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Volume 67 (2015)
- Issue 4 Pages 1295-
- Issue 3 Pages 877-
- Issue 2 Pages 433-
- 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 67, Issue 2
Displaying 1-18 of 18 articles from this issue
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Yoshihiro Mizuta, Takao Ohno2015 Volume 67 Issue 2 Pages 433-452
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSIn the present paper we discuss the boundedness of the maximal operator in the Lorentz space of variable exponent defined by the symmetric decreasing rearrangement in the sense of Almut [1]. As an application of the boundedness of the maximal operator, we establish the Sobolev inequality by using Hedberg's trick in his paper [10].View full abstractDownload PDF (218K) -
Ching Hung Lam, Che Sheng Su2015 Volume 67 Issue 2 Pages 453-476
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSIn this article, we study Griess algebras generated by two pairs of Ising vectors (a0, a1) and (b0, b1) such that each pair generates a 3A-algebra U3A and their intersection contains the W3-algebra \mathcal{W}(4/5) ≅ L(4/5,0) ⊕ L(4/5,3). We show that there are only 3 possibilities, up to isomorphisms and they are isomorphic to the Griess algebras of the VOAs VF(1A), VF(2A) and VF(3A) constructed by Höhn–Lam–Yamauchi.View full abstractDownload PDF (309K) -
Shigenori Matsumoto2015 Volume 67 Issue 2 Pages 477-501
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSWe consider an orientation preserving homeomorphism h of S2 which admits a repellor denoted ∞ and an attractor −∞ such that h is not a North-South map and that the basins of ∞ and −∞ intersect. We study various aspects of the rotation number of h: S2\{±∞} → S2\{±∞}, especially its relationship with the existence of periodic orbits.View full abstractDownload PDF (380K) -
Michela Artebani, Alessandra Sarti2015 Volume 67 Issue 2 Pages 503-533
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSIn this paper we study automorphisms of order four on K3 surfaces. We give a classification of the non-symplectic ones when either the square of the automorphism is symplectic, or its fixed locus contains a curve of positive genus, or its fixed locus contains at least a curve and all the curves fixed by its square are rational. We provide partial results in the other cases.View full abstractDownload PDF (321K) -
Qingying Xue, Xiuxiang Peng, Kôzô Yabuta2015 Volume 67 Issue 2 Pages 535-559
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSLet m ≥ 2 and define the multilinear Littlewood–Paley g-function by
In this paper, we establish the strong Lp1(w1) × ⋯ × Lpm(wm) to Lp(ν\vec{ω}) boundedness and weak type Lp1(w1) × ⋯ × Lpm(wm) to Lp,∞(ν\vec{ω}) estimate for the multilinear g-function. The weighted strong and end-point estimates for the iterated commutators of g-function are also given. Here ν\vec{ω} = ∏mi=1ωp/pii and each wi is a nonnegative function on ℝn.
View full abstractDownload PDF (322K) -
Niko Marola, William P. Ziemer2015 Volume 67 Issue 2 Pages 561-579
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSWe consider some measure-theoretic properties of functions belonging to a Sobolev-type class on metric measure spaces that admit a Poincaré inequality and are equipped with a doubling measure. The properties we have selected to study are those that are related to area formulas.View full abstractDownload PDF (257K) -
Mujdat Agcayazi, Amiran Gogatishvili, Kerim Koca, Rza Mustafayev2015 Volume 67 Issue 2 Pages 581-593
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSIn this paper maximal commutators and commutators of maximal functions with functions of bounded mean oscillation are investigated. New pointwise estimates for these operators are proved.View full abstractDownload PDF (205K) -
Oskar Kędzierski, Jarosław A. Wiśniewski2015 Volume 67 Issue 2 Pages 595-608
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSA generalized Euler sequence over a complete normal variety X is the unique extension of the trivial bundle V ⊗ \mathcal{O}X by the sheaf of differentials ΩX, given by the inclusion of a linear space V ⊂ Ext1X(\mathcal{O}X, ΩX). For Λ, a lattice of Cartier divisors, let ℛΛ denote the corresponding sheaf associated to V spanned by the first Chern classes of divisors in Λ. We prove that any projective, smooth variety on which the bundle ℛΛ splits into a direct sum of line bundles is toric. We describe the bundle ℛΛ in terms of the sheaf of differentials on the characteristic space of the Cox ring, provided it is finitely generated. Moreover, we relate the finiteness of the module of sections of ℛΛ and of the Cox ring of Λ.View full abstractDownload PDF (605K) -
Kazuhiko Aomoto, Yoshinori Machida2015 Volume 67 Issue 2 Pages 609-636
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSThe twisted de Rham complex associated with hypergeometric integral of a power product of polynomials is quasi-isomorphic to the corresponding logarithmic complex. We show in this article that the latter has a double filtration with respect to degrees of polynomials and exterior algebras. By a combinatorial method we prove the quasi-isomorphism between the twisted de Rham cohomology and a specially filtered subcomplex in case of polynomials of the same degree. This fact gives a more detailed structure of a basis for the twisted de Rham cohomology.View full abstractDownload PDF (267K) -
Sergey Neshveyev, Makoto Yamashita2015 Volume 67 Issue 2 Pages 637-662
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSGiven a compact semisimple Lie group G of rank r, and a parameter q > 0, we can define new associativity morphisms in Rep(Gq) using a 3-cocycle Φ on the dual of the center of G, thus getting a new tensor category Rep(Gq)Φ. For a class of cocycles Φ we construct compact quantum groups Gτq with representation categories Rep(Gq)Φ. The construction depends on the choice of an r-tuple τ of elements in the center of G. In the simplest case of G = SU(2) and τ = −1, our construction produces Woronowicz's quantum group SU−q(2) out of SUq(2). More generally, for G = SU(n), we get quantum group realizations of the Kazhdan–Wenzl categories.View full abstractDownload PDF (339K) -
Christophe Eyral, Mutsuo Oka2015 Volume 67 Issue 2 Pages 663-698
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSWe compute the fundamental groups π1(ℙ2 \ C) for all complex curves C of degree 7 defined by an equation of the form
where ∑ℓj=1 νj = ∑mi=1 λi is the degree of the curve, c ∈ ℝ \ {0}, and β1,…,βℓ (respectively α1,…,αm) mutually distinct real numbers.
