二次的

In this paper, after the introduction of the basic concepts and the main results on K〓 theory, relative K〓 theory and the theory of classical groups of degree 2 which is related to K〓 theory, we study the problems of the computation of K〓 for the ring of integers of quadratic imaginary fields, examples of subrings of quadratic fields which are not universal for GE〓 and generating set of the Cokernel of the canonical homomorphism from K〓 to K〓.

本文在介绍了K〓理论和相对K〓理论以及与K〓理论有关的2阶典型群的基本概念及主要成果之后，对于虚二次域代数整环的K〓群的计算，非GE〓泛的虚二次域的子环以及K〓到K〓的自然同态的余核的生成元集等问题进行了研究。

The book is divided into 14 chapters, including Introduction, continuous control system theory, process and discrete sampling, Z transform, sampled-data systems, discrete approximation of continuous system the equivalent, based on mathematical transform the classical design method, based on state space pole placement design methodology, multi-variable system of quadratic optimal control, quantitative effects, the choice of sampling period, the digital control system modeling, digital control system for a variety of design methods, variables quadratic optimal control systems, sampling cycle of selection, non-linear control of the problem, as well as digital control system, a typical application - Disk drive servo control design.

全书共分14章，内容包括概论、连续控制系统理论、采样过程和离散化、Z变换、采样数据系统、连续系统的近似离散等效、基于数学变换的经典设计方法、基于状态空间的极点配置设计方法、多变量系统的二次型最优控制、量化效应、采样周期的选择、数字控制系统的建模问题、数字控制系统的各种设计方法、变量系统的二次型最优控制、采样周期的选择、非线性控制的有关问题，以及数字控制系统的一个典型应用——磁盘驱动器的伺服控制设计等。

Firstly, we prove that if we select nodes properly, and let the distance between these nodes sufficiently small, cubic polynomial spline can approximate a continuously differentiable function, which with continuous derivatives of second order and discontinuity of the first kind in the derivatives of fourth order, to any desirable accuracy. This result lays a theoretical foundation for representing trajectories by splines and double orthogonal basis.

一是证明了适当选取节点并使节点距充分小时，三次多项式样条可以逼近具有二次连续导数的分段四次连续可微函数到足够的精度，这一结论为用样条和双正交基表示弹道打下了理论基础。

In order to discuss the rationality of various warping displacement modes, second-degree parabola, cubic parabola, fourth-degree parabola and cosine function are selected respectively. It has been demonstrated that these displacement modes have limitation to some extent, and a more reasonable mode needs to be developed.

为了探讨各种剪滞翘曲位移模式的合理性，分别选取二次抛物线、三次抛物线、四次抛物线及余弦函数等翘曲位移模式进行计算；结果表明，这些翘曲位移模式在一定程度上均存在不足，目前还缺乏一种更加合理的位移模式。

Then, a modifiable cubic polynomial curve is presented based on the basis functions, and the relation between the curve and the classical Bézier curves is discussed.

然后，基于该调配函数生成了一类可调控的三次多项式曲线，并讨论了该曲线与二次Bézier曲线及三次Bézier曲线之间的关系。

They are ①cubic plane curve constituted with projective pencil of lines and line eonic

进而证明三个定理：①一次线束和其射影对应的二次线束，所对应直线交点的轨迹为三次平面曲线

Thermal oxidation treatment can increase the surface hardness and elastic modulus significantly and reduce the E /H ratio of the TC4, which indicate the treatment can enhance the wear resistance of TC4 alloy. Long time treatment can increase the thickness of the oxide layer, but the outside layer is apt to desquamate during the scratching. The oxide layer closing to substrate has better bonding properties, but microcrack forms as a result of high stress loading, which lead the layer to flake off completely.

