Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Super-Hamiltonian Structures and Conservation Laws of a New Six-Component Super-Ablowitz-Kaup-Newell-Segur Hierarchy Wed, 20 Aug 2014 07:59:29 +0000 http://www.hindawi.com/journals/aaa/2014/214709/ A six-component super-Ablowitz-Kaup-Newell-Segur (-AKNS) hierarchy is proposed by the zero curvature equation associated with Lie superalgebras. Supertrace identity is used to furnish the super-Hamiltonian structures for the resulting nonlinear superintegrable hierarchy. Furthermore, we derive the infinite conservation laws of the first two nonlinear super-AKNS equations in the hierarchy by utilizing spectral parameter expansions. PACS: 02.30.Ik; 02.30.Jr; 02.20.Sv. Fucai You, Jiao Zhang, and Yan Zhao Copyright © 2014 Fucai You et al. All rights reserved. Strong Convergence of the Split-Step Theta Method for Stochastic Delay Differential Equations with Nonglobally Lipschitz Continuous Coefficients Wed, 20 Aug 2014 07:09:09 +0000 http://www.hindawi.com/journals/aaa/2014/157498/ This paper is concerned with the convergence analysis of numerical methods for stochastic delay differential equations. We consider the split-step theta method for nonlinear nonautonomous equations and prove the strong convergence of the numerical solution under a local Lipschitz condition and a coupled condition on the drift and diffusion coefficients. In particular, these conditions admit that the diffusion coefficient is highly nonlinear. Furthermore, the obtained results are supported by numerical experiments. Chao Yue and Chengming Huang Copyright © 2014 Chao Yue and Chengming Huang. All rights reserved. Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative Wed, 20 Aug 2014 06:03:43 +0000 http://www.hindawi.com/journals/aaa/2014/283019/ An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented. The order of the derivative is considered as , for the space and time domain, respectively. The fractional derivative of Caputo type is considered. In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case. In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form. In order that the equation preserves the physical units of the system two auxiliary parameters and are introduced characterizing the existence of fractional space and time components, respectively. A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parameters and . The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior. José Francisco Gómez Aguilar and Margarita Miranda Hernández Copyright © 2014 José Francisco Gómez Aguilar and Margarita Miranda Hernández. All rights reserved. Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation Wed, 20 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/178672/ The regularization of the shock wave solution to the Riemann problem for the relativistic Burgers equation is considered. For Riemann initial data consisting of a single decreasing jump, we find that the regularization of nonlinear convective term cannot capture the correct shock wave solution. In order to overcome it, we consider a new regularization technique called the observable divergence method introduced by Mohseni and discover that it can capture the correct shock wave solution. In addition, we take the Helmholtz filter for the fully explicit computation. Ting Zhang and Chun Shen Copyright © 2014 Ting Zhang and Chun Shen. All rights reserved. Dissipative Nonlinear Schrödinger Equation for Envelope Solitary Rossby Waves with Dissipation Effect in Stratified Fluids and Its Solution Tue, 19 Aug 2014 10:42:05 +0000 http://www.hindawi.com/journals/aaa/2014/643652/ We solve the so-called dissipative nonlinear Schrödinger equation by means of multiple scales analysis and perturbation method to describe envelope solitary Rossby waves with dissipation effect in stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency, and effect are important factors to form the envelope solitary Rossby waves. By employing trial function method, the asymptotic solution of dissipative nonlinear Schrödinger equation is derived. Based on the solution, the effect of dissipation on the evolution of envelope solitary Rossby wave is also discussed. The results show that the dissipation causes a slow decrease of amplitude of envelope solitary Rossby waves and a slow increase of width, while it has no effect on the propagation velocity. That is quite different from the KdV-type solitary waves. It is notable that dissipation has certain influence on the carrier frequency. Yunlong Shi, Baoshu Yin, Hongwei Yang, Dezhou Yang, and Zhenhua Xu Copyright © 2014 Yunlong Shi et al. All rights reserved. Asymptotic Behavior of the Coupled Nonlinear Schrödinger Lattice