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Open Access Article
1 - Connected and Hyperconnected Generalized Topological Spaces
I. Basdouri R. Messaoud A. MissaouiA. Csaszar introduced and extensively studied the notion of generalized opensets. Following Csazar, we introduce a new notion hyperconnected. We study some specificproperties about connected and hyperconnected in generalized topological spaces. Finally, wecharacterize t MoreA. Csaszar introduced and extensively studied the notion of generalized opensets. Following Csazar, we introduce a new notion hyperconnected. We study some specificproperties about connected and hyperconnected in generalized topological spaces. Finally, wecharacterize the connected component in generalized topological spaces. Manuscript profile -
Open Access Article
2 - On quasi-baer modules
M. Shafiee-MousaviLet $R$ be a ring, $\sigma$ be an endomorphism of $R$ and $M_R$ be a $\sigma$-rigid module. Amodule $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ isgenerated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer mod MoreLet $R$ be a ring, $\sigma$ be an endomorphism of $R$ and $M_R$ be a $\sigma$-rigid module. Amodule $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ isgenerated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if andonly if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,\sigma]]$. Manuscript profile -
Open Access Article
3 - Construction of strict Lyapunov function for nonlinear parameterised perturbed systems
B. Ghanmi M. A. HammamiIn this paper, global uniform exponential stability of perturbed dynamical systemsis studied by using Lyapunov techniques. The system presents a perturbation term which isbounded by an integrable function with the assumption that the nominal system is globallyuniformly MoreIn this paper, global uniform exponential stability of perturbed dynamical systemsis studied by using Lyapunov techniques. The system presents a perturbation term which isbounded by an integrable function with the assumption that the nominal system is globallyuniformly exponentially stable. Some examples in dimensional two are given to illustrate theapplicability of the main results. Manuscript profile -
Open Access Article
4 - On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex reflection group $G_7$
M. Y. Chreif M. AbdulrahimWe consider a 2-dimensional representation of the Hecke algebra $H(G_7, u)$, where$G_7$ is the complex reflection group and $u$ is the set of indeterminates$u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3)$.After specializing the indetrminates to non zero complex numbers, we then MoreWe consider a 2-dimensional representation of the Hecke algebra $H(G_7, u)$, where$G_7$ is the complex reflection group and $u$ is the set of indeterminates$u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3)$.After specializing the indetrminates to non zero complex numbers, we then determine a necessary and sufficient condition that guarantees the irreducibility of the complex specializationof the representation of the Hecke algebra $H(G_7, u)$. Manuscript profile -
Open Access Article
5 - Preorder Relators and Generalized Topologies
H. ArianpoorIn this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. We introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some MoreIn this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. We introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some of their important properties. Manuscript profile -
Open Access Article
6 - Dynamical distance as a semi-metric on nuclear configuration space
M. RahimiIn this paper, we introduce the concept of dynamical distance on a nuclear configuration space. We partition the nuclear conguration space into disjoint classes. This classification coincides with the classical partitioning of molecular systems via the concept ofconjuga MoreIn this paper, we introduce the concept of dynamical distance on a nuclear configuration space. We partition the nuclear conguration space into disjoint classes. This classification coincides with the classical partitioning of molecular systems via the concept ofconjugacy of dynamical systems. It gives a quantitative criterion to distinguish differentmolecular structures. Manuscript profile -
Open Access Article
7 - On the commuting graph of some non-commutative rings with unity
F. Ramezani E. Vatandoost‎‎Let $R$ be a non-commutative ring with unity‎. ‎The commuting graph‎ of $R$ denoted by $\Gamma(R)$‎, ‎is a graph with a vertex set‎‎$R\setminus Z(R)$ and two vertices $a$ and $b$ are adjacent if and only if‎$ab=ba$‎. ‎In More‎‎Let $R$ be a non-commutative ring with unity‎. ‎The commuting graph‎ of $R$ denoted by $\Gamma(R)$‎, ‎is a graph with a vertex set‎‎$R\setminus Z(R)$ and two vertices $a$ and $b$ are adjacent if and only if‎$ab=ba$‎. ‎In this paper‎, ‎we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n \in \lbrace 4,5 \rbrace$‎. It is shown that‎, ‎$\Gamma(R)$ is the disjoint union of complete graphs‎. Finally‎, ‎we prove that there are exactly five commuting‎‎graphs of non-commutative rings with unity up to twenty vertices and they are $3K_2,3K_4,7K_2‎, ‎K_2 \cup 2K_6$ and $4K_2 \cup K_6$‎. Manuscript profile
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