Scientific Research Publishing

Read  full  paper  at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53792#.VNMhYSzQrzE Author(s)   Rengang Shi 1,2 , Haitian Yang 3   Affiliation(s) 1 Department of Applied Mathematics, Dalian University of Technology, Dalian, China . 2 College of Science, China University of Petroleum, Qingdao, China . 3 Department of Engineering Mechanics, Dalian University of Technology, Dalian, China . ABSTRACT In this paper, a new kind of energy identities for the Maxwell equations with periodic boundary conditions is proposed and then proved rigorously by the energy methods. By these identities, several modified energy identities of the ADI-FDTD scheme for the two dimensional (2D) Maxwell equations with the periodic boundary conditions are derived. Also by these identities it is proved that 2D-ADI-FDTD is approximately energy conserved and unconditionally stable in the discrete L 2 and H 1 norms. Experiments are provided an...

Read  full  paper  at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53343#.VL3KrSzQrzE Author(s)    A. A. Martynyuk Affiliation(s) S.P. Timoshenko Institute of Mechanics of NAS of Ukraine, Kyiv, Ukraine . ABSTRACT In this paper the estimates for norms of solutions to nonlinear systems are obtained via an integral inequality. As an application we considered affine control systems and systems of equations for synchronization of motions.   KEYWORDS Nonlinear Systems , Novel Bounds for Solutions , Stability , Synchronization Cite this paper Martynyuk, A. (2015) Novel Bounds for Solutions of Nonlinear Differential Equations. Applied Mathematics , 6 , 182-194. doi: 10.4236/am.2015.61018 .   References [ 1 ] Bellman, R. (1953) Stability Theory of Differential Equations. Dover Publications, New York, 166 p.   [ 2 ] Martynyuk, A.A., Lakshmikantham, V. and Leela, S. (1979) Stability of Motion:...

Read  full  paper  at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53159#.VLXf1MnQrzE Author(s)    Ibrahim Khalifa , Hassan Barakat * , Hamdy A. El-Mansy , Soliman A. Soliman Affiliation(s) Department of Food Science, Faculty of Agriculture, Benha University, 13736 Moshtohor, Qaliuobia, Egypt . ABSTRACT Utilization of potato processing residues to produce a low caloric cupcake in present study was targeted. The functional properties of wheat flour (WF 72%) and dried potato peel varieties [Hermus (PPH) and Russet (PPR)] were carried out. Consequently, WF was partially substituted by both potato peels (PP) at 5% - 20% to prepare mixtures for cupcake making. Approximate chemical composition and physical characteristics were determined. Rheological parameters of prepared formulas were assayed using Mixolab. Moreover, total phenolic compounds (TPC) and relative antioxidant activity (AOA) were evaluated. Quality parameters ...

Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=47024#.VGLxSmfHRK0 Author(s) Jessica Li Affiliation(s) Kent Place School, Summit, USA . ABSTRACT The Lotka-Volterra predator-prey model is widely used in many disciplines such as ecology and economics. The model consists of a pair of first-order nonlinear differential equations. In this paper, we first analyze the dynamics, equilibria and steady state oscillation contours of the differential equations and study in particular a well-known problem of a high risk that the prey and/or predator may end up with extinction. We then introduce exogenous control to reduce the risk of extinction. We propose two control schemes. The first schem...

Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50913#.VFB-HlfHRK0 Author(s) Huahua Cao , Shujing Gao , Xiangyu Zhang , Youquan Luo Affiliation(s) College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China . ABSTRACT From the lifecycle of schistosome, the phenomenon of time delay is widespread. In this paper, a two-dimensional system is studied that incorporates two time delays which are the incubation period of human and snail, respectively. Our purpose is to demonstrate that the time delays are harmless for stability of equilibria of the system. Further, sufficient conditions of stability of equilibria are obtained. ...