Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Positivity of Fundamental Matrix and Exponential Stability of Delay Differential System Thu, 28 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/490816/ The classical Wazewski theorem established that nonpositivity of all nondiagonal elements is necessary and sufficient for nonnegativity of the fundamental (Cauchy) matrix and consequently for applicability of the Chaplygin approach of approximate integration for system of linear ordinary differential equations Results on nonnegativity of the Cauchy matrix for system of delay differential equations which were based on nonpositivity of all diagonal elements, were presented in the previous works. Then examples, which demonstrated that nonpositivity of nondiagonal coefficients is not necessary for systems of delay equations, were found. In this paper first sufficient results about nonnegativity of the Cauchy matrix of the delay system without this assumption are proven. A necessary condition of nonnegativity of the Cauchy matrix is proposed. On the basis of these results on nonnegativity of the Cauchy matrix, necessary and sufficient conditions of the exponential stability of the delay system are obtained. Alexander Domoshnitsky, Roman Shklyar, Mikhail Gitman, and Valery Stolbov Copyright © 2014 Alexander Domoshnitsky et al. All rights reserved. Retracted: Three Homoclinic Solutions for Second-Order -Laplacian Differential System Wed, 27 Aug 2014 13:30:27 +0000 http://www.hindawi.com/journals/aaa/2014/798572/ Abstract and Applied Analysis Copyright © 2014 Abstract and Applied Analysis. All rights reserved. Generalized Stampacchia Vector Variational-Like Inequalities and Vector Optimization Problems Involving Set-Valued Maps Wed, 27 Aug 2014 12:02:34 +0000 http://www.hindawi.com/journals/aaa/2014/948270/ We first obtain that subdifferentials of set-valued mapping from finite-dimensional spaces to finite-dimensional possess certain relaxed compactness. Then using this weak compactness, we establish gap functions for generalized Stampacchia vector variational-like inequalities which are defined by means of subdifferentials. Finally, an existence result of generalized weakly efficient solutions for vector optimization problem involving a subdifferentiable and preinvex set-valued mapping is established by exploiting the existence of a solution for the weak formulation of the generalized Stampacchia vector variational-like inequality via a Fan-KKM lemma. Yanfei Chai, Sanyang Liu, and Guotao Wang Copyright © 2014 Yanfei Chai et al. All rights reserved. Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes Wed, 27 Aug 2014 11:15:42 +0000 http://www.hindawi.com/journals/aaa/2014/954658/ A higher order compact difference (HOC) scheme with uniform mesh sizes in different coordinate directions is employed to discretize a two- and three-dimensional Helmholtz equation. In case of two dimension, the stencil is of 9 points while in three-dimensional case, the scheme has 27 points and has fourth- to fifth-order accuracy. Multigrid method using Gauss-Seidel relaxation is designed to solve the resulting sparse linear systems. Numerical experiments were conducted to test the accuracy of the sixth-order compact difference scheme with Multigrid method and to compare it with the standard second-order finite-difference scheme and fourth-order compact difference scheme. Performance of the scheme is tested through numerical examples. Accuracy and efficiency of the new scheme are established by using the errors norms . Fazal Ghaffar, Noor Badshah, and Saeed Islam Copyright © 2014 Fazal Ghaffar et al. All rights reserved. Normal Form for High-Dimensional Nonlinear System and Its Application to a Viscoelastic Moving Belt Wed, 27 Aug 2014 09:11:59 +0000 http://www.hindawi.com/journals/aaa/2014/879564/ This paper is concerned with the computation of the normal form and its application to a viscoelastic moving belt. First, a new computation method is proposed for significantly refining the normal forms for high-dimensional nonlinear systems. The improved method is described in detail by analyzing the four-dimensional nonlinear dynamical systems whose Jacobian matrices evaluated at an equilibrium point contain three different cases, that are, (i) two pairs of pure imaginary eigenvalues, (ii) one nonsemisimple double zero and a pair of pure imaginary eigenvalues, and (iii) two nonsemisimple double zero eigenvalues. Then, three explicit formulae are derived, herein, which can be used to compute the coefficients of the normal form and the associated nonlinear transformation. Finally, employing the present method, we study the nonlinear oscillation of the viscoelastic moving belt