Hokkaido Mathematical Journal

No. 2

URAKAWA, Hajime;

$CR$ rigidity of pseudo harmonic maps and pseudo biharmonic maps.

Hokkaido Mathematical Journal, 46 (2017) pp.141-187

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Abstract

The $CR$ analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with pseudo parallel pseudo mean curvature vector fields, will be characterized.

MSC(Primary)	58E20
MSC(Secondary)	53C43;
Uncontrolled Keywords	isometric immersion; harmonic map; biharmonic map; pseudo-harmonic map; pseudo-biharmonic map;

ZHOU, Zhenqiang;

A note on skew group categories.

Hokkaido Mathematical Journal, 46 (2017) pp.189-207

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Abstract

Let $G$ be a finite group, and $\mathscr{C}$ a $G$-abelian category. We prove that the skew group category $\mathscr{C}(G)$ is an abelian category under the condition that the order $|G|$ is invertible in $\mathscr{C}$. When the order $|G|$ is not invertible in $\mathscr{C}$, an example is given to show that $\mathscr{C}(G)$ is not an abelian category.

MSC(Primary)	18E10
MSC(Secondary)	16B50;
Uncontrolled Keywords	$G$-abelian category; skew group category; idempotent completion;

FURUTA, Koji;

A moment problem on rational numbers.

Hokkaido Mathematical Journal, 46 (2017) pp.209-226

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Abstract

We give integral representations of positive and negative definite functions defined on an interval in a certain subsemigroup of the semigroup of rational numbers.

MSC(Primary)	43A35
MSC(Secondary)	44A60; 47A57;
Uncontrolled Keywords	moment problem; positive definite function; semigroup;

IIYORI, Nobuo; SAWABE, Masato;

Homology of a certain associative algebra.

Hokkaido Mathematical Journal, 46 (2017) pp.227-256

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Abstract

Let $R$ be a commutative ring, and let $A$ be an associative $R$-algebra possessing an $R$-free basis $B$. In this paper, we introduce a homology $H_{n}(A,B)$ associated to a pair $(A,B)$ under suitable hypotheses. It depends on not only $A$ itself but also a choice of $B$. In order to define $H_{n}(A,B)$, we make use of a certain submodule of the $(n+1)$-fold tensor product of $A$. We develop a general theory of $H_{n}(A,B)$. Various examples of a pair $(A,B)$ and $H_{n}(A,B)$ are also provided.

MSC(Primary)	16E40
MSC(Secondary)
Uncontrolled Keywords	Homology; $R$-algebra; Tensor product;

WAKASA, Kyouhei;

The lifespan of solutions to wave equations with weighted nonlinear terms in one space dimension.

Hokkaido Mathematical Journal, 46 (2017) pp.257-276

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Abstract

In this paper, we consider the initial value problem for nonlinear wave equation with weighted nonlinear terms in one space dimension. Kubo & Osaka & Yazici [4] studied global solvability of the problem under different conditions on the nonlinearity and initial data, together with an upper bound of the lifespan for the problem. The aim of this paper is to improve the upper bound of the lifespan and to derive its lower bound which shows the optimality of our new upper bound.

MSC(Primary)	35L71
MSC(Secondary)	35E15; 35A01; 35A09; 35B44;
Uncontrolled Keywords	nonlinear wave equation; lifespan; one space dimension;