Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2024-04-30
Utilizing coupling strategy to generate a new simple 7d hyperchaotic system and its circuit application
Saad Fawzi Al-AzzawiAbstract : By utilizing coupling the strategy in the 5D Sprott B system, a new no equilibrium 7D hyperchaotic system is introduced. Despite the proposed system being simple with twelve-term, including solely two cross product nonlinearities, it displays extremely rich dynamical features such as hidden attractors and the dissipative and conservative nature. Besides, this system has largest Kaplan-Yorke dimension compared with to the work available in the literature. The dynamical properties are fully investigated via Matlab 2021 software from several aspects of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, offset boosting and so on. Moreover, the corresponding circuit is done through Multisim 14.2 software and preform to verify the new 7D system. The numerical simulations wit carryout via both software are agreement which indicates the efficiency of the proposed system.
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2024-04-30
On a special class of matrix rings
Arnab BhattacharjeeAbstract : In this paper, we continue to explore an idea presented in \cite{bhatt2020} and introduce a new class of matrix rings called \emph{staircase} matrix rings which has applications in noncommutative ring theory. We show that these rings preserve the notions of reduced, symmetric, reversible, IFP, reflexive, abelian rings, etc.
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2022-07-31
Metrizability and submetrizability for point-open, open-point and bi-point-open topologies on $C(X,Y)$
Barkha, Azhuthil Raghavan PrasannanAbstract : We characterize metrizability and submetrizability for point-open, open-point and bi-point-open topologies on scalebox{0.98}{$C(X,Y)$}, where scalebox{0.98}{$C(X,Y)$} denotes the set of all continuous functions from space $X$ to $Y$; $X$ is a completely regular space and $Y$ is a locally convex space.
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2024-04-30
Invariant null rigged hypersurfaces of indefinite nearly ${\alpha}$-Sasakian manifolds
Mohamed H. A. Hamed, Fortune Massamba
Abstract : We introduce invariant rigged null hypersurfaces of indefinite almost contact manifolds, by paying attention to those of indefinite nearly $\alpha$-Sasakian manifolds. We prove that, under some conditions, there exist leaves of the integrable screen distribution of the ambient manifolds admitting nearly $\alpha$-Sasakian structures.
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2024-04-30
A new criterion for moment infinitely divisible weighted shifts
Hong T. T. TrinhAbstract : In this paper we present the weighted shift operators having the property of moment infinite divisibility. We first review the monotone theory and conditional positive definiteness. Next, we study the infinite divisibility of sequences. A sequence of real numbers $\gamma$ is said to be infinitely divisible if for any $p>0$, the sequence $\gamma^p = \{ \gamma_n^p \}_{n=0}^{\infty}$ is positive definite. For sequences $\alpha = \{\alpha_n\}^{\infty}_{n=0}$ of positive real numbers, we consider the weighted shift operators $W_{\alpha}$. It is also known that $W_{\alpha}$ is moment infinitely divisible if and only if the sequences $\{\gamma_n\}_{n=0}^{\infty}$ and $\{\gamma_{n+1}\}_{n=0}^{\infty}$ of $W_{\alpha}$ are infinitely divisible. Here $\gamma$ is the moment sequence associated with $\alpha$. We use conditional positive definiteness to establish a new criterion for moment infinite divisibility of $W_{\alpha}$, which only requires infinite divisibility of the sequence $\{\gamma_n\}_{n=0}^{\infty}$. Finally, we consider some examples and properties of weighted shift operators having the property of $(k,0)$-CPD; that is, the moment matrix $M_{\gamma}(n,k)$ is CPD for any $n \ge 0$.
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2024-04-30
Nonlinear mixed $\ast$-Jordan type $n$-derivations on $\ast$-algebras
Raof Ahmad Bhat, Abbas Hussain Shikeh, Mohammad Aslam SiddeequeAbstract : Let $ \mathfrak{R}$ be a $\ast$-algebra with unity $I$ and a nontrivial projection $P_1$. In this paper, we show that under certain restrictions if a map $ \Psi : \mathfrak{R} \to \mathfrak{R}$ satisfies \begin{align*} &\ \Psi ( S_1 \diamond S_2 \diamond \cdots \diamond S_{n-1} \bullet S_n) \\ =&\ \sum_{k = 1}^{n} S_1 \diamond S_2 \diamond \cdots \diamond S_{k-1} \diamond \Psi( S_k)\diamond S_{k+1} \diamond \cdots \diamond S_{n-1} \bullet S_n \end{align*} for all $ S_{n-2}, S_{n-1}, S_n \in \mathfrak{R} $ and $S_i=I$ for all $i \in \{1,2,\hdots, n-3\}$, where $n\geq 3$, then $ \Psi$ is an additive $\ast$-derivation.
