应用复变函数论的方法，简洁地给出了的一切有理数解和一切整数解公式。
In this paper, the general rational solutions and the general integer solutions of are given.
复变函数论的方法，对复合材料的圆盘状裂纹的轴对称性扩展问题进行研究。
By the theory of complex functions, a penny-shaped crack on axially symmetric propagating problems for composite materials was studied.
针对前向神经网络泛化问题，从函数论的角度分析了影响前向神经网络泛化性能的因素。
To investigate generalization capability of feedforward neural networks, the influencing factors of generalization capability of feedforward neural networks are analyzed according to function theory.
本文用复变函数论的映射方法证明了一个普遍意义的矢量性物理量的合成公式，并证明了一个易于判定的充要条件。
In this paper, the generalized vector composite formulas are proved by the mapping method of complex function, and a necessary and sufficient condition that can be used easily is proved too.
解析函数是复变函数论主要的研究对象，而解析函数的五个等价条件又贯穿了我们对复变函数论学习的全过程。
Analytic functions of complex variable function is the main object of study, and the five equivalent conditions of analytic functions penetrate the whole process of learning of complex function.
采用复变函数论，对反平面条件下的动态裂纹扩展问题进行研究。
By the application of complex functions theory, the dynamic crack propagation problems under the condition of anti-plane were investigated.
亚纯函数与整函数的分解理论是单复变函数论中一个令人感兴趣的课题。
The factorization theory of meromorphic and entire functions is one of interesting problems in complex analytic function theory.
本文主要介绍了偏微分方程一些边值问题的函数论方法。
In this paper, we attempt to introduce mainly the solvability of several boundary value problems for partial differential equations by using function theoretic methods.
数学课程的主题情境分析可以给学习者导引出一个整体思路及框架，有利于实变函数论课程的教学与学习。
The analysis of subject context in the mathematics course gives the learners a complete thinking and frame, which is good for the teaching and studying of Real Variable Function Theoty.
摘要最大模原理在复变函数论中占有重要的地位，是研究解析函数的有力工具。
Maximum modulus principle plays an important role in the complex analytics, and it is a powerful tool in studying the analytic function.
促进了这两个新的数论函数的研究。
Properties of the two new arithmetical functions are developed.
的函数论方法与亏指标理论。
Tichmarsh's functional method and the deficiency index theory.
实变函数论是现代分析必不可少的理论基础。
Functions of real variable is an essential basic theory in modern analysis.
结果给出两个新的数论函数均值的渐近公式。
Results Two new asymptotic formulae on their mean value are given.
研究一个关于n原根的数论函数的渐近性质，给出了一个较为精确的渐近公式。
In this paper, we have studied the asymptotic formula of a number theoretic function about the primitive roots modulo n, and given a more precise asymptotic formula.
算术函数的均值问题在解析数论研究中占有十分重要的位置，许多著名的数论难题都与之密切相关。
Mean value problems of arithmetical functions play an important role in the study of analytic number theory, and they relate to many famous number theoretic problems.
主要讨论了《实变函数论》中定理：“可数个可数集之并是可数集”的多种证明。
This paper give the proofs of the Keal Function "a theorem that sum aggregate enumerable set is countable aggregate".
目的研究两个新的数论函数的性质。
为了判断整数是否为拟亲和数，文章在讨论费玛数和数论函数性质的基础上，找到了一种验证一个整数是否是拟亲和数的方法，从而证明了费玛数不与其他正整数构成拟亲和数对的结论。
In this paper, we find out a kind of method of verifying whether an integer is quasi-amicable or not, and prove the Fermat numbers are never perfect or part of an quasi-amicable pair.
1957年从法国归来的熊庆来先生负责建立了函数论研究组。
In 1957, Professor Xiong Qinglai, who returned from France, founded the research group of the theory of functions.
利用解析方法研究了平方剩余数的若干性质，并给出了平方剩余数对于两个常用数论函数的几个均值公式。
By using the analytic method some properties of the square residues are studied, and several (interesting) mean value formulas are given.
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.
该软件包提供了基本的数学和数论函数，可对不同安全强度的算法进行实现。
The package provides math and Numerical Theory functions, which could support the implementation of algorithm on different security level.
空谈形成一种从经典数论解释在怪物有限群和模函数之间的神秘的连接的方式。
Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory.
高斯函数是一个非常重要的数论函数，其应用非常广泛。
高斯函数是一个非常重要的数论函数，其应用非常广泛。
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