Discrete Dynamics in Nature and Society http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. A Novel Algorithm to Scheduling Optimization of Melting-Casting Process in Copper Alloy Strip Production Wed, 07 Oct 2015 07:26:14 +0000 http://www.hindawi.com/journals/ddns/2015/147980/ Melting-casting is the first process in copper alloy strip production. The schedule scheme on this process affects the subsequent processes greatly. In this paper, we build the multiobjective model of melting-casting scheduling problem, which considers minimizing the makespan and total weighted earliness and tardiness penalties comprehensively. A novel algorithm, which we called Multiobjective Artificial Bee Colony/Decomposition (MOABC/D) algorithm, is proposed to solve this model. The algorithm combines the framework of Multiobjective Evolutionary Algorithm/Decomposition (MOEA/D) and the neighborhood search strategy of Artificial Bee Colony algorithm. The results on instances show that the proposed MOABC/D algorithm outperforms the other two comparison algorithms both on the distributions of the Pareto front and the priority in the optimal selection results. Xiaohui Yan, Zhicong Zhang, Jianwen Guo, Shuai Li, and Kaishun Hu Copyright © 2015 Xiaohui Yan et al. All rights reserved. Fault Detection for Linear Discrete Time-Varying Descriptor Systems with Missing Measurements Mon, 05 Oct 2015 09:38:13 +0000 http://www.hindawi.com/journals/ddns/2015/867206/ This paper deals with the problem of fault detection for a class of linear discrete time-varying descriptor systems with missing measurements, and the missing measurements are described by a Bernoulli random binary switching sequence. We first translate the fault detection problem into an indefinite quadratic form problem. Then, a sufficient and necessary condition on the existence of the minimum is derived. Finally, an observer-based fault detection filter is obtained such that the minimum is positive and its parameter matrices are calculated recursively by solving a matrix differential equation. A numerical example is given to demonstrate the efficiency of the proposed method. Guangfu Deng and Huihong Zhao Copyright © 2015 Guangfu Deng and Huihong Zhao. All rights reserved. Average Consensus in Networks of Neutral Dynamical Agents with Fixed and Switching Topologies Mon, 05 Oct 2015 09:34:16 +0000 http://www.hindawi.com/journals/ddns/2015/252050/ This paper addresses the average consensus problem of neutral multiagent systems in undirected networks with fixed and switching topologies. For the case of fixed topology, necessary and sufficient conditions to average consensus are established by decoupling the neutral multiagent system in terms of the eigenvalues of the Laplacian matrix. For the case of switching topology, sufficient conditions to average consensus are given in terms of linear matrix inequalities to determine the allowable upper bound of the time-varying communication delay. Finally, two examples are worked out to explain the effectiveness of the theoretical results. Yingying Wu and Yuangong Sun Copyright © 2015 Yingying Wu and Yuangong Sun. All rights reserved. New Delay-Range-Dependent Robust Exponential Stability Criteria of Uncertain Impulsive Switched Linear Systems with Mixed Interval Nondifferentiable Time-Varying Delays and Nonlinear Perturbations Mon, 05 Oct 2015 08:40:50 +0000 http://www.hindawi.com/journals/ddns/2015/406420/ We investigate the problem of robust exponential stability analysis for uncertain impulsive switched linear systems with time-varying delays and nonlinear perturbations. The time delays are continuous functions belonging to the given interval delays, which mean that the lower and upper bounds for the time-varying delays are available, but the delay functions are not necessary to be differentiable. The uncertainties under consideration are nonlinear time-varying parameter uncertainties and norm-bounded uncertainties, respectively. Based on the combination of mixed model transformation, Halanay inequality, utilization of zero equations, decomposition technique of coefficient matrices, and a common Lyapunov functional, new delay-range-dependent robust exponential stability criteria are established for the systems in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed method. Piyapong Niamsup, Narongsak Yotha, and Kanit Mukdasai Copyright © 2015 Piyapong Niamsup et al. All rights reserved. Study on Wireless Network Communication in Stage Hydraulic Monitoring System Based on Internet of Things Mon, 05 Oct 2015 06:42:40 +0000 http://www.hindawi.com/journals/ddns/2015/652183/ A novel stage hydraulic monitoring system based on Internet of Things (IoT) is proposed in this paper. Compared with the traditional wired system, the proposed system is a flexible working method and can save