under parametric excitations. The stability and bifurcation of the nonlinear vibration system are studied. Through the illustrative example, the feasibility and merit of this novel method are also demonstrated and discussed. S. P. Chen and Y. H. Qian Copyright © 2014 S. P. Chen and Y. H. Qian. All rights reserved. Solution of Several Functional Equations on Nonunital Semigroups Using Wilson’s Functional Equations with Involution Wed, 27 Aug 2014 09:09:54 +0000 http://www.hindawi.com/journals/aaa/2014/463918/ Let S be a nonunital commutative semigroup, an involution, and the set of complex numbers. In this paper, first we determine the general solutions of Wilson’s generalizations of d’Alembert’s functional equations   and on nonunital commutative semigroups, and then using the solutions of these equations we solve a number of other functional equations on more general domains. Jaeyoung Chung and Prasanna K. Sahoo Copyright © 2014 Jaeyoung Chung and Prasanna K. Sahoo. All rights reserved. Euler Polynomials and Combinatoric Convolution Sums of Divisor Functions with Even Indices Wed, 27 Aug 2014 07:59:51 +0000 http://www.hindawi.com/journals/aaa/2014/289187/ We study combinatoric convolution sums of certain divisor functions involving even indices. We express them as a linear combination of divisor functions and Euler polynomials and obtain identities , , and . As applications of these identities, we give several concrete interpretations in terms of the procedural modelling method. Daeyeoul Kim, Abdelmejid Bayad, and Joongsoo Park Copyright © 2014 Daeyeoul Kim et al. All rights reserved. An Illusion: “A Suzuki Type Coupled Fixed Point Theorem” Wed, 27 Aug 2014 07:53:08 +0000 http://www.hindawi.com/journals/aaa/2014/235731/ We admonish to be careful on studying coupled fixed point theorems since most of the reported fixed point results can be easily derived from the existing corresponding theorems in the literature. In particular, we notice that the recent paper [Semwal and Dimri (2014)] has gaps and the announced result is false. The authors claimed that their result generalized the main result in [Ðoric and Lazović (2011)] but, in fact, the contrary case is true. Finally, we present a fixed point theorem for Suzuki type (, r)-admissible contractions. Hamed H. Alsulami, Erdal Karapınar, Marwan A. Kutbi, and Antonio-Francisco Roldán-López-de-Hierro Copyright © 2014 Hamed H. Alsulami et al. All rights reserved. The Schur-Convexity of the Generalized Muirhead-Heronian Means Wed, 27 Aug 2014 07:50:26 +0000 http://www.hindawi.com/journals/aaa/2014/706518/ We give a unified generalization of the generalized Muirhead means and the generalized Heronian means involving three parameters. The Schur-convexity of the generalized Muirhead-Heronian means is investigated. Our main result implies the sufficient conditions of the Schur-convexity of the generalized Heronian means and the generalized Muirhead means. Yong-Ping Deng, Shan-He Wu, Yu-Ming Chu, and Deng He Copyright © 2014 Yong-Ping Deng et al. All rights reserved. A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition Wed, 27 Aug 2014 07:33:58 +0000 http://www.hindawi.com/journals/aaa/2014/384241/ As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns. Yafei Song, Xiaodan Wang, Lei Lei, and Aijun Xue Copyright © 2014 Yafei Song et al. All rights reserved. Periodic Solutions of Multispecies Mutualism System with Infinite Delays Wed, 27 Aug 2014 06:07:36 +0000 http://www.hindawi.com/journals/aaa/2014/127876/ We studied the delayed periodic mutualism system with Gilpin-Ayala effect. Some new and interesting sufficient conditions are obtained to guarantee the existence of periodic solution for the multispecies mutualism system with infinite delays. Our method is based on Mawhin's coincidence degree. To the best knowledge of the authors, there is no paper considering the existence of periodic solutions for n-species mutualism system with infinite delays. Wenbo Zhao, Caocuan Ma, Taotao Zheng, and Xiao-Ke Sun Copyright © 2014 Wenbo Zhao et al. All rights reserved. Numerical Reduced Variable Optimization Methods via Implicit Functional Dependence with Applications Wed, 27 Aug 2014 06:05:34 +0000 http://www.hindawi.com/journals/aaa/2014/108184/ A systematic theoretical basis is developed that optimizes an arbitrary number of variables for (i) modeling data and (ii) the determination of stationary points of a function of several variables by the optimization of an auxiliary function of a single variable deemed the most significant on physical, experimental or mathematical grounds from which all the other optimized variables may be derived. Algorithms that focus on a reduced variable set avoid problems associated