查询词典 quadratic function

This article mainly discussed between the quadratic function and Yuan two inequalities, a Yuan quadratic equation relation and the application.

本文主要谈了二次函数与一元二次不等式、一元二次方程之间的联系及其应用。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational, basic, differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式，给出了这几个不等式的一些应用实例，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational ,basic , differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality and Minkowski inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式和闵可夫斯基不等式以及这几个不等式的应用，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

Chapter one is "Introduction". On the basis of summarizing the history of the study of the pictophonetic characters, we suppose some theoretical principle, such as the principle of the correspondence between the form and the meaning of the individual graph of Chinese characters, the principle of the total graphs of Chinese characters being a character-formation system, and the principle of the optimum development of the character -formation system in the history, and som analytic methods, such as the methods of structrue-function analysis, form-position analysis and meaning factor analysis, in the study of the pictophonetic characters. Chapter two is titled"General knwledge of the pictophonetic character." We discuss their origins, nature and some standards of distingnishing them, introduce the knowledge about the editions of SHUO WEN JIE ZI, analyse the functions of the modules of pictophonetic characters in detail, discuss concretely the function of phonetic graphs showing origins and pronunciations, the function of meaning graphs showing meanings and analogies, and the function of distinguishment when the two kinds of graphs are conbined. Chapter three is"The system of meaning graphs of Xiao Zhuan system."After we describe the structure of the meaning graph system, the relations between meaning graphs, the distributions of the function of meaning graphs showing meanings, and the frequency of all this kind of graphs, we get a table of all meaning graphs, a table of the frequency. Chapter four is"The system of phonetic graphs of Xiao Zhuan system."We describe the structure of the phonetic graph system, the relations between phonetic graphs, and between their function showing origins and their function showing pronunciations, and their frequency, then we get ageneral table of phonetic graphs and table of their frequency. Chapter five is "conclusion". We think that systematical methodology is useful in describing and analysing the formation system of Chinese characters. The methodology is adaptable in describing the formation system of modern Chinese characters as well as the historical character systems, adaptable in describing horizontally as well as comparing vertically. Only when we finish the systematical vertical compare on the base of systematical horizontal decription, could we know the true history of the system of Chinese characters, recover the rule of the system's development, and supply the theoretical supports for the scientifical arrangement of modern Chinese characters.

第一部分—绪论，在总结形声字研究历史状况的基础上，提出了研究形声系统的理论原则和分析方法，即汉字个体字符形义统一的思想，汉字字符集合构形系统的思想，汉字构形系统历史演变系统优化的思想等三项理论原则和结构功能分析法，形位分析法，义素分析法等三种分析方法，还扼要地介绍了具体的工作程序和论文的主要内容；第二部分—形声字概述，论述了形声字的来源、性质和鉴别标准，介绍了对《说文解字》正篆形声字说解中的传抄讹误，版本异文，说解错误校勘和考证的经过，详细分析了形声字构件的功能，具体讨论了声符的示源功能与示音功能，义符的示意功能与类化功能以及声符与义符组合中的相互区别功能；第三部分—小篆字系的义符系统，从义符系统的构成、义符间的相互关系，义符示意功能的分布及义符的构字频度等不同侧面，对义符系统进行了全面的描写，产生了义符总表、义符间意义关系总表和义符构字频度总表；第四部分—小篆字系形声字的声符系统，从声符系统的构成、声符间的相互关系，声符的示源功能与示音功能的关系以及声符的构字频度等不同侧面，对声符系统进行了全面描写，产生了声符总表和声符构字频度总表；第五部分—结束语，在全面测查小篆字系形声字的基础上，对研究汉字的方法和现代汉字发展方向的问题提出了一些看法，认为系统论的方法是描写和分析汉字构形系统行之有效的方法，系统论方法，不仅适用于历史上文字系统的描写，也适用于现代汉字构形系统的描写，不仅适用了断代描写，也适用于历史比较，只有在对汉字断代系统描写的基础上进行系统的历史比较，才能认清汉字系统历史演变的真相，揭示汉字系统发展的客观规律，为科学地整理现代汉字提供理论上的依据。

On the basis of extending the concepts of the derived function, primitive function and integration of interval-valued function to complex interval-valued function and using the descomposition theorem of complex fuzzy set, the derived function, primitive function and integration of complex fuzzy set-valued function and some properties of them are proved.

