Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
Most Downloaded
HOME
VIEW ARTICLES
Most Downloaded
VIEW ARTICLES
Most Downloaded
-
2023-05-31
When all permutations are combinatorial similarities
Viktoriia Bilet, Oleksiy DovgosheyAbstract : Let \((X, d)\) be a semimetric space. A permutation \(\Phi\) of the set \(X\) is a combinatorial self similarity of \((X, d)\) if there is a bijective function \(f \colon d(X \times X) \to d(X \times X)\) such that \[ d(x, y) = f(d(\Phi(x), \Phi(y))) \] for all \(x\), \(y \in X\). We describe the set of all semimetrics \(\rho\) on an arbitrary nonempty set \(Y\) for which every permutation of \(Y\) is a combinatorial self similarity of \((Y, \rho)\).
-
2023-03-31
Uniqueness results on meromorphic functions and their difference operators sharing targets with weight
Thu Thuy Hoang, Hong Nhat Nguyen, Duc Thoan PhamAbstract : Let $f$ be a nonconstant meromorphic function of hyper-order strictly less than 1, and let $c\in\mathbb C\setminus\{0\}$ such that $f(z + c) \not\equiv f(z)$. We prove that if $f$ and its exact difference $\Delta_cf(z) = f(z + c) - f(z)$ share partially $0, \infty$ CM and share 1 IM, then $\Delta_cf = f$, where all 1-points with multiplicities more than 2 do not need to be counted. Some similar uniqueness results for such meromorphic functions partially sharing targets with weight and their shifts are also given. Our results generalize and improve the recent important results.
-
2023-09-30
Structure of idempotents in polynomial rings and matrix rings
Juan Huang, Tai Keun Kwak, Yang Lee, Zhelin PiaoAbstract : An idempotent $e$ of a ring $R$ is called {\it right} (resp., {\it left}) {\it semicentral} if $er=ere$ (resp., $re =ere$) for any $r\in R$, and an idempotent $e$ of $R\backslash \{0,1\}$ will be called {\it right} (resp., {\it left}) {\it quasicentral} provided that for any $r\in R$, there exists an idempotent $f=f(e,r)\in R\backslash \{0,1\}$ such that $er=erf$ (resp., $re=fre$). We show the whole shapes of idempotents and right (left) semicentral idempotents of upper triangular matrix rings and polynomial rings. We next prove that every nontrivial idempotent of the $n$ by $n$ full matrix ring over a principal ideal domain is right and left quasicentral and, applying this result, we can find many right (left) quasicentral idempotents but not right (left) semicentral.
-
2023-07-31
Copure projective modules over FGV-domains and Gorenstein Pr\"{u}fer domains
Shiqi XingAbstract : In this paper, we prove that a domain $R$ is an FGV-domain if every finitely generated torsion-free $R$-module is strongly copure projective, and a coherent domain is an FGV-domain if and only if every finitely generated torsion-free $R$-module is strongly copure projective. To do this, we characterize G-Pr\"{u}fer domains by G-flat modules, and we prove that a domain is G-Pr\"{u}fer if and only if every submodule of a projective module is G-flat. Also, we study the $D+M$ construction of G-Pr\"{u}fer domains. It is seen that there exists a non-integrally closed G-Pr\"{u}fer domain that is neither Noetherian nor divisorial.
-
2023-07-31
An extension of Schneider's characterization theorem for ellipsoids
Dong-Soo Kim, Young Ho KimAbstract : Suppose that $M$ is a strictly convex hypersurface in the $(n+1)$-dimensional Euclidean space ${\mathbb E}^{n+1}$ with the origin $o$ in its convex side and with the outward unit normal $N$. For a fixed point $p \in M$ and a positive constant $t$, we put $\Phi_t$ the hyperplane parallel to the tangent hyperplane $\Phi$ at $p$ and passing through the point $q=p-tN(p)$. We consider the region cut from $M$ by the parallel hyperplane $\Phi_t$, and denote by $I_p(t)$ the $(n+1)$-dimensional volume of the convex hull of the region and the origin $o$. Then Schneider's characterization theorem for ellipsoids states that among centrally symmetric, strictly convex and closed surfaces in the 3-dimensional Euclidean space ${\mathbb E}^{3}$, the ellipsoids are the only ones satisfying $I_p(t)=\phi(p)t$, where $\phi$ is a function defined on $M$. Recently, the characterization theorem was extended to centrally symmetric, strictly convex and closed hypersurfaces in ${\mathbb E}^{n+1}$ satisfying for a constant $\beta$, $I_p(t)=\phi(p)t^{\beta}$. In this paper, we study the volume $I_p(t)$ of a strictly convex and complete hypersurface in ${\mathbb E}^{n+1}$ with the origin $o$ in its convex side. As a result, first of all we extend the characterization theorem to strictly convex and closed (not necessarily centrally symmetric) hypersurfaces in ${\mathbb E}^{n+1}$ satisfying $I_p(t)=\phi(p)t^{\beta}$. After that we generalize the characterization theorem to strictly convex and complete (not necessarily closed) hypersurfaces in ${\mathbb E}^{n+1}$ satisfying $I_p(t)=\phi(p)t^{\beta}$.
-
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.
