Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. On Perturbations of Generators of -Semigroups Thu, 30 Oct 2014 09:27:32 +0000 http://www.hindawi.com/journals/aaa/2014/213020/ We present a perturbation result for generators of -semigroups which can be considered as an operator theoretic version of the Weiss-Staffans perturbation theorem for abstract linear systems. The results are illustrated by applications to the Desch-Schappacher and the Miyadera-Voigt perturbation theorems and to unbounded perturbations of the boundary conditions of a generator. Martin Adler, Miriam Bombieri, and Klaus-Jochen Engel Copyright © 2014 Martin Adler et al. All rights reserved. Agent-Based Model to Study and Quantify the Evolution Dynamics of Android Malware Infection Tue, 28 Oct 2014 11:40:14 +0000 http://www.hindawi.com/journals/aaa/2014/623436/ In the last years the number of malware Apps that the users download to their devices has risen. In this paper, we propose an agent-based model to quantify the Android malware infection evolution, modeling the behavior of the users and the different markets where the users may download Apps. The model predicts the number of infected smartphones depending on the type of malware. Additionally, we will estimate the cost that the users should afford when the malware is in their devices. We will be able to analyze which part is more critical: the users, giving indiscriminate permissions to the Apps or not protecting their devices with antivirus software, or the Android platform, due to the vulnerabilities of the Android devices that permit their rooted. We focus on the community of Valencia, Spain, although the obtained results can be extrapolated to other places where the number of Android smartphones remains fairly stable. Juan Alegre-Sanahuja, Javier Camacho, Juan Carlos Cortés López, Francisco-José Santonja, and Rafael Jacinto Villanueva Micó Copyright © 2014 Juan Alegre-Sanahuja et al. All rights reserved. Strong Convergence of Modified Algorithms Based on the Regularization for the Constrained Convex Minimization Problem Tue, 28 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/870102/ As is known, the regularization method plays an important role in solving constrained convex minimization problems. Based on the idea of regularization, implicit and explicit iterative algorithms are proposed in this paper and the sequences generated by the algorithms can converge strongly to a solution of the constrained convex minimization problem, which also solves a certain variational inequality. As an application, we also apply the algorithm to solve the split feasibility problem. Ming Tian and Jun-Ying Gong Copyright © 2014 Ming Tian and Jun-Ying Gong. All rights reserved. Analysis of the Properties of Adjoint Equations and Accuracy Verification of Adjoint Model Based on FVM Mon, 27 Oct 2014 13:50:21 +0000 http://www.hindawi.com/journals/aaa/2014/407468/ There are two different approaches on how to formulate adjoint numerical model (ANM). Aiming at the disputes arising from the construction methods of ANM, the differences between nonlinear shallow water equation and its adjoint equation are analyzed; the hyperbolicity and homogeneity of the adjoint equation are discussed. Then, based on unstructured meshes and finite volume method, a new adjoint model was advanced by getting numerical model of the adjoint equations directly. Using a gradient check, the correctness of the adjoint model was verified. The results of twin experiments to invert the bottom friction coefficient (Manning’s roughness coefficient) indicate that the adjoint model can extract the observation information and produce good quality inversion. The reason of disputes about construction methods of ANM is also discussed in the paper. Yaodeng Chen, Ruizhi Zhang, Yufang Gao, and Changna Lu Copyright © 2014 Yaodeng Chen et al. All rights reserved. On the Dynamics of a Nonautonomous Predator-Prey Model with Hassell-Varley Type Functional Response Mon, 27 Oct 2014 13:21:26 +0000 http://www.hindawi.com/journals/aaa/2014/864678/ The dynamic behaviors of a nonautonomous system for migratory birds with Hassell-Varley type functional response and the saturation incidence rate are studied. Under quite weak assumptions, some sufficient conditions are obtained for the permanence and extinction of the disease. Moreover, the global attractivity of the model is discussed by constructing a Lyapunov function. Numerical simulations which support our theoretical analysis are also given. Yan Zhang, Shujing Gao, and Kuangang Fan Copyright © 2014 Yan Zhang et al. All rights reserved. Strong Convergence Theorems for Mixed Equilibrium Problem