Journal of the Mathematical Society of Japan

Algebraic structures on quasi-primary states in superconformal algebras

Go YAMAMOTO

2005 Volume 57 Issue 2 Pages 309-332
Published: 2005
Released on J-STAGE: December 25, 2008

DOIhttps://doi.org/10.2969/jmsj/1158242061

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Operator Product Expansions give algebraic structures on subspaces of quasi-primary vectors in superconformal algebras. The structures characterize the structures of superconformal algebras if they meet a criteria, while in some cases the spaces of quasi-primary vectors are finite dimensional. As an application the complete list of simple physical conformal superalgebras is given by classifying the corresponding algebraic structures on finite dimensional vector spaces. The list contains a one-parameter family of superconformal algebras with 4 supercharges that is simple for general values.

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On a variational problem for soap films with gravity and partially free boundary

Miyuki KOISO, Bennett PALMER

2005 Volume 57 Issue 2 Pages 333-355
Published: 2005
Released on J-STAGE: December 25, 2008

DOIhttps://doi.org/10.2969/jmsj/1158242062

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We pose a variational problem for surfaces whose solutions are a geometric model for thin films with gravity which is partially supported by a given contour. The energy functional contains surface tension, a gravitational energy and a wetting energy, and the Euler-Lagrange equation can be expressed in terms of the mean curvature of the surface, the curvatures of the free boundary and a few other geometric quantities. Especially, we study in detail a simple case where the solutions are vertical planar surfaces bounded by two vertical lines. We determine the stability or instability of each solution.

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On arithmetic subgroups of a \mathQ-rank 2 form of \bm{SU}(2, 2) and their automorphic cohomology

Takahiro HAYATA, Joachim SCHWERMER

2005 Volume 57 Issue 2 Pages 357-385
Published: 2005
Released on J-STAGE: December 25, 2008

DOIhttps://doi.org/10.2969/jmsj/1158242063

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The cohomology H^*(Γ, E) of an arithmetic subgroup Γ of a connected reductive algebraic group G defined over \mathQ can be interpreted in terms of the automorphic spectrum of Γ. In this frame there is a sum decomposition of the cohomology into the cuspidal cohomology ( i.e., classes represented by cuspidal automorphic forms for G) and the so called Eisenstein cohomology. The present paper deals with the case of a quasi split form G of \mathQ-rank two of a unitary group of degree four. We describe in detail the Eisenstein series which give rise to non-trivial cohomology classes and the cuspidal automorphic forms for the Levi components of parabolic \mathQ-subgroups to which these classes are attached. Mainly the generic case will be treated, i.e., we essentially suppose that the coefficient system E is regular.

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Uniqueness theorems for parabolic equations and Martin boundaries for elliptic equations in skew product form

Minoru MURATA

2005 Volume 57 Issue 2 Pages 387-413
Published: 2005
Released on J-STAGE: December 25, 2008

DOIhttps://doi.org/10.2969/jmsj/1158242064

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We give a method to determine Martin boundaries of product domains for elliptic equations in skew product form via Widder type uniqueness theorems for parabolic equations. It is shown that the fiber of the Martin boundary at infinity of the base space degenerates into one point if any nonnegative solution to the Dirichlet problem for a corresponding parabolic equation with zero initial and boundary data is identically zero. We apply it in a unified way to several concrete examples to explicitly determine Martin boundaries for them.

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Borel summability of formal solutions of some first order singular partial differential equations and normal forms of vector fields

Sunao OUCHI

2005 Volume 57 Issue 2 Pages 415-460
Published: 2005
Released on J-STAGE: December 25, 2008

DOIhttps://doi.org/10.2969/jmsj/1158242065

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Let L=∑_{i=1}^d X_i(z) ∂_{z_i} be a holomorphic vector field degenerating at z=0 such that Jacobi matrix ((∂ X_i/∂ z_j)(0)) has zero eigenvalues. Consider Lu=F(z, u) and let ˜{u}(z) be a formal power series solution. We study the Borel summability of ˜{u}(z), which implies the existence of a genuine solution u(z) such that u(z)∼ ˜{u}(z) as z → 0 in some sectorial region. Further we treat singular equations appearing in finding normal forms of singular vector fields and study to simplify L by transformations with Borel summable functions.

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Homotopy classification of twisted complex projective spaces of dimension 4

Juno MUKAI, Kohhei YAMAGUCHI

2005 Volume 57 Issue 2 Pages 461-489
Published: 2005
Released on J-STAGE: December 25, 2008

DOIhttps://doi.org/10.2969/jmsj/1158242066

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We study the existence problem of a 2n dimensional Poincaré complex whose linebreak homology is isomorphic to that of n dimensional complex projective space when n=4.

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One-parametric selfinjective algebras

Rafal BOCIAN, Andrzej SKOWRONSKI

2005 Volume 57 Issue 2 Pages 491-512
Published: 2005
Released on J-STAGE: December 25, 2008

DOIhttps://doi.org/10.2969/jmsj/1158242067

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In continuation of our papers \cite{bib:BoSk}, \cite{bib:BoSk1} we complete the classification of all one-parametric selfinjective algebras over algebraically closed fields which admit simply connected Galois coverings.

