In this paper, we propose a Hepatitis C virus transmissions model with time delay. Firstly, we get the condition for the existence and local stability of equilibria of the system. Secondly, by choosing the time delay τ as a bifurcation parameter, we show that Hopf bifurcation will occur as the time delay τ passes through some critical values. Thirdly, by use of normal form theory and central manifold argument, we establish the direction and stability of Hopf bifurcation. At last, some numerical simulations is provided to verify the theoretical results.

For any abelian group A, a graph G = (V;E) is said to be A-magic if there exists a labeling ` : E(G) ! A n f0g such that the induced vertex set labeling `+ : V (G) ! A defined by

is a constant map. A graph G = (V, E) is said to be a-sum A magic if there there exists an a 2 A such that `+(v) = a for all v ∈ V . In particular, if a is the identity element 0, we say that G is zero-sum A magic. In this paper we will consider the Klein-four group V4 = {0; a; b; c} and investigate a class of V4 magic shell related graphs that belongs to the following categories:

(i) Va, the class of a-sum V4 magic graphs,

(ii) V0, the class of zero-sum V4 magic graphs,

(iii) Va, 0, the class of graphs which are both a-sum and zero -sum V4 magic

The effect of the density of the liquid on the sloshing in partially filled tanks is studied. The liquid is assumed to be almost-homogeneous (i.e. a liquid whose density in equilibrium is practically a linear function of the height, which differs very little from a constant). In this case the linearized Euler’s equation of the liquid is presented and analyzed, the relevant operators are studied. The Weyl’s criterion is used for computing the spectrum of the fundamental operator . We obtain nonclassically spectrum with continuous part filling an interval.

The biharmonic equations arise in many applications such as elasticity, fluid mechanics, and many other areas. In this paper, the combination of Explicit Decoupled Group (EDG) method with Successive Over Relaxation (SOR) is proposed for solving the biharmonic equation by reducing this equation into a coupled second order Poisson equations. Thus, this pair of Poisson equations can be easily solved using finite difference method, which discretizes the solution domain into a finite number of grids. The sparse linear system derived is usually solved by iterative methods which always take advantage of the existence of zeros in the coefficient matrix. However, such methods yield high number of iterations for convergence especially if the number of grid points is very large. To overcome of this problem, EDG SOR method formulated to accelerate the rate of convergence for the solution of these iterative methods. The numerical experiments carried out confirm the superiority of the introduced method over the classical standard five point SOR formula in terms of number of iterations and execution time.

Nodal cilia play an important role in the left-right symmetry breaking at the early stage of the mammal embryos and show an apparent rotational motion. This study is about the flow induced by cilia sweeping out circular/elliptical cones above a no-slip plane in the low Reynolds number regime. Using the regularized Stokeslet method, we examine the properties of flows generated by a single cilium and multiple cilia, especially two cilia, which are assumed to be anchored to the embryonic heart wall. For a short-term Lagrangian fluid tracer trajectory, epicycles are presented as a nodal cilium precesses in either a circular cone or a non-circular cone shape. For the long-term behavior, the trajectory is periodic around both the circular and elliptical cones. Compared to the circular cone cases, the vertical variances are enhanced in elliptical cone cases. Besides tracer trajectories, fluid velocity elds are presented to demonstrate the flow structure. When two cilia are considered in the system, the flow structure is analyzed for the dierent phase angles and relative orientation of the elliptical cones.

This paper demonstrates the use of radial basis networks (RBF), cellular neural networks (CNN) and genetic algorithm (GA) for automatic classication of plant leaves. A genetic neuronal system herein attempted to solve some of the inherent challenges facing current software being employed for plant leaf classication. The image segmentation module in this work was genetically optimized to bring salient features in the images of plants leaves used in this work. The combination of GA-based CNN with RBF in this work proved more ecient than the existing systems that use conventional edge operators such as Canny, LoG, Prewitt, and Sobel operators. The results herein showed that GA-based CNN edge detector outperforms other edge detector in terms of speed and classication accuracy.

In this paper, the discrete Adomian decomposition method (DADM) is applied to obtain the approximate solution of fuzzy convection-diusion equation (FCDE). The numerical results are compared with the exact solution. It is shown that this method is accurate and eective for FCDE. Also, the analytical-approximate solution of this equation by Adomian decomposition method (ADM) is oered.