并推导出一种判断裂缝位置的泛函分析法。
A functional analysis method to determine the position of a crack is proposed.
随机不动点定理在随机泛函分析中起重要作用。
Random fixed point theorems are of fundamental importance in probabilistic functional analysis.
对偶不变性结果是泛函分析空间理论的核心内容。
Duality invariance is the core of the space theory of functional analysis.
泛函分析和算子代数；量子化方法和路径积分；变分技术。
Functional Analysis and Operator Algebras; Quantization Methods and Path Integration; Variational Techniques.
目前，非线性泛函分析已经成为现代数学中的一个重要分支。
At present, nonlinear functional analysis has been one of the most important branch of learning in modern mathematics.
谱论是泛函分析的一个近代重要分支，由矩阵特征值构思出算子的谱。
Spectral theory is an important branch of functional analysis in modern times the operator spectra projected from matrix eigenvalue.
数学(分析)：数学分析方面，学到实分析、泛函分析和复分析层次。
Mathematics (analytical) : I have learned analytical mathematics up to real analysis, functional analysis and complex analysis.
同时设立了泛函分析、数理逻辑等研究组，以加强相应理论学科的研究。
It also set up the research groups on functional analysis and mathematical logic to intensify the theoretical study of relevant subjects.
随机赋范空间中的共鸣定理将可能成为随机泛函分析与概率论的新应用工具。
The random principle of uniform boundedness will be also to devoted to the possible of applications of random functional analysis and probability theory, as a new tool.
非线性泛函分析序集一般原理及其应用的研究是非线性泛函分析的重要研究课题。
The study for the general principle on ordered sets in nonlinear functional analysis and its applications is an important problem in nonlinear functional analysis.
从泛函分析的角度出发，将航空发动机排气温度预测问题转换为一种泛函逼近问题。
From the perspective of functional analysis, the prediction of the aeroengine exhaust gas temperature could be seen as a functional approximation problem in nature.
本文论述了两列向量组等价的一些充分必要条件，并应用泛函分析的理论进行分析。
In this paper, some necessary and sufficient condition about the equivalence of two column vector groups has been discussed.
近代数学的一些学科，如代数结构理论与泛函分析可以在矩阵论中寻找到它们的根源。
Some subjects of modern mathematics, such as the algebraic structure theory and functional analysis, would be found in the Matrix theory.
利用泛函分析的技巧讨论了一类对具有连续时滞非线性积分微分方程周期解的稳定性。
The stability of periodic solutions of a kind of nonlinear integral-differential equations with continuous delay is discussed in this paper mainly by the method of functional analysis.
信号与系统的泛函分析是以泛函理论为工具描述和研究信号与系统特性的近代分析方法。
Functional analysis of signal and system is a modern analytical method which is used for describing and studying the properties of signals and systems by means of functional analysis theory.
本文主要利用非线性泛函分析的拓扑度方法来研究时间测度上几类动力方程的正解存在性。
This thesis mainly investigates the existence of positive solutions for some class of dynamic equations on time scales by using topological degree of nonlinear functional analysis.
运用泛函分析和积分方程理论，证明了系统解的存在性与唯一性，得到系统解的解析表达式。
Applying the theory of integral equation and functional analysis, we prove the existence and uniqueness of the system solution to the equation, and get the analytical expression of the solution.
应用非线性泛函分析的理论和方法研究了一类二阶线性微分方程，证明了周期衰减解的存在性。
The second-order nonlinear differential equations are studied and the existence of the periodic degenerate solution is proved with the principle of the functional analysis.
本文把复变函数的围道积分应用于泛函分析，对一般的线性闭算子得到了算子值函数的中值定理。
In this paper, the author USES the contour integral in analytic function to functional analysis, and obtains the mean value theorem of operator-valued functions.
从18世纪末一直到20世纪20年代，是泛函分析从最初的隐含要素到各个基本要素逐渐齐备的萌芽阶段。
From the 18th century until the 20th century, 20 years, is implicit from the initial elements of functional analysis to the various basic elements of a gradual complete embryonic stage.
运用泛函分析的方法 ，通过分析系统主算子的谱特征 ，给出一类具有备用部件的可修人机系统解的渐近稳定性证明 。
By using functional method, the asymptotic stabitity of a solution of a repairable standby human-machine system is proved, by studing spectral properties of the operator corresponding to this system.
从教学管理和内容处理等方面阐述作为分析学课群主要组成的实变函数论与泛函分析课程的建设，以建设课程群的思路对课程进行全面、综合、深入的建设，提高课程建设质量和效益。
It puts forward a new concept to comprehensively and deeply build curricula group in the meantime when to build a course, so as to promote the quality and benefit of curricula construction.
泛函空间理论是成熟的多维空间数学理论，是多维空间分析和表达的有力工具。
Functional analysis theory is a mature hyperspace mathematics theory. It is a potent tool for multidimensional space analysis and expression.
从卷积型变分原理的泛函出发，通过分析泛函中的各项，推导出求解动力响应问题的时-空有限元法，并将其应用于梁的动力问题中。
Based on Gurtin type variational principle a finite element method for initial value problems is presented by functional analysis. It is used for problems of beams dynamics.
建立了直井中钻柱屈曲的平衡方程及对应的泛函表达式，并首次采用有限元法对斜直井中钻柱屈曲的整个过程进行了分析。
The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite element method.
其次，利用随机分析技巧和拟有界条件，建立了伊藤随机泛函微分方程解的延拓定理；
Furthermore, a continuation theorem for stochastic functional differential equations of Ito-type is given by using stochastic analysis technique and the quasi-boundedness condition.
通过对泛函网络的分析，提出了一种序列泛函网络模型及学习算法，而网络的泛函参数利用梯度下降法来进行学习。
In this paper, by analyzing the functional network, a new model and learning algorithm of the serial functional networks is proposed.
文中阐述了方法的基本原理，并就稳定泛函和正则参数的选择等关键问题作了分析和论述。
The principle of the method is introduced and some key points, i. e. the selection of the stabilization functional and the regularization parameter, are discussed in the paper.
文中阐述了方法的基本原理，并就稳定泛函和正则参数的选择等关键问题作了分析和论述。
The principle of the method is introduced and some key points, i. e. the selection of the stabilization functional and the regularization parameter, are discussed in the paper.
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