几何结构

Linear Algebra is mainly a subject which studies the linear structure of finite dimensional linear space and its linear transformation while linear concept is in itself from the old Euclid Geometry. The concept of "Linear Space" is a kind of algebraic abstract. In many fields of modern engineering project and technology, because of the influence of computer and graph showing, the algebraic disposal of geometric questions, the visual disposal of algebraic questions, algebra and geometry are tightly combined.

线性代数主要是研究有限维线性空间及其线性变换这一代数结构的学科，而线性概念究其根源则是来自古老的Euclid几何，线性空间概念是几何空间的一种代数抽象，在现代工程技术的许多领域里，由于计算机及图形显示的强大威力，几何问题的代数化处理，代数问题的可视化处理，把代数与几何更加紧密地结合在一起。

With respect to syntax, the roles of tagmeme in the structure of word and sentence and Chomsky's Generative-Transformational Grammar are discussed. The spatial relation theory and existing research achievements are investigated. Having noticed the shortage of the capability of topological and metrical relation in the description of spatial information structure, the author proposes Combinational Qualitative Geometry based on the two invariables under ordinary transformations, distance ratio and direction difference, the CQG-based spatial relation system between topological and metrical constraint is thus constructed, on which several spatial relations such as parallel, perpendicularity, co-linearity, sequence and direct neighborhood are derived. Based on extended theory of spatial relation, the language anamorphosis is analyzed from the aspects of phonetics, semantics and syntax. The mere geometric and formalized spatial relation is then integrated with concrete geographic ontology to accommodate richer and indicative spatial configuration of spatial information in the different geographic context. Finally a syntax framework for spatial information is put forward.

在语法结构方面，首先阐述了法位和法素在语法结构词法和句法中的地位和作用，以及Chomsky生成转换语法的核心内容；详细介绍了地理信息系统空间关系理论及现有的研究成果；在分析现有的拓扑关系和量度关系对空间信息结构描述能力不足的基础上，提出了基于长度比和角度差两个不变量的组合定性几何，以此建立了介于拓扑及量度约束之间的组合定性关系体系，并以此为基础派生出平行、垂直、共线、次序、直接邻近等空间关系描述；本文基于扩展的空间关系理论，详细讨论了空间关系在语音、语法和语义三个方面的语言变体，将纯几何和纯形式化的空间关系与具体的地理本体结合起来，可以获得更为丰富的、更能反映空间关系在不同语言上下文中具体体现的组合关系；最后给出了一个空间信息的语法结构的基本框架。

It provided a correct and reasonable mathematical model for the analysis of the ultimate bearing capacity and crankle stability of the thin-walled structure.

论文在比较了两种运动描述方法（完全拉格朗日法和更新拉格朗日法）异同点并分析了非线性几何关系及大变形下的弹性物理关系的基础上，基于增量虚功原理推导了几何非线性空间梁元单元切线刚度矩阵，采取分模块形式，分别表示了轴力、弯矩、双力矩对几何矩阵的贡献；通过球面显式荷载增量迭代式弧长法求解方法编制程序，很好地实现了几何非线性增量荷载的自动步长选择及全过程跟踪，为薄壁杆系结构的极限承载力分析和弯扭失稳分析，提供了较为精确合理的分析力学模型。

The variable geometry truss mechanisms have been studied extensively and systematically by this project. The research plan has been completed all sidedly, and expected results have been obtained. Three new kinds of combination decahedrons and a new class of variable geometry truss mechanism, which is composed of an octahedron and three tetrahedrons connected in parallel form, are proposed. The position analyses for decahedrons, dodecahedrons, triple-octahedrons, combinations decahedron and a new type of structure of variable geometry truss mechanisms are presented by introducing additional extra linear displacement sensors and using resultant elimination and homotopy continuation algorithms. The method of kinematical analysis of variable geometry truss mechanisms is established.

