查询词典 functional analysis

Nonlinear functional analysis is not only profound theory but also widelyused research discipline in mathematics, in the context of nonlinear problemsof mathematics and natural sciences, a number of theories and methods of dil-ing with nonlinear problems have been established.

非线性泛函分析是数学中既有深刻理论又有广泛应用的研究学科，以数学和自然科学中出现的非线性问题为背景，建立了处理非线性问题的若干理论和方法。

Nonlinear functional Analysis is an important branch of morderm math-matics .

中文摘要：非线性泛函分析是现代分析数学的—个重要分支。

The whole contents is divided into five chapters. In chapter 1, as the beginning of this paper, we offered some relative knowledge, such as the cone theory and semi-order method in nonlinear functional analysis. Moreover, we established a new fixed point theorem of the mixed monotone iterative operator.

全文共分成五章：第一章作为准备知识给出了本文要用到的相关知识内容，其中包括非线性泛函分析中的锥理论及半序方法，并建立了新的混合单调算子不动点定理。

The singular differential equation has developed on the basis of nonlinear functional analysis, because it can explain a lot of natural phenomenal, more and more mathematicans are devoting their times to the study of sigular differential equation.

以非线性泛函分析为基础而发展起来的奇异微分方程理论因其能很好的解释自然界中的各种各样的自然现象而倍受关注。

And control problems such as optimal import rate control, optimal harvesting control, optimal birth control are investigated. By means of nonlinear functional analysis, differential equations, integral equations, and modern control theory, a number of research results are obtained, which are theoretically valuable and provide a solid ground for the practical use of our models.

本文系统讨论了几类年龄依赖的单种群和多种群动力系统，综合应用非线性泛函分析、微分方程、积分方程以及分布参数系统控制论等理论与方法，深入地研究了这些系统的解的存在性、唯一性以及非负有界性；研究了这些种群动力系统的最优输入率、收获率和出生率控制问题，获得了一批重要的理论成果。

In this paper, the algorithm of BFGS has been used to solve the problem, which was demonstrated by the results of NFEA and the nonlinear functional analysis logically.

其次，针对支架的弹塑性大变形分析过程容易出现负刚度导致分析终止的问题，本研究采用BFGS算法解决了该问题，并且利用非线性泛函定理证明了起始刚度正定，BFGS算法能使刚度始终保持正定。

Missirlis in article [1]. At the same time, a sufficient condition for convergence of the PSD method is given to be compared when the coefficient matrix A of the linear system Ax = b is a symmetric, positively defective matrix. In §3.2, an example is given to state that the range of our sufficient condition is wider than theorem 3.3 of article [1]. On the other hand, following a.n analogous approach of [14] and starting the functional relationshipwe have a perfect analysis for the PSD method to converge and optimum valves for the involved parameters under different conditions.Under the assumptions that A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are real,we get necessary and sufficient conditions for the PSD method to convergence.The result is equal to theorem 1 of article [9].Under the same condition, we can see the optimal parameter and of corresponding spectral radius of thePSD method in [8]:(2)When A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are imaginary or zero,we get necessary and sufficient conditions for the PSD method to convergence.In chapter 3, the optimal parameter and of corresponding spectral radius of the PSD method are given by table 3.3. Moreover, under the assumption 0

Missirlis在文献[1]中定理3.3的不准确，同时给出了当线性方程组Ax=b的系数矩阵A为对称正定阵时，PSD迭代法收敛的一个充分条件与之比较，并且在§2.3中用实例说明了对于一部分矩阵而言本文得到的充分条件广于[1]中定理3.3的充分条件；另一方面，按照文献[14]的方法，我们从PSD迭代法的特征值λ与其Jacobi迭代矩阵B的特征值μ的关系式：出发，在不同条件下对PSD迭代法的收敛性和最优参数以及最优谱半径进行了完整的分析：(1)在系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为实数的条件下，给出了PSD迭代法收敛的充分必要条件，此结果与[9]中的定理1等价，此时最优参数及最优谱半径由[8]得：(2)第三章表3.3中给出了，当系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为纯虚数或零时的PSD迭代法的收敛范围和最优参数，并且我们可以得到当0

The analysis result of IR and fluorescence indicated that Eu3phen had been grafted on polypropylene backbone successfully and that of DSC and WAXS revealed that this functional group act as nucleator to increase the crystallization rate effectively and destroy the integrity of crystalline as well.

IR和荧光分析结果表明该配合物已成功接枝到PP链上。而DSC和WAXS分析结果则表明功能化基因的加入起到类似成核剂的作用，有效提高PP的结晶速率，但同时也破坏了PP晶区的规整性。

ABSTRACT:Objective To explore the feasibility of functional magnetic resonance imaging in analysis of olfaction function with modified OEP-98C olfactometer and event-related design.

目的 探讨以改进后的OEP-98C型嗅觉诱发电位仪作为嗅觉刺激器，事件相关设计的嗅觉功能磁共振成像分析嗅觉功能的可行性。

Objective To explore the feasibility of functional magnetic resonance imaging in analysis of olfaction function with modified OEP-98C olfactometer and event-related design.

目的探讨以改进后的OEP-98C型嗅觉诱发电位仪作为嗅觉刺激器，事件相关设计的嗅觉功能磁共振成像分析嗅觉功能的可行性。方法采用改进后适应磁共振环境的OEP-98C型嗅觉诱发电位仪作为嗅觉刺激器对6名右利手年轻男性志愿者进行嗅觉刺激。

Chinese traditional virtue is humility and wariness,the compliment and praise to the others should be declination

中国人的传统美德是谦虚谨慎，对别人的恭维和夸奖应是推辞。如

We bought this house on the never-never.

我们以分期付款的方式买下这座房子。