长时间的高温氧化可以增加氧化层的厚度，但在划擦过程中氧化层发生两次脱落，表明氧化层由外表层和次外层组成，外层结合力差，易发生一次脆性剥落，内层与基体的结合强度较高，但在较大载荷作用下会产生微裂纹，导致氧化层的二次剥落。

In general, the design work with traditional measures is done by hand, which cannot meet the needs of the technology and manufacture. So the author has developed a CAD hydraulic design software fit for lower specific speed axial flow runner, which is easily operated by users.The main research work of this paper is as follows:1 Analyzing the main reason of axial flow power station cannot work well under littler volume of flow in some season and putting forward an improving scheme, pointing out the characters of design under abnormal factors.2 Combined with the development of the industry in our country, the abnormal hydraulic design method of propeller turbine is discussed based on present literature, data and experiment results.3 Guided by the design method of software engineering, a suit of hydraulic design software of Lower Specific Speed Axial Flow Runner is programmed by the object-oriented programming language Visual Basic and a straightforward, concise and standard Windows human-computer dialogue interface is designed for the system, which makes the operation of the system very convenient.4 ActiveX Automation technology is adopted as the interface with AutoCAD and the hydraulic drawings are edited, modified by AutoCAD until hydraulic model drawings according with the demand of engineering practice are output.5 To resolve practice problem, the author has designed a lower specific speed axial flow runner for Duowa Power Station through an example.

论文的主要内容有：1 深入分析很多轴流定桨式水电站枯水季节小流量下不能发电的主要原因，提出减容改造方案，并指出超常规条件下的改造设计特点。2 结合国情及行业发展需要，参考现有资料、文献和前人的研究成果，进行低比转速轴流式转轮叶片水力设计方法的研究，对轴流式转轮叶片的奇点分布法水力设计进行了全面的探索，结合现代计算机技术，找到了一种针对特殊条件的轴流式转轮叶片水力设计方法。3 仔细比较多种AutoCAD二次开发工具后，结合本课题的特点，选用Visual Basic语言，综合应用软件工程的设计思想，进行低比转速轴流式转轮叶片水力设计软件的编制，为系统设计了直观、简洁和标准的Windows人机对话界面，便于用户操作；编程时在考虑到设计条件特殊性的同时，尽量做到程序的通用性，使之可用于解决同一类问题；另外，大部分程序还可移植到普通轴流式转轮叶片水力设计中，具有良好的适应性。4 利用ActiveX Automation技术与AutoCAD接口，对AutoCAD进行二次开发，在AutoCAD下实现水力图的自动生成和编辑，直至输出符合实际工程要求的木模图。5 通过算例，为多哇水电站设计了一个低比转速轴流定桨式转轮，解决其在枯水期小流量下不能发电的问题。

But , when we changeour trainofthought , we can find that sometimes using mathematical Analysis is a better solution to the linear algebraic problems.In thispaper, use the propertyofcontinuous function andimproper integralof infinite interval and to solve some matrix and quadratic form problems.Algebraic ideas andmethodstosolvemathematical analysisproblems are indicated by several specific examples. Close contactof differentmathematical analysis fields is shown.

该文探讨运用数学分析的有关知识（如：函数连续性、无穷区间的广义积分）和方法解决高等代数中的某些复杂、繁琐的问题；通过具体的实例，阐述高等代数的思想和方法在解决数学分析问题中的作用，揭示不同的数学领域之间的密切联系，例如：二次型与正交变换是代数学的基本内容，其用途十分广泛，而重积分的计算往往存在技术性的困难，若利用"二次型"与"正交变换"的有关理论去解决某些重积分的计算问题是颇有功效的。

Summary: The concept of matrix and its determinant computing, matrix determinant, matrix sub-block with the elementary transformation, invertible matrix, rank of matrix; vector and its computation, the linear relationship between vector, vector group of rank; linear equations of the nature and structure of linear equations; matrix eigenvalue and eigenvector, similar to matrix and matrix diagonalization conditions, the standard quadratic form with the normal forms, quadratic and symmetric matrix There are qualitative.

内容提要：行列式矩阵的概念及其运算，方阵的行列式，矩阵的分块与初等变换，可逆矩阵，矩阵的秩；向量及其运算，向量间的线性关系，向量组的秩；线性方程组的性质与结构，线性方程组的求解；矩阵的特征值与特征向量，相似矩阵与矩阵可对角化条件，二次型的标准形与规范形，二次型和对称阵的有定性。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。