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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 1
Displaying 1-12 of 12 articles from this issue
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Yoshihiro Shibata, Senjo Shimizu2007 Volume 59 Issue 1 Pages 1-34
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSIn this paper, we obtain local energy decay estimates and Lp-Lq estimates of the solutions to the Stokes equations with Neumann boundary condition which is obtained as a linearized equation of the free boundary problem for the Navier-Stokes equations. Comparing with the non-slip boundary condition case, we have a better decay estimate for the gradient of the semigroup because of the null force at the boundary.View full abstractDownload PDF (334K) -
Tadashi Tomaru2007 Volume 59 Issue 1 Pages 35-80
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSLet (X,o) be a normal complex surface singularity. We define an invariant pe(X,o) for (X,o) in terms of pencils of compact complex curves. Similarly, for a pair of (X,o) and h∈$¥mathfrak m$X,o (the maximal ideal of $¥mathscr{O}$X,o), we define an invariant pe(X,o,h). We call pe(X,o) (resp. pe(X,o,h)) the pencil genus of (X,o) (resp. a pair of (X,o) and h). In this paper, we give a method to construct pencils of compact complex curves by gluing a resolution space of (X,o) and resolution spaces of some cyclic quotient singularities. Using this, we prove some formulae on pe(X,o,h) and estimate pe(X,o). We also characterize Kodaira singularities in terms of pe(X,o,h).View full abstractDownload PDF (566K) -
Evelia Rosa García Barroso, Andrzej Lenarcik, Arkadiusz Ploski2007 Volume 59 Issue 1 Pages 81-96
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe introduce an equivalence of plane curve germs which is weaker than Zariski's equisingularity and prove that the set of all Newton diagrams of a germ is an invariant of this equivalence. Then we show how to construct all Newton diagrams of a plane many-branched singularity starting with some invariants of branches and their orders of contact.View full abstractDownload PDF (208K) -
Kouyemon Iriye2007 Volume 59 Issue 1 Pages 97-112
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe study a stable suspension order of a universal phantom map out of a space. We prove that it is infinite if X is a non-trivial finite Postnikov space, a classifying space of connected Lie group or a loop space on a connected Lie group with torsion. We also show that the loop spaces on the exceptional Lie groups E6 and E7 are stably indecomposable.View full abstractDownload PDF (220K) -
Humihiko Watanabe2007 Volume 59 Issue 1 Pages 113-126
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSTwo-by-two matrix functions, which are the lifts of the local solutions of the matrix hypergeometric differential equation of SL type at 0,1,∞ to the upper half plane by the lambda function, are introduced. Each component of these matrix functions is represented by a definite integral with a power product of theta functions as integrand, which we call in this paper Wirtinger integral. Transformations of the matrix functions under some modular transformations are established by exploiting classical formulas of theta functions. These are regarded as formulas of monodromy or connection of the hypergeometric function of Gauss.View full abstractDownload PDF (207K) -
Reinhard Farwig, Hideo Kozono, Hermann Sohr2007 Volume 59 Issue 1 Pages 127-150
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe investigate the nonstationary Navier-Stokes equations for an exterior domain Ω⊂R3 in a solution class Ls (0,T;Lq(Ω)) of very low regularity in space and time, satisfying Serrin's condition $¥frac{2}{s}$+$¥frac{3}{q}$=1 but not necessarily any differentiability property. The weakest possible boundary conditions, beyond the usual trace theorems, are given by u|∂Ω=g∈Ls (0,T;W-1/q,q(∂Ω)), and will be made precise in this paper. Moreover, we suppose the weakest possible divergence condition k=divu∈Ls(0,T;Lr(Ω)), where $¥frac{1}{3}$+$¥frac{1}{q}$=$¥frac{1}{r}$.View full abstractDownload PDF (279K) -
Hidehisa Alikawa2007 Volume 59 Issue 1 Pages 151-177
