Through weierstrass circle of students the importance of uniform convergence was made known . 通过威阿斯塔斯周围的学生，人们知道了一致收敛性的重要性。
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Uniform approximation for combinations of gauss - weierstrass operators 算子线性组合的一致逼近
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In 1869 charles m ray , the french counterpart of weierstrass , gave a definition of the irrationals 1869年charles meray ，作为weierstrass的法国对等人物，给出无理数的一个定义。
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Fortunately , we have contrived mathematics in which the definition of limit is given by great mathematicians louis cauchy and weierstrass , and what surprises us is that the demon has a seraphic appearance 这个“魔鬼”无处不在，数学家们历经千年的磨砺，直到19世纪柯西和魏尔斯特拉斯给出极限的精确定义，才完成“降魔”过程，令人惊异的是它竟然有着天使一样美丽的脸庞。
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Futhermore , fractal analysis has achieved some important development . several fractal functions , such as the weierstrass functions , the besicovitch functions , the rademacher functions , the takagi functions , etc , and their graph dimensions and fractal properties are investigated extensively due to the special fractal structures 几个分形函数， weierstrass函数， besicovitch函数， rademacher函数， takagi函数等，由于它们所特有的分形性质，在分形研究中占有重要地位，因此，它们的分形维数、图象模拟的研究，也成为当前的重要课题。
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( 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
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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。
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The combination of fractional calculus with fractal analysis , in other words , appling fractional calculus to analyze fractal structures of graphs of some special functions , is a crucial problem in this direction . the present paper mainly investigates the relationship between the fractional calculus and the fractal functions 第二章研究一类weierstrass函数w ( t ) 、它的分数阶积分函数g ( t ) 、分数阶微分函数n ( t )的图象的维数估计，以及besicovitch函数图象的维数与分数阶微积分的关系。
