New Development of Singularity Theory
| Project/Area Number |
17K05245
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Yokohama National University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
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| Keywords | ウルフ図形 / フロンタル / 距離二乗写像 / 持ち上げ可能ベクトル場 / 特異点 / 可微分写像 / 球面双対変換, / isometry, / 球面ウルフ図形， / ウルフ図形， / Kato's chaos, / orthotomic, / anti-orthotomic, / フロンタル． / 球面双対変換 / ヤコビアン二乗関数芽 / 一般化された距離二乗写像 / Lowerable vector field / Convex integrand / 安定写像 / convex integrand |
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| Outline of Final Research Achievements |
I studied topics in each of the following five projects. Although three fiscal years was a relatively short period, I succeeded to obtain the result of publishing as many as 12 peer-reviewed papers during the research period of this study. Moreover, since eight of the above 12 papers are international co-authored papers, I can say that the original purpose of this study "To develop Singularities Theory in a new way with an emphasis on international joint research" was achieved.
(1) Studies on Wulff shapes and related topics from the viewpoint of Singularity theory. (2) Studies on distance-squared mappings and related topics. (3) Studies on liftable vector fields and related topics. (4) Studies on special mappings derived from Singularity Theory from the viepoint of Chaos Theory. (5) Studies on applications of frontal.
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| Academic Significance and Societal Importance of the Research Achievements |
上記の五つの研究プロジェクトのうち「（１）ウルフ図形とその周辺の特異点論的研究」と「（２）距離二乗写像とその周辺」のプロジェクトは，世界的にみても同様の研究が見当たらない状況の中で注目を集めつつあり，十分な学術的意義がある，と言える．
また,「（５）フロンタルの応用の研究」はフロンタルの新しい研究方向を切り開くものであり，表面科学等に新しい知見を与えるとともに，数学以外の分野にフロンタルの重要性を知らしめることとなった意義を持つ．
尚，いずれの研究プロジェクトにおいても，既存の特異点論には存在しない観点からの研究が実践されており，特異点論の有用性を拡大した意義もある．
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Report
(4 results)
Research Products
(31 results)
