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Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2024-10-31
On graded radical ideals of graded non-commutative rings
Susan F. EL-Deken, Nico Groenewald
Abstract : Let $G$ be a group and $R$ a $G$-graded ring$.$ In 2023, Al-Shorman et al. introduced the concept of graded $J$-ideals of a $G$ -graded commutative ring and several characterizations of this concept were investigated. The notion of gr-$n$-ideals in a $G$-graded commutative ring was introduced by Al-Zoubi et al. and studied. In this note, we introduce the concept of a graded $\rho$-ideal (gr-$\rho$-ideal) for a graded special radical $\rho_{G}$ and show that the results of graded $J$-ideals and graded $n$-ideals are special cases of a more general situation. We prove that most of the results in graded commutative rings of the above-mentioned papers are satisfied for non-commutative $G$-graded rings as a special case.
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2024-10-31
Antinormal operators and antinormality of composition operators on $L^2(X)$
Arvind Bhatt, Harish Chandra, Mohammad Irshad KhanAbstract : In this article, we show that if $T\in \mathcal{B}(H)$ is an antinormal operator, $M$ is a reducing subspace for $T$ and $i(T|_M)$ and $i(T)$ are of the same sign, then $T|_M$ is also antinormal. We also characterize the antinormality of composition operators on $L^2(X)$ for a $\sigma$-finite measure space $X$.
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2024-10-31
Coefficient bounds using Faber Polynomial for a New Subclass of Meromorphic Bi-Univalent Functions
Thambidurai Janani, Sibel Yalçın Abstract : A recently introduced subclass of meromorphic bi-univalent functions class $\Sigma'$ is considered for the study and coefficient estimates $|b_0|, |b_1|$ and $|b_2|$ are determined in the present investigation. Further, the coefficient estimate $|b_n|$ is obtained for functions in the new subclass $\Sigma'$ using Faber polynomials. Various remarks of the results are also specified in generalized form.
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2024-10-31
Sharp bounds for the initial coefficients for certain families of bi-univalent functions
Ahmad Motamednezhad, Safa SalehianAbstract : In our study, we present the well known family ${\mathcal N}_\Sigma^\mu(\lambda)$ of $\Sigma$, which is the family of bi-univalent functions in the open unit disk ${\mathbb U}$. We obtain sharp estimates for the first three Taylor-Maclaurin coefficients $|a_2|$, $|a_3|$, $|a_4|$. Fekete-Szeg\"{o} functional problem is also established. Furthermore, we consider the family ${\mathcal B}_{1,\Sigma}(\mu,\lambda,\gamma)$ of bi-univalent functions in the open unit disk ${\mathbb U}$. The results presented in this paper would generalize and improve some recent works of several earlier authors.
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2024-10-31
On the measure of non strict cosingularity and the theory of operator matrix
Naila Bouida, Ines WalhaAbstract : Measure of non strict cosingularity appears as one of the most particular class of Fredholm perturbation allowing to draft an interesting use in the analysis of spectral properties of linear operators in particular operator matrix field. The main purpose of this paper is to establish some new stability results of perturbed lower semi-Fredholm (semi-Weyl) operators linked to the use of measure of non strict cosingularity and the theory of Fredholm inverse. Moreover, we apply our results in order to investigate a new framework of the characterization of some essential spectra of unbounded block $3\times 3$ operator matrix with maximal domain.
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2024-10-31
Spectral properties of the sum of two operators matrices via relatively Fredholmness perturbations
Sana BouzidiAbstract : In this paper, we deal with the theory of the relatively Fredholm perturbations which allows us to provide a new criteria to characterize some essential spectra of the sum of two $2\times 2$ blocks of operators matrices. Particularly, our developed results provide an amelioration of the work done by M. Marletta and C. Tretter [M. Marletta and C. Tretter, Essential spectra of coupled systems of differential equations and applications in hydrodynamics, J. Diff. Equ. 243 (2007), 36--69].
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2024-10-31
Study on Lorentzian para-Kenmotsu manifold with $k$-almost Yamabe solitons
Chandrashekharappa Aishwarya, Venkatesha VenkateshaAbstract : The focus of this article is to explore the concepts of $k$-almost Yamabe and gradient $k$-almost Yamabe solitons on three-dimensional Lorentzian para-Kenmotsu manifolds, with the aim of providing a comprehensive analysis.
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2024-10-31
A study of harmonicity on cotangent bundle with Berger-type deformed Sasaki metric over standard K"{a}hler manifold
Kheireddine Biroud, Abderrahim ZaganeAbstract : In this paper, we present some results concerning the harmonicity on the cotangent bundle equipped with the Berger-type deformed Sasaki metric over standard K"{a}hler manifolds. We establish necessary and sufficient conditions under which a covector field is harmonic map or is harmonic covector with respect to the Berger-type deformed Sasaki metric and we construct some examples of harmonic covector fields. We also study the harmonicity of a covector field along a map between Riemannian manifolds, the target manifold being standard K"{a}hler equipped with the Berger-type deformed Sasaki metric on its cotangent bundle. After that, we discuss the harmonicity of the composition of the projection map of the cotangent bundle of a Riemannian manifold with a map from this manifold into another Riemannian manifold, the source manifold being standard K"{a}hler whose cotangent bundle is endowed with the Berger-type deformed Sasaki metric.