and Asymptotically -Nonexpansive Mapping in Banach Spaces Mon, 27 Oct 2014 12:56:15 +0000 http://www.hindawi.com/journals/aaa/2014/965737/ This paper aims to use a hybrid algorithm for finding a common element of a fixed point problem for a finite family of asymptotically nonexpansive mappings and the set solutions of mixed equilibrium problem in uniformly smooth and uniformly convex Banach space. Then, we prove some strong convergence theorems of the proposed hybrid algorithm to a common element of the above two sets under some suitable conditions. Bin-Chao Deng, Tong Chen, and Yi-Lin Yin Copyright © 2014 Bin-Chao Deng et al. All rights reserved. The Stochastic -Method for Nonlinear Stochastic Volterra Integro-Differential Equations Mon, 27 Oct 2014 12:46:54 +0000 http://www.hindawi.com/journals/aaa/2014/583930/ The stochastic -method is extended to solve nonlinear stochastic Volterra integro-differential equations. The mean-square convergence and asymptotic stability of the method are studied. First, we prove that the stochastic -method is convergent of order in mean-square sense for such equations. Then, a sufficient condition for mean-square exponential stability of the true solution is given. Under this condition, it is shown that the stochastic -method is mean-square asymptotically stable for every stepsize if and when , the stochastic -method is mean-square asymptotically stable for some small stepsizes. Finally, we validate our conclusions by numerical experiments. Peng Hu and Chengming Huang Copyright © 2014 Peng Hu and Chengming Huang. All rights reserved. Inequalities for Convex Functions on Simplexes and Their Cones Mon, 27 Oct 2014 08:59:22 +0000 http://www.hindawi.com/journals/aaa/2014/690803/ The aim of this paper is to present the fundamental inequalities for convex functions on Euclidean spaces. The work is based on the geometry of the simplest convex sets and properties of convex functions. Some obtained inequalities are applied to demonstrate a natural way of generalizing the Hermite-Hadamard inequality. Zlatko Pavić and Shanhe Wu Copyright © 2014 Zlatko Pavić and Shanhe Wu. All rights reserved. Tetris Tight Frames Construction via Hadamard Matrices Mon, 27 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/917491/ We present a new method to construct unit norm tight frames by applying altered Hadamard matrices. Also we determine an elementary construction which can be used to produce a unit norm frame with prescribed spectrum of frame operator. A. Abdollahi and M. Monfaredpour Copyright © 2014 A. Abdollahi and M. Monfaredpour. All rights reserved. Operator Fractional Brownian Motion and Martingale Differences Mon, 27 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/791537/ It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays an important role in both applications and theory. In this paper, we study the relation between them. We construct an approximation sequence of operator fractional Brownian motion based on a martingale difference sequence. Hongshuai Dai, Tien-Chung Hu, and June-Yung Lee Copyright © 2014 Hongshuai Dai et al. All rights reserved. A Note on Best Approximation in 0-Complete Partial Metric Spaces Thu, 23 Oct 2014 11:55:25 +0000 http://www.hindawi.com/journals/aaa/2014/979170/ We study the existence and uniqueness of best proximity points in the setting of 0-complete partial metric spaces. We get our results by showing that the generalizations, which we have to consider, are obtained from the corresponding results in metric spaces. We introduce some new concepts and consider significant theorems to support this fact. Marta Demma, Mohamed Jleli, Bessem Samet, and Calogero Vetro Copyright © 2014 Marta Demma et al. All rights reserved. Improving Vehicle Ride and Handling Using LQG CNF Fusion Control Strategy for an Active Antiroll Bar System Thu, 23 Oct 2014 07:48:39 +0000 http://www.hindawi.com/journals/aaa/2014/698195/ This paper analyses a comparison of performance for an active antiroll bar (ARB) system using two types of control strategy. First of all, the LQG control strategy is investigated and then a novel LQG CNF fusion control method is developed to improve the performances on vehicle ride and handling for an active antiroll bar system. However, the ARB system has to balance the trade-off between ride and handling performance, where the CNF consists of a linear feedback law and a nonlinear feedback law. Typically, the linear feedback is designed to yield a quick response at the initial stage, while the nonlinear feedback law is used to smooth out overshoots in the system output when it approaches the target reference. The half car model is combined with