Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Some New Lacunary Strong Convergent Vector-Valued Sequence Spaces Thu, 24 Jul 2014 13:23:04 +0000 http://www.hindawi.com/journals/aaa/2014/858504/ We introduce some vector-valued sequence spaces defined by a Musielak-Orlicz function and the concepts of lacunary convergence and strong ()-convergence, where is an infinite matrix of complex numbers. We also make an effort to study some topological properties and some inclusion relations between these spaces. M. Mursaleen, A. Alotaibi, and Sunil K. Sharma Copyright © 2014 M. Mursaleen et al. All rights reserved. PSO-RBF Neural Network PID Control Algorithm of Electric Gas Pressure Regulator Thu, 24 Jul 2014 11:18:05 +0000 http://www.hindawi.com/journals/aaa/2014/731368/ The current electric gas pressure regulator often adopts the conventional PID control algorithm to take drive control of the core part (micromotor) of electric gas pressure regulator. In order to further improve tracking performance and to shorten response time, this paper presents an improved PID intelligent control algorithm which applies to the electric gas pressure regulator. The algorithm uses the improved RBF neural network based on PSO algorithm to make online adjustment on PID parameters. Theoretical analysis and simulation result show that the algorithm shortens the step response time and improves tracking performance. Yuanchang Zhong, Xu Huang, Pu Meng, and Fachuan Li Copyright © 2014 Yuanchang Zhong et al. All rights reserved. Best Proximity Point for --Proximal Contractive Multimaps Thu, 24 Jul 2014 09:32:06 +0000 http://www.hindawi.com/journals/aaa/2014/181598/ We extend the notions of --proximal contraction and -proximal admissibility to multivalued maps and then using these notions we obtain some best proximity point theorems for multivalued mappings. Our results extend some recent results by Jleli and those contained therein. Some examples are constructed to show the generality of our results. Muhammad Usman Ali, Tayyab Kamran, and Naseer Shahzad Copyright © 2014 Muhammad Usman Ali et al. All rights reserved. A Fixed Point Theorem for Multivalued Mappings with -Distance Thu, 24 Jul 2014 09:20:15 +0000 http://www.hindawi.com/journals/aaa/2014/497092/ We mainly study fixed point theorem for multivalued mappings with -distance using Wardowski’s technique on complete metric space. Let be a metric space and let be a family of all nonempty bounded subsets of . Define by Considering -distance, it is proved that if is a complete metric space and is a multivalued certain contraction, then has a fixed point. Özlem Acar and Ishak Altun Copyright © 2014 Özlem Acar and Ishak Altun. All rights reserved. Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions Thu, 24 Jul 2014 08:53:16 +0000 http://www.hindawi.com/journals/aaa/2014/194962/ This paper investigates the excess-of-loss reinsurance and investment problem for a compound Poisson jump-diffusion risk process, with the risk asset price modeled by a constant elasticity of variance (CEV) model. It aims at obtaining the explicit optimal control strategy and the optimal value function. Applying stochastic control technique of jump diffusion, a Hamilton-Jacobi-Bellman (HJB) equation is established. Moreover, we show that a closed-form solution for the HJB equation can be found by maximizing the insurer’s exponential utility of terminal wealth with the independence of two Brownian motions and . A verification theorem is also proved to verify that the solution of HJB equation is indeed a solution of this optimal control problem. Then, we quantitatively analyze the effect of different parameter impacts on optimal control strategy and the optimal value function, which show that optimal control strategy is decreasing with the initial wealth and decreasing with the volatility rate of risk asset price. However, the optimal value function is increasing with the appreciation rate of risk asset. De-Lei Sheng, Ximin Rong, and Hui Zhao Copyright © 2014 De-Lei Sheng et al. All rights reserved. Robust Exponential Stability of Impulsive Stochastic Neural Networks with Leakage Time-Varying Delay Thu, 24 Jul 2014 08:46:27 +0000 http://www.hindawi.com/journals/aaa/2014/831027/ This paper investigates mean-square robust exponential stability of the equilibrium point of stochastic neural