Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. A New Method for Solving Supervised Data Classification Problems Thu, 27 Nov 2014 13:14:23 +0000 http://www.hindawi.com/journals/aaa/2014/318478/ Supervised data classification is one of the techniques used to extract nontrivial information from data. Classification is a widely used technique in various fields, including data mining, industry, medicine, science, and law. This paper considers a new algorithm for supervised data classification problems associated with the cluster analysis. The mathematical formulations for this algorithm are based on nonsmooth, nonconvex optimization. A new algorithm for solving this optimization problem is utilized. The new algorithm uses a derivative-free technique, with robustness and efficiency. To improve classification performance and efficiency in generating classification model, a new feature selection algorithm based on techniques of convex programming is suggested. Proposed methods are tested on real-world datasets. Results of numerical experiments have been presented which demonstrate the effectiveness of the proposed algorithms. Parvaneh Shabanzadeh and Rubiyah Yusof Copyright © 2014 Parvaneh Shabanzadeh and Rubiyah Yusof. All rights reserved. Secure OpenID Authentication Model by Using Trusted Computing Thu, 27 Nov 2014 08:33:09 +0000 http://www.hindawi.com/journals/aaa/2014/561487/ The growth of Internet online services has been very quick in recent years. Each online service requires Internet users to create a new account to use the service. The problem can be seen when each user usually needs more than one service and, consequently, has numerous accounts. These numerous accounts have to be managed in a secure and simple way to be protected against identity theft. Single sign-on (SSO) and OpenID have been used to decrease the complexity of managing numerous accounts required in the Internet identity environment. Trusted Platform Module (TPM) and Trust Multitenancy are great trusted computing-based technologies to solve security concerns in the Internet identity environment. Since trust is one of the pillars of security in the cloud, this paper analyzes the existing cloud identity techniques in order to investigate their strengths and weaknesses. This paper proposes a model in which One Time Password (OTP), TPM, and OpenID are used to provide a solution against phishing as a common identity theft in cloud environment. E. Ghazizadeh, Z. S. Shams Dolatabadi, R. Khaleghparast, M. Zamani, A. A. Manaf, and M. S. Abdullah Copyright © 2014 E. Ghazizadeh et al. All rights reserved. Assessment of an Average Controller for a DC/DC Converter via Either a PWM or a Sigma-Delta-Modulator Wed, 26 Nov 2014 08:59:38 +0000 http://www.hindawi.com/journals/aaa/2014/196010/ Sliding mode control is a discontinuous control technique that is, by its nature, appropriate for controlling variable structure systems, such as the switch regulated systems employed in power electronics. However, when designing control laws based on the average models of these systems a modulator is necessary for their experimental implementation. Among the most widely used modulators in power electronics are the pulse width modulation (PWM) and, more recently, the sigma-delta-modulator (-modulator). Based on the importance of achieving an appropriate implementation of average control laws and the relevance of the trajectory tracking task in DC/DC power converters, for the first time, this research presents the assessment of the experimental results obtained when one of these controllers is implemented through either a PWM or a -modulator to perform such a task. A comparative assessment based on the integral square error (ISE) index shows that, at frequencies with similar efficiency, the -modulator provides a better tracking performance for the DC/DC Buck converter. In this paper, an average control based on differential flatness was used to perform the experiments. It is worth mentioning that a different trajectory tracking controller could have been selected for this research. R. Silva-Ortigoza, F. Carrizosa-Corral, J. J. Gálvez-Gamboa, M. Marcelino-Aranda, D. Muñoz-Carrillo, and H. Taud Copyright © 2014 R. Silva-Ortigoza et al. All rights reserved. Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables Tue, 25 Nov 2014 11:14:25 +0000 http://www.hindawi.com/journals/aaa/2014/619035/ Leptospirosis is an infectious disease that damages the liver and kidneys, found mainly in dogs and farm animals and caused by bacteria. In this paper, we present the optimal control problem applied to a dynamical leptospirosis infected vector and human population by using multiple control variables. First, we show the existence of the control problem and then use analytical and numerical techniques to investigate the existence cost effective control efforts for prevention of indirect and direct transmission of this disease. In order to do this, we consider three control functions two for human and one for vector population. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method. Muhammad Altaf Khan, Saeed Islam, Sher Afzal Khan, Ilyas Khan, Sharidan Shafie, and Taza Gul Copyright © 2014 Muhammad Altaf Khan et al. All rights reserved. Combining Interval Branch and Bound and Stochastic Search Mon, 24 Nov 2014 13:46:16 +0000 http://www.hindawi.com/journals/aaa/2014/861765/ This paper presents global optimization algorithms that incorporate the idea of an interval branch and bound and the stochastic search algorithms. Two algorithms for unconstrained problems are proposed, the hybrid interval simulated annealing and the combined interval branch and bound and genetic algorithm. The numerical experiment shows better results compared to Hansen’s algorithm and simulated annealing in terms of the storage, speed, and number of function evaluations. The convergence proof is described. Moreover, the idea of both algorithms suggests a structure for an integrated interval branch and bound and genetic algorithm for constrained problems in which the algorithm is described and tested. The aim is to capture one of the solutions with higher accuracy and lower cost. The results show better quality of the solutions with less number of function evaluations compared with the traditional GA. Dhiranuch Bunnag Copyright © 2014 Dhiranuch Bunnag. All rights reserved. An Analysis of Relationship among Income Inequality, Poverty, and Income Mobility, Based on Distribution Functions Mon, 24 Nov 2014 07:37:28 +0000 http://www.hindawi.com/journals/aaa/2014/186564/ Many studies show that the relationship among income inequality, poverty, and income mobility needs to be further discussed. Meanwhile, some researches on Distribution Function offer new perspective and methods to analyze this issue. First, this paper expresses the relationship among the Gini coefficient, poverty ratio, and income mobility of 5 common Distribution Functions through math deduction; this finding cannot be found in relevant literatures. Furthermore, an empirical research result proves that the income distribution of urban residents in the period from 2005 to 2010 fits Log-Logistic Distribution. On the basis of the above analysis and empirical data, the paper explores the relations of income inequality, poverty, and income mobility of urban residents and draws some useful conclusions. Jiandong Chen, Yaqing Si, Fengying Li, and Aifeng Zhao Copyright © 2014 Jiandong Chen et al. All rights reserved. Blow-Up Solutions and Global Solutions to Discrete -Laplacian Parabolic Equations Mon, 24 Nov 2014 07:27:14 +0000 http://www.hindawi.com/journals/aaa/2014/351675/ We discuss the conditions under which blow-up occurs for the solutions of discrete -Laplacian parabolic equations on networks with boundary as follows: , ; , ; , where , , , and the initial data is nontrivial on . The main theorem states that the solution to the above equation satisfies the following: (i) if and , then the solution blows up in a finite time, provided , where and ; (ii) if , then the nonnegative solution is global; (iii) if , then the solution is global. In order to prove the main theorem, we first derive the comparison principles for the solution of the equation above, which play an important role throughout this paper. Moreover, when the solution blows up, we give an estimate for the blow-up time and also provide the blow-up rate. Finally, we give some numerical illustrations which exploit the main results. Soon-Yeong Chung and Min-Jun Choi Copyright © 2014 Soon-Yeong Chung and Min-Jun Choi. All rights reserved. Automatic Gauge Control in Rolling Process Based on Multiple Smith Predictor Models Mon, 24 Nov 2014 07:16:30 +0000 http://www.hindawi.com/journals/aaa/2014/872418/ Automatic rolling process is a high-speed system