Hokkaido Mathematical Journal

No. 2

HANAMURA, Masaki; KIMURA, Kenichiro; TERASOMA, Tomohide;

Integrals of logarithmic forms on semi-algebraic sets and a generalized Cauchy formula Part II: Generalized Cauchy formula.

Hokkaido Mathematical Journal, 54 (2025) pp.185-253

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Abstract

This paper is the continuation of the paper arXiv:1509.06950, which is Part I under the same title. In this paper, we prove a generalized Cauchy formula for the integrals of logarithmic forms on products of projective lines, and give an application to the construction of Hodge realization of mixed Tate motives.

Keywords	Semi-algebraic sets; Generalized Cauchy formula; Mixed Tate motives; Hodge realization;
msc2020(primary)	14P10; 14C15; 14C30;
msc2020(secondary)	14C25;

SHI, Jiangtao; TIAN, Yunfeng;

On finite groups in which some maximal invariant subgroups have indices a prime or the square of a prime.

Hokkaido Mathematical Journal, 54 (2025) pp.255-261

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Abstract

Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms, we first prove some results on the solvability of finite groups in which some maximal $A$-invariant subgroups have indices a prime or the square of a prime. Our results generalize Hall's theorem and some other known results. Moreover, we obtain a complete characterization of finite groups in which every non-nilpotent maximal $A$-invariant subgroup that contains the normalizer of some $A$-invariant Sylow subgroup has index a prime.

Keywords	maximal $A$-invariant subgroup; normalizer; non-nilpotent maximal $A$-invariant subgroup; solvable; normal $p$-complement;
msc2020(primary)	20D10; 20D20;

CHEN, Yining; WANG, Yufeng; YU, Jianshe;

Existence and stability of periodic solutions in a mosquito population suppression model based on the release of Wolbachia-infected males.

Hokkaido Mathematical Journal, 54 (2025) pp.263-294

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Abstract

In this paper, we study a mosquito population suppression model based on impulsive and periodic releases of Wolbachia-infected males, and consider the situation that the waiting period $T$ is not longer than the sexual lifespan $\bar{T}$ of the released males. We find that the origin of the model is always asymptotically stable. When $T=\bar{T}$, we establish the existence and analyze the stability of the equilibrium points for the model. When $T < \bar{T}$, the dynamics of the model exhibit rich behaviors. We obtain sufficient conditions for the existence of global asymptotically stable origin, a unique periodic solution, or exactly two periodic solutions, and analyze the stability of each periodic solution. Numerical examples also demonstrate the rich dynamics of the model.

Keywords	Wolbachia-infected males; Mosquito population suppression; Periodic solutions; Asymptotic stability;
msc2020(primary)	34C25; 34D05; 34D23;

ANDO, Masanori; AOKAGE, Kazuya;

A combinatorial approach to Harada's conjecture II of the groups related to the symmetric groups.

Hokkaido Mathematical Journal, 54 (2025) pp.295-317

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Abstract

Harada conjectured that the product of the sizes of all conjugacy classes is divided by the product of the degrees of all irreducible characters for any finite group. When the group is the symmetric group $S_n$ and the alternating group $A_n$, this conjecture is presented by the hook length properties of the Young diagram (cf. [1]). We show the conjecture for the covering groups $\widetilde{S_n}$ and $\widetilde{A_n}$ $(n\geq 4)$.

Keywords	Bijection; Glaisher map; Harada's conjecture II; Spin representations;
msc2020(primary)	05A17; 20C25; 20C30;

IKEHATA, Masaru;

The enclosure method using a single point on the graph of the response operator for the Stokes system.

Hokkaido Mathematical Journal, 54 (2025) pp.319-343

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Abstract

An inverse obstacle problem governed by the Stokes system in the time domain is considered. Two types of extraction formulae about the geometry of an unknown obstacle are given by using the most recent version of the time domain enclosure method in a unified style. Each of the formulae employs only a single set of velocity and the Cauchy stress fields over a finite time interval on the surface of the region where a viscous incompressible fluid occupies.

Keywords	enclosure method; inverse obstacle problem; Stokes system; fluid;
msc2020(primary)	35R30; 76M21; 76D07;