networks with leakage time-varying delays and impulsive perturbations. By using Lyapunov functions and Razumikhin techniques, some easy-to-test criteria of the stability are derived. Two examples are provided to illustrate the efficiency of the results. Chunge Lu and Linshan Wang Copyright © 2014 Chunge Lu and Linshan Wang. All rights reserved. A Closed-Loop Supply Chain Problem with Retailing and Recycling Competition Thu, 24 Jul 2014 07:37:00 +0000 http://www.hindawi.com/journals/aaa/2014/509825/ We investigate a durable product retailing and recycling problem in a closed-loop supply chain consisting of a single manufacturer and two competitive retailers, in which the manufacturer collects used products via retailers from the consumers and has sufficient channel power over the retailers to act as a Stackelberg leader; the retailers compete in retail products and recycling used products. In order to analyze the impact of retailing and recycling competitions on the profits of the manufacturer and the competitive retailers, two collection models (coordinated collection (Model C) and decentralized collection (Model D)) are established, respectively. Then, based on game theory, we derive the optimal retail price, the optimal repurchase price, and the optimal profits of the manufacturer and the retailers. The managerial insights demonstrate that more intense retailing competition induces the increase of the manufacturer's profits in both forward and reverse channels and retailers' profits in the forward channel and the decrease of retailers' profits in the reverse channel, while more intense recycling competition induces the decrease of the profits of the manufacturer and retailers in both forward and reverse channels. Finally, numerical examples are given to illustrate the effectiveness of the proposed models. Chuanchao Xu, Bo Li, Yanfei Lan, and Yi Tang Copyright © 2014 Chuanchao Xu et al. All rights reserved. Iterative Algorithms for Mixed Equilibrium Problems, System of Quasi-Variational Inclusion, and Fixed Point Problem in Hilbert Spaces Thu, 24 Jul 2014 07:19:40 +0000 http://www.hindawi.com/journals/aaa/2014/271208/ We introduce a new iterative algorithm for approximating a common element of the set of solutions for mixed equilibrium problems, the set of solutions of a system of quasi-variational inclusion, and the set of fixed points of an infinite family of nonexpansive mappings in a real Hilbert space. Strong convergence of the proposed iterative algorithm is obtained. Our results generalize, extend, and improve the results of Peng and Yao, 2009, Qin et al. 2010 and many authors. Poom Kumam and Thanyarat Jitpeera Copyright © 2014 Poom Kumam and Thanyarat Jitpeera. All rights reserved. On Some Classes of Double Difference Sequences of Interval Numbers Thu, 24 Jul 2014 07:18:15 +0000 http://www.hindawi.com/journals/aaa/2014/516956/ The aim of this paper is to introduce some interval valued double difference sequence spaces by means of Musielak-Orlicz function . We also determine some topological properties and inclusion relations between these double difference sequence spaces. S. A. Mohiuddine, Kuldip Raj, and Abdullah Alotaibi Copyright © 2014 S. A. Mohiuddine et al. All rights reserved. New Mono- and Biaccelerator Iterative Methods with Memory for Nonlinear Equations Thu, 24 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/705674/ Acceleration of convergence is discussed for some families of iterative methods in order to solve scalar nonlinear equations. In fact, we construct mono- and biparametric methods with memory and study their orders. It is shown that the convergence orders 12 and 14 can be attained using only 4 functional evaluations, which provides high computational efficiency indices. Some illustrations will also be given to reverify the theoretical discussions. T. Lotfi, F. Soleymani, S. Shateyi, P. Assari, and F. Khaksar Haghani Copyright © 2014 T. Lotfi et al. All rights reserved. Implicit Numerical Solutions for Solving Stochastic Differential Equations with Jumps Thu, 24 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/159107/ To realize the applications of stochastic differential equations with jumps, much attention has recently been paid to the construction of efficient numerical solutions of the equations. Considering the fact that the use of the