Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Windowed Fourier Frames to Approximate Two-Point Boundary Value Problems Mon, 26 Jan 2015 09:20:57 +0000 http://www.hindawi.com/journals/aaa/2015/153010/ Boundary value problems arise while modeling various physical and engineering reality. In this communication we investigate windowed Fourier frames focusing two-point BVPs. We approximate BVPs using windowed Fourier frames. We present some numerical results to demonstrate the efficiency of such frame functions to approximate BVPs. Abdullah Aljouiee and Samir Kumar Bhowmik Copyright © 2015 Abdullah Aljouiee and Samir Kumar Bhowmik. All rights reserved. Eigenvalues of Vectorial Sturm-Liouville Problems with Parameter Dependent Boundary Conditions Mon, 26 Jan 2015 07:34:01 +0000 http://www.hindawi.com/journals/aaa/2015/796086/ We generalize the regularized sampling method introduced in 2005 by the author to compute the eigenvalues of scalar Sturm-Liouville problems (SLPs) to the case of vectorial SLP with parameter dependent boundary conditions. A few problems are worked out to illustrate the effectiveness of the method and show by the same token that we have indeed a general method capable of handling with ease very broad classes of SLPs, whether scalar or vectorial. Bilal Chanane Copyright © 2015 Bilal Chanane. All rights reserved. Analysis of a Fractal Boundary: The Graph of the Knopp Function Thu, 22 Jan 2015 13:07:45 +0000 http://www.hindawi.com/journals/aaa/2015/587347/ A usual classification tool to study a fractal interface is the computation of its fractal dimension. But a recent method developed by Y. Heurteaux and S. Jaffard proposes to compute either weak and strong accessibility exponents or local regularity exponents (the so-called p-exponent). These exponents describe locally the behavior of the interface. We apply this method to the graph of the Knopp function which is defined for as , where and . The Knopp function itself has everywhere the same p-exponent . Nevertheless, using the characterization of the maxima and minima done by B. Dubuc and S. Dubuc, we will compute the p-exponent of the characteristic function of the domain under the graph of F at each point and show that p-exponents, weak and strong accessibility exponents, change from point to point. Furthermore we will derive a characterization of the local extrema of the function according to the values of these exponents. Mourad Ben Slimane and Clothilde Mélot Copyright © 2015 Mourad Ben Slimane and Clothilde Mélot. All rights reserved. Variational Analysis, Optimization, and Fixed Point Theory 2014 Mon, 19 Jan 2015 12:45:34 +0000 http://www.hindawi.com/journals/aaa/2015/312823/ Jen-Chih Yao, Abdul Latif, Chong Li, and Adrian Petrusel Copyright © 2015 Jen-Chih Yao et al. All rights reserved. -Solvability of the Dirichlet Problem for Elliptic Equations with Singular Data Mon, 19 Jan 2015 12:43:45 +0000 http://www.hindawi.com/journals/aaa/2015/635035/ We give an overview on some results concerning the unique solvability of the Dirichlet problem in , , for second-order linear elliptic partial differential equations in nondivergence form and with singular data in weighted Sobolev spaces. We also extend such results to the planar case. Loredana Caso, Roberta D’Ambrosio, and Maria Transirico Copyright © 2015 Loredana Caso et al. All rights reserved. Sharp Power Mean Bounds for Sándor Mean Thu, 15 Jan 2015 07:58:35 +0000 http://www.hindawi.com/journals/aaa/2015/172867/ We prove that the double inequality holds for all with if and only if and …, where and are the Sándor and th power means of and , respectively. Yu-Ming Chu, Zhen-Hang Yang, and Li-Min Wu Copyright © 2015 Yu-Ming Chu et al. All rights reserved. An Obstacle Problem for Noncoercive Operators Thu, 15 Jan 2015 07:13:37 +0000 http://www.hindawi.com/journals/aaa/2015/890289/ We study the obstacle problem for second order nonlinear equations whose model appears in the stationary diffusion-convection problem. We assume that the growth coefficient of the convection term lies in the Marcinkiewicz space -. Luigi Greco, Gioconda Moscariello, and Gabriella Zecca Copyright © 2015 Luigi Greco et al. All rights reserved. VanderLaan Circulant Type Matrices Thu, 15 Jan 2015 06:29:37 +0000 http://www.hindawi.com/journals/aaa/2015/329329/ Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, and -circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The exact determinants of VanderLaan circulant type matrices are given by structuring transformation matrices, determinants of well-known tridiagonal matrices, and tridiagonal-like matrices. The explicit inverse matrices of these special matrices are obtained by structuring transformation matrices, inverses of known tridiagonal matrices, and quasi-tridiagonal matrices. Three kinds of norms and lower bound for the spread of VanderLaan circulant and left circulant matrix are given separately. And we gain the spectral norm of VanderLaan -circulant matrix. Hongyan Pan and Zhaolin Jiang Copyright © 2015 Hongyan Pan and Zhaolin Jiang. All rights reserved. Solving Delay Differential Equations by an Accurate Method with Interpolation Wed, 14 Jan 2015 14:32:35 +0000 http://www.hindawi.com/journals/aaa/2015/676939/ We use the reproducing kernel method (RKM) with interpolation for finding approximate solutions of delay differential equations. Interpolation for delay differential equations has not been used by this method till now. The numerical approximation to the exact solution is computed. The comparison of the results with exact ones is made to confirm the validity and efficiency. Ali Akgül and Adem Kiliçman Copyright © 2015 Ali Akgül and Adem Kiliçman. All rights reserved. Attracting and Quasi-Invariant Sets of Cohen-Grossberg Neural Networks with Time Delay in the Leakage Term under Impulsive Perturbations Wed, 14 Jan 2015 06:56:58 +0000 http://www.hindawi.com/journals/aaa/2015/491801/ A class of impulsive Cohen-Grossberg neural networks with time delay in the leakage term is investigated. By using the method of -matrix and the technique of delay differential inequality, the attracting and invariant sets of the networks are obtained. The results in this paper extend and improve the earlier publications. An example is presented to illustrate the effectiveness of our conclusion. Guiying Chen and Linshan Wang Copyright © 2015 Guiying Chen and Linshan Wang. All rights reserved. New Trends on Fractional and Functional Differential Equations Tue, 13 Jan 2015 08:29:29 +0000 http://www.hindawi.com/journals/aaa/2015/635714/ Dumitru Baleanu, Ali H. Bhrawy, and Robert A. Van Gorder Copyright © 2015 Dumitru Baleanu et al. All rights reserved. Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators Mon, 12 Jan 2015 13:01:08 +0000 http://www.hindawi.com/journals/aaa/2015/263748/ We consider the following state dependent boundary-value problem , ; , where is the standard Riemann-Liouville fractional derivative of order , , , , the function is defined as , and the function is defined as , are continuous on and , . Using Banach contraction mapping principle and Leray-Schauder continuation principle, we obtain some sufficient conditions for the existence and uniqueness of the positive solutions for the above fractional order differential equations, which extend some references. Dongyuan Liu, Zigen Ouyang, and Huilan Wang Copyright © 2015 Dongyuan Liu et al. All rights reserved. Analysis of Iterative Learning Control for a Class of Linear Discrete-Time Switched Systems Sun, 11 Jan 2015 14:15:12 +0000 http://www.hindawi.com/journals/aaa/2015/464175/ An iterative learning control scheme is applied to a class of linear discrete-time switched systems with arbitrary switching rules. The application is based on the assumption that the switched system repetitively operates over a finite time interval. By taking advantage of the super vector approach, convergence is discussed when noise is free and robustness is analyzed when the controlled system is disturbed by bounded noise. The analytical results manifest that the iterative learning control algorithm is feasible and effective for the linear switched system. To support the theoretical analysis, numerical simulations are made. Xuan Yang and Xiaoe Ruan Copyright © 2015 Xuan Yang and Xiaoe