Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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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.
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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.
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2023-11-30
Partial sums and inclusion relations for starlike functions associated with an evolute of a nephroid curve
Gurpreet Kaur, Sumit NagpalAbstract : A class of normalized univalent functions $f$ defined in an open unit disk of the complex plane is introduced and studied such that the values of the quantity $zf'(z)/f(z)$ lies inside the evolute of a nephroid curve. The inclusion relations of the newly defined class with other subclasses of starlike functions and radius problems concerning the second partial sums are investigated. All the obtained results are sharp.
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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.
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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 \((Y, \rho)\).
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2023-09-30
Spin structures on complex projective spaces and circle actions
Donghoon JangAbstract : It is known that the complex projective space $\mathbb{CP}^n$ admits a spin structure if and only if $n$ is odd. In this paper, we provide another proof that $\mathbb{CP}^{2m}$ does not admit a spin structure, by using a circle action.
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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.
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2023-11-30
The $u$-$S$-global dimensions of commutative rings
Wei Qi, Xiaolei ZhangAbstract : Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. First, we introduce and study the $u$-$S$-projective dimension and $u$-$S$-injective dimension of an $R$-module, and then explore the $u$-$S$-global dimension $u$-$S$-\gld$(R)$ of a commutative ring $R$, i.e., the supremum of $u$-$S$-projective dimensions of all $R$-modules. Finally, we investigate $u$-$S$-global dimensions of factor rings and polynomial rings.
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2023-05-31
MacWilliams-type identities on vectorial Boolean functions with bent components and applications
Jong Yoon HyunAbstract : In this paper, we focus on establishing the MacWilliams-type identities on vectorial Boolean functions with bent component functions. As their applications, we provide a bound for the non-existence of vectorial dual-bent functions with prescribed minimum degree, and several Gleason-type theorems are presented as well.
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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.
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Bisectors in the Heisenberg group I
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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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Annihilator ideals of simple modules of restricted quantized enveloping algebra
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Complex symmetric weighted composition-differentiation operators on $H^2$
Lian Hu, Songxiao Li, Rong Yang
Bull. Korean Math. Soc. 2023; 60(5): 1141-1154
https://doi.org/10.4134/BKMS.b220215
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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 -
UN rings and group rings
Kanchan Jangra, Dinesh Udar
Bull. Korean Math. Soc. 2023; 60(1): 83-91
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On the $p$-adic valuation of generalized harmonic numbers
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Bull. Korean Math. Soc. 2023; 60(4): 933-955
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Sharp inequalities involving the Chen-Ricci inequality for slant Riemannian submersions
Mehmet Akif Akyol, Nergiz (Önen) Poyraz
Bull. Korean Math. Soc. 2023; 60(5): 1155-1179
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