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Volume 53 (2001)
- Issue 4 Pages 745-
- Issue 3 Pages 501-
- Issue 2 Pages 261-
- Issue 1 Pages 1-
Predecessor
- Proceedings of the Physico-Mathematical Society of Japan. 3rd Series
- Proceedings of the Tokyo Mathematico-Physical Society. 2nd Series
- Tokyo Sugaku-Butsurigakukwai Kiji-Gaiyo
- Tokyo Sugaku-Butsurigakkwai Hokoku
- Tokyo Sugaku-Butsurigaku Kwai Kiji
- Tokyo Sugaku-Butsurigaku Kwai Kiji
- Tokyo Sugaku Kaisya Zasshi
Volume 53, Issue 4
Displaying 1-11 of 11 articles from this issue
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Dedicated to Professor Kyuûya MASUDA on the occasion of his 60-th birthdayMitsuharu ÔTANI, Yoshie SUGIYAMA2001 Volume 53 Issue 4 Pages 745-789
Published: 2001
Released on J-STAGE: January 23, 2007
JOURNAL FREE ACCESSThe existence of time local C∞-solutions is shown for Cauchy problem of the porous medium equations. Our arguments rely on the“ L∞-energy method”developed in our previous paper [{16}] and a new method based on the theory of evolution equations in the L2-framework which enables us to handle with perturbations which can be decomposed into monotone parts and small parts in Sobolev spaces of higher order.View full abstractDownload PDF (294K) -
Hiroki SATO2001 Volume 53 Issue 4 Pages 791-811
Published: 2001
Released on J-STAGE: January 23, 2007
JOURNAL FREE ACCESSIn this paper we consider J[oslash]rgensen's inequality for classical Schottky groups of real types, that is, the third, sixth and eighth types. The infimum of J[oslash]rgensen's numbers for the groups of the third, sixth and eighth types are 4, 16 and 16, respectively.View full abstractDownload PDF (173K) -
Bert van GEEMEN2001 Volume 53 Issue 4 Pages 813-833
Published: 2001
Released on J-STAGE: January 23, 2007
JOURNAL FREE ACCESSTo a Hodge structure V of weight k with CM by a field K we associate Hodge structures V-n/2 of weight k+n for n positive and, under certain circumstances, also for n negative. We show that these 'half twists' come up naturally in the Kuga-Satake varieties of weight two Hodge structures with CM by an imaginary quadratic fieldView full abstractDownload PDF (164K) -
Jianhua ZHENG, Yuzan HE2001 Volume 53 Issue 4 Pages 835-845
Published: 2001
Released on J-STAGE: January 23, 2007
JOURNAL FREE ACCESSIn this paper, we discuss factorization of the solutions of some linear ordinary differential equations with transcendental entire coefficients. We give a condition which shows that the solutions for some differential equations are prime, for some are factorizable.View full abstractDownload PDF (117K) -
Yusuke OKUYAMA2001 Volume 53 Issue 4 Pages 847-874
Published: 2001
Released on J-STAGE: January 23, 2007
JOURNAL FREE ACCESSWe study the non-linearlizability conjecture (NLC) for polynomials at non-Brjuno irrationally indifferent fixed points. A polynomial is n-subhyperbolic if it has exactly n recurrent critical points corresponding to irrationally indifferent cycles, other ones in the Julia set are preperiodic and no critical orbit in the Fatou set accumulates to the Julia set. In this article, we show that NLC and, more generally, the cycle-version of NLC are true in a subclass of n-subhyperbolic polynomials. As a corollary, we prove the cycle-version of the Yoccoz Theorem for quadratic polynomials.
