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Journal of the Mathematical Society of Japan
- Vol.69(2017)
- Vol.68(2016)
- Vol.67(2015)
- Vol.66(2014)
- Vol.65(2013)
- Vol.64(2012)
- Vol.63(2011)
- Vol.62(2010)
- Vol.61(2009)
- Vol.60(2008)
- Vol.59(2007)
- Vol.58(2006)
- Vol.57(2005)
- Vol.56(2004)
- Vol.55(2003)
- Vol.54(2002)
- Vol.53(2001)
- Vol.52(2000)
- Vol.51(1999)
- Vol.50(1998)
- Vol.49(1997)
- Vol.48(1996)
- Vol.47(1995)
- Vol.46(1994)
- Vol.45(1993)
- Vol.44(1992)
- Vol.43(1991)
- Vol.42(1990)
- Vol.41(1989)
- Vol.40(1988)
- Vol.39(1987)
- Vol.38(1986)
- Vol.37(1985)
- Vol.36(1984)
- Vol.35(1983)
- Vol.34(1982)
- Vol.33(1981)
- Vol.32(1980)
- Vol.31(1979)
- Vol.30(1978)
- Vol.29(1977)
- Vol.28(1976)
- Vol.27(1975)
- Vol.26(1974)
- Vol.25(1973)
- Vol.24(1972)
- Vol.23(1971)
- Vol.22(1970)
- Vol.21(1969)
- Vol.20(1968)
- Vol.19(1967)
- Vol.18(1966)
- Vol.17(1965)
- Vol.16(1964)
- Vol.15(1963)
- Vol.14(1962)
- Vol.13(1961)
- Vol.12(1960)
- Vol.11(1959)
- Vol.10(1958)
- Vol.9(1957)
- Vol.8(1956)
- Vol.7(1955)
- Vol.6(1954)
- Vol.5(1953)
- Vol.4(1952)
- Vol.3(1951)
  - No.2 p.259-
  - No.1 p.1-
- Vol.2(1950 - 1951)
  - No.3-4 p.1･･･
  - No.1-2 p.1-
- Vol.1(1948 - 1950)

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 Kaisya Zasshi

Journal of the Mathematical Society of Japan Vol. 69(2017) No. 3

Extension theorem for rough paths via fractional calculus

Yu Ito

Released: August 04, 2017

p.893-912

On the basis of fractional calculus, we introduce an integral of weakly controlled paths, which is a generalization of integrals in the context of rough path analysis. As an application, we provide an alternative proof of Lyons' extension theorem for geometric Hölder rough paths together with an explicit expression of the extension map.

Some consequences from Proper Forcing Axiom together with large continuum and the negation of Martin's Axiom

Teruyuki Yorioka

Released: August 04, 2017

p.913-943

Recently, David Asperó and Miguel Angel Mota discovered a new method of iterated forcing using models as side conditions. The side condition method with models was introduced by Stevo Todorčević in the 1980s. The Asperó–Mota iteration enables us to force some Π₂-statements over H(ℵ₂) with the continuum greater than ℵ₂. In this article, by using the Asperó–Mota iteration, we prove that it is consistent that ℧ fails, there are no weak club guessing ladder systems, 𝔭 = add($\mathcal{N}$) = 2^ℵ₀ > ℵ₂ and MA_ℵ₁ fails.

Poset pinball, GKM-compatible subspaces, and Hessenberg varieties

Megumi Harada, Julianna Tymoczko

Released: August 04, 2017

p.945-994

This paper has three main goals. First, we set up a general framework to address the problem of constructing module bases for the equivariant cohomology of certain subspaces of GKM spaces. To this end we introduce the notion of a GKM-compatible subspace of an ambient GKM space. We also discuss poset-upper-triangularity, a key combinatorial notion in both GKM theory and more generally in localization theory in equivariant cohomology. With a view toward other applications, we present parts of our setup in a general algebraic and combinatorial framework. Second, motivated by our central problem of building module bases, we introduce a combinatorial game which we dub poset pinball and illustrate with several examples. Finally, as first applications, we apply the perspective of GKM-compatible subspaces and poset pinball to construct explicit and computationally convenient module bases for the S¹-equivariant cohomology of all Peterson varieties of classical Lie type, and subregular Springer varieties of Lie type A. In addition, in the Springer case we use our module basis to lift the classical Springer representation on the ordinary cohomology of subregular Springer varieties to S¹-equivariant cohomology in Lie type A.

Geometry of the Gromov product: Geometry at infinity of Teichmüller space

Hideki Miyachi

Released: August 04, 2017

p.995-1049

This paper is devoted to studying transformations on metric spaces. It is done in an effort to produce qualitative version of quasi-isometries which takes into account the asymptotic behavior of the Gromov product in hyperbolic spaces. We characterize a quotient semigroup of such transformations on Teichmüller space by use of simplicial automorphisms of the complex of curves, and we will see that such transformation is recognized as a “coarsification” of isometries on Teichmüller space which is rigid at infinity. We also show a hyperbolic characteristic that any finite dimensional Teichmüller space does not admit (quasi)-invertible rough-homothety.

