Journal of Applied Mathematics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. On Nonnegative Moore-Penrose Inverses of Perturbed Matrices Mon, 20 May 2013 14:47:07 +0000 http://www.hindawi.com/journals/jam/2013/680975/ Nonnegativity of the Moore-Penrose inverse of a perturbation of the form is considered when . Using a generalized version of the Sherman-Morrison-Woodbury formula, conditions for to be nonnegative are derived. Applications of the results are presented briefly. Iterative versions of the results are also studied. Shani Jose and K. C. Sivakumar Copyright © 2013 Shani Jose and K. C. Sivakumar. All rights reserved. Approximate Controllability of Fractional Integrodifferential Evolution Equations Mon, 20 May 2013 14:40:29 +0000 http://www.hindawi.com/journals/jam/2013/291816/ This paper addresses the issue of approximate controllability for a class of control system which is represented by nonlinear fractional integrodifferential equations with nonlocal conditions. By using semigroup theory, p-mean continuity and fractional calculations, a set of sufficient conditions, are formulated and proved for the nonlinear fractional control systems. More precisely, the results are established under the assumption that the corresponding linear system is approximately controllable and functions satisfy non-Lipschitz conditions. The results generalize and improve some known results. R. Ganesh, R. Sakthivel, N. I. Mahmudov, and S. M. Anthoni Copyright © 2013 R. Ganesh et al. All rights reserved. Recursive Identification for Dynamic Linear Systems from Noisy Input-Output Measurements Mon, 20 May 2013 13:07:56 +0000 http://www.hindawi.com/journals/jam/2013/318786/ Errors-in-variables (EIV) model is a kind of model with not only noisy output but also noisy input measurements, which can be used for system modeling in many engineering applications. However, the identification for EIV model is much complicated due to the input noises. This paper focuses on the adaptive identification problem of real-time EIV models. Some derivation errors in an accuracy research of the popular Frisch scheme used for EIV identification have been pointed out in a recent study. To solve the same modeling problem, a new algorithm is proposed in this paper. A Moving Average (MA) process is used as a substitute for the joint impact of the mutually independent input and output noises, and then system parameters and the noise properties are estimated in the view of the time domain and frequency domain separately. A recursive form of the first step calculation is constructed to improve the calculation efficiency and online computation ability. Another advantage of the proposed algorithm is its applicableness to different input processes situations. Numerical simulations are given to demonstrate the efficiency and robustness of the new algorithm. Dan Fan and Kueiming Lo Copyright © 2013 Dan Fan and Kueiming Lo. All rights reserved. Fixed Point Theory of Weak Contractions in Partially Ordered Metric Spaces Mon, 20 May 2013 11:22:38 +0000 http://www.hindawi.com/journals/jam/2013/302438/ We prove two new fixed point theorems in the framework of partially ordered metric spaces. Our results generalize and improve many recent fixed point theorems in the literature. Chi-Ming Chen, Jin-Chirng Lee, and Chao-Hung Chen Copyright © 2013 Chi-Ming Chen et al. All rights reserved. New Results on Robust Stability and Stabilization of Linear Discrete-Time Stochastic Systems with Convex Polytopic Uncertainties Sun, 19 May 2013 14:55:03 +0000 http://www.hindawi.com/journals/jam/2013/368259/ This paper addresses the robust stability for a class of linear discrete-time stochastic systems with convex polytopic uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of linear discrete-time stochastic control systems is given. Numerical examples are included to illustrate the effectiveness of our results. P. Niamsup and G. Rajchakit Copyright © 2013 P. Niamsup and G. Rajchakit. All rights reserved. Adaptive Integral Observer-Based Synchronization for Chaotic Systems with Unknown Parameters and Disturbances Sun, 19 May 2013 13:58:29 +0000 http://www.hindawi.com/journals/jam/2013/501421/ Considering the effects of external perturbations on the state vector and the output of the original system, this paper proposes a new adaptive integral observer method to deal with chaos synchronization between the drive and response systems with unknown parameters. The analysis and proof are given by means of the Lyapunov stability theorem and Barbalat lemma. This approach has fewer constraints because many parameters related to chaotic system can be unknown, as shown in the paper. Numerical simulations are performed in the end and the results show that the proposed method is not only suitable to the representative chaotic systems but also applied to some neural network chaotic systems. Xiuchun Li, Jianhua Gu, and Wei Xu Copyright © 2013 