Tohoku Mathematical Journal, Second Series
Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735
Volume 68, Issue 1
Displaying 1-7 of 7 articles from this issue
  • Zhi-Ming Ma, Wei Sun, Li-Fei Wang
    2016 Volume 68 Issue 1 Pages 1-27
    Published: March 30, 2016
    Released on J-STAGE: October 20, 2021
    JOURNAL FREE ACCESS

    We present a Fukushima type decomposition in the setting of general quasi-regular semi-Dirichlet forms. The decomposition is then employed to give a transformation formula for martingale additive functionals. Applications of the results to some concrete examples of semi-Dirichlet forms are given at the end of the paper. We discuss also the uniqueness question about the Doob-Meyer decomposition on optional sets of interval type.

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  • Akio Kodama
    2016 Volume 68 Issue 1 Pages 29-45
    Published: March 30, 2016
    Released on J-STAGE: October 20, 2021
    JOURNAL FREE ACCESS

    In this paper, we completely determine the structure of the holomorphic automorphism group of a generalized Hartogs triangle and obtain natural generalizations of some results due to Landucci and Chen-Xu. These give affirmative answers to some open problems posed by Jarnicki and Pflug.

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  • Akio Kodama
    2016 Volume 68 Issue 1 Pages 47-48
    Published: March 30, 2016
    Released on J-STAGE: October 20, 2021
    JOURNAL FREE ACCESS
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  • Tetsuya Ito
    2016 Volume 68 Issue 1 Pages 49-71
    Published: March 30, 2016
    Released on J-STAGE: October 20, 2021
    JOURNAL FREE ACCESS

    We give a new method to construct isolated left orderings of groups whose positive cones are finitely generated. Our construction uses an amalgamated free product of two groups having an isolated ordering. We construct a lot of new examples of isolated orderings, and give an example of isolated left orderings with various properties which previously known isolated orderings do not have.

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  • Kosuke Naokawa, Masaaki Umehara, Kotaro Yamada
    2016 Volume 68 Issue 1 Pages 73-90
    Published: March 30, 2016
    Released on J-STAGE: October 20, 2021
    JOURNAL FREE ACCESS

    Along cuspidal edge singularities on a given surface in Euclidean 3-space $\boldsymbol{R}^3$, which can be parametrized by a regular space curve $\hat\gamma (t)$, a unit normal vector field $\nu$ is well-defined as a smooth vector field of the surface. A cuspidal edge singular point is called generic if the osculating plane of $\hat\gamma (t)$ is not orthogonal to $\nu$. This genericity is equivalent to the condition that its limiting normal curvature $\kappa_\nu$ takes a non-zero value. In this paper, we show that a given generic (real analytic) cuspidal edge $f$ can be isometrically deformed preserving $\kappa_\nu$ into a cuspidal edge whose singular set lies in a plane. Such a limiting cuspidal edge is uniquely determined from the initial germ of the cuspidal edge.

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  • Suyoung Choi, Hanchul Park
    2016 Volume 68 Issue 1 Pages 91-138
    Published: March 30, 2016
    Released on J-STAGE: October 20, 2021
    JOURNAL FREE ACCESS

    A fundamental result of toric geometry is that there is a bijection between toric varieties and fans. More generally, it is known that some classes of manifolds having well-behaved torus actions, say toric objects, can be classified in terms of combinatorial data containing simplicial complexes.

    In this paper, we investigate the relationship between the topological toric manifolds over a simplicial complex $K$ and those over the complex obtained by simplicial wedge operations from $K$. Our result provides a systematic way to classify toric objects associated with the class of simplicial complexes obtained from a given $K$ by wedge operations. As applications, we completely classify smooth toric varieties with a few generators and show their projectivity. We also study smooth real toric varieties.

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  • Kyoung Hwan Choi, Jang Hyun Jo, Jae Min Moon
    2016 Volume 68 Issue 1 Pages 139-159
    Published: March 30, 2016
    Released on J-STAGE: October 20, 2021
    JOURNAL FREE ACCESS

    The purpose of this paper is to give positive answers to some questions which are related to Fox, Rhodes, Gottlieb-Fox, and Gottlieb-Rhodes groups. Firstly, we show that for a compactly generated Hausdorff based $G$-space $(X,x_0,G)$ with free and properly discontinuous $G$-action, if $(X,x_0,G)$ is homotopically $n$-equivariant, then the $n$-th Gottlieb-Rhodes group $G\sigma_n (X,x_0,G)$ is isomorphic to the $n$-th Gottlieb-Fox group $G\tau_n (X/G,p (x_0))$. Secondly, we prove that every short exact sequence of groups is $n$-Rhodes-Fox realizable for any positive integer $n$. Finally, we present some positive answers to restricted realization problems for Gottlieb-Fox groups and Gottlieb-Rhodes groups.

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