泛函分析

耳蜗模型的Volterra泛函分析

Volterra Functional Analysis for the Cochlear Model

Clifford泛函分析概要

The Essentials of Clifford Functional Analysis

利用广义Lyapunov泛函分析了其闭环系统的稳定性，给出了其闭环系统渐近稳定的充分条件。

The stability of the close loop systems is analyzed by singular Lyapunov function .

非线性离散时间耳蜗力学建模、Volterra泛函分析及在语声处理中的应用

Nonlinear Discrete-Time Cochlear Mechanics : Modelling and Its Volterra Functional Analysis with Applications to Speech Signal Processing

利用指数二分性理论和泛函分析方法来处理第一变分方程在R上有多于一个非平凡有界解下的奇摄动系统的同宿轨道分支问题。

With the theory of dichotomy and functional analysis , the paper studies the homoclinic orbits bifurcation of the Auto-Odd-Perturbation System of the first variational equation that has more than one non-trivial bounded solution .

抽象对偶系统中映射级数的λ（X）-赋值收敛是分析学中各领域级数收敛的统一形式，对其内在的相互关系和本质属性（及不变性）的研究，是泛函分析的重要研究内容。

λ( X ) - evaluation convergence of mapping series is the normal form for convergence of series in every area , and the study on its relationship or invariant is an important content of functional analysis .

Al6（OH）（18）（H2O）6的结构及成键方位的从头算及密度泛函分析Ⅱ

Ab Initio and DFT Studies on the Structure and Bonding Orientation of the Favorable Growth Unit Al_6 ( OH ) _ ( 18 ) ( H_2O ) _6 of Al ( OH ) _3 Crystals Precipitating ⅱ

Kakutani不动点定理的泛函分析证法

Functional Analysis Methods of Proving Kakutani Fixed Point Theorem

硕士学位论文《关于算子代数B（X）的K群的相关研讨》是泛函分析学科Banach空间理论与算子理论有机结合进行研讨的产物。

Master 's academic article " Study on the K-groups of operator algebras B ( X ) " is the organic combinative result of the study on the theory of Banach space and the operator theory of functional analysis .

研究了次范整线性空间的性质，引入Q空间的概念，将泛函分析学中的开映射定理、逆算子定理与闭图象定理推广到次范整线性空间之中。

Some properties of sub-normed linear spaces are discussed and by introducing the concept of a Q-space , analogues of the inverse operator theorem , the open mapping theorem and the closed graph theorem are established in sub-normed linear space setting .

f的局部精细点概念是f的正则点的推广。由于它的引进解决了许多非线性泛函分析的问题，如局部共轭定理和现代分析学中的秩定理等等。

Since the concept of locally fine point , which is the generalized regular point , was introduced , many problems in nonlinear functional analysis have been solved , such as the conjugacy problem , the rank theorem in advanced calculus and so on .

小波变换（WT）是八十年代中后期发展起来的一项新的应用数学的分支，数学界公认它是泛函分析、样条分析、调和分析、数值分析、Fourier分析的完美结晶。

Wavelet transform ( WT ) is a new branch in applied mathematics . Research fellows generally accepted that it is a perfect colligation of functional analysis , belt transect analysis , numerical analysis , harmonic analysis and Fourier analysis .

泛函分析学中的有界线性算子定理，Hahn-Banach定理以及共鸣定理都可以移植于次范整线性空间之中。

Analogues the bounded linear operator theorem , the Hahn-Banach theorem and the resonance theorem are established in sub-normed Z-linear space .

从论述经典力学中的Hamiltonian原理的推广开始，概述泛函分析中算子理论和非平衡热力学变分原理基于场的变分的新发展。

This paper discusses the limitations of extension of classical Hamiltonian Principle to continuous systems , then reviews the new developments of operational theory in functional analysis and variational principles in non equilibrium thermodynamics based on field variation .