the cost. Furthermore, it has the low power consumption, high safety, and large scale network. The real-time pressure and flow data can be collected by using the nodes in ZigBee network. The fault detection and diagnosis process was used in this study, which was facilitated by measuring pressure of flow. When the monitored data exceeds the normal range, some failure may occur in the stage hydraulic system. If any failure occurs in the circuit, the maintainers can be informed immediately, which can greatly improve maintenance efficiency, ensuring the failure to be eliminated in time. Meanwhile, we can take advantage of wireless sensor network (WSN) to connect the multiple loops and then monitor the loops by using ZigBee technology, which greatly improves the efficiency of monitoring. Yue Dong, Hui Ren, Jianghui Dong, and Liping Wang Copyright © 2015 Yue Dong et al. All rights reserved. Kalman Filtering for Discrete Stochastic Systems with Multiplicative Noises and Random Two-Step Sensor Delays Sun, 04 Oct 2015 14:11:02 +0000 http://www.hindawi.com/journals/ddns/2015/809734/ This paper is concerned with the optimal Kalman filtering problem for a class of discrete stochastic systems with multiplicative noises and random two-step sensor delays. Three Bernoulli distributed random variables with known conditional probabilities are introduced to characterize the phenomena of the random two-step sensor delays which may happen during the data transmission. By using the state augmentation approach and innovation analysis technique, an optimal Kalman filter is constructed for the augmented system in the sense of the minimum mean square error (MMSE). Subsequently, the optimal Kalman filtering is derived for corresponding augmented system in initial instants. Finally, a simulation example is provided to demonstrate the feasibility and effectiveness of the proposed filtering method. Dongyan Chen, Yonglong Yu, Long Xu, and Xiaohui Liu Copyright © 2015 Dongyan Chen et al. All rights reserved. Controlling the Stochastic Sensitivity in Nonlinear Discrete-Time Systems with Incomplete Information Sun, 04 Oct 2015 14:04:04 +0000 http://www.hindawi.com/journals/ddns/2015/658048/ For stochastic nonlinear discrete-time system with incomplete information, a problem of the stabilization of equilibrium is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations. Lev Ryashko and Irina Bashkirtseva Copyright © 2015 Lev Ryashko and Irina Bashkirtseva. All rights reserved. Index for Stochastic Linear Discrete-Time Systems Sun, 04 Oct 2015 11:50:22 +0000 http://www.hindawi.com/journals/ddns/2015/953831/ This paper discusses the index problem for stochastic linear discrete-time systems. A necessary and sufficient condition of index is given for such systems in finite horizon. It is proved that when the index is greater than a given value, the feasibility of index is equivalent to the solvability of a constrained difference equation. The above result can be applied to the fault detection observer design. Finally, some examples are presented to illustrate the proposed theoretical results. Yan Li, Weihai Zhang, and Xikui Liu Copyright © 2015 Yan Li et al. All rights reserved. Study on a Twice Transfer Alignment Based on Dual Model Sun, 04 Oct 2015 11:09:11 +0000 http://www.hindawi.com/journals/ddns/2015/943065/ This paper proposes a twice rapid transfer alignment algorithm based on dual models in order to solve the problems such as long convergence time, poor accuracy, and heavy computation burden resulting from the traditional nonlinear error models. The quaternion matching method based on quaternion error model along with the extended Kalman filter (EKF) is applied to deal with the large misalignment in the first phase. Then in the second transfer alignment phase, velocity plus attitude matching method as well as classical Kalman filter is adopted. The simulation and the results of vehicle tests demonstrate that this method combines the advantages of both nonlinear and linear error models with the guarantee of accuracy and fastness. Shuai Chen, Runwu Zhong, Xiaohui Liu, and Ahmed Alsaedi Copyright © 2015 Shuai Chen et al. All rights reserved. Analysis of Spatiotemporal Dynamic and Bifurcation in a Wetland Ecosystem Sun, 04 Oct 2015 11:03:44 +0000 http://www.hindawi.com/journals/ddns/2015/185432/ A wetland ecosystem is studied theoretically and numerically to reveal the rules of dynamics which can be quite accurate to better describe the observed spatial regularity of tussock vegetation. Mathematical theoretical works mainly investigate the stability of constant steady states, the existence of nonconstant steady states, and bifurcation, which can deduce a standard parameter control relation and in return can provide a theoretical basis for the numerical simulation. Numerical analysis