explicit methods often results in instability and inaccurate approximations in solving stochastic differential equations, we propose two implicit methods, the θ-Taylor method and the balanced θ-Taylor method, for numerically solving the stochastic differential equation with jumps and prove that the numerical solutions are convergent with strong order 1.0. For a linear scalar test equation, the mean-square stability regions of the methods are derived. Finally, numerical examples are given to evaluate the performance of the methods. Ying Du and Changlin Mei Copyright © 2014 Ying Du and Changlin Mei. All rights reserved. Some New Classes of Generalized Difference Strongly Summable -Normed Sequence Spaces Defined by Ideal Convergence and Orlicz Function Wed, 23 Jul 2014 12:51:59 +0000 http://www.hindawi.com/journals/aaa/2014/621383/ We study some new generalized difference strongly summable n-normed sequence spaces using ideal convergence and an Orlicz function in connection with de la Vallèe Poussin mean. We give some relations related to these sequence spaces also. Adem Kılıçman and Stuti Borgohain Copyright © 2014 Adem Kılıçman and Stuti Borgohain. All rights reserved. Study on Knowledge Propagation in Complex Networks Based on Preferences, Taking Wechat as Example Wed, 23 Jul 2014 11:38:43 +0000 http://www.hindawi.com/journals/aaa/2014/543734/ As platform based on users’ relationship to acquire, share, and propagate knowledge, Wechat develops very rapidly and becomes an important channel to spread knowledge. This new way to propagate knowledge is quite different from the traditional media way which enables knowledge to be spread surprisingly in Wechat. Based on complex network theory and the analysis of the factors which influence the knowledge propagation in Wechat, this paper summarizes the behavior preferences of Wechat users in knowledge propagation and establishes a Wechat knowledge propagation model. By the simulation experiment, this paper tests the model established and finds some important thresholds in knowledge propagation in Wechat. The findings are valuable for further studying the knowledge propagation in Wechat and provide theoretical proof for forecasting the scale and influence of knowledge propagation. Si-hua Chen and Wei He Copyright © 2014 Si-hua Chen and Wei He. All rights reserved. A Comparative Study of Marketing Channel Multiagent Stackelberg Model Based on Perfect Rationality and Fairness Preference Wed, 23 Jul 2014 11:02:10 +0000 http://www.hindawi.com/journals/aaa/2014/527458/ This paper studies channel consisting of a manufacturer and two retailers. As a basis for comparison, the first, multiagent Stackelberg model has been structured based on perfect rationality. Further, fairness preference theory will be embedded in marketing channel multiagent Stackelberg model, and the results show that if the retailers have a jealous fairness preference, the manufacturer will reduce the wholesale price, retailers will increase the effort level, product sales will be increased, and the total channel utility and manufacturers’ utility will be pareto improvement, but the pareto improvement of retailers’ utility is associated with the interval of jealousy fairness preference coefficient. If the retailers have a sympathetic fairness preference, the manufacturer increases wholesale price, retailers reduce the effort level, and the total channel utility, manufacturer’s utility, and retailers’ utility are less than that of the no fairness preference utility. Kaihong Wang, Xu Yang, Yiwan Sun, and Chuan Ding Copyright © 2014 Kaihong Wang et al. All rights reserved. Symmetries, Associated First Integrals, and Double Reduction of Difference Equations Wed, 23 Jul 2014 10:58:15 +0000 http://www.hindawi.com/journals/aaa/2014/490165/ We determine the symmetry generators of some ordinary difference equations and proceeded to find the first integral and reduce the order of the difference equations. We show that, in some cases, the symmetry generator and first integral are associated via the “invariance condition.” That is, the first integral may be invariant under the symmetry of the original difference equation. When this condition is satisfied, we may proceed to double reduction of the difference equation. L. Ndlovu, M. Folly-Gbetoula, A. H. Kara, and A. Love Copyright © 2014 L. Ndlovu