Xiuchun Li et al. All rights reserved. On Characterizations of Fourier Frames and Tilings Sun, 19 May 2013 13:57:29 +0000 http://www.hindawi.com/journals/jam/2013/845072/ We give some characterizations of Fourier frames and tilings and obtain a more general form of characterizations of spectra and tilings. Dao-Xin Ding and Hai-Xiong Li Copyright © 2013 Dao-Xin Ding and Hai-Xiong Li. All rights reserved. Fuzzy Multiobjective Traffic Light Signal Optimization Sun, 19 May 2013 10:10:19 +0000 http://www.hindawi.com/journals/jam/2013/249726/ Traffic congestion is a major concern for many cities throughout the world. In a general traffic light controller, the traffic lights change at a constant cycle time. Hence it does not provide an optimal solution. Many traffic light controllers in current use are based on the “time-of-the-day” scheme, which use a limited number of predetermined traffic light patterns and implement these patterns depending upon the time of the day. These automated systems do not provide an optimal control for fluctuating traffic volumes. In this paper, the fuzzy traffic light controller is used to optimize the control of fluctuating traffic volumes such as oversaturated or unusual load conditions. The problem is solved by genetic algorithm, and a new defuzzification method is introduced. The performance of the new defuzzification method (NDM) is compared with the centroid point defuzzification method (CPDM) by using ANOVA. Finally, an illustrative example is presented to show the competency of proposed algorithm. N. Shahsavari Pour, H. Asadi, and M. Pour Kheradmand Copyright © 2013 N. Shahsavari Pour et al. All rights reserved. Multiscale Analysis on the Pricing of Intensity-Based Defaultable Bonds Thu, 16 May 2013 18:28:31 +0000 http://www.hindawi.com/journals/jam/2013/287425/ This paper studies the pricing of intensity-based defaultable bonds where the volatility of default intensity is assumed to be random and driven by two different factors varying on fast and slow time scales. Corrections to the constant intensity of default are obtained and then how these corrections influence the term structure of interest rate derivatives is shown. The results indicate that the fast scale correction produces a more significant impact on the bond price than the slow scale correction and the impact tends to increase as time to maturity increases. Sun-Hwa Cho, Jeong-Hoon Kim, and Yong-Ki Ma Copyright © 2013 Sun-Hwa Cho et al. All rights reserved. Positive Implicative Ideals of BCK-Algebras Based on Intersectional Soft Sets Thu, 16 May 2013 15:45:06 +0000 http://www.hindawi.com/journals/jam/2013/853907/ The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of int-soft positive implicative ideals is introduced, and related properties are investigated. Relations between an int-soft ideal and an int-soft positive implicative ideal are established. Characterizations of an int-soft positive implicative ideal are obtained. Extension property for an int-soft positive implicative ideal is constructed. The -product and -product of int-soft positive implicative ideals are considered, and the soft intersection (resp., union) of int-soft positive implicative ideals is discussed. Eun Hwan Roh and Young Bae Jun Copyright © 2013 Eun Hwan Roh and Young Bae Jun. All rights reserved. Stress Analysis of Osteoporotic Lumbar Vertebra Using Finite Element Model with Microscaled Beam-Shell Trabecular-Cortical Structure Wed, 15 May 2013 08:04:41 +0000 http://www.hindawi.com/journals/jam/2013/285165/ Osteoporosis is a disease in which low bone mass and microarchitectural deterioration of bone tissue lead to enhanced bone fragility and susceptibility to fracture. Due to the complex anatomy of the vertebral body, the difficulties associated with obtaining bones for in vitro experiments, and the limitations on the control of the experimental parameters, finite element models have been developed to analyze the biomechanical properties of the vertebral body. We developed finite element models of the L2 vertebra, which consisted of the endplates, the trabecular lattice, and the cortical shell, for three age-related grades (young, middle, and old) of osteoporosis. The compressive strength and stiffness results revealed that we had developed a valid model that was consistent with the results of previous experimental and computational studies. The von-Mises stress, which was assumed to predict the risk of a burst fracture, was also determined for the three age groups. The results showed that the von-Mises stress was substantially higher under relatively high levels of compressive loading, which suggests that patients with osteoporosis should be cautious of fracture risk even during daily activities. Yoon Hyuk Kim, Mengying Wu, and Kyungsoo Kim Copyright © 2013 Yoon Hyuk Kim et al. All rights reserved. A Mathematical Programming Model for Cell Formation Problem with Machine Replication Tue, 14 May 