Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Positivity, Betweenness, and Strictness of Operator Means Sun, 24 May 2015 12:14:36 +0000 http://www.hindawi.com/journals/aaa/2015/851568/ An operator mean is a binary operation assigned to each pair of positive operators satisfying monotonicity, continuity from above, the transformer inequality, and the fixed-point property. It is well known that there are one-to-one correspondences between operator means, operator monotone functions, and Borel measures. In this paper, we provide various characterizations for the concepts of positivity, betweenness, and strictness of operator means in terms of operator inequalities, operator monotone functions, Borel measures, and certain operator equations. Pattrawut Chansangiam Copyright © 2015 Pattrawut Chansangiam. All rights reserved. Semiglobal Finite-Time Synchronization of Complex Dynamical Networks via Periodically Intermittent Control Wed, 20 May 2015 07:31:46 +0000 http://www.hindawi.com/journals/aaa/2015/381078/ This paper studies the finite-time synchronization problem for a class of complex dynamical networks by means of periodically intermittent control. Based on some analysis techniques and finite-time stability theory, some novel and effective finite-time synchronization criteria are given in terms of a set of linear matrix inequalities. Particularly, the previous synchronization problem by using periodically intermittent control has been extended in this paper. Finally, numerical simulations are presented to verify the theoretical results. Yihan Fan, Hongmei Liu, and Jun Mei Copyright © 2015 Yihan Fan et al. All rights reserved. A Cubic Set Theoretical Approach to Linear Space Wed, 13 May 2015 11:46:53 +0000 http://www.hindawi.com/journals/aaa/2015/523129/ The main motivation of this paper is to introduce the notion of cubic linear space. This inspiration is received from the structure of cubic sets. The notions of R-intersection, R-union, P-intersection, and P-union of cubic linear spaces are defined and we provide some results on these. We further introduce the notion of internal cubic linear space and external cubic linear space and establish some results on them. S. Vijayabalaji and S. Sivaramakrishnan Copyright © 2015 S. Vijayabalaji and S. Sivaramakrishnan. All rights reserved. Quantitative Estimates for Positive Linear Operators in terms of the Usual Second Modulus Mon, 11 May 2015 12:02:23 +0000 http://www.hindawi.com/journals/aaa/2015/915358/ We give accurate estimates of the constants appearing in direct inequalities of the form   , , ,  and   where is a positive linear operator reproducing linear functions and acting on real functions defined on the interval , is a certain subset of such functions, is the usual second modulus of , and is an appropriate weight function. We show that the size of the constants mainly depends on the degree of smoothness of the functions in the set and on the distance from the point to the boundary of . We give a closed form expression for the best constant when is a certain set of continuous piecewise linear functions. As illustrative examples, the Szàsz-Mirakyan operators and the Bernstein polynomials are discussed. José A. Adell and A. Lekuona Copyright © 2015 José A. Adell and A. Lekuona. All rights reserved. Analysis of Water Hammer with Different Closing Valve Laws on Transient Flow of Hydrogen-Natural Gas Mixture Wed, 06 May 2015 09:46:30 +0000 http://www.hindawi.com/journals/aaa/2015/510675/ Water hammer on transient flow of hydrogen-natural gas mixture in a horizontal pipeline is analysed to determine the relationship between pressure waves and different modes of closing and opening of valves. Four types of laws applicable to closing valve, namely, instantaneous, linear, concave, and convex laws, are considered. These closure laws describe the speed variation of the hydrogen-natural gas mixture as the valve is closing. The numerical solution is obtained using the reduced order modelling technique. The results show that changes in the pressure wave profile and amplitude depend on the type of closing laws, valve closure times, and the number of polygonal segments in the closing function. The pressure wave profile varies from square to triangular and trapezoidal shape depending on the type of closing laws, while the amplitude of pressure waves reduces as the closing time is reduced and the numbers of polygonal segments are increased. The instantaneous and convex closing laws give rise to minimum and maximum pressure, respectively. Norazlina Subani and Norsarahaida Amin Copyright © 2015 Norazlina Subani and Norsarahaida Amin. All rights reserved. Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy Thu, 30 Apr 2015 13:21:46 +0000 http://www.hindawi.com/journals/aaa/2015/725674/ A novel bioinspired control strategy design is proposed for generalized synchronization of nonlinear chaotic systems, combining the bioinspired stability theory, fuzzy modeling, and a novel, simple-form Lyapunov control function design of derived high efficient, heuristic and bioinspired controllers. Three main contributions are concluded: (1) apply the bioinspired stability theory to further analyze the stability of fuzzy error systems; the high performance of controllers has been shown in previous study by Li and Ge 2009, (2) a new Lyapunov control function based on bioinspired stability theory is designed to achieve synchronization without using traditional LMI method, which is a simple linear homogeneous function of states and the process of designing controller to synchronize two fuzzy chaotic systems becomes much simpler, and (3) three different situations of synchronization are proposed; classical master and slave Lorenz systems, slave Chen’s system, and Rossler’s system as functional system are illustrated to further show the effectiveness and feasibility of our novel strategy. The simulation results show that our novel control strategy can be applied to different and complicated control situations with high effectiveness. Shih-Yu Li, Shi-An Chen, Chin-Teng Lin, Li-Wei Ko, Cheng-Hsiung Yang, and Heng-Hui Chen Copyright © 2015 Shih-Yu Li et al. All rights reserved. A New Method for Proving Existence Theorems for Abstract Hammerstein Equations Thu, 30 Apr 2015 11:12:22 +0000 http://www.hindawi.com/journals/aaa/2015/627260/ An abstract Hammerstein equation is an equation of the form . A new method is introduced to prove the existence of a solution of this equation where and are nonlinear accretive (monotone) operators. The method does not involve the complicated technique of factorizing a linear map via a Hilbert space and does not involve the use of deep variational techniques. C. E. Chidume, C. O. Chidume, and Ma’aruf Shehu Minjibir Copyright © 2015 C. E. Chidume et al. All rights reserved. On the Equivalence of Differential Equations in the Sense of Coincidence Reflecting Functions Tue, 28 Apr 2015 06:32:30 +0000 http://www.hindawi.com/journals/aaa/2015/456364/ We use a new method for constructing some differential equations which are equivalent to a given equation in the sense of having the same reflecting function. We completely solve the problem: when is a polynomial differential equation equivalent to a given polynomial differential equation? Many sufficient conditions have been established for one differential equation to be equivalent to a given differential equation. We apply the obtained results to study the boundary value problem of two equivalent differential equations. Zhengxin Zhou Copyright © 2015 Zhengxin Zhou. All rights reserved. Applications of Fractional -Calculus to Certain Subclass of Analytic -Valent Functions with Negative Coefficients Wed, 22 Apr 2015 13:37:30 +0000 http://www.hindawi.com/journals/aaa/2015/273236/ By making use of the concept of fractional -calculus, we firstly define -extension of the generalization of the generalized Al-Oboudi differential operator. Then, we introduce new class of -analogue of -valently closed-to-convex function, and, consequently, new class by means of this new general differential operator. Our main purpose is to determine the general properties on such class and geometric properties for functions belonging to this class with negative coefficient. Further, the -extension of interesting properties, such as distortion inequalities, inclusion relations, extreme points, radii of generalized starlikeness, convexity and close-to-convexity, quasi-Hadamard properties, and invariant properties, is obtained. Finally, we briefly indicate the relevant connections of our presented results to the former results. Ben Wongsaijai and Nattakorn Sukantamala Copyright © 2015 Ben Wongsaijai and Nattakorn Sukantamala. All rights reserved. New Trends in Nonlinear Control Systems and Applications Tue, 21 Apr 2015 07:04:24 +0000 http://www.hindawi.com/journals/aaa/2015/637632/ Zhitao Liu, Deqing Huang, Yifan Xing, Chuanke Zhang, Zhengguang Wu, and Xiaofu Ji Copyright © 2015 Zhitao Liu et al. All rights reserved. Optimal Control: Theory and Application to Science, Engineering, and Social Sciences Mon, 20 Apr 2015 13:37:59 +0000 http://www.hindawi.com/journals/aaa/2015/890527/ Davide La Torre, Herb Kunze, Manuel Ruiz-Galan, Tufail Malik, and Simone Marsiglio Copyright © 2015 Davide La Torre et al. All rights reserved. Dynamical Aspects of Initial/Boundary Value Problems for Ordinary Differential Equations 2014 Sun, 19 Apr 2015 12:07:01 +0000 http://www.hindawi.com/journals/aaa/2015/287490/ Jifeng Chu, Yongli Song, Juntao Sun, Patricia J. Y. Wong, and Yonghui Xia Copyright © 2015 Jifeng Chu et al. All rights reserved. Advances on