| Project/Area Number |
13640137
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokai University |
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Principal Investigator |
URABE Masatsugu Tokai University, School of Marine Science and Technology, Associate Professor, 海洋学部, 助教授 (30256177)
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| Co-Investigator(Kenkyū-buntansha) |
HOSONO Kiyoshi Tokai University, Scool of Science, Associate Professor, 理学部, 助教授 (40238754)
FUJU Nobuhiko Tokai University, Scool of Science, Professor, 理学部, 教授 (60228955)
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| Project Period (FY) |
2001 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2001: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | Mathematics / Applied Mathematics / Combinatorics / Combinatorial Geometry / Discrete Geometry / Convex Decomposition / Point Set / Erdos-Szekeres / 計算幾何学 |
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| Research Abstract |
We have studied some combinatorial properties on convex polygons by a given point set in the research project ; giant-in-aid for scientific research (C)(2). In particular, we studied the following five problems.
1.Partitioning a point set into convex polygons : In our paper "On a partition into convex polygons" which has accepted to DAM in 1996, we introduced some partitioning properties ; disjoint partition, empty partition and general partition. In 2001. we have succeeded to improve the bound for disjoint partition problem with Professor K.Hosono who is one of the investigators in this research project. About empty partition, we also improved the bounds after we attended the International Congress of Mathematicians 2002 in China. We gave the talk concerning this topic on the other international conference in 2002, and this paper was accepted.
2.On the existence of a convex polygon with a specified number of interior points : The paper about this topics was accepted to DM in 2001, and w
… More
e studied more the existence of such convex polygon with K.Hosono and G.Karolyi who is a Hungarian mathematician. In 2001, we talked around it, and this manuscript was accepted to Discrete Geometry (A.Bezdek ed.) in 2003.
3.On the number of disjoint convex k-gons for a planar point set : We estimated the number of convex k-gons for a planar point set. For a convex quadrilateral, in particular, we studied, and the paper accepted in 2001. In this paper, we introduced useful partitioning method for a given point set, and then the number of convex quadrilaterals is increase in the above problem 1.
4.On convex decompositions of points : We seek a partition of a given point into convex cells such that the union of the cells forms a simple polygon and every point is on the boundary. The paper concerning this topics was accepted the international journal in 2001.
5.On a triangle with the maximum area in a planar point set : After I attended the international conference in 2002, I studied this problem with some colleagues in our private seminar. It is the problem about the ratio between the maximum area of an empty triangle with vertices in a planar point set and the area of the convex hull of the points. We gave the talk about this problem in the Indonesia -Japan joint conference in 2003, and submitted this manuscript. Less
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