查询词典 foundation of geometry

The linear system optimum control theory distributes one of parameter systembasic topics,in domains and so on aerospace,national defense,finance,communicationhas the widespread application prospect.simultaneously, because the research tech-nique involves to foundation mathematics theories and so on the functional analysis,analysis situs,geometry, algebra.

线性系统的最优控制理论是分布参数系统的基本课题之一，在航空航天、国防、金融、通讯等领域有着广泛的应用前景。同时，由于研究手法涉及到泛函分析、拓扑学、几何学、代数学等基础数学理论。

Advanced mathematics is one of the most important foundation lessons in each univercity, its content of course includes the calculus,the space analytic geometry and the vector algebra step,etc..

摘 要：高等数学是各大高校最重要的基础课之一，其教学内容包含微积分、空间解析几何与向量代数初步、场论初步等等。

The higher mathematics curriculum is a college engineering course undergraduate course each specialized student's compulsory important basic theory class, through this curriculum study, causes the student to obtain: Circular function calculus study, the space analytic geometry and the vector algebra, the function of many variables calculus study, the infinite series, aspect and so on ordinary differential equation basic concepts, the elementary theory and the fundamental operation skill, and further obtain mathematics knowledge for the study successor curriculum to lay the essential mathematics foundation,During instruction knowledge, must train the student through each teaching link to have the abstract thinking ability, logic reasoning ability, spatial imagination ability gradually and studies independently ability, but also must pay attention specially trains the student to have the quite skilled operational capability and the synthesis utilization studies the knowledge to analyze the question and to solve the question ability.

高等数学课程是高等学校工科本科各专业学生的一门必修的重要基础理论课，通过本课程的学习，使学生获得：一元函数微积分学，空间解析几何与向量代数，多元函数微积分学，无穷级数，常微分方程等方面的基本概念、基本理论和基本运算技能，为学习后继课程和进一步获得数学知识奠定必要的数学基础，在传授知识的同时，要通过各个教学环节逐步培养学生具有抽象思维能力、逻辑推理能力、空间想象能力和自学能力，还要特别注意培养学生具有比较熟练的运算能力和综合运用所学知识去分析问题和解决问题的能力。主要是其中的一些专有名词查不到，比如一元函数等

The interpolate algorithms of three-order NURBS curve and double three-orders NURBS surface are presented. The expressions of partial derivative and normal curvature of NURBS surface are derived by the theory of differential geometry. The geometric characteristics of different curvature area of the free-form surfaces are analyzed in detail. All these work lays a theoretical foundation for constructing the cutter location calculating model of free-form surfaces NC machining. 2 On the basis of analyzing the methods of cutter path generation, the standard of evaluating the various methods of cutter path generation is presented. The method of generating cutter path with constant scallop height is presented for the first time.

本文以提高复杂曲面多坐标数控加工精度和加工效率为目的，在对国内外研究现状进行深入分析的基础上，对数控编程中各环节的关键技术问题进行了深入研究，主要内容包括以下几方面： 1 分析了复杂曲面各种造型方法的优缺点，给出了根据各种边界条件所确定自由曲面的NURBS表示方法以及三次NURBS曲线曲面反算算法；用微分几何理论推导了NURBS曲面的偏导矢及法曲率计算表达式；对曲面不同曲率特性区域的几何特征进行了深入分析，为建立复杂曲面的数控加工刀位计算模型奠定了理论基础。

Its theoretic foundation is integration geometry, random theory of set, topology, modern probability, algebra, theory of set, graph theory, and so on.

其最基本的数学理论基础是积分几何和随机集论，同时还涉及到拓扑学、现代概率论、近代代数、集合论、图论等一系列数学分支。

Main Curriculums: Higher Mathematics, Engineering Mathematics, College Physics, English, Descriptive Geometry and Building Cartography, Program Design and Arithmetic, Introduction to Java, Network Database, Numerical Analysis, Tensor Analysis, Specialty English, Document Retrieval and Utilization, Introduction to Mechanics, Theoretical Mechanics,Mechanics of Materials,Structural Mechanics,Computational Mechanics and Engineering Software, Theory of Plate and Shell, Theory of Elasticity, Composite Mechanics, Advanced Structural Mechanics,Plastic Mechanics of Structural Engineering, Fluid Mechanics, Experimental Mechanics, Vibration Theory, Soil Mechanics and Foundation, Steel Structures, Concrete Structures, Engineering Construction and Engineering Estimate, Engineering Signal Analysis and Processing, CAD of Structure, Design of Structural Optimization, Modern Testing Technologies.

