Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2022-11-30
Tamed exhaustion functions and Schwarz type lemmas for almost Hermitian manifolds
Weike YuAbstract : In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish a related Schwarz type lemma for almost holomorphic maps between two almost Hermitian manifolds. As corollaries, we deduce several versions of Schwarz and Liouville type theorems for almost holomorphic maps.
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2022-05-31
On eigensharpness and almost eigensharpness of lexicographic products of some graphs
Ahmad Abbasi, Mona Gholamnia~TaleshaniAbstract : The minimum number of complete bipartite subgraphs \linebreak needed to partition the edges of a graph $G$ is denoted by $b(G)$. A known lower bound on $b(G)$ states that $b(G)\geq \max\lbrace p(G), q(G)\rbrace$, where $p(G)$ and $q(G)$ are the numbers of positive and negative eigenvalues of the adjacency matrix of $G$, respectively. When equality is attained, $G$ is said to be eigensharp and when $b(G) =\max \lbrace p(G), q(G)\rbrace + 1$, $G$ is called an almost eigensharp graph. In this paper, we investigate the eigensharpness and almost eigensharpness of lexicographic products of some graphs.
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2023-07-31
On the structure of certain subset of Farey sequence
Xing-Wang Jiang, Ya-Li LiAbstract : Let $F_n$ be the Farey sequence of order $n$. For $S\subseteq F_n$, let $\mathcal{Q}(S)$ be the set of rational numbers $x/y$ with $x,y\in S,~x\leq y$ and $y\neq 0$. Recently, Wang found all subsets $S$ of $F_n$ with $|S|=n+1$ for which $\mathcal{Q}(S)\subseteq F_n$. Motivated by this work, we try to determine the structure of $S\subseteq F_n$ such that $|S|=n$ and $\mathcal{Q}(S)\subseteq F_n$. In this paper, we determine all sets $S\subseteq F_n$ satisfying these conditions for $n\in\{p,2p\}$, where $p$ is prime.
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2023-05-31
MacWilliams-type identities on vectorial Boolean functions with bent components and applications
Jong Yoon HyunAbstract : In this paper, we focus on establishing the MacWilliams-type identities on vectorial Boolean functions with bent component functions. As their applications, we provide a bound for the non-existence of vectorial dual-bent functions with prescribed minimum degree, and several Gleason-type theorems are presented as well.
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2023-03-31
Prime-producing polynomials related to class number one problem of number fields
Jun Ho LeeAbstract : First, we recall the results for prime-producing polynomials related to class number one problem of quadratic fields. Next, we give the relation between prime-producing cubic polynomials and class number one problem of the simplest cubic fields and then present the conjecture for the relations. Finally, we numerically compare the ratios producing prime values for several polynomials in some interval.
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2023-01-31
On certain estimates for rough generalized parametric Marcinkiewicz integrals
Daiqing ZhangAbstract : This paper is devoted to establishing certain $L^p$ bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels given by $h\in\Delta_\gamma(\mathbb{R}_{+})$ and $\Omega\in W\mathcal{F}_\beta({\rm S}^{n-1})$ for some $\gamma,\,\beta\in(1,\infty]$. As applications, the corresponding results for the generalized parametric Marcinkiewicz integral operators related to the Littlewood-Paley $g_\lambda^{*}$ functions and area integrals are also presented.
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2023-05-31
Generalized $m$-quasi-Einstein structure in almost Kenmotsu manifolds
Mohan Khatri, Jay Prakash SinghAbstract : The goal of this paper is to analyze the generalized $m$-quasi-Einstein structure in the context of almost Kenmotsu manifolds. Firstly we showed that a complete Kenmotsu manifold admitting a generalized $m$-quasi-Einstein structure $(g,f,m,\lambda)$ is locally isometric to a hyperbolic space $\mathbb{H}^{2n+1}(-1)$ or a warped product $\widetilde{M}\times_\gamma\mathbb{R}$ under certain conditions. Next, we proved that a $(\kappa,\mu)'$-almost Kenmotsu manifold with $h'\neq0$ admitting a closed generalized $m$-quasi-Einstein metric is locally isometric to some warped product spaces. Finally, a generalized $m$-quasi-Einstein metric $(g,f,m,\lambda)$ in almost Kenmotsu 3-H-manifold is considered and proved that either it is locally isometric to the hyperbolic space $\mathbb{H}^3(-1)$ or the Riemannian product $\mathbb{H}^2(-4)\times\mathbb{R}$.