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On a mean value formula for the approximate functional equation of \bm{ξ(s)} in the critical strip

Shao-Ji FENG

2005 Volume 57 Issue 2 Pages 513-521
Published: 2005
Released on J-STAGE: December 25, 2008

DOIhttps://doi.org/10.2969/jmsj/1158242068

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In a recent paper, Isao Kiuchi and Naoki Yanagisawa studied the even power moments of the error term in the approximate functional equation for ξ(s). They got a mean value formula with an error term O(T^1/2-kσ), and then they conjecture that this term could be replaced by E_{k, σ}T^1/2-kσ(1+o(1)) with constant E_{k, σ} depending on k and σ. In this paper, we disprove this conjecture by showing that the error term should be f(T)T^1/2-kσ+o(T^1/2-kσ) with f(T) oscillating.

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Hyperspaces with the Hausdorff Metric and Uniform ANR's

Masayuki KURIHARA, Katsuro SAKAI, Masato YAGUCHI

2005 Volume 57 Issue 2 Pages 523-535
Published: 2005
Released on J-STAGE: December 25, 2008

DOIhttps://doi.org/10.2969/jmsj/1158242069

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For a metric space X =(X, d), let \Cld_H(X) be the space of all nonempty closed sets in X with the topology induced by the Hausdorff extended metric: d_H(A, B) =max\bigg{\sup_{x∈ B}d(x, A), \ \sup_{x∈ A}d(x, B)\bigg} ∈ [0, ∞]. On each component of \Cld_H(X), d_H is a metric (i.e., d_H(A, B) < ∞). In this paper, we give a condition on X such that each component of \Cld_H(X) is a uniform AR (in the sense of E.Michael). For a totally bounded metric space X, in order that \Cld_H(X) is a uniform ANR, a necessary and sufficient condition is also given. Moreover, we discuss the subspace \Dis_H(X) of \Cld_H(X) consisting of all discrete sets in X and give a condition on X such that each component of \Dis_H(X) is a uniform AR and \Dis_H(X) is homotopy dense in \Cld_H(X).

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Chart description and a new proof of the classification theorem of genus one Lefschetz fibrations

Seiichi KAMADA, Yukio MATSUMOTO, Takao MATUMOTO, Keita WAKI

2005 Volume 57 Issue 2 Pages 537-555
Published: 2005
Released on J-STAGE: December 25, 2008

DOIhttps://doi.org/10.2969/jmsj/1158242070

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We introduce a graphical method, called the chart description, to describe the monodromy representation of a genus one Lefschetz fibration. Using this method, we give a new and purely combinatorial proof of the classification theorem of genus one Lefschetz fibrations.

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Laplace approximations for large deviations of diffusion processes on Euclidean spaces

Song LIANG

2005 Volume 57 Issue 2 Pages 557-592
Published: 2005
Released on J-STAGE: December 25, 2008

DOIhttps://doi.org/10.2969/jmsj/1158242071

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Consider a class of uniformly elliptic diffusion processes { X_t }_{t ≥ 0} on Euclidean spaces \bm{R}^d . We give an estimate of E^P_x \bigl[ exp (T ¶hi ({1}/{T} ∈t_0^T δ_{X_t} dt)) \big| X_T =y \bigr] as T → ∞ up to the order 1 + o(1), where δ_• means the delta measure, and ¶hi is a function on the set of measures on \bm{R}^d . This is a generalization of the works by Bolthausen-Deuschel-Tamura \cite{B-D-T} and Kusuoka-Liang \cite{K-L_Torus}, which studied the same problems for processes on compact state spaces.

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Homogenization for stochastic partial differential equations derived from nonlinear filterings with feedback

Naoyuki ICHIHARA

2005 Volume 57 Issue 2 Pages 593-603
Published: 2005
Released on J-STAGE: December 25, 2008

DOIhttps://doi.org/10.2969/jmsj/1158242072

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We discuss the homogenization of stochastic partial differential equations whose coefficients are rapidly oscillating and are perturbed by a diffusion process. Such class of equations appear in nonlinear filtering problems with feedback. We specify the constant coefficients of the limit equation. The constants are essentially different from the case where the coefficients do not contain perturbed factors.

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Relations between principal functions of \bm{p}-hyponormal operators

Dedicated to Professor Sin-Ei Takahasi on his sixtieth birthday

Muneo CHO, Tadasi HURUYA

2005 Volume 57 Issue 2 Pages 605-618
Published: 2005
Released on J-STAGE: December 25, 2008

DOIhttps://doi.org/10.2969/jmsj/1158242073

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Let T =U|T| be a bounded linear operator with the associated polar decomposition on a separable infinite dimensional Hilbert space. For 0 < t < 1, let T_t =|T|^tU|T|^1-t and \fg_T and \fg_{T_t} be the principal functions of T and T_t, respectively. We show that, if T is an invertible semi-hyponormal operator with trace class commutator [|T|, U], then \fg_T =\fg_{T_t} almost everywhere on \bm{C}. As a biproduct we reprove Berger's theorem and index properties of invertible p-hyponormal operators.

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