#### Journal of the Mathematical Society of Japan

Journal Information

ISSN
:
0025-5645

Published by: The Mathematical Society of Japan
(10.2969)

Total articles ≅ 3,335

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#### Latest articles in this journal

Published: 22 October 2021

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.

Published: 22 October 2021

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 $n \leq 3$.

Published: 22 October 2021

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.

Published: 22 October 2021

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.

Published: 22 October 2021

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.

Published: 22 October 2021

Journal of the Mathematical Society of Japan, Volume 73; https://doi.org/10.2969/jmsj/83148314

Published: 22 October 2021

Journal of the Mathematical Society of Japan, Volume 73; https://doi.org/10.2969/jmsj/84348434

Published: 22 October 2021

Journal of the Mathematical Society of Japan, Volume 73; https://doi.org/10.2969/jmsj/83928392

Published: 22 October 2021

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).

Published: 22 October 2021

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.