Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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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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2023-01-31
Homology and Serre class in $\mathrm{D}(R)$
Zhicheng WangAbstract : Let $\mathcal{S}$ be a Serre class in the category of modules and $\mathfrak{a}$ an ideal of a commutative Noetherian ring $R$. We study the containment of Tor modules, Koszul homology and local homology in $\mathcal{S}$ from below. With these results at our disposal, by specializing the Serre class to be Noetherian or zero, a handful of conclusions on Noetherianness and vanishing of the foregoing homology theories are obtained. We also determine when $\mathrm{Tor}_{s+t}^R(R/\mathfrak{a},X)\cong\mathrm{Tor}_{s}^R(R/\mathfrak{a},\mathrm{H}_{t}^\mathfrak{a}(X))$.
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2022-07-31
Integral operators on Ces\`{a}ro function spaces
Kwok-Pun Ho
Abstract : This paper studies the boundedness of integral operators on the Ces\`{a}ro function spaces. As applications of the main result, we obtain the Hilbert inequalities, the boundedness of the Erd\'{e}lyi-Kober fractional integrals and the Mellin fractional integrals on the Ces\`{a}ro function spaces.
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2022-09-30
On the geometry of complex metallic Norden manifolds
Adara Monica Blaga, Rakesh Kumar, Rachna RaniAbstract : We study almost complex metallic Norden manifolds and their adapted connections with respect to an almost complex metallic Norden structure. We study various connections like special connection of the first type, special connection of the second type, Kobayashi-Nomizu metallic Norden type connection, Yano metallic Norden type connection etc., on almost complex metallic Norden manifolds. We establish classifications of almost complex metallic Norden manifolds by using covariant derivative of the almost complex metallic Norden structure and also by using torsion tensor on the canonical connections.
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2022-07-31
Complete characterization of odd factors via the size, spectral radius or distance spectral radius of graphs
Shuchao Li, Shujing MiaoAbstract : Given a graph $G,$ a $\{1,3,\ldots,2n-1\}$-factor of $G$ is a spanning subgraph of $G$, in which each degree of vertices is one of $\{1,3,\ldots,2n-1\}$, where $n$ is a positive integer. In this paper, we first establish a lower bound on the size (resp.~the spectral radius) of $G$ to guarantee that $G$ contains a $\{1,3,\ldots,2n-1\}$-factor. Then we determine an upper bound on the distance spectral radius of $G$ to ensure that $G$ has a $\{1,3,\ldots,2n-1\}$-factor. Furthermore, we construct some extremal graphs to show all the bounds obtained in this contribution are best possible.
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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
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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2022-09-30
Second main theorem with weighted counting functions and uniqueness theorem
Liu YangAbstract : In this paper, we obtain a second main theorem for holomorphic curves and moving hyperplanes of $\mathbf{P}^{n}(\mathbf{C})$ where the counting functions are truncated multiplicity and have different weights. As its application, we prove a uniqueness theorem for holomorphic curves of finite growth index sharing moving hyperplanes with different multiple values.
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2022-07-31
On complete convergence for weighted sums of coordinatewise negatively associated random vectors in Hilbert spaces
Vu Thi Ngoc Anh, Nguyen Thi Thanh HienAbstract : This paper establishes the {Baum--Katz} type theorem and the {Marcinkiewicz--Zymund} type strong law of large numbers for sequences of coordinatewise negatively associated and identically distributed random vectors $\{X,X_n,n\ge1\}$ taking values in a Hilbert space $H$ with general normalizing constants $b_n=n^{\alpha}\widetilde L(n^{\alpha})$, where $\widetilde L(\cdot)$ is the de Bruijn conjugate of a slowly varying function $L(\cdot).$ The main result extends and unifies many results in the literature. The sharpness of the result is illustrated by two examples.
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2024-01-31
Well-Posedness and asymptotic behavior of partly dissipative reaction diffusion systems with memory
Vu Trong Luong, Nguyen Duong ToanAbstract : In this paper, we consider the asymptotic behavior of solutions for the partly dissipative reaction diffusion systems of the FitzHugh-Nagumo type with hereditary memory and a very large class of nonlinearities, which have no restriction on the upper growth of the nonlinearity. We first prove the existence and uniqueness of weak solutions to the initial boundary value problem for the above-mentioned model. Next, we investigate the existence of a uniform attractor of this problem, where the time-dependent forcing term $h \in L^2_b(\mathbb{R}; H^{-1}(\mathbb{R}^N))$ is the only translation bounded instead of translation compact. Finally, we prove the regularity of the uniform attractor $\mathcal{A}$, i.e., $\mathcal{A}$ is a bounded subset of $ H^2(\mathbb{R}^N)\times H^1(\mathbb{R}^N)\times L^2_\mu(\mathbb{R}^+, H^2(\mathbb{R}^N))$. The results in this paper will extend and improve some previously obtained results, which have not been studied before in the case of non-autonomous, exponential growth nonlinearity and contain memory kernels.
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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
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Integral operators on Ces\`{a}ro function spaces
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Bull. Korean Math. Soc. 2022; 59(4): 905-915
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B\'ezout rings and weakly B\'ezout rings
Haitham El~Alaoui
Bull. Korean Math. Soc. 2022; 59(4): 843-852
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Finiteness and vanishing results on hypersurfaces with finite index in $\mathbb{R}^{n+1}$: a revision
Nguyen Van Duc
Bull. Korean Math. Soc. 2022; 59(3): 709-723
https://doi.org/10.4134/BKMS.b210426
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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 -
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
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Copure projective modules over FGV-domains and Gorenstein Pr\"{u}fer domains
Shiqi Xing
Bull. Korean Math. Soc. 2023; 60(4): 971-983
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Prime-producing polynomials related to class number one problem of number fields
Jun Ho Lee
Bull. Korean Math. Soc. 2023; 60(2): 315-323
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