2013 17:55:23 +0000 http://www.hindawi.com/journals/jam/2013/285759/ Cell formation (CF) is a crucial aspect in the design of cellular manufacturing (CM) systems. This paper develops a comprehensive mathematical programming model for the cell formation problem, where product demands, cell size limits, sequence of operations, multiple units of identical machines, machine capacity, or machine cost are all considered. In this model, the intercell moves are restricted to be unidirectional from one cell to the downstream cells, without backtracking. The proposed model is investigated through several numerical examples. To evaluate the solution quality of the proposed model, it is compared with some well-known cell formation methods from the literature, by using group capability index (GCI) as a performance measure. The results and comparisons indicate that the proposed model produces solution with a higher performance. Reza Raminfar, Norzima Zulkifli, and Mohammadreza Vasili Copyright © 2013 Reza Raminfar et al. All rights reserved. Positive Macroscopic Approximation for Fast Attribute Reduction Tue, 14 May 2013 13:47:45 +0000 http://www.hindawi.com/journals/jam/2013/837281/ Attribute reduction is one of the challenging problems facing the effective application of computational intelligence technology for artificial intelligence. Its task is to eliminate dispensable attributes and search for a feature subset that possesses the same classification capacity as that of the original attribute set. To accomplish efficient attribute reduction, many heuristic search algorithms have been developed. Most of them are based on the model that the approximation of all the target concepts associated with a decision system is dividable into that of a single target concept represented by a pair of definable concepts known as lower and upper approximations. This paper proposes a novel model called macroscopic approximation, considering all the target concepts as an indivisible whole to be approximated by rough set boundary region derived from inconsistent tolerance blocks, as well as an efficient approximation framework called positive macroscopic approximation (PMA), addressing macroscopic approximations with respect to a series of attribute subsets. Based on PMA, a fast heuristic search algorithm for attribute reduction in incomplete decision systems is designed and achieves obviously better computational efficiency than other available algorithms, which is also demonstrated by the experimental results. Zheng-Cai Lu, Zheng Qin, Qiao Jing, and Lai-Xiang Shan Copyright © 2013 Zheng-Cai Lu et al. All rights reserved. High Efficient Numerical Methods for Viscous and Nonviscous Wave Problems Tue, 14 May 2013 11:05:41 +0000 http://www.hindawi.com/journals/jam/2013/267106/ This paper is concerned with accurate and efficient numerical methods for solving viscous and nonviscous wave problems. The paper first introduces a new second-order PR-ADI like scheme. For an efficient simulation, the scheme is also extended to a high-order compact PRADI like method. Both of them have the advantages of unconditional stability, less impact of the perturbing terms on the accuracy, and being convenient to compute the boundary values of the intermediates. Besides this, the compact scheme has high-order accuracy and costs less in computational time. Numerical results are presented to show the accuracy and efficiency of the new algorithms. Xiujie Lv, Jinggang Qin, and Tongke Wang Copyright © 2013 Xiujie Lv et al. All rights reserved. A Numerical Method for Delayed Fractional-Order Differential Equations Tue, 14 May 2013 10:10:44 +0000 http://www.hindawi.com/journals/jam/2013/256071/ A numerical method for nonlinear fractional-order differential equations with constant or time-varying delay is devised. The order here is an arbitrary positive real number, and the differential operator is with the Caputo definition. The general Adams-Bashforth-Moulton method combined with the linear interpolation method is employed to approximate the delayed fractional-order differential equations. Meanwhile, the detailed error analysis for this algorithm is given. In order to compare with the exact analytical solution, a numerical example is provided to illustrate the effectiveness of the proposed method. Zhen Wang Copyright © 2013 Zhen Wang. All rights reserved. Car Delay Model near Bus Stops with Mixed Traffic Flow Tue, 14 May 2013 08:58:58 +0000 http://www.hindawi.com/journals/jam/2013/437637/ This paper proposes a model for estimating car delays at bus stops under mixed traffic using probability theory and queuing theory. The roadway is divided to serve motorized and nonmotorized traffic streams. Bus stops are located on the nonmotorized lanes. When buses dwell at the stop, they block the bicycles. Thus, two conflict points between car stream and other traffic stream are identified. The first conflict point occurs as bicycles