a linear single track model with roll dynamics which are used for the analysis and simulation of ride and handling. The performances of the control strategies are compared and the simulation results show the LQG CNF fusion improves the performances in vehicle ride and handling. N. Zulkarnain, H. Zamzuri, Y. M. Sam, S. A. Mazlan, and S. M. H. F. Zainal Copyright © 2014 N. Zulkarnain et al. All rights reserved. The Semimartingale Approach to Almost Sure Stability Analysis of a Two-Stage Numerical Method for Stochastic Delay Differential Equation Thu, 23 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/621359/ Almost sure exponential stability of the split-step backward Euler (SSBE) method applied to an Itô-type stochastic differential equation with time-varying delay is discussed by the techniques based on Doob-Mayer decomposition and semimartingale convergence theorem. Numerical experiments confirm the theoretical analysis. Qian Guo and Xueyin Tao Copyright © 2014 Qian Guo and Xueyin Tao. All rights reserved. Mathematical Modelling of the Spread and Control of Onchocerciasis in Tropical Countries: Case Study in Nigeria Wed, 22 Oct 2014 14:13:11 +0000 http://www.hindawi.com/journals/aaa/2014/631658/ Onchocerciasis, also known as river blindness and Robles disease, is a parasitic disease caused by Onchocerca volvulus, a nematode (roundworm), and it is endemic in tropical countries like Nigeria. The objective of this paper is to discuss the mathematical formulation underpinning the spread and control of this disease on one hand. On the other hand, we make use of some new analytical methods to derive the solution of the resulting set of equations. The numerical results are presented to test the efficiency and the accuracy of both methods. The techniques used for solving these problems are friendly, very easy, and less time consuming. The numerical solutions in both cases display the biological behaviour of the real life situation. Ikechukwu Chiwueze Oguoma and Thomas Mbah Acho Copyright © 2014 Ikechukwu Chiwueze Oguoma and Thomas Mbah Acho. All rights reserved. Multiplicity of Solutions to a Potential Operator Equation and Its Applications Wed, 22 Oct 2014 06:52:25 +0000 http://www.hindawi.com/journals/aaa/2014/947139/ We consider the multiplicity of solutions for operator equation involving homogeneous potential operators. With the help of Nehari manifold and fibering maps, we prove that such equation has at least two nontrivial solutions. Furthermore, we apply this result to prove the existence of two nonnegative solutions for three types of quasilinear elliptic systems involving (p, q)-Laplacian operator and concave-convex nonlinearities. Jincheng Huang Copyright © 2014 Jincheng Huang. All rights reserved. Pricing of Two Kinds of Power Options under Fractional Brownian Motion, Stochastic Rate, and Jump-Diffusion Models Tue, 21 Oct 2014 11:47:17 +0000 http://www.hindawi.com/journals/aaa/2014/259297/ Option pricing is always one of the critical issues in financial mathematics and economics. Brownian motion is the basic hypothesis of option pricing model, which questions the fractional property of stock price. In this paper, under the assumption that the exchange rate follows the extended Vasicek model, we obtain the closed form of the pricing formulas for two kinds of power options under fractional Brownian Motion (FBM) jump-diffusion models. Kaili Xiang, Yindong Zhang, and Xiaotong Mao Copyright © 2014 Kaili Xiang et al. All rights reserved. Multiple Model ILC for Continuous-Time Nonlinear Systems Tue, 21 Oct 2014 09:55:47 +0000 http://www.hindawi.com/journals/aaa/2014/984742/ Multiple model iterative learning control (MMILC) method is proposed to deal with the continuous-time nonlinear system with uncertain and iteration-varying parameters. In this kind of control strategy, multiple models are established to cover the uncertainty of system; a switching mechanism is used to decide the most appropriate model for system in current iteration. For system operating iteratively in a fixed time interval with uncertain or jumping parameters, this kind of MMILC can improve the transient response and control property greatly. Asymptotical convergence is demonstrated theoretically, and the control effectiveness is illustrated by numerical simulation. Xiaoli Li, Kang Wang, and Yang Li Copyright © 2014 Xiaoli Li et al. All rights reserved. Distortion of Quasiregular Mappings and Equivalent Norms on Lipschitz-Type Spaces Tue, 21 Oct 2014 07:28:46 +0000 http://www.hindawi.com/journals/aaa/2014/895074/ We prove a quasiconformal analogue of Koebe’s theorem related to the average Jacobian and use a normal family argument