We also study several specific examples of n-subhyperbolic polynomials. Here we also show the scaling invariance of the Brjuno condition: if an irrational number α satisfies the Brjuno condition, then so do mα for every positive integer m.View full abstractDownload PDF (406K) -
Dedicated to Professor Kiyoshi Mochizuki on the occasion of his 60th birthdayHideo KUBO, Kôji KUBOTA2001 Volume 53 Issue 4 Pages 875-912
Published: 2001
Released on J-STAGE: January 23, 2007
JOURNAL FREE ACCESSWe give a new a priori estimate for a classical solution of the inhomogeneous wave equation in \bm{R}n× \bm{R}, where n=2, 3. As an application of the estimate, we study the asymptotic behavior as t→±∞ of solutions u(x, t) and v(x, t) to a system of semilinear wave equations: ∂t2u-Δ u=|v|p, \ ∂t2v-Δ v=|u|q in \bm{R}n× \bm{R}, where (n+1)/(n-1)<p≤ q with n=2 or n=3. More precisely, it is known that there exists a critical curve Γ=Γ(p, q, n)=0 on the p- q plane such that, when Γ>0, the Cauchy problem for the system has a global solution with small initial data and that, when Γ≤ 0, a solution of the problem generically blows up in finite time even if the initial data are small. In this paper, when Γ>0, we construct a global solution (u(x, t), v(x, t)) of the system which is asymptotic to a pair of solutions to the homogeneous wave equation with small initial data given, as t→-∞, in the sense of both the energy norm and the pointwise convergence. We also show that the scattering operator exists on a dense set of a neighborhood of 0 in the energy space.View full abstractDownload PDF (236K) -
Zygmunt POGORZALY2001 Volume 53 Issue 4 Pages 913-918
Published: 2001
Released on J-STAGE: January 23, 2007
JOURNAL FREE ACCESSThere is proved that the Hochschild cohomology algebras of finite- dimensional self-injective K-algebras over a field K are invariants of stable equivalences of Morita type.View full abstractDownload PDF (72K) -
Mohammad OBIEDAT2001 Volume 53 Issue 4 Pages 919-932
Published: 2001
Released on J-STAGE: January 23, 2007
JOURNAL FREE ACCESSLet KO(\bm{C}Pm) be the KO-ring of the complex projective space \bm{C}Pm. By means of methods of rational D-series [{4}], a formula for the J-orders of elements of KO(\bm{C}Pm) is given. Explicit formulas are given for computing the J-orders of the canonical generators of KO(\bm{C}Pm) and the J-order of any complex line bundle over \bm{C}PmView full abstractDownload PDF (129K) -
Hideo KOJIMA2001 Volume 53 Issue 4 Pages 933-955
Published: 2001
Released on J-STAGE: January 23, 2007
JOURNAL FREE ACCESSIn this article we study nonsingular rational open surfaces of logarithmic Kodaira dimension zero with connected boundaries at infinity defined over an algebraically closed field of arbitrary characteristic. We establish a classification theory of nonsingular affine surfaces of logarithmic Kodaira dimension zero and give a characterization of A*1× A*1 in arbitrary characteristic.View full abstractDownload PDF (203K) -
Marc HUTTNER, Tapani MATALA-AHO2001 Volume 53 Issue 4 Pages 957-974
Published: 2001
Released on J-STAGE: January 23, 2007
JOURNAL FREE ACCESSThis paper is devoted to the study of rational approximations of the ratio η(λ)/omega(λ), where omega(λ) and η(λ) are the real period and real quasi-period, respectively, of the elliptic curve y2=x(x-1)(x-λ). Using monodromy principle for hypergeometric function in the logarithm case we obtain rational approximations of (η/omega)(λ) with λ∈ \bm{Q} and we shall find new measures of irrationality, both in the archimedean and non archimedean case.View full abstractDownload PDF (128K) -
Dedicated to Professor Masayoshi Kamata on his 60th birthdayToshio SUMI2001 Volume 53 Issue 4 Pages 975-990
Published: 2001
Released on J-STAGE: January 23, 2007
JOURNAL FREE ACCESSLet G be a finite group. A gap G-module V is a finite dimensional real G-representation space satisfying the following two conditions:
(1) The following strong gap condition holds: \dim VP>2\dim VH for all P< H≤ G such that P is of prime power order, which is a sufficient condition to define a G-surgery obstruction group and a G-surgery obstruction.
(2) V has only one H-fixed point 0 for all large subgroups H, namely H∈ \mathscr{L}(G). A finite group G not of prime power order is called a gap group if there exists a gap G-module. We discuss the question when the direct product K× L is a gap group for two finite groups K and L. According to [{5}], if K and K× C2 are gap groups, so is K× L. In this paper, we prove that if K is a gap group, so is K× C2. Using [{5}], this allows us to show that if a finite group G has a quotient group which is a gap group, then G itself is a gap group. Also, we prove the converse: if K is not a gap group, then K× D2n is not a gap group. To show this we define a condition, called NGC, which is equivalent to the non-existence of gap modules.View full abstractDownload PDF (152K)
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