Ruan. All rights reserved. Imperative Remarks for “On Common Coupled Fixed Point Theorems for Comparable Mappings in Ordered Partially Metric Spaces” and an Answer to the Question: How to Smooth It Away Mon, 05 Jan 2015 13:44:50 +0000 http://www.hindawi.com/journals/aaa/2015/730268/ We show that the main result in the work by Mutlu et al. is not true. We explain point by point some of its main mistakes and we propose an alternative version to smooth away the defects of it. Hamed H. Alsulami, Erdal Karapınar, and Antonio Francisco Roldán Lόpez de Hierro Copyright © 2015 Hamed H. Alsulami et al. All rights reserved. A Coincidence Best Proximity Point Problem in -Metric Spaces Mon, 05 Jan 2015 13:40:11 +0000 http://www.hindawi.com/journals/aaa/2015/243753/ The aim of this paper is to initiate the study of coincidence best proximity point problem in the setup of generalized metric spaces. Some results dealing with existence and uniqueness of a coincidence best proximity point of mappings satisfying certain contractive conditions in such spaces are obtained. An example is provided to support the result proved herein. Our results generalize, extend, and unify various results in the existing literature. M. Abbas, A. Hussain, and P. Kumam Copyright © 2015 M. Abbas et al. All rights reserved. Erratum to “Influence of Removable Devices’ Heterouse on the Propagation of Malware” Mon, 05 Jan 2015 13:11:07 +0000 http://www.hindawi.com/journals/aaa/2015/379532/ Xie Han, Yi-Hong Li, Li-Ping Feng, and Li-Peng Song Copyright © 2015 Xie Han et al. All rights reserved. On the Riesz Basisness of Systems Composed of Root Functions of Periodic Boundary Value Problems Thu, 01 Jan 2015 10:12:12 +0000 http://www.hindawi.com/journals/aaa/2015/945049/ We consider the nonself-adjoint Sturm-Liouville operator with and either periodic or antiperiodic boundary conditions. We obtain necessary and sufficient conditions for systems of root functions of these operators to be a Riesz basis in in terms of the Fourier coefficients of . Alp Arslan Kıraç Copyright © 2015 Alp Arslan Kıraç. All rights reserved. Uncertain Dynamical Systems 2014 Wed, 31 Dec 2014 13:46:19 +0000 http://www.hindawi.com/journals/aaa/2014/746741/ Ivanka Stamova, Haydar Akca, and Gani Stamov Copyright © 2014 Ivanka Stamova et al. All rights reserved. Z Specification of Gate and Apron Control Management at Airport Wed, 31 Dec 2014 06:29:19 +0000 http://www.hindawi.com/journals/aaa/2014/530619/ Modelling of an air traffic control (ATC) system is an open issue and has become a challenging problem due to its complexity and increase of traffic at airports and in airspace. Consequently, automated ATC systems are suggested to improve efficiency ensuring the safety standards. It is reported that the number of collisions that occurred at airports surface is three times larger than in airspace. Further, it is observed that gates and aprons congestions cause significant delays at airports; hence, effective monitoring and guidance mechanisms are required to control ground air traffic. In this paper, formal procedure of managing air traffic from gate to enter in the active area of airport for taxiing is provided using Z notation. An integration of gate and apron controllers is described to manipulate the information for correct decision making and flow management. Graph theory is used for representation of airport topology and appropriate routs. In static part of the model, safety properties are described in terms of invariants over the critical data types. In dynamic model, the state space is updated by defining pre- and postconditions ensuring the safety. Formal specification is analysed using Z/Eves tool. Nazir Ahmad Zafar, Fahad Alhumaidan, and Sher Afzal Khan Copyright © 2014 Nazir Ahmad Zafar et al. All rights reserved. Erratum to “Local Fractional Functional Method for Solving Diffusion Equations on Cantor Sets” Thu, 25 Dec 2014 00:10:34 +0000 http://www.hindawi.com/journals/aaa/2014/249298/ Yuan Cao, Wei-Gang Ma, and Lian-Chuan Ma Copyright © 2014 Yuan Cao et al. All rights reserved. Iterative Fixed-Point Methods for Solving Nonlinear Problems: Dynamics and