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In curve and surface modeling, Bernstein polynomial compositions are widely used for various geometric operations. So it is important to investigate them both in theory and practice.

在曲线曲面造型中，Bernstein多项式复合被广泛用于许多几何操作，因而具有重要的理论和实际意义。

With respect to phonetics, Distinctive Features for the phonetic syncopation of spatial information are extracted based on Bertin's retinal variables. The importance of geographic reality, cognitive laws and geometric laws in the syncopation is pointed out following the thorough inspection of the physical characteristics of spatial information and a phonetic hierarchy of phoneme、 phoneme combination is proposed after the summarization of different methods of syncopation in Psychology, Pattern Recognition, Mathematic Morphology and Cartography, which provides linguistic interpretation for cartographic symbol design and understanding. With respect to the property that map symbol is represented as the combination of attribute and geometry in digital form of spatial information, suprasegmental phoneme as unit is proposed which deals with the high level phonetic units and their structure with the bend of curve and the simple area of complex area as primitive.

在语音结构方面，基于Bertin的视觉变量，提取了产生空间信息语音切分的区别特征；对空间信息的物理特征进行了详尽分析，指出了地理真实、认知规律和几何规律在语音切分中的重要作用；在总结心理学、模式识别、数学形态学和地图学等相关切分理论的基础上，提出了空间信息音位系统以及音位组合规律，为地图符号设计与理解提供了语言学解释；针对地图符号通常在空间信息中表现为属性和形态相结合的特点，提出在超音段音位层次上重点关注以线切分单元——弯曲和复杂面切分单元——弯曲构成的简单面为基本元素的语音高级层次及其结构。

Inspired by the wavelets,we introduce the concept of geometric wavelets.We transform the compression into a best uniform approximation which is familiar to us in mathematic,we approximate the signal with polynomials.

受小波方法的启发，我们引入了几何小波的概念，将压缩问题转化为逼近理论中熟知的最佳一致逼近问题。

The bifurcation theory on dynamic systems is introduced to the study of the basic geometric properties of redundant robots.

在冗余度机器人机构综合方面，首次提出了根据杆参数的分叉特征，设计工作空间内部无不可避奇异的机器人杆参数的新方法。

Ringel realized positive parts of semisimple Lie algebras in the framework of Ringel-Hall algebras. The main result of this thesis is to build a geometric and topological model over triangulated categories such as derived categories and stable module categories of repetitive algebras. We defines a Lie bracket by Euler characteristics of constructible subsets and thus realizes infinite dimensional Lie algebras of various types with non-degenerated bilinear form.

本文的主要结果是在导出范畴和重复代数的稳定模范畴等三角范畴水平上建立相应的几何-拓扑模型，并利用相应可构集的欧拉示性数定义了一个Hall代数的交换子乘法，从而在三角范畴水平上实现了一大类无限维李代数的整体构造，并且这类李代数本质上都具有非退化的不变双线性型。

NMath Stats contains a data table class with functions for computing descriptive statistics, such as mean, variance, standard deviation, percentile, median, quartiles, geometric mean, harmonic mean, RMS, kurtosis, skewness, and many more; PDF, CDF, inverse CDF, and random variable moments for a variety of probability distributions, including normal, Poisson, chi-square, gamma, beta, Student's t, F, binomial, and negative binomial; Combinatorial functions, such as factorial, log factorial, binomial coefficient, and log binomial; Multiple linear regression; Basic hypothesis tests, such as z-test, t-test, and F-test, with calculation of p-values, critical values, and confidence intervals; One-way and two-way analysis of variance and analysis of variance with repeated measures; Multivariate statistical analyses, including principal component analysis and hierarchical cluster analysis.

nmath统计包含一个数据表的阶层与职能计算描述性统计，如平均，方差，标准差，百分位，中位数， 25 ％，几何平均数，调和的意思是，有效值，峭度，偏度，还有更多的； PDF格式，民防部队，逆民防部队，并随机变量矩的各种概率分布，包括正常，泊松，卡方检定，伽玛，测试版，学生的吨，男，二项式，并负二项分布；组合的功能，例如阶乘，日志阶乘，二项式系数，并登入二项式；多元线性回归；基本假设测试，如的Z测试， t检验， F检验，计算p值，临界值，和置信区间；之一，双向和双方法方差分析和方差分析与反复的措施；多元统计分析，包括主成分分析和聚类分析。

In this paper,singularity is used to study the classification of singularities of the binormal curves and focal surfaces of a spacelike in Minkowski 3-space,and also establish the relationships between singularities of these and geometric invariants of curves under the action of Lorentzian group.

应用奇点理论方法对三维Minkowski空间内由空间型曲线生成的副法线标型和可展焦曲面的奇点进行了分类，并且研究了在Lorenzian群作用下的空间型曲线的几何学不变量同这些奇点之间的关系。

To construct a wall is to bisect a space into 0 and 1, however0 and 1. I like to create an in-between-space, therefore myvery simple but looks complex due to its geometric form.

建造一堵墙犹如把空间分成0和1，然而空间本质上在0与1之间是存在着许多灰色阶层的，我想要创造出属于中间层的空间，因此我的作品都是很基本的（我有一个项目，原理很简单但看起来很复杂，原因在于其几何构成）。

Geometric parameters such as bond length, bond angle and molecular volume were carefully investigated, as most of the acyclic alkanes under study are not yet synthesized.

研究还测定了它们的几何参数，如键长，键角，分子体积等，它们中的绝大多数分子目前还没有被合成。

This method will spilt the polygon and we can use this property to proceed Boolean operation of geometric polygon.

本论文中所使用的计算几何理论为二元空间分割法，此方法会对本身多边形进行分割，我们可以利用这个特性去进行几何图形的布林运算。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。