Hokkaido Mathematical Journal

No. 3

DATT, Gopal; PANDEY, Shesh Kumar;

Slant Toeplitz operators on the Lebesgue space of $n$-dimensional torus.

Hokkaido Mathematical Journal, 49 (2020) pp.363-389

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Abstract

In this paper, we introduce the $k$-th order slant Toeplitz operator on the Lebesgue space $L^2(\mathbb{T}^n)$ for a fixed integer $k\ge2$ and also investigate certain algebraic properties of the $k$-th order slant Toeplitz operator on the Lebesgue space $L^2(\mathbb{T}^n)$. The complete characterization of the $k$-th order slant Toeplitz operator is also given. Finally, norms and the spectral radius of the introduced operator are discussed.

MSC(Primary)	47B35
MSC(Secondary)
Uncontrolled Keywords	slant Toeplitz operator; Lebesgue space; $n$-dimensional torus;

ANDO, Masanori;

Inferior Regular Partitions and Glaisher Correspondence.

Hokkaido Mathematical Journal, 49 (2020) pp.391-398

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Abstract

We define $r$-inferior regular partition which is a restriction of partition. Its generating function equals to that of the number of operations in the Glaisher correspondence. Using this result, we prove Mizukawa-Yamada's identity separately. Moreover we extend this identity to $m$-tuple version.

MSC(Primary)	05E10
MSC(Secondary)	11P83;
Uncontrolled Keywords	$r$-inferior regular partition; Glaisher correspondence;

HOSHI, Yuichiro;

Reconstruction of profinite graphs from profinite groups of PIPSC-type.

Hokkaido Mathematical Journal, 49 (2020) pp.399-430

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Abstract

In the present paper, we study profinite groups of PIPSC-type, i.e., abstract profinite groups isomorphic to the extensions determined by outer representations of PIPSC-type. In particular, we establish a “group-theoretic” algorithm for constructing, from a profinite group of PIPSC-type that is noncuspidal, a certain profinite graph.

MSC(Primary)	14H30
MSC(Secondary)
Uncontrolled Keywords	combinatorial anabelian geometry; semi-graph of anabelioids of PSC-type; profinite group of PIPSC-type;

KAWAMURA, Masaya;

On Kähler-like almost Hermitian metrics and the almost Hermitian curvature flow.

Hokkaido Mathematical Journal, 49 (2020) pp.431-450

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Abstract

We introduce a Kähler-like almost Hermitian metric and an almost balanced metric. We prove that on a Kähler-like almost Hermitian manifold, we have an identity between the first derivative of the torsion $(1,0)$-tensor and the Nijenhuis tensor. By applying the identity, then we figure out what the equivalent condition of being almost balanced on a compact Kähler-like almost Hermitian manifold is. We apply the result to a 2-step nilpotent Lie algebra, and also to the almost Hermitian curvature flow (AHCF). We obtain a lower bound for the scalar curvature along (AHCF). Also we have some results on the monotonicity of the volume along (AHCF) by studying the relation between the volume and the scalar curvature.

MSC(Primary)	32Q60
MSC(Secondary)	53C15; 53C55;
Uncontrolled Keywords	almost Hermitian manifolds; Kähler-like metrics; Chern connection;

GARUNKŠTIS, Ramūnas; STEUDING, Jörn;

On primeness of the Selberg zeta-function.

Hokkaido Mathematical Journal, 49 (2020) pp.451-462

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Abstract

In this note we prove that the Selberg zeta-function associated to a compact Riemann surface is pseudo-prime and right-prime in the sense of a decomposition.

MSC(Primary)	11M36
MSC(Secondary)
Uncontrolled Keywords	Selberg zeta-function; compact Riemann surface;

SHIRALI, Maryam; MOMTAHAN, Ehsan; SAFAEEYAN, Saeed;

Perpendicular graph of modules.

Hokkaido Mathematical Journal, 49 (2020) pp.463-479

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Abstract

Let $R$ be a ring and $M$ be an $R$-module. Two modules $A$ and $B$ are called orthogonal, written $A\perp B$, if they do not have non-zero isomorphic submodules. We associate a graph $\Gamma_{\bot}(M)$ to $M$ with vertices $\mathcal{M}_{\perp}=\{(0)\neq A\leq M \mid \exists B\neq (0) \;\mbox{such that}\; A\perp B\}$, and for distinct $A,B\in \mathcal{M}_{\perp}$, the vertices $A$ and $B$ are adjacent if and only if $A\perp B$. The main object of this article is to study the interplay of module-theoretic properties of $M$ with graph-theoretic properties of $\Gamma_{\bot}(M)$. An algorithm is given to generate perpendicular graphs of $\mathbb{Z}_n$.

MSC(Primary)	05C25
MSC(Secondary)	16D10;
Uncontrolled Keywords	Type dimension; Complete graph; bipartite graph;

NAKAMURA, Makoto; SATO, Yuya;

Remarks on global solutions for the semilinear diffusion equation in the de Sitter spacetime.

Hokkaido Mathematical Journal, 49 (2020) pp.481-508

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Abstract

The Cauchy problem for the semilinear diffusion equation is considered in the de Sitter spacetime with the spatial zero-curvature. Global solutions and their asymptotic behaviors for small initial data are obtained for positive and negative Hubble constants. The effects of the spatial expansion and contraction are studied on the problem.

MSC(Primary)	35K58
MSC(Secondary)	35G20; 35Q75;
Uncontrolled Keywords	semilinear diffusion equation; de Sitter spacetime; global solution;