Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2023-01-31
Some functional identities arising from derivations
Abdellah Mamouni, Lahcen Oukhtite, Mohammed ZerraAbstract : This paper considers some functional identities related to derivations of a ring $R$ and their action on the centre of $R/P$ where $P$ is a prime ideal of $R.$ It generalizes some previous results that are in the same spirit. Finally, examples proving that our restrictions cannot be relaxed are given.
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2022-10-31
Note on the multifractal measures of Cartesian product sets
Najmeddine Attia, Rihab Guedri, Omrane GuizaniAbstract : In this paper, we shall be concerned with evaluation of multifractal Hausdorff measure ${\mathcal H}^{q,t}_\mu$ and multifractal packing measure ${\mathcal P}^{q,t}_\mu$ of Cartesian product sets by means of the measure of their components. This is done by investigating the density result introduced in \cite{Olsen95}. As a consequence, we get the inequalities related to the multifractal dimension functions, proved in \cite{Olsen96}, by using a unified method for all the inequalities. Finally, we discuss the extension of our approach to studying the multifractal Hewitt-Stromberg measures of Cartesian product sets.
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2023-07-31
Coloring links by the symmetric group of degree three
Kazuhiro Ichihara, Eri MatsudoAbstract : We consider the number of colors for colorings of links by the symmetric group $S_3$ of degree $3$. For knots, such a coloring corresponds to a Fox 3-coloring, and thus the number of colors must be 1 or 3. However, for links, there are colorings by $S_3$ with 4 or 5 colors. In this paper, we show that if a 2-bridge link admits a coloring by $S_3$ with 5 colors, then the link also admits such a coloring with only 4 colors.
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2023-01-31
On lightlike hypersurfaces of cosymplectic space form
Ejaz Sabir Lone, Pankaj PandeyAbstract : The main purpose of this paper is to study the lightlike hypersurface $(M,\bar{g})$ of cosymplectic space form $\bar{M}(c)$. In this paper, we computed the Gauss and Codazzi formulae of $(M,\bar{g})$ of cosymplectic manifold $(\bar{M},g)$. We showed that we can't obtain screen semi-invariant lightlike hypersurface (SCI-LH) of $\bar{M}(c)$ with parallel second fundamental form $h$, parallel screen distribution and $c\neq 0$. We showed that if second fundamental form $h$ and local second fundamental form $B$ are parallel, then $(M,\bar{g})$ is totally geodesic. Finally we showed that if $(M,\bar{g})$ is umbilical, then cosymplectic manifold $(\bar{M},g)$ is flat.
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2023-07-31
Generalized $(C,r)$-Hankel operator and $(R,r)$-Hankel operator on general Hilbert spaces
Jyoti Bhola, Bhawna GuptaAbstract : Hankel operators and their variants have abundant applications in numerous fields. For a non-zero complex number $r$, the $r$-Hankel operators on a Hilbert space $\mathcal{H}$ define a class of one such variant. This article introduces and explores some properties of two other variants of Hankel operators namely $k^{th}$-order $(C,r)$-Hankel operators and $k^{th}$-order $(R,r)$-Hankel operators $(k \geq 2)$ which are closely related to $r$-Hankel operators in such a way that a $k^{th}$-order $(C,r)$-Hankel matrix is formed from $r^k$-Hankel matrix on deleting every consecutive $(k-1)$ columns after the first column and a $k^{th}$-order $(R, r^k)$-Hankel matrix is formed from $r$-Hankel matrix if after the first column, every consecutive $(k-1)$ columns are deleted. For $|r| \neq 1$, the characterizations for the boundedness of these operators are also completely investigated. Finally, an appropriate approach is also presented to extend these matrices to two-way infinite matrices.
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2022-10-31
Ground state sign-changing solutions for nonlinear Schr\"{o}dinger-Poisson system with indefinite potentials
Shubin Yu, Ziheng ZhangAbstract : This paper is concerned with the following Schr\"{o}dinger-\linebreak Poisson system$$\left\{\begin{array}{ll} -{\Delta}u+V(x)u+K(x){\phi}u=a(x)|u|^{p-2}u &\mbox{in}\ \mathbb{R}^3, \\[0.1cm] -{\Delta}{\phi}=K(x)u^{2}&\mbox{in}\ \mathbb{R}^3, \\[0.1cm]\end{array}\right.$$where $4<p<6$. For the case that $K$ is nonnegative, $V$ and $a$ are indefinite, we prove the above problem possesses one ground state sign-changing solutionwith exactly two nodal domains by constraint variational method and quantitative deformation lemma. Moreover, we show that the energy of sign-changing solutions islarger than that of the ground state solutions. The novelty of this paper is that the potential $a$ is indefinite and allowed to vanish at infinity. In this sense, we complementthe existing results obtained by Batista and Furtado \cite{BF18}.
