查询词典 generalized function

Firstly,based on the generalized function,φ-mapping topological currentare rigorously proved to be of delta-function formδand can be labelledby the nodal indices of the vector field,namely by Hopf indices and Brouwerdegrees of this vector field,which reveals the inner relationships between ourtheory and the topology of vector bundle.A singular divergence theorem isalso presented.

论文首先以广函数为基础严格证明了，φ-映射拓扑流具有δ函数形式，并且可以向量场的零点指标表征，即以其Hopf数和Brouwer度拓扑量子化，从而揭示了它与向量丛的拓扑学之间的内在联系。

In the third section, the asymptotic behaviors of the solution for the generalized Burgers equation with convective function and nonconvective function are analyzed, respectively, both of which tend to the corresponding steady equation.

分别讨论了广义Burgers方程(0.2)在有对流流函数f及无对流流函数时解的渐进行为，它们分别趋于相应定常问题的解。

Based on the theory of nonequilibrium statistics and density operator equation, the generalized master characteristic function for the nonextensive reaction-diffusion systems affected by pressure is derived by equation satisfied by calculating the time variation of probability distribution function, where the pressure of the nonextensive systems is given in the framework of Tsallis statistics.

依据非平衡统计及密度算子方程，通过计算概率分布函数的时间变化，得到了非广延反应扩散系统在压力作用时其特征函数满足的广义主方程，其中非广延反应扩散系统的压力在Tsallis统计的框架下给出。与唯象理论中的主方程比较，新得到的方程不仅依赖于非广延参量q而且有更多的非线性项，因此更具有普遍性。

The matrix =( xi, xjp having the e-th power of the greatest common P-divisorp of xi and xj as its-entry is called the e-th power GCD matrix on S. The matrix = having the e-th power of the least common P-multiple p of xi and xj as its-entry is called the e-th power LCM matrix on 5. We obtained the following results:(1) is nonsingular for any set S;(2) If S is an FC set, then the determined of has formula Det =Jpe(x1)...Jpe, where the function Jpe is the generalized Jordan totient function;(3) A formula of the inverse of is given when S is an FC set;(4) If S is an FC set, then |.

以_P的e次方为第i行j列元素的矩阵称为定义在S上的e次幂GCD矩阵，记为；以_P的e次方为第i行j列元素的矩阵称为S上的e次幂LCM矩阵，记为，我们得到了如下结果：①定义在集合S上的e次幂GCD矩阵是非奇异的；②若S是R上的FC集，则S上的e次幂GCD矩阵的行列式Det=J_p~e(x_1)J_P~e(x_2)…，J_p~e，其中J_p~e为R上的Jordan函数；③当S为FC集时，得到了的逆矩阵~-1的表达式；④证明了当S是FC集时，整除，即等于与R上另一个矩阵的乘积。

While the standard Airy function, used frequently in the uniform asymptotic formulas for classical orthogonal polynomials, behaves like the exponential function on one side and the trigonometric functions on the other side of an extreme zero,the q-Airy polynomial behaves like the q-Airy function on one side and the q-Theta function on the other side.

在经典正交多项式的一致渐近公式中我们通常要用到Airy函数，这个Airy函数在一个极端零点的一边表现为指数函数，另一边又表现为三角函数。同样地，q-Airy多项式在一边表现为q-Airy函数，另一边又表现为q-Theta函数。

This paper compares periodic set with almost periodic set, and properties of periodic function with that of almost periodic function through analysing the definitions of periodic function and almost perodic function, and then draws some important conclusions.

利用周期函数与概周期函数的定义，把周期函数的周期集与概周期函数的概周期集进行了比较，把周期函数与概周期函数的性质进行了比较，并得出一些重要结论。

A main feature in developing the theory is that the scope is expanding: from almost periodic function, asymptotically almost periodic function, weakly almost periodic function to pseudo almost periodic function which was introduced by Professor Zhang in 1992. Every extension consumedly enlarges the theory and their applications.

