Communications of the
Korean Mathematical Society

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

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  • 2023-01-31

    On the structure of a $k$-annihilating ideal hypergraph of commutative rings

    Shaymaa S. Essa, Husam Q. Mohammad

    Abstract : In this paper we obtain a new structure of a $k$-annihilating ideal hypergraph of a reduced ring $R$, by determine the order and size of a hypergraph $\mathcal{AG}_{k}(R)$. Also we describe and count the degree of every nontrivial ideal of a ring $R$ containing in vertex set $\mathcal{A}(R,k)$ of a hypergraph $\mathcal{AG}_{k}(R)$. Furthermore, we prove the diameter of $\mathcal{AG}_{k}(R)$ must be less than or equal to 2. Finally, we determine the minimal dominating set of a $k$-annihilating ideal hypergraph of a ring $R$.

  • 2022-10-31

    Common fixed point results for generalized orthogonal $F$-Suzuki contraction for family of multivalued mappings in orthogonal $b$-metric spaces

    Bahru Tsegaye Leyew, Oluwatosin Temitope Mewomo

    Abstract : In this paper, we introduce a new class of mappings called the generalized orthogonal $F$-Suzuki contraction for a family of multivalued mappings in the setup of orthogonal $b$-metric spaces. We established the existence of some common fixed point results without using any commutativity condition for this new class of mappings in orthogonal $b$-metric spaces. Moreover, we illustrate and support these common fixed point results with example. The results obtained in this work generalize and extend some recent and classical related results in the existing literature.

  • 2022-10-31

    On functions starlike with respect to $n$-ply symmetric, conjugate and symmetric conjugate points

    Somya Malik, Vaithiyanathan Ravichandran

    Abstract : For given non-negative real numbers $\alpha_k$ with $ \sum_{k=1}^{m}\alpha_k =1$ and normalized analytic functions $f_k$, $k=1,\dotsc,m$, defined on the open unit disc, let the functions $F$ and $F_n$ be defined by $ F(z):=\sum_{k=1}^{m}\alpha_k f_k (z)$, and $F_{n}(z):=n^{-1}\sum_{j=0}^{n-1} e^{-2j\pi i/n} F(e^{2j\pi i/n} z)$. This paper studies the functions $f_k$ satisfying the subordination $zf'_{k} (z)/F_{n} (z) \prec h(z)$, where the function $h$ is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

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  • 2022-04-30

    A note on static manifolds and almost Ricci solitons

    Reihaneh Ahmadzadeh, Hajar Ghahremani-Gol

    Abstract : In this short paper, we investigate the existence of non-trivial almost Ricci solitones on static manifolds. As a result we show any compact nontrivial static manifold is isometric to a Euclidean sphere.

  • 2022-04-30

    Homogeneous conditions for stochastic tensors

    Bokhee Im, Jonathan D. H. Smith

    Abstract : Fix an integer $nge 1$. Then the simplex $Pi_n$, Birkhoff polytope $Omega_n$, and Latin square polytope $Lambda_n$ each yield projective geometries obtained by identifying antipodal points on a sphere bounding a ball centered at the barycenter of the polytope. We investigate conditions for homogeneous coordinates of points in the projective geometries to locate exact vertices of the respective polytopes, namely crisp distributions, permutation matrices, and quasigroups or Latin squares respectively. In the latter case, the homogeneous conditions form a crucial part of a recent projective-geometrical approach to the study of orthogonality of Latin squares. Coordinates based on the barycenter of $Omega_n$ are also suited to the analysis of generalized doubly stochastic matrices, observing that orthogonal matrices of this type form a subgroup of the orthogonal group.

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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.

  • 2022-10-31

    Riemannian submersions whose total space is endowed with a torse-forming vector field

    \c{S}emsi Eken~Meri\c{c}, Erol K{\i}l{\i}\c{c}

    Abstract : In the present paper, a Riemannian submersion $\pi$ between Riemannian manifolds such that the total space of $\pi$ endowed with a torse-forming vector field $\nu$ is studied. Some remarkable results of such a submersion whose total space is Ricci soliton are given. Moreover, some characterizations about any fiber of $\pi$ or the base manifold $B$ to be an almost quasi-Einstein are obtained.

  • 2022-04-30

    Subclasses of analytic functions defined by Lommel operator

    c{S}ahsene Altinkaya, Rizwan Salim Badar, Khalida Inayat Noor

    Abstract : We use convolution techniques to define certain classes of starlike functions which are associated with Lommel operator. Some inclusion results are investigated. It is also shown that these classes are invariant under Bernardi integral operator.

  • 2023-07-31

    The dimension graph for modules over commutative rings

    Shiroyeh Payrovi

    Abstract : Let $R$ be a commutative ring and $M$ be an $R$-module. The dimension graph of $M$, denoted by $DG(M)$, is a simple undirected graph whose vertex set is $Z(M)\setminus {\rm Ann}(M)$ and two distinct vertices $x$ and $y$ are adjacent if and only if $\dim M/(x, y)M=\min\{\dim M/xM, \dim M/yM\}$. It is shown that $DG(M)$ is a disconnected graph if and only if (i) ${\rm Ass}(M)=\{\mathfrak p, \mathfrak q\}$, $Z(M)=\mathfrak p\cup \mathfrak q$ and ${\rm Ann}(M)=\mathfrak p\cap \mathfrak q$. (ii) $\dim M=\dim R/\mathfrak p=\dim R/\mathfrak q$. (iii) $\dim M/xM=\dim M$ for all $x\in Z(M)\setminus {\rm Ann}(M)$. Furthermore, it is shown that ${\rm diam}(DG(M))\leq 2$ and ${\rm gr}({DG(M)})=3$, whenever $M$ is Noetherian with $|Z(M)\setminus {\rm Ann}(M)| \geq 3$ and $DG(M)$ is a connected graph.

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  • 2023-04-30

    The measurability of Hewitt-Stromberg measures and dimensions

    Zied Douzi, Bilel Selmi, Haythem Zyoudi

    Abstract : The aim of this paper is to study the descriptive set-theoretic complexity of the Hewitt-Stromberg measure and dimension maps.

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January, 2024
Vol.39 No.1

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