查询词典 generalized almost periodic function

In the third chapter,we prove two general symmetric identities involving the generalized degenerate Bernoulli polynomials and sums of generalized falling factorials by applying their generating functions,these results extend some known identities,and give an relationship of the generalized degenerate Bernoulli polynomials.

第三章，利用广义退化的Bernoulli多项式以及广义阶乘求和的生成函数，证明了两个对称恒等式，推广了一些已知的结论，并得到广义退化的Bernoulli多项式的一个闭形式。

For the one-dimensional p-Laplacian with indefinite weights, four sequences of periodic and anti-periodic eigenvalues are given by introducing the rotation number function, and these eigenvalues are the endpoints of the preimage intervals of the rotation number function at nonnegative integers.

本文以带变号权函数和带变号势函数的一维p-Laplacian为基本模型，系统地阐述了特征值的旋转数方法、带正权Dirichlet特征值的最佳估计、特征值在正则和奇异渐近半线性方程的可解性中的应用、Fucik谱的旋转数方法以及Fucik谱在周期解的扭转性和多解性中的应用。

Through the Radon transformation of the normally ordered Wigner operator we introduce two mutually conjugate intermediate coordinate- momentum representations. Based on them we construct the appropriate quantum phase space theory which includes the new Wigner operator adapting to this space and construct the appropriate generalized Fredholm operator equation and then find its solution. We then deriving the Hermite polynomials operator identities by applying the Fredholm equation. We also reveal the connection between the generalized Wigner operator and the 2-dimension normal distribution in statistics, which is useful to study the quantum tomogram. As the application of the entanglement Husimi operator theory we calculate the Wigner function and the Husimi function of the one- and two-mode combination squeezed state , study their characters through drawing the three-dimensional graphics.

由正规序Wigner算符的拉登变换引入了两个互为共轭的中介坐标-动量表象，在此基础上我们建立了相应的量子相空间理论，其中包括引入适合该空间的新的Wigner算符；并在该表象的基础上，建立了广义Fredholm算符方程，求出了它的解，并运用该方程导出有关厄米多项式的算符公式；揭示广义Wigner算符与统计学中的随机变量的二维正态分布形式上的相似，这对于研究量子态的tomogram(是英文Tomography的派生词)有用。

In Part 5, the stability of linear large-scale singular dynamic system is investigated by using the method of vector generalized Lyapunov function and the sum type of scalar generalized Lyapunov function, respectively.

首先研究线性广义系统二次型李雅普诺夫函数的存在性；然后建立按线性近似系统决定非线性广义系统稳定性的准则；进而改进广义李雅普诺夫函数法以研究广义系统的稳定性；最后提出利用非线性函数的偏导数矩阵判别非线性微分-代数系统稳定性的若干简便判据。

On the basis of the achieved result and the effect of stress such as minor principal stress, intermediate principal stress, hydrostatic pressure, stress Lode degree, a generalized hyperbolic failure function adapted naturally with the envelope form of Mohr-Coulomb criterion is proposed for brittle rocks; and a smooth failure function acquired by Yu Maohong is also presented. Thus, a generalized polyaxial strain energy strength criterion is created.

在分析脆性岩石强度的静水压力、中间主应力、最小主应力以及应力Lode角等4种效应的基础上，提出子午面上与Mohr-Coulomb准则包络线自然衔接的广义双曲线型破坏函数及八面体偏平面上光滑角隅型破坏函数，从而建立非线性广义多轴应变能强度准则。

For a class of nondifferentiable generalized fractional programming problems with the norm \$‖Bx‖\-p\$ in the objective function involving, a new incomplete Lagrange function is given, and the saddle point optimal criteria are proven by using the existing necessary optimality conditions, under the assumptions of the class of generalized (\$F,α,ρ,d\$)-convexity.

对于一类目标函数中含范数‖Bx‖p的非可微广义分式规划，给出了一个新的非完全Lagrange函数，并利用已有的最优性必要条件，在一类广义-凸性的条件下，证明了鞍点最优性准则。

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。

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。

We are forbidden from giving money to these shoeless, skinny children, as this will perpetuate begging.

向光着脚，骨瘦如柴的孩子施舍是不可以的，因为要招来无休无止的乞讨。

It would be hard not to fall victim to some sharpeyed policeman.

要想不被某个目光锐利的警察抓到，谈何容易。