查询词典 piecewise continuous function

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。

Math: any binary relation that is complete, transitive, and continuous can be represented by a continuous real-valued utility function

效用指数，效用函数的存在性：理性是必要条件；连续性是充分条件，效用函数也是连续函数。

Week 4 The definition of continuous, the nature of continuous function, integral of elementary functions, the nature of elementary functions on closed interval

第4周 连续的定义，连续函数的性质，初等函数的连续性，闭区间上连续函数的性质。

Compared with the discrete distribution, we defined a comparison function for continuous distribution, and pointed out the relationship between the discrete distribution and continuous distribution.

仿照离散分布，定义了连续分布的比较函数，并沟通了离散和连续分布的伴随关系。

In view of continuous function problems, it is first proved that the-ES algorithm based on uniform distribution converges in probability in a weaker condition by means of the central limit theorem. Then it is proved that the-ES algorithm which adopts the general continuous random variables as its variable operators converges in probability.

针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的-ES算法依概率收效，然后给出了采用一般连续性随机变量作为变异算子的-ES算法依概率收效的证明。

In view of continuous function problems,it is first proved that the-ES algorithm based on uniform distribution converges in probability in a weaker condition by means of the central limit theorem.Then it is proved that the-ES algorithm which adopts the general continuous random variables as its variable operators converges in probability.

针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的-ES算法依概率收敛，然后给出了采用一般连续性随机变量作为变异算子的-ES算法依概率收敛的证明。

If each term of the series u1+u2+…un+…is continuous on the interval［a,b］, and this series is uniformly convergent on［a,b］, then its sum function is also continuous on ［a,b］.

若级数u1+u2+…un+…的每一项在［a，b］上连续，而且这级数在［a，b］上一致收敛，则它的和函数也在［a，b］上连续

Lastly,Using the extension theory of〓-algebras founded and developed by Brown-Douglas-Fillmore in 70s,inparticular,using the homotopy invariance of the extensions and the indexformule of Toeplitz operator matrices,the paper characterized the automorphismgroup of the continuous function symbol Toeplitz 〓-algebra in terms of thetopological degrees of the continuous mappings on the n-dimensional sphere.

最后，本文利用Brown-Douglas-Fillmore在七十年代建立并发展起来的C*-代数扩张理论，尤其是扩张的同伦不变性，以及Toeplitz算子矩阵的指标公式，通过球面上连续映射的拓扑度，刻划了高维球面Hardy空间上连续符号Toeplitz 〓代数的自同构群。

Theorem 2 If the functionis continuous and increasing on the interval, then its inverse function is also continuous and increasing on the corresponding interval.

定理 2 如果函数在区间上单调增加且连续，那么它的反函数也在对应的区间上单调增加且连续。

In part 3, utilizing the existing Lipschitz results and the property of Yosida approximation of monotone and continuous function, we prove the existence and uniqueness theorem of a general backward stochastic differential equation with monotone and continuous coefficient.

第三部分在系数仅满足单调连续这样一个新条件下，我们综合运用单调连续函数的Yosida逼近的性质以及Lipschitz条件下的已有结果，证明了一般形式的倒向随机微分方程解的存在唯一性。

What was it that made you want to change sider ?

是什么使你临阵倒戈？

I don't know what he wants, but let's play along with him.

我不知道他要干什么，可我