Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2022-07-31
A generalization of ${\mathcal A}_2$-groups
Junqiang ZhangAbstract : In this paper, we determine the finite $p$-group such that the intersection of its any two distinct minimal nonabelian subgroups is a maximal subgroup of the two minimal nonabelian subgroups, and the finite $p$-group in which any two distinct ${\mathcal A}_1$-subgroups generate an ${\mathcal A}_2$-subgroup. As a byproduct, we answer a problem proposed by Berkovich and Janko.
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2023-03-31
On meromorphic solutions of nonlinear partial differential-difference equations of first order in several complex variables
Qibin Cheng, Yezhou Li, Zhixue LiuAbstract : This paper is concerned with the value distribution for meromorphic solutions $f$ of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions $f$ are uniquely determined by the poles of $f$ and the zeros of $f-c, f-d$ (counting multiplicities) for two distinct small functions $c, d$.
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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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2023-11-30
Isotropic mean Berwald Finsler warped product metrics
Mehran Gabrani, Bahman Rezaei, Esra Sengelen SevimAbstract : It is our goal in this study to present the structure of isotropic mean Berwald Finsler warped product metrics. We bring out the rich class of warped product Finsler metrics behaviour under this condition. We show that every Finsler warped product metric of dimension $n\geq 2$ is of isotropic mean Berwald curvature if and only if it is a weakly Berwald metric. Also, we prove that every locally dually flat Finsler warped product metric is weakly Berwaldian. Finally, we prove that every Finsler warped product metric is of isotropic Berwald curvature if and only if it is a Berwald metric.
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2022-07-31
Knots in homology lens spaces determined by their complements
Kazuhiro Ichihara
, Toshio SaitoAbstract : In this paper, we consider the knot complement problem for not null-homologous knots in homology lens spaces. Let $M$ be a homology lens space with $H_1(M; \mathbb{Z}) \cong \mathbb{Z}_p$ and $K$ a not null-homologous knot in $M$. We show that, $K$ is determined by its complement if $M$ is non-hyperbolic, $K$ is hyperbolic, and $p$ is a prime greater than 7, or, if $M$ is actually a lens space $L(p,q)$ and $K$ represents a generator of $H_1(L(p,q))$.
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2024-03-31
Geometric inequalities for affine connections on Riemannian manifolds
Huiting Chang, Fanqi ZengAbstract : Using a Reilly type integral formula due to Li and Xia \cite{LiXia2017}, we prove several geometric inequalities for affine connections on Riemannian manifolds. We obtain some general De Lellis-Topping type inequalities associated with affine connections. These not only permit to derive quickly many well-known De Lellis-Topping type inequalities, but also supply a new De Lellis-Topping type inequality when the $1$-Bakry-\'{E}mery Ricci curvature is bounded from below by a negative function. On the other hand, we also achieve some Lichnerowicz type estimate for the first (nonzero) eigenvalue of the affine Laplacian with the Robin boundary condition on Riemannian manifolds.
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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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2022-11-30
Hopf hypersurfaces of the homogeneous nearly K\"{a}hler $\mathbb{S}^3\times\mathbb{S}^3$ satisfying certain commuting conditions
Xiaomin Chen, Yifan YangAbstract : In this article, we first introduce the notion of commuting Ricci tensor and pseudo-anti commuting Ricci tensor for Hopf hypersurfaces in the homogeneous nearly K\"{a}hler $\mathbb{S}^3\times\mathbb{S}^3$ and prove that the mean curvature of hypersurface is constant under certain assumptions. Next, we prove the nonexistence of Ricci soliton on Hopf hypersurface with potential Reeb vector field, which improves a result of Hu et al.~on the nonexistence of Einstein Hopf hypersurfaces in the homogeneous nearly K\"{a}hler $\mathbb{S}^3\times\mathbb{S}^3$.
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2022-11-30
On the Pocklington-Peralta square root algorithm in finite fields
Chang Heon Kim, Namhun Koo, Soonhak KwonAbstract : We present a new square root algorithm in finite fields which is a variant of the Pocklington-Peralta algorithm. We give the complexity of the proposed algorithm in terms of the number of operations (multiplications) in finite fields, and compare the result with other square root algorithms, the Tonelli-Shanks algorithm, the Cipolla-Lehmer algorithm, and the original Pocklington-Peralta square root algorithm. Both the theoretical estimation and the implementation result imply that our proposed algorithm performs favorably over other existing algorithms. In particular, for the NIST suggested field P-224, we show that our proposed algorithm is significantly faster than other proposed algorithms.
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2022-09-30
Einstein-type manifolds with complete divergence of Weyl and Riemann tensor
Seungsu Hwang, Gabjin YunAbstract : In this paper, we study Einstein-type manifolds generalizing static spaces and $V$-static spaces. We prove that if an Einstein-type manifold has non-positive complete divergence of its Weyl tensor and non-negative complete divergence of Bach tensor, then $M$ has harmonic Weyl curvature. Also similar results on an Einstein-type manifold with complete divergence of Riemann tensor are proved.
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Szeg\"{o} projections for Hardy spaces in quaternionic Clifford analysis
Fuli He
, Song Huang, Min KuBull. Korean Math. Soc. 2022; 59(5): 1215-1235
https://doi.org/10.4134/BKMS.b210688 -
The K\"{a}hler Different of a Set of Points in~$\mathbb{P}^{m}\!\times\mathbb{P}^{n}$
Nguyen T. Hoa, Tran N. K. Linh, Le N. Long, Phan T. T. Nhan, Nguyen T. P. Nhi
Bull. Korean Math. Soc. 2022; 59(4): 929-949
https://doi.org/10.4134/BKMS.b210544 -
S-curvature and geodesic orbit property of invariant $(\alpha_{1},\alpha_{2})$-metrics on spheres
Huihui An, Zaili Yan, Shaoxiang Zhang
Bull. Korean Math. Soc. 2023; 60(1): 33-46
https://doi.org/10.4134/BKMS.b210835 -
Hopf hypersurfaces of the homogeneous nearly K\"{a}hler $\mathbb{S}^3\times\mathbb{S}^3$ satisfying certain commuting conditions
Xiaomin Chen, Yifan Yang
Bull. Korean Math. Soc. 2022; 59(6): 1567-1594
https://doi.org/10.4134/BKMS.b210904
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Rings with a right duo factor ring by an ideal contained in the center
Jeoung Soo Cheon, Tai Keun Kwak, Yang Lee, Zhelin Piao, Sang Jo Yun
Bull. Korean Math. Soc. 2022; 59(3): 529-545
https://doi.org/10.4134/BKMS.b201014 -
Two-weight norm estimates for square functions associated to fractional Schr{\"o}dinger operators with Hardy potential
Tongxin Kang, Yang Zou
Bull. Korean Math. Soc. 2023; 60(6): 1567-1605
https://doi.org/10.4134/BKMS.b220752 -
Singularity formation for a nonlinear variational sine-Gordon equation in a multidimensional space
Fengmei Qin, Kyungwoo Song, Qin Wang
Bull. Korean Math. Soc. 2023; 60(6): 1697-1704
https://doi.org/10.4134/BKMS.b220859 -
Weak factorizations of $H^1(\mathbb{R}^n)$ in terms of multilinear fractional integral operator on variable Lebesgue spaces
Zongguang Liu, Huan Zhao
Bull. Korean Math. Soc. 2023; 60(6): 1439-1451
https://doi.org/10.4134/BKMS.b220496
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