et al. All rights reserved. Global Asymptotic Stability of Impulsive CNNs with Proportional Delays and Partially Lipschitz Activation Functions Wed, 23 Jul 2014 09:36:28 +0000 http://www.hindawi.com/journals/aaa/2014/832892/ This paper researches global asymptotic stability of impulsive cellular neural networks with proportional delays and partially Lipschitz activation functions. Firstly, by means of the transformation , the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Secondly, we provide novel criteria for the uniqueness and exponential stability of the equilibrium point of the latter by relative nonlinear measure and prove that the exponential stability of equilibrium point of the latter implies the asymptotic stability of one of the former. We furthermore obtain a sufficient condition to the uniqueness and global asymptotic stability of the equilibrium point of the former. Our method does not require conventional assumptions on global Lipschitz continuity, boundedness, and monotonicity of activation functions. Our results are generalizations and improvements of some existing ones. Finally, an example and its simulations are provided to illustrate the correctness of our analysis. Xueli Song and Jigen Peng Copyright © 2014 Xueli Song and Jigen Peng. All rights reserved. Solvability for a Coupled System of Fractional Integrodifferential Equations with -Point Boundary Conditions on the Half-Line Wed, 23 Jul 2014 09:29:09 +0000 http://www.hindawi.com/journals/aaa/2014/297314/ The aim of this paper is to study the solvability for a coupled system of fractional integrodifferential equations with multipoint fractional boundary value problems on the half-line. An example is given to demonstrate the validity of our assumptions. Payam Nasertayoob, S. Mansour Vaezpour, and Dumitru Baleanu Copyright © 2014 Payam Nasertayoob et al. All rights reserved. Sharp Bounds for Neuman Means by Harmonic, Arithmetic, and Contraharmonic Means Wed, 23 Jul 2014 09:24:42 +0000 http://www.hindawi.com/journals/aaa/2014/914242/ We give several sharp bounds for the Neuman means and ( and ) in terms of harmonic mean H (contraharmonic mean C) or the geometric convex combination of arithmetic mean A and harmonic mean H (contraharmonic mean C and arithmetic mean A) and present a new chain of inequalities for certain bivariate means. Zhi-Jun Guo, Yu-Ming Chu, Ying-Qing Song, and Xiao-Jing Tao Copyright © 2014 Zhi-Jun Guo et al. All rights reserved. Improved Quantum Genetic Algorithm in Application of Scheduling Engineering Personnel Wed, 23 Jul 2014 07:22:57 +0000 http://www.hindawi.com/journals/aaa/2014/164961/ To verify the availability of the improved quantum genetic algorithm in solving the scheduling engineering personnel problem, the following work has been carried out: the characteristics of the scheduling engineering personnel problem are analyzed, the quantum encoding method is proposed, and an improved quantum genetic algorithm is applied to address the issue. Taking the low efficiency and the bad performance of the conventional quantum genetic algorithm into account, a universal improved quantum genetic algorithm is introduced to solve the scheduling engineering personnel problem. Finally, the examples are applied to verify the effectiveness and superiority of the improved quantum genetic algorithm and the rationality of the encoding method. Huaixiao Wang, Ling Li, Jianyong Liu, Yong Wang, and Chengqun Fu Copyright © 2014 Huaixiao Wang et al. All rights reserved. Solving Split Common Fixed-Point Problem of Firmly Quasi-Nonexpansive Mappings without Prior Knowledge of Operators Norms Wed, 23 Jul 2014 07:18:00 +0000 http://www.hindawi.com/journals/aaa/2014/389689/ Very recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms for the split common fixed-point problem concerned two bounded linear operators. However, to employ Moudafi’s algorithms, one needs to know a prior norm (or at least an estimate of the norm) of the bounded linear operators. To estimate the norm of an operator is very difficult, if it is not an impossible task. It is the purpose of this paper to introduce a viscosity iterative algorithm with a way of selecting the stepsizes such that the implementation of the algorithm does not need any prior information about the operator norms. We prove the strong convergence of the proposed