with multiple minima and maxima that arise because of the large numbers of parameters. For (i), both approximate and exact methods are presented, where the single controlling variable k of all the other variables passes through the local stationary point of the least squares metric. For (ii), an exact theory is developed whereby the solution of the optimized function of an independent variation of all parameters coincides with that due to single parameter optimization of an auxiliary function. The implicit function theorem has to be further qualified to arrive at this result. A nontrivial real world application of the above implicit methodology to rate constant and final concentration parameter determination is made to illustrate its utility. This work is more general than the reduction schemes for conditional linear parameters since it covers the nonconditional case as well and has potentially wide applicability. Christopher Gunaseelan Jesudason Copyright © 2014 Christopher Gunaseelan Jesudason. All rights reserved. An Efficient Computation of Effective Ground Range Using an Oblate Earth Model Wed, 27 Aug 2014 05:58:05 +0000 http://www.hindawi.com/journals/aaa/2014/459790/ An effcient method is presented to calculate the ground range of a ballistic missile trajectory on a nonrotating Earth. The spherical Earth model does not provide good approximation of distance between two locations on the surface of Earth. We used oblate spheroid Earth model because it provides better approximations. The effective ground range of a ballistic missile is an arc-length of a planner elliptic (or circle) curve which passes through the launch and target points on the surface of Earth model. A general formulation is presented to calculate the arc-length of an elliptic (or circle) curve which is the intersection of oblate Earth model and a plane. Explicit formulas are developed to calculate the coordinates of center of the ellipse as well as major and minor axes which are necessary ingredients for the calculation of effective ground range. Dalal A. Maturi, Malik Zaka Ullah, Shahid Ahmad, and Fayyaz Ahmad Copyright © 2014 Dalal A. Maturi et al. All rights reserved. On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications Wed, 27 Aug 2014 05:52:39 +0000 http://www.hindawi.com/journals/aaa/2014/795456/ Some new weakly singular versions of discrete nonlinear inequalities are established, which generalize some existing weakly singular inequalities and can be used in the analysis of nonlinear Volterra type difference equations with weakly singular kernels. A few applications to the upper bound and the uniqueness of solutions of nonlinear difference equations are also involved. Kelong Cheng, Chunxiang Guo, and Qingke Zeng Copyright © 2014 Kelong Cheng et al. All rights reserved. On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature Rules Wed, 27 Aug 2014 05:47:37 +0000 http://www.hindawi.com/journals/aaa/2014/436164/ Based upon the fast computation of the coefficients of the interpolation polynomials at Chebyshev-type points by FFT, together with the efficient evaluation of the modified moments by forward recursions or by Oliver’s algorithms, this paper presents fast and stable interpolating integration algorithms, by using the coefficients and modified moments, for Clenshaw-Curtis, Fejér’s first- and second-type rules for Jacobi weights or Jacobi weights multiplied by a logarithmic function. Numerical examples illustrate the stability, efficiency, and accuracy of these quadratures. Shuhuang Xiang, Guo He, and Haiyong Wang Copyright © 2014 Shuhuang Xiang et al. All rights reserved. A Numerical Method for Computing the Principal Square Root of a Matrix Wed, 27 Aug 2014 05:46:15 +0000 http://www.hindawi.com/journals/aaa/2014/525087/ It is shown how the mid-point iterative method with cubical rate of convergence can be applied for finding the principal matrix square root. Using an identity between matrix sign function and matrix square root, we construct a variant of mid-point method which is asymptotically stable in the neighborhood of the solution. Finally, application of the presented approach is illustrated in solving a matrix differential equation. F. Soleymani, S. Shateyi, and F. Khaksar Haghani Copyright © 2014 F. Soleymani et al. All rights reserved. Precise Asymptotics on Second-Order Complete Moment Convergence of Uniform Empirical Process Wed, 27 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/143581/ Let be a sequence of iid U[0, 1]-distributed random variables, and define the uniform empirical process , . When the nonnegative function satisfies some regular monotone conditions, it proves that . Junshan Xie and Lin He Copyright © 2014 Junshan Xie and Lin He. All rights reserved. The Iteration Solution of Matrix Equation Subject to a Linear Matrix Inequality Constraint Wed, 27 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/705830/ We propose a feasible and effective iteration method to find solutions to the matrix equation subject to a matrix inequality constraint , where means that the matrix is nonnegative. And the global convergence results are obtained. Some numerical results are reported to illustrate the applicability of the method. Na Huang and Changfeng Ma Copyright © 2014 Na Huang and Changfeng Ma. All rights reserved. Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems Wed, 27 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/350682/ In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples. Neng Wan, Ke Du, Tao Chen, Sentang Zhang, and Gongnan Xie Copyright © 2014 Neng Wan et al. All rights reserved. The Existence of Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equations Wed, 27 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/681513/ We consider the existence of positive solutions for the nonlinear fractional differential equations boundary value problem where is a real number, is the Riemann-Liouville fractional derivative of order , and is a given continuous function. Our analysis relies on the fixed point index theory in cones. Yanli Chen and Yongxiang Li Copyright © 2014 Yanli Chen and Yongxiang Li. All rights reserved. Nonlinear Time-Delay Suspension Adaptive Neural Network Active Control Wed, 27 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/765871/ Considering the time-delay in control input channel and the nonlinear spring stiffness characteristics of suspension, a quarter-vehicle magneto rheological active suspension nonlinear model with time-delay is established in this paper. Based on the time-delay nonlinear model, an adaptive neural network structure for magneto rheological active suspension is presented. By recognizing and training the adaptive neural network, the adaptive neural network active suspension controller is obtained. Simulation results show that the presented method can guarantee that the quarter-vehicle magneto rheological active suspension system has satisfying performance on the E_level very poor ground. Yue Zhu and Sihong Zhu Copyright © 2014 Yue Zhu and Sihong Zhu. All rights reserved. Krasnosel’skii Type Hybrid Fixed Point Theorems and Their Applications to Fractional Integral Equations Wed, 27 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/710746/ Some hybrid fixed point theorems of Krasnosel’skii type, which involve product of two operators, are proved in partially ordered normed linear spaces. These hybrid fixed point theorems are then applied to fractional integral equations for proving the existence of solutions under certain monotonicity conditions blending with the existence of the upper or lower solution. H. M. Srivastava, Sachin V. Bedre, S. M. Khairnar, and B. S. Desale Copyright © 2014 H. M. Srivastava et al. All rights reserved. Predictive Compensation for Wireless Networked System with Time Delay and Packet Dropout Based on T-S Model Tue, 26 Aug 2014 12:25:33 +0000 http://www.hindawi.com/journals/aaa/2014/953039/ Based on the T-S model, a predictive compensation scheme including timer and counter for wireless networked system with long time delay and data packet dropout is proposed in this paper. By the separation principle, the state observation predictor and the state feedback controller are designed separately. For the case of fixed delay, the stability of the closed-loop networked control systems is discussed. Simulation by inverted pendulum system illustrates the effectiveness of the proposed method in wireless networked system based on T-S model. Le Wang, Haipeng Pan, Jinfeng Gao, and Dongdong Chen Copyright © 2014 Le Wang et al. All rights reserved. Algorithms for Finding Inverse of Two Patterned Matrices over Tue, 26 Aug 2014 11:20:21 +0000 http://www.hindawi.com/journals/aaa/2014/840435/ Circulant matrix families have become an important tool in network engineering. In this paper, two new patterned matrices over which include row skew first-plus-last right circulant matrix and row first-plus-last left circulant matrix are presented. Their basic properties are discussed. Based on Newton-Hensel lifting and Chinese remaindering, two different algorithms are obtained. Moreover, the cost in terms of bit operations for each algorithm is given. Xiaoyu Jiang and Kicheon Hong Copyright © 2014 Xiaoyu Jiang and Kicheon Hong. All rights reserved. Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function in Spaces Tue, 26 Aug 2014 11:18:45 +0000 http://www.hindawi.com/journals/aaa/2014/621857/ One-weight inequalities with general weights for Riemann-Liouville transform and -dimensional fractional integral operator in variable exponent Lebesgue spaces defined on are investigated. In particular, we derive necessary and sufficient conditions governing one-weight inequalities for these operators on the cone of nonnegative decreasing functions in spaces. Muhammad Sarwar, Ghulam Murtaza, and Irshaad Ahmed Copyright © 2014 Muhammad Sarwar et al. All rights reserved. Safe Control for Spiral Recovery of Unmanned Aerial Vehicle Tue, 26 Aug 2014 09:35:08 +0000 http://www.hindawi.com/journals/aaa/2014/983624/ With unmanned aerial vehicles (UAVs) widely used in both military and civilian fields, many events affecting their safe flying have emerged. That UAV’s entering into the spiral is such a typical safety issue. To solve this safety problem, a novel recovery control approach is proposed. First, the factors of spiral are analyzed. Then, based on control scheduling of state variables and nonlinear dynamic inversion control laws, the spiral recovery controller is designed to accomplish guidance and control of spiral recovery. Finally, the simulation results have illustrated that the proposed control method can ensure the UAV autonomous recovery from spiral effectively. Chang-Jian Ru and Rui-Xuan Wei Copyright © 2014 Chang-Jian Ru and Rui-Xuan Wei. All rights reserved. Super-Hamiltonian Structures and Conservation Laws of a New Six-Component Super-Ablowitz-Kaup-Newell-Segur Hierarchy Wed, 20 Aug 2014 07:59:29 +0000 http://www.hindawi.com/journals/aaa/2014/214709/ A six-component super-Ablowitz-Kaup-Newell-Segur (-AKNS) hierarchy is proposed by the zero curvature equation associated with Lie superalgebras. Supertrace identity is used to furnish the super-Hamiltonian structures for the resulting nonlinear superintegrable hierarchy. Furthermore, we derive the infinite conservation laws of the first two nonlinear super-AKNS equations in the hierarchy by utilizing spectral parameter expansions. PACS: 02.30.Ik; 02.30.Jr; 02.20.Sv. Fucai You, Jiao Zhang, and Yan Zhao Copyright © 2014 Fucai You et al. All rights reserved. Strong Convergence of the Split-Step Theta Method for Stochastic Delay Differential Equations with Nonglobally Lipschitz Continuous Coefficients Wed, 20 Aug 2014 07:09:09 +0000 http://www.hindawi.com/journals/aaa/2014/157498/ This paper is concerned with the convergence analysis of numerical methods for stochastic delay differential equations. We consider the split-step theta method for nonlinear nonautonomous equations and prove the strong convergence of the numerical solution under a local Lipschitz condition and a coupled condition on the drift and diffusion coefficients. In particular, these conditions admit that the diffusion coefficient is highly nonlinear. Furthermore, the obtained results are supported by numerical experiments. Chao Yue and Chengming Huang Copyright © 2014 Chao Yue and Chengming Huang. All rights reserved. Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative Wed, 20 Aug 2014 06:03:43 +0000 http://www.hindawi.com/journals/aaa/2014/283019/ An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented. The order of the derivative is considered as , for the space and time domain, respectively. The fractional derivative of Caputo type is considered. In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case. In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form. In order that the equation preserves the physical units of the system two auxiliary parameters and are introduced characterizing the existence of fractional space and time components, respectively. A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parameters and . The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior. José Francisco Gómez Aguilar and Margarita Miranda Hernández Copyright © 2014 José Francisco Gómez Aguilar and Margarita Miranda Hernández. All rights reserved. Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation Wed, 20 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/178672/ The regularization of the shock wave solution to the Riemann problem for the relativistic Burgers equation is considered. For Riemann initial data consisting of a single decreasing jump, we find that the regularization of nonlinear convective term cannot capture the correct shock wave solution. In order to overcome it, we consider a new regularization technique called the observable divergence method introduced by Mohseni and discover that it can capture the correct shock wave solution. In addition, we take the Helmholtz filter for the fully explicit computation. Ting Zhang and Chun Shen Copyright © 2014 Ting Zhang and Chun Shen. All rights reserved.