查询词典 analytic function

The process of our study links some of the most basic questions about C〓 with beautiful classical results from analyticfunction theory. For instance, it is essential Littlewood subordination theorem that assures that composition operators act boundedly on many analytic function spaces. And there are close connections between the compactness of C〓 and the existence of angular derivatives of ψ at points of 〓D. It involves the classical Julia-Careatheodory theorem, Denjoy-Wolff theorem and Nevanlinna counting functions and so on. It makes many old theorems in analytic-function theory getting some new meanings, and bestows upon functional analysis an interesting class of linear operators. This thesis consists of six chapters as follows: Chapter 1 is a preparatory in nature.

从而建立了C〓的算子性质与解析函数论中许多漂亮的经典结果之间的联系，如许多解析函数空间上复合算子的有界性本质上往往是著名的Littlewood从属原理，复合算子的紧性与其诱导映射在边界〓D上的角导数之间有着紧密的联系等等，这样自然而然地涉及到经典函数论中的Julia-Caratheodory定理，Denjoy-Wolff定理及Nevanlinna计数函数等等一些结果，并以此赋予函数论中许多古老问题以新意，同时也为泛函分析提供了一类十分具体的线性算子。

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。

The linear function applicable scope is broad, when the reservoir turnover water volume and the time, the student leaves the staircase mouth population and the time and the time and the motion communication speech spends the comparison and so on the relational question has the important application;The study linear function, may deepen in the life the linear question understanding and the understanding, is helpful in solves some simple function problem; The linear function some problem solving method has the universality in mathematics, the linear function related theory may use for to solve some other mathematics problem, For instance the dual linear equation group, a Yuan inequality, a Yuan quadratic equation most value question and some complex mathematics question, the light is studies the linear function the theory is insufficient, the key is can utilize actual the linear function goes is our final goal.

一次函数的适用范围广，在蓄水池的进出水量与时间、学生出楼梯口人数与时间与时间和移动通讯的话费比较等的关系问题时均有重要的应用；学习一次函数，可以加深生活中线性问题的认识与理解，有助于解决一些简单的函数问题；一次函数的一些解题方法在数学中具有普遍性，一次函数的有关理论可以用来解决一些其它的数学问题，比如二元一次方程组、一元一次不等式、一元二次方程的最值问题及一些复杂的数学问题，光是学习一次函数的理论是不够的，关键是能把一次函数运用到实际中去才是我们最终的目的。

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。

The results indicated that the weight determined by analytic hierarchy process was in accord with the actual needs; fuzzy evaluation could easily make quantative comprehensive results; f-function values estimated on the basis of analytic hierarchy process and fuzzy transformation were convenient for giving the quality order of different unblended cigarette samples.

结果表明：层次分析法确定各单项指标的权重符合实际的评吸要求，模糊综合评价容易给出定量的综合评价结果，在此基础上计算f函数值便于对不同的单料烟样品进行排序。

The information integrated pattern based on PDM/PLM in the course ofmanufacture is put forward. Under the constraints of building CAPP platform, thearchitecture of CAPP platform is established. The models of decision making andfunction for process planning are given. Then the development means of CAPP basedSmarTeam are extracted.3. The structure of modular product life cycle is established. Toward the divisionand planning of the General Modules oriented product family, theCAD/CAPP integrated model of flexible module based on feature and CAD/CAPPmapping model based on process planning match board are set up. The keytechnologies of Solidworks/SmarTeam/CAPP integration are studies.4. From the point of view of process match board and step match board, theprocess of creating to process planning match board is studied. As an example, themachining process planning of up beam of hydraulic press machines is used tointroduce the establishment of process planning match board by means of inferencebased on expert knowledge. The organize model about the process planning matchboard oriented product family is brought forward.5. The multi-decision methods of CAPP system based on analytic hierarchy aregiven.. On the basis of uniform data model, the sub-machining process planning ofpart is auto-created by means of analytic hierarchy, The step decision methods basedon AHP is put forward.6. For the design/manufacture information in the course of product life cycle, thetree structure based on Object-Oriented and static model based UML are founded. Themethod of establishing design/manufacture information management system isbrought forward. The commercial PLM software—SmarTeam is regarded asdevelopment platform, on basis of which, the design/manufacture informationmanagement system is built, and the multi-view mapping technique ofdesign/manufacture information model is studies.7. A computer-aided CAPP platform based on PDM/PLM is founded, and itsstructure, function, work flow is illustrated. Some example of the system areintroduced.

