Arab Journal of Mathematical Sciences最新文献

Mason introduced the notion of reflexive property of rings as a generalization of reduced rings. For a ring endomorphism $\alpha$, Krempa studied $\alpha$-rigid rings as an extension of reduced rings. In this note, we introduce the notion of $\alpha$-quasi reflexive rings as a generalization of $\alpha$-rigid rings and a natural extension of the reflexive property to ring endomorphisms. We investigate various properties of these rings and also study ring theoretic extensions such as polynomial rings, trivial extensions, right (left) quotient rings, Dorroh extensions etc. over these rings.

In a graph $G$, a vertex $w\in V\left(G\right)$ resolves a pair of vertices $u,v\in V\left(G\right)$ if $d(u,w)\ne d(v,w)$. A resolving set of $G$ is a set of vertices $S$ such that every pair of distinct vertices in $V\left(G\right)$ is resolved by some vertex in $S$. The minimum cardinality among all the resolving sets of $G$ is called the metric dimension of $G$, denoted by $\beta \left(G\right)$. The metric dimension of a wheel has been obtained in an earlier paper (Shanmukha et al., 2002). In this paper, the metric dimension of the family of generalized wheels is obtained. Further, few properties of the metric dimension of the corona product of graphs have been discussed and some relations between the metric dimension of a graph and its generalized corona product are established.

A formula for calculating moments for wavelet packets is derived and a sufficient condition for moments of wavelet packets to be vanishing is obtained. Also, the convolution and cross-correlation theorems for Hilbert transform of wavelets are proved. Finally, using MRA of $L^2\left(R\right)$, some results on the vanishing moments of the scaling functions, wavelets and their convolution in two dimension are given.

In this paper, we use Schauder’s fixed point to establish the existence of at least one solution for a functional nonlocal stochastic differential equation under sufficient conditions in the space of all square integrable stochastic processes with a finite second moment. We state and prove the conditions which guarantee the uniqueness of the solution. We solve a nonlinear example analytically and obtain the initial condition which makes the solution passes through a random position with a given normal distribution at a specified time. Also, the Milstein scheme to this example is studied.

A nonlinear modified form of Bass model involving the interactions of non-adopter and adopter populations has been proposed to describe the process of diffusion of a new technology in the presence of evaluation period (time delay). The basic aim is to model the diffusion of those technologies which require higher investments, and which require government subsidies for promotions in the various markets. We use government incentives and the costs in the form of external factors, as well as the internal word of mouth that considerably influence the non-adopters decisions. A qualitative analysis has been performed to determine the stability of the various equilibria. The Hopf bifurcation occurs near the positive equilibrium when the time delay passes some critical values. By applying the normal form theory and the center manifold reduction for functional differential equations, explicit formulae presenting stability properties of bifurcating periodic solutions have been computed. Moreover, the intra-specific competition has played an important role in establishing the maturity stage in the innovation diffusion model. Numerical analysis has been carried out to justify the correctness of our analytical findings.

A class of third order singularly perturbed convection diffusion type equations with integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is of almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the theoretical estimates.