System Tue, 19 Aug 2014 10:39:54 +0000 http://www.hindawi.com/journals/aaa/2014/514850/ This paper studies asymptotic behavior of solutions for the coupled nonlinear Schrödinger lattice system. We obtain the existence and stability of compact attractor by means of tail estimates method and finite-dimensional approximations. Hengyan Li and Xin Zhao Copyright © 2014 Hengyan Li and Xin Zhao. All rights reserved. Distance from Bloch-Type Functions to the Analytic Space Tue, 19 Aug 2014 09:30:44 +0000 http://www.hindawi.com/journals/aaa/2014/610237/ The analytic space can be embedded into a Bloch-type space. We establish a distance formula from Bloch-type functions to , which generalizes the distance formula from Bloch functions to BMOA by Peter Jones, and to by Zhao. Cheng Yuan and Cezhong Tong Copyright © 2014 Cheng Yuan and Cezhong Tong. All rights reserved. α-Coupled Fixed Points and Their Application in Dynamic Programming Tue, 19 Aug 2014 08:33:19 +0000 http://www.hindawi.com/journals/aaa/2014/593645/ We introduce the definition of α-coupled fixed point in the space of the bounded functions on a set S and we present a result about the existence and uniqueness of such points. Moreover, as an application of our result, we study the problem of existence and uniqueness of solutions for a class of systems of functional equations arising in dynamic programming. J. Harjani, J. Rocha, and K. Sadarangani Copyright © 2014 J. Harjani et al. All rights reserved. A Computational Study of an Implicit Local Discontinuous Galerkin Method for Time-Fractional Diffusion Equations Tue, 19 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/898217/ We propose, analyze, and test a fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional diffusion equation. The proposed method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. By choosing the numerical fluxes carefully, we prove that our scheme is unconditionally stable and convergent. Finally, numerical examples are performed to illustrate the effectiveness and the accuracy of the method. Leilei Wei and Xindong Zhang Copyright © 2014 Leilei Wei and Xindong Zhang. All rights reserved. Double Sequence Spaces by Means of Orlicz Functions Mon, 18 Aug 2014 13:13:09 +0000 http://www.hindawi.com/journals/aaa/2014/260326/ We define some classes of double entire and analytic sequences by means of Orlicz functions. We study some relevant algebraic and topological properties. Further some inclusion relations among the classes are also examined. Abdullah Alotaibi, M. Mursaleen, and Kuldip Raj Copyright © 2014 Abdullah Alotaibi et al. All rights reserved. The Almost Sure Asymptotic Stability and Boundedness of Stochastic Functional Differential Equations with Polynomial Growth Condition Mon, 18 Aug 2014 12:10:42 +0000 http://www.hindawi.com/journals/aaa/2014/629426/ Stability and boundedness are two of the most important topics in the study of stochastic functional differential equations (SFDEs). This paper mainly discusses the almost sure asymptotic stability and the boundedness of nonlinear SFDEs satisfying the local Lipschitz condition but not the linear growth condition. Here we assume that the coefficients of SFDEs are polynomial or dominated by polynomial functions. We give sufficient criteria on the almost sure asymptotic stability and the boundedness for this kind of nonlinear SFDEs. Some nontrivial examples are provided to illustrate our results. Lichao Feng and Shoumei Li Copyright © 2014 Lichao Feng and Shoumei Li. All rights reserved. Optimal Pole Assignment of Linear Systems by the Sylvester Matrix Equations Mon, 18 Aug 2014 11:19:23 +0000 http://www.hindawi.com/journals/aaa/2014/301375/ The problem of state feedback optimal pole assignment is to design a feedback gain such that the closed-loop system has desired eigenvalues and such that certain quadratic performance index is minimized. Optimal pole assignment controller can guarantee both good dynamic response and well robustness properties of the closed-loop system. With the help of a class of linear matrix equations, necessary and sufficient conditions for the existence of a solution to the optimal pole assignment problem are proposed in this paper. By properly choosing the free parameters in the parametric solutions to this class of linear matrix equations, complete solutions to the optimal pole assignment problem can be obtained. A numerical example is used to illustrate the effectiveness of the proposed approach. Hua-Feng He, Guang-Bin Cai, and Xiao-Jun Han Copyright © 2014 Hua-Feng He et al. All rights reserved. Prediction Model of Interval Grey Numbers with a Real Parameter and Its Application Mon, 18 Aug 2014 11:13:48 +0000 