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標題: 空間的尺度分析 (I)
Dimensional Analysis in Mathematics (I)
作者: 盧俊豪
Lu, Jun-Hao
關鍵字: Dimensional Analysis
出版社: 應用數學系所
引用: [1] Tom M. Apostol., Mathematical Analysis (2nd ed.), Addison-Wesley, 1974. [2] Richard L. Wheeden. and Antoni Zygmund., Measure and Integral: an introduction to Real Analysis, New York: Marcel Dekker, 1977. [3] H. L. Royden., Real Analysis (3rd ed.), New York: Macmillan, 1988. [4] Gerald B. Folland., Real Analysis: modern techniques and their applications, New York: Wiley, 1984. [5] Frank Jones., Lebesgue Integration on Eucliden spaces, Boston: Jones and Bartlett, 1993. [6] John B. Fraleigh., A first course in abstract algebra (4th ed.), Addison-Wesley, 1989. [7] P. W. Bridgman., Dimensional Analysis, New York: AMS Press, 1978. [8] Chi-Kun Lin., Applications of dimensional analysis to differential equations, inequalities and the related topics, Department of applied Mathematics National Chiao Tung University. [9] J. M. Marstrand., The dimension of Cartesian product sets, Proc. Cambridge Philos. Soc. 50, (1954). 198-202. [10] Donald L. Cohn., Measure theory, Boston: Birkhauser, 1980.
摘要: P. W. Bridgman 在其所著的Dimensional Analysis [7]書中提出以下物理觀點: "物理上Dimensional Analysis 之目的在於能夠找出各種可測量物體或物理現象的相關 性"。在本篇論文中,我們從這個物理觀念中導出數學完備賦距空間的尺度,以期建立 一套數學空間尺度分析的嚴密理論。
In this thesis, we introduce the dimensional analysis to mathematics from the concept in physics which is “The purpose of dimensional analysis is to give certain information about the relations which hold between the measurable quantities associated with various phenomena.” (See P. W. Bridgman [7], p17.). Thus, the purpose of our study is to establish theoretic theory of the dimensional analysis in mathematics.
其他識別: U0005-0106200910514900
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