indicates that the theoretical works are correct and the wetland ecosystem can show rich dynamical behaviors not only regular spatial patterns. Our results further deepen and expand the study of dynamics in the wetland ecosystem. In addition, it is successful to display tussock formation in the wetland ecosystem may have important consequences for aquatic community structure, especially for species interactions and biodiversity. All these results are expected to be useful in the study of the dynamic complexity of wetland ecosystems. Yi Wang, Min Zhao, Hengguo Yu, Chuanjun Dai, Debing Mei, Qi Wang, and Zengling Ma Copyright © 2015 Yi Wang et al. All rights reserved. An Alternate Iterative Differential Evolution Algorithm for Parameter Identification of Chaotic Systems Sun, 04 Oct 2015 11:01:54 +0000 http://www.hindawi.com/journals/ddns/2015/740721/ Parameter estimation of chaotic systems plays a key role for control and synchronization of chaotic systems. At first, the parameter estimation of chaotic systems is mathematically formulated as a global continuous optimization problem. Then through integrating two differential mutation strategies, an improved greedy selection mechanism and a population diversity balance scheme, an alternate iterative differential algorithm, called AIDE, is presented to solve the problem in this paper. Subsequently, experiments are tested on a set of cases of parameter estimation of chaotic systems and the results show that AIDE is better than or at least equal to DE/rand/1/bin, DE/best/1/bin, and other four well-known algorithms in all cases. Wanli Xiang, Xuelei Meng, and Meiqing An Copyright © 2015 Wanli Xiang et al. All rights reserved. Losslessness of Nonlinear Stochastic Discrete-Time Systems Sun, 04 Oct 2015 11:00:53 +0000 http://www.hindawi.com/journals/ddns/2015/594010/ This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Itô-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. By the stochastic lossless theory, we show that a nonlinear stochastic discrete-time system can be lossless via state feedback if and only if it has relative degree and lossless zero dynamics. The effectiveness of the proposed results is illustrated by a numerical example. Xikui Liu, Yan Li, and Ning Gao Copyright © 2015 Xikui Liu et al. All rights reserved. A New Comparison Principle for Impulsive Functional Differential Equations Sun, 04 Oct 2015 11:00:12 +0000 http://www.hindawi.com/journals/ddns/2015/139828/ We establish a new comparison principle for impulsive differential systems with time delay. Then, using this comparison principle, we obtain some sufficient conditions for several stabilities of impulsive delay differential equations. Finally, we present an example to show the effectiveness of our results. Gang Li, Weizhong Ling, and Changming Ding Copyright © 2015 Gang Li et al. All rights reserved. The Least Algebraic Connectivity of Graphs Sun, 04 Oct 2015 10:59:51 +0000 http://www.hindawi.com/journals/ddns/2015/756960/ The algebraic connectivity of a graph is defined as the second smallest eigenvalue of the Laplacian matrix of the graph, which is a parameter to measure how well a graph is connected. In this paper, we present two unique graphs whose algebraic connectivity attain the minimum among all graphs whose complements are trees, but not stars, and among all graphs whose complements are unicyclic graphs, but not stars adding one edge, respectively. Guisheng Jiang, Guidong Yu, and Jinde Cao Copyright © 2015 Guisheng Jiang et al. All rights reserved. The Dynamics of a Delayed Predator-Prey Model with Double Allee Effect Sun, 04 Oct 2015 10:57:14 +0000 http://www.hindawi.com/journals/ddns/2015/102597/ We study the dynamics of a delayed predator-prey model with double Allee effect. For the temporal model, we showed that there exists a threshold of time delay in predator-prey interactions; when time delay is below the threshold value, the positive equilibrium is stable. However, when time delay is above the threshold value, the positive equilibrium is unstable and period solution will emerge. For the spatiotemporal model, through numerical simulations, we show that the model dynamics exhibit rich parameter space Turing structures. The obtained results show that this system has rich dynamics; these patterns show that it is useful for a delayed predator-prey model with double Allee effect to reveal the spatial dynamics in the real model. Boli Xie, Zhijun Wang, Yakui Xue, and Zhenmin Zhang Copyright © 2015 Boli Xie et al. All rights reserved. Dynamics Analysis of a Delayed Rumor Propagation Model in an Emergency-Affected Environment Sun, 04 Oct 2015 09:41:44 +0000 http://www.hindawi.com/journals/ddns/2015/269561/ Rumors influence people’s decisions in an emergency-affected environment. How to describe the spreading mechanism is significant. In this paper, we propose a delayed rumor propagation model in emergencies. By taking the delay as the bifurcation parameter, the local stability of the boundary equilibrium point and the positive equilibrium point is investigated and the conditions of Hopf bifurcation are obtained. