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Volume 58 (2006)
- Issue 4 Pages 927-
- Issue 3 Pages 617-
- Issue 2 Pages 299-
- 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 58, Issue 1
Displaying 1-12 of 12 articles from this issue
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Kojun Abe, Kazuhiko Fukui, Takeshi Miura2006 Volume 58 Issue 1 Pages 1-15
Published: 2006
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe study the structure of the group of equivariant Lipschitz homeomorphisms of a smooth G-manifold M which are isotopic to the identity through equivariant Lipschitz homeomorphisms with compact support. First we show that the group is perfect when M is a smooth free G-manifold. Secondly in the case of Cn with the canonical U(n)-action, we show that the first homology group admits continuous moduli. Thirdly we apply the result to the case of the group L(C, 0) of Lipschitz homeomorphisms of C fixing the origin.View full abstractDownload PDF (234K) -
Koji Tojo2006 Volume 58 Issue 1 Pages 17-53
Published: 2006
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSIt is known that each 3-symmetric space admits an invariant almost complex structure J, so-called a canonical almost complex structure. By making use of simple graded Lie algebras and an affine Lie algebra, we classify half dimensional, totally real (with respect to J) and totally geodesic submanifolds of compact 3-symmetric spaces.View full abstractDownload PDF (322K) -
Fumio Hazama2006 Volume 58 Issue 1 Pages 55-82
Published: 2006
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSThe structure of the ring of Hodge cycles on a certain family of abelian varieties of CM-type is investigated. This leads to an interesting combinatorial problem related to posets based on complete p-ary trees. A complete solution to the problem is given for the case p=2.View full abstractDownload PDF (289K) -
Masaharu Nishio, Masahiro Yamada2006 Volume 58 Issue 1 Pages 83-96
Published: 2006
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSLet bpα, 0<α≤1, be the parabolic Bergman space, the Banach space of solutions of parabolic equations (∂/∂ t+(-Δ)α)u=0 on the upper half space Rn+1+ which have finite Lp norms. We study Carleson type measures on bpα and give a necessary and sufficient condition for a measure μ on Rn+1+ to be of Carleson type on bpα. As an application, we characterize bounded Toeplitz operators in the space b2α.View full abstractDownload PDF (224K) -
Karin Erdmann, Andrzej Skowronski2006 Volume 58 Issue 1 Pages 97-128
Published: 2006
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe determine the Calabi-Yau dimension of the stable module categories of all symmetric algebras of tame representation type over an algebraically closed field, and derive some consequences.View full abstractDownload PDF (340K) -
Yuu Hariya2006 Volume 58 Issue 1 Pages 129-151
Published: 2006
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSIn [3], Kotani proved analytically that expectations for additive functionals of Brownian motion {Bt, t≥0} of the form
E0 [ f(Bt)g (∫t0 φ(Bs)ds) ]
have the asymptotics t-3/2 as t→∞ for some suitable non-negative functions φ, f and g. This generalizes, in the asymptotic form, Yor's explicit formula [10] for exponential Brownian functionals.