algorithms for split common fixed-point problem governed by the firmly quasi-nonexpansive operators. As a consequence, we obtain strong convergence theorems for split feasibility problem and split common null point problems of maximal monotone operators. Our results improve and extend the corresponding results announced by many others. Jing Zhao and Hang Zhang Copyright © 2014 Jing Zhao and Hang Zhang. All rights reserved. Existence Results and the Monotone Iterative Technique for Nonlinear Fractional Differential Systems with Coupled Four-Point Boundary Value Problems Wed, 23 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/242591/ By establishing a comparison result and using the monotone iterative technique combined with the method of upper and lower solutions, we investigate the existence of solutions for nonlinear fractional differential systems with coupled four-point boundary value problems. Yujun Cui and Yumei Zou Copyright © 2014 Yujun Cui and Yumei Zou. All rights reserved. Parallel-Batch Scheduling with Two Models of Deterioration to Minimize the Makespan Wed, 23 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/495187/ We consider the bounded parallel-batch scheduling with two models of deterioration, in which the processing time of the first model is and of the second model is . The objective is to minimize the makespan. We present time algorithms for the single-machine problems, respectively. And we propose fully polynomial time approximation schemes to solve the identical-parallel-machine problem and uniform-parallel-machine problem, respectively. Cuixia Miao Copyright © 2014 Cuixia Miao. All rights reserved. The Gerber-Shiu Expected Penalty Function for the Risk Model with Dependence and a Constant Dividend Barrier Wed, 23 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/730174/ We consider a compound Poisson risk model with dependence and a constant dividend barrier. A dependence structure between the claim amount and the interclaim time is introduced through a Farlie-Gumbel-Morgenstern copula. An integrodifferential equation for the Gerber-Shiu discounted penalty function is derived. We also solve the integrodifferential equation and show that the solution is a linear combination of the Gerber-Shiu function with no barrier and the solution of an associated homogeneous integrodifferential equation. Donghai Liu, Zaiming Liu, and Dan Peng Copyright © 2014 Donghai Liu et al. All rights reserved. Time- and Event-Driven Communication Process for Networked Control Systems: A Survey Wed, 23 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/261738/ In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time- and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes. Lei Zou, Zidong Wang, Hongli Dong, Yurong Liu, and Huijun Gao Copyright © 2014 Lei Zou et al. All rights reserved. Analytic Formulation for the Sound Absorption of a Panel Absorber under the Effects of Microperforation, Air Pumping, Linear Vibration and Nonlinear Vibration Wed, 23 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/906506/ This study includes the first work about the absorption of a panel absorber under the effects of microperforation, air pumping, and linear and nonlinear vibrations. In practice, thin perforated panel absorber is backed by a flexible wall to enhance the acoustic performance within the room. The panel is easily excited to vibrate nonlinearly and the wall can vibrate linearly. However, the assumptions of linear panel vibration and no wall vibration are adopted in many research works. The development of the absorption formula is based on the classical approach and the electroacoustic analogy, in which the impedances of microperforation, air pumping, and linear and nonlinear vibrations are in parallel and connected to that of the air cavity in series. Unlike those finite element, numerical integration, and multiscale solution methods and so forth, the analytic formula to calculate the absorption of a panel absorber does not require heavy computation effort and is suitable for engineering calculation purpose. The theoretical result obtained from the proposed method shows reasonable agreement with that from a previous numerical integration method. It can be concluded that the overall absorption bandwidth of a panel absorber with an appropriate configuration can be optimized