具有平衡結構的多重組合型 Stokes 定理 Multiple Combinatorial Stokes' Theorem with Balanced Structure

dc.contributor 施茂祥 zh_TW
dc.contributor Mau-Hsiang Shih en_US
dc.contributor.author 陳建宏 zh_TW
dc.contributor.author Chien-Hung Chen en_US
dc.date.accessioned 2019-09-05T01:19:22Z
dc.date.available 2010-6-4
dc.date.available 2019-09-05T01:19:22Z
dc.date.issued 2008
dc.description.abstract 複體組合學在拓撲,非線性分析,賽局論和數理經濟學中扮演非常重要的角色。1967年樊土畿教授使用挨門挨戶原則證明了在擬流形上組合型的 Stokes 定理,1993年施茂祥教授與李是男教授從幾何觀點發展一般位置映射,pi平衡集、pi次平衡集之相關理論,並且利用這些結果來證明在單純形上具有多重集值標號之組合公式,1998年李是男教授與施茂祥教授將樊土畿的組合公式一般化到多重標號,證明具有多重標號組合型的 Stokes 定理,於是我們提出下列問題:是否存在一個統合的定理能包含樊教授與施教授和李教授的結果呢? 在這篇論文中,我們利用關聯函數的方法證明在擬流形上具有平衡結構的多重組合型 Stokes 定理,我們也獲得具有平衡結構的多重組合型 Sperner 引理。 zh_TW
dc.description.abstract Combinatorics of complexes plays an important role in topology, nonlinear analysis, game theory, and mathematical economics. In 1967, Ky Fan used door-to-door principle to prove a combinatorial Stokes' theorem on pseudomanifolds. In 1993, Shih and Lee developed the geometric context of general position maps, -balanced and -subbalanced sets and used them to prove a combinatorial formula for multiple set-valued labellings on simplexes. On the other hand, in 1998, Lee and Shih proved a multiple combinatorial Stokes' theorem, generalizing the Ky Fan combinatorial formula to multiple labellings. That raises a question : Does there exist a unified theorem underlying Ky Fan's theorem and Shih and Lee's results? In this dissertation, we prove a multiple combinatorial Stokes' theorem with balanced structure. Our method of proof is based on an incidence function. As a consequence, we obtain a multiple combinatorial Sperner's lemma with balanced structure. en_US
dc.description.sponsorship 數學系 zh_TW
dc.identifier GN0890400022
dc.identifier.uri http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22GN0890400022%22.&%22.id.&
dc.identifier.uri http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101845
dc.language 英文
dc.subject 擬流形 zh_TW
dc.subject 一般位置映射 zh_TW
dc.subject 組合型Stokes定理 zh_TW
dc.subject 組合型Sperner引理 zh_TW
dc.subject 平衡集 zh_TW
dc.subject 次平衡集 zh_TW
dc.subject 多重集值標號 zh_TW
dc.subject 三角分割 zh_TW
dc.subject pseudomanifold en_US
dc.subject general position map en_US
dc.subject combinatorial Stokes' theorem en_US
dc.subject combinatorial Sperner's lemma en_US
dc.subject balanced set en_US
dc.subject subbalanced set en_US
dc.subject multiple set-valued labelling en_US
dc.subject triangulation en_US
dc.title 具有平衡結構的多重組合型 Stokes 定理 zh_TW
dc.title Multiple Combinatorial Stokes' Theorem with Balanced Structure en_US
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