View full abstractDownload PDF (1287K) -
Suyoung Choi, Hanchul Park2015 Volume 67 Issue 2 Pages 699-720
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSIn this paper, we introduce new combinatorial invariants of any finite simple graph, which arise in toric topology. We compute the i-th (rational) Betti number of the real toric variety associated to a graph associahedron Pℬ(G). It can be calculated by a purely combinatorial method (in terms of graphs) and is denoted by ai(G). To our surprise, for specific families of the graph G, our invariants are deeply related to well-known combinatorial sequences such as the Catalan numbers and Euler zigzag numbers.View full abstractDownload PDF (368K) -
Satoshi Koike, Laurentiu Paunescu2015 Volume 67 Issue 2 Pages 721-751
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSIn this paper we study fundamental directional properties of sets under the assumption of condition (SSP) (introduced in [3]). We show several transversality theorems in the singular case and an (SSP)-structure preserving theorem. As a geometric illustration, our transversality results are used to prove several facts concerning complex analytic varieties in 3.3. Also, using our results on sets with condition (SSP), we give a classification of spirals in the appendix 5.
The (SSP)-property is most suitable for understanding transversality in the Lipschitz category. This property is shared by a large class of sets, in particular by subanalytic sets or by definable sets in an o-minimal structure.View full abstractDownload PDF (294K) -
Pierre-Marie Poloni2015 Volume 67 Issue 2 Pages 753-761
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSWe provide counterexamples to the stable equivalence problem in every dimension d ≥ 2. That means that we construct hypersurfaces H1, H2 ⊂ ℂd+1 whose cylinders H1 × ℂ and H2 × ℂ are equivalent hypersurfaces in ℂd+2, although H1 and H2 themselves are not equivalent by an automorphism of ℂd+1. We also give, for every d ≥ 2, examples of two non-isomorphic algebraic varieties of dimension d which are biholomorphic.View full abstractDownload PDF (212K) -
Tomoyuki Shirai2015 Volume 67 Issue 2 Pages 763-787
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSWe introduce Ginibre-type point processes as determinantal point processes associated with the eigenspaces corresponding to the so-called Landau levels. The Ginibre point process, originally defined as the limiting point process of eigenvalues of the Ginibre complex Gaussian random matrix, can be understood as a special case of Ginibre-type point processes. For these point processes, we investigate the asymptotic behavior of the variance of the number of points inside a growing disk. We also investigate the asymptotic behavior of the conditional expectation of the number of points inside an annulus given that there are no points inside another annulus.View full abstractDownload PDF (285K) -
Yiqiang Zhou, Michał Ziembowski2015 Volume 67 Issue 2 Pages 789-796
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSMotivated by a recent result of Mazurek and Ziembowski in [21] that every left distributive ring is Armendariz, in this paper we present methods of constructing Armendariz modules using a distributive module. We prove that, for a bimodule RVA, RV being distributive implies that VA is Armendariz, and that every right module over a right distributive ring is Armendariz. These results can be used to construct new Armendariz rings. Examples are provided to illustrate and delimit the results obtained.View full abstractDownload PDF (193K) -
Krzysztof Klosin2015 Volume 67 Issue 2 Pages 797-860
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSLet K = Q(i√DK) be an imaginary quadratic field of discriminant −DK. We introduce a notion of an adelic Maass space \mathcal{S}Mk,−k/2 for automorphic forms on the quasi-split unitary group U(2,2) associated with K and prove that it is stable under the action of all Hecke operators. When DK is prime we obtain a Hecke-equivariant descent from \mathcal{S}Mk,−k/2 to the space of elliptic cusp forms Sk−1(DK, χK), where χK is the quadratic character of K. For a given ϕ ∈ Sk−1(DK, χK), a prime ℓ > k, we then construct (mod ℓ) congruences between the Maass form corresponding to ϕ and Hermitian modular forms orthogonal to \mathcal{S}Mk,−k/2 whenever valℓ(Lalg(Symm2ϕ, k)) > 0. This gives a proof of the holomorphic analogue of the unitary version of Harder's conjecture. Finally, we use these congruences to provide evidence for the Bloch–Kato conjecture for the motives Symm2ρϕ(k−3) and Symm2ρϕ(k), where ρϕ denotes the Galois representation attached to ϕ.View full abstractDownload PDF (563K) -
Mauro C. Beltrametti, Antonio Lanteri, Andrew J. Sommese2015 Volume 67 Issue 2 Pages 861-875
Published: 2015
Released on J-STAGE: May 13, 2015
JOURNAL FREE ACCESSLet (X,L) be a smooth polarized variety of dimension n. Let A ∈ |L| be an effective irreducible divisor, and let Σ be the singular locus of A. We assume that Σ is a smooth subvariety of dimension k ≥ 2, and codimension c ≥ 3, consisting of non-degenerate quadratic singularities. We study positivity conditions for adjoint bundles KX+tL with t ≥ n−3. Several explicit examples motivate the discussion.View full abstractDownload PDF (244K)
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