Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2023-10-31
on weakly cyclic generalized $B$-symmetric manifolds
Mohabbat Ali, Aziz Ullah Khan, Quddus Khan, Mohd VasiullaAbstract : The object of the present paper is to introduce a type of non-flat Riemannian manifold, called a weakly cyclic generalized $B$-symmetric manifold $(WCGBS)_{n}$. We obtain a sufficient condition for a weakly cyclic generalized $B$-symmetric manifold to be a generalized quasi Einstein manifold. Next we consider conformally flat weakly cyclic generalized $B$-symmetric manifolds. Then we study Einstein $(WCGBS)_{n}$ $(n>2)$. Finally, it is shown that the semi-symmetry and Weyl semi-symmetry are equivalent in such a manifold.
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2023-04-30
A simple proof for a result on $n$-Jordan homomorphisms
Choonkil Park, Abbas Zivari-KazempourAbstract : In this short note, we give a simple proof of the main theorem of \cite{Cheshmavar} which states that every $n$-Jordan homomorphism $h:A\longrightarrow B$ between two commutative algebras $A$ and $B$ is an $n$-homomorphism.
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2022-07-31
On partial sums of four parametric Wright function
Muhey U DinAbstract : Special functions and Geometric function theory are close related to each other due to the surprise use of hypergeometric function in the solution of the Bieberbach conjecture. The purpose of this paper is to provide a set of sufficient conditions under which the normalized four parametric Wright function has lower bounds for the ratios to its partial sums and as well as for their derivatives. The sufficient conditions are also obtained by using Alexander transform. The results of this paper are generalized and also improved the work of M. Din et al.~cite{din}. Some examples are also discussed for the sake of better understanding of this article.
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2023-10-31
Geometry of a semi-symmetric recurrent metric connection
Jaeman KimAbstract : In the present paper, we study a semi-symmetric recurrent metric connection and verify its various geometric properties.
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2024-01-31
The homological properties of regular injective modules
Wei Qi, Xiaolei ZhangAbstract : Let $R$ be a commutative ring. An $R$-module $E$ is said to be regular injective provided that $\Ext_R^1(R/I,E)=0$ for any regular ideal $I$ of $R$. We first show that the class of regular injective modules have the hereditary property, and then introduce and study the regular injective dimension of modules and regular global dimension of rings. Finally, we give some homological characterizations of total rings of quotients and Dedekind rings.
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2023-01-31
Functions subordinate to the exponential function
Priya G. Krishnan, Vaithiyanathan Ravichandran, Ponnaiah SaikrishnanAbstract : We use the theory of differential subordination to explore various inequalities that are satisfied by an analytic function $p$ defined on the unit disc so that the function $p$ is subordinate to the function $e^z$. These results are applied to find sufficient conditions for the normalised analytic functions $f$ defined on the unit disc to satisfy the subordination $zf'(z)/f(z) \prec e^z$.
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2023-10-31
Nonlinear maps preserving the mixed product $_*[X\diamond Y, Z]$ on $*$-algebras
Raof Ahmad Bhat, Abbas Hussain Shikeh, Mohammad Aslam SiddeequeAbstract : Let $\mathfrak{A}$ and $\mathfrak{B}$ be unital prime $*$-algebras such that $\mathfrak{A}$ contains a nontrivial projection. In the present paper, we show that if a bijective map $\Theta:\mathfrak{A}\to\mathfrak{B}$ satisfies $\Theta(_*[X\diamond Y, Z])={}_*[\Theta(X)\diamond \Theta(Y), \Theta(Z)]$ for all $X, Y, Z\in\mathfrak{A}$, then $\Theta$ or $-\Theta$ is a $*$-ring isomorphism. As an application, we shall characterize such maps in factor von Neumann algebras.
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2023-04-30
A note on statistical manifolds with torsion
Hwajeong KimAbstract : Given a linear connection $\nabla$ and its dual connection $\nabla^*$, we discuss the situation where $\nabla +\nabla^* = 0$. We also discuss statistical manifolds with torsion and give new examples of some type for linear connections inducing the statistical manifolds with non-zero torsion.
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2023-04-30
Generalized hyperbolic geometric flow
Shahroud Azami, Ghodratallah Fasihi~Ramandi, Vahid PirhadiAbstract : In the present paper, we consider a kind of generalized hyperbolic geometric flow which has a gradient form. Firstly, we establish the existence and uniqueness for the solution of this flow on an $n$-dimensional closed Riemannian manifold. Then, we give the evolution of some geometric structures of the manifold along this flow.
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2023-04-30
Simple formulations on circulant matrices with alternating Fibonacci
Sugi GuritmanAbstract : In this article, an alternating Fibonacci sequence is defined from a second-order linear homogeneous recurrence relation with constant coefficients. Then, the determinant, inverse, and eigenvalues of the circulant matrices with entries in the first row having the formation of the sequence are formulated explicitly in a simple way. In this study, the method for deriving the formulation of the determinant and inverse is simply using traditional elementary row or column operations. For the eigenvalues, the known formulation from the case of general circulant matrices is simplified by considering the specialty of the sequence and using cyclic group properties. We also propose algorithms for the formulation to show how efficient the computations are.
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Equality in degrees of compactness: Schauder's theorem and $s$-numbers
Asuman Guven Aksoy, Daniel Akech Thiong
Commun. Korean Math. Soc. 2023; 38(4): 1127-1139
https://doi.org/10.4134/CKMS.c230003 -
Study of gradient solitons in three dimensional Riemannian manifolds
Gour Gopal Biswas, Uday Chand De
Commun. Korean Math. Soc. 2022; 37(3): 825-837
https://doi.org/10.4134/CKMS.c210046 -
Infinitely many homoclinic solutions for damped vibration systems with locally defined potentials
Wafa Selmi, Mohsen Timoumi
Commun. Korean Math. Soc. 2022; 37(3): 693-703
https://doi.org/10.4134/CKMS.c210008 -
A characterization of finite factorization positive monoids
Harold Polo
Commun. Korean Math. Soc. 2022; 37(3): 669-679
https://doi.org/10.4134/CKMS.c210270
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S-coherent property in trivial extension and in amalgamated duplication
MOHAMED CHHITI, SALAH EDDINE MAHDOU
Commun. Korean Math. Soc. 2023; 38(3): 705-714
https://doi.org/10.4134/CKMS.c220260 -
The $p$-part of divisor class numbers for cyclotomic function fields
Daisuke Shiomi
Commun. Korean Math. Soc. 2023; 38(3): 715-723
https://doi.org/10.4134/CKMS.c220271 -
The dimension of the maximal spectrum of some ring extensions
Rachida EL KHALFAOUI, Najib Mahdou
Commun. Korean Math. Soc. 2023; 38(4): 983-992
https://doi.org/10.4134/CKMS.c220332 -
Existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system
Nguyen Viet Tuan
Commun. Korean Math. Soc. 2023; 38(3): 741-754
https://doi.org/10.4134/CKMS.c220080
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