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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2022-09-30
Brouwer degree for mean field equation on graph
Yang LiuAbstract : Let $u$ be a function on a connected finite graph $G=(V, E)$. We consider the mean field equation \begin{equation}\label{5} -\Delta u=\rho\bigg{(}\frac{he^u}{\int_V he^ud\mu}-\frac{1}{|V|}\bigg{)}, \end{equation} where $\Delta$ is $\mu$-Laplacian on the graph, $\rho\in \mathbb{R}\backslash\{0\}$, $h: V\ra\mathbb{R^+}$ is a function satisfying $\min_{x\in V}h(x)>0$. Following Sun and Wang \cite{S-w}, we use the method of Brouwer degree to prove the existence of solutions to the mean field equation $(\ref{5})$. Firstly, we prove the compactness result and conclude that every solution to the equation $(\ref{5})$ is uniformly bounded. Then the Brouwer degree can be well defined. Secondly, we calculate the Brouwer degree for the equation $(\ref{5})$, say \begin{equation*}d_{\rho,h}=\left\{\begin{array}{lll} -1,\quad \rho>0,\\ \ 1,\quad \ \rho
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2022-09-30
Unique range sets without Fujimoto's hypothesis
Bikash ChakrabortyAbstract : This paper studies the uniqueness of two non-constant meromorphic functions when they share a finite set. Moreover, we will give an existence of unique range sets for meromorphic functions that are the zero sets of some polynomials that do not necessarily satisfy the Fujimoto's hypothesis ([6]).
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2022-07-31
On right regularity of commutators
Da Woon Jung, Chang Ik Lee, Yang Lee, Sangwon Park, Sung Ju Ryu, Hyo Jin SungAbstract : We study the structure of right regular commutators, and call a ring $R$ {\it strongly $C$-regular} if $ab-ba\in (ab-ba)^2R$ for any $a, b\in R$. We first prove that a noncommutative strongly $C$-regular domain is a division algebra generated by all commutators; and that a ring (possibly without identity) is strongly $C$-regular if and only if it is Abelian $C$-regular (from which we infer that strong $C$-regularity is left-right symmetric). It is proved that for a strongly $C$-regular ring $R$, (i) if $R/W(R)$ is commutative, then $R$ is commutative; and (ii) every prime factor ring of $R$ is either a commutative domain or a noncommutative division ring, where $W(R)$ is the Wedderburn radical of $R$.
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2023-05-31
Bach almost solitons in paraSasakian geometry
Uday Chand De, Gopal GhoshAbstract : If a paraSasakian manifold of dimension $(2n+1)$ represents Bach almost solitons, then the Bach tensor is a scalar multiple of the metric tensor and the manifold is of constant scalar curvature. Additionally it is shown that the Ricci operator of the metric $g$ has a constant norm. Next, we characterize 3-dimensional paraSasakian manifolds admitting Bach almost solitons and it is proven that if a 3-dimensional paraSasakian manifold admits Bach almost solitons, then the manifold is of constant scalar curvature. Moreover, in dimension 3 the Bach almost solitons are steady if $r=-6$; shrinking if $r>-6$; expanding if $r
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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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2023-07-31
Hypersurfaces with prescribed mean curvature in measure metric space
Zhengmao ChenAbstract : For any given function $f$, we focus on the so-called prescribed mean curvature problem for the measure $e^{-f(|x|^2)}dx$ provided that $e^{-f(|x|^2)}\in L^1(\mathbb{R}^{n+1})$. More precisely, we prove that there exists a smooth hypersurface $M$ whose metric is $ds^2=d\rho^2+\rho^2d\xi^2$ and whose mean curvature function is \begin{equation*} \frac{1}{n}\frac{u^p}{\rho^\beta}e^{f(\rho^2)}\psi(\xi) \end{equation*} for any given real constants $p$, $\beta$ and functions $f$ and $\psi$ where $u$ and $\rho$ are the support function and radial function of $M$, respectively. Equivalently, we get the existence of a smooth solution to the following quasilinear equation on the unit sphere $\mathbb{S}^{n}$, \begin{equation*} \sum\limits_{i,j}(\delta_{ij}-\frac{\rho_i\rho_j}{\rho^2+|\nabla\rho|^2})(-\rho_{ji} +\frac{2}{\rho}\rho_j\rho_i +\rho\delta_{ji})=\psi\frac{\rho^{2p+2-n-\beta} e^{f(\rho^2)}}{(\rho^2+|\nabla \rho|^2)^{\frac{p}{2}}} \end{equation*} under some conditions. Our proof is based on the powerful method of continuity. In particular, if we take $f(t)=\frac{t}{2}$, this may be prescribed mean curvature problem in Gauss measure space and it can be seen as an embedded result in Gauss measure space which will be needed in our forthcoming papers on the differential geometric analysis in Gauss measure space, such as Gauss-Bonnet-Chern theorem and its application on positive mass theorem and the Steiner-Weyl type formula, the Plateau problem and so on.