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2024-10-31
Monads on Cartesian products of projective spaces
Damian Muindi MaingiAbstract : In this paper we establish the existence of monads on Cartesian products of projective spaces that inject onto an odd dimensional projective spaces.We first construct monads on $\mathbb{P}^1\times\cdots\times\mathbb{P}^1\times\mathbb{P}^3\times\cdots\times\mathbb{P}^3\times\mathbb{P}^5\times\cdots\times\mathbb{P}^5$,then proceed to prove stability of the kernel bundle associated to the monad and simplicity of the cohomology vector bundle.Lastly we establish the existence of monads on $\mathbb{P}^{a_1}\times\cdots\times\mathbb{P}^{a_n }$, where $a_1<a_2<\cdots<a_n$, alternatingeven and odd or at least $a_i$ $0<i\leq{n}$ is odd.
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2024-10-31
Characteristics of Lorentzian-Para Kenmotsu spacetime manifolds
Vinay Kumar, Rajendra PrasadAbstract : The primary objectives of this paper is to study a special type of spacetime known as Lorentzian para-Kenmotsu (LPK) spacetime, characterized by a coefficient $ \alpha $, satisfying curvature conditions $ \mathcal{C}(X,Y)\cdot \xi=0 $ and $\mathsf{R}(X,Y)\cdot \mathcal{S} = 0$. We study the conditions under which the generalized $\mathcal {Z} $-tensor becomes almost pseudo-$ \mathcal {Z} $-symmetric spacetime. Finally, we provide an example of (LPK) spacetime with a coefficient $ \alpha $ that satisfies certain notable results.
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2024-10-31
A study on the deformed Riemann extensions
Filiz OcakAbstract : The purpose of this paper is to define a deformed Riemann extension using energy density on the cotangent bundle and to investigate applications of this metric.
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2024-10-31
A theorem on almost Hermitian manifolds
Jaeman KimAbstract : In this paper, we give some sufficient conditions for an almost Hermitian manifold to be K"ahler.
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2024-10-31
On the classification of periodic weaves and universal cover of links in thickened surfaces
Sonia MahmoudiAbstract : A \textit{periodic weave} is the lift of a particular link embedded in a thickened surface of genus $g \geq 1$ to the universal cover. Its components are infinite unknotted simple open curves that can be partitioned in at least two distinct \textit{sets of threads}. The classification of periodic weaves can be reduced to the one of their generating cells, namely their \textit{weaving motifs}. However, this classification cannot be achieved through the classical theory of links in thickened surfaces since periodicity in the universal cover is not encoded. In this paper, we first introduce the notion of hyperbolic periodic weaves, which generalizes our doubly periodic weaves embedded in the Euclidean thickened plane. Then, Tait's first and second conjectures are extended to minimal reduced alternating weaving motifs and proved using a generalized Kauffman bracket polynomial defined for periodic weaving diagrams of $\mathbb{E}^2$ and generalized to $\mathbb{H}^2$. The first conjecture states that any minimal alternating reduced weaving motif has the minimum possible number of crossings, while the second one formulates that two such oriented weaving motifs have the same writhe.
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2024-10-31
New classes of graphs with strongly almost trivial embeddings
Ryo HanakiAbstract : A spatial embedding $f$ of a graph $G$ is strongly almost trivial if $f$ is nontrivial and there exists a projection $hat{f}$ of $f$ such that only trivial spatial embeddings are obtained from $hat{f}|_H$ by assigning over/under information to transversal double points for any proper subgraph $H$ of $G$. We present new classes of graphs which have strongly almost trivial embeddings.
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2024-10-31
Measure-valued solutions for stochastic differential equations on Hilbert Spaces driven by L'evy measure and their optimal control
Nasir U. AhmedAbstract : In this paper we consider a general class of nonlinear stochastic differential equations on Hilbert spaces determined by nonstandard infinitesimal generators (drift, diffusion, jump-kernel) and driven by L'evy process (measure). The infinitesimal generators are assumed to be only continuous and bounded on bounded sets. Under such relaxed assumptions, these equations do not have solutions in the usual sense (classical, strong, mild and weak). We prove existence of measure-valued solutions and consider several control problems (including control of the range of vector measures) and prove existence of partially observed optimal feedback controls. This paper is an extension of our previous studies on similar problems for deterministic as well as stochastic differential equations driven by cylindrical Brownian motion.
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2024-10-31
Rhombic numerical radius inequalities for Hilbert $C^{*}$-Modules
Nordine Bounader, Mohammed HassaouyAbstract : In this paper, a new definition of the Rhombic numerical radius of two adjointable operators in Hilbert $C^{*}$-module space will be introduced, and some inequalities between the operator norm and the Rhombic numerical radius will be discussed, as well as some new results. The results of the present paper can be utilized to generalize some new refinements of the Rhombic numerical radius inequalities of two bounded operators on Hilbert spaces to bounded adjointable operators on Hilbert $C^{*}$-module spaces.
October, 2024 | Volume 39, No. 4
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The homology regarding to e-exact sequences
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Conformal hemi-slant submersions from cosymplectic manifolds
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A characterization of zero divisors and topological divisors of zero in $C[a,b]$ and $\ell^\infty$
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On Noetherian pseudo-prime spectrum of a topological le-module
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Conformal hemi-slant submersions from cosymplectic manifolds
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Commun. Korean Math. Soc. 2023; 38(1): 205-221
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