Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2024-01-31
$S$-versions and $S$-generalizations of idempotents, pure ideals and Stone type theorems
Bayram Ali Ersoy, Ünsal Tekir, Eda YıldızAbstract : Let $R$ be a commutative ring with nonzero identity and $M$ be an $R$-module. In this paper, we first introduce the concept of $S$-idempotent element of $R$. Then we give a relation between $S$-idempotents of $R$ and clopen sets of $S$-Zariski topology. After that we define $S$-pure ideal which is a generalization of the notion of pure ideal. In fact, every pure ideal is $S$-pure but the converse may not be true. Afterwards, we show that there is a relation between $S$-pure ideals of $R$ and closed sets of $S$-Zariski topology that are stable under generalization.
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2024-01-31
Periodic shadowable points
Namjip Koo, Hyunhee Lee, Nyamdavaa TsegmidAbstract : In this paper, we consider the set of periodic shadowable points for homeomorphisms of a compact metric space, and we prove that this set satisfies some properties such as invariance and being a $G_{\delta}$ set. Then we investigate implication relations related to sets consisting of shadowable points, periodic shadowable points and uniformly expansive points, respectively. Assume that the set of periodic points and the set of periodic shadowable points of a homeomorphism on a compact metric space are dense in $X$. Then we show that a homeomorphism has the periodic shadowing property if and only if so is the restricted map to the set of periodic shadowable points. We also give some examples related to our results.
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2024-01-31
Regular $t$-balanced Cayley maps on split metacyclic $2$-groups
Haimiao Chen, Jingrui ZhangAbstract : A regular $t$-balanced Cayley map on a group $\Gamma$ is an embedding of a Cayley graph on $\Gamma$ into a surface with certain special symmetric properties. We completely classify regular $t$-balanced Cayley maps for a class of split metacyclic $2$-groups.
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2023-03-31
A note on comparison principle for elliptic obstacle problems with $L^{1}$-data
Kyeong Song, Yeonghun YounAbstract : In this note, we study a comparison principle for elliptic obstacle problems of $p$-Laplacian type with $L^1$-data. As a consequence, we improve some known regularity results for obstacle problems with zero Dirichlet boundary conditions.
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2023-03-31
Hankel determinants for starlike functions with respect to symmetrical points
Nak Eun Cho, Young Jae Sim, Derek K. ThomasAbstract : We prove sharp bounds for Hankel determinants for starlike functions $f$ with respect to symmetrical points, i.e., $f$ given by $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ for $z\in \mathbb{D}$ satisfying $$ Re\dfrac{zf'(z)}{f(z)-f(-z)}>0, \quad z\in \mathbb{D}. $$ We also give sharp upper and lower bounds when the coefficients of $f$ are real.
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2023-03-31
$\Delta$-transitivity for semigroup actions
Tiaoying ZengAbstract : In this paper, we study $\Delta$-transitivity, $\Delta$-weak mixing and $\Delta$-mixing for semigroup actions and give several characterizations of them, which generalize related results in the literature.
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2024-03-31
Six dimensional almost complex torus manifolds with Euler number six
Donghoon Jang, Jiyun ParkAbstract : An almost complex torus manifold is a $2n$-dimensional compact connected almost complex manifold equipped with an effective action of a real $n$-dimensional torus $T^n \simeq (S^1)^n$ that has fixed points. For an almost complex torus manifold, there is a labeled directed graph which contains information on weights at the fixed points and isotropy spheres. Let $M$ be a 6-dimensional almost complex torus manifold with Euler number 6. We show that two types of graphs occur for $M$, and for each type of graph we construct such a manifold $M$, proving the existence. Using the graphs, we determine the Chern numbers and the Hirzebruch $\chi_y$-genus of $M$.
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2023-01-31
Zero sums of dual Toeplitz products on the orthogonal complement of the Dirichlet space
Young Joo LeeAbstract : We consider dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space on the unit disk. We give a characterization of when a finite sum of products of two dual Toeplitz operators is equal to $0$. Our result extends several known results by using a unified way.
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2024-01-31
Complex moments and the distribution of values of $L(1, \chi_{u})$ in even characteristic
Sunghan Bae, Hwanyup JungAbstract : In this paper, we announce that the strategy of comparing the complex moments of $L(1,\chi_{u})$ to that of a random Euler product $L(1, {\mb X})$ is also valid in even characteristic case. We give an asymptotic formulas for the complex moments of $L(1,\chi_{u})$ in a large uniform range. We also give $\Omega$-results for the extreme values of $L(1,\chi_{u})$.
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2024-01-31
The kernels of the linear maps of finite group algebras
Dan YanAbstract : Let $G$ be a finite group, $K$ a split field for $G$, and $L$ a linear map from $K[G]$ to $K$. In our paper, we first give sufficient and necessary conditions for $\operatorname{Ker}L$ and $\operatorname{Ker}L\cap Z(K[G])$, respectively, to be Mathieu-Zhao spaces for some linear maps $L$. Then we give equivalent conditions for $\operatorname{Ker}L$ to be Mathieu-Zhao spaces of $K[G]$ in term of the degrees of irreducible representations of $G$ over $K$ if $G$ is a finite Abelian group or $G$ has a normal Sylow $p$-subgroup $H$ and $L$ are class functions of $G/H$. In particular, we classify all Mathieu-Zhao spaces of the finite Abelian group algebras if $K$ is a split field for $G$.
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Lens spaces admitting minimal symplectic fillings with the second Betti number one
Heesang Park, Dongsoo Shin
Bull. Korean Math. Soc. 2023; 60(1): 113-122
https://doi.org/10.4134/BKMS.b210923 -
A note on the properties of pseudo-weighted Browder spectrum
Preeti Dharmarha, Sarita Kumari
Bull. Korean Math. Soc. 2023; 60(1): 123-135
https://doi.org/10.4134/BKMS.b210931 -
On the structure of certain subset of Farey sequence
Xing-Wang Jiang, Ya-Li Li
Bull. Korean Math. Soc. 2023; 60(4): 915-931
https://doi.org/10.4134/BKMS.b220396 -
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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Estimate for bilinear Calder\'{o}n-Zygmund operator and its commutator on product of variable exponent spaces
Guanghui Lu, Shuangping Tao
Bull. Korean Math. Soc. 2022; 59(6): 1471-1493
https://doi.org/10.4134/BKMS.b210839 -
$p$-Biharmonic hypersurfaces in Einstein space and conformally flat space
Ahmed Mohammed Cherif, Khadidja Mouffoki
Bull. Korean Math. Soc. 2023; 60(3): 705-715
https://doi.org/10.4134/BKMS.b220347 -
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 -
Prime-producing polynomials related to class number one problem of number fields
Jun Ho Lee
Bull. Korean Math. Soc. 2023; 60(2): 315-323
https://doi.org/10.4134/BKMS.b220094
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