查询词典 existence theorem of implicit function

By using cross-iteration technique and the Schauder fixed point theorem, the existence theorem of travelling wave solutions of this system is established.

针对反应项的不同单调性，引进交互迭代格式，利用Schauder不动点定理建立了行波解的存在性定理，并将所得结论应用到时滞竞争系统。

In chapter II,the preliminary knowledgefor accomplishing this research is presented,and the well-posed problem ofthe thin-plate flow of non-Newtonian viscous fluids is testified.By using themonotone operator theory and Schauder's fixed point theorem,the generalizedsolution's existence and uniqueness theorem for the thin-plate flow problem ofnon-Newtonian viscous fluids is obtained under reasonable conditions.

第二章给出了进行本项研究所需的一些预备知识，对非牛顿粘性流体薄板流问题广义解的适定性进行了研究，应用单调算子理论和不动点定理，在合理的条件下，证明了非牛顿粘性流体薄板流问题广义解的存在性，唯一性定理。

We discussed the stability of the system balance, used the Poincare-Bendixson's annular region theorem to prove the existence, and used the Zhang Zhifen unicity theorem to prove the uniqueness of limit cycle, at the same time give meaning to the corresponding conclusions on the ecology.

讨论了系统平衡点的稳定性，用Bendixson环域定理证明极限环的存在性，借助张芷芬唯一性定理证明极限环的唯一性，同时对相应结论的生态学意义给予说明。

The existence and uniqueness of the limit cycle are proved by applying Poincare-Bendixson theorem and Zhang Zhifen's Uniqueness theorem.

运用Poincare-Bendixson环域定理，证明了极限环的存在性。这用张芷芬惟一性定理，注明了极限环的惟一性。

By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.

应用局部凸H－空间内具有闭零调值的上半连续集值映象的Fan－Glicksberg型不动点定理和极大化定理，对无限最优化总理2和约束对策问题在没有线性结构的局部凸H－空间内证明了解的某些新的存在定理，这些定理改进和推广了最近文献中的许多重要结果。

This result is browden to n-dimentional case in chapter 2 first and an existence theorem (theorem 2.1) for linearly increasing solutions is given.

第二章将此结果推广到高维情形，给出了一个线性增长解的存在性定理(定理2.1)；另外，本章还给出了方程存在对数增长解的两个定理(定理2.2—2.3)。

Chapter 4 is devoted to the existence and multiplicity of homoclinic for self-adjoint nonlinear second order difference equations by using "Mountain Pass " theorem and "Symmetry Mountain Pass "theorem in critical point theory.

第四章应用临界点理论中的山路引理与对称山路引理研究了一类自共轭非线性二阶差分方程的同宿轨的存在性与多重性。

With the help of the fundamental theory to singular measure differential system, Green's function matrix expression of solution and well-posed boundary condition are given, together with discussing the properties of the Green's function matrix under the influence of impulsive effect In section 5, based on Lyapunov function method, we investigate that the existence of the first boundary value problem to second-order singular system by macthing the solutions to the second boundary value problem; and the existence and uniqueness of three-point boundary value problem to third order singular system by macthing the solutions to two-piont boundary value problem.

第五部分借助Lyapunov函数法，通过将第二类边值问题的解对结成第一类边值问题的解，得到了二阶广义系统的第一类边值问题解的存在性；通过将两点边值问题的解对结成三点边值问题的解，得到了三阶广义系统的三点边值问题解的存在性和唯一性。

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。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

Objective To investigate the relationship between ovum fertilization rate and sperm morphology, acrosome reaction in IVF and to explore the influence of parameters of sperm on fertilization rate.

目的 研究体外受精(in vitro fertilization，IVF)中精子形态、顶体反应与卵子受精率之间的关系，分析精子各参数在IVF受精率方面的参考意义。

A: I hear Mr. White wants to run for the Presidency!

我听说怀特先生要参加总统竞选！