定理证明

• ( 5 ) the constructively sufficient conditions of the approximating c1 functions and the explicit formula dealing with the approximation precision and the number of fuzzy rules are given for one kind of general fuzzy systems , using the methods different from the former ones which are based on the stone - weierstrass theory , therefore , the constructively sufficient conditions are also generalized from polynomial function to c1 function
  ( 5 )针对一类一般的模糊系统，采用与通常的基于stone - weierstrass定理证明模糊逼近器不同的方法，首次给出了它们逼近c ~ 1函数的构造性充分条件，并给出了逼近精度与模糊规则条数之间关系的显式表达式
• The paper combines artificial neural network , fuzzy inference system , system identification , and does a thorough research on fuzzy - neural network . the research results are as follows : in this paper , we propose a new neuro - fuzzy systems with laplace ( probability density function ) membership function , and proved its universal approximation property by using weierstrass theorem . we get excellent modeling results for nonlinear systems by applying the new neuro - fuzzy model
  本文融合了人工神经网络、模糊推理系统、系统辨识等理论，并围绕神经网络和模糊推理的结合体? ?模糊神经网络，展开了深入地研究，主要完成了如下研究工作：本文提出一种新型的带laplace (概率密度函数)型隶属函数的模糊神经网络模型，并应用微分中值定理和weierstrass定理证明它的通用逼近性。
• ( 1 ) the paper has studied the contractive mapping genetic algorithm , which can be converged to a global optimal solution proved by fixed - point theorem of banach space . it remedies the shortage of standard genetic algorithm . furthermore , the paper discusses the genetic operation in the algorithm such as the coding , select , cross over and mutation etc . it will be help to the next work about fusion with the neural network
  本文融合神经网络技术和遗传算法，对轨道交通引起的地面振动进行了正分析和反演，并利用计算机技术实现了地面振动的三维动画模拟，这主要包括： ( 1 )研究了压缩映射遗传算法，利用banach空间的不动点定理证明了压缩映射遗传算法可以收敛到全局最优值，弥补了标准遗传算法不能收敛至全局最优值的不足。
• Both positive diffusive coefficients and some zero diffusive coefficient cases are considered . finally , for partial decoupling systems , such as competitive - cooperative model with time delay and delayed epidemic model , we employ the new cross - iteration method , together with schauder fixed point theorem , to establish the existence of traveling wave solutions . both partial quasi - monotonicity and partial non - quasimonotonicity cases are considered separately
  对于时滞格微分方程，利用schauder不动点定理证明了其波前解的存在性，减少了对上解的限制条件，给出了上、下解在有限个点不连续时，行波解存在的条件；并将时滞反应扩散方程的结论推广到相应的时滞格微分方程组上。
• Studying on the shakedown theories and plastic deformation of contact surface layer the shakedown of contact surface layer is related to the strain - hardening models of materials , such as isotropic hardening , kinematic - hardening , and mixed - hardening . the existing results based on experiments and theory show that the shearing strain behavior of contact surface layer caused by friction can be comparatively described with kinematic - hardening
  研究中，围绕强化后接触表面疲劳问题，从强化模型选择、接触表层安定性存在的条件及其失效规律，进行了详细的概念定义、定理证明及推论演算等理论工作，为接触表面层安定性的数值模拟和疲劳分析奠定了理论基础。
• Several widely used uncertainty measures based on rough set theory and information entropy are compared and analyzed . we prove that these measures exist inconsistency in evaluating uncertainty of rules and give a necessary condition of occurring the inconsistency . the further direction of building more efficient uncertainty measure is also proposed
  对目前广泛应用的基于粗集理论和信息熵的几种规则不确定性度量准则进行了比较分析，通过定理证明了它们之间存在不一致性以及发生不一致时的必要条件，提出了下一步构建更有效的不确定性度量的方向。
• Finally , this paper introduces the concepts of subl - cusl , algebraic subl - domain , l - cusl embedding and projection pair for domains . making use of the representation theorem for algebraic l - domains , this paper proves that the category of algebraic l - domains with projection pairs for domains as morphisms is eqivalent to the category of l - cusls and l - cusl embeddings
  最后，本文引入了子l - cusl ，子代数l - domain ， l - cusl嵌入和domain上的投射对等相关的几个概念，并通过代数l - domain的表示定理证明了以l - cusl为对象， l - cusl嵌入为态射的范畴lcusl ~ *与以代数l - domain为对象， domain上的投射对为态射的范畴aldom ~ *是等价的两个范畴。
• The thesis consists of four sections . in section one , we introduce some background of the topic , in section two we review some basic and recent results about the structure and hierarchies of the computably enumerable degrees which are closely related to our topic - the algebraic structure of the plus cupping turing degrees , in section three , we outline the basic principles of the priority tree argument , one of the main frameworks and tools of theorem proving in computability theory , and in section four , we prove a new result concerning the algebraic structure of the plus cupping turing degrees that there exist two computably enumerable degrees a , b such that a , b ? pc , and the join a v b of a and b is high
  本篇论文分为4个部分：第一部分介绍了这个领域的一些背景知识；第二部分主要回顾了前人在研究可计算枚举度的结构和层谱时所取得的一些基本和最新结果，这些结果与我们的主题?加杯图灵度的代数结构密切相关；在第三部分中，我们概要的描述了优先树方法的基本原理，此方法是可计算性理论中定理证明的一个重要框架和工具；第四部分证明了一个加杯图灵度代数结构的新结果：存在两个可计算枚举度a ， b ，满足a ， b pc ，而且a和b的并a b是一个高度。