Communications of the
Korean Mathematical Society

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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  • 2023-07-31

    S-coherent property in trivial extension and in amalgamated duplication


    Abstract : Bennis and El Hajoui have defined a (commutative unital) ring $R$ to be $S$-coherent if each finitely generated ideal of $R$ is a $S$-finitely presented $R$-module. Any coherent ring is an $S$-coherent ring. Several examples of $S$-coherent rings that are not coherent rings are obtained as byproducts of our study of the transfer of the $S$-coherent property to trivial ring extensions and amalgamated duplications.

  • 2022-04-30

    Certain reduction and transformation formulas for the Kamp'{e} de F'{e}riet function

    Medhat A. Rakha, Arjun K. Rathie

    Abstract : In 2014, Liu and Wang established a large number of interesting reduction, transformation and summation formulas for the Kamp'{e} de F'{e}riet function. Inspired by the work, we aim to find further several transformation and reduction formulas for the Kamp'{e} de F'{e}riet function. Theses formulas are mainly based on the formulas given by Liu and Wang cite{33}.

  • 2023-07-31

    Areas of polygons with vertices from Lucas sequences on a plane

    SeokJun Hong, SiHyun Moon, Ho Park, SeoYeon Park, SoYoung Seo

    Abstract : Area problems for triangles and polygons whose vertices have Fibonacci numbers on a plane were presented by A. Shriki, O. Liba, and S. Edwards et al. In 2017, V. P. Johnson and C. K. Cook addressed problems of the areas of triangles and polygons whose vertices have various sequences. This paper examines the conditions of triangles and polygons whose vertices have Lucas sequences and presents a formula for their areas.

  • 2023-04-30

    On sharp general coefficient estimates for $\vartheta$-spirallike functions

    \c{S}ahsene Altinkaya, Tu\u{g}ba Yavuz

    Abstract : This paper attempts to investigate a new subfamily \linebreak $\mathcal{ST}_{\vartheta ,\sigma}\left( \alpha ,\beta ,\gamma ,\mu \right) $ of spirallike functions endowed with Mittag-Leffler and Wright functions. The paper further investigates sharp coefficient bounds for functions that belong to this class.

  • 2023-01-31

    Existence theorems for critical degenerate equations involving the Grushin operators

    Huong Thi Thu Nguyen, Tri Minh Nguyen

    Abstract : In this paper we prove the existence of nontrivial weak solutions to the boundary value problem \begin{align*} - G_1 u & =u^3 + f(x,y,u) \quad \text{ in } \Omega ,\\ u &\geq 0 \quad \text{ in } \Omega ,\\ u & =0 \quad \text{ on } \partial\Omega , \end{align*} where $\Omega $ is a bounded domain with smooth boundary in $\mathbb{R}^3$, $G_1 $ is a Grushin type operator, and $f(x,y,u)$ is a lower order perturbation of $u^3$ with $f(x,y,0)=0$. The nonlinearity involved is of critical exponent, which differs from the existing results in \cite{Tri:2018,TriLuyen:2020}.

  • 2022-10-31

    Liouville theorems for the multidimensional fractional Bessel operators

    Vanesa Galli, Sandra Molina, Alejandro Quintero

    Abstract : In this paper, we establish Liouville type theorems for the fractional powers of multidimensional Bessel operators extending the results given in \cite{GMQ18}. In order to do this, we consider the distributional point of view of fractional Bessel operators studied in \cite{Mo18}.

  • 2023-07-31

    Existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system

    Nguyen Viet Tuan

    Abstract : In this paper, we study the existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system with subcritical growth \begin{equation*} \begin{cases} -\Delta_\lambda u -\mu v =|v|^{p-1}v &\;\text{ in } \Omega,\\ -\Delta_\lambda v -\mu u=|u|^{q-1}u &\;\text{ in } \Omega,\\ u = v = 0 &\;\text{ on } \partial\Omega, \end{cases} \end{equation*} where $p, q>1$ and $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$, $N\ge 3$. Here $\Delta_\lambda$ is the strongly degenerate elliptic operator. The existence of at least a nontrivial solution is obtained by variational methods while the nonexistence of positive solutions are proven by a contradiction argument.

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  • 2023-04-30

    H-quasi-hemi-slant submersions

    Sumeet Kumar, Sushil Kumar, Rajendra Prasad, Aysel Turgut Vanli

    Abstract : In this paper, h-quasi-hemi-slant submersions and almost h-quasi-hemi-slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds are introduced. Fundamental results on h-quasi-hemi-slant submersions: the integrability of distributions, geometry of foliations and the conditions for such submersions to be totally geodesic are investigated. Moreover, some non-trivial examples of the h-quasi-hemi-slant submersion are constructed.

  • 2023-10-31

    Nonlinear maps preserving the mixed product $_*[X\diamond Y, Z]$ on $*$-algebras

    Raof Ahmad Bhat, Abbas Hussain Shikeh, Mohammad Aslam Siddeeque

    Abstract : Let $\mathfrak{A}$ and $\mathfrak{B}$ be unital prime $*$-algebras such that $\mathfrak{A}$ contains a nontrivial projection. In the present paper, we show that if a bijective map $\Theta:\mathfrak{A}\to\mathfrak{B}$ satisfies $\Theta(_*[X\diamond Y, Z])={}_*[\Theta(X)\diamond \Theta(Y), \Theta(Z)]$ for all $X, Y, Z\in\mathfrak{A}$, then $\Theta$ or $-\Theta$ is a $*$-ring isomorphism. As an application, we shall characterize such maps in factor von Neumann algebras.

  • 2023-01-31

    Pr\"ufer conditions vs EM conditions

    Emad Abuosba, Mariam Al-Azaizeh, Manal Ghanem

    Abstract : In this article we relate the six Pr\"{u}fer conditions with the EM conditions. We use the EM-conditions to prove some cases of equivalence of the six Pr\"{u}fer conditions. We also use the Pr\"{u}fer conditions to answer some open problems concerning EM-rings.

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January, 2024
Vol.39 No.1

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