which always requires high-speed control and communication capabilities. Meanwhile, it is also a typical complex electromechanical system; distributed control has become the mainstream of computer control system for rolling mill. Generally, the control system adopts the 2-level control structure—basic automation (Level 1) and process control (Level 2)—to achieve the automatic gauge control. In Level 1, there is always a certain distance between the roll gap of each stand and the thickness testing point, leading to the time delay of gauge control. Smith predictor is a method to cope with time-delay system, but the practical feedback control based on traditional Smith predictor cannot get the ideal control result, because the time delay is hard to be measured precisely and in some situations it may vary in a certain range. In this paper, based on adaptive Smith predictor, we employ multiple models to cover the uncertainties of time delay. The optimal model will be selected by the proposed switch mechanism. Simulations show that the proposed multiple Smith model method exhibits excellent performance in improving the control result even for system with jumping time delay. Jiangyun Li, Kang Wang, and Yang Li Copyright © 2014 Jiangyun Li et al. All rights reserved. Low-Rank Representation-Based Object Tracking Using Multitask Feature Learning with Joint Sparsity Sun, 23 Nov 2014 13:19:02 +0000 http://www.hindawi.com/journals/aaa/2014/147353/ We address object tracking problem as a multitask feature learning process based on low-rank representation of features with joint sparsity. We first select features with low-rank representation within a number of initial frames to obtain subspace basis. Next, the features represented by the low-rank and sparse property are learned using a modified joint sparsity-based multitask feature learning framework. Both the features and sparse errors are then optimally updated using a novel incremental alternating direction method. The low-rank minimization problem for learning multitask features can be achieved by a few sequences of efficient closed form update process. Since the proposed method attempts to perform the feature learning problem in both multitask and low-rank manner, it can not only reduce the dimension but also improve the tracking performance without drift. Experimental results demonstrate that the proposed method outperforms existing state-of-the-art tracking methods for tracking objects in challenging image sequences. Hyuncheol Kim and Joonki Paik Copyright © 2014 Hyuncheol Kim and Joonki Paik. All rights reserved. On One 2-Valued Transformation: Its Invariant Measure and Application to Masked Dynamical Systems Wed, 19 Nov 2014 08:12:55 +0000 http://www.hindawi.com/journals/aaa/2014/513061/ We consider one family of 2-valued transformations on the interval [0, 1] with measure , endowed with a set of weight functions. We construct invariant measure for this multivalued dynamical system with weights and show the interplay between such systems and masked dynamical systems, which leads to image processing. P. I. Troshin Copyright © 2014 P. I. Troshin. All rights reserved. Bifurcation Structure in a Bimodal Piecewise Linear Business Cycle Model Wed, 19 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/401319/ We study the bifurcation structure of the parameter space of a 1D continuous piecewise linear bimodal map which describes dynamics of a business cycle model introduced by Day-Shafer. In particular, we obtain the analytical expression of the boundaries of several periodicity regions associated with attracting cycles of the map (principal cycles and related fin structure). By crossing these boundaries the map displays robust chaos. Viktor Avrutin, Iryna Sushko, and Fabio Tramontana Copyright © 2014 Viktor Avrutin et al. All rights reserved. Parabolic Equations of Infinite Order with Data Tue, 18 Nov 2014 11:25:40 +0000 http://www.hindawi.com/journals/aaa/2014/646721/ We prove an existence result of a nonlinear parabolic equation under Dirichlet null boundary conditions in Sobolev spaces of infinite order, where the second member belongs to . Mohammed Housseine Abdou, Moussa Chrif, and Said El Manouni Copyright © 2014 Mohammed Housseine Abdou et al. All rights reserved. Robust Adaptive Stabilization of Nonholonomic Mobile Robots with Bounded Disturbances Mon, 17 Nov 2014 12:55:23 +0000 