Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2025-01-31
A construction of wobbly divisors of nilpotency index greater than 2
Insong Choe; George H. HitchingAbstract : For a smooth projective curve $C$, let $U_C(n, d)$ be the moduli space of semistable bundles over $C$ of rank $n$ and degree $d$. A vector bundle $V$ in $U_C(n,d)$ is called \textit{wobbly} if there is a nonzero nilpotent $K_C$-valued endomorphism $\phi: V \to V \otimes K_C$. Drinfeld's conjecture predicts that the wobbly locus has pure codimension one. This has been proven for $n=2$, for which case the involved endomorphisms have nilpotency index 2. In this paper, we construct irreducible wobbly components of codimension 1 and nilpotency index greater than 2, under a certain numerical condition on $n$ and $d$.
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2025-01-31
On weakly quasi-$S$-primary ideals
Samir GuesmiAbstract : This article introduces the concept of weakly quasi-$S$-primary ideals, which generalize both weakly $S$-primary and quasi-$S$-primary ideals. We define an ideal $P$ of a ring $R$ to be {\em weakly quasi-$S$-primary} if there exists $s \in S$ such that for all $x, y \in R$ if $0 \neq xy \in P$, then either $sx \in \sqrt{P}$ or $sy \in \sqrt{P}$. We investigate various properties and characterizations of weakly quasi-$S$-primary ideals, and provide numerous examples and counterexamples. We also study the behavior of these ideals under homomorphisms, in rings of fractions, in idealizations, and in amalgamated rings.
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2025-01-31
Some identities in $3$-prime near-rings with derivations
Abdelkarim BouaAbstract : In this paper, we study new differential identities of $3$-prime near-rings associated with derivations. Our paper extends some identities already cited in the literature and draws inspiration from important sources such as [5] and [10]. Furthermore, examples are given to prove that the restrictions imposed on the hypotheses of the various theorems were necessary and not just a formality.
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2025-01-31
Dual Hilbert coefficient and width of the dual fiber cone relative to an Artinian module
Ton That Quoc TanAbstract : Let $(R,{\frak m})$ be a quasi-local ring and $M$ be a co-Cohen-Macaulay Artinian $R$-module with ${\mathrm{Ndim}} M = d > 0$. Suppose $I$ is an ideal of $R$ such that $\lambda(0:_M I) < \infty$. In this paper, we establish formulas for the first dual Hilbert coefficient $g'_1(I,M)$, a dual form of [4, Theorem 4.3 and 5.3], under the assumption the width of the dual fiber cone ${\mathcal{F}'}(I,M)$ is at least $d-1$.
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2025-01-31
Derivations acting on symmetric elements with central values
Hiba Fihi; Abdellah Mamouni; Khalid OuarghiAbstract : Our purpose in this paper is to prove that the set of hermitian elements, defined by commutativity conditions involving derivations over prime rings with involution $*$, are either central elements or their square are central elements. Furthermore, we can find the same results for the set of skew-hermitian elements.
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2025-01-31
Derivations on distributive bilattices
Mohammad M. Atallah; Eman G. RezkAbstract : In this paper, a derivation is defined on a reduct or two reducts of a distributive bilattice, with and without a relationship between derivations on reducts. The concept of a differential distributive bilattice is introduced. The algebraic structure and properties are investigated. Characterization and Construction theorems are proved.
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2025-01-31
Value sharing and uniqueness of certain classes of meromorphic functions
Samar Halder; Pulak SahooAbstract : We study the uniqueness problem of two different classes of meromorphic functions sharing two distinct values. Our results extend and complement the result of Li [12], and at the same time extend results due to Hao and Chen [7], and Wu and Hu [16]. Another result in this paper, besides finding a possible answer to a question raised in [1], extends and complements a recent result of Banerjee and Kundu [1] and that of Han [6].
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2025-01-31
An extension of a normality criterion leading to a counterexample to the converse of Bloch's principle
Nikhil Bharti
; Kuldeep Singh CharakAbstract : In this paper, a criterion for normality of a family of meromorphic functions involving differential polynomials is obtained which generalizes a result of Deng et al. (J. Aust. Math. Soc. 91 (2011), 313--322). As a consequence, a counterexample to the converse of Bloch's principle is also obtained. In addition, we prove some normality criterion generalizing a result of Chen et al. (Acta Math. Sci. 36 (2016), 87--93). Wherever possible, examples are provided to demonstrate sharpness of results.