课题组对变几何桁架机构进行了深入的研究，全面地完成了研究计划，取得了预期的成果；提出了三种新的十面体组合机构以及由一个八面体和三个四面体组成的新型变几何桁架机构的结构形式；应用结式消元、附加传感器和同伦方法等提出了十面体、十二面体、三重八面体、组合十面体和新型变几何桁架机构的位置分析方法；建立了变几何桁架机构运动分析的一般方法；建立了简洁的凯恩和拉格伦日动力学的模型；应用有限元和子结构方法，提出了变几何柞架机构弹性动力学模型，导出了逆动力学方程的显式形式；设计和研制了一台可折叠的八面体变几何杵架机构装置等。

Then we re-sampling all signals defined on the surface of the original triangle mesh at the vertices of the spherical subdivision mesh and get a set of discrete geometry signals with subdivision topology which can be compressed by using spherical wavelet.

于是，在参数域内位于细分网格顶点处对定义在参数网格表面上的各种几何信号进行重采样，可得到新的具有细分结构的几何信号近似表示原始几何信号，以此满足球面细分小波对处理对象的细分结构要求，从而使得用球面细分小波对几何信号进行压缩得以实现。

The vector has the rich actual background and the widespread application function, it has the algebra and the geometry dual statuses, causes the algebra geometrization, the geometry algebra, has communicated the algebra, the geometry and the trigonometric function, has the good analysis method and the complete structure.

向量具有丰富的实际背景和广泛的应用功能，它具有代数和几何双重身份，使代数几何化、几何代数化，沟通了代数、几何与三角函数，具有良好的分析方法和完整的结构。

Based on the relationship between the structure and function, a lot of research have been performed on predicting base-pair which is indispensable to the RNA three-dimensional strcutrue. The tools and methods in Combinatorics and Statistics will play important roles in studying linear sequences of biomolocular units . Similarly, we can present the geometric representation of biological sequences and structures. So the genometric topology and group theory are important also.

根据RNA的结构与功能的关系，在预测碱基配对的类型方面进行了相当多的研究，这也是确定RNA三维构象的必不可少的一部分，组合学和统计学的工具和方法在研究生物序列和生物结构上起到了很大的作用，同样我们可以用几何方法来表示生物序列和二级结构，几何拓扑和群论也起到了很大的作用。

Although this structure is comparatively complex, it still can be divided into sub-strctures to study. This paper puts forward for the first time the loop geometric model of MBWK fabric reinforced composite. And based on this research, the total structural model for the MBWK fabric reinforced composite was also derived subsequently. In addition, the Non-Uniform Rational B-Spline Curve NURBS for abbriv.

我们经过合理分解复合材料的内部结构，对实际结构作了必要的简化之后，得到了可以进行几何和力学分析的结构单元，也就是说，线圈结构可以用数学方法描述，所以本论文第一次提出了MBWK织物增强复合材料线圈结构的几何模型并分析了这种复合材料整体的结构形态特点。

Researchment on Cable Dome begin with the Concept Design, which including geometric stability, ratio of rise to span, space between struts, height of struts, space between strop, inclination between ridge cable, etc.

对索穹顶结构设计技术的研究首先从概念设计开始，概念设计包括结构的几何稳定性判断、跨度和矢高的关系、压杆的间距、压杆的高度、环索的间距、脊索间夹角等，后面几个部分其实也可以归结为结构几何参数的优化问题。

Basic symbols;Coatings;Definition;Definitions;Dimensions;Drawing specifications;Drawings;Engineering drawings;Finishes;Geometric;Geometrical product specification;GPS;Graphic representation;Graphic symbols;Inscriptions in a drawing;Letterings;Machining;Machining tolerances;Marks;Product specifications;Production processes;Products documentation;Ratings;Reference length;Reference lines;Representation of characters;Roughness;Roughness value;Specification;Statement;Surface properties;Surface roughness;Surface texture;Surface treatment;Surface-roughness measurement;Surfaces;Symbols;Technical drawing;Treatment;Wear-quantity

中文标题产品几何量技术规范。技术产品文件中表面结构的表示方式中文主题词图形表示；参考长度；尺寸；加工公差；表面性质；产品规范；覆层；制图规范；精整；表面粗糙度；粗糙度；表面粗糙度测定；表面结构；磨损量；图纸标题；表面处理；技术制图；几何的；基准线；图形符号；符号；标记；加工工艺；文字书写；产品文件；定义；表面；粗糙度值；工程图；额定值；产品几何量技术规范；GPS；叙述；处理；图纸；机械加工；字符表示；基础符号；规范验收

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。