Doubly transitive groups and cyclic quandles

Leandro Vendramin

Released: August 04, 2017

p.1051-1057

We prove that for n > 2 there exists a quandle of cyclic type of size n if and only if n is a power of a prime number. This establishes a conjecture of S. Kamada, H. Tamaru and K. Wada. As a corollary, every finite quandle of cyclic type is an Alexander quandle. We also prove that finite doubly transitive quandles are of cyclic type. This establishes a conjecture of H. Tamaru.

Fractional integral operators with homogeneous kernels on Morrey spaces with variable exponents

Kwok-Pun Ho

Released: August 04, 2017

p.1059-1077

We establish the mapping properties of the fractional integral operators with homogeneous kernels on Morrey spaces with variable exponents.

On usual, virtual and welded knotted objects up to homotopy

Benjamin Audoux, Paolo Bellingeri, Jean-Baptiste Meilhan, Emmanuel Wagner

Released: August 04, 2017

p.1079-1097

We consider several classes of knotted objects, namely usual, virtual and welded pure braids and string links, and two equivalence relations on those objects, induced by either self-crossing changes or self-virtualizations. We provide a number of results which point out the differences between these various notions. The proofs are mainly based on the techniques of Gauss diagram formulae.

Shifted products of Fourier coefficients of Siegel cusp forms of degree two

Winfried Kohnen, Jyoti Sengupta

Released: August 04, 2017

p.1099-1103

We prove a non-negativity result for shifted products of two Fourier coefficients of a Siegel Hecke eigenform of degree two not in the Maass space.

Modules over quantized coordinate algebras and PBW-bases

Toshiyuki Tanisaki

Released: August 04, 2017

p.1105-1156

Around 1990 Soibelman constructed certain irreducible modules over the quantized coordinate algebra. A. Kuniba, M. Okado, Y. Yamada [8] recently found that the relation among natural bases of Soibelman's irreducible module can be described using the relation among the PBW-type bases of the positive part of the quantized enveloping algebra, and proved this fact using case-by-case analysis in rank two cases. In this paper we will give a realization of Soibelman's module as an induced module, and give a unified proof of the above result of [8]. We also verify Conjecture 1 of [8] about certain operators on Soibelman's module.

Structure and equivalence of a class of tube domains with solvable groups of automorphisms

Satoru Shimizu

Released: August 04, 2017

p.1157-1177

In the study of the holomorphic equivalence problem for tube domains, it is fundamental to investigate tube domains with polynomial infinitesimal automorphisms. To apply Lie group theory to the holomorphic equivalence problem for such tube domains T_Ω, investigating certain solvable subalgebras of 𝔤(T_Ω) plays an important role, where 𝔤(T_Ω) is the Lie algebra of all complete polynomial vector fields on T_Ω. Related to this theme, we discuss in this paper the structure and equivalence of a class of tube domains with solvable groups of automorphisms. Besides, we give a concrete example of a tube domain whose automorphism group is solvable and contains nonaffine automorphisms.

Hypergroup structures arising from certain dual objects of a hypergroup

Herbert Heyer, Satoshi Kawakami

Released: August 04, 2017

p.1179-1195

In the present paper hypergroup structures are investigated on distinguished dual objects related to a given hypergroup K, especially to a semi-direct product hypergroup K = H ⋊_α G defined by an action α of a locally compact group G on a commutative hypergroup H. Typical dual objects are the sets of equivalence classes of irreducible representations of K, of infinite-dimensional irreducible representations of type I hypergroups K, and of quasi-equivalence classes of type II₁ factor representations of non-type I hypergroups K. The method of proof relies on the notion of a character of a representation of K = H ⋊_α G.

A class of minimal submanifolds in spheres

Marcos Dajczer, Theodoros Vlachos

Released: August 04, 2017

p.1197-1212

We introduce a class of minimal submanifolds Mⁿ, n ≥ 3, in spheres 𝕊ⁿ⁺² that are ruled by totally geodesic spheres of dimension n − 2. If simply-connected, such a submanifold admits a one-parameter associated family of equally ruled minimal isometric deformations that are genuine. As for compact examples, there are plenty of them but only for dimensions n = 3 and n = 4. In the first case, we have that M³ must be a 𝕊¹-bundle over a minimal torus T² in 𝕊⁵ and in the second case M⁴ has to be a 𝕊²-bundle over a minimal sphere 𝕊² in 𝕊⁶. In addition, we provide new examples in relation to the well-known Chern-do Carmo–Kobayashi problem since taking the torus T² to be flat yields minimal submanifolds M³ in 𝕊⁵ with constant scalar curvature.