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2025-01-31
A class of Eulerian integrals involving generalized hypergeometric functions with applications
Shoukat Ali; Deepak Kumar; Subrat ParidaAbstract : This paper aims to evaluate a general class of Eulerian integrals involving the Aleph function and Rathie I-function. Further, various particular cases are considered as applications of our derived main results.
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2025-01-31
Linear maps which are $\theta$-centralizers at zero or identity products
Abbas Zivari-KazempourAbstract : Let $A$ be a unital Banach algebra and let $\theta: A\longrightarrow A$ be a homomorphism. In this paper, we study linear maps $T: A\longrightarrow A$ which are $\theta$-centralizers at zero or identity products, and under special hypotheses we show that every such linear map is a $\theta$-centralizer. Zero and identity Jordan products preservers, and a more restrictive version of them are also discussed.
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2025-01-31
On dispersive quantization and fractalization for the Kawahara equation
Seongyeon KimAbstract : In this paper, we investigate the dichotomous behavior of solutions to the Kawahara equation with bounded variation initial data, analogous to the Talbot effect. Specifically, we observe that the solution is quantized at rational times, whereas at irrational times, it is a nowhere continuous differentiable function with a fractal profile. This phenomenon, however, has not been explored for the Kawahara equation, which is a fifth-order KdV type equation. To achieve this, we derive smoothing estimates for the nonlinear Duhamel solution, which, when combined with the known results on the linear solution, provides a mathematical description of the Talbot effect.
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2025-01-31
Variational inequality problem with hyperbolic scalars
Amjad Ali; Romesh Kumar; Aditi SharmaAbstract : In this paper, we initiate the study of variational inequalities with hyperbolic scalars. We study some basic properties of variational inequalities and hyperbolic version of Lax-Milgram theorem for $\mathbb{D}$-Hilbert spaces.
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2025-01-31
A study on certain classes of multivalent analytic functions with fixed second coefficients
Fayzah Awad Alshehri; Abeer O. Badghaish; Amani Z. Bajamal; Abdel Moneim Y. LashinAbstract : This paper examines two novel subclasses of multivalent analytic functions in the open unit disc, characterized by fixed second coefficients. These subclasses interestingly unify several previously introduced and studied subclasses. We establish some argument properties and discuss the integral operator for functions in these subclasses. Our results include new findings that generalize and refine the related works of various authors.
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2025-01-31
Ricci solitons as lightlike hypersurfaces endowed with a concircular vector field
Arfah Arfah; Gül TUĞ Abstract : In this study, we investigate some properties of the lightlike hypersurfaces endowed with a concircular vector field. We give some conditions related to them for being a Ricci soliton. Also, we give some equations related to such hypersurfaces in an $(n+2)$-dimensional semi-Riemannian manifold with constant curvature. Lastly, we calculate the principal curvatures of a screen homothetic lightlike hypersurface which is also a Ricci soliton.
January, 2025 | Volume 40, No. 1
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A characterization of zero divisors and topological divisors of zero in $C[a,b]$ and $\ell^\infty$
Harish Chandra, Anurag Kumar Patel
Commun. Korean Math. Soc. 2023; 38(2): 451-459
https://doi.org/10.4134/CKMS.c220108 -
Transversal lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds
Shiv Sharma Shukla, Vipul Singh
Commun. Korean Math. Soc. 2023; 38(4): 1191-1213
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Unitary analogues of a generalized number-theoretic sum
Traiwat Intarawong, Boonrod Yuttanan
Commun. Korean Math. Soc. 2023; 38(2): 355-364
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A simple proof for a result on $n$-Jordan homomorphisms
Choonkil Park, Abbas Zivari-Kazempour
Commun. Korean Math. Soc. 2023; 38(2): 487-490
https://doi.org/10.4134/CKMS.c220136
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Unitary analogues of a generalized number-theoretic sum
Traiwat Intarawong, Boonrod Yuttanan
Commun. Korean Math. Soc. 2023; 38(2): 355-364
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The dimension graph for modules over commutative rings
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Commun. Korean Math. Soc. 2023; 38(3): 733-740
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A study of differential identities on $\sigma$-prime rings
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Commun. Korean Math. Soc. 2023; 38(3): 679-693
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Hyers-Ulam stability of fractional stochastic differential equations with random impulse
Dumitru Baleanu, Banupriya Kandasamy, Ramkumar Kasinathan, Ravikumar Kasinathan, Varshini Sandrasekaran
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