专业课：高等数学、工程数学、普通物理、英语、政治、画法几何及建筑制图、程序设计与算法语言、Java基础、网络数据库、数值分析、张量分析、专业英语、科技文献检索、力学概论、理论力学、材料力学、结构力学、计算力学与工程软件、板壳理论、弹性力学、复合材料力学、高等结构力学、结构工程塑性力学、流体力学、实验力学、振动理论、土力学与地基基础、钢结构、混凝土结构、工程施工与概预算、工程信号分析与处理、结构CAD、结构优化设计、现代测试技术等。

In this dissertation, InGaAs/InGaAsP/InP MQW microdisk laser and its characterization were presented. Some conclusions are as following: the characteristics of lasing threshold was discussed by using rate equation. The dependent relations between threshold and cavity volume, spontaneous emission coupling efficiency β were investigated. The whispering gallery mode and spontaneous emission in a microdisk geometry were then studied. Almost all spontaneous emission was coupled into the lowest order TE mode when the normalized thickness of photonics well was between 0.15 and 0.5. The design principle and device process of InGaAs/InGaAsP/InP MQW microdisk laser were presented. The microdisk lasers with the diameter of 8μm, 4. 5μm and 2μm were succesfully fabricated by using etching techniques. The pulse lasing thresholds for the microdisk with the diameter of 8μm and 4. 5μm were 170μW and 15μW, a record results compared with the published in the literature. The cw lasing threshold for a 2-μm-diameter microdisk was only a few μW. We haven't found similar report up to now. To solve the problem of directional output in a microdisk laser, the power coupling efficiency in a double disk geometry was investigated with the theory of waveguide mode couple. A new structure of electrically pumped microdisk laser with output waveguide was designed, making a foundation for the practical use of microdisk laser.

本文主要研究InGaAs/InGaAsP/InP多量子阱半导体碟型激光器的研制和特性表征，并取得如下结果：利用速率方程理论讨论了激光器激射阈值的特性，分析了阈值与腔体积和自发发射耦合系数β之间的关系；讨论了微碟光子阱结构中的自发发射特性和微碟中WGM模式特性；光子阱结构在其归一化厚度在0.15-0.5之间时，几乎全部自发发射进入到最低阶TE模式中；研究了InGaAs/InGaAsP/InP多量子阱微碟激光器的结构设计原理和器件的制备工艺；利用刻蚀方法成功制备出直径分别为8μm、4.5μm、2μm的碟型微腔激光器；直径8μm和4.5μm的微碟脉冲光泵浦激射阈值分别为170μW、15μW，是目前所见文献报导中比较低的；直径2μm的微碟连续光泵浦激射阈值仅几μW，目前尚未见到达到类似结果的研究报导；为解决微碟激光器激射光定向引出的问题，通过波导耦合模理论分析了双层碟之间功率耦合效率；据此设计了新型带耦合输出波导的电泵浦微腔激光器，为进一步研制可实用的电泵浦微腔激光器打下基础。

CoCreate Modeling 2008 builds on that foundation and adds new capabilities to improve the cross-sectional design of components with rotational geometry, such as spindles.

这些新功能可减少针对旋转几何物件许多重复的定义步骤，而只需要简单的动作就可以完成，如此一来您可以更快地设计出更好的产品。

A cusp catastrophe model is presented to describe the behavior of sliding along one deep incompetent structural plane of a gravity dam foundation, and the sufficient conditions leading to instability are discussed. It is found that the instability of sliding relies mainly on the stiffness ratio k, the homogeneity index of the medium m and the geometry-mechanic parameter ξ and that the reliability of the traditional limit analysis method is deficient.

通过建立的模型分析，发现坝基滑动失稳主要取决于软弱面上复杂弹脆性介质和应变软化介质在应变软化拐点处的刚度比k、材料的均匀性指标m及几何－力学参数ξ；并给出了发生突变失稳的充分力学判据，指出传统的刚体极限平衡分析法存在一定的缺陷。

Later, Riemann generalized Gauss's theory on surfaces to higher dimensional spaces (called "manifolds") and established Riemannian geometry which constitutes the foundation of Einstein's General Relativity theory.

Riemann将Gauss的理论推广到高维空间而创立了Riemann几何并为Einstein的广义相对论奠定了基础。

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。