使用泛函分析理论压缩映射原理对SCFGA进行了收敛性分析；

Make convergence analysis of SCFGA using the principle of Contractive Mapping in functional analysis theory ;

使用泛函分析方法，特别是Banach空间上的线性算子理论，证明了严格占优本征值的存在性，以及系统解的渐近稳定性，线性稳定性和指数稳定性。

By means of functional analysis , particularly , the linear operator theory on Banach space , the existence of the strictly dominant eigenvalue is proved , showing the asymptotic stability , the linear stability and the exponential stability of the solution .

本文讨论了Kakutani不动点定理的泛函分析证法，给出了它的一个较简洁的证明。

In this paper , we discuss the functional analysis methods of proving kakutani fixed point theorem and give a briefer proof of kakutani fixed point theorem .

Fredholm算子是泛函分析算子理论中的一个基本且重要的概念，在偏微分方程等学科方面有重要的应用，在对空间的分类和维数的研究中起着关键的作用。

As an important fundamental concept in generalized functional and analytical operator theory , Fredholm operator has been used in differential coefficient equations and other fields . It is of vital importance for the research of space classification and dimensions .

本文建立了耳蜗的非线性运动方程及相应的状态空间方程，并首次利用Volterra泛函分析方法，获得了非线性耳蜗模型满足任意精度的频域解析解。

In this paper , the nonlinear motion equation and the corresponding state space equation of the cochlea are established , and the Volterra functional series method is firstly used to obtain the analytic solution in frequency domain which may be arbitrarily closed to the accurate one .

用线性算子的理论将人口发展的偏微分方程模型转化为抽象的Cauchy问题，并用泛函分析中的C0半群理论来研究该系统解的存在性和收敛性。

In this paper , we transform the model of the partial differential equation of the population developing system to the abstract Cauchy question . We discuss the solution existence and convergence of the system by the semi-group of class C_0 in function analysis .

描述一般经济均衡理论的主要内容，指出证明该理论的关键所在，简略讨论Kakutani不动点定理的泛函分析证法。

We describe the main contents of the theory of general economic equilibrium , point out the key to its proof , and discuss briefly the functional analysis methods of proving Kakutani fired point theorem .

主要利用泛函分析中的Mazur定理和分离的思想，证明了状态方程解的存在唯一性，并论证了对于给定的目标泛函，在一定条件下最优捕获控制的存在性。

By applying Mazur theory of functional analysis and the ideal of separation , we get the existence and uniqueness for the solution and the existence of the optimal control for given cost function under some assumptions .

在本章中，运用离散泛函分析理论，结合先验估计、Brouwer不动点原理证明了相应差分格式解的存在唯一性、收敛性和稳定性。

In this chapter , the existence and uniqueness of the solution to the scheme , the convergence and stability to the scheme are proved by using discrete functional analysis theory , the apriority estimate method and the Brouwer fixed-point theory .

利用泛函分析的方法，特别是L1空间的线性算子理论，得到了方程解的存在性、唯一性和严格的正性。

We consider the problem of finding the solutions to these equations . By using the methods of functional analysis , especially the theory of linear operator in an L_1 space , we obtain the existence , uniqueness and strict positivity of the solution .

泛函分析方法在联合逼近问题中的应用

The Application of the Methods of Functional Analysis in Simultaneous Approximation

泛函分析中定理教学的改革尝试

Reform Tries at Teaching and Learning of Theorems in Functional Analysis

泛函分析在数据同化伴随方法中的应用

The Application of Functional Analysis in the Accompany Way of Data Assimilation

泛函分析在裂缝简支梁损伤检测及参数识别中的应用

Application of Functional Analysis to Simple-supported-beam Crack Damage Detection and Parameters Verification

范数是泛函分析中最基本、最重要的概念之一。

Norm is a very fundamental and important notion in functional analysis .

随机泛函分析中可交换映象的随机不动点定理

Random Fixed Point Theorems for Commuting Random Operators in Probabilistic Functional Analysis