http://www.hindawi.com/journals/aaa/2014/456975/ The stabilization problem of nonholonomic mobile robots with unknown system parameters and environmental disturbances is investigated in this paper. Considering the dynamic model and the kinematic model of mobile robots, the transverse function approach is adopted to construct an additional control parameter, so that the closed-loop system is not underactuated. Then the adaptive backstepping method and the parameter projection technique are applied to design the controller to stabilize the system. At last, simulation results demonstrate the effectiveness of our proposed controller schemes. Gang Chen, Tingting Gao, Jiangshuai Huang, and Qicai Zhou Copyright © 2014 Gang Chen et al. All rights reserved. Event-Triggered Control for Multiagent Systems with the Problem of Packet Losses and Communication Delays When Using the Second-Order Neighbors’ Information Mon, 17 Nov 2014 10:53:14 +0000 http://www.hindawi.com/journals/aaa/2014/616530/ This paper mainly investigates the event-triggered control for discrete-time multiagent systems with the problem of packet losses and communication delays when both the first-order and the second-order neighbors’ information are used. Event-triggered control laws are adopted so as to reduce the frequency of individual actuation updating under the sampled-data framework for discrete-time agent dynamics. The communication graph is undirected and the loss of data across each communication link occurs at certain probability, which is governed by a Bernoulli process. It is found that the distributed consensus speeds up by using the second-order neighbors’ information when packet losses and communication delays occur. Numerical examples are given to demonstrate the effectiveness of the proposed methods. Chuan Yan, Mei Yu, Guangming Xie, and Yu Liu Copyright © 2014 Chuan Yan et al. All rights reserved. An Adaptive Approach to Solutions of Fredholm Integral Equations of the Second Kind Mon, 17 Nov 2014 10:34:32 +0000 http://www.hindawi.com/journals/aaa/2014/629179/ As an approach to approximate solutions of Fredholm integral equations of the second kind, adaptive hp-refinement is used firstly together with Galerkin method and with Sloan iteration method which is applied to Galerkin method solution. The linear hat functions and modified integrated Legendre polynomials are used as basis functions for the approximations. The most appropriate refinement is determined by an optimization problem given by Demkowicz, 2007. During the calculations -projections of approximate solutions on four different meshes which could occur between coarse mesh and fine mesh are calculated. Depending on the error values, these procedures could be repeated consecutively or different meshes could be used in order to decrease the error values. Nebiye Korkmaz and Zekeriya Güney Copyright © 2014 Nebiye Korkmaz and Zekeriya Güney. All rights reserved. Further Application of -Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions Mon, 17 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/468065/ We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeister function and its generalizations, denoted by GCP() where and are -differentiable. We describe -differentials of some GCP functions based on the generalized Fisher-Burmeister function and its generalizations, and their merit functions. Under appropriate conditions on the -differentials of and , we show that a local/global minimum of a merit function (or a “stationary point” of a merit function) is coincident with the solution of the given generalized complementarity problem. When specializing GCP to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved for , semismooth, and locally Lipschitzian. Wei-Zhe Gu and Mohamed A. Tawhid Copyright © 2014 Wei-Zhe Gu and Mohamed A. Tawhid. All rights reserved. Convex Combination Inequalities of the Line and Plane Sun, 16 Nov 2014 09:42:50 +0000 http://www.hindawi.com/journals/aaa/2014/916243/ The paper deals with convex combinations, convex functions, and Jensen’s functionals. The main idea of this work is to present the given convex combination by using two other convex combinations with minimal number of points. For example, as regards the presentation of the planar combination, we use two trinomial combinations. Generalizations to higher dimensions are also considered. Zlatko Pavić, Shanhe Wu, and Štefanija