Abstract : In this paper, we study almost cosymplectic manifolds with nullity distributions admitting Riemann solitons and gradient almost Riemann solitons. First, we consider Riemann soliton on $(\kappa, \mu)$-almost cosymplectic manifold $M$ with $\kappa<0$ and we show that the soliton is expanding with $\lambda = \frac{\kappa}{2n-1}(4n-1)$ and $M$ is locally isometric to the Lie group $G_\rho$. Finally, we prove the non-existence of gradient almost Riemann soliton on a $(\kappa, \mu)$-almost cosymplectic manifold of dimension greater than 3 with $\kappa < 0$.
Abstract : In this paper, we prove the Hyers-Ulam stability and Mittag-Leffler-Hyers-Ulam stability of a differential equation of Logistic growth in a population by applying Laplace transforms method.
Abstract : For each positive integer $ n $, a square congruence graph $ S(n) $ is the graph with vertex set $ H=\left\lbrace 1,2,3,\ldots,n\right\rbrace $ and two vertices $ a , b $ are adjacent if they are distinct and $ a^{2}\equiv b^{2}\pmod n$. In this paper we investigate some structural properties of square congruence graph and we obtain the relationship between clique number, chromatic number and maximum degree of square congruence graph. Also we study square congruence graph with $ p $ vertices or $ 2p $ vertices for any prime number $ p$.
Abstract : 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.
Abstract : 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.
Abstract : Hankel operators and their variants have abundant applications in numerous fields. For a non-zero complex number $r$, the $r$-Hankel operators on a Hilbert space $\mathcal{H}$ define a class of one such variant. This article introduces and explores some properties of two other variants of Hankel operators namely $k^{th}$-order $(C,r)$-Hankel operators and $k^{th}$-order $(R,r)$-Hankel operators $(k \geq 2)$ which are closely related to $r$-Hankel operators in such a way that a $k^{th}$-order $(C,r)$-Hankel matrix is formed from $r^k$-Hankel matrix on deleting every consecutive $(k-1)$ columns after the first column and a $k^{th}$-order $(R, r^k)$-Hankel matrix is formed from $r$-Hankel matrix if after the first column, every consecutive $(k-1)$ columns are deleted. For $|r| \neq 1$, the characterizations for the boundedness of these operators are also completely investigated. Finally, an appropriate approach is also presented to extend these matrices to two-way infinite matrices.
Abstract : We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin \cite{P1}. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism $f$ of a compact smooth manifold $M$ has the robustly pointwise inverse pseudo-orbit tracing property, $f$ is structurally stable. (ii) For a $C^1$ generic diffeomorphism $f$ of a compact smooth manifold $M$, if $f$ has the pointwise inverse pseudo-orbit tracing property, $f$ is structurally stable. (iii) If a diffeomorphism $f$ has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set $\Lambda$, then $\Lambda$ is hyperbolic for $f$. Finally, (iv) for $C^1$ generically, if a diffeomorphism $f$ has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set $\Lambda$, then $\Lambda$ is hyperbolic for $f$. In addition, we investigate cases of volume preserving diffeomorphisms.
Abstract : Let $R$ be a commutative graded ring with nonzero identity and $n$ a positive integer. Our principal aim in this paper is to introduce and study the notions of graded $n$-irreducible and strongly graded $n$-irreducible ideals which are generalizations of $n$-irreducible and strongly $n$-irreducible ideals to the context of graded rings, respectively. A proper graded ideal $I$ of $R$ is called graded $n$-irreducible (respectively, strongly graded $n$-irreducible) if for each graded ideals $I_{1}, \ldots,I_{n+1}$ of $R$, $I=I_{1} \cap \cdots \cap I_{n+1}$ (respectively, $I_{1} \cap \cdots \cap I_{n+1} \subseteq I$ ) implies that there are $n$ of the $I_{i}$ 's whose intersection is $I$ (respectively, whose intersection is in $I$). In order to give a graded study to this notions, we give the graded version of several other results, some of them are well known. Finally, as a special result, we give an example of a graded $n$-irreducible ideal which is not an $n$-irreducible ideal and an example of a graded ideal which is graded $n$-irreducible, but not graded $(n-1)$-irreducible.
Abstract : Magnetic curves are the trajectories of charged particals \linebreak which are influenced by magnetic fields and they satisfy the Lorentz equation. It is important to find relationships between magnetic curves and other special curves. This paper is a study of magnetic curves and this kind of relationships. We give the relationship between $\beta $-magnetic curves and Mannheim, Bertrand, involute-evolute curves and we give some geometric properties about them. Then, we study this subject for $\gamma $-magnetic curves. Finally, we give an evaluation of what we did.
Abstract : In the present paper, following the pullback approach to Finsler geometry, we study intrinsically the $C^v$-reducible and generalized $C^v$-reducible Finsler spaces. Precisely, we introduce a coordinate-free formulation of these manifolds. Then, we prove that a Finsler manifold is $C^v$-reducible if and only if it is $C$-reducible and satisfies the $\mathbb{T}$-condition. We study the generalized $C^v$-reducible Finsler manifold with a scalar $\pi$-form $\mathbb{A}$. We show that a Finsler manifold $(M,L)$ is generalized $C^v$-reducible with $\mathbb{A}$ if and only if it is $C$-reducible and $\mathbb{T}=\mathbb{A}$. Moreover, we prove that a Landsberg generalized $C^v$-reducible Finsler manifold with a scalar $\pi$-form $\mathbb{A}$ is Berwaldian. Finally, we consider a special $C^v$-reducible Finsler manifold and conclude that a Finsler manifold is a special $C^v$-reducible if and only if it is special semi-$C$-reducible with vanishing $\mathbb{T}$-tensor.
Adnan Abbasi, Md Arshad Madni, Muzibur Rahman Mozumder
Commun. Korean Math. Soc. 2023; 38(3): 679-693
https://doi.org/10.4134/CKMS.c220240
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
Uday Chand De, Mohammad Nazrul Islam Khan
Commun. Korean Math. Soc. 2023; 38(4): 1233-1247
https://doi.org/10.4134/CKMS.c230006
Rachida EL KHALFAOUI, Najib Mahdou
Commun. Korean Math. Soc. 2023; 38(4): 983-992
https://doi.org/10.4134/CKMS.c220332
Bui Thi Hong Cam, Nguyen Minh Tri, Do Ngoc Yen
Commun. Korean Math. Soc. 2023; 38(3): 649-661
https://doi.org/10.4134/CKMS.c220160
Asmaa Orabi Mohammed, Medhat Ahmed Rakha, Arjun K. Rathie
Commun. Korean Math. Soc. 2023; 38(3): 807-819
https://doi.org/10.4134/CKMS.c220217
Uday Chand De, Dipankar Hazra
Commun. Korean Math. Soc. 2024; 39(1): 201-210
https://doi.org/10.4134/CKMS.c230105
El Mehdi Bouba , Yassine EL-khabchi, Mohammed Tamekkante
Commun. Korean Math. Soc. 2024; 39(1): 93-104
https://doi.org/10.4134/CKMS.c230134
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