阐述课题提出的目的和意义，明确了本文研究的主要内容。2、提出基于PDM/PLM的制造过程信息化集成模式；在平台式CAPP系统的设计约束模型基础上，构建了平台式CAPP系统的体系结构；并给出工艺决策模型和功能模型；最后提出基于SmarTeam的CAPP开发模式和实现策略。3、建立模块化产品生命周期模型的组织结构；针对面向产品族的广义模块的划分和规划方法，建立基于特征的柔性模块CAD/CAPP集成模型及基于工艺模板的CAD/CAPP映射模型；研究Solidworks/SmarTeam/CAPP集成的关键技术。4、从工序模板和工步模板的角度研究了工艺模板的创建过程；以液压机上梁模块机加工为例，采用基于专家知识的推理技术实现了工艺模板的创成；提出了面向产品族的工艺模板分层结构树的组织模式。5、提出基于分层规划的多模式工艺决策流程；在统一数据模型的基础上，从特征层和零件层分层规划，实现了零件加工子工艺的自动创成；提出基于AHP的工步排序决策方法。6、针对产品生命周期中的设计/制造信息，建立了面向对象的类树结构和基于UML的静态结构模型；提出基于PDM/PLM软件的设计/制造信息管理系统的构建方法；以商品化PLM软件SmarTeam作为开发平台，开发了基于SmarTeam的设计/制造信息管理原型系统；研究设计/制造信息模型多视图映射机制。7、开发了基于PDM/PLM的平台式CAPP原型系统，构建了系统的功能模型，并对系统的主要功能进行说明，给出系统的运行实例。

Also, if a complex analytic function is defined in an open ball around a point x 0, its power series expansion at x 0 is convergent in the whole ball. This is not true in general for real analytic functions.

复解析函数则不同：凡复解析函数必为全纯函数（即复可导，以实变量表示则是满足柯西-黎曼方程），反之亦然，因此全纯函数与解析函数在复分析中是同一类对象。

Textbook is not only the primary basis for students to grasp knowledge and method but also resort and carrier to train capability. New textbook has been tested in some provinces and cities since 1997, some educational and teaching concepts in new textbook inosculates with new mathematics course which is being tested now, it has taken great role for the transition of teachers' teaching idea and students' learning way. This paper will analyze Plane Analytic Geometry high school textbook of 2004 edition which is published by People's Education Publishing House in some aspects such as content structure, educational function, psychological characteristic according with student cognizance and teaching through the method of content analysis, investigation, comparison and statistical analysis . The paper's purpose is to excavate the potential value of the textbook and understand educational idea and concept of new textbook so that students can grasp more basic thought of analytic geometry in teaching and can learn studying and discovering and solving problem ,at the same time it builds a kind of independent, disquisitive, cooperative and lifelong learning pattern.

教材既是学生掌握知识和方法的主要依据，又是培养学生能力的凭借和载体，自1997年新教材在部分省市实验以来，新教材中所体现的一些教育教学理念与现在正在实验的高中数学新课程相吻合，对教师的教学观念和学生的学习方式的转变都起到了很大的作用，本文将对人民教育出版社2004版普通高中教材中的平面解析几何部分通过内容分析法、调查研究、比较研究、统计分析等研究方法从教材的内容结构、教育功能、符合学生认知心理特点、教学等几个方面进行分析，目的是挖掘教材内容的潜在价值，真正领会新教材所蕴涵的教育思想和理念，以使教师在教学中能够让学生更多的掌握解析几何的基本思想，以培养学生学会学习、学会发现问题和解决问题，为学生构建一种自主的、探究的、合作的、终身的学习模式。

Fostering the concept of multi-culture firmly and mastering the development of advanced culture correctly are conductive to resisting terrorism, separatism of nationalities and ultraism of religion, which is of great academic theoretical, immediate and profound historical si...

牢固树立多元文化的理念和正确把握先进文化的发展方向，有助于在世界范围内自觉地抵制恐怖主义，民族分裂主义和宗教极端主义。不仅具有重大的学术理论意义，而且也具有重大的现实意义和深远的历史意义。

But if anyone walks in the night, he stumbles, because the light is not in him.

11：10 若在黑夜行走，就必碰跌，因为那光不在他里面。