The linear stability of an incompressible planar layer in the presence of nonuniform horizontal magnetic field is studied for three sequences of equilibrium configurations. It is found that the Alfven continuum is fundamental for the... more
The linear stability of an incompressible planar layer in the presence of nonuniform horizontal magnetic field is studied for three sequences of equilibrium configurations. It is found that the Alfven continuum is fundamental for the understanding of the linear stability. Complete stabilization is only obtained when min sigma sq A (z) 0 in the layer where d rho/dz 0, and
The purpose of this paper is to study the linear stability of an incompressible horizontal layer of fluid in the presence of a non-uniform horizontal magnetic field and to show that the Alfvén continuum of frequencies is fundamental for... more
The purpose of this paper is to study the linear stability of an incompressible horizontal layer of fluid in the presence of a non-uniform horizontal magnetic field and to show that the Alfvén continuum of frequencies is fundamental for the understanding of the linear stability.
... It is well-known that this differential equation possesses a singularity at the level where the local Alfv6n frequency or the local cusp frequency equals the frequency of the oscillation (see eg, Appert et al., 1975; Chen and... more
... It is well-known that this differential equation possesses a singularity at the level where the local Alfv6n frequency or the local cusp frequency equals the frequency of the oscillation (see eg, Appert et al., 1975; Chen and Hasegawa, 1974; Adam, 1977; E1 Mekki et al., 1978; Rae ...
In this paper, the probability that two elements of a finite ring have product zero is considered. The bounds of this probability are found for an arbitrary finite commutative ring with identity 1. An explicit formula for this probability... more
In this paper, the probability that two elements of a finite ring have product zero is considered. The bounds of this probability are found for an arbitrary finite commutative ring with identity 1. An explicit formula for this probability in the case of, the ring of integers modulo, is obtained.
Let R be a finite ring. The zero divisors of R are defined as two nonzero elements of R, say x and y where xy = 0. Meanwhile, the probability that two random elements in a group commute is called the commutativity degree of the group.... more
Let R be a finite ring. The zero divisors of R are defined as two nonzero elements of R, say x and y where xy = 0. Meanwhile, the probability that two random elements in a group commute is called the commutativity degree of the group. Some generalizations of this concept have been done on various groups, but not in rings. In this study, a variant of probability in rings which is the probability that two elements of a finite ring have product zero is determined for some ring of matrices over integers modulo n. The results are then applied into graph theory, specifically the zero divisor graph. This graph is defined as a graph where its vertices are zero divisors of R and two distinct vertices x and y are adjacent if and only if xy = 0. It is found that the zero divisor graph of R is a directed graph.
Let $G$ be a finite group. The intersection graph of $G$ is a graph whose vertex set is the set of all proper non-trivial subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $H\cap K \neq \{e\}$, where $e$... more
Let $G$ be a finite group. The intersection graph of $G$ is a graph whose vertex set is the set of all proper non-trivial subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $H\cap K \neq \{e\}$, where $e$ is the identity of the group $G$. In this paper, we investigate some properties and exploring some topological indices such as Wiener, Hyper-Wiener, first and second Zagreb, Schultz, Gutman and eccentric connectivity indices of the intersection graph of $D_{2n}$ for $n=p^2$, $p$ is prime. We also find the metric dimension and the resolving polynomial of the intersection graph of $D_{2p^2}$.
A non-commuting graph of a finite group $G$ is a graph whose vertices are non-central elements of $G$ and two vertices are adjacent if they don't commute in $G$. In this paper, we study the non-commuting graph of the group $U_{6n}$... more
A non-commuting graph of a finite group $G$ is a graph whose vertices are non-central elements of $G$ and two vertices are adjacent if they don't commute in $G$. In this paper, we study the non-commuting graph of the group $U_{6n}$ and explore some of its properties including the independent number, clique and chromatic numbers. Also, the general formula of the resolving polynomial of the non-commuting graph of the group $U_{6n}$ are provided. Furthermore, we find the detour index, eccentric connectivity, total eccentricity and independent polynomials of the graph.