Klarić Copyright © 2014 Zlatko Pavić et al. All rights reserved. Multiple Symmetric Results for Quasilinear Elliptic Systems Involving Singular Potentials and Critical Sobolev Exponents in Sun, 16 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/430976/ This paper deals with a class of quasilinear elliptic systems involving singular potentials and critical Sobolev exponents in . By using the symmetric criticality principle of Palais and variational methods, we prove several existence and multiplicity results of G-symmetric solutions under certain appropriate hypotheses on the potentials and parameters. Zhiying Deng and Yisheng Huang Copyright © 2014 Zhiying Deng and Yisheng Huang. All rights reserved. Multiplicity of Positive Solutions for a Second-Order Elliptic System of Kirchhoff Type Wed, 12 Nov 2014 08:43:30 +0000 http://www.hindawi.com/journals/aaa/2014/280130/ We study elliptic problems of Kirchhoff type in . Using variational tools, we establish the existence of at least two nontrivial and nonnegative solutions. S. Khademloo, E. Valipour, and A. Babakhani Copyright © 2014 S. Khademloo et al. All rights reserved. An Improved Differential Evolution Algorithm for Maritime Collision Avoidance Route Planning Wed, 12 Nov 2014 08:09:10 +0000 http://www.hindawi.com/journals/aaa/2014/614569/ High accuracy navigation and surveillance systems are pivotal to ensure efficient ship route planning and marine safety. Based on existing ship navigation and maritime collision prevention rules, an improved approach for collision avoidance route planning using a differential evolution algorithm was developed. Simulation results show that the algorithm is capable of significantly enhancing the optimized route over current methods. It has the potential to be used as a tool to generate optimal vessel routing in the presence of conflicts. Yu-xin Zhao, Wang Li, Shaojun Feng, Washington Y. Ochieng, and Wolfgang Schuster Copyright © 2014 Yu-xin Zhao et al. All rights reserved. Counting Closed Orbits for the Dyck Shift Wed, 12 Nov 2014 07:51:40 +0000 http://www.hindawi.com/journals/aaa/2014/304798/ The prime orbit theorem and Mertens’ theorem are proved for a shift dynamical system of infinite type called the Dyck shift. Different and more direct methods are used in the proof without any complicated theoretical discussion. Fahad Alsharari, Mohd Salmi Md. Noorani, and Habibulla Akhadkulov Copyright © 2014 Fahad Alsharari et al. All rights reserved. Estimates of Invariant Metrics on Pseudoconvex Domains of Finite Type in Wed, 12 Nov 2014 06:52:27 +0000 http://www.hindawi.com/journals/aaa/2014/697160/ Let be a smoothly bounded pseudoconvex domain in and assume that is a point of finite 1-type in the sense of D’Angelo. Then, there are an admissible curve , connecting points   and , and a quantity , along , which bounds from above and below the Bergman, Caratheodory, and Kobayashi metrics in a small constant and large constant sense. Sanghyun Cho and Young Hwan You Copyright © 2014 Sanghyun Cho and Young Hwan You. All rights reserved. Multiple Positive Solutions of Nonlinear Boundary Value Problem for Finite Fractional Difference Wed, 12 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/147975/ We consider a discrete fractional nonlinear boundary value problem in which nonlinear term is involved with the fractional order difference. And we transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions. Yansheng He, Mingzhe Sun, and Chengmin Hou Copyright © 2014 Yansheng He et al. All rights reserved. Dynamics of the Zeros of Analytic Continued -Euler Polynomials Tue, 11 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/537864/ In this paper, we study that the -Euler numbers and -Euler polynomials are analytic continued to and . We investigate the new concept of dynamics of the zeros of analytic continued polynomials related to solution of Bernoulli equation. Finally, we observe an interesting phenomenon of “scattering” of the zeros of . C. S. Ryoo Copyright © 2014 C. S. Ryoo. All rights reserved. An Improved Adaptive Tracking Controller of Permanent Magnet Synchronous Motor Tue, 11 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/987308/ This paper proposes a new adaptive fuzzy neural control to suppress chaos and also to achieve the speed tracking control in a permanent magnet synchronous motor (PMSM) drive system with unknown parameters and