Integrodifferential Equations and Transforms Sun, 19 Apr 2015 09:03:25 +0000 http://www.hindawi.com/journals/aaa/2015/462905/ H. M. Srivastava, Xiao-Jun Yang, Dumitru Baleanu, Juan J. Nieto, and Jordan Hristov Copyright © 2015 H. M. Srivastava et al. All rights reserved. Optimal Control of Renewable Resources Based on the Effective Utilization Rate Thu, 16 Apr 2015 14:15:30 +0000 http://www.hindawi.com/journals/aaa/2015/369493/ The effective utilization rate of exploited renewable resources affects the final total revenue and the further exploitation of renewable resources. Considering the effective utilization rate, we propose an optimal control model for the exploitation of the renewable resources in this study. Firstly, we can prove that the novel model is nonsingular compared with the singular basic model. Secondly, we solve the novel model and obtain the optimal solution by Bang-Bang theory. Furthermore, we can determine the optimal total resources and the maximal total revenue. Finally, a numerical example is provided to verify the obtained theoretical results. Rui Wu, Zhengwei Shen, and Fucheng Liao Copyright © 2015 Rui Wu et al. All rights reserved. Corrigendum to “Krasnosel’skii Type Hybrid Fixed Point Theorems and Their Applications to Fractional Integral Equations” Thu, 16 Apr 2015 13:03:00 +0000 http://www.hindawi.com/journals/aaa/2015/467569/ H. M. Srivastava, Sachin V. Bedre, S. M. Khairnar, and B. S. Desale Copyright © 2015 H. M. Srivastava et al. All rights reserved. Reliable Control for Uncertain Singular Systems with Randomly Occurring Time-Varying Delay and Actuator Faults Thu, 16 Apr 2015 11:49:59 +0000 http://www.hindawi.com/journals/aaa/2015/238692/ The problem of reliable control is investigated for uncertain continuous singular systems with randomly occurring time-varying delay and actuator faults in this work. The delay occurs in a random way, and such randomly occurring delay obeys certain mutually uncorrelated Bernoulli distributed white noise sequences. The uncertainties under consideration are norm-bounded, and may vary with time. Then, with the constructed Lyapunov function, a sufficient condition is given to ensure the unforced system is mean-square exponentially stable and the corresponding controller can be derived from such condition, and the actuator faults problem is guaranteed. A numerical example is provided to show the effectiveness of the methods. Yu-Lin Li, Lin-Sheng Li, Zhi-Cheng Zhao, and Jing-Gang Zhang Copyright © 2015 Yu-Lin Li et al. All rights reserved. Approximate Controllability of Semilinear Impulsive Evolution Equations Thu, 16 Apr 2015 11:24:47 +0000 http://www.hindawi.com/journals/aaa/2015/797439/ We prove the approximate controllability of the following semilinear impulsive evolution equation: where , and are Hilbert spaces, , is a bounded linear operator, are smooth functions, and is an unbounded linear operator in which generates a strongly continuous semigroup . We suppose that is bounded and the linear system is approximately controllable on for all . Under these conditions, we prove the following statement: the semilinear impulsive evolution equation is approximately controllable on . Hugo Leiva Copyright © 2015 Hugo Leiva. All rights reserved. Fractional Cauchy Problem with Caputo Nabla Derivative on Time Scales Thu, 16 Apr 2015 08:22:52 +0000 http://www.hindawi.com/journals/aaa/2015/486054/ The definition of Caputo fractional derivative is given and some of its properties are discussed in detail. After then, the existence of the solution and the dependency of the solution upon the initial value for Cauchy type problem with fractional Caputo nabla derivative are studied. Also the explicit solutions to homogeneous equations and nonhomogeneous equations are derived by using Laplace transform method. Jiang Zhu and Ling Wu Copyright © 2015 Jiang Zhu and Ling Wu. All rights reserved. On the Fourier-Transformed Boltzmann Equation with Brownian Motion Thu, 16 Apr 2015 07:10:53 +0000 http://www.hindawi.com/journals/aaa/2015/318618/ We establish a global existence theorem, and uniqueness and stability of solutions of the Cauchy problem for the Fourier-transformed Fokker-Planck-Boltzmann equation with singular Maxwellian kernel, which may be viewed as a kinetic model for the stochastic time-evolution of characteristic functions governed by Brownian motion and collision dynamics. Yong-Kum Cho and Eunsil Kim Copyright © 2015 Yong-Kum Cho and Eunsil Kim. All rights reserved. Nonlinear Analysis: Optimization Methods, Convergence Theory, and Applications Thu, 16 Apr 2015 06:28:03 +0000 http://www.hindawi.com/journals/aaa/2015/429595/ Gonglin Yuan, Gaohang Yu, Neculai Andrei, Yunhai Xiao, and Li Zhang Copyright © 2015 Gonglin Yuan et al. All rights reserved. The Existence and Uniqueness of Global Solutions to the