Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . 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. The Generalized Projective Riccati Equations Method for Solving Nonlinear Evolution Equations in Mathematical Physics Thu, 06 Nov 2014 12:55:52 +0000 http://www.hindawi.com/journals/aaa/2014/259190/ We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics. E. M. E. Zayed and K. A. E. Alurrfi Copyright © 2014 E. M. E. Zayed and K. A. E. Alurrfi. All rights reserved. The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems Thu, 06 Nov 2014 11:44:20 +0000 http://www.hindawi.com/journals/aaa/2014/469587/ We investigate the stochastic linear complementarity problem affinely affected by the uncertain parameters. Assuming that we have only limited information about the uncertain parameters, such as the first two moments or the first two moments as well as the support of the distribution, we formulate the stochastic linear complementarity problem as a distributionally robust optimization reformation which minimizes the worst case of an expected complementarity measure with nonnegativity constraints and a distributionally robust joint chance constraint representing that the probability of the linear mapping being nonnegative is not less than a given probability level. Applying the cone dual theory and S-procedure, we show that the distributionally robust counterpart of the uncertain complementarity problem can be conservatively approximated by the optimization with bilinear matrix inequalities. Preliminary numerical results show that a solution of our method is desirable. Liyan Xu, Bo Yu, and Wei Liu Copyright © 2014 Liyan Xu et al. All rights reserved. A Series Solution for Heat Conduction Problem with Phase Change in a Finite Slab Tue, 04 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/684293/ A two-dimensional differential transform method is applied to solve one-dimensional phase change problems in a slab of finite thickness, which is subjected to convective thermal loading at one surface and a constant prescribed temperature at the other. In the problems, the initial temperature of the slab does not necessarily have to be the same as the fusion temperature. A series solution is derived for the temperature profile in the melting or solidifying slab with temperature-dependent thermal conductivity and volumetric heat capacity. The latent heat effect of the phase change is incorporated into the temperature-dependent heat capacity. Numerical results demonstrate the effects of the temperature-dependent parameters on the transient temperature profile of the slab. Ryoichi Chiba Copyright © 2014 Ryoichi Chiba. All rights reserved. Positive Solutions for -Type Singular Fractional Differential System with Coupled Integral Boundary Conditions Mon, 03 Nov 2014 09:08:18 +0000 http://www.hindawi.com/journals/aaa/2014/142391/ We study the positive solutions of the -type fractional differential system with coupled integral boundary conditions. The conditions for the existence of positive solutions to the system are established. In addition, we derive explicit formulae for the estimation of the positive solutions and obtain the unique positive solution when certain additional conditions hold. An example is then given to demonstrate the validity of our main results. Ying Wang, Lishan Liu, Xinguang Zhang, and Yonghong Wu Copyright © 2014 Ying Wang et al. All rights reserved. Semicontinuity of the Solution Mapping to a Parametric Generalized Weak Ky Fan Inequality Mon, 03 Nov 2014 09:07:35 +0000 http://www.hindawi.com/journals/aaa/2014/451521/ Under new assumptions, which do not contain any information about the solution set, the upper and lower semicontinuity of the solution mapping to a class of parametric generalized weak Ky Fan inequality are established by using a nonlinear scalarization technique. These results extend and improve the recent ones in the literature. Some examples are given to illustrate our results. Y. D. Xu Copyright © 2014 Y. D. Xu. All rights reserved. On Perturbations of Generators of -Semigroups Thu, 30 Oct 2014 09:27:32 +0000 http://www.hindawi.com/journals/aaa/2014/213020/ We present a perturbation result for generators of -semigroups which can be considered as an operator theoretic version of the Weiss-Staffans perturbation theorem for abstract linear systems. The results are illustrated by applications to the Desch-Schappacher and the Miyadera-Voigt perturbation theorems and to unbounded perturbations of the boundary conditions of a generator. Martin Adler, Miriam Bombieri, and Klaus-Jochen Engel Copyright © 2014 Martin Adler et al. All rights reserved. Agent-Based Model to Study and Quantify the Evolution Dynamics of Android Malware Infection Tue, 28 Oct 2014 11:40:14 +0000 http://www.hindawi.com/journals/aaa/2014/623436/ In the last years the number of malware Apps that the users download to their devices has risen. In this paper, we propose an agent-based model to quantify the Android malware infection evolution, modeling the behavior of the users and the different markets where the users may download Apps. The model predicts the number of infected smartphones depending on the type of malware. Additionally, we will estimate the cost that the users should afford when the malware is in their devices. We will be able to analyze which part is more critical: the users, giving indiscriminate permissions to the Apps or not protecting their devices with antivirus software, or the Android platform, due to the vulnerabilities of the Android devices that permit their rooted. We focus on the community of Valencia, Spain, although the obtained results can be extrapolated to other places where the number of Android smartphones remains fairly stable. Juan Alegre-Sanahuja, Javier Camacho, Juan Carlos Cortés López, Francisco-José Santonja, and Rafael Jacinto Villanueva Micó Copyright © 2014 Juan Alegre-Sanahuja et al. All rights reserved. Strong Convergence of Modified Algorithms Based on the Regularization for the Constrained Convex Minimization Problem Tue, 28 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/870102/ As is known, the regularization method plays an important role in solving constrained convex minimization problems. Based on the idea of regularization, implicit and explicit iterative algorithms are proposed in this paper and the sequences generated by the algorithms can converge strongly to a solution of the constrained convex minimization problem, which also solves a certain variational inequality. As an application, we also apply the algorithm to solve the split feasibility problem. Ming Tian and Jun-Ying Gong Copyright © 2014 Ming Tian and Jun-Ying Gong. All rights reserved.