-
2022-11-30
Estimate for bilinear Calder\'{o}n-Zygmund operator and its commutator on product of variable exponent spaces
Guanghui Lu, Shuangping TaoAbstract : The goal of this paper is to establish the boundedness of bilinear Calder\'{o}n-Zygmund operator $BT$ and its commutator $[b_{1},b_{2},BT]$ which is generated by $b_{1}, b_{2}\in\mathrm{BMO}(\mathbb{R}^{n})$ (or $\dot{\Lambda}_{\alpha}(\mathbb{R}^{n})$) and the $BT$ on generalized variable exponent Morrey spaces $\mathcal{L}^{p(\cdot),\varphi}(\mathbb{R}^{n})$. Under assumption that the functions $\varphi_{1}$ and $\varphi_{2}$ satisfy certain conditions, the authors proved that the $BT$ is bounded from product of spaces $\mathcal{L}^{p_{1}(\cdot),\varphi_{1}}(\mathbb{R}^{n}) \times\mathcal{L}^{p_{2}(\cdot),\varphi_{2}}(\mathbb{R}^{n})$ into space $\mathcal{L}^{p(\cdot),\varphi}(\mathbb{R}^{n})$. Furthermore, the boundedness of commutator $[b_{1},b_{2},BT]$ on spaces $L^{p(\cdot)}(\mathbb{R}^{n})$ and on spaces $\mathcal{L}^{p(\cdot),\varphi}(\mathbb{R}^{n})$ is also established.
-
2023-09-30
Certain properties of the class of univalent functions with real coefficients
Milutin Obradovic, Nikola TuneskiAbstract : Let $\mathcal U^+$ be the class of analytic functions $f$ such that $\frac{z}{f(z)}$ has real and positive coefficients and $f^{-1}$ be its inverse. In this paper we give sharp estimates of the initial coefficients and initial logarithmic coefficients for $f$, as well as, sharp estimates of the second and the third Hankel determinant for $f$ and $f^{-1}$. We also show that the Zalcman conjecture holds for functions $f$ from $\mathcal U^+$.
-
2023-11-30
Representations over Green algebras of weak Hopf algebras based on Taft algebras
Liufeng CaoAbstract : In this paper, we study the Green ring $r(\mathfrak{w}^0_n)$ of the weak Hopf algebra $\mathfrak{w}^0_n$ based on Taft Hopf algebra $H_n(q)$. Let $R(\mathfrak{w}^0_n):=r(\mathfrak{w}^0_n)\otimes_\mathbb{Z}\mathbb{C}$ be the Green algebra corresponding to the Green ring $r(\mathfrak{w}^0_n)$. We first determine all finite dimensional simple modules of the Green algebra $R(\mathfrak{w}^0_n)$, which is based on the observations of the roots of the generating relations associated with the Green ring $r(\mathfrak{w}^0_n)$. Then we show that the nilpotent elements in $r(\mathfrak{w}^0_n)$ can be written as a sum of finite dimensional indecomposable projective $\mathfrak{w}^0_n$-modules. The Jacobson radical $J(r(\mathfrak{w}^0_n))$ of $r(\mathfrak{w}^0_n)$ is a principal ideal, and its rank equals $n-1$. Furthermore, we classify all finite dimensional non-simple indecomposable $R(\mathfrak{w}^0_n)$-modules. It turns out that $R(\mathfrak{w}^0_n)$ has $n^2-n+2$ simple modules of dimension 1, and $n$ non-simple indecomposable modules of dimension 2.
-
2023-09-30
Differences of weighted composition operators on Bergman spaces induced by doubling weights
Jiale ChenAbstract : We characterize the boundedness and compactness of differences of weighted composition operators acting from weighted Bergman spaces $A^p_{\omega}$ to Lebesgue spaces $L^q(d\mu)$ for all $0<p,q<\infty$, where $\omega$ is a radial weight on the unit disk admitting a two-sided doubling condition.
Most Read
-
Uniqueness of meromorphic solutions of a certain type of difference equations
Jun-Fan Chen, Shu-Qing Lin
Bull. Korean Math. Soc. 2022; 59(4): 827-841
https://doi.org/10.4134/BKMS.b210490 -
The recurrent hypercyclicity criterion for translation $C_0$-semigroups on complex sectors
Yuxia Liang, Zhi-Yuan Xu, Ze-Hua Zhou
Bull. Korean Math. Soc. 2023; 60(2): 293-305
https://doi.org/10.4134/BKMS.b210802 -
Second main theorem with weighted counting functions and uniqueness theorem
Liu Yang
Bull. Korean Math. Soc. 2022; 59(5): 1105-1117
https://doi.org/10.4134/BKMS.b210620 -
Complete characterization of odd factors via the size, spectral radius or distance spectral radius of graphs
Shuchao Li, Shujing Miao
Bull. Korean Math. Soc. 2022; 59(4): 1045-1067
https://doi.org/10.4134/BKMS.b210613
Most Downloaded
-
UN rings and group rings
Kanchan Jangra, Dinesh Udar
Bull. Korean Math. Soc. 2023; 60(1): 83-91
https://doi.org/10.4134/BKMS.b210917 -
Bach almost solitons in paraSasakian geometry
Uday Chand De, Gopal Ghosh
Bull. Korean Math. Soc. 2023; 60(3): 763-774
https://doi.org/10.4134/BKMS.b220366 -
On Chowla's hypothesis implying that $L(s,\chi)>0$ for $s>0$ for real characters $\chi$
St\'ephane R. Louboutin
Bull. Korean Math. Soc. 2023; 60(1): 1-22
https://doi.org/10.4134/BKMS.b210464 -
Residual supersingular Iwasawa theory over quadratic imaginary fields
Parham Hamidi
Bull. Korean Math. Soc. 2023; 60(4): 1035-1059
https://doi.org/10.4134/BKMS.b220461
Editorial Office
✕
BKMS
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd