Japanese journal of mathematics. New series

Japanese journal of mathematics. New series

Online ISSN : 1861-3624
Print ISSN : 0289-2316

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Volume 11, Issue 1

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On compact complex 3-folds with lines

Masahide KATO

1985 Volume 11 Issue 1 Pages 1-58
Published: 1985
Released on J-STAGE: December 16, 2008

DOIhttps://doi.org/10.4099/math1924.11.1

JOURNAL FREE ACCESS

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Stochastic calculus for a class of evolution equations

Kunio NISHIOKA

1985 Volume 11 Issue 1 Pages 59-102
Published: 1985
Released on J-STAGE: December 16, 2008

DOIhttps://doi.org/10.4099/math1924.11.59

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Irreducible representations of a class of unbounded operator algebras

Subhash J. BHATT

1985 Volume 11 Issue 1 Pages 103-108
Published: 1985
Released on J-STAGE: December 16, 2008

DOIhttps://doi.org/10.4099/math1924.11.103

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The stable behavior of the augmentation quotients of some groups of order p⁴, III

Ken-Ichi TAHARA, Tsuneyo YAMADA

1985 Volume 11 Issue 1 Pages 109-130
Published: 1985
Released on J-STAGE: December 16, 2008

DOIhttps://doi.org/10.4099/math1924.11.109

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In this section we list up the stable behavior of the augmentation quotients for all p-groups of order p⁴, p an odd prime.
1) G=(Z_p)⁴(Passi[6, Theorem 4.7])
n₀=3p-2, π=1, Q_n₀(G)=(Z_p)^p³+p²+p+1.
2) G=(Z_p)²×Z_p² (Horibe and Tahara [3, Proposition 4.5])
n₀=3p-2, π=1, Q_n₀(G)=(Z_p)^2p²+p-1⊕Z_p².
3) G=(Z_p²)² (Proposition 4.5)
n₀=p²+p-1, π=1, Q_n₀(G)=(Z_p)^p²-1⊕(Z_p²)^p+1.
4) G=Z_p×Z_p³ (Tahara and Yamada [11, Proposition 5.6])
n₀=3p-2, π=1, Q_n₀(G)=(Z_p)^3p-2⊕Z_p³.
5) G=Z_p⁴ (Passi [6, Theorem 3.1])
n₀=1, π=1, Q_n₀(G)=Z_p⁴.
6) G=Z_p×‹x, y, z|x^p=y^p=z^p=[z, x]=[z, y]=1, [y, x]=z›
(Horibe and Tahara [3, Proposition 3.1])
n₀=3p-2, π=2, Q_n₀+i(G)=(Z_p)^{(1/2)(p+1)(p²+p+1)+i}, i=0, 1.
7) G=‹x, y, z, w||x^p=y^p=z^p=w^p=[w, x]=[w, y]=[w, z]=1 [z, y]=1, [y, x]=z, [z, x]=w›
(G. Losey and N. Losey [4, Proposition 3.2])
n₀=4p-3, π=6, Q_n₀+i(G)=(Z_p)^s_n₀+i(G)
Case 1. p≡1 mod 3,
s_n₀+i(G)=K(i=0, 4), K+1(i=1, 2, 3), K+2(i=5),
where K=1+p+_??_(p²-1)+_??_(p³-1),
Case 2. p≡2 mod 3,
s_n₀+i(G)=L(i=0), L+2(i=1, 5), L+1(i=2, 3, 4),
where L=1+p+_??_(p²-1)+_??_(p³-2).
8) G=‹x, y, z|x^p=y^p=z^p²=[y, x]=[z^p, x]=1, [z, x]=y, [z, y]=z^p›
(Horibe and Tahara [3, Proposition 5.3])
n₀=4p-3, π=2, Q_n₀+i(G)=(Z_p)^{(1/2)(3p²+2p+1)+i}, i=0, 1.

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Linear partial differential equations with regular singularities in all variables

Toru TSUTSUI

1985 Volume 11 Issue 1 Pages 131-143
Published: 1985
Released on J-STAGE: December 16, 2008

DOIhttps://doi.org/10.4099/math1924.11.131

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Entire positive solutions of singular semilinear elliptic equations

Takasi KUSANO, Charles A. SWANSON

1985 Volume 11 Issue 1 Pages 145-155
Published: 1985
Released on J-STAGE: December 16, 2008

DOIhttps://doi.org/10.4099/math1924.11.145

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Singularities of solutions of the Cauchy problem for hyperbolic systems in Gevrey classes

Seiiehiro WAKABAYASHI

1985 Volume 11 Issue 1 Pages 157-201
Published: 1985
Released on J-STAGE: December 16, 2008

DOIhttps://doi.org/10.4099/math1924.11.157

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