merge to the motorized lane to avoid waiting behind the stopping buses. The second occurs as buses merge back to the motorized lane. The average car delay is estimated as the sum of the average delay at these two conflict points and the delay resulting from following the slower bicycles that merged into the motorized lane. Data are collected to calibrate and validate the developed model from one site in Beijing. The sensitivity of car delay to various operation conditions is examined. The results show that both bus stream and bicycle stream have significant effects on car delay. At bus volumes above 200 vehicles per hour, the curbside stop design is not appropriate because of the long car delays. It can be replaced by the bus bay design. Yang Xiaobao, Huan Mei, and Gao Ziyou Copyright © 2013 Yang Xiaobao et al. All rights reserved. Relaxed Viscosity Approximation Methods with Regularization for Constrained Minimization Problems Mon, 13 May 2013 17:44:59 +0000 http://www.hindawi.com/journals/jam/2013/531859/ We introduce a new relaxed viscosity approximation method with regularization and prove the strong convergence of the method to a common fixed point of finitely many nonexpansive mappings and a strict pseudocontraction that also solves a convex minimization problem and a suitable equilibrium problem. Lu-Chuan Ceng, Hong-Kun Xu, and Ching-Feng Wen Copyright © 2013 Lu-Chuan Ceng et al. All rights reserved. Three New Stochastic Local Search Metaheuristics for the Annual Crop Planning Problem Based on a New Irrigation Scheme Mon, 13 May 2013 16:33:19 +0000 http://www.hindawi.com/journals/jam/2013/158538/ Annual Crop Planning (ACP) is an NP-hard-type optimization problem in agricultural planning. It involves finding optimal solutions concerning the seasonal allocations of a limited amount of agricultural land amongst the various competing crops that are required to be grown on it. This study investigates the effectiveness of employing three new local search (LS) metaheuristic techniques in determining solutions to an ACP problem at a new Irrigation Scheme. These three new LS metaheuristic techniques are the Best Performance Algorithm (BPA), Iterative Best Performance Algorithm (IBPA), and the Largest Absolute Difference Algorithm (LADA). The solutions determined by these LS metaheuristic techniques are compared against the solutions of two other well-known LS metaheuristic techniques in the literature. These techniques are Tabu Search (TS) and Simulated Annealing (SA). The comparison with TS and SA was to determine the relative merits of the solutions found by BPA, IBPA, and LADA. The results show that TS performed as the overall best. However, LADA determined the best solution that was the most economically feasible. Sivashan Chetty and Aderemi Oluyinka Adewumi Copyright © 2013 Sivashan Chetty and Aderemi Oluyinka Adewumi. All rights reserved. Developing a Series Solution Method of -Difference Equations Mon, 13 May 2013 15:14:14 +0000 http://www.hindawi.com/journals/jam/2013/743973/ The series solution is widely applied to differential equations on but is not found in -differential equations. Applying the Taylor and multiplication rule of two generalized polynomials, we develop a series solution of linear homogeneous -difference equations. As an example, the series solution method is used to find a series solution of the second-order -difference equation of Hermite’s type. Hsuan-Ku Liu Copyright © 2013 Hsuan-Ku Liu. All rights reserved. Bounds on the Distance Energy and the Distance Estrada Index of Strongly Quotient Graphs Mon, 13 May 2013 15:01:59 +0000 http://www.hindawi.com/journals/jam/2013/681019/ The notion of strongly quotient graph (SQG) was introduced by Adiga et al. (2007). In this paper, we obtain some better results for the distance energy and the distance Estrada index of any connected strongly quotient graph (CSQG) as well as some relations between the distance Estrada index and the distance energy. We also present some bounds for the distance energy and the distance Estrada index of CSQG whose diameter does not exceed two. Additionally, we show that our results improve most of the results obtained by Güngör and Bozkurt (2009) and Zaferani (2008). Ş. Burcu Bozkurt, Chandrashekara Adiga, and Durmuş Bozkurt Copyright © 2013 Ş. Burcu Bozkurt et al. All rights reserved. Fractional-Order Control of First Order Plants with Guaranteed Time Specifications Mon, 13 May 2013 08:26:30 +0000 http://www.hindawi.com/journals/jam/2013/197186/ Cardiospheres (CSs) are self-assembling multicellular clusters from the cellular outgrowth from cardiac explants cultured in nonadhesive substrates. They contain a core of primitive, proliferating cells, and an outer layer of mesenchymal/stromal cells and differentiating cells that express cardiomyocyte proteins and connexin 43. Because CSs contain both primitive cells and committed progenitors for the three major cell types present