here to prove a quasiregular analogue of this result in certain domains in -dimensional space. As an application, we establish that Lipschitz-type properties are inherited by a quasiregular function from its modulo. We also prove some results of Hardy-Littlewood type for Lipschitz-type spaces in several dimensions, give the characterization of Lipschitz-type spaces for quasiregular mappings by the average Jacobian, and give a short review of the subject. Miodrag Mateljević Copyright © 2014 Miodrag Mateljević. All rights reserved. Dynamics of a Predator-Prey System with a Mate-Finding Allee Effect Mon, 20 Oct 2014 13:09:12 +0000 http://www.hindawi.com/journals/aaa/2014/673424/ We consider a ratio-dependent predator-prey system with a mate-finding Allee effect on prey. The stability properties of the equilibria and a complete bifurcation analysis, including the existence of a saddle-node, a Hopf bifurcation, and, a Bogdanov-Takens bifurcations, have been proved theoretically and numerically. The blow-up method has been applied to investigate the structure of a neighborhood of the origin. Our mathematical results show the mate-finding Allee effect can reduce the complexity of system behaviors by making the complicated equilibrium less complicated, and it can be a destabilizing force as well, which makes the system has a high possibility of being threatened with extinction in ecology. Ruiwen Wu and Xiuxiang Liu Copyright © 2014 Ruiwen Wu and Xiuxiang Liu. All rights reserved. A Note on the Minimal Period Problem for Second Order Hamiltonian Systems Mon, 20 Oct 2014 12:25:22 +0000 http://www.hindawi.com/journals/aaa/2014/385381/ We study periodic solutions of second order Hamiltonian systems with even potential. By making use of generalized Nehari manifold, some sufficient conditions are obtained to guarantee the multiplicity and minimality of periodic solutions for second order Hamiltonian systems. Our results generalize the outcome in the literature. Huafeng Xiao Copyright © 2014 Huafeng Xiao. All rights reserved. Global Dynamics of a Discretized Heroin Epidemic Model with Time Delay Mon, 20 Oct 2014 08:50:19 +0000 http://www.hindawi.com/journals/aaa/2014/742385/ We derive a discretized heroin epidemic model with delay by applying a nonstandard finite difference scheme. We obtain positivity of the solution and existence of the unique endemic equilibrium. We show that heroin-using free equilibrium is globally asymptotically stable when the basic reproduction number , and the heroin-using is permanent when the basic reproduction number . Xamxinur Abdurahman, Ling Zhang, and Zhidong Teng Copyright © 2014 Xamxinur Abdurahman et al. All rights reserved. A New Fractional-Order Chaotic Complex System and Its Antisynchronization Mon, 20 Oct 2014 06:43:32 +0000 http://www.hindawi.com/journals/aaa/2014/326354/ We propose a new fractional-order chaotic complex system and study its dynamical properties including symmetry, equilibria and their stability, and chaotic attractors. Chaotic behavior is verified with phase portraits, bifurcation diagrams, the histories, and the largest Lyapunov exponents. And we find that chaos exists in this system with orders less than 5 by numerical simulation. Additionally, antisynchronization of different fractional-order chaotic complex systems is considered based on the stability theory of fractional-order systems. This new system and the fractional-order complex Lorenz system can achieve antisynchronization. Corresponding numerical simulations show the effectiveness and feasibility of the scheme. Cuimei Jiang, Shutang Liu, and Chao Luo Copyright © 2014 Cuimei Jiang et al. All rights reserved. A Survey of Modelling and Identification of Quadrotor Robot Mon, 20 Oct 2014 06:36:49 +0000 http://www.hindawi.com/journals/aaa/2014/320526/ A quadrotor is a rotorcraft capable of hover, forward flight, and VTOL and is emerging as a fundamental research and application platform at present with flexibility, adaptability, and ease of construction. Since a quadrotor is basically considered an unstable system with the characteristics of dynamics such as being intensively nonlinear, multivariable, strongly coupled, and underactuated, a precise and practical model is critical to control the vehicle which seems to be simple to operate. As a rotorcraft, the dynamics of a quadrotor is mainly dominated by the complicated aerodynamic effects of the rotors. This paper gives a tutorial of the platform configuration, methodology of modeling, comprehensive nonlinear model, the aerodynamic effects, and model identification for a quadrotor. Xiaodong Zhang, Xiaoli Li, Kang Wang, and Yanjun Lu Copyright © 2014 Xiaodong