and widened by making use of the positive effects of microperforation, air pumping, and panel vibration. Y. Y. Lee Copyright © 2014 Y. Y. Lee. All rights reserved. Some Retarded Difference Inequalities of Product Form and Their Application Tue, 22 Jul 2014 11:22:04 +0000 http://www.hindawi.com/journals/aaa/2014/158375/ A class of new nonlinear retarded difference inequalities is established. An application of the obtained inequalities to the estimation of finite difference equations is given. Zongyi Hou, Shanhe Wu, and Wu-Sheng Wang Copyright © 2014 Zongyi Hou et al. All rights reserved. A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations Tue, 22 Jul 2014 11:18:57 +0000 http://www.hindawi.com/journals/aaa/2014/105414/ Standard application of similarity method to find solutions of PDEs mostly results in reduction to ODEs which are not easily integrable in terms of elementary or tabulated functions. Such situations usually demand solving reduced ODEs numerically. However, there are no systematic procedures available to utilize these numerical solutions of reduced ODE to obtain the solution of original PDE. A practical and tractable approach is proposed to deal with such situations and is applied to obtain approximate similarity solutions to different cases of an initial-boundary value problem of unsteady gas flow through a semi-infinite porous medium. Mazhar Iqbal, M. T. Mustafa, and Azad A. Siddiqui Copyright © 2014 Mazhar Iqbal et al. All rights reserved. Fixed Point Results for α-ψ-Contractive Mappings Including Almost Contractions and Applications Tue, 22 Jul 2014 09:30:44 +0000 http://www.hindawi.com/journals/aaa/2014/869123/ In the recent paper (B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for --contractive type mappings, Nonlinear Analysis. Theory, Methods and Applications, 75 (2012), 2154-2165.), the authors introduced the concept of -admissible maps on metric spaces. Using this new concept, they presented some nice fixed point results. Also, they gave an existence theorem for integral equation to show the usability of their result. Then, many authors focused on this new concept and obtained a lot of fixed point results, which are used for existence theorems. In this paper, we not only extend some of the recent results about this direction but also generalize them. Then, we give some examples to show our results are proper extensions. Furthermore, we use our results to obtain the existence and uniqueness result for a solution of fourth order two-point boundary value problem. Gonca Durmaz, Gülhan Mınak, and Ishak Altun Copyright © 2014 Gonca Durmaz et al. All rights reserved. Stability and Dynamical Analysis of a Biological System Tue, 22 Jul 2014 09:07:37 +0000 http://www.hindawi.com/journals/aaa/2014/952840/ This study considers the spatiotemporal dynamics of a reaction-diffusion phytoplankton-zooplankton system with a double Allee effect on prey under a homogeneous boundary condition. The qualitative properties are analyzed, including the local stability of all equilibria and the global asymptotic property of the unique positive equilibrium. We also discuss the Hopf bifurcation and the steady state bifurcation of the system. These results are expected to help understand the complexity of the Allee effect and the interaction between phytoplankton and zooplankton. Xinhong Pan, Min Zhao, Yapei Wang, Hengguo Yu, Zengling Ma, and Qi Wang Copyright © 2014 Xinhong Pan et al. All rights reserved. Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions Tue, 22 Jul 2014 08:55:51 +0000 http://www.hindawi.com/journals/aaa/2014/490161/ This work investigates traveling waves for a class of delayed cellular neural networks with nonmonotonic output functions on the one-dimensional integer lattice . The dynamics of each given cell depends on itself and its nearest left or right neighborhood cells with distributed delay due to, for example, finite switching speed and finite velocity of signal transmission. Our technique is to construct two appropriate nondecreasing functions to squeeze the nonmonotonic output functions. Then we construct a suitable wave profiles set and derive the existence of traveling wave solutions by using Schauder's fixed point theorem. Zhi-Xian Yu, Rong Yuan, Cheng-Hsiung Hsu, and Ming-Shu Peng Copyright © 2014 Zhi-Xian Yu et al. All rights reserved.