查询词典 weierstrass point

Comprehensively analysis of the notes of Weierstrass\' students on the lecture of "Introduction to analytic function", function theoretic system is clearly reconstructed.

详尽分析了魏尔斯特拉斯学生的"解析函数导论"课堂笔记，更加清晰地重构魏尔斯特拉斯函数理论体系。

Focus on the origin of Weierstrass\' Complex Analysis, considering to external and internal causes are the development of complex function in 19~ century reviewed, and three basic approaches lead to complex analysis, namely, algebraic analysis, integral and geometry are introduced.

指出了德国数学组合分析与古德曼的级数工作以及分析严格化要求的共同影响，构成了魏尔斯特拉斯发展复变函数理论的动机。2。

Its universal approximation has been proved by using differential intermediate value theorem and Weierstrass theorem.

笔者采用微分中值定理和Weierstrass定理证明它的通用逼近性。

The contents of the abstract of the short Communication is:"The paper gives a complete differential partition to a Euclidean straight line with a fixed frame, and three axioms for the integral of infinitesimals indexed by real numbers; proves in standard mathematics there are positive infinitesimals outside of real number set; Gives cosmic, macro and micro counterexamples to two axioms in Jordan, Carathéodory, and Lebesgue measure theory; transforms Weierstrass limit into Huang limit, Cantor continuum into Huang continuum, and Newton-Leibniz formula into Huang formula."

这个短的发言的摘要的内容如下："此文对一条确定了固定标架的欧几里德直线给出了完整的微分分拆，并对以实数为标号的无穷小的积分给出了三条公理；在标准数学中证明了在实数集合之外存在正的无穷小；对若当，卡拉特欧多里和勒贝格测度论中的两条公理给出了宇观的，宏观的和微观的反例；将外尔斯特拉斯极限改进为黄氏极限，将康托连续统改进为黄氏连续统，和将牛顿－莱布尼茨公式改进为黄氏公式。"

If one makes some omissions in Chapter 4, for example, the proof of the theorem of Lindemann—Weierstrass, one is likely to have several weeks left after the completion of this material.

并且在讲授过程中可以不讲引言中有关递归定理的证明，第一章的有关自由群的小节，第二章和第三章的最后一节。

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。

These rough surfaces have been analyzed by a fractal theory,and a three-dimensional Weierstrass-Mandelbrot function has been used to simulate the topographies of the rough surfaces.

这些参数是基于所测样品大小和仪器测量精度得出的，而分形理论的处处连续不可导及其自相似性则显示出了很好的互补特性[3，4]。

The contents of the abstract of the short Communication is:"The paper gives a complete differential partition to a Euclidean straight line with a fixed frame, and three axioms for the integral of infinitesimals indexed by real numbers; proves in standard mathematics there are positive infinitesimals outside of real number set; Gives cosmic, macro and micro counterexamples to two axioms in Jordan, Carathéodory, and Lebesgue measure theory; transforms Weierstrass limit into Huang limit, Cantor continuum into Huang continuum, and Newton-Leibniz formula into Huang formula."

这个短的发言的摘要的内容如下：&此文对一条确定了固定标架的欧几里德直线给出了完整的微分分拆，并对以实数为标号的无穷小的积分给出了三条公理；在标准数学中证明了在实数集合之外存在正的无穷小；对若当，卡拉特欧多里和勒贝格测度论中的两条公理给出了宇观的，宏观的和微观的反例；将外尔斯特拉斯极限改进为黄氏极限，将康托连续统改进为黄氏连续统，和将牛顿－莱布尼茨公式改进为黄氏公式。&

Solveing to some extent problem to define hidden layer node number of feed forward networks,and makeing successfully it to apply to solve weierstrass theorem of that is polynomial approach continuous function;and establishing dynamic mathematical neural networks of Romberg integration.

从而在一定程度上解决了前向神经网络隐层结点数无法确定的难题，并成功地将其运用于解决用多项式逼近连续函数的魏尔斯特拉斯定理，并建立了龙贝格求定积分的动态数学神经网络模型。

Sb can combine with Cu and P to form a low melting point compound which lowers the melting point of binary Cu-8P eutectic alloy by nearly 200℃. Bi and Cu can create compounds with low melting point(270℃) distributing at the boundaries and that is the reason why the melting point of (Cu-8P)-Bi is lower than that of binary Cu-8P eutectic alloy. The eutectic cluster can be refined with the addition of Fe, and that is the reason why the addition of Fe can decrease the melting point of Cu-8P alloy. Two means of decreasing the melting point of Cu-8P are found.

一定量的Sb与Cu， P形成低熔点相，从而大幅降低了Cu-8P合金的熔点，使其熔点降低近200℃；加入少量Bi后， Bi与Cu在共晶团晶界上形成熔点为270℃左右的低熔点化合物，且Bi的加入明显细化Cu-8P合金共晶团，从而使Cu-8P合金的熔点降低；加入Fe能明显细化Cu-8P合金的共晶团，使层片间距由8μm减为2μm以下，并使共晶团由层片状向短棒状转变，虽然Fe与Cu形成熔点为806℃的高温相，但Fe的细化作用使得Cu-8P合金的熔点降低，但降低幅度不大。

The receding calculations and experiment analyses in this subject are built on the blood cast of pig tongue.

本研究课题的前期工作是采用猪舌血管铸型模拟人舌而进行的数值计算与实验分析。

"Each human infection constitutes an opportunity for genetic modification of the virus through reassortment, mutation, or both...."

&每一次人类的感染都暗藏着一次基因修改的机会，无论是通过病毒的整合、突变或者兼而有之。。。。&