区的上下界。

Note that, since these operators commute with the particle number operator., the 2 × 2 = 4-dimensional Hilbert space has a 2-dimensional subspace,, in which a canonical spin representation is realized.

注意，由于这些算符与粒子数算符对易，2× 2 = 4 维的Hilbert空间有一个2维的子空间，其中有一个正则自旋表象。

We prove that any irreduciblesymmetric self-dual Lie algebra 〓 whose Cartan subalgebra consists of semi-simpleelements is in one of the following classes:(1)〓 is simple;(2)〓 is 1-dimensional;(3)〓is solvable.

第五节讨论Cartan子代数由半单元构成的对称自对偶李代数的结构，证明了不可约对称自对偶李代数g如果它的Cartan子代数由半单元构成，那么它只能是下列情形之一：（1）g为单李代数；（2）g是1维的；（3）g是可解的。

The discrete velocity ordinate method in the kinetic theory of gases is developed and applied to discretize the correspo

借助非定常时间分裂法和无波动无自由参数的NND耗散格式，建立直接求解微观分子速度分布函数的有限差分数值格式；研究并发展可用于离散速度坐标点选取和离散速度空间宏观取矩的高斯─埃尔米特无穷积分方法、等均间隔的牛顿─柯斯复合积分法、以勒让德多项式的根为积分结点的高斯─勒让德数值积分法，并应用于不同马赫数绕流模拟；通过对不同流域一维激波管问题、二维圆柱绕流问题和三维球体绕流的计算研究，并将计算结果与其他途径得到的研究结果诸如DSMC模拟值、N-S解及有关实验数据进行比较分析，创建了一套能有效模拟稀薄流到连续流不同流域气体流动问题简化的统一数值算法研究框架

For the purpose to figure out location and function relations of three-dimensional syphon's unfolded curve with any bend angle, any diameter and any section, and to make integration of design and manufacturing for three dimensional big-diameter syphon, methods of engineering mathematics and analytic geometry are provided. Syphon's unfolded curve function in three-dimensional station is analyzed and built; the corresponding MATLAB procedures are compiled at the same time.

为了解决弯管在弯曲角度、直径、节数等变化时的三维弯管展平曲线的坐标位置以及函数关系问题，以实现大直径弯管的三维设计与制造的自动化、一体化，通过利用工程数学及画法解析几何的方法，分析和建立了弯管在三维状态下的展平曲线方程，同时编写了相应的MATLAB程序。

By using the Clifford matrix expression of n dimensional sense preserving M bius transformations, the trace s and norms of the Clifford matrix and chordal norms are discussed.

利用n维Mobius变换的Cliford矩阵表示，讨论了n维空间的Cliford矩阵的迹和范数以及弦范数，得到了它们在n维空间上一些不等式及它们间的相互关系。

Based on the estimation of the directions of arrival and the Doppler frequencies of the sources, a quaternion model was proposed, which made the estimation of the DOA and the Doppler frequencies similar to that of one-dimensional azimuths so as to avoid direct and indirect pairing with the complex model.

针对阵列信号处理中方向角、多普勒频率的同时估计问题，提出了方向角、多普勒频率的四元数模型，使估计方向角、多普勒频率二维问题与估计一维问题相类似，从而避免了在经典的二维复数模型估计中直接或间接的配对。

Based on a new three-dimensional topology-related grain growth rate equation proposed recently by MacPherson and Srolovitz, a set of analytical quasi-stationary grain size distributions were obtained.

以MacPherson-Srolovitz提出的三维个体晶粒长大拓扑依赖速率方程以及三维晶粒组织的晶粒尺寸--晶粒面数间的抛物线型统计关系为基础，导出了相应的描述三维准稳态晶粒尺寸分布的函数族。

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。