| Project/Area Number |
12640167
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | GIFU UNIVERSITY |
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Principal Investigator |
TAKEUCHI Shigeru Gifu University, faculty of education, professor, 教育学部, 教授 (30021330)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIMOTO Yoshio Gifu University, faculty of education, associate professor, 教育学部, 助教授 (90192731)
SHIMIZU Satoru Tohoku University, graduate school, associate professor, 大学院・理学系研究科, 助教授 (90178971)
HATADA Kazuyuki Gifu University, faculty of education, professor, 教育学部, 教授 (40144000)
YAMADA Masahiro Gifu University, faculty of education, associate professor, 教育学部, 助教授 (00263666)
AIKI Toyohiko Gifu University, faculty of education, associate professor, 教育学部, 助教授 (90231745)
志賀 潔 岐阜大学, 工学部, 教授 (10022683)
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| Project Period (FY) |
2000 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2003: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2002: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2001: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2000: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | CR LIE GROUP ACTION / CR LIE ALGEBRA / LINEAR CR LIE GROUP / CR ADAPTED COMPLEXIFICATION / CATEGORY OF GROUP ACTION / CR GROUP MANIFOLD / CATEGORICAL COMPLEXIFICATION / CR REAL FORM / CR実形式 / 無限次元CRベクトル空間 / 双対カテゴリー / 複素化 / 圏論的単射 / 圏論的像 / 圏論的全射 / CR多様体 / CR関数空間 / CRベクトル空間 / CR写像 / CRカテゴリー / カテゴリ的複素化 / カテゴリ的単射 / カテゴリ的像 / カテゴリ的全射 / CR接空間 |
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| Research Abstract |
(1)Takeuchi studied the basic relations of the CR structures of the manifolds and its adapted complexifications or CR forms from categorical points of view, and obtained some affirmative results on epics, monics and images in the CR category. He also studied the serious situations in mathematics education not only in Japan but also world wide, e.g in Latin America and south east Asia.
(2)Kazuyuki Hatada studied metric properties of geometric simplices and generalized the formula among the ditance of the point in a triangle from the vertices to higher dimensional simplices. He also studied p-adic properties of p-adic limits of sequences defined by norms and traces of algebraic integers and p-adic modular forms.
(3)Shimizu studied the holomorphic vector fields of tube domains and obtained the criterion of the their completeness, clarified the their Lie algebra structures solved the holomorphic equivalence problem affirmatively and gave a characterization of a certain type of Stein manifolds by their automorphism groups.
(4)Fujimoto proved if a nonsingular projective 3-fold of non-negative Kodaira dimension admits a non trivial endomorphism, its finite unramified covering to be a smooth family of abelian varieies and gave a sufficient condition for an endornorphism of the product manifold of a minimal variety X with a non minimal one Y to split into product for the case of 3-dimensional Y.
(5)Aiki studied the models for shape memory alloys described by subdifferentials of indicator functions, obtained the existence and uniqueness of the solution of one-phase Stefan problems with nonlinear boundary conditions described by maximal monotone operators.
(6)Yamada, analyzing the Carleson inequality, obtained more general results than before and introduced the similar condition corresponding to the (A_p) one in Bergman space, which is the Banach space of harmonic functions.
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