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2023-03-31
Conjugacy classification of $n$-dimensional M\"obius group
Binlin Dai, Zekun LiAbstract : In this paper, we study the $n$-dimensional M\"obius transformation. We obtain several conjugacy invariants and give a conjugacy classification for $n$-dimensional M\"obius transformation.
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2022-07-31
Positive solution and ground state solution for a Kirchhoff type equation with critical growth
Caixia Chen, Aixia QianAbstract : In this paper, we consider the following Kirchhoff type equation on the whole space $$\left\{\aligned &-(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}dx)\triangle u = u^{5} + \lambda k(x)g(u), \ x\in \mathbb{R}^{3},\\ & u\in\mathcal{D}^{1,2}(\mathbb{R}^{3}),\endaligned\right.$$ where $\lambda>0$ is a real number and $k, g$ satisfy some conditions. We mainly investigate the existence of ground state solution via variational method and concentration-compactness principle.
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2022-09-30
Some polynomials with unimodular roots
Art\= uras DubickasAbstract : In this paper we consider a sequence of polynomials defined by some recurrence relation. They include, for instance, Poupard polynomials and Kreweras polynomials whose coefficients have some combinatorial interpretation and have been investigated before. Extending a recent result of Chapoton and Han we show that each polynomial of this sequence is a self-reciprocal polynomial with positive coefficients whose all roots are unimodular. Moreover, we prove that their arguments are uniformly distributed in the interval $[0,2\pi)$.
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On toric Hamiltonian $T$-spaces with anti-symplectic involutions
Jin Hong Kim
Bull. Korean Math. Soc. 2022; 59(3): 671-683
https://doi.org/10.4134/BKMS.b210406 -
Irreducibility of the moduli space for the quotient singularity $\frac{1}{2k+1}(k+1,1,2k)$
Seung-Jo Jung
Bull. Korean Math. Soc. 2022; 59(6): 1409-1422
https://doi.org/10.4134/BKMS.b210797 -
Multiplicative functions commutable with binary quadratic forms $x^2 \pm xy + y^2$
Poo-Sung Park
Bull. Korean Math. Soc. 2023; 60(1): 75-81
https://doi.org/10.4134/BKMS.b210915 -
A note on Artinian local rings
Kui Hu, Hwankoo Kim, Dechuan Zhou
Bull. Korean Math. Soc. 2022; 59(5): 1317-1325
https://doi.org/10.4134/BKMS.b210759
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Relationship between the structure of a factor ring $R/P$ and derivations of $R$
Karim Bouchannafa, Moulay Abdallah Idrissi, Lahcen Oukhtite
Bull. Korean Math. Soc. 2023; 60(5): 1281-1293
https://doi.org/10.4134/BKMS.b220654 -
Uniqueness results on meromorphic functions and their difference operators sharing targets with weight
Thu Thuy Hoang, Hong Nhat Nguyen, Duc Thoan Pham
Bull. Korean Math. Soc. 2023; 60(2): 461-473
https://doi.org/10.4134/BKMS.b220190 -
Classification of twisted product lightlike submanifolds
Sangeet Kumar, Megha Pruthi
Bull. Korean Math. Soc. 2023; 60(4): 1003-1016
https://doi.org/10.4134/BKMS.b220452 -
Structure of idempotents in polynomial rings and matrix rings
Juan Huang, Tai Keun Kwak, Yang Lee, Zhelin Piao
Bull. Korean Math. Soc. 2023; 60(5): 1321-1334
https://doi.org/10.4134/BKMS.b220692
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