uncertainties. The control scheme consists of fuzzy neural and compensatory controllers. The fuzzy neural controller with online parameter tuning is used to estimate the unknown nonlinear models and construct linearization feedback control law, while the compensatory controller is employed to attenuate the estimation error effects of the fuzzy neural network and ensure the robustness of the controlled system. Moreover, due to improvement in controller design, the singularity problem is surely avoided. Finally, numerical simulations are carried out to demonstrate that the proposed control scheme can successfully remove chaotic oscillations and allow the speed to follow the desired trajectory in a chaotic PMSM despite the existence of unknown models and uncertainties. Tat-Bao-Thien Nguyen, Teh-Lu Liao, Hang-Hong Kuo, and Jun-Juh Yan Copyright © 2014 Tat-Bao-Thien Nguyen et al. All rights reserved. Nonlinear Analysis and Geometric Function Theory Mon, 10 Nov 2014 12:40:36 +0000 http://www.hindawi.com/journals/aaa/2014/656957/ Ljubomir B. Ćirić, Samuel Krushkal, Qamrul Hasan Ansari, David Kalaj, and Vesna Manojlović Copyright © 2014 Ljubomir B. Ćirić et al. All rights reserved. Global Optimization for the Sum of Certain Nonlinear Functions Mon, 10 Nov 2014 12:22:05 +0000 http://www.hindawi.com/journals/aaa/2014/408918/ We extend work by Pei-Ping and Gui-Xia, 2007, to a global optimization problem for more general functions. Pei-Ping and Gui-Xia treat the optimization problem for the linear sum of polynomial fractional functions, using a branch and bound approach. We prove that this extension makes possible to solve the following nonconvex optimization problems which Pei-Ping and Gui-Xia, 2007, cannot solve, that the sum of the positive (or negative) first and second derivatives function with the variable defined by sum of polynomial fractional function by using branch and bound algorithm. Mio Horai, Hideo Kobayashi, and Takashi G. Nitta Copyright © 2014 Mio Horai et al. All rights reserved. High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential Mon, 10 Nov 2014 11:23:03 +0000 http://www.hindawi.com/journals/aaa/2014/274859/ Let be the basis of space of horizontal vector fields in a Carnot group . We prove high order Fefferman-Phong type inequalities in . As applications, we derive a priori estimates for the nondivergence degenerate elliptic operators with coefficients and a potential belonging to an appropriate Stummel type class introduced in this paper. Some of our results are also new even for the usual Euclidean space. Pengcheng Niu and Kelei Zhang Copyright © 2014 Pengcheng Niu and Kelei Zhang. All rights reserved. High Balanced Biorthogonal Multiwavelets with Symmetry Mon, 10 Nov 2014 07:55:25 +0000 http://www.hindawi.com/journals/aaa/2014/154269/ Balanced multiwavelet transform can process the vector-valued data sparsely while preserving a polynomial signal. Yang et al. (2006) constructed balanced multiwavelets from the existing nonbalanced ones. It will be proved, however, in this paper that if the nonbalanced multiwavelets have antisymmetric component, it is impossible for the balanced multiwavelets by the method mentioned above to have symmetry. In this paper, we give an algorithm for constructing a pair of biorthogonal symmetric refinable function vectors from any orthogonal refinable function vector, which has symmetric and antisymmetric components. Then, a general scheme is given for high balanced biorthogonal multiwavelets with symmetry from the constructed pair of biorthogonal refinable function vectors. Moreover, we discuss the approximation orders of the biorthogonal symmetric refinable function vectors. An example is given to illustrate our results. Youfa Li, Shouzhi Yang, Yanfeng Shen, and Gengrong Zhang Copyright © 2014 Youfa Li et al. All rights reserved. New Periodic Solutions for the Singular Hamiltonian System Sun, 09 Nov 2014 07:56:18 +0000 http://www.hindawi.com/journals/aaa/2014/703539/ By use of the Cerami-Palais-Smale condition, we generalize the classical Weierstrass minimizing theorem to the singular case by allowing functions which attain infinity at some values. As an application, we study certain singular second-order Hamiltonian systems with strong force potential at the origin and show the existence of new periodic solutions with fixed periods. Yi Liao Copyright © 2014 Yi Liao. All rights reserved.