in the heart, that is, cardiomyocytes, endothelial cells, and smooth muscle cells, and because they are derived from percutaneous endomyocardial biopsies, they represent an attractive cell source for cardiac regeneration. In preclinical studies, CS-derived cells (CDCs) delivered to infarcted hearts resulted in improved cardiac function. CDCs have been tested safely in an initial phase-1 clinical trial in patients after myocardial infarction. Whether or not CDCs are superior to purified populations, for example, c-kit+ cardiac stem cells, or to gene therapy approaches for cardiac regeneration remains to be evaluated. F. J. Castillo-Garcia, A. San Millan-Rodriguez, V. Feliu-Batlle, and L. Sanchez-Rodriguez Copyright © 2013 F. J. Castillo-Garcia et al. All rights reserved. Splitting Matching Pursuit Method for Reconstructing Sparse Signal in Compressed Sensing Sun, 12 May 2013 18:55:57 +0000 http://www.hindawi.com/journals/jam/2013/804640/ In this paper, a novel method named as splitting matching pursuit (SMP) is proposed to reconstruct -sparse signal in compressed sensing. The proposed method selects    largest components of the correlation vector , which are divided into split sets with equal length . The searching area is thus expanded to incorporate more candidate components, which increases the probability of finding the true components at one iteration. The proposed method does not require the sparsity level to be known in prior. The Merging, Estimation and Pruning steps are carried out for each split set independently, which makes it especially suitable for parallel computation. The proposed SMP method is then extended to more practical condition, e.g. the direction of arrival (DOA) estimation problem in phased array radar system using compressed sensing. Numerical simulations show that the proposed method succeeds in identifying multiple targets in a sparse radar scene, outperforming other OMP-type methods. The proposed method also obtains more precise estimation of DOA angle using one snapshot compared with the traditional estimation methods such as Capon, APES (amplitude and phase estimation) and GLRT (generalized likelihood ratio test) based on hundreds of snapshots. Liu Jing, Han ChongZhao, Yao XiangHua, and Lian Feng Copyright © 2013 Liu Jing et al. All rights reserved. On the Positive Definite Solutions of a Nonlinear Matrix Equation Sun, 12 May 2013 15:10:23 +0000 http://www.hindawi.com/journals/jam/2013/676978/ The positive definite solutions of the nonlinear matrix equation are discussed. A necessary and sufficient condition for the existence of positive definite solutions for this equation is derived. Then, the uniqueness of the Hermitian positive definite solution is studied based on an iterative method proposed in this paper. Lastly the perturbation analysis for this equation is discussed. Panpan Liu, Shugong Zhang, and Qingchun Li Copyright © 2013 Panpan Liu et al. All rights reserved. A Modified -Median Model for the Emergency Facilities Location Problem and Its Variable Neighbourhood Search-Based Algorithm Sun, 12 May 2013 15:04:06 +0000 http://www.hindawi.com/journals/jam/2013/375657/ Emergency incidents, including natural disasters, terrorist attacks, public health outbreaks, and industrial and mining accidents, and so forth, result in severe human casualties and property losses. Emergency facilities, which provide relief materials and services, play an important role in rescue management. The decision of where to locate the emergency rescue facilities is very important, as it determines the efficiency and effectiveness of the emergency management process. This paper develops a modified -median problem model that accounts for rescue time limitations. A variable neighbourhood search- (VNS-) based algorithm is developed for the model considered. The modified VNS algorithm exhibits good performance on -median benchmark problems. A case from Western China is studied, and a reasonable location decision is then made for emergency rescue facilities using the modified VNS algorithm. The paper also compares the results with and without considering the rescue time limitation. Menghao Xi, Feng Ye, Zhong Yao, and Qiuhong Zhao Copyright © 2013 Menghao Xi et al. All rights reserved. Dynamics Analysis of an HIV Infection Model including Infected Cells in an Eclipse Stage Sun, 12 May 2013 13:56:45 +0000 http://www.hindawi.com/journals/jam/2013/419593/ In this paper, an HIV infection model including an eclipse stage of infected cells is considered. Some quicker cells in this stage become productively infected cells, a portion of these cells are reverted to the uninfected class, and others will be latent down in the body. We consider CTL-response delay in this model and analyze the effect of time delay on stability of equilibrium. It is shown that the uninfected equilibrium and CTL-absent infection equilibrium are globally asymptotically stable for both ODE and