几何基础

As an important algebraic subject, rings are the base on Algebraic Geometry and Algebraic Number Theory.

环作为一门重要的代数学科是代数几何和代数数论的基础，有许多其它相关学科领域都涉及到环。

Basic Mathematics has undergone an amazing evolution and born fruit on fields such as algebra, functional analysis, dynamic system, algebraic number theory and differential geometry.

基础数学的研究经过多年工作积累，在代数学、泛函分析、动力系统，代数数论，微分几何等领域在国内外有一定影响。

Based on the theory, the differential geometry of statistical model proposed by Amari is generalized from probability space to Sugeno measure space, and a new notion of fuzzy manifold based on Sugeno measure is proposed, including the fundamental differential-geometrical structures of statistical models, the tangent space, and the Riemannian metric in a fuzzy manifold.

第四章介绍了Sugeno测度空间上随机变量的数字特征，在此基础上将学者Amari提出的统计流形从概率测度空间推广到Sugeno测度空间，提出了一种基于Sugeno测度的模糊流形分析方法，包括Sugeno模糊模型的基本微分几何结构，模糊流形中的切空间、黎曼度量。

By changing the value of the blade thickness, cone angle, lead and height of fillet weld, influences of these parameters on the strength and displacement of the screw conveyor are investigated which form the base for optimization of the conveyor structure.

论文还通过调整螺旋输送器的叶片壁厚、半锥角、导程和焊角高等几何结构参数，研究了各参数的变化对螺旋输送器强度和变形的影响，为结构优化设计奠定了基础。

On the basis of OCM, segmentation based on curvature radium is presented in the paper, in which curvature radium is calculated using parametric-surface fitting, and detecting edge points is realized from orthogonal direction, which ensure the integrality of edge points. Since the data is organized by cross-line in OCM, a new arithmetic, Double-direction Angle Difference arithmetic, is brought forward, which can pick up edge points more quickly.

物体的表面一般由多个曲面相交组成，要建立完整的几何模型，需要对测量数据进行区域分割——区分不同曲面的数据，现有的区域分割大多是对单视图的图像式测量数据进行的，但完整的CAD模型需要联合多个视图产生，本文在上面提出的三维正交模型的基础上，提出了三种区域分割方法：第一种方法是基于曲率半径的数据分区方法，通过二次参数曲面拟合计算局部曲率半径，从正交的多个方向进行检测，保证了边点提取的完整性。

First the math theory of machining simulation is studied, and the set structure of NC machining simulation system whose components, including time, input, output and so on, are defined. Hereby we set up the hierarchy structure, the logical structure, the static model and the dynamic model of simulation system. The construction method of sweep entity of cutter and rotation parts is researched, and their differential geometry invariants are calculated. NC code is unscrambled, and the recursion division arithmetic of time segment is put forward, which is the driven data of the movement or rotation parts. The CLDATA should be interference-free. To examine if there is interference between cutter flank and the work piece, an arithmetic that discussed the existence of intersecting curve between them is put forward. To examine if there is interference between two turrets, an arithmetic that discussed the existence of intersection set between two polygons is put forward.

首先研究加工过程仿真的数学基础，然后定义数控加工仿真系统的集合结构及时间集、输入集、输出集等概念，建立加工仿真的层次结构和逻辑结构，阐述双刀车削仿真系统的静态模型和动态模型建立方法，分析刀具扫描体和旋转部件扫描体的建立方法及其微分几何性质；研究NC代码解读技术和双刀加工时间段递归子分划技术，为驱动各仿真单元作数据准备；通过讨论后刀面和工件表面交线的存在性判断刀具后刀面与工件间是否干涉，通过求多边形的交集判断刀架与刀架是否干涉。

The two fractal parameters (amplitude B and fractal dimension D) in the new model represent the roughness of primary and higher order asperities of stationary profiles, respectively.

接着在节理表面形状的精确测定基础上，根据分形理论的变量图法，建立了描述岩石节理表面几何形状的新的分形模型。

First, based on all that have been mentioned above, the geometric constant D, which was introduced to characterize the quantitative difference between Birkhoff orthogonality and isosceles orthogonality, is studied further. Moreover, attainability as well as continuity and monotony of D in two-dimensional sequence spaces are presented.

基于上述原因，本文首先在已有结论的基础上，对用以刻画等腰正交和Birkhoff正交性之间量化差异的几何常数D进行了进一步的研究，解决了D的可达性，二维序列空间中D的连续性与单调性等问题。

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。

Recently, we defined the uniruledness of symplectic manifolds and proved that symplectic uniruledness is invariant under symplectic birational

最近，我们给出了Uniruled辛流形的定义并证明了其在辛双有理变换下的不变性，为今后进一步从事辛双有理几何的研究打下了基础。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。