查询词典 theorem of implicit functions

The study of exceptional set has a history of half a century. In reference (2), Lento extended the famous Picard Theorem and Presented the concept of exceptional set of entire functions and meromorphic functions. And the exceptional set in his result was an infinite sequence of complex numbers.

例外集问题的研究，已有半个世纪的历史，在文献〔2〕中，Lehto推广了著名的Picard定理，并首次提出例外集的概念，在他的结论中，例外集为一无穷复数序列。

The study of exceptional set has a history of half a century. In reference (2), Lento extended the famous Picard Theorem and Presented the concept of exceptional set of entire functions and meromorphic functions.

例外集问题的研究，已有半个世纪的历史，在文献〔2〕中，Lehto推广了著名的Picard定理，并首次提出例外集的概念，在他的结论中，例外集为一无穷复数序列。

Liouville"s Theorem on entire functions is proposed as a proving method for theta function identities. Several identities are exemplified, such as the quintuple and septuple product identities; four symmetric difference identities related to the Ramanujan"s congruence modulo 11 on the partition function; as well as two theta function identities on the Rogers-Ramanujan functions G and H.

作者提出利用Liouville定理作为证明theta函数恒等式的基本方法，并以Watson五重积，Hirschhorn七重积恒等式，四个与分拆函数中Ramanujan的模11同余有关的对称差恒等式，以及两个与Rogers-Ramanujan函数G，H有关的theta函数恒等式为范例，论证这种方法的有效性。

A minimax theorem generally involves three assumption conditions: space structures on sets X and Y, the continuity of the functions and the concavity and convexity of functions.

一个极大极小定理一般涉及三个假设条件：集合X和Y的空间结构，函数的连续性和函数的凹凸性。

As an appliance, by applying the addition defined in this paper, the uniqueness theorem of meromorphic functions obtained by Yang Lo is generalized which consider its multiple values to multiple valued algebroidal functions.

本文明确地定义了加、乘运算，并证明了运算后的结果仍是代数体函数。为进一步的研究完善了理论基础。关于亚纯函数的唯一性定理有许多非常好的成果仁'1。杨乐创造了一种方法，结合重值更深人的研究了亚纯函数的值分布〔，一'了。

In chapter 6, we discussed the wavefront solution of a kind of lattice differential equation which derives from diverse fields. We obtained the wavefront solution by using sup-subsolution iteration when the coupled functions are quasimonotone, and by applying Schauder fixed point theorem, we also obtained the wavefront solution when the coupled functions have a different quasimonotone property.

在第六章中，我们对一类从实际问题中抽象出来的二阶时滞格微分方程的行波解进行了讨论，用单调迭代的方法讨论了耦合函数具有拟单调性时行波解的存在性，用不动点的方法讨论了耦合函数具有指数拟单调性时行波解的存在性。

We also proved corresponding results on normal functions and a uniqueness theorem of entire functions.

此外，还证明了相应于正规函数以及整函数的唯一性定理方面的的结果。

We introduce the concepts of differential and integral of fuzzycomplex functions on the space〓,and get their properties.We provethe depictive theorem of differentiable fuzzy complex functions.

在模糊复数度量空间〓上重新引进模糊复函数的微分概念和积分概念，给出了其微积分的基本性质，证明了模糊复函数可微的刻划定理。

Engineering design problems have two characteristics: the design variables are often monotonic in the objective function and constraints. Moreover, the objective function and constraints are often implicit functions which cannot be expressed explicitly in terms of design variables.

工程最佳化设计问题通常有两个特性：设计变数在目标函数与限制条件常具有单调性，且其目标函数与限制条件常为内隐式函数，也就是不能以设计变数来表示其外显形式。

In this algorithm, first, the nonlinear kernel mapping is used to map the face data into an implicit feature space, and then a linear transformation which produces orthogonal basis functions is performed to preserve locality geometric structures of the face image.

该算法首先利用核的方法提取人脸图像中的非线性信息，并将其投影在一个高维非线性空间，在保证各向量正交的同时，通过局部保持投影算法做一线性映射，从而更好地提取人脸非线性局部邻域结构特征。

After explaining total design of automated test system for microcircuit , the thesis introduces GPIB standard .

文章在说明了微电路模块自动测试系统的总体设计后，对GPIB标准进行了介绍。

He interceded in my behalf.

他替我说情。