In the present paper, we discuss this generalization probabilistically, by using a time-change argument. We may easily see from our argument that this asymptotics t-3/2 comes from the transition probability of 3-dimensional Bessel process.View full abstractDownload PDF (251K) -
Pierre Matet2006 Volume 58 Issue 1 Pages 153-181
Published: 2006
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe study combinatorics on Pκ(λ) under the assumption that cov(Mκ,λ<κ)>λ<κ.View full abstractDownload PDF (315K) -
Christian Krattenthaler, Tanguy Rivoal2006 Volume 58 Issue 1 Pages 183-210
Published: 2006
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSIn 1879, Thomae discussed the relations between two generic hypergeometric 3F2-series with argument 1. It is well-known since then that, in combination with the trivial ones which come from permutations of the parameters of the hypergeometric series, Thomae had found a set of 120 relations. More recently, Rhin and Viola asked the following question (in a different, but equivalent language of integrals): If there exists a linear dependence relation over Q between two convergent 3F2-series with argument 1, with integral parameters, and whose values are irrational numbers, is this relation a specialisation of one of the 120 Thomae relations? A few years later, Sato answered this question in the negative, by giving six examples of relations which cannot be explained by Thomae's relations. We show that Sato's counter-examples can be naturally embedded into two families of infinitely many 3F2-relations, both parametrised by three independent parameters. Moreover, we find two more infinite families of the same nature. The families, which do not seem to have been recorded before, come from certain 3F2-transformation formulae and contiguous relations. We also explain in detail the relationship between the integrals of Rhin and Viola and 3F2-series.View full abstractDownload PDF (310K) -
Lucian Badescu, Mauro C. Beltrametti2006 Volume 58 Issue 1 Pages 211-230
Published: 2006
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSLet Y be a smooth curve embedded in a complex projective manifold X of dimension n&\ge;2 with ample normal bundle NY|X. For every p&\ge;0 let αp denote the natural restriction maps Pic(X)→Pic(Y(p)), where Y(p) is the p-th infinitesimal neighbourhood of Y in X. First one proves that for every p&\ge;1 there is an isomorphism of abelian groups Coker(αp)$\cong$Coker(α0)$\oplus$Kp(Y,X), where Kp(Y,X) is a quotient of the C-vector space Lp(Y,X):=$\bigoplus$i=1p H1(Y, Si(NY|X)*) by a free subgroup of Lp(Y,X) of rank strictly less than the Picard number of X. Then one shows that L1(Y,X)=0 if and only if Y$\cong$P1 and NY|X$\cong\mathscr{O}_{\bm{P}^1}(1)^{\oplus n-1}$ (i.e. Y is a quasi-line in the terminology of [4]). The special curves in question are by definition those for which dimCL1(Y,X)=1. This equality is closely related with a beautiful classical result of B. Segre [25]. It turns out that Y is special if and only if either Y$\cong$P1 and NY|X$\cong\mathscr{O}_{\bm{P}^1}(2)\oplus\mathscr{O}_{\bm{P}^1}(1)^{\oplus n-2}$, or Y is elliptic and deg(NY|X)=1. After proving some general results on manifolds of dimension n≥2 carrying special rational curves (e.g. they form a subclass of the class of rationally connected manifolds which is stable under small projective deformations), a complete birational classification of pairs (X,Y) with X surface and Y special is given. Finally, one gives several examples of special rational curves in dimension n≥3.View full abstractDownload PDF (287K) -
Pier Domenico Lamberti, Massimo Lanza de Cristoforis2006 Volume 58 Issue 1 Pages 231-245
Published: 2006
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe consider the Dirichlet and the Neumann eigenvalue problem for the Laplace operator on a variable nonsmooth domain, and we prove that the elementary symmetric functions of the eigenvalues splitting from a given eigenvalue upon domain deformation have a critical point at a domain with the shape of a ball. Correspondingly, we formulate overdetermined boundary value problems of the type of the Schiffer conjecture.View full abstractDownload PDF (213K) -
Hiroaki Aikawa, Kentaro Hirata, Torbjörn Lundh2006 Volume 58 Issue 1 Pages 247-274
Published: 2006
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSWe show that a John domain has finitely many minimal Martin boundary points at each Euclidean boundary point. The number of minimal Martin boundary points is estimated in terms of the John constant. In particular, if the John constant is bigger than $\sqrt3$/2, then there are at most two minimal Martin boundary points at each Euclidean boundary point. For a class of John domains represented as the union of convex sets we give a sufficient condition for the Martin boundary and the Euclidean boundary to coincide.View full abstractDownload PDF (330K) -
Hiroyuki Tasaki2006 Volume 58 Issue 1 Pages 275-297
Published: 2006
Released on J-STAGE: November 05, 2008
JOURNAL FREE ACCESSThe set $\mathscr{R}$(B) of submanifolds conjugate to a given reflective submanifold B in a Riemannian symmetric space M has a structure of symmetric space. Using this structure, for a submanifold N in M we establish integral formulae which represent the integrals of the functions C $\mapsto$ vol(N∩C) on $\mathscr{R}$(B) by some extrinsic geometric amounts of N.View full abstractDownload PDF (256K)
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