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Volume 59 (2007)
- Issue 4 Pages 913-
- Issue 3 Pages 603-
- Issue 2 Pages 301-
- 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 59, Issue 3
Displaying 1-15 of 15 articles from this issue
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Masayuki Asaoka2007 Volume 59 Issue 3 Pages 603-648
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe define invariants of two dimensional C2 projectively Anosov diffeomorphisms. The invariants are defined by the topology of the space of circles tangent to an invariant subbundle and are preserved under homotopy of projectively Anosov diffeomorphisms. As an application, we show that the invariant subbundle is not uniquely integrable and two distinct periodic orbits exist if certain invariants do not vanish.View full abstractDownload PDF (552K) -
Wataru Ichinose2007 Volume 59 Issue 3 Pages 649-668
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSThe definitions of the Feynman path integral for the Pauli equation and more general equations in configuration space and in phase space are proposed, probably for the first time. Then it is proved rigorously that the Feynman path integrals are well-defined and are the solutions to the corresponding equations. These Feynman path integrals are defined by the time-slicing method through broken line paths, which is familiar in physics. Our definitions of these Feynman path integrals and our results give the extension of ones for the Schrödinger equation.View full abstractDownload PDF (241K) -
Toshiyuki Kobayashi2007 Volume 59 Issue 3 Pages 669-691
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSMotivated by recent developments on visible actions on complex manifolds, we raise a question whether or not the multiplication of three subgroups L, G′ and H surjects a Lie group G in the setting that G/H carries a complex structure and contains G′/G′∩H as a totally real submanifold.
Particularly important cases are when G/L and G/H are generalized flag varieties, and we classify pairs of Levi subgroups (L,H) such that LG′H=G, or equivalently, the real generalized flag variety G′/H∩G′ meets every L-orbit on the complex generalized flag variety G/H in the setting that (G,G′)=(U(n),O(n)). For such pairs (L,H), we introduce a herringbone stitch method to find a generalized Cartan decomposition for the double coset space L$¥backslash$G/H, for which there has been no general theory in the non-symmetric case. Our geometric results provides a unified proof of various multiplicity-free theorems in representation theory of general linear groups.View full abstractDownload PDF (273K) -
Tsuyoshi Miezaki, Hiroshi Nozaki, Junichi Shigezumi2007 Volume 59 Issue 3 Pages 693-706
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe locate all of the zeros of the Eisenstein series associated with the Fricke groups Γ*0(2) and &\Gamma;*0(3) in their fundamental domains by applying and expanding the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (“On the zeros of Eisenstein series”, 1970).View full abstractDownload PDF (213K) -
Jae Ho Choi, Yong Chan Kim, Toshiyuki Sugawa2007 Volume 59 Issue 3 Pages 707-727
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSIn this article, we provide a new method solving the Fekete-Szegö problem for classes of close-to-convex functions defined in terms of subordination. As an example, we apply it to the class of strongly close-to-convex functions.View full abstractDownload PDF (242K) -
Alexander Stoimenow2007 Volume 59 Issue 3 Pages 729-749
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe describe several classes of Montesinos links up to mutation and 5-move equivalence, and obtain from this a Jones and Kauffman polynomial test for a Montesinos link.View full abstractDownload PDF (295K) -
Ryosuke Yamamoto2007 Volume 59 Issue 3 Pages 751-761
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe study open books (or open book decompositions) of a closed oriented 3-manifold which support overtwisted contact structures. We focus on a simple closed curve along which one can perform Stallings twist, called “twisting loop”. We show that the existence of a twisting loop on the fiber surface of an open book is equivalent up to positive stabilization to the existence of an overtwisted disk in the contact manifold supported by the open book. We also show a criterion for overtwistedness using a certain arc properly embedded in the fiber surface, which is an extension of Goodman's one.View full abstractDownload PDF (648K) -
Hisaaki Fujita, Yosuke Sakai, Daniel Simson2007 Volume 59 Issue 3 Pages 763-795