Zhang et al. All rights reserved. Erratum to “Resilient Finite-Time Controller Design of a Class of Stochastic Nonlinear Systems” Mon, 20 Oct 2014 06:27:13 +0000 http://www.hindawi.com/journals/aaa/2014/217579/ Zhiguo Yan Copyright © 2014 Zhiguo Yan. All rights reserved. Ground States for the Schrödinger Systems with Harmonic Potential and Combined Power-Type Nonlinearities Sun, 19 Oct 2014 12:15:48 +0000 http://www.hindawi.com/journals/aaa/2014/317571/ We consider a class of coupled nonlinear Schrödinger systems with potential terms and combined power-type nonlinearities. We establish the existence of ground states, by using a variational method. As an application, some symmetry results for ground states of Schrödinger systems with harmonic potential terms are obtained. Baiyu Liu Copyright © 2014 Baiyu Liu. All rights reserved. A Note on Entire Functions That Share Two Small Functions Sun, 19 Oct 2014 11:15:24 +0000 http://www.hindawi.com/journals/aaa/2014/601507/ This note is to show that if is a nonconstant entire function that shares two pairs of small functions ignoring multiplicities with its first derivative , then there exists a close linear relationship between and . This result is a generalization of some results obtained by Rubel and Yang, Mues and Steinmetz, Zheng and Wang, and Qiu. Moreover, examples are provided to show that the conditions in the result are sharp. Jun-Fan Chen Copyright © 2014 Jun-Fan Chen. All rights reserved. Control for a Networked Control Model of Systems with Two Additive Time-Varying Delays Sun, 19 Oct 2014 10:18:27 +0000 http://www.hindawi.com/journals/aaa/2014/923436/ This paper is concerned with control for a networked control model of systems with two additive time-varying delays. A new Lyapunov functional is constructed to make full use of the information of the delays, and for the derivative of the Lyapunov functional a novel technique is employed to compute a tighter upper bound, which is dependent on the two time-varying delays instead of the upper bounds of them. Then the convex polyhedron method is proposed to check the upper bound of the derivative of the Lyapunov functional. The resulting stability criteria have fewer matrix variables but less conservatism than some existing ones. The stability criteria are applied to designing a state feedback controller, which guarantees that the closed-loop system is asymptotically stable with a prescribed disturbance attenuation level. Finally examples are given to show the advantages of the stability criteria and the effectiveness of the proposed control method. Hanyong Shao, Zhengqiang Zhang, Xunlin Zhu, and Guoying Miao Copyright © 2014 Hanyong Shao et al. All rights reserved. Maps Preserving Peripheral Spectrum of Generalized Jordan Products of Self-Adjoint Operators Sun, 19 Oct 2014 09:44:10 +0000 http://www.hindawi.com/journals/aaa/2014/192040/ Let and   be standard real Jordan algebras of self-adjoint operators on complex Hilbert spaces   and  , respectively. For  , let   be a fixed sequence with and assume that at least one of the terms in appears exactly once. Define the generalized Jordan product   on elements in  . Let be a map with the range containing all rank-one projections and trace zero-rank two self-adjoint operators. We show that satisfies that for all , where stands for the peripheral spectrum of , if and only if there exist a scalar and a unitary operator such that for all , or for all , where is the transpose of for an arbitrarily fixed orthonormal basis of . Moreover, whenever is odd. Wen Zhang and Jinchuan Hou Copyright © 2014 Wen Zhang and Jinchuan Hou. All rights reserved. Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays Sun, 19 Oct 2014 06:28:45 +0000 http://www.hindawi.com/journals/aaa/2014/689573/ We investigate a nonautonomous two-species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis. Chao Liu and Yuanke Li Copyright © 2014 Chao Liu and Yuanke Li. All rights reserved. Pullback Attractor for Nonautonomous Ginzburg-Landau Equation with Additive Noise Sun, 19 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/921750/ Long time behavior of stochastic Ginzburg-Landau equations with nonautonomous deterministic external forces, dispersion coefficients, and nonautonomous perturbations is studied. The domain is taken as a bounded interval in . By making use of Sobolev embeddings and Gialiardo-Nirenberg inequality we obtain the existence and upper semicontinuity of the pullback attractor in for the equation. The upper semicontinuity shows the stability of attractors under perturbations. Yangrong Li and Hongyong Cui Copyright © 2014 Yangrong Li and Hongyong Cui. All rights reserved.