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现代分析
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  modern analysis
    Nonlinear functional analysis is an important branch of modern analysis mathematics, because it can explain all kinds of natural phenomenon, more and more mathematicans are spending their time on it.
    非线性泛函分析是现代分析数学的一个重要分支,因其能很好的解释自然界中的各种各样的自然现象从而受到了越来越多的数学工作者的关注。
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    Nonlinear functional analysis is an important branch of modern analysis mathematics, because it can explain all kinds of natural phenomenal, more and more mathematics are devoting their time to it.
    非线性泛函分析是现代分析数学的一个重要分支,因其能很好的解释自然界中各种各样的自然现象受到了越来越多的数学工作者的广泛关注。
短句来源
    Based on the above-mentioned study background and compared with the Kolmogorov model used the theory of modern analysis, analytical probability and martingale convergence theory, this paper does the works as following:1. Perfect the properties of the probability on MV-algebra.
    本文与Kolmogorov模型相对比运用了现代分析和分析概率论中的理论内容及鞅的收敛定理,在现有的研究基础上,主要做了下面几个方面的工作: 1.进一步完善了MV-代数中概率测度的性质;
短句来源
    Nonlinear functional analysis is an important branch of modern analysis mathematics, because it can explain all kinds of natural phenomenal, more and more mathematicians are devoting their time to it.
    非线性泛函分析是现代分析数学的一个重要分支,因其能很好的解释自然界中的各种各样的自然现象受到了越来越多的数学工作者的关注。
短句来源
    Functions of real variable is an essential basic theory in modern analysis.
    实变函数论是现代分析必不可少的理论基础 .
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  “现代分析”译为未确定词的双语例句
    Nonlinear functional analysis has been one of the most important branches of learning in modern mathematics at present.
    非线性泛函分析是现代分析数学中的一个重要分支学科,它为解决当今科技领域中出现的各种非线性问题提供了富有成效的理论工具。 在处理实际问题所对应的各种非线性积分方程和微分方程中发挥着不可替代的作用。
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    Nonlinear functional Analysis is an important branch of morderm mathmatics.
    非线性泛函分析是现代分析数学的一个重要分支。
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    During the development of solving such problems, since the 18th century, nonlinear partial differential equations has been one of the most important and active research fields in Modern mathematics.
    自18世纪以来,在解决这些非线性问题的过程中,逐渐形成了现代分析数学中一个非常重要的分支-非线性偏微分方程.它是当今数学界极为活跃的一个方面。
短句来源
    In later years, all sorts of nonlinear problems have resulted from mathematics, physics, chemistry, biology, medicine, economics engineering, cybernetics and so on. During the development of solving such problems, nonlinear functional analysis has been one of the most important research fields in modern mathematics.
    近年来,在数学,物理学,化学,生物学,医学,经济学,工程学,控制论等许多科学领域出现了各种各样的非线性问题,在解决这些非线性问题的过程中,逐渐形成了现代分析数学中一个非常重要的分支-非线性泛函分析。
短句来源
    Nonlinear functional analysis is an important branch of morderm analysis mathmatics, because it can explain all kinds of natural phenomenal, more and more mathematicans are devoting their time to it.
    非线性泛函分析是现代分析数学的一个重要分支,因其能很好的解释自然界中的各种各样的自然现象受到了越来越多的数学工作者的关注。
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  modern analysis
The microstructure of the epoxy resin polymer cement materials was studied and their hydration and hardening characteristics were discussed by means of modern analysis measures such as SEM, XRD and Hg-intrusion micromeritics.
      
Modern analysis of trace elements has been carried out for many years.
      
The prospects of a modern analysis of nanostructure evolution during the processing of polymer materials by means of scattering from synchrotron radiation are demonstrated in examples.
      
Modern analysis techniques on the extended data base are used for further insight.
      
In particular I have tried to emphasize the instability of the Port-Royal semantics - the ways in which their theory of terms vacillates between earlier views and something closer to a modern analysis.
      
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This paper analyses and compares with the three typical sorts of division of a circle.They were made respectively by Chinese Liu Hui, Japanese Seki and Greek Heron. Particularly, We give a new explanation to the "in formation" of liu Hiu's notes. By using modern anlysis (which is similar to Heron's method), the circumference formula defined by Liu Hui and Seki is strictly proved. The precision of their formula is estimated. It is remarkable , that the method used by Liu Hui and Seki to improve the precision,...

This paper analyses and compares with the three typical sorts of division of a circle.They were made respectively by Chinese Liu Hui, Japanese Seki and Greek Heron. Particularly, We give a new explanation to the "in formation" of liu Hiu's notes. By using modern anlysis (which is similar to Heron's method), the circumference formula defined by Liu Hui and Seki is strictly proved. The precision of their formula is estimated. It is remarkable , that the method used by Liu Hui and Seki to improve the precision, cortains the idea of extrapolation to the limit which was appeared anly in the beginning of this century.

本文对我国刘徽、日本关孝和及希腊海伦三位古代数学家在圆周率研究中的三种典型的割圆术作了分析比较.尤其是刘徽注中所说的“消息”一词作出了一种新的解释.对刘徽、关孝和的思想所定义的圆周长,以现代分析所常用的圆周长的定义为基础(即与海伦类似的方法)作了严格的证明.并对刘徽和关孝和的公式作了精度估计.文中指出了刘徽和关孝和的割圆术中提高精度的做法已具有本世纪初才提出的外推极限法思想.

In this paper, we put forward and prove theorme 1 of the paper, which is ra-tional popularization about fermat theorem of classical analysis in modern analysis. Throughtheorme 1, we give a condition of that mid-value formula is true in medern analysis. Inaddition, we point out that mid - value formula is not true in modern analysis. Combining every items of the contents, we explain the reason why mid - value formula is not true inmedern analysis.

本文给出并证明了文中的定理1,该定理是经典分析中的Fermat定理在现代分析学中的合理推广。据此又给出了一个中值公式在抽象分析中成立的充分条件。最后,指出了经典分析中的中值定理在抽象分析中不成立。文中各项内容相结合,较深刻地说明了中值定理在抽象分析学中不成立的原因。

Let E and F be Banach spaces, and f:UE→F be a C 1 map where U is an open set in E . It is well known that the set of all of regular points of f is an open set in E . Since the concept of locally fine point, which is the generalized regular point, was introduced, many problems in nonlinear functional analysis have been solved, such as the conjugacy problem, the rank theorem in advanced calculus and so on. So locally fine point is a significant concept to take the place of regular...

Let E and F be Banach spaces, and f:UE→F be a C 1 map where U is an open set in E . It is well known that the set of all of regular points of f is an open set in E . Since the concept of locally fine point, which is the generalized regular point, was introduced, many problems in nonlinear functional analysis have been solved, such as the conjugacy problem, the rank theorem in advanced calculus and so on. So locally fine point is a significant concept to take the place of regular points. In this paper, it is proved that the set of all of the locally fine points of f in U is also an open set in E .

设 E和 F是 Banach空间 ,让 f是定义在 E中开集 U到 F的一个 C1映射。非线性泛函分析中一个著名的结果是 f的正则点全体是 E中的一个开子集。f 的局部精细点概念是 f 的正则点的推广。由于它的引进解决了许多非线性泛函分析的问题 ,如局部共轭定理和现代分析学中的秩定理等等。因此局部精细点的概念是代替正则点的一个重要的概念。经讨论证明 ,f在 U中的局部精细点全体也是 E中的一个开子集

 
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