| Project/Area Number |
18K03414
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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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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Kobe University |
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Principal Investigator |
Sawa Masanori 神戸大学, システム情報学研究科, 准教授 (50508182)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | cubature / 最適実験計画 / ユークリッドデザイン / 再生核 / corner vector method / cubature公式 / 直交多項式 / Euclidean Design / Cubature formula / 応答曲面計画 / Cubature公式 / Euclidean design / 古典直交多項式 / Christoffel-Darboux核 / Sobolevの定理 / D型ワイル群 / 実験計画法 / Fisher型不等式 / 組合せデザイン / 最適計画 / 再生核ヒルベルト空間 / 解析的デザイン理論 |
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| Outline of Final Research Achievements |
This study provides a framework that unifies construction theories of cubature, Euclidean designs and optimum rotatable designs, and makes further progress on the existence problems of such objects. A main research achievement is the development of two basic constructions, namely so-called corner-vector construction and thinning construction for Weyl group of type D, which has been published in some international journals like Graphs and Combinatorics. Another main achievement is the treatise "Euclidean Design Theory", which is the first treatise compiling constructions of optimum designs in the framework of cubature and reproducing kernels, and which has been a reason for 34th Ogawa Prize from the Japan Statistical Society.
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| Academic Significance and Societal Importance of the Research Achievements |
最適デザインに関する専門書の多くは凸最適化とのつながりを意識してまとめられたものであるのに対して，本研究の集大成ともいえる専門書 Euclidean Design Theory (Springer Briefs in Statistics, 2019) は最適デザインの構成理論を再生核やcubatureの枠組みで体系的にまとめたはじめての書であり，最適デザインとその周辺分野に斬新な視点を提供している．本研究の成果の一つに，品質管理などの分野で有用な中心複合計画やボックスベーンケン計画の応答曲面計画としての次数の決定があり，応用上の反響も期待される．
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