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, some numerical simulations are also given to illustrate our theoretical results. Chunru Li and Zujun Ma Copyright © 2015 Chunru Li and Zujun Ma. All rights reserved. A New Hybrid Algorithm for Bankruptcy Prediction Using Switching Particle Swarm Optimization and Support Vector Machines Thu, 01 Oct 2015 13:14:24 +0000 http://www.hindawi.com/journals/ddns/2015/294930/ Bankruptcy prediction has been extensively investigated by data mining techniques since it is a critical issue in the accounting and finance field. In this paper, a new hybrid algorithm combining switching particle swarm optimization (SPSO) and support vector machine (SVM) is proposed to solve the bankruptcy prediction problem. In particular, a recently developed SPSO algorithm is exploited to search the optimal parameter values of radial basis function (RBF) kernel of the SVM. The new algorithm can largely improve the explanatory power and the stability of the SVM. The proposed algorithm is successfully applied in the bankruptcy prediction problem, where experiment data sets are originally from the UCI Machine Learning Repository. The simulation results show the superiority of proposed algorithm over the traditional SVM-based methods combined with genetic algorithm (GA) or the particle swarm optimization (PSO) algorithm alone. Yang Lu, Nianyin Zeng, Xiaohui Liu, and Shujuan Yi Copyright © 2015 Yang Lu et al. All rights reserved. Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear Source Thu, 01 Oct 2015 11:48:05 +0000 http://www.hindawi.com/journals/ddns/2015/143718/ This paper deals with the global existence of solutions to a strongly coupled parabolic-parabolic system of chemotaxis arising from the theory of reinforced random walks. More specifically, we investigate the attraction-repulsion chemotaxis model with fast diffusive term and nonlinear source subject to the Neumann boundary conditions. Such fast diffusion guarantees the global existence of solutions for any given initial value in a bounded domain. Our main results are based on the method of energy estimates, where the key estimates are obtained by a technique originating from Moser’s iterations. Moreover, we notice that the cell density goes to the maximum value when the diffusion coefficient of the cell density tends to infinity. Yingjie Zhu and Fuzhong Cong Copyright © 2015 Yingjie Zhu and Fuzhong Cong. All rights reserved. Imbalanced Data Sets Classification Based on SVM for Sand-Dust Storm Warning Thu, 01 Oct 2015 11:14:37 +0000 http://www.hindawi.com/journals/ddns/2015/562724/ In view of the SVM classification for the imbalanced sand-dust storm data sets, this paper proposes a hybrid self-adaptive sampling method named SRU-AIBSMOTE algorithm. This method can adaptively adjust neighboring selection strategy based on the internal distribution of sample sets. It produces virtual minority class instances through randomized interpolation in the spherical space which consists of minority class instances and their neighbors. The random undersampling is also applied to undersample the majority class instances for removal of redundant data in the sample sets. The comparative experimental results on the real data sets from Yanchi and Tongxin districts in Ningxia of China show that the SRU-AIBSMOTE method can obtain better classification performance than some traditional classification methods. Yonghua Xie, Yurong Liu, and Qingqiu Fu Copyright © 2015 Yonghua Xie et al. All rights reserved. Qualitative Analysis of a Quadratic Integrate-and-Fire Neuron Model with State-Dependent Feedback Control Thu, 01 Oct 2015 09:54:26 +0000 http://www.hindawi.com/journals/ddns/2015/836402/ Spiking neuron models which exhibit rich dynamics are usually defined by hybrid dynamical systems. It is revealed that mathematical analysis of these models has important significance. Therefore, in this work, we provide a comprehensively qualitative analysis for a quadratic integrate-and-fire model by using the theories of hybrid dynamical system. Firstly, the exact impulsive and phase sets are defined according to the phase portraits of the proposed model, and then the Poincaré map is constructed. Furthermore, the conditions for the existence and stability of an order 1 periodic solution are provided. Moreover, the existence and nonexistence of an order periodic solution have been studied theoretically and numerically, and the results show that the system has periodic solutions with any period. Finally, some biological implications of the mathematical results are discussed. Guangyao Tang, Jin Yang, and Sanyi Tang Copyright © 2015 Guangyao Tang et al. All rights reserved. Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps Thu, 01 Oct 2015 09:50:28 +0000 http://www.hindawi.com/journals/ddns/2015/586783/ The discrete logistic map is one of the most famous discrete chaotic maps which has widely spread applications. This paper investigates a set of four generalized logistic maps where the conventional map is a special case. The proposed maps have extra degrees of freedom which provide different chaotic characteristics and increase the design flexibility required for many applications such as quantitative financial modeling. Based on the maximum chaotic range of the output, the proposed maps can be classified as positive logistic map, mostly positive logistic map, negative logistic map, and mostly negative logistic map. Mathematical analysis for each generalized map includes bifurcation diagrams relative to all parameters, effective range of parameters, first bifurcation point, and the maximum Lyapunov exponent (MLE). Independent, vertical, and horizontal scales of the bifurcation diagram are discussed for each generalized map as well as a new bifurcation diagram related to one of the added parameters. A systematic procedure to design two-constraint logistic map is discussed and validated through four different examples. Wafaa S. Sayed, Ahmed G. Radwan, and Hossam A. H. Fahmy Copyright © 2015 Wafaa S. Sayed et al. All rights reserved. Robust Distributed Filtering for Nonlinear Systems with Sensor Saturations and Fractional Uncertainties with Digital Simulation Thu, 01 Oct 2015 09:47:55 +0000 http://www.hindawi.com/journals/ddns/2015/160683/ This paper is concerned with the robust distributed filtering problem for nonlinear systems subject to sensor saturations and fractional parameter uncertainties. A sufficient condition is derived for the filtering error system to reach the required performance in terms of recursive linear matrix inequality method. An iterative algorithm is then proposed to obtain the filter parameters recursively by solving the corresponding linear matrix inequality. A numerical example is presented to show the effectiveness of the proposed method. Dong Liu, Guangfu Tang, Zhiyuan He, Yan Zhao, and Hui Pang Copyright © 2015 Dong Liu et al. All rights reserved. Spatial Spread of Tuberculosis through Neighborhoods Segregated by Socioeconomic Position: A Stochastic Automata Model Thu, 01 Oct 2015 09:46:43 +0000 http://www.hindawi.com/journals/ddns/2015/583819/ Transmission of the agent of tuberculosis, Mycobacterium tuberculosis, is dependent on social context. A discrete spatial model representing neighborhoods segregated by levels of crowding and immunocompetence is constructed and used to evaluate prevention strategies, based on a number of assumptions about the spatial dynamics of tuberculosis. A cellular automata model is used to (a) construct neighborhoods of different densities, (b) model stochastically local interactions among individuals, and (c) model the spread of tuberculosis within and across neighborhoods over time. Since infected people may become progressively sick but also heal through treatment, the transition among stages was modeled with transition probabilities. A moderate level of successful treatment (40%) dramatically reduced the number of infections across all neighborhoods. Increasing the treatment in neighborhoods of a lower socioeconomic level from 40% to 90% results in an additional decrease of approximately 25% in the number of infected individuals overall. In conclusion, we find that a combination of a moderate level of successful treatment across all areas with more focused treatment efforts in lower socioeconomic areas resulted in the least number of infections over time. David Rehkopf, Alice Furumoto-Dawson, Anthony Kiszewski, and Tamara Awerbuch-Friedlander Copyright © 2015 David Rehkopf et al. All rights reserved. Dynamic Navigation Method with Multisubstations Based on Doppler Shift Thu, 01 Oct 2015 09:45:41 +0000 http://www.hindawi.com/journals/ddns/2015/245837/ The mobile terminals must be compensated for the Doppler effect in their moving communication. This special characteristic of mobile communication can be developed in some new applications. This paper proposes methods to realize mobile navigation calculation via Doppler shifts. It gives the theory of relationship between the motion parameters, like directions and speed, and frequency shifts caused by multibase stations. The simulation illustrates how to compute the movement parameters of numerical calculation and what should be care for the problem near angle 90 degree. It also gives an application with Google map and dynamical locating position and