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSGiven a positive integer n≥2, an arbitrary field K and an n-block q=[q(1)|…|q(n)] of n×n square matrices q(1),…,q(n) with coefficients in K satisfying certain conditions, we define a multiplication ·q : Mn(K)$¥otimes$K Mn(K)→Mn(K) on the K-module Mn(K) of all square n×n matrices with coefficients in K in such a way that ·q defines a K-algebra structure on Mn(K). We denote it by Mqn(K), and we call it a minor q-degeneration of the full matrix K-algebra Mn(K). The class of minor degenerations of the algebra Mn(K) and their modules are investigated in the paper by means of the properties of q and by applying quivers with relations. The Gabriel quiver of Mqn(K) is described and conditions for q to be Mqn(K) a Frobenius algebra are given. In case K is an infinite field, for each n≥4 a one-parameter K-algebraic family {Cμ}μ∈K* of basic pairwise non-isomorphic Frobenius K-algebras of the form Cμ=Mqμn(K) is constructed. We also show that if Aq=Mqn(K) is a Frobenius algebra such that J(Aq)3=0, then Aq is representation-finite if and only if n=3, and Aq is tame representation-infinite if and only if n=4.View full abstractDownload PDF (380K) -
Andreas Arvanitoyeorgos, Filip Defever, George Kaimakamis2007 Volume 59 Issue 3 Pages 797-809
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSSubmanifolds satisfying Δ$¥vec H$=λ$¥vec H$ are named by B. Y. Chen submanifolds with proper mean curvature vector. We prove that a hypersurface of the pseudo-Euclidean space Es4 with Δ$¥vec H$=λ$¥vec H$ and diagonalizable shape operator, has constant mean curvature.View full abstractDownload PDF (192K) -
Kuniaki Horie2007 Volume 59 Issue 3 Pages 811-824
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSLet S be a non-empty finite set of prime numbers, and let F be an abelian extension over the rational field such that the Galois group of F over some subfield of F with finite degree is topologically isomorphic to the additive group of the direct product of the p-adic integer rings for all p in S. Let m be a positive integer that is neither congruent to 2 modulo 4 nor divisible by any prime number outside S but divisible by all prime numbers in S. Let Ω denote the composite of pn-th cyclotomic fields for all p in S and all positive integers n. In our earlier paper [3], it is shown that there exist only finitely many prime numbers l for which the l-class group of F is nontrivial and the m-th cyclotomic field contains the decomposition field of l in Ω. We shall prove more precise results providing us with an effective upper bound for a prime number l such that the l-class group of F is nontrivial and that the m-th cyclotomic field contains the decomposition field of l in Ω.View full abstractDownload PDF (236K) -
Nobuhiro Innami2007 Volume 59 Issue 3 Pages 825-835
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSLet M be a complete glued surface whose sectional curvature is greater than or equal to k and $¥triangle$pqr a geodesic triangle domain with vertices p, q, r in M. We prove a compression theorem that there exists a distance nonincreasing map from $¥triangle$pqr onto the comparison triangle domain $¥widetilde{¥triangle}$pqr in the two-dimensional space form with sectional curvature k. Using the theorem, we also have some compression theorems and an application to a circular billiard ball problem on a surface.View full abstractDownload PDF (184K) -
Takayuki Kubo2007 Volume 59 Issue 3 Pages 837-859
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe consider the nonstationary Stokes and Navier-Stokes equations in an aperture domain Ω⊂Rn, n≥2. For this purpose, we prove Lp-Lq type estimate of the Stokes semigroup in the aperture domain. Our proof is based on the local energy decay estimate obtained by investigation of the asymptotic behavior of the resolvent of the Stokes operator near the origin. We apply them to the Navier-Stokes initial value problem in the aperture domain. As a result, we can prove the global existence of a unique solution to the Navier-Stokes problem with the vanishing flux condition and some decay properties as t→∞, when the initial velocity is sufficiently small in the Ln space. Moreover we can prove the time-local existence of a unique solution to the Navier-Stokes problem with the non-trivial flux condition.View full abstractDownload PDF (281K) -
Kazuhiro Ishige, Yoshitsugu Kabeya2007 Volume 59 Issue 3 Pages 861-898
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe consider the initial-boundary value problem
(P) {$¥frac{∂}{∂t}$u = Δu-V(|x|)u in ΩL×(0,∞),
μu+(1-μ)$¥frac{∂}{∂ν}$u = 0 on ∂ΩL×(0,∞),
u(·,0) = φ(·)∈Lp(ΩL), p≥1,
where ΩL={x∈RN:|x|>L}, N≥2, L>0, 0≤μ≤1, &\ u; is the outer unit normal vector to ∂ΩL, and V is a nonnegative smooth function such that V(r)=O(r-2) as r→∞. In this paper, we study the decay rates of the derivatives ∇xju of the solution u to (P) as t→∞.View full abstractDownload PDF (329K) -
Takeshi Izawa2007 Volume 59 Issue 3 Pages 899-910
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSFor a holomorphic map F:X→Y and a non-singular foliation on Y, we give a residue formula which measures singularities of the lifted foliation on X by applying the Baum-Bott residue formula.View full abstractDownload PDF (202K) -
Benoît Audoubert, Tu Chanh Nguyen, Mutsuo Oka2007 Volume 59 Issue 3 Pages 911-912
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSDownload PDF (112K)
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