Communications of the
Korean Mathematical Society

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

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  • 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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  • 2023-10-31

    Transversal lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds

    Shiv Sharma Shukla, Vipul Singh

    Abstract : In this paper, we introduce and study two new classes of lightlike submersions, called radical transversal and transversal lightlike submersions between an indefinite Sasakian manifold and a lightlike manifold. We give examples and investigate the geometry of distributions involved in the definitions of these lightlike submersions. We also study radical transversal and transversal lightlike submersions from an indefinite Sasakian manifold onto a lightlike manifold with totally contact umbilical fibers.

  • 2022-01-31

    On common and sequential fixed points via asymptotic regularity

    Ravindra Kishor Bisht, Sayantan Panja, Kushal Roy, Mantu Saha

    Abstract : In this paper, we introduce some new classes of generalized mappings and prove some common fixed point theorems for a pair of asymptotically regular mappings. Our results extend and improve various well-known results due to Kannan, Reich, Wong, Hardy and Rogers, 'Ciri'c, Jungck, G'ornicki and many others. In addition to it, a sequential fixed point for a mapping which is the point-wise limit of a sequence of functions satisfying 'Ciri'c-Proinov-G'ornicki type mapping has been proved. Supporting examples have been given in strengthening hypotheses of our established theorems.

  • 2023-07-31

    Hyers-Ulam stability of fractional stochastic differential equations with random impulse

    Dumitru Baleanu, Banupriya Kandasamy, Ramkumar Kasinathan, Ravikumar Kasinathan, Varshini Sandrasekaran

    Abstract : The goal of this study is to derive a class of random impulsive non-local fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.

  • 2023-04-30

    On graded $J$-ideals over graded rings

    Tamem Al-Shorman, Malik Bataineh, Ece Yetkin Celikel

    Abstract : The goal of this article is to present the graded $J$-ideals of $G$-graded rings which are extensions of $J$-ideals of commutative rings. A graded ideal $P$ of a $G$-graded ring $R$ is a graded $J$-ideal if whenever $x,y\in h(R)$, if $xy\in P$ and $x\not\in J(R)$, then $y\in P$, where $h(R)$ and $J(R)$ denote the set of all homogeneous elements and the Jacobson radical of $R$, respectively. Several characterizations and properties with supporting examples of the concept of graded $J$-ideals of graded rings are investigated.

  • 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 $R$.

  • 2022-01-31

    Infra-topologies revisited: logic and clarification of basic notions

    Tomasz Witczak

    Abstract : In this paper we adhere to the definition of emph{infra-topological} space as it was introduced by Al-Odhari. Namely, we speak about families of subsets which contain $emptyset$ and the whole universe $X$, being at the same time closed under finite intersections (but not necessarily under arbitrary or even finite unions). This slight modification allows us to distinguish between new classes of subsets (infra-open, ps-infra-open and i-genuine). Analogous notions are discussed in the language of closures. The class of minimal infra-open sets is studied too, as well as the idea of generalized infra-spaces. Finally, we obtain characterization of infra-spaces in terms of modal logic, using some of the notions introduced above.

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  • 2022-01-31

    Semi-invariant submanifolds of codimension 3 in a complex space form in terms of the structure Jacobi operator

    U-Hang Ki, Hiroyuki Kurihara

    Abstract : Let $M$ be a semi-invariant submanifold of codimension $3$ with almost contact metric structure $(phi, xi, eta, g)$ in a complex space form $M_{n +1} (c), c e 0$. We denote by $A$ and $R_{xi}$ the shape operator in the direction of distinguished normal vector field and the structure Jacobi operator with respect to the structure vector $xi$, respectively. Suppose that the third fundamental form $t$ satisfies $dt (X,Y) =2 heta g (phi X, Y)$ for a scalar $ heta (< 2 c)$ and any vector fields $X$ and $Y$ on $M$. In this paper, we prove that if it satisfies $R_{xi} A =A R_{xi}$ and at the same time $ abla_{xi} R_{xi} =0$ on $M$, then $M$ is a Hopf hypersurface of type ($A$) provided that the scalar curvature $s$ of $M$ holds $s -2(n -1)c leq 0$.

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  • 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.

  • 2022-07-31

    Solitons of K"{A}hlerian Norden space-time manifolds

    Praveena Manjappa Mundalamane, Bagewadi Channabasappa Shanthappa, Mallannara Siddalingappa Siddesha

    Abstract : We study solitons of K"{a}hlerian Norden space-time manifolds and Bochner curvature tensor in almost pseudo symmetric K"{a}hlerian space-time manifolds. It is shown that the steady, expanding or shrinking solitons depend on different relations of energy density/isotropic pressure, the cosmological constant, and gravitational constant.

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October, 2023
Vol.38 No.4

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