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2022-11-30
Glift codes over chain ring and non-chain ring $R_{e,s}$
Elif Segah Oztas
Abstract : In this paper, Glift codes, generalized lifted polynomials, matrices are introduced. The advantage of Glift code is ``distance preserving" over the ring $\mathcal{R}$. Then optimal codes can be obtained over the rings by using Glift codes and lifted polynomials. Zero divisors are classified to satisfy ``distance preserving" for codes over non-chain rings. Moreover, Glift codes apply on MDS codes and MDS codes are obtained over the ring $\mathcal{R}$ and the non-chain ring $\mathcal{R}_{e,s}$.
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2022-09-30
The Matrix representation of a composition operator on the Hardy space
Young-Bok ChungAbstract : We formulate the matrix representation of a composition operator on the Hardy space of the unit disc with the symbol which is a Riemann map of the unit disc, with respect to a special orthonormal basis.
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2023-11-30
On a generalization of unit regular rings
Tahire OzenAbstract : In this paper, we introduce a class of rings generalizing unit regular rings and being a subclass of semipotent rings, which is called idempotent unit regular. We call a ring $R$ an idempotent unit regular ring if for all $r\in R-J(R)$, there exist a non-zero idempotent $e$ and a unit element $u$ in $R$ such that $er=eu$, where this condition is left and right symmetric. Thus, we have also that there exist a non-zero idempotent $e$ and a unit $u$ such that $ere=eue$ for all $r\in R-J(R)$. Various basic characterizations and properties of this class of rings are proved and it is given the relationships between this class of rings and some well-known classes of rings such as semiperfect, clean, exchange and semipotent. Moreover, we obtain some results about when the endomorphism ring of a module in a class of left $R$-modules $X$ is idempotent unit regular.
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A new characterization of type $(A)$ and ruled real hypersurfaces in nonflat complex space forms
Yaning Wang
Bull. Korean Math. Soc. 2022; 59(4): 897-904
https://doi.org/10.4134/BKMS.b210514 -
Integral operators on Ces\`{a}ro function spaces
Kwok-Pun Ho
Bull. Korean Math. Soc. 2022; 59(4): 905-915
https://doi.org/10.4134/BKMS.b210522 -
B\'ezout rings and weakly B\'ezout rings
Haitham El~Alaoui
Bull. Korean Math. Soc. 2022; 59(4): 843-852
https://doi.org/10.4134/BKMS.b210492 -
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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Copure projective modules over FGV-domains and Gorenstein Pr\"{u}fer domains
Shiqi Xing
Bull. Korean Math. Soc. 2023; 60(4): 971-983
https://doi.org/10.4134/BKMS.b220431 -
An extension of Schneider's characterization theorem for ellipsoids
Dong-Soo Kim, Young Ho Kim
Bull. Korean Math. Soc. 2023; 60(4): 905-913
https://doi.org/10.4134/BKMS.b220393 -
When all permutations are combinatorial similarities
Viktoriia Bilet, Oleksiy Dovgoshey
Bull. Korean Math. Soc. 2023; 60(3): 733-746
https://doi.org/10.4134/BKMS.b220355 -
Certain properties of the class of univalent functions with real coefficients
Milutin Obradovic, Nikola Tuneski
Bull. Korean Math. Soc. 2023; 60(5): 1253-1263
https://doi.org/10.4134/BKMS.b220643
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