KUWADA Masahide Hiroshima Univ., Faculty of Integrated Arts and Sciences, Professor, 総合科学部, 教授 (10144891)
FUJIKOSHI Yasunori Hiroshima Univ., Graduate School of Science, Professor, 大学院・教育学研究科, 教授 (40033849)
FUJIHARA Ryoshuku Univ.of Thukuba, Graduate School of System and Information Engineering, Professor, 社会工学系, 教授 (30165443)
JIMBO Masakazu Nagoya Univ., Graduate School of Information Science, Professor, 大学院・情報科学研究科, 教授 (50103049)
MISHIMA Miwako Gifu Univ., Information and Multimedia Center, Associate Professor, 総合情報メディアセンター, 助教授 (00283284)
|Budget Amount *help
¥3,200,000 (Direct Cost : ¥3,200,000)
Fiscal Year 2004 : ¥1,000,000 (Direct Cost : ¥1,000,000)
Fiscal Year 2003 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 2002 : ¥1,100,000 (Direct Cost : ¥1,100,000)
This is a 3-year research project and this year is final. The activity done for the period is summarized as follows. Research results on this project were presented in many conferences (including international conferences on statistics and combinatorics) to communicate with other researchers and then we have received many positive comments or suggestions. Such conferences and meetings are organized, in Japan, at Gifu Univ., Keio Univ., Chiba Univ., Univ.of Tsukuba, Embassy of Poland, Meijou Univ., Fuji.Univ., Meisei Univ., Shimane Univ., Kyoto Univ., Hokkaido Univ., Shirahama and Ise areas, while, outside Japan, at Newcastle Univ. in Australia, Bedlewo in Poland, Portland in USA, Taupo in New Zealand, Guilin in China. Most of them are presented as invited papers. We have obtained many useful and fruitful comments or information to develop our project further during such experience.
Some of our main results are explained below.
1.Some methods of construction are obtained for the following
classes of block designs and combinatorial structures : group divisible designs, diallel crosses for comparative experiments, rectangular designs, difference families, frames of block size 4 and index 3.
2.Systematic characterization of balanced incomplete block designs and symmetric balanced incomplete block designs are given in terms of design parameters. A characterization for certain group divisible designs are also given.
3.For various popular definitions on balancedness in block designs in literature, we proposed a unified terminology to develop a new theory for analysis.
4.We clarify combinatorial structures of balanced nested block designs, balanced arrays and resolvable block designs, and provide their constructions.
5.We propose a new property, i.e., addition structure, of a balanced incomplete block design and present several methods of constructing such block designs. This problem is now extended to consider two-parameters' situation. Also, large sets of balanced incomplete block designs are investigated with their characterizations. Less