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe find explicit multiplicity-free branching rules of some series of irreducible finite dimensional representations of simple Lie algebras $¥mathfrak g$ to the fixed point subalgebras $¥mathfrak g$σ of outer automorphisms σ. The representations have highest weights which are scalar multiples of fundamental weights or linear combinations of two scalar ones. Our list of pairs of Lie algebras ($¥mathfrak g$, $¥mathfrak g$σ) includes an exceptional symmetric pair (E6, F4) and also a non-symmetric pair (D4, G2) as well as a number of classical symmetric pairs. Some of the branching rules were known and others are new, but all the rules in this paper are proved by a unified method. Our key lemma is a characterization of the “middle” cosets of the Weyl group of $¥mathfrak g$ in terms of the subalgebras $¥mathfrak g$σ on one hand, and the length function on the other hand.View full abstractDownload PDF (310K) -
Jong Bum Lee, Xuezhi Zhao2007 Volume 59 Issue 1 Pages 179-184
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe prove that the sets of homotopy minimal periods for expanding maps on n-dimensional infra-nilmanifolds are uniformly cofinite, i.e., there exists a positive integer m0, which depends only on n, such that for any integer m≥m0, for any n-dimensional infra-nilmanifold M, and for any expanding map f on M, any self-map on M homotopic to f has a periodic point of least period m, namely, [m0,∞)⊂HPer(f). This extends the main result, Theorem 4.6, of [13] from periods to homotopy periods.View full abstractDownload PDF (155K) -
Cris Poor, David S. Yuen2007 Volume 59 Issue 1 Pages 185-222
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSSimple homomorphisms to elliptic modular forms are defined on the ring of Siegel modular forms and linear relations on the Fourier coefficients of Siegel modular forms are implied by the codomains of these homomorphisms. We use the linear relations provided by these homomorphisms to compute the Siegel cusp forms of degree n and weight k in some new cases: (n,k)=(4,14), (4,16), (5,8), (5,10), (6,8). We also compute enough Fourier coefficients using this method to determine the Hecke eigenforms in the nontrivial cases. We also put the open question of whether our technique always succeeds in a precise form. As a partial converse we prove that the Fourier series of Siegel modular forms are characterized among all formal series by the codomain spaces of these homomorphisms and a certain boundedness condition.View full abstractDownload PDF (436K) -
Shin-ichi Oguni2007 Volume 59 Issue 1 Pages 223-237
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe define new L2-invariants which we call secondary Novikov-Shubin invariants. We calculate the first secondary Novikov-Shubin invariants of finitely generated groups by using random walk on Cayley graphs and see in particular that these are invariant under quasi-isometry.View full abstractDownload PDF (208K) -
Toshiaki Hattori2007 Volume 59 Issue 1 Pages 239-264
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe find new generalizations of Dirichlet's theorem to real quadratic fields and quartic fields with two complex places, which are closely related to geometry of products of hyperbolic spaces.View full abstractDownload PDF (291K) -
Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara, Kotaro Yamada2007 Volume 59 Issue 1 Pages 265-299
Published: 2007
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSAfter Gálvez, Martínez and Milán discovered a (Weierstrass-type) holomorphic representation formula for flat surfaces in hyperbolic 3-space H3, the first, third and fourth authors here gave a framework for complete flat fronts with singularities in H3. In the present work we broaden the notion of completeness to weak completeness, and of front to p-front. As a front is a p-front and completeness implies weak completeness, the new framework and results here apply to a more general class of flat surfaces.
This more general class contains the caustics of flat fronts - shown also to be flat by Roitman (who gave a holomorphic representation formula for them) - which are an important class of surfaces and are generally not complete but only weakly complete. Furthermore, although flat fronts have globally defined normals, caustics might not, making them flat fronts only locally, and hence only p-fronts. Using the new framework, we obtain characterizations for caustics.View full abstractDownload PDF (564K)
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