Degenerations and fibrations of Riemann surfaces associated with regular polyhedra and soccer ball

Ryota Hirakawa, Shigeru Takamura

Released: August 04, 2017

p.1213-1233

To each of regular polyhedra and a soccer ball, we associate degenerating families (degenerations) of Riemann surfaces. More specifically: To each orientation-preserving automorphism of a regular polyhedron (and also of a soccer ball), we associate a degenerating family of Riemann surfaces whose topological monodromy is the automorphism. The complete classification of such degenerating families is given. Besides, we determine the Euler numbers of their total spaces. Furthermore, we affirmatively solve the compactification problem raised by Mutsuo Oka — we explicitly construct compact fibrations of Riemann surfaces that compactify the above degenerating families. Their singular fibers and Euler numbers are also determined.

Absolutely k-convex domains and holomorphic foliations on homogeneous manifolds

Maurício Corrêa Jr., Arturo Fernández-Pérez

Released: August 04, 2017

p.1235-1246

We consider a holomorphic foliation ℱ of codimension k ≥ 1 on a homogeneous compact Kähler manifold X of dimension n > k. Assuming that the singular set Sing(ℱ) of ℱ is contained in an absolutely k-convex domain U ⊂ X, we prove that the determinant of normal bundle det(N_ℱ) of ℱ cannot be an ample line bundle, provided [n/k] ≥ 2k + 3. Here [n/k] denotes the largest integer ≤ n/k.

Forcing-theoretic aspects of Hindman's Theorem

Jörg Brendle, Luz María García Ávila

Released: August 04, 2017

p.1247-1280

We investigate the partial order (FIN)^ω of infinite block sequences, ordered by almost condensation, from the forcing-theoretic point of view. This order bears the same relationship to Hindman's Theorem as $\mathcal{P}$(ω)/fin does to Ramsey's Theorem. While ($\mathcal{P}$(ω)/fin)² completely embeds into (FIN)^ω, we show this is consistently false for higher powers of $\mathcal{P}$(ω)/fin, by proving that the distributivity number 𝔥₃ of ($\mathcal{P}$(ω)/fin)³ may be strictly smaller than the distributivity number 𝔥_FIN of (FIN)^ω. We also investigate infinite maximal antichains in (FIN)^ω and show that the least cardinality 𝔞_FIN of such a maximal antichain is at least the smallest size of a nonmeager set of reals. As a consequence, we obtain that 𝔞_FIN is consistently larger than 𝔞, the least cardinality of an infinite maximal antichain in $\mathcal{P}$(ω)/fin.

Analytic semigroups for the subelliptic oblique derivative problem

Kazuaki Taira

Released: August 04, 2017

p.1281-1330

This paper is devoted to a functional analytic approach to the subelliptic oblique derivative problem for second-order, elliptic differential operators with a complex parameter λ. We prove an existence and uniqueness theorem of the homogeneous oblique derivative problem in the framework of L^p Sobolev spaces when | λ | tends to ∞. As an application of the main theorem, we prove generation theorems of analytic semigroups for this subelliptic oblique derivative problem in the L^p topology and in the topology of uniform convergence. Moreover, we solve the long-standing open problem of the asymptotic eigenvalue distribution for the subelliptic oblique derivative problem. In this paper we make use of Agmon's technique of treating a spectral parameter λ as a second-order elliptic differential operator of an extra variable on the unit circle and relating the old problem to a new one with the additional variable.

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Volume And Issue List
Journal of the Mathematical Society of Japan

Predecessor

Journal of the Mathematical Society of Japan Vol. 69(2017) No. 3

Extension theorem for rough paths via fractional calculus

Some consequences from Proper Forcing Axiom together with large continuum and the negation of Martin's Axiom

Poset pinball, GKM-compatible subspaces, and Hessenberg varieties

Geometry of the Gromov product: Geometry at infinity of Teichmüller space

Doubly transitive groups and cyclic quandles

Fractional integral operators with homogeneous kernels on Morrey spaces with variable exponents

On usual, virtual and welded knotted objects up to homotopy

Shifted products of Fourier coefficients of Siegel cusp forms of degree two

Modules over quantized coordinate algebras and PBW-bases

Structure and equivalence of a class of tube domains with solvable groups of automorphisms

Hypergroup structures arising from certain dual objects of a hypergroup

A class of minimal submanifolds in spheres

Degenerations and fibrations of Riemann surfaces associated with regular polyhedra and soccer ball

Absolutely k-convex domains and holomorphic foliations on homogeneous manifolds

Forcing-theoretic aspects of Hindman's Theorem

Analytic semigroups for the subelliptic oblique derivative problem

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Volume And Issue List Journal of the Mathematical Society of Japan

Predecessor

Journal of the Mathematical Society of Japan Vol. 69(2017) No. 3

System Maintenance

Announcement From J-STAGE

Journal Tools

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Volume And Issue List
Journal of the Mathematical Society of Japan