Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2023-09-30
Relationship between the structure of a factor ring $R/P$ and derivations of $R$
Karim Bouchannafa, Moulay Abdallah Idrissi, Lahcen OukhtiteAbstract : The purpose of this paper is to study the relationship between the structure of a factor ring $R/P$ and the behavior of some derivations of $R$. More precisely, we establish a connection between the commutativity of $R/P$ and derivations of $R$ satisfying specific identities involving the prime ideal $P$. Moreover, we provide an example to show that our results cannot be extended to semi-prime ideals.
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2023-07-31
Classification of twisted product lightlike submanifolds
Sangeet Kumar, Megha PruthiAbstract : In this paper, we introduce the idea of twisted product lightlike submanifolds of semi-Riemannian manifolds and provide non-trivial examples of such lightlike submanifolds. Then, we prove the non-existence of proper isotropic or totally lightlike twisted product submanifolds of a semi-Riemannian manifold. We also show that for a twisted product lightlike submanifold of a semi-Riemannian manifold, the induced connection $\nabla$ is not a metric connection. Further, we prove that a totally umbilical $SCR$-lightlike submanifold of an indefinite Kaehler manifold $\tilde{M}$ does not admit any twisted product $SCR$-lightlike submanifold of the type $M_{\perp}\times_{\phi}M_{T}$, where $M_{\perp}$ is a totally real submanifold and $M_{T}$ is a holomorphic submanifold of $\tilde{M}$. Consequently, we obtain a geometric inequality for the second fundamental form of twisted product $SCR$-lightlike submanifolds of the type $M_{T}\times_{\phi}M_{\perp}$ of an indefinite Kaehler manifold $\tilde{M}$, in terms of the gradient of $\ln \phi$, where $\phi$ stands for the twisting function. Subsequently, the equality case of this inequality is discussed. Finally, we construct a non-trivial example of a twisted product $SCR$-lightlike submanifold in an indefinite Kaehler manifold.
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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
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 $\mathcal U^+$.
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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 $I_p(t)=\phi(p)t^{\beta}$.
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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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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.
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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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2023-09-30
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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Uniqueness of meromorphic solutions of a certain type of difference equations
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The recurrent hypercyclicity criterion for translation $C_0$-semigroups on complex sectors
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A model of retirement and consumption-portfolio choice
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Bach almost solitons in paraSasakian geometry
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