Communications of the
Korean Mathematical Society

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

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  • 2022-04-30

    Some results on $S$-accr pairs

    Ahmed Hamed, Achraf Malek

    Abstract : Let $Rsubseteq T$ be an extension of a commutative ring and $Ssubseteq R$ a multiplicative subset. We say that $(R, T)$ is an $S$-accr (a commutative ring $R$ is said to be $S$-accr if every ascending chain of residuals of the form $(I:B)subseteq (I:B^2)subseteq (I:B^3)subseteqcdots$ is $S$-stationary, where $I$ is an ideal of $R$ and $B$ is a finitely generated ideal of $R$) pair if every ring $A$ with $Rsubseteq Asubseteq T$ satisfies $S$-accr. Using this concept, we give an $S$-version of several different known results.

  • 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.

  • 2022-07-31

    Infinitely many homoclinic solutions for damped vibration systems with locally defined potentials

    Wafa Selmi, Mohsen Timoumi

    Abstract : In this paper, we are concerned with the existence of infinitely many fast homoclinic solutions for the following damped vibration system $$ddot{u}(t)+q(t)dot{u}(t)-L(t)u(t)+ abla W(t,u(t))=0, forall tinmathbb{R}, leqno(1)$$ where $qin C(mathbb{R},mathbb{R})$, $Lin C(mathbb{R},mathbb{R}^{N^{2}})$ is a symmetric and positive definite matix-valued function and $Win C^{1}(mathbb{R} imesmathbb{R}^{N},mathbb{R})$. The novelty of this paper is that, assuming that $L$ is bounded from below unnecessarily coercive at infinity, and $W$ is only locally defined near the origin with respect to the second variable, we show that $(1)$ possesses infinitely many homoclinic solutions via a variant symmetric mountain pass theorem.

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  • 2022-10-31

    Classification of Solvable Lie groups whose non-trivial coadjoint orbits are of Codimension $1$

    Hieu Van Ha, Duong Quang Hoa, Vu Anh Le

    Abstract : We give a complete classification of simply connected and solvable real Lie groups whose nontrivial coadjoint orbits are of codimension 1. This classification of the Lie groups is one to one corresponding to the classification of their Lie algebras. Such a Lie group belongs to a class, called the class of MD-groups. The Lie algebra of an MD-group is called an MD-algebra. Some interest properties of MD-algebras will be investigated as well.

  • 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.

  • 2022-07-31

    A characterization of finite factorization positive monoids

    Harold Polo

    Abstract : We provide a characterization of the emph{positive monoids} (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

  • 2022-10-31

    Notes on $(LCS)_n$-manifolds satisfying certain conditions

    Shyam Kishor, Pushpendra Verma

    Abstract : The object of the present paper is to study the properties of conharmonically flat $(LCS)_n$-manifold, special weakly Ricci symmetric and generalized Ricci recurrent $(LCS)_n$-manifold. The existence of such a manifold is ensured by non-trivial example.

  • 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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  • 2022-07-31

    Semi-neutral groupoids and $BCK$-algebras

    Hee Sik Kim, Joseph Neggers, Young Joo Seo

    Abstract : In this paper, we introduce the notion of a left-almost-zero groupoid, and we generalize two axioms which play important roles in the theory of $BCK$-algebra using the notion of a projection. Moreover, we investigate a Smarandache disjointness of semi-leftoids.

  • 2023-04-30

    Unitary analogues of a generalized number-theoretic sum

    Traiwat Intarawong, Boonrod Yuttanan

    Abstract : In this paper, we investigate the sums of the elements in the finite set $\{x^{k}:1\leq x\leq\frac{n}{m},\gcd_u(x,n)=1\}$, where $k$, $m$ and $n$ are positive integers and $\gcd_u(x,n)$ is the unitary greatest common divisor of $x$ and $n$. Moreover, for some cases of $k$ and $m$, we can give the explicit formulae for the sums involving some well-known arithmetic functions.

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January, 2024
Vol.39 No.1

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