Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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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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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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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 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
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
On the number of equivalence classes of bi-partitions arising from the color change
Byungchan KimAbstract : We introduce a new class of bi-partition function $c_k(n)$, which counts the number of bi-color partitions of $n$ in which the second color only appears at the parts that are multiples of $k$. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo $k$. We show that the generating function for $c_k(n)$ involves the partial theta function and obtain the following congruences: \begin{align*} c_2 (27n+26) &\equiv 0 \pmod{3} \\ \intertext{and} c_3 (4n + 2 ) &\equiv 0 \pmod{2}. \end{align*}
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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
When every finitely generated regular ideal is finitely presented
MOHAMED CHHITI, SALAH EDDINE MAHDOUAbstract : In this paper, we introduce a weak version of coherent that we call regular coherent property. A ring is called regular coherent, if every finitely generated regular ideal is finitely presented. We investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as trivial ring extensions, pullbacks and amalgamated. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.
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2024-04-30
A generalization of the symmetry property of a ring via its endomorphism
Fatma Kaynarca
, H. Melis Tekin Akcin Abstract : Lambek introduced the concept of symmetric rings to expand the commutative ideal theory to noncommutative rings. In this study, we propose an extension of symmetric rings called strongly $\alpha$-symmetric rings, which serves as both a generalization of strongly symmetric rings and an extension of symmetric rings. We define a ring $R$ as strongly $\alpha$-symmetric if the skew polynomial ring $R[x;\alpha]$ is symmetric. Consequently, we provide proofs for previously established outcomes regarding symmetric and strongly symmetric rings, directly derived from the results we have obtained. Furthermore, we explore various properties and extensions of strongly $\alpha$-symmetric rings.
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2024-04-30
On the convergence of Ishikawa iteration with errors for real continuous functions
Kittithat Boonpot, Satit SaejungAbstract : We point out an error appeared in the paper of Yuan et al.~\cite{YCQ} and present a correction of their result under a more general assumption. Moreover, we discuss the validity of the conditions imposed on the sequences of error terms.
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2024-04-30
Geometric properties of starlikeness involving hyperbolic cosine function
Om P. Ahuja, Asena Çetinkaya, Sushil KumarAbstract : In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.
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2024-04-30
Parallel shrinking projection method for fixed point and generalized equilibrium problems on Hadamard manifold
HAMMED ANUOLUWAPO ABASS, KAZEEM OLAWALE OYEWOLEAbstract : In this article, we propose a shrinking projection algorithm for solving a finite family of generalized equilibrium problem which is also a fixed point of a nonexpansive mapping in the setting of Hadamard manifolds. Under some mild conditions, we prove that the sequence generated by the proposed algorithm converges to a common solution of a finite family of generalized equilibrium problem and fixed point problem of a nonexpansive mapping. Lastly, we present some numerical examples to illustrate the performance of our iterative method. Our results extends and improve many related results on generalized equilibrium problem from linear spaces to Hadamard manifolds. The result discuss in this article extends and complements many related results in the literature.
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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
Horadam polynomials for a new subclass of Sakaguchi-type bi-univalent functions defined by $({p},{q})$-derivative operator
Vanithakumari B, SARAVANAN G , Baskaran S , Sibel Yalcin Abstract : In this paper, a new subclass, $\mathcal{SC}_{\sigma}^{\mu,{p},{q}}({r},{s};x)$, of Sakaguchi-type analytic bi-univalent functions defined by $({p},{q})$-derivative operator using Horadam polynomials is constructed and investigated. The initial coefficient bounds for $|a_{2}|$ and $|a_{3}|$ are obtained. Fekete-Szeg\"{o} inequalities for the class are found. Finally, we give some corollaries.
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2024-04-30
Some properties of critical point equations metrics on the statistical manifolds
Hajar Ghahremani-Gol, Mohammad Amin SedghiAbstract : The aim of this paper is to investigate some properties of the critical points equations on the statistical manifolds. We obtain some geometric equations on the statistical manifolds which admit critical point equations. We give a relation only between potential function and difference tensor for a CPE metric on the statistical manifolds to be Einstein.
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2024-04-30
Riemannian submersions whose total manifold admits $h$-almost Ricci-Yamabe soliton
Mehraj Ahmad Lone, Towseef Ali WaniAbstract : In this paper, we study Riemannian submersions whose total manifold admits $h$-almost Ricci-Yamabe soliton. We characterize the fibers of the submersion and see under what conditions the fibers form $h$-almost Ricci-Yamabe soliton. Moreover, we find the necessary condition for the base manifold to be an $h$-almost Ricci-Yamabe soliton and Einstein manifold. Later, we compute scalar curvature of the total manifold and using this we find the necessary condition for $h$-almost Yamabe solition to be shrinking, expanding and steady. At the end, we give a non-trivial example.
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2024-04-30
Invariant null rigged hypersurfaces of indefinite nearly ${\alpha}$-Sasakian manifolds
Mohamed H. A. Hamed, Fortune MassambaAbstract : 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
Unsteady flow of Bingham fluid in a two dimensional elastic domain
Mosbah Kaddour, Farid Messelmi, Saf SalimAbstract : The main goal of this work is to study an initial boundary value problem relating to the unsteady flow of a rigid, viscoplastic, and incompressible Bingham fluid in an elastic bounded domain of $\mathbb{R}^{2}$. By using the approximation sequences of the Faedo-Galerkin method together with the regularization techniques, we obtain the results of the existence and uniqueness of local solutions.
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2024-04-30
Chooser options on various underlying options
Wonjoong Kim, JINYOUNG LEEAbstract : We consider chooser options written on various underlying assets other than vanilla call and put options. Specifically, we deal with (i) the chooser option written on the power call and put options, and (ii) the chooser option written on the exchange options. We provide explicit formulas for the prices of these chooser options whose underlying assets are either power options or exchange options, rather than the vanilla call and put options.
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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.
April, 2024 | Volume 39, No. 2
Most Read
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The homology regarding to e-exact sequences
Ismael Akray, Amin Mahamad Zebari
Commun. Korean Math. Soc. 2023; 38(1): 21-38
https://doi.org/10.4134/CKMS.c210349 -
Conformal hemi-slant submersions from cosymplectic manifolds
Vinay Kumar, Rajendra Prasad, Sandeep Kumar Verma
Commun. Korean Math. Soc. 2023; 38(1): 205-221
https://doi.org/10.4134/CKMS.c210433 -
Knotoids, pseudo knotoids, Braidoids and pseudo braidoids on the torus
Ioannis Diamantis
Commun. Korean Math. Soc. 2022; 37(4): 1221-1248
https://doi.org/10.4134/CKMS.c210169 -
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
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Conformal hemi-slant submersions from cosymplectic manifolds
Vinay Kumar, Rajendra Prasad, Sandeep Kumar Verma
Commun. Korean Math. Soc. 2023; 38(1): 205-221
https://doi.org/10.4134/CKMS.c210433 -
The homology regarding to e-exact sequences
Ismael Akray, Amin Mahamad Zebari
Commun. Korean Math. Soc. 2023; 38(1): 21-38
https://doi.org/10.4134/CKMS.c210349 -
On Noetherian pseudo-prime spectrum of a topological le-module
Anjan Kumar Bhuniya, Manas Kumbhakar
Commun. Korean Math. Soc. 2023; 38(1): 1-9
https://doi.org/10.4134/CKMS.c210057 -
Unitary analogues of a generalized number-theoretic sum
Traiwat Intarawong, Boonrod Yuttanan
Commun. Korean Math. Soc. 2023; 38(2): 355-364
https://doi.org/10.4134/CKMS.c220139
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