http://www.hindawi.com/journals/aaa/2014/939404/ Grey prediction models have become common methods which are widely employed to solve the problems with “small examples and poor information.” However, modeling objects of existing grey prediction models are limited to the homogenous data sequences which only contain the same data type. This paper studies the methodology of building prediction models of interval grey numbers that are grey heterogeneous data sequence, with a real parameter. Firstly, the position of the real parameter in an interval grey number sequence is discussed, and the real number is expanded into an interval grey number by adopting the method of grey generation. On this basis, a prediction model of interval grey number with a real parameter is deduced and built. Finally, this novel model is successfully applied to forecast the concentration of organic pollutant DDT in the atmosphere. The analysis and research results in this paper extend the object of grey prediction from homogenous data sequence to grey heterogeneous data sequence. Those research findings are of positive significance in terms of enriching and improving the theory system of grey prediction models. Bo Zeng, Chuan Li, Xue-Yu Zhou, and Xian-Jun Long Copyright © 2014 Bo Zeng et al. All rights reserved. Certain Class of Generating Functions for the Incomplete Hypergeometric Functions Mon, 18 Aug 2014 09:27:05 +0000 http://www.hindawi.com/journals/aaa/2014/714560/ Generating functions play an important role in the investigation of various useful properties of the sequences which they generate. In this paper, we aim to establish certain generating functions for the incomplete hypergeometric functions introduced by Srivastava et al. (2012). All the derived results in this paper are general and can yield a number of (known and new) results in the theory of generating functions. Junesang Choi and Praveen Agarwal Copyright © 2014 Junesang Choi and Praveen Agarwal. All rights reserved. Oscillations in Difference Equations with Deviating Arguments and Variable Coefficients Mon, 18 Aug 2014 08:32:39 +0000 http://www.hindawi.com/journals/aaa/2014/902616/ New sufficient conditions for the oscillation of all solutions of difference equations with several deviating arguments and variable coefficients are presented. Examples illustrating the results are also given. G. E. Chatzarakis, H. Péics, and I. P. Stavroulakis Copyright © 2014 G. E. Chatzarakis et al. All rights reserved. Bounded Doubly Close-to-Convex Functions Mon, 18 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/804095/ We consider a new class of bounded doubly close-to-convex functions. Coefficient bounds, distortion theorems, and radius of convexity for the class are investigated. A corresponding class of doubly close-to-starlike functions is also considered. Dorina Răducanu Copyright © 2014 Dorina Răducanu. All rights reserved. A Numerical Solution for Hirota-Satsuma Coupled KdV Equation Sun, 17 Aug 2014 13:16:58 +0000 http://www.hindawi.com/journals/aaa/2014/819367/ A Petrov-Galerkin method and product approximation technique are used to solve numerically the Hirota-Satsuma coupled Korteweg-de Vries equation, using cubic -splines as test functions and a linear -spline as trial functions. The implicit midpoint rule is used to advance the solution in time. Newton’s method is used to solve the block nonlinear pentadiagonal system we have obtained. The resulting schemes are of second order accuracy in both directions, space and time. The von Neumann stability analysis of the schemes shows that the two schemes are unconditionally stable. The single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitons, three solitons, and birth of solitons is also discussed. M. S. Ismail and H. A. Ashi Copyright © 2014 M. S. Ismail and H. A. Ashi. All rights reserved. Krein Space-Based Fault Estimation for Discrete Time-Delay Systems Thu, 14 Aug 2014 14:13:52 +0000 http://www.hindawi.com/journals/aaa/2014/935216/ This paper investigates the finite-time fault estimation problem for linear time-delay systems, where the delay appears in both state and measurement equations. Firstly, the design of finite horizon fault estimation is converted into a minimum problem of certain quadratic form. Then we introduce a stochastic system in Krein space, and a sufficient and necessary condition for the minimum is derived by applying innovation analysis approach and projection theory. Finally, a solution to the fault estimation is obtained by recursively computing a partial difference Riccati equation, which has the same dimension as the original system. Compared with the conventional augmented approach, the solving of