Please use this identifier to cite or link to this item:
https://ah.lib.nccu.edu.tw/handle/140.119/32582
DC Field | Value | Language |
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dc.contributor.advisor | 陳天進 | zh_TW |
dc.contributor.advisor | Chen, Ten-Ging | en_US |
dc.contributor.author | 陳耿彥 | zh_TW |
dc.contributor.author | Chen, Keng-Yan | en_US |
dc.creator | 陳耿彥 | zh_TW |
dc.creator | Chen, Keng-Yan | en_US |
dc.date | 2007 | en_US |
dc.date.accessioned | 2009-09-17T05:47:35Z | - |
dc.date.available | 2009-09-17T05:47:35Z | - |
dc.date.issued | 2009-09-17T05:47:35Z | - |
dc.identifier | G0093751501 | en_US |
dc.identifier.uri | https://nccur.lib.nccu.edu.tw/handle/140.119/32582 | - |
dc.description | 博士 | zh_TW |
dc.description | 國立政治大學 | zh_TW |
dc.description | 應用數學研究所 | zh_TW |
dc.description | 93751501 | zh_TW |
dc.description | 96 | zh_TW |
dc.description.abstract | 在這篇論文裡,我們利用值分佈的理論來探討半純函數的共值與唯一性的問題,本文包含了以下的結果:將Jank與Terglane有關三個A類中的半純函數唯一性的結果推廣到任意q個半純函數的情形;證明了C. C. Yang的一個猜測;建構了一類半純函數恰有兩個虧值,而且算出它們的虧格;將\nNevanlinna 五個值的定理推廣至兩個半純函數部分共值的情形;探討純函數\n與其導數的共值問題;最後,證明了兩個半純函數共四個值且重數皆不同的定\n理。 | zh_TW |
dc.description.abstract | In this thesis, we study the sharing value problems and the\nuniqueness problems of meromorphic functions in the theory of value distribution. In fact, this thesis contains the following results: We generalize a unicity condition of three meromorphic functions given by Jank and Terglane in class A to the case of arbitrary q meromorphic functoins. An elementary proof of a conjecture of C. C. Yang is provided. We construct a class of meromorphic functions with exact two deficient values and their deficiencies are explicitly computed. We generalize the Nevanlinna`s five-value theorem to the cases that two meromorphic functions partially share either five or more values, or five or\nmore small functions. In each case, we formulate a way to measure how far these two meromorphic functions are from sharing either values or small functions, and use this measurement to prove a uniqueness theorem. Also, we prove some uniqueness theorems on entire functions that share a pair of values (a,-a) with their derivatives, which are reformulations of some important results about uniqueness of entire functions that share values with their derivatives. Finally, we prove that if two distinct non-constant meromorphic functions $f$ and $g$ share four distinct values a_1, a_2, a_3, a_4 DM such that each a_i-point is either a (p,q)-fold or (q,p)-fold point of f and g, then (p,q) is either (1,2) or (1,3) and f, g are in some particular forms. | en_US |
dc.description.tableofcontents | 謝辭......................................................i\n\nAbstract................................................iii\n\n中文摘要..................................................iv\n\n1 Introduction............................................1\n\n2 Basic Theory of Value Distribution......................4\n\n 2.1 Poisson-Jensen`s Formula............................4\n\n 2.2 The Nevanlinna`s First Fundamental Theorem..........6\n\n 2.3 The Nevanlinna`s Second Fundamental Theorem.........8\n\n 2.4 The Estimation of S(r,f)............................9\n\n 2.5 Deficient Value of Meromorphic Functions...........12\n\n 2.6 Some Well-Known Results on Four Value Problem......13\n\n3 Unicity of Meromorphic Functions of Class A............15\n\n 3.1 Introduction.......................................15\n\n 3.2 Some Facts About Meromorphic Functions of Class A..17\n\n 3.3 Main Results and Proofs............................18\n\n 3.4 A Conjecture.......................................20\n\n4 On a Conjecture of C. C. Yang..........................22\n\n 4.1 Introduction.......................................22\n\n 4.2 Some Lemmas........................................24\n\n 4.3 Main Result and Proof..............................25\n\n5 The Deficient Values of a Class of Meromorphic Functions\n .......................................................28\n\n 5.1 Introduction.......................................28\n\n 5.2 The Deficient Values of Rational Functions.........30\n\n 5.3 The Proof of Theorem A.............................31\n\n 5.4 The Proof of Theorem B.............................35\n\n6 Some Generalization of Nevanlinna`s Five-Values Theorem \n .......................................................41\n\n 6.1 Introduction.......................................41\n\n 6.2 Meromorphic Functions Partially Share Values.......43\n\n 6.3 Meromorphic Functions Partially Share Small Functions\n ...................................................45\n\n7 On the Uniqueness of Entire Functions and Their \n Derivatives............................................49\n\n 7.1 Introduction.......................................49\n\n 7.2 Lemmas and Known Results...........................50\n\n 7.3 Main Results and Proofs............................52\n\n8 Some Results on Meromorphic Functions Sharing Four Values\n DM.....................................................65\n\n 8.1 Introduction.......................................65\n\n 8.2 Key Examples and Facts.............................66\n\n 8.3 Main Result and Proof..............................68\n\nReferences...............................................69 | zh_TW |
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dc.language.iso | en_US | - |
dc.source.uri | http://thesis.lib.nccu.edu.tw/record/#G0093751501 | en_US |
dc.subject | 值分佈理論 | zh_TW |
dc.subject | 半純函數 | zh_TW |
dc.subject | value distribution theory | en_US |
dc.subject | meromorphic function | en_US |
dc.title | 半純函數的唯一性 | zh_TW |
dc.title | Some Results on the Uniqueness of Meromorphic Functions | en_US |
dc.type | thesis | en |
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item.languageiso639-1 | en_US | - |
item.fulltext | With Fulltext | - |
item.openairecristype | http://purl.org/coar/resource_type/c_46ec | - |
item.grantfulltext | open | - |
item.openairetype | thesis | - |
item.cerifentitytype | Publications | - |
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