从概周期函数、渐进概周期函数、弱概周期函数，一直到张传义教授在上世纪九十年代初提出的伪概周期函数，每一次函数范围的扩展都大大地丰富了概周期函数的理论和其应用前景。

Methods 42 children with CP (26 males, 16 females, average age 49.5±21.5 months, 11 children with spastic quadriplegia, 22 with spastic diplegia, 5 with spastic hemiplegia, 2 with athetosis and 2 with dystonia) were assessed with Gross Motor Function Classification System and Gross Motor Function Measure for the assessment and classification of gross motor function. Pediatric Evaluation of Disability Inventory PEDD was used to assess the ADL. The ADL of children with different levels of GMFCS and the correlat ion between gross mot or function and ADL were analyzed. Results The more severe of GMFCS, the less standard score of PEDI.

方法对 42例脑瘫患儿（男性26例、女性16例，年龄49.5±21.5个月；痉挛型四肢瘫11例、痉挛型双瘫22例、痉挛型偏瘫5例、徐动型2例、肌张力障碍型2例）采用脑瘫粗大运动功能分级系统和粗大运动功能测试量表进行粗大运动功能分级和评估；采用能力低下儿童评定量表进行日常生活能力评定，分析不同GMFCS等级脑瘫患儿的日常生活能力表现，以及粗大运动功能与日常生活能力之间的相关性。

Events,Operation and Relation of Sets, Classical Probability, Geometrical Probability , Statistical Stability of a Frequency, Axioms of Probability, Conditional Probability, Total Probability Theorem, Bayes' Rule,Independent Events,Independent Repeated Trials, One Dimensional Random Variables, Discrete Random Variables, Distribution Function of a Random Variables , Continuous Random Variables, Normal Distribution, Distribution of a Function of a Random Variable, Multidimensional Random Variables, Joint Distribution Function, Marginal Distribution Function,Discrete Two—Dimensional Random Variables,Continuous Two—Dimensional Random Variables, Independent Random Variables, Distribution of Functions of Random Variables,Expectation,Variance, Covariance, Coefficient of Correlation, Bivariate Normal Distribution, Law of Large Numbers, The Central Limit Theorems, Sample and Population ,Chi—Squared, T and F Distributions , Sampling Distributions , Point Estimation , Interval Estimation , Testing Hypotheses , A Test of Significance for Parameters in a Single Sample From a Normally Distributed Population , A Test of Significance for Parameters in Two Sample From Normally Distributed Populations .

本课程的主要内容：概率的概念与运算、随机变量及其分布、随机变量的数字特征与极限定理、数理统计的基本概念、估计和检验的基本方法，随机事件与概率随机事件、事件的关系与运算、几何概率、统计概率等，条件概率、全概率公式、贝叶斯公式、事件的独立性、二项概率公式，随机变量的概念、离散型随机变量、随机变量的分布函数、连续型随机变量、随机变量函数的分布，多维随机变量及其分布函数、边缘分布函数、随机变量的独立性、二维随机变量函数的分布，数学期望、方差、协方差和相关系数、大数定律、中心极限定理，总体与样本， X 2-分布、 t-分布和 F-分布，统计量及抽样分布，假设检验的基本概念、单个正态总体参数的显著性检验、两个正态总体参数的显著性检验。

Second, in the viewpoint of crypto analysis, the practical requirement for the cryptographic function is to construct the function that can resist all the known crypto analysis and attacks. In advanced, the main cryptographic properties are compared, and the relation among these cryptographic properties is analyzed, including the trade-off ones. Get the conclusion that the construction of cryptographic Boolean function is to find out the proper Boolean function in the whole vector space under the restriction of several cryptographic properties required for the security system.

然后本文从密码分析的角度，讨论了密码函数的实际需求，即构造能够抵抗已有密码分析与攻击的布尔函数；分析了布尔函数的主要的密码学性质，并比较了这些性质之间的相互关系，包括制约的关系；得出了构造布尔函数的实质的结论，即在向量空间中构造全体布尔函数，以所需的若干密码学性质作为限制条件，用有限域上的多项式、Walsh谱、Hadamard矩阵等数学工具找出适当的布尔函数用于加密体制的设计。

Many will continue to choose to live in duality and in conflict.

许多人将继续选择活在二元对立性和冲突中。

I find that students of the University of Physical Education all wear sportswear at first sight.

我发现：体育大学的学生乍一看，都是穿运动衣，大家都一样