Applications Wed, 24 Dec 2014 13:07:38 +0000 http://www.hindawi.com/journals/aaa/2014/313061/ Juan R. Torregrosa, Alicia Cordero, Vinay Kanwar, and Jisheng Kou Copyright © 2014 Juan R. Torregrosa et al. All rights reserved. Convergence of Infinite Family of Multivalued Quasi-Nonexpansive Mappings Using Multistep Iterative Processes Wed, 24 Dec 2014 09:10:35 +0000 http://www.hindawi.com/journals/aaa/2014/781704/ We prove strong and weak convergence results using multistep iterative sequences for countable family of multivalued quasi-nonexpansive mappings by using some conditions in uniformly convex real Banach space. The results presented extended and improved the corresponding result of Zhang et al. (2013), Bunyawat and Suantai (2012), and some others from finite family, one countable family, and two countable families to -number of countable families of multivalued quasi-nonexpansive mappings. Also we used a numerical example in C++ computational programs to prove that the iterative scheme we used has better rate of convergence than other existing iterative schemes. Renu Chugh and Sanjay Kumar Copyright © 2014 Renu Chugh and Sanjay Kumar. All rights reserved. Study of a Biparametric Family of Iterative Methods Wed, 24 Dec 2014 06:42:26 +0000 http://www.hindawi.com/journals/aaa/2014/141643/ The dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the -iterative methods and the well-known Chebyshev-Halley family. We find the analytical expressions for the fixed and critical points by solving 6-degree polynomials. We use the free critical points to get the parameter planes and, by observing them, we specify some values of with clear stable and unstable behaviors. B. Campos, A. Cordero, Á. A. Magreñán, J. R. Torregrosa, and P. Vindel Copyright © 2014 B. Campos et al. All rights reserved. Integrable Couplings: Generation, Hamiltonian Structures, Conservation Laws, and Applications Wed, 24 Dec 2014 06:30:09 +0000 http://www.hindawi.com/journals/aaa/2014/356350/ Huanhe Dong, Wen-Xiu Ma, Yufeng Zhang, and Tingting Chen Copyright © 2014 Huanhe Dong et al. All rights reserved. Existence and Algorithm for the Systems of Hierarchical Variational Inclusion Problems Tue, 23 Dec 2014 14:11:37 +0000 http://www.hindawi.com/journals/aaa/2014/589679/ We study the existence and approximation of a solution for a system of hierarchical variational inclusion problems in Hilbert spaces. In this study, we use Maingé’s approach for finding the solutions of the system of hierarchical variational inclusion problems. Our result in this paper improves and generalizes some known corresponding results in the literature. Nopparat Wairojjana and Poom Kumam Copyright © 2014 Nopparat Wairojjana and Poom Kumam. All rights reserved. Approximation Theory and Numerical Analysis Mon, 22 Dec 2014 12:40:09 +0000 http://www.hindawi.com/journals/aaa/2014/390983/ Sofiya Ostrovska, Elena Berdysheva, Grzegorz Nowak, and Ahmet Yaşar Özban Copyright © 2014 Sofiya Ostrovska et al. All rights reserved. Finite-Time Control and Estimation for Complex and Practical Dynamical Systems Mon, 22 Dec 2014 12:29:38 +0000 http://www.hindawi.com/journals/aaa/2014/369328/ Hui Zhang, Junmin Wang, Hamid Reza Karimi, Peng Shi, and Zexu Zhang Copyright © 2014 Hui Zhang et al. All rights reserved. Recent Advances in Symmetry Groups and Conservation Laws for Partial Differential Equations and Applications Mon, 22 Dec 2014 12:22:42 +0000 http://www.hindawi.com/journals/aaa/2014/457145/ Maria Gandarias, Mariano Torrisi, Maria Bruzón, Rita Tracinà, and Chaudry Masood Khalique Copyright © 2014 Maria Gandarias et al. All rights reserved. Fuzzy Linear and Nonlinear Integral Equations: Numerical Methods Mon, 22 Dec 2014 12:05:26 +0000 http://www.hindawi.com/journals/aaa/2014/147351/ Reza Ezzati, Soheil Salahshour, Ronald R. Yager, and Morteza Khodabin Copyright © 2014 Reza Ezzati et al. All rights reserved. Advanced Nonlinear Dynamics of Population Biology and Epidemiology Mon, 22 Dec 2014 12:01:47 +0000 http://www.hindawi.com/journals/aaa/2014/214514/ Weiming Wang, Yun Kang, Malay Banerjee, and Kaifa Wang Copyright © 2014 Weiming Wang et al. All rights reserved.