DDE model. And we get the global stability of the CTL-present equilibrium for ODE model. For DDE model, we have proved that the CTL-present equilibrium is locally asymptotically stable in a range of delays and also have studied the existence of Hopf bifurcations at the CTL-present equilibrium. Numerical simulations are carried out to support our main results. Shengyu Zhou, Zhixing Hu, Wanbiao Ma, and Fucheng Liao Copyright © 2013 Shengyu Zhou et al. All rights reserved. The Application of the Homotopy Analysis Method and the Homotopy Perturbation Method to the Davey-Stewartson Equations and Comparison between Them and Exact Solutions Sun, 12 May 2013 10:57:30 +0000 http://www.hindawi.com/journals/jam/2013/326473/ We introduce two powerful methods to solve the Davey-Stewartson equations: one is the homotopy perturbation method (HPM) and the other is the homotopy analysis method (HAM). HAM is a strong and easy to use analytic tool for nonlinear problems. Comparison of the HPM results with the HAM results, and compute the absolute errors between the exact solutions of the DS equations with the HPM solutions and HAM solutions are obtained. Hassan A. Zedan, W. Barakati, and Nada Hamad Copyright © 2013 Hassan A. Zedan et al. All rights reserved. Thermal Diffusion and Diffusion Thermo Effects on the Viscous Fluid Flow with Heat and Mass Transfer through Porous Medium over a Shrinking Sheet Sun, 12 May 2013 07:59:35 +0000 http://www.hindawi.com/journals/jam/2013/584534/ The motion of the viscous, incompressible fluid through a porous medium with heat and mass transfer over a shrinking sheet is investigated. The cross-diffusion effect between temperature and concentration is considered. This phenomenon is modulated mathematically by a set of partial differential equations which govern the continuity, momentum, heat, and mass. These equations are transformed to a set of ordinary differential equations by using similarity solutions. The analytical solutions of these equations are obtained. The velocity, temperature, and concentration of the fluid as well as the heat and mass transfer with shear stress at the sheet are obtained as a function of the physical parameters of the problem. The effects of Prandtl number, mass transfer parameter, the wall shrinking parameter, the permeability parameter, and Dufour and Soret numbers on temperature and concentration are studied. Also, the effects of mass transfer parameter, permeability parameter, and shrinking strength on the velocity and shear stress are discussed. These effects are illustrated graphically through a set of figures. Nabil Eldabe and Mahmoud Abu Zeid Copyright © 2013 Nabil Eldabe and Mahmoud Abu Zeid. All rights reserved. A New Construction of Multisender Authentication Codes from Polynomials over Finite Fields Thu, 09 May 2013 17:13:15 +0000 http://www.hindawi.com/journals/jam/2013/320392/ Multisender authentication codes allow a group of senders to construct an authenticated message for a receiver such that the receiver can verify the authenticity of the received message. In this paper, we construct one multisender authentication code from polynomials over finite fields. Some parameters and the probabilities of deceptions of this code are also computed. Xiuli Wang Copyright © 2013 Xiuli Wang. All rights reserved. Adaptive Neural Sliding Mode Control of Active Power Filter Thu, 09 May 2013 16:49:14 +0000 http://www.hindawi.com/journals/jam/2013/341831/ A radial basis function (RBF) neural network adaptive sliding mode control system is developed for the current compensation control of three-phase active power filter (APF). The advantages of the adaptive control, neural network control, and sliding mode control are combined together to achieve the control task; that is, the harmonic current of nonlinear load can be eliminated and the quality of power system can be well improved. Sliding surface coordinate function and sliding mode controller are used as input and output of the RBF neural network, respectively. The neural network control parameters are online adjusted through gradient method and Lyapunov theory. Simulation results demonstrate that the adaptive RBF sliding mode control can compensate harmonic current effectively and has strong robustness to disturbance signals. Juntao Fei and Zhe Wang Copyright © 2013 Juntao Fei and Zhe Wang. All rights reserved. Strong Convergence Theorems for Solutions of Equations of Hammerstein Type Thu, 09 May 2013 14:50:35 +0000 http://www.hindawi.com/journals/jam/2013/541079/ We consider an auxiliary operator, defined in a real Hilbert space in terms of and , that is, monotone and Lipschitz mappings (resp., monotone and bounded mappings). We use an explicit iterative process that converges strongly to a solution of equation of Hammerstein type. Furthermore, our results improve related results in the literature. Chih-Sheng Chuang Copyright © 2013 Chih-Sheng Chuang. All rights reserved.