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トロピカルNevanlinna-Cartan理論の完成と複素解析的手法への還元
https://doi.org/10.24517/00053761
https://doi.org/10.24517/00053761ea9edba7-e125-49cb-8a26-4968f97fb8a4
名前 / ファイル | ライセンス | アクション |
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TE-PR-TOGE-K-kaken 2017-5p.pdf (186.0 kB)
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Item type | 報告書 / Research Paper(1) | |||||
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公開日 | 2019-03-15 | |||||
タイトル | ||||||
タイトル | トロピカルNevanlinna-Cartan理論の完成と複素解析的手法への還元 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | Formulation of the tropical Navanlinna-Cartan theory and their returns for complex analytic methods | |||||
言語 | ||||||
言語 | jpn | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_18ws | |||||
資源タイプ | research report | |||||
ID登録 | ||||||
ID登録 | 10.24517/00053761 | |||||
ID登録タイプ | JaLC | |||||
著者別表示 |
Toge, Kazuya
× Toge, Kazuya |
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提供者所属 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 金沢大学理工研究域電子情報通信学系 | |||||
書誌情報 |
平成28(2016)年度 科学研究費補助金 基盤研究(C) 研究成果報告書 en : 2016 Fiscal Year Final Research Report 巻 2013-04-01 - 2017-03-31, p. 5p., 発行日 2017-08-25 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | 解析的な函数はそのべき級数表示を通して数学のみならず理工学の幅広い分野で利用されている。それらの多くは複素平面全体に有理型に接続でき、指数函数や楕円函数などの特徴的な方程式の解として与えられる。これら超越函数を統一的に取り扱うためRolf Nevanlinnaが値分布論を完成して90年が経過した。本研究では解析函数のみがこれら応用を実現し得るのかとの問題を、Nevanllinna理論さらにはその正則曲線への拡張であるHenri Cartanの値分布理論を、実数直線上で定義された区分的線型な連続関数と正則曲線の値分布論に変換し、そのmax-plusべき級数展開からも類似した応用可能性を確認した。 | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | There are known many applications of analytic functions not only to mathematics but also to a broad range of fields in science and engineering, where the essential role is played by power series expansion. Actually, most of them are functions which permit meromorphic continuation over the whole complex plane and solve some distinctive equations such as differential equations for exponential or elliptic functions. It was 90 years ago when Rolf Nevanlinna established his theory on value distribution of the tanscendental meromorphic functions. Our study observed the question whether such contributions can be done only with complex analysis or there is a possible replacement of the role. It is our main result that we have formulated the tropical analogues of the complex analytic counterparts as a sort of dictionary in a satisfactly fashion for our purpose. In fact, it is found that there is a chance for similar applications by some tropical entire functions with max-plus series expansion. | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 研究課題/領域番号:25400131, 研究期間(年度):2013-04-01 - 2017-03-31 | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 出典:「トロピカルNevanlinna-Cartan理論の完成と複素解析的手法への還元」研究成果報告書 課題番号25400131 (KAKEN:科学研究費助成事業データベース(国立情報学研究所)) (https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-25400131/25400131seika/)を加工して作成 |
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著者版フラグ | ||||||
出版タイプ | AM | |||||
出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||
関連URI | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://kaken.nii.ac.jp/search/?qm=30260558 | |||||
関連名称 | https://kaken.nii.ac.jp/search/?qm=30260558 | |||||
関連URI | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-25400131/ | |||||
関連名称 | https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-25400131/ | |||||
関連URI | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-25400131/25400131seika/ | |||||
関連名称 | https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-25400131/25400131seika/ |