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      /  一道140年的數學難題獲解決
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註冊日: 2005-09-03
發表數: 48


 一道140年的數學難題獲解決

【大紀元4月1日訊】(大紀元記者郭潔報導)一個難倒數學家們近140年的數學難題,已由倫敦帝國大學一研究員解決。

根據每日科學(ScienceDaily)報導,保角變換(保形映射)將複雜的形狀改為較為簡單的圓形來加以分析,19世紀中葉,兩位數學家合力研究出著名的「舒瓦茲-克里斯托夫公式」(Schwarz-Christoffel formula),進行保形映射的研究。此理論工具的應用相當廣泛,比如在航空學上模擬空氣經過複雜形狀機翼的流態,在神經學上用來顯示人腦複雜的灰色神經組織。

但是「舒瓦茲-克里斯托夫公式」卻有漏洞,不能用於包含孔洞的形狀或者不規則形狀。

倫敦帝國大學(Imperial College London)應用數學系的克勞帝(Darren Crowdy)教授克服了此公式的缺陷,使其適用於更複雜的形狀,因而在工業上的運用將更為廣泛。

source:
http://www.epochtimes.com/b5/8/4/1/n2066258.htm




140-year-old Math Problem Solved

ScienceDaily (Mar. 4, 2008) — A problem which has defeated mathematicians for almost 140 years has been solved by a researcher at Imperial College London. Professor Darren Crowdy, Chair in Applied Mathematics, has made the breakthrough in an area of mathematics known as conformal mapping, a key theoretical tool used by mathematicians, engineers and scientists to translate information from a complicated shape to a simpler circular shape so that it is easier to analyse.

This theoretical tool has a long history and has uses in a large number of fields including modelling airflow patterns over intricate wing shapes in aeronautics. It is also currently being used in neuroscience to visualise the complicated structure of the grey matter in the human brain.

A formula, now known as the Schwarz-Christoffel formula, was developed by two mathematicians in the mid-19th century to enable them to carry out this kind of mapping. However, for 140 years there has been a deficiency in this formula: it only worked for shapes that did not contain any holes or irregularities.

Now Professor Crowdy has made additions to the famous Schwarz-Christoffel formula which mean it can be used for these more complicated shapes. He explains the significance of his work, saying:

"This formula is an essential piece of mathematical kit which is used the world over. Now, with my additions to it, it can be used in far more complex scenarios than before. In industry, for example, this mapping tool was previously inadequate if a piece of metal or other material was not uniform all over - for instance, if it contained parts of a different material, or had holes."

Professor Crowdy's work has overcome these obstacles and he says he hopes it will open up many new opportunities for this kind of conformal mapping to be used in diverse applications.

"With my extensions to this formula, you can take account of these differences and map them onto a simple disk shape for analysis in the same way as you can with less complex shapes without any of the holes," he added.

Professor Crowdy's improvements to the Schwarz-Christoffel formula were published in the March-June 2007 issue of Mathematical Proceedings of the Cambridge Philosophical Society.

Journal reference: 'Schwarz-Christoffel mappings to unbounded multiply connected polygonal regions,' Math. Proc. Camb. Phil. Soc. (2007), 142, 319.

Adapted from materials provided by Imperial College London, via EurekAlert!, a service of AAAS.

source:
http://www.sciencedaily.com/releases/2008/03/080303110214.htm


http://www3.imperial.ac.uk/newsandeventspggrp/imperialcollege/newssummary/news_3-3-2008-15-25-28


http://mathworld.wolfram.com/ConformalMapping.html


Schwarz-Christoffel mapping中文版:
http://zh.wikipedia.org/wiki/%E6%96%BD%E7%93%A6%E8%8C%A8-%E5%85%8B%E9%87%8C%E6%96%AF%E6%89%98%E8%B4%B9%E5%B0%94%E6%98%A0%E5%B0%84

Schwarz-Christoffel mapping英文版:
http://en.wikipedia.org/wiki/Schwarz-Christoffel_mapping

Talk: Schwarz-Christoffel_mapping:
http://en.wikipedia.org/wiki/Talk:Schwarz-Christoffel_mapping


PlaneMath: Schwarz-Christoffel transformation (circular version) :
http://planetmath.org/encyclopedia/SchwarzChristoffelTransformationCircularVersion.html

 2008-04-02 20:42個人資料


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