a high dimension Riccati equation is avoided. Xinmin Song and Xuehua Yan Copyright © 2014 Xinmin Song and Xuehua Yan. All rights reserved. A Few Integrable Couplings of Some Integrable Systems and ()-Dimensional Integrable Hierarchies Thu, 14 Aug 2014 14:13:08 +0000 http://www.hindawi.com/journals/aaa/2014/932672/ Two high-dimensional Lie algebras are presented for which four ()-dimensional expanding integrable couplings of the D-AKNS hierarchy are obtained by using the Tu scheme; one of them is a united integrable coupling model of the D-AKNS hierarchy and the AKNS hierarchy. Then ()-dimensional DS hierarchy is derived by using the TAH scheme; in particular, the integrable couplings of the DS hierarchy are obtained. Binlu Feng, Yufeng Zhang, and Huanhe Dong Copyright © 2014 Binlu Feng et al. All rights reserved. Spectrums of Solvable Pantograph Differential-Operators for First Order Thu, 14 Aug 2014 13:06:14 +0000 http://www.hindawi.com/journals/aaa/2014/837565/ By using the methods of operator theory, all solvable extensions of minimal operator generated by first order pantograph-type delay differential-operator expression in the Hilbert space of vector-functions on finite interval have been considered. As a result, the exact formula for the spectrums of these extensions is presented. Applications of obtained results to the concrete models are illustrated. Z. I. Ismailov and P. Ipek Copyright © 2014 Z. I. Ismailov and P. Ipek. All rights reserved. A New Algorithm for System of Integral Equations Thu, 14 Aug 2014 12:03:12 +0000 http://www.hindawi.com/journals/aaa/2014/236065/ We develop a new algorithm to solve the system of integral equations. In this new method no need to use matrix weights. Beacause of it, we reduce computational complexity considerable. Using the new algorithm it is also possible to solve an initial boundary value problem for system of parabolic equations. To verify the efficiency, the results of computational experiments are given. Abdujabar Rasulov, Adem Kilicman, Zainidin Eshkuvatov, and Gulnora Raimova Copyright © 2014 Abdujabar Rasulov et al. All rights reserved. Complex Boundary Value Problems of Nonlinear Differential Equations 2014 Thu, 14 Aug 2014 11:56:35 +0000 http://www.hindawi.com/journals/aaa/2014/496350/ Xinguang Zhang, Yong Hong Wu, Dragoș-Pãtru Covei, and Xinan Hao Copyright © 2014 Xinguang Zhang et al. All rights reserved. Global and Blow-Up Solutions for a Class of Nonlinear Parabolic Problems under Robin Boundary Condition Thu, 14 Aug 2014 11:09:25 +0000 http://www.hindawi.com/journals/aaa/2014/241650/ We discuss the global and blow-up solutions of the following nonlinear parabolic problems with a gradient term under Robin boundary conditions: , in , , on , , in , where is a bounded domain with smooth boundary . Under some appropriate assumption on the functions , , , , and and initial value , we obtain the sufficient conditions for the existence of a global solution, an upper estimate of the global solution, the sufficient conditions for the existence of a blow-up solution, an upper bound for “blow-up time,” and an upper estimate of “blow-up rate.” Our approach depends heavily on the maximum principles. Lingling Zhang and Hui Wang Copyright © 2014 Lingling Zhang and Hui Wang. All rights reserved. Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays Thu, 14 Aug 2014 07:02:57 +0000 http://www.hindawi.com/journals/aaa/2014/958140/ A class of Lotka-Volterra mutualistic system with time delays of benefit and feedback delays is introduced. By analyzing the associated characteristic equation, the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained under all possible combinations of two or three delays selecting from multiple delays. Not only explicit formulas to determine the properties of the Hopf bifurcation are shown by using the normal form method and center manifold theorem, but also the global continuation of Hopf bifurcation is investigated by applying a global Hopf bifurcation result due to Wu (1998). Numerical simulations are given to support the theoretical results. Xin-You Meng and Hai-Feng Huo Copyright © 2014 Xin-You Meng and Hai-Feng Huo. All rights reserved. Robust Stabilization of Linear Switching Systems with Both Input and Communication Delays Thu, 14 Aug 2014 07:01:58 +0000 http://www.hindawi.com/journals/aaa/2014/906917/ This work is concerned with stabilization control of a class of linear switching systems with time-delays in both the input and the communication channels. It is observed that the time-delay in communication channel leads to the mismatch between the plant and the controller. Such a phenomenon can be accounted for by reconstructing switching