Communications of the
Korean Mathematical Society
CKMS

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

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  • 2023-01-31

    Geometric inequalities for warped products submanifolds in generalized complex space forms

    Mohd Aquib, Mohd Aslam, Michel Nguiffo Boyom, Mohammad Hasan Shahid

    Abstract : In this article, we derived Chen's inequality for warped product bi-slant submanifolds in generalized complex space forms using semi-symmetric metric connections and discuss the equality case of the inequality. Further, we discuss non-existence of such minimal immersion. We also provide various applications of the obtained inequalities.

  • 2022-07-31

    Commutativity criteria of prime rings involving two endomorphisms

    Souad Dakir, Abdellah Mamouni, Mohammed Tamekkante

    Abstract : This paper treats the commutativity of prime rings with involution over which elements satisfy some specific identities involving endomorphisms. The obtained results cover some well-known results. We show, by given examples, that the imposed hypotheses are necessary.

  • 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

    A note on statistical manifolds with torsion

    Hwajeong Kim

    Abstract : Given a linear connection $\nabla$ and its dual connection $\nabla^*$, we discuss the situation where $\nabla +\nabla^* = 0$. We also discuss statistical manifolds with torsion and give new examples of some type for linear connections inducing the statistical manifolds with non-zero torsion.

  • 2023-01-31

    Ricci $\rho$-soliton in a perfect fluid spacetime with a gradient vector field

    Dibakar Dey, Pradip Majhi

    Abstract : In this paper, we studied several geometrical aspects of a perfect fluid spacetime admitting a Ricci $\rho$-soliton and an $\eta$-Ricci $\rho$-soliton. Beside this, we consider the velocity vector of the perfect fluid space time as a gradient vector and obtain some Poisson equations satisfied by the potential function of the gradient solitons.

  • 2022-10-31

    Ground state sign-changing solutions for nonlinear Schr\"{o}dinger-Poisson system with indefinite potentials

    Shubin Yu, Ziheng Zhang

    Abstract : This paper is concerned with the following Schr\"{o}dinger-\linebreak Poisson system$$\left\{\begin{array}{ll} -{\Delta}u+V(x)u+K(x){\phi}u=a(x)|u|^{p-2}u  &\mbox{in}\ \mathbb{R}^3, \\[0.1cm] -{\Delta}{\phi}=K(x)u^{2}&\mbox{in}\ \mathbb{R}^3, \\[0.1cm]\end{array}\right.$$where $4<p<6$. For the case that $K$ is nonnegative, $V$ and $a$ are indefinite, we prove the above problem possesses one ground state sign-changing solutionwith exactly two nodal domains by constraint variational method and quantitative deformation lemma. Moreover, we show that the energy of sign-changing solutions islarger than that of the ground state solutions. The novelty of this paper is that the potential $a$ is indefinite and allowed to vanish at infinity. In this sense, we complementthe existing results obtained by Batista and Furtado \cite{BF18}.

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  • 2023-01-31

    Numerical method for a system of Caputo fractional differential equations with non-local boundary conditions

    S. Joe Christin Mary, Ayyadurai Tamilselvan

    Abstract : A class of systems of Caputo fractional differential equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a uniform mesh is proposed. Supremum norm is used to derive an error estimate which is of order $\kappa-1$, $1

  • 2023-01-31

    On covering and quotient maps for $\mathcal{I}^{\mathcal{K}}$-convergence in topological spaces

    Debajit Hazarika, Ankur Sharmah

    Abstract : In this article, we show that the family of all $\mathcal{I}^\mathcal{K}$-open subsets in a topological space forms a topology if $\mathcal{K}$ is a maximal ideal. We introduce the notion of $\mathcal{I}^\mathcal{K}$-covering map and investigate some basic properties. The notion of quotient map is studied in the context of $\mathcal{I}^\mathcal{K}$-convergence and the relationship between $\mathcal{I}^\mathcal{K}$-continuity and $\mathcal{I}^\mathcal{K}$-quotient map is established. We show that for a maximal ideal $\mathcal{K}$, the properties of continuity and preserving $\mathcal{I}^\mathcal{K}$-convergence of a function defined on $X$ coincide if and only if $X$ is an $\mathcal{I}^\mathcal{K}$-sequential space.

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  • 2023-01-31

    The $u$-$S$-weak global dimensions of commutative rings

    Xiaolei Zhang

    Abstract : In this paper, we introduce and study the $u$-$S$-weak global dimension $u$-$S$-w.gl.dim$(R)$ of a commutative ring $R$ for some multiplicative subset $S$ of $R$. Moreover, the $u$-$S$-weak global dimensions of factor rings and polynomial rings are investigated.

  • 2022-01-31

    A note on defectless extensions of henselian valued fields

    Azadeh Nikseresht

    Abstract : A valued field $(K,v)$ is called defectless if each of its finite extensions is defectless. In cite{a.k.o.2002}, Aghigh and Khanduja posed a question on defectless extensions of henselian valued fields: ``if every simple algebraic extension of a henselian valued field $(K,v)$ is defectless, then is it true that $(K,v)$ is defectless?'' They gave an example to show that the answer is ``no'' in general. This paper explores when the answer to the mentioned question is affirmative. More precisely, for a henselian valued field $(K,v)$ such that each of its simple algebraic extensions is defectless, we investigate additional conditions under which $(K,v)$ is defectless.

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October, 2023
Vol.38 No.4

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