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 $R$.

  • 2023-10-31

    The dimension of the maximal spectrum of some ring extensions

    Rachida EL KHALFAOUI, Najib Mahdou

    Abstract : Let $A$ be a ring and $\mathcal{J} = \{\text{ideals $I$ of $A$} \,|\, J(I) = I\}$. The Krull dimension of $A$, written $\dim A$, is the sup of the lengths of chains of prime ideals of $A$; whereas the dimension of the maximal spectrum, denoted by $\dim_\mathcal{J} A$, is the sup of the lengths of chains of prime ideals from $\mathcal{J}$. Then $\dim_{\mathcal{J}} A\leq \dim A$. In this paper, we will study the dimension of the maximal spectrum of some constructions of rings and we will be interested in the transfer of the property $J$-Noetherian to ring extensions.

  • 2023-04-30

    Results associated with the Schwarz lemma on the boundary

    B\"{u}lent Nafi \"{O}rnek

    Abstract : In this paper, some estimations will be given for the analytic functions belonging to the class $\mathcal{R}\left( \alpha \right) $. In these estimations, an upper bound and a lower bound will be determined for the first coefficient of the expansion of the analytic function $h(z)$ and the modulus of the angular derivative of the function $\frac{zh^{\prime }(z)}{ h(z)}$, respectively. Also, the relationship between the coefficients of the analytical function $h(z)$ and the derivative mentioned above will be shown.

  • 2023-01-31

    An exponentially fitted method for two parameter singularly perturbed parabolic boundary value problems

    Gemechis File Duressa, Tariku Birabasa Mekonnen

    Abstract : This article devises an exponentially fitted method for the numerical solution of two parameter singularly perturbed parabolic boundary value problems. The proposed scheme is able to resolve the two lateral boundary layers of the solution. Error estimates show that the constructed scheme is parameter-uniformly convergent with a quadratic numerical rate of convergence. Some numerical test examples are taken from recently published articles to confirm the theoretical results and demonstrate a good performance of the current scheme.

  • 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.

  • 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.

  • 2022-10-31

    On strong exponential limit shadowing property

    Ali Darabi

    Abstract : In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that $\Omega$-stable diffeomorphisms and $\mathcal{\mathcal{L}}$-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.

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  • 2023-07-31

    On nonnil-SFT rings

    Ali Benhissi, Abdelamir Dabbabi

    Abstract : The purpose of this paper is to introduce a new class of rings containing the class of SFT-rings and contained in the class of rings with Noetherian prime spectrum. Let $A$ be a commutative ring with unit and $I$ be an ideal of $A$. We say that $I$ is SFT if there exist an integer $k\geq 1$ and a finitely generated ideal $F\subseteq I$ of $A$ such that $x^k\in F$ for every $x\in I$. The ring $A$ is said to be nonnil-SFT, if each nonnil-ideal (i.e., not contained in the nilradical of $A$) is SFT. We investigate the nonnil-SFT variant of some well known theorems on SFT-rings. Also we study the transfer of this property to Nagata's idealization and the amalgamation algebra along an ideal. Many examples are given. In fact, using the amalgamation construction, we give an infinite family of nonnil-SFT rings which are not SFT.

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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

  • 2022-10-31

    Circle approximation using parametric polynomial curves of high degree in explicit form

    Young Joon Ahn

    Abstract : In this paper we present a full circle approximation method using parametric polynomial curves with algebraic coefficients which are curvature continuous at both endpoints. Our method yields the $n$-th degree parametric polynomial curves which have a total number of $2n$ contacts with the full circle at both endpoints and the midpoint. The parametric polynomial approximants have algebraic coefficients involving rational numbers and radicals for degree higher than four. We obtain the exact Hausdorff distances between the circle and the approximation curves.

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April, 2024
Vol.39 No.2

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