signal for the overall closed-loop system. Therefore, we derive some sufficient stability conditions by using multiple Lyapunov functions approach and, moreover, present a robust controller design methodology. A numerical example is presented to demonstrate the effectiveness of the proposed method. Lili Jia and Zunbing Sheng Copyright © 2014 Lili Jia and Zunbing Sheng. All rights reserved. Hermite-Hadamard Type Inequalities for Superquadratic Functions via Fractional Integrals Thu, 14 Aug 2014 07:00:52 +0000 http://www.hindawi.com/journals/aaa/2014/851271/ We use basic properties of superquadratic functions to obtain some new Hermite-Hadamard type inequalities via Riemann-Liouville fractional integrals. For superquadratic functions which are also convex, we get refinements of existing results. Guangzhou Li and Feixiang Chen Copyright © 2014 Guangzhou Li and Feixiang Chen. All rights reserved. On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations Thu, 14 Aug 2014 06:53:55 +0000 http://www.hindawi.com/journals/aaa/2014/350529/ This paper presents a new application of the homotopy analysis method (HAM) for solving evolution equations described in terms of nonlinear partial differential equations (PDEs). The new approach, termed bivariate spectral homotopy analysis method (BISHAM), is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. The applicability of the new approach has been demonstrated by application on several examples of nonlinear evolution PDEs, namely, Fisher’s, Burgers-Fisher’s, Burger-Huxley’s, and Fitzhugh-Nagumo’s equations. Comparison with known exact results from literature has been used to confirm accuracy and effectiveness of the proposed method. S. S. Motsa Copyright © 2014 S. S. Motsa. All rights reserved. On Fractional Derivatives and Primitives of Periodic Functions Thu, 14 Aug 2014 05:57:42 +0000 http://www.hindawi.com/journals/aaa/2014/392598/ We prove that the fractional derivative or the fractional primitive of a -periodic function cannot be a -periodic function, for any period , with the exception of the zero function. I. Area, J. Losada, and J. J. Nieto Copyright © 2014 I. Area et al. All rights reserved. Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation Thu, 14 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/643640/ This paper deals with the stabilization problem of first-order hyperbolic partial differential equations (PDEs) with spatial-temporal actuation over the full physical domains. We assume that the interior actuator can be decomposed into a product of spatial and temporal components, where the spatial component satisfies a specific ordinary differential equation (ODE). A Volterra integral transformation is used to convert the original system into a simple target system using the backstepping-like procedure. Unlike the classical backstepping techniques for boundary control problems of PDEs, the internal actuation can not eliminate the residual term that causes the instability of the open-loop system. Thus, an additional differential transformation is introduced to transfer the input from the interior of the domain onto the boundary. Then, a feedback control law is designed using the classic backstepping technique which can stabilize the first-order hyperbolic PDE system in a finite time, which can be proved by using the semigroup arguments. The effectiveness of the design is illustrated with some numerical simulations. Xin Yu, Chao Xu, Huacheng Jiang, Arthi Ganesan, and Guojie Zheng Copyright © 2014 Xin Yu et al. All rights reserved. Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control Wed, 13 Aug 2014 14:21:08 +0000 http://www.hindawi.com/journals/aaa/2014/970205/ We establish a master-slave oligopoly game model with an upstream monopoly whose output is considered and two downstream oligopolies whose prices are considered. The existence and the local stable region of the Nash equilibrium point are investigated. The complex dynamic properties, such as bifurcation and chaos, are analyzed using bifurcation diagrams, the largest Lyapunov exponent diagrams, and the strange attractor graph. We further analyze the long-run average profit of the three firms and find that they are all optimal in the stable region. In addition, delay feedback control method and limiter control method are used in nondelayed model to control chaos. Furthermore, a delayed master-slave oligopoly game model is considered, and the three firms’ profit in various conditions is analyzed. We find that suitable delayed parameters are important for eliminating chaos and maximizing the profit of the players. Junhai Ma, Fang Zhang, and Yanyan He Copyright © 2014 Junhai Ma et al. All rights reserved.