Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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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 TamilselvanAbstract : 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
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2024-01-31
On strongly quasi $J$-ideals of commutative rings
El Mehdi Bouba
, Yassine EL-khabchi, Mohammed Tamekkante Abstract : Let $R$ be a commutative ring with identity. In this paper, we introduce a new class of ideals called the class of strongly quasi $J$-ideals lying properly between the class of $J$-ideals and the class of quasi $J$-ideals. A proper ideal $I$ of $R$ is called a strongly quasi $J$-ideal if, whenever $a$, $b\in R$ and $ab\in I$, then $a^{2}\in I$ or $b\in {\rm Jac}(R)$. Firstly, we investigate some basic properties of strongly quasi $J$-ideals. Hence, we give the necessary and sufficient conditions for a ring $R$ to contain a strongly quasi $J$-ideals. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the primary ideals, the prime ideals and the maximal ideals. Finally, we give an idea about some strongly quasi $J$-ideals of the quotient rings, the localization of rings, the polynomial rings and the trivial rings extensions.
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2022-10-31
Circle approximation using parametric polynomial curves of high degree in explicit form
Young Joon AhnAbstract : 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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2023-10-31
Nonlinear maps preserving the mixed product $_*[X\diamond Y, Z]$ on $*$-algebras
Raof Ahmad Bhat, Abbas Hussain Shikeh, Mohammad Aslam SiddeequeAbstract : 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.
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2023-07-31
A study of differential identities on $\sigma$-prime rings
Adnan Abbasi, Md Arshad Madni, Muzibur Rahman MozumderAbstract : Let $\mathcal{R}$ be a $\sigma$-prime ring with involution $\sigma$. The main \linebreak objective of this paper is to describe the structure of the $\sigma$-prime ring $\mathcal{R}$ with involution $\sigma$ satisfying certain differential identities involving three derivations $\psi_1, \psi_2$ and $\psi_3$ such that $\psi_1[t_1,\sigma(t_1)]+[\psi_2(t_1),\psi_2(\sigma(t_1))] + [\psi_3(t_1),\sigma(t_1)]\in \mathcal{J}_Z$ for all $t_1\in \mathcal{R}$. Further, some other related results have also been discussed.
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2024-01-31
Generalized derivations in ring with involution involving symmetric and skew symmetric elements
Souad DAKIR, Hajar EL MIR, Abdellah MAMOUNIAbstract : In this paper we will demonstrate some results on a prime ring with involution by introducing two generalized derivations acting on symmetric and skew symmetric elements. This approach allows us to generalize some well known results. Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.
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2023-10-31
On graded $(m, n)$-closed submodules
Rezvan VarmazyarAbstract : Let $A$ be a $G$-graded commutative ring with identity and $M$ a graded $A$-module. Let $m, n$ be positive integers with $m>n$. A proper graded submodule $L$ of $M$ is said to be graded $(m, n)$-closed if $a^{m}_g\cdot x_t\in L$ implies that $a^{n}_g\cdot x_t\in L$, where $a_g\in h(A)$ and $x_t\in h(M)$. The aim of this paper is to explore some basic properties of these class of submodules which are a generalization of graded $(m, n)$-closed ideals. Also, we investigate $GC^{m}_n-rad$ property for graded submodules.
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2024-01-31
Spacetimes admitting divergence free $m$-projective curvature tensor
Uday Chand De, Dipankar HazraAbstract : This paper is concerned with the study of spacetimes satisfying $\mathrm{div}\mathcal{M}=0$, where ``div" denotes the divergence and $\mathcal{M}$ is the $m$-projective curvature tensor. We establish that a perfect fluid spacetime with $\mathrm{div}\mathcal{M}=0$ is a generalized Robertson-Walker spacetime and vorticity free; whereas a four-dimensional perfect fluid spacetime becomes a Robertson-Walker spacetime. Moreover, we establish that a Ricci recurrent spacetime with $\mathrm{div}\mathcal{M}=0$ represents a generalized Robertson-Walker spacetime.
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2022-10-31
On the semi-local convergence of contraharmonic-mean Newton's method (CHMN)
Ioannis K. Argyros, Manoj Kumar SinghAbstract : The main objective of this work is to investigate the study of the local and semi-local convergence of the contraharmonic-mean Newton's method (CHMN) for solving nonlinear equations in a Banach space. We have performed the semi-local convergence analysis by using generalized conditions. We examine the theoretical results by comparing the CHN method with the Newton's method and other third order methods by Weerakoon et al.~using some test functions. The theoretical and numerical results are also supported by the basins of attraction for a selected test function.
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2023-07-31
Convergence of sequences in generalized topological spaces via filter
Julio C. Ramos-Fernández, Ennis Rosas, Margot Salas-BrownAbstract : In this paper a generalization of convergent sequences in connection with generalized topologies and filters is given. Additionally, properties such as uniqueness, behavior related to continuous functions are established and notions relative to product spaces.
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Generalizing some Fibonacci--Lucas relations
Junghyun Hong, Jongmin Lee, Ho Park
Commun. Korean Math. Soc. 2023; 38(1): 89-96
https://doi.org/10.4134/CKMS.c220015 -
Uniqueness of meromorphic function with its $k$-th derivative sharing two small functions under different weights
Abhijit Banerjee, Arpita Kundu
Commun. Korean Math. Soc. 2023; 38(2): 525-545
https://doi.org/10.4134/CKMS.c220168 -
On graded $J$-ideals over graded rings
Tamem Al-Shorman, Malik Bataineh, Ece Yetkin Celikel
Commun. Korean Math. Soc. 2023; 38(2): 365-376
https://doi.org/10.4134/CKMS.c220169 -
Simple formulations on circulant matrices with alternating Fibonacci
Sugi Guritman
Commun. Korean Math. Soc. 2023; 38(2): 341-354
https://doi.org/10.4134/CKMS.c220110
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$\star$-conformal Ricci solitons on almost coK\"{a}hler manifolds
Tarak Mandal, Avijit Sarkar
Commun. Korean Math. Soc. 2023; 38(3): 865-880
https://doi.org/10.4134/CKMS.c220145 -
Joint essential numerical spectrum and Jeribi essential numerical spectrum of linear operators in Banach spaces
Bouthaina Abdelhedi, Wissal Boubaker, Nedra Moalla
Commun. Korean Math. Soc. 2023; 38(4): 1029-1044
https://doi.org/10.4134/CKMS.c220019 -
Areas of polygons with vertices from Lucas sequences on a plane
SeokJun Hong, SiHyun Moon, Ho Park, SeoYeon Park, SoYoung Seo
Commun. Korean Math. Soc. 2023; 38(3): 695-704
https://doi.org/10.4134/CKMS.c220245 -
Energy decay for a viscoelastic equation with Balakrishnan-Taylor damping involving infinite memory and nonlinear time-varying delay terms in dynamical boundary
soufiane Benkouider, Abita Rahmoune
Commun. Korean Math. Soc. 2023; 38(3): 943-966
https://doi.org/10.4134/CKMS.c220225
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