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2024-04-30
Study of quotient near-rings with additive maps
Abdelkarim Boua, Abderrahmane Raji, Abdelilah ZerbaneAbstract : We consider $\mathcal{N}$ to be a $3$-prime field and $\mathcal{P}$ to be a prime ideal of $\mathcal{N}.$ In this paper, we study the commutativity of the quotient near-ring $\mathcal{N}/\mathcal{P}$ with left multipliers and derivations satisfying certain identities on $P$, generalizing some well-known results in the literature. Furthermore, an example is given to illustrate the necessity of our hypotheses.
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2024-04-30
A weaker notion of the finite factorization property
Henry Jiang, Shihan Kanungo, Hwisoo KimAbstract : An (additive) commutative monoid is called atomic if every given non-invertible element can be written as a sum of atoms (i.e., irreducible elements), in which case, such a sum is called a factorization of the given element. The number of atoms (counting repetitions) in the corresponding sum is called the length of the factorization. Following Geroldinger and Zhong, we say that an atomic monoid $M$ is a length-finite factorization monoid if each $b \in M$ has only finitely many factorizations of any prescribed length. An additive submonoid of $\mathbb{R}_{\ge 0}$ is called a positive monoid. Factorizations in positive monoids have been actively studied in recent years. The main purpose of this paper is to give a better understanding of the non-unique factorization phenomenon in positive monoids through the lens of the length-finite factorization property. To do so, we identify a large class of positive monoids which satisfy the length-finite factorization property. Then we compare the length-finite factorization property to the bounded and the finite factorization properties, which are two properties that have been systematically investigated for more than thirty years.
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2024-04-30
Cohen-Macaulay dimension for complexes
Fatemeh Mohammadi Aghjeh MashhadAbstract : In this paper, our focus lies in exploring the concept of Cohen-Macaulay dimension within the category of homologically finite complexes. We prove that over a local ring $(R,\fm)$, any homologically finite complex $X$ with a finite Cohen-Macaulay dimension possesses a finite \emph{$CM$-resolution}. This means that there exists a bounded complex $G$ of finitely generated $R$-modules, such that $G$ is isomorphic to $X$ and each nonzero $G_i$ within the complex $G$ has zero Cohen-Macaulay dimension.
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2024-04-30
A survey of lengths of linear groups with respect to certain generating sets
Nguyen Thi Thai HaAbstract : In this paper, we summarise and present results on involution lengths and commutator lengths of certain linear groups such as special linear groups, projective linear groups, upper triangle matrix groups and Vershik-Kerov groups. Some open problems motivated by these results are also proposed.
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Certain study of generalized $B$ curvature tensor within the framework of Kenmotsu manifold
Rahuthanahalli Thimmegowda Naveen Kumar, Basavaraju Phalaksha Murthy, Puttasiddappa Somashekhara, Venkatesha Venkatesha
Commun. Korean Math. Soc. 2023; 38(3): 893-900
https://doi.org/10.4134/CKMS.c220287 -
Quantization for a probability distribution generated by an infinite iterated function system
Lakshmi Roychowdhury, Mrinal Kanti Roychowdhury
Commun. Korean Math. Soc. 2022; 37(3): 765-800
https://doi.org/10.4134/CKMS.c210266 -
New volume comparison with almost Ricci soliton
Shahroud azami, Sakineh Hajiaghasi
Commun. Korean Math. Soc. 2022; 37(3): 839-849
https://doi.org/10.4134/CKMS.c210097 -
The $u$-$S$-weak global dimensions of commutative rings
Xiaolei Zhang
Commun. Korean Math. Soc. 2023; 38(1): 97-112
https://doi.org/10.4134/CKMS.c220016
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Space of homeomorphisms under regular topology
Mir Aaliya, Sanjay Mishra
Commun. Korean Math. Soc. 2023; 38(4): 1299-1307
https://doi.org/10.4134/CKMS.c220349 -
Existence theorems for critical degenerate equations involving the Grushin operators
Huong Thi Thu Nguyen, Tri Minh Nguyen
Commun. Korean Math. Soc. 2023; 38(1): 137-151
https://doi.org/10.4134/CKMS.c220030 -
On the generalized Ornstein-Uhlenbeck operators with regular and singular potentials in weighted $L^{p}$-spaces
Imen Metoui
Commun. Korean Math. Soc. 2024; 39(1): 149-160
https://doi.org/10.4134/CKMS.c230133 -
Properties of functions with bounded rotation associated with lima\c{c}on class
Kanwal Jabeen, Afis Saliu
Commun. Korean Math. Soc. 2022; 37(4): 995-1007
https://doi.org/10.4134/CKMS.c210273
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