2在国际上最先引入了复模糊集合与复模糊数的基本概念，证明了它们的基本代数运算的封闭性，并且其运算可通过α水平复集合的相应运算来进行

The total of these two sorts of functions is called S-functions The indicial function, sinusoidal function, cosinusoidal function, hyperbolic sinusoidal function, hyperbolic cosinusoidal function, trigonometric function of n-order and hyperbolic function of n-order etch are all belong to S-functions.

指数函数、正弦函数、余弦函数、双曲正弦、双曲余弦、n阶三角函数和n阶双曲函数等。都是S－函数的特殊形式。文中证明了关于S－函数及其各阶导数的性质的三个定理。

Driver system for the stability of nonlinear and non-use of the theory of linear quadratic control law studies, select the ball location, speed and rod angle, angular velocity of the four variables as state variables, output variables for the ball position and bar angle, the establishment of linear state space equation and after the designs of clubs based on LQR control law, the design process simple and easy to realize the control law, simulation results show that the linear quadratic regulator robustness and stability.

球杆系统翻译，求高人针对球杆系统的非线性和不稳定性运用最优二次型理论进行控制律的研究，选取小球位置、速度和横杆角度、角速度四个变量为状态变量，输出变量为小球的位置和横杆的角度，建立状态空间方程并进行线性化后设计了基于LQR的球杆系统控制律，设计过程简单，控制律的实现容易，仿真结果表明了最优二次型调节器的鲁棒性和稳定性。

Applying LMI technique, quadratic stability theory, and H〓 control theory, three methods of robust stability analysis and robust controller design for uncertain fuzzy systems are proposed respectively. Among them, LMI based technique can analyze the uncertainties raised in the premises and in the consequent of fuzzy systems. The resulting stabilizing state feedback controllers have maximum stability margins for both kinds of uncertainties. Quadratic stability theory based approach can apply LMI technique and other methods to design fuzzy controllers. H〓 control theory based design can get H〓 controller with constant disturbance attenuation for each local subsystem. Using the given stability criterion of generalized systems, the robust stability of fuzzy systems can be checked.

其中，基于LMI的方法可分析由模糊系统的前件或后件引起的不确定性，得到的稳定的状态反馈控制器对这两类不确定性具有最大的稳定裕度；基于二次稳定理论的方法可应用LMI技术和其它方法设计模糊控制器；基于H〓控制理论的方法可得到各局部子系统具一定干扰抑制性能的鲁棒H〓控制器，而全局系统的鲁棒稳定性可应用所给出的稳定条件进行检验。

In this paper, three robust estimators: robust best invariant quadratic unbiased estimator, robust minimum norm quadratic unbiased estimator and robust Helmert estimator have been designed. Finally, this paper states that these three classical estimators are particular cases of the RBIQUE.

导出了稳健最优不变二次无偏估计、稳健最小范数二次无偏估计、稳健Helmert估计，并说明了最优不变二次无偏估计、最小范数二次无偏估计以及Helmert估计等均是稳健最优不变二次无偏估计的特例。

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。

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

在侵犯著作权案件中，如果被控侵权行为人虽未经著作权人的同意，使用甚至抄袭了受著作权保护的作品或作品的片段，但若情节轻微，未对该作品的正常使用产生任何实质不利的影响，亦未对权利人的权利造成实质性的损害，则应适用&不计琐细原则&，免除行为人的责任，以寻求在权利人利益与著作权法所体现的社会公共利益之间的平衡。

This new product will become our best seller.

这个新产品会成为我们最畅销的产品。