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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 王藹農 | |
dc.contributor.author | Yi-Yu Lin | en |
dc.contributor.author | 林羿佑 | zh_TW |
dc.date.accessioned | 2021-06-17T03:25:19Z | - |
dc.date.available | 2018-05-31 | |
dc.date.copyright | 2018-05-31 | |
dc.date.issued | 2018 | |
dc.date.submitted | 2018-05-22 | |
dc.identifier.citation | 1.G.Hardy,J.E.Littlewood&George Pólya,Inequalities,2nd,cambridege university press,Cambridge,1952.
2.嚴鎮軍,史濟懷,高中數學競賽教程,初版,九章出版社,台北市,1993。 3.胡大同,嚴鎮軍,國際數學奧林匹克大陸隊訓練教材,二版,九章出版社,台北市,1993。 4.Robert V.Hogg,Elliot A. Tanis,Probability And Statistical Inference,7th,Pearson Education,New Jersy,2006. 5.Tom M.Apostol,Mathematical Analysis,2 nd,Pearson Education Taiwan,Taipei,2005. 6.Salas ,Hill, Etgon,Calculus,9th,John Wiley & Sons,Hoboken,2003. 7.維基百科擬群。取自https://zh.wikipedia.org/wiki/%E6%8B%9F%E7%BE%A4 8.維基百科最小平方法。取自https://zh.wikipedia.org/wiki/%E6%9C%80%E5%B0%8F%E4%BA%8C%E4%B9%98%E6%B3%95 9.維基百科迭代冪次。取自https://zh.wikipedia.org/wiki/%E8%BF%AD%E4%BB%A3%E5%86%AA%E6%AC%A1 10.維基百科超運算。取自 https://zh.wikipedia.org/wiki/%E8%B6%85%E8%BF%90%E7%AE%97 11.Wikipedia,Stein method, Retrieved from https://en.wikipedia.org/wiki/Stein%27s_method 12.Stackexchange0-norm https://math.stackexchange.com/questions/13125/what-is-the-0-norm | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/69724 | - |
dc.description.abstract | 我發現不同的平均型不等式可以嵌入到微積分裡,形成它們獨特的積分公式,微分公式,均值定理,泰勒展式,黎曼分割。以及離散統計量,連續統計量,範數皆可如此構造。平均型不等式、積分型算子、微分型算子、黎曼分割、離散統計量、連續統計量、範數這七種結構會形成一一對應關係。並且可以做維度的推廣。
第一部分描述嵌入可以形成微積分空間,第二部分描述第一部分可以自然誘導出加減乘除的推廣,第三部分描述一種新方法可以用作統計函數的擬合。 | zh_TW |
dc.description.abstract | I found that inequalities can be embedded in Calculus to form their unique theorems such as its integration, differentiation, Mean-Value Theorem, Taylor Expansion, Riemann partition. And discrete statistics, continuous statistics and norms can also embedded. Average type inequalities, integration operators, differential operators, Riemann partitions , discrete statistics, continuous statistics ,and norms will have one-one onto correspondence. And it can have higher dimension extension. The first part states the embedding which forms Calculus space, the second part states the first part can naturally induce extension of addition, subtraction, multiplication, and division. And the third part states a method which can handle probability distribution fitting. | en |
dc.description.provenance | Made available in DSpace on 2021-06-17T03:25:19Z (GMT). No. of bitstreams: 1 ntu-107-R03221014-1.pdf: 1308337 bytes, checksum: add8aae2cb7277c08752dd7c3c34147b (MD5) Previous issue date: 2018 | en |
dc.description.tableofcontents | 口試委員會審定書 ………………………………………………………………………………. i
誌謝 ………………………………………………………………………………. ii 中文摘要 ………………………………………………………………………………. iii 英文摘要 ………………………………………………………………………………. iv 第一章 Introduction…………………………………………………………………………….. 1 第二章 Part I Analysis …………………………………………………. 3 第三章 Part II Algebra …………………………………………………. 10 第四章 Part III Statistic ………………………………………………… 33 第五章 Conclusion ………………………………………………… 44 參考文獻 ……………………………………………………………….. 45 附錄……………………………………………………………………………………………………….. 46 | |
dc.language.iso | en | |
dc.title | 微積分的推廣,加減乘除的推廣,以及統計擬合 | zh_TW |
dc.title | The Extension of calculus, Extension of Addition, subtraction, multiplication, division and probability
distribution fitting | en |
dc.type | Thesis | |
dc.date.schoolyear | 106-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 張海潮,夏俊雄 | |
dc.subject.keyword | 算子,平均數,不等式,超冪運算,低超冪運算,迭代冪次,擬群, | zh_TW |
dc.subject.keyword | operators,average,inequalities,hyperoperations,lower hyperoperations,Tetration,quasigroup, | en |
dc.relation.page | 80 | |
dc.identifier.doi | 10.6342/NTU201800843 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2018-05-23 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 數學研究所 | zh_TW |
顯示於系所單位: | 數學系 |
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ntu-107-1.pdf 目前未授權公開取用 | 1.28 MB | Adobe PDF |
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