This paper researches the three - layered b - spline neural network , which is commonly used in engineering and presents a constructive algorithm for selecting the number of the hidden nodes . it is proved that the proposes algorithm can be used to build a b - spline neural network with minimum hidden nodes to approximate any continuous function defined on compact set to a prescribed accuracy 本文研究了工程上常用的三层b样条神经网络,采用构造性的方法证明了b样条神经网络的全局逼近能力,并且给出了构造几乎最小隐节点的算法,从而在理论上为b样条神经网络的使用提供了依据。
This paper also points out the consistency that can be generalized more than one dimension . so , we achieve the large sample property - consistency of this class of model on the fixed design . in this paper , for fixed design points xi ; under the assumption that the unknown function g is continuous function and the moment of random error exists and is finity , we discuss and show that the estimators n , gn and n2 for , g and 2 have strong consistency , p th - mean consistency for more general nonparametric weighted fuction 本论文在x ;是固定设计的情况下,假定未知函数9 ( ? )连续,对非参数权函数的条件更为一般和基本,并对随机误差e ;的矩的要求有限,讨论并证明了在这些条件下, p ; g ( ? )的估计量札lin ( ? )及误差方差a ’的估计量枯相合性和叭三2 )阶平均相合性
In the analyse course , two elasticity theory methods , the finite element method and the variation method are employed . and the variation method solution is a continuous function describing the distribution of the stress and strain as a whole , which can be helpful to the design of similar gauge 本文在对弹性元件进行力学分析时,采用了弹性力学有限单元法和变分法,由变分法产生的解是整体应力应变分布的连续函数表达式,该表达式可供今后同类型力传感器的设计计算借鉴。
An important property of sobrification is given . by discussing the spectra of complete lattices , a theoretical foundation of sobrification of spaces is obtained . thus we know that the category of sober spaces is a reflective subcategory of the category of all the topological spaces with continuous functions 通过对完备格的谱理论的简单讨,为一般的拓扑空间及偏序集的sober匕做了理论上的铺垫z指出了拓扑空间的sober化函子是从sob到top的包含函子的左拌随,理想完备化函子是从alg到pos的遗忘函子的左拌随
On the other hand , the conformal deformation ' s problem is to find a metric on h2 ( - 1 ) , conformal to g , with the given function k as its gaussian curvature , that is , it is important for us to study the solvability of the conformal gauss curvature equation in geometry analysis . the problem that the conformal gauss curvature equation may have a solution for every nonegative holder continuous function k ( x ) is also an open problem ) = e ~ ( 2u ) g使k是( ? )的高斯曲率,即共形高斯曲率方程的可解性研究是几何分析中的一个重要问题。当预定的函数k取正值时,共形高斯曲率方程解的存在性命题作为一个猜测至今未得到解决。
The main contributions of this paper are as follows : ? by employing the fuzzy logical system which can approximate any nonlinear continuous function with arbitrary , we synthesize the state feedback robust stabilization controller , the output feedback robust stabilization controller , the nonlinear state observer and the decentralized output tracking controller for a class of complex systems with interconnections , which can ensure the states , state errors , tracking errors and all estimate parameter errors to be uniformly ultimately bounded ( uub ) in all control layouts 本文的主要工作和研究成果如下:利用模糊逻辑系统和自适应思想分析处理复杂互联系统中的不确定性,完成了一类复杂互联系统的状态反馈鲁棒镇定设计、输出反馈鲁棒镇定设计、状态观测器设计和输出跟踪控制器设计,并证明了所设计的鲁棒控制器可保证被控系统的状态、状态误差、跟踪误差及各类参数估计一致终极有界。
A kind of operator of trigonometric interpolation polynomials with bivariate product was constructed based on an equidistant node set , so that the operator could be converged uniformly to bivariate continuous functions with periodicity of 27 on whole plane , and the convergence order of the approximation would be optimal for a body of functions with arbitrary - ordered continuous partial deritives 摘要构造了一类基于等距结点组上的二元三角插值多项式算子,使得该算子在全平面上一致收敛到每个以2为周期的二元连续函数,并且对具有任意阶连续偏导数的函数全体的逼近具有最佳收敛阶。
The second , the molecule dynamic method ( md ) has been used to investigate the nature of at high temperature and pressure . the primary results is ( 4 ) that is really a reduced minorant but not a continuous function of temperature ? there a interrupt where material transfer its state from solid to liquid . the third , some methods which to get directly by experiments and their results have been discussed 第二方面,以分子动力学方法研究了晶格随比容和温度的变化规律问题,获得的主要认识为( : 4 )晶格(至少对于铜、铝)的确是温度的函数,并且是弱函数,但不是温度的单调(下降)函数? ?其基本变化规律在固液相变点有一间断(跳升) 。
In the new method the uncertainty of the system to be controlled is normalized firstly , and then the partition of unity that is subordinated to a open covering of state variables compact set is constructed , and the approximation is realized by using its property that can approximate nonlinear continuous function with arbitrary precision , then the decentralized adaptive robust controller of complex systems and adaptive laws of approximate parameter estimation are designed 该方法首先对被控系统中的不确定性进行归一化处理,进而构造出从属于状态变量的紧致域的一组开覆盖的单位分解,利用其具有以任意精度逼近非线性连续函数的性质,实现了对被控系统不确定性的近似逼近,然后设计了复杂系统的分散鲁棒控制器和参数估计的自适应律,并证明了这种控制器使被控系统的状态及参数估计误差一致终极有界。
Neural network has the ability of learning and expressing any nonlinear relation . it can approximate any continuous function and their any order derivatives with any precision if it has the correct layers of networks and the correct number of hidden units . so the identification of dynamic character of time - varying , nonlinear plants has a kind of simple and effective means . the critical problem of control of time - varying , nonlinear plants is resolved . so all kinds of advanced control means based on neural network is an effective way that resolve the control problem of modern power station 神经网络具有表示任意非线性关系和学习等能力,通过恰当选择网络层次和隐层单元数能够以任意精度逼近任意连续函数及其各阶导数。为时变、非线性对象的动态特性的辩识提供了简单而有效的一般性的方法,解决了时变、非线性对象控制中的瓶颈问题。因此基于神经网络的各种先进控制技术是解决现代电站中控制难题的一条有效途径。
In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be a "discontinuous function".