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be critical keys to understanding of the collisional and dynamical evolution
of the main belt asteroids.
Acknowledgments
A large part of the result presented in this paper is based on our observa-
tions with the VATT (the Alice P. Lennon Telescope and the Thomas J.
Bannan Astrophysics Facility). We thank Elizabeth Green, Paula White,
Ed Olszewski and Andy Odell for our observing use at the Steward 90-inch
telescope. The authors owe a lot to many people who helped us observe
and analyze our asteroid data: Shigeru Takahashi, Mansur A. Ibrahimov,
Budi Dermawan, Tsuko Nakamura, Toshifumi Yanagisawa, Masanori Hirai,
Seidai Miyasaka, Hideo Fukushima, Hideo Sato, and Yusuke Sato, as well
as Beatrice Mueller who benefited us with stimulating discussions. Two ref-
erees, Alberto Cellino and Maria J. Lopez-Gonzalez, suggested directions
which bettered the quality of this paper a great deal. Detailed and construc-
tive review by Yolande McLean has considerably improved the English pre-
sentation of this paper. This study is supported by the Grant-in-Aid of the
Ministry of Education of Japan (16740259/2004-2005). F.Y. acknowledges
financial support from the Sumitomo Foundation (030755/2003-2004).
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