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2024-01-31
3-Hom-Lie superbialgebras and 3-Hom-Lie classical Yang-Baxter equations
Issam Bartouli, Imed Basdouri, Gaith Chaabane, Mohamed Fadous, Jean LerbetAbstract : 3-Lie algebras are in close relationships with many fields. In this paper we are concerned with the study of 3-Hom-Lie super algebras, the concepts of 3-Hom-Lie coalgebras and how they make a 3-Hom-Lie superbialgebras, we study the structures of such categories of algebras and the relationships between each others. We study a super twisted 3-ary version of the Yang-Baxter equation, called the super 3-Lie classical Hom-Yang-Baxter equation (3-Lie CHYBE), which is a general form of 3-Lie classical Yang-Baxter equation and prove that the superbialgebras induced by the solutions of the super 3-Lie CHYBE induce the coboundary local cocycle 3-Hom-Lie superbialgebras.
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2024-01-31
Cyclic codes of length $p^s$ over $\frac{\mathbb{F}_{p^m}[u]}{\langle u^e \rangle}$
Roghayeh Mohammadi Hesari, Masoumeh Mohebbei, Rashid Rezaei, Karim SameiAbstract : Let $R_e=\frac{\mathbb{F}_{p^m}[u]}{\langle u^e \rangle}$, where $p$ is a prime number, $ e $ is a positive integer and $u^e=0$. In this paper, we first characterize the structure of cyclic codes of length $p^s$ over $R_e$. These codes will be classified into $2^e $ distinct types. Among other results, in the case that $e=4$, the torsion codes of cyclic codes of length $ p^s $ over $ R_4$ are obtained. Also, we present some examples of cyclic codes of length $p^s $ over $R_e$.
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2023-04-30
On graded $J$-ideals over graded rings
Tamem Al-Shorman, Malik Bataineh, Ece Yetkin CelikelAbstract : 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.
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2022-10-31
Golden para-contact metric manifolds
Gherici Beldjilali, Habib BouzirAbstract : The purpose of the present paper is to introduce a new class of almost para-contact metric manifolds namely, Golden para-contact metric manifolds. Then, we are particularly interested in a more special type called Golden para-Sasakian manifolds, where we will study their fundamental properties and we present many examples which justify their study.
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Sharp estimates on the third order Hermitian-Toeplitz determinant for Sakaguchi classes
Sushil Kumar, Virendra Kumar
Commun. Korean Math. Soc. 2022; 37(4): 1041-1053
https://doi.org/10.4134/CKMS.c210332 -
Characterizations of (Jordan) derivations on Banach algebras with local actions
Jiankui Li, Shan Li, Kaijia Luo
Commun. Korean Math. Soc. 2023; 38(2): 469-485
https://doi.org/10.4134/CKMS.c220123 -
Maximal chain of ideals and $n$-maximal ideal
Hemin A. Ahmad, Parween A. Hummadi
Commun. Korean Math. Soc. 2023; 38(2): 331-340
https://doi.org/10.4134/CKMS.c220097 -
Solitons of K"{A}hlerian Norden space-time manifolds
Praveena Manjappa Mundalamane, Bagewadi Channabasappa Shanthappa, Mallannara Siddalingappa Siddesha
Commun. Korean Math. Soc. 2022; 37(3): 813-824
https://doi.org/10.4134/CKMS.c200471
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Local-global principle and generalized local cohomology modules
Bui Thi Hong Cam, Nguyen Minh Tri, Do Ngoc Yen
Commun. Korean Math. Soc. 2023; 38(3): 649-661
https://doi.org/10.4134/CKMS.c220160 -
Generalized Padovan sequences
Jhon J. Bravo, Jose L. Herrera
Commun. Korean Math. Soc. 2022; 37(4): 977-988
https://doi.org/10.4134/CKMS.c210367 -
A note on certain transformation formulas related to Appell, Horn and Kamp\'{e} de F\'{e}riet functions
Asmaa Orabi Mohammed, Medhat Ahmed Rakha, Arjun K. Rathie
Commun. Korean Math. Soc. 2023; 38(3): 807-819
https://doi.org/10.4134/CKMS.c220217 -
On strongly quasi $J$-ideals of commutative rings
El Mehdi Bouba
, Yassine EL-khabchi, Mohammed Tamekkante Commun. Korean Math. Soc. 2024; 39(1): 93-104
https://doi.org/10.4134/CKMS.c230134
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