In this paper we study some growth properties of iterated entire functions which improve some earlier results.

In this paper, we present the comparative study of Haar wavelet collocation method (HWCM) and Finite Element Method (FEM) for the numerical solution of parabolic type partial differential equations such as 1-D singularly perturbed convection-dominated diffusion equation and 2-D Transient heat conduction problems validated against exact solution. The distinguishing feature of HWCM is that it provides a fast converging series of easily computable components. Compared with FEM, this approach needs substantially shorter computational time, at the same time meeting accuracy requirements. It is found that higher accuracy can be attained by increasing the level of Haar wavelets. As Consequences, it avoids more computational costs, minimizes errors and speeds up the convergence, which has been justified in this paper through the error analysis.

In this article, we use the extended rational ( )- expansion function method to construct exact solutions for some nonlinear partial differential equations in mathematical physics via the (2+1)- dimensional Wu-Zhang equations, the KdV equation, and generalized Hirota–Satsuma coupled KdV equation in terms of the hyperbolic functions, trigonometric functions and rational function, when satisfies a nonlinear second order ordinary differential equation. When the parameters are taken some special values, the solitary wave are derived from the traveling waves. This method is reliable, simple and gives many new exact solutions.

This paper deals with the finite-time chaos synchronization of the delay hyperchaotic Lü systen with uncertain parameters. Based on the finite time stability theory, a control law is proposed to realize finite- time chaos synchronization for the delay hyperchaotic Lü systen with uncertain parameters. The controller is simple, robust and only part parameters are required to be bounded. Numerical simulation results are given to demonstrate the effectiveness of the proposed finite-time chaos synchronization scheme.

Taking the drought stress and normal irrigation fields where plant the same varieties of corn, an experiment by drilling soil was conducted to study the effects of drought stress on characteristics of the soil gravimetric moisture content, water storage and water consumption. The result showed that the effect of drought stress enhanced significantly after the tasseling stage, the soil moisture was markedly lower than that in the normal irrigation field. During the reproductive period, the soil water storage of drought stress area was lower than the normal irrigation field, and the variation of the soil water storage in shallow layer was bigger and smaller in the deep layer. Moreover, the drought stress influenced on the maize yield seriously, and the indexes of maize yield under the drought stress were significantly lower than the normal water treatment, the hundred grain weight decreased by 23.3%, and the grain yield fell by 35.6%.

Cloud-computing service providers are currently viewed as the best solution to the global need for massive data systems because of their superior flexibility, scalability, and cost benefits. Cloud computing that is enabled by virtualized services is still constrained, however, by the capacities of the underlying physical systems that are combined into sharable pools of resources. The next challenge for computation systems will arise when even the cloud is not sufficient. What comes after cloud migration and adoption? In this paper, we examine how service providers can manage cloud storage resources and costs when the amount of collected data to be retained grows exponentially, to the point that it strains even virtualized resource capacities. We assess the analytical frameworks being developed to identify which storage architectures can best accommodate the specific needs of large data storage consumers. We also investigate the areas in which these fail to fully address the problem, and propose solutions. We argue that a cloud storage framework that addresses data volume, data growth trends over time, and requirements for storage management will enable service providers to manage cloud storage resources and costs in such a manner that the cloud will continue to offer the greatest benefits for the storage of massive data systems.