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JOURNAL OF MATHEMATICS THE UNIVERSITY OF TOKUSHIMA VOLUME 41 2007 PUBLISHED BY THE UNIVERSITY OF TOKUSHIMA TOKUSHIMA, JAPAN ISSN 1346 - 7387

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Page 1: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

JOURNAL OF MATHEMATICSTHE UNIVERSITY OF TOKUSHIMA

VOLUME 41

2007

PUBLISHED BY THEUNIVERSITY OF TOKUSHIMA

TOKUSHIMA, JAPAN

ISSN 1346-7387

Page 2: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

This journal is devoted to the publication of original research papers of our university staff and their joint researchers. One volume is published in each school year. The journal is the new series of “Journal of Mathematics, Tokushima Univer-sity”and“Journal of Gakugei, Tokushima University”.“Journal of Gakugei, Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started in 2001. The volume number of the journal succeeds to that of the former series. The contents of all papers of the journals from 1967 can be seen at the web

site :

http://www-math.ias.tokushima-u.ac.jp/

Any communication with the journal should be addressed to :

The Editorial Committee of Journal of Mathematics The University of Tokushima 1-1, Minamijosanjima-cho Tokushima-shi, 770-8502 JAPAN

Page 3: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

CONTENTS

Page 4: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

J. Math. Univ. Tokushima Vol. 41 (2007), 1-11

1

Page 5: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara2 Pandiagonal Constant Sum Matrices 3

Page 6: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara2 Pandiagonal Constant Sum Matrices 3

Page 7: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara4 Pandiagonal Constant Sum Matrices 5

Page 8: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara4 Pandiagonal Constant Sum Matrices 5

Page 9: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara6 Pandiagonal Constant Sum Matrices 7

Page 10: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara6 Pandiagonal Constant Sum Matrices 7

Page 11: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara8 Pandiagonal Constant Sum Matrices 9

Page 12: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara8 Pandiagonal Constant Sum Matrices 9

Page 13: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara10 Pandiagonal Constant Sum Matrices 11

Page 14: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara10 Pandiagonal Constant Sum Matrices 11

Page 15: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started
Page 16: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

J. Math. Univ. Tokushima Vol. 41 (2007), 13-23

13

Page 17: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara14 Signed Graphs and Hushimi Trees 15

Page 18: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara14 Signed Graphs and Hushimi Trees 15

Page 19: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara16 Signed Graphs and Hushimi Trees 17

Page 20: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara16 Signed Graphs and Hushimi Trees 17

Page 21: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara18 Signed Graphs and Hushimi Trees 19

Page 22: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara18 Signed Graphs and Hushimi Trees 19

Page 23: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara20 Signed Graphs and Hushimi Trees 21

Page 24: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara20 Signed Graphs and Hushimi Trees 21

Page 25: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara22 Signed Graphs and Hushimi Trees 23

Page 26: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Toru Ishihara22 Signed Graphs and Hushimi Trees 23

Page 27: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started
Page 28: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

J. Math. Univ. Tokushima Vol. 41 (2007), 25-31

25

Page 29: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Shin-ichi Katayama26 On Finite Simple Groups of Cude Order 27

Page 30: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Shin-ichi Katayama26 On Finite Simple Groups of Cude Order 27

Page 31: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Shin-ichi Katayama28 On Finite Simple Groups of Cude Order 29

Page 32: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Shin-ichi Katayama28 On Finite Simple Groups of Cude Order 29

Page 33: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Shin-ichi Katayama30 On Finite Simple Groups of Cude Order 31

Page 34: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Shin-ichi Katayama30 On Finite Simple Groups of Cude Order 31

Page 35: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started
Page 36: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

J. Math. Univ. Tokushima Vol. 41 (2007), 33-41

33

Page 37: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Hiroki Sumida-Takahashi34 Examples of the Iwasawa Invariants and the Higher K-groups 35

Page 38: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Hiroki Sumida-Takahashi34 Examples of the Iwasawa Invariants and the Higher K-groups 35

Page 39: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Hiroki Sumida-Takahashi36 Examples of the Iwasawa Invariants and the Higher K-groups 37

Page 40: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Hiroki Sumida-Takahashi36 Examples of the Iwasawa Invariants and the Higher K-groups 37

Page 41: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Hiroki Sumida-Takahashi38 Examples of the Iwasawa Invariants and the Higher K-groups 39

Page 42: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Hiroki Sumida-Takahashi38 Examples of the Iwasawa Invariants and the Higher K-groups 39

Page 43: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Hiroki Sumida-Takahashi40 Examples of the Iwasawa Invariants and the Higher K-groups 41

Page 44: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Hiroki Sumida-Takahashi40 Examples of the Iwasawa Invariants and the Higher K-groups 41

Page 45: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started
Page 46: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

J. Math. Univ. Tokushima Vol. 41 (2007), 43-57

43

Page 47: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono44 L1 Estimates for the Dissipative Wave Equation 45

Page 48: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono44 L1 Estimates for the Dissipative Wave Equation 45

Page 49: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono46 L1 Estimates for the Dissipative Wave Equation 47

Page 50: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono46 L1 Estimates for the Dissipative Wave Equation 47

Page 51: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono48 L1 Estimates for the Dissipative Wave Equation 49

Page 52: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono48 L1 Estimates for the Dissipative Wave Equation 49

Page 53: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono50 L1 Estimates for the Dissipative Wave Equation 51

Page 54: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono50 L1 Estimates for the Dissipative Wave Equation 51

Page 55: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono52 L1 Estimates for the Dissipative Wave Equation 53

Page 56: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono52 L1 Estimates for the Dissipative Wave Equation 53

Page 57: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono54 L1 Estimates for the Dissipative Wave Equation 55

Page 58: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono54 L1 Estimates for the Dissipative Wave Equation 55

Page 59: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono56 L1 Estimates for the Dissipative Wave Equation 57

Page 60: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

Kosuke Ono56 L1 Estimates for the Dissipative Wave Equation 57

Page 61: JOURNAL OF MATHEMATICS...Tokushima University”was published from 1951 to 1966.“Journal of Math-ematics, Tokushima University”was published from 1967 to 2000. The new series started

平成19年12月14日 印 刷平成19年12月21日 発 行

発 行 者

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鳴門市撫養町黒崎字松島242番地

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徳島大学 総合科学部 数理科学教室工 学 部 数 学 教 室

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