Journal of the Mathematical Society of Japan

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ISSN : 0025-5645
Published by: The Mathematical Society of Japan (10.2969)
Total articles ≅ 3,335
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Tai Melcher
Journal of the Mathematical Society of Japan, Volume 73, pp 1-27; https://doi.org/10.2969/jmsj/84678467

Abstract:
We construct a class of iterated stochastic integrals with respect to Brownian motion on an abstract Wiener space which allows for the definition of Brownian motions on a general class of infinite-dimensional nilpotent Lie groups based on abstract Wiener spaces. We then prove that a Cameron–Martin type quasi-invariance result holds for the associated heat kernel measures in the non-degenerate case, and give estimates on the associated Radon–Nikodym derivative. We also prove that a log Sobolev estimate holds in this setting.
Yifei Chen
Journal of the Mathematical Society of Japan, Volume 73, pp 1-14; https://doi.org/10.2969/jmsj/83898389

Abstract:
We answer a conjecture raised by Caucher Birkar of singularities of weighted blowups of $\mathbb{A}^{n}$ for $n \leq 3$.
Benjamin Bode, Seiichi Kamada
Journal of the Mathematical Society of Japan, Volume 73, pp 1-34; https://doi.org/10.2969/jmsj/84618461

Abstract:
We present an algorithm that takes as input any element $B$ of the loop braid group and constructs a polynomial $f:\mathbb{R}^5 \to \mathbb{R}^2$ such that the intersection of the vanishing set of $f$ and the unit 4-sphere contains the closure of $B$. The polynomials can be used to create real analytic time-dependent vector fields with zero divergence and closed flow lines that move as prescribed by $B$. We also show how a family of surface braids in $\mathbb{C} \times S^1 \times S^1$ without branch points can be constructed as the vanishing set of a holomorphic polynomial $f:\mathbb{C}^3 \to \mathbb{C}$ on $\mathbb{C} \times S^1 \times S^1 \subset \mathbb{C}^3$. Both constructions allow us to give upper bounds on the degree of the polynomials.
Toshiyuki Katsura, Natsuo Saito
Journal of the Mathematical Society of Japan, Volume 73, pp 1-9; https://doi.org/10.2969/jmsj/85058505

Abstract:
We consider the multicanonical systems $|mK_{S}|$ of quasi-elliptic surfaces with Kodaira dimension 1 in characteristic 2. We show that for any $m \geq 6$ $|mK_{S}|$ gives the structure of quasi-elliptic fiber space, and 6 is the best possible number to give the structure for any such surfaces.
Toshihiro Nakanishi
Journal of the Mathematical Society of Japan, Volume 73, pp 1-32; https://doi.org/10.2969/jmsj/84998499

Abstract:
We introduce coordinate systems to the Teichmüller space of the twice-punctured torus and give matrix representations for the points of Teichmüller space. The coordinate systems allow representation of the mapping class group of the twice punctured torus as a group of rational transformations and provide several applications to the mapping class group and also to Kleinian groups.
Yohei Fujishima, Kazuhiro Ishige
Journal of the Mathematical Society of Japan, Volume 73, pp 1-33; https://doi.org/10.2969/jmsj/84728472

Abstract:
Let $(u, v)$ be a solution to a semilinear parabolic system $$ \mbox{(P)} \qquad \left\{ \begin{array}{ll} \partial_t u = D_1 \Delta u+v^p \quad \mbox{in} \quad \mathbf{R}^N \times (0,T),\\ \partial_t v = D_2 \Delta v+u^q \quad \mbox{in}\quad \mathbf{R}^N \times (0,T),\\ u,v \ge 0 \quad \mbox{in} \quad \mathbf{R}^N \times (0,T),\\ (u(\cdot,0),v(\cdot,0)) = (\mu,\nu) \quad \mbox{in} \quad \mathbf{R}^N, \end{array} \right. $$ where $N \ge 1$, $T > 0$, $D_1 > 0$, $D_2 > 0$, $0 < p \le q$ with $pq > 1$ and $(\mu, \nu)$ is a pair of Radon measures or nonnegative measurable functions in $\mathbf{R}^N$. In this paper we study qualitative properties of the initial trace of the solution $(u, v)$ and obtain necessary conditions on the initial data $(\mu, \nu)$ for the existence of solutions to problem (P).
Shinichiro Kobayashi
Journal of the Mathematical Society of Japan, Volume 73, pp 1-11; https://doi.org/10.2969/jmsj/85088508

Abstract:
In this paper, we derive an upper bound for higher eigenvalues of the normalized Laplace operator associated with a symmetric finite graph in terms of lower eigenvalues.
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