direction on a mobile phone by public wireless network. Given the simulation analysis and navigation test, the results show that this method has a good effect. Jianyang Zhao, Weihong Ding, Zujun Ding, Lianfeng Shen, and Jin Zhao Copyright © 2015 Jianyang Zhao et al. All rights reserved. The Kirchhoff Index of Some Combinatorial Networks Thu, 01 Oct 2015 08:46:46 +0000 http://www.hindawi.com/journals/ddns/2015/340793/ The Kirchhoff index Kf() is the sum of the effective resistance distances between all pairs of vertices in . The hypercube and the folded hypercube are well known networks due to their perfect properties. The graph , constructed from , is the line graph of the subdivision graph . In this paper, explicit formulae expressing the Kirchhoff index of and are found by deducing the characteristic polynomial of the Laplacian matrix of in terms of that of . Jia-Bao Liu, Xiang-Feng Pan, Jinde Cao, and Fu-Tao Hu Copyright © 2015 Jia-Bao Liu et al. All rights reserved. Robustness Analysis of Hybrid Stochastic Neural Networks with Neutral Terms and Time-Varying Delays Thu, 01 Oct 2015 08:31:38 +0000 http://www.hindawi.com/journals/ddns/2015/278571/ We analyze the robustness of global exponential stability of hybrid stochastic neural networks subject to neutral terms and time-varying delays simultaneously. Given globally exponentially stable hybrid stochastic neural networks, we characterize the upper bounds of contraction coefficients of neutral terms and time-varying delays by using the transcendental equation. Moreover, we prove theoretically that, for any globally exponentially stable hybrid stochastic neural networks, if additive neutral terms and time-varying delays are smaller than the upper bounds arrived, then the perturbed neural networks are guaranteed to also be globally exponentially stable. Finally, a numerical simulation example is given to illustrate the presented criteria. Chunmei Wu, Junhao Hu, and Yan Li Copyright © 2015 Chunmei Wu et al. All rights reserved. Dynamics of Planar Systems That Model Stage-Structured Populations Thu, 01 Oct 2015 07:08:23 +0000 http://www.hindawi.com/journals/ddns/2015/137182/ We study a general discrete planar system for modeling stage-structured populations. Our results include conditions for the global convergence of orbits to zero (extinction) when the parameters (vital rates) are time and density dependent. When the parameters are periodic we obtain weaker conditions for extinction. We also study a rational special case of the system for Beverton-Holt type interactions and show that the persistence equilibrium (in the positive quadrant) may be globally attracting even in the presence of interstage competition. However, we determine that with a sufficiently high level of competition, the persistence equilibrium becomes unstable (a saddle point) and the system exhibits period two oscillations. N. Lazaryan and H. Sedaghat Copyright © 2015 N. Lazaryan and H. Sedaghat. All rights reserved. Existence and Stability of Solutions for Hadamard-Stieltjes Fractional Integral Equations Wed, 30 Sep 2015 16:23:54 +0000 http://www.hindawi.com/journals/ddns/2015/317094/ We give some existence results and Ulam stability results for a class of Hadamard-Stieltjes integral equations. We present two results: the first one is an existence result based on Schauder’s fixed point theorem and the second one is about the generalized Ulam-Hyers-Rassias stability. Saïd Abbas, Eman Alaidarous, Mouffak Benchohra, and Juan J. Nieto Copyright © 2015 Saïd Abbas et al. All rights reserved. Adomian Decomposition Method Combined with Padé Approximation and Laplace Transform for Solving a Model of HIV Infection of CD4+T Cells Wed, 30 Sep 2015 13:54:01 +0000 http://www.hindawi.com/journals/ddns/2015/584787/ The classical Adomian decomposition method (ADM) is implemented to solve a model of HIV infection of CD4+T cells. The results indicate that the approximate solution by using the ADM is the same as that by using the Laplace ADM, but it can be obtained in a more efficient way. We also use Padé approximation and Laplace transform as a posttreatment technique to obtain the result of the ADM. The advantage of the posttreatment is illustrated by numerical experiments. Fang Chen and Qing-Quan Liu Copyright © 2015 Fang Chen and Qing-Quan Liu. All rights reserved. Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation Wed, 30 Sep 2015 07:15:25 +0000 http://www.hindawi.com/journals/ddns/2015/791304/ We study reaction-diffusion equations with a general reaction function on one-dimensional lattices with continuous or discrete time , . We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time) exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity. Petr Stehlík and Jonáš Volek Copyright © 2015 Petr Stehlík and Jonáš Volek. All rights reserved.