Abstract : 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 $d$.
Abstract : 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.
Abstract : 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.
Abstract : 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 $d-1$.
Abstract : 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.
Abstract : 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.
Abstract : 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].
Abstract : 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.
Abstract : 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.
Abstract : 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.
Abstract : 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.
Abstract : 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.
Abstract : 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.
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.
Harish Chandra, Anurag Kumar Patel
Commun. Korean Math. Soc. 2023; 38(2): 451-459
https://doi.org/10.4134/CKMS.c220108
Shiv Sharma Shukla, Vipul Singh
Commun. Korean Math. Soc. 2023; 38(4): 1191-1213
https://doi.org/10.4134/CKMS.c220309
Traiwat Intarawong, Boonrod Yuttanan
Commun. Korean Math. Soc. 2023; 38(2): 355-364
https://doi.org/10.4134/CKMS.c220139
Choonkil Park, Abbas Zivari-Kazempour
Commun. Korean Math. Soc. 2023; 38(2): 487-490
https://doi.org/10.4134/CKMS.c220136
Traiwat Intarawong, Boonrod Yuttanan
Commun. Korean Math. Soc. 2023; 38(2): 355-364
https://doi.org/10.4134/CKMS.c220139
Shiroyeh Payrovi
Commun. Korean Math. Soc. 2023; 38(3): 733-740
https://doi.org/10.4134/CKMS.c220273
Adnan Abbasi, Md Arshad Madni, Muzibur Rahman Mozumder
Commun. Korean Math. Soc. 2023; 38(3): 679-693
https://doi.org/10.4134/CKMS.c220240
Dumitru Baleanu, Banupriya Kandasamy, Ramkumar Kasinathan, Ravikumar Kasinathan, Varshini Sandrasekaran
Commun. Korean Math. Soc. 2023; 38(3): 967-982
https://doi.org/10.4134/CKMS.c220231
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