连续可微性

This article uses the implicit function theorem and the properties of analytic functions,with less limitations for the uniqueness,continuity,continuous differentiability of the implicit functions,and gets the sufficient and necessary conditions of the existence of implicit functions by simplifying them.

从常用隐函数存在性定理出发，放宽对隐函数唯一、连续、连续可微等性质的限制，利用解析函数的性质将其展拓，得到广义隐函数存在的充分必要条件和广义隐函数的分布特征。

By weakening the premise of the convexity of the objective function required in paper[7], we prove the sufficient desent property and the global convergence with the strong Wolfe line search.

在第二章中，我们参照文献[7]中的方法，提出了一类与HS算法相关的共轭梯度算法，并减弱了文[7]中要求目标函数二阶连续可微且为凸的前提条件，采用强Wolfe线搜索，在较弱的条件下证明了这一类算法具有充分下降性和全局收敛性。

Ablish two decision theorems of relative compactness for unbounded function groups in an infinite interval.

sect；2.3我们建立了判定无穷区间上抽象无界连续函数组和抽象无界可微函数组相对紧性的充分必要条件，并对无穷区间上抽象二阶微分方程两点边值问题无界解的存在性做了研究。

Limits, Continuity, Derivatives, and Integration of Single Variable, Integration Techniques, Applications of Derivatives and Integrals, Infinite Sequences and Series, Multivariable Function and Their Derivative, Multiple Integrals, Integration in Vector Fields.

课程内容：单变数函数之极限、连续、微分、积分，积分技巧，微分与积分的应用，无穷数列与级数，多变数函数之偏微分、可微性，多重积分，极值问题，向量场积分。

In chapter 3 constructs firstlya new differential merit function by a perturbation structure of VIP and study theproperties of this merit function.Based on this merit function,a continuation-typeNewton method is proposed,which use the technique of inexact linear search forassuring its global convergence,and improves essentially the method of Taji,Fukushima and Ibaraki which can only solve the strong monotone VIP,and has locallyquadratic convergent rate under some condition.

第三章利用变分不等式问题的一种扰动结构构造了新的可微效用函数，并研究了效用函数的性质；在此基础上，给出了一类求解一般单调变分不等式问题的连续型Newton方法CN，方法采用了不精确的线性搜索技术以确保整体收敛性，从本质上改进了Taji、Fukushima和Ibaraki方法只能求解强单调变分不等式问题的局限性，同时又保持了局部二次收敛率。

W ithout assuming the boundedness, monotonicity, differentiability and Lipschitz continuity of the active functions, an algebraic criterion to ensure existence and globally exponential stability of periodic solutions was obtained.

在 放松该类神经网络激活函数的有界性、单调递增性、可微性及Lipschitz连续等条件下，得到了该类神经网络周期解的存在性与全局指数稳定的代数判据。

Based on the sizeof the set of perturbed minimal points in the variational principle, the differentiability of lower semicontinuous functions is examined by means of approximation of the infconvolution sequence.

摘要通过函数的下卷积函数列的逼近方法，在变分原理中从扰动最小值点集的"大小"入手，研究了下半连续函数的可微性。

In chapter 2, we firstly introduce the model of a discrete-time neural network with generalized input-output function. The model generalizes the input-output function in transiently chaotic neural network to a class of continuous, differentiable and monotone increasing functions. Secondly we study the uniformly asymptotical stability of equilibrium in the non-autonomous model. Finally, several examples and numerical simulations are given to illustrate and reinforce our theories. In chapter 3, we firstly introduce a specific class of discrete-time neural network models with sinusoidal activation function.

在本文的第二章中，首先介绍了一类具有广义输入输出函数的非自治离散神经网络模型，该模型把瞬时混沌神经网络模型中的输入输出函数推广到了一般的单调递增且连续可微的函数；其次，利用Schauder不动点原理和利用Lyapunov函数逆定理依次证明了模型平衡点的存在性和该模型在时变权值下的一致渐近稳定性；最后，对几个具体的例子进行数值模拟，数值模拟的结果更好地说明了我们的结论。

The model generalizes the input-output function in transiently chaotic neural network to a class of continuous, differentiable and monotone increasing functions. Secondly we study the uniformly asymptotical stability of equilibrium in the non-autonomous model. Finally, several examples and numerical simulations are given to illustrate and reinforce our theories. In chapter 3, we firstly introduce a specific class of discrete-time neural network models with sinusoidal activation function.

在本文的第二章中，首先介绍了一类具有广义输入输出函数的非自治离散神经网络模型，该模型把瞬时混沌神经网络模型中的输入输出函数推广到了一般的单调递增且连续可微的函数；其次，利用Schauder不动点原理和利用Lyapunov函数逆定理依次证明了模型平衡点的存在性和在时变权值下的一致渐近稳定性；最后，对几个具体的例子进行数值模拟，数值模拟的结果更好地说明了我们的结论。

As the shape optimization design of structural element sections belong to structural optimization,which has its own traits such as discreteness, nondifferentiable and non-convexity,while the traditional optimal methods are not applicable.

结构截面形状优化设计属于工程结构优化问题，由于工程结构优化问题具有离散性、不可微性和非凸性等特点，而传统的优化算法对所优化的问题往往要求连续、可微、非凹等前提条件，所以已不再适合用于工程结构优化问题的求解。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。