Initial Value Problem for the System of Nonlinear Integropartial Differential Equations in Spatial Economics: The Dynamic Continuous Dixit-Stiglitz-Krugman Model in an Urban-Rural Setting Wed, 15 Apr 2015 14:10:19 +0000 http://www.hindawi.com/journals/aaa/2015/760136/ Assume that economic activities are conducted in a bounded continuous domain where workers move toward regions that offer higher real wages and away from regions that offer below-average real wages. The density of real wages is calculated by solving the nominal wage equation of the continuous Dixit-Stiglitz-Krugman model in an urban-rural setting. The evolution of the density of workers is described by an unknown function of the replicator equation whose growth rate is equal to the difference between the density of real wages and the average real wage. Hence, the evolution of the densities of workers and real wages is described by the system of the nominal wage equation and the replicator equation. This system of equations is an essentially new kind of system of nonlinear integropartial differential equations in the theory of functional equations. The purpose of this paper is to obtain a sufficient condition for the initial value problem for this system to have a unique global solution. Minoru Tabata and Nobuoki Eshima Copyright © 2015 Minoru Tabata and Nobuoki Eshima. All rights reserved. A Smoothing Inexact Newton Method for Nonlinear Complementarity Problems Wed, 15 Apr 2015 11:15:02 +0000 http://www.hindawi.com/journals/aaa/2015/731026/ A smoothing inexact Newton method is presented for solving nonlinear complementarity problems. Different from the existing exact methods, the associated subproblems are not necessary to be exactly solved to obtain the search directions. Under suitable assumptions, global convergence and superlinear convergence are established for the developed inexact algorithm, which are extensions of the exact case. On the one hand, results of numerical experiments indicate that our algorithm is effective for the benchmark test problems available in the literature. On the other hand, suitable choice of inexact parameters can improve the numerical performance of the developed algorithm. Zhong Wan, HuanHuan Li, and Shuai Huang Copyright © 2015 Zhong Wan et al. All rights reserved. A Note on Continuity of Solution Set for Parametric Weak Vector Equilibrium Problems Wed, 15 Apr 2015 07:06:05 +0000 http://www.hindawi.com/journals/aaa/2015/503091/ We consider the parametric weak vector equilibrium problem. By using a weaker assumption of Peng and Chang (2014), the sufficient conditions for continuity of the solution mappings to a parametric weak vector equilibrium problem are established. Examples are provided to illustrate the essentialness of imposed assumptions. As advantages of the results, we derive the continuity of solution mappings for vector optimization problems. Pakkapon Preechasilp and Rabian Wangkeeree Copyright © Pakkapon Preechasilp and Rabian Wangkeeree. All rights reserved. On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation Tue, 14 Apr 2015 17:02:54 +0000 http://www.hindawi.com/journals/aaa/2015/219616/ We develop the Newton-Kantorovich method to solve the system of nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method. Hameed Husam Hameed, Z. K. Eshkuvatov, Anvarjon Ahmedov, and N. M. A. Nik Long Copyright © 2015 Hameed Husam Hameed et al. All rights reserved. On the Relation between Phase-Type Distributions and Positive Systems Tue, 14 Apr 2015 11:51:02 +0000 http://www.hindawi.com/journals/aaa/2015/731261/ The relation between phase-type representation and positive system realization in both the discrete and continuous time is discussed. Using the Perron-Frobenius theorem of nonnegative matrix theory, a transformation from positive realization to phase-type realization is derived under the excitability condition. In order to explain the connection, some useful properties and characteristics such as irreducibility, excitability, transparency, and order reduction for positive realization and phase-type representation are discussed. In addition, the connection between the phase-type renewal process and the feedback positive system is discussed in the stabilization concept. Kyungsup Kim Copyright © 2015 Kyungsup Kim. All rights reserved. Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk Wed, 01 Apr 2015 14:10:23 +0000 http://www.hindawi.com/journals/aaa/2015/209307/ We consider the reducing subspaces of on , where , , and for . We prove that each reducing subspace of is a direct sum of some minimal reducing subspaces. We also characterize the minimal reducing subspaces in the cases that and , respectively. Finally, we give a complete description of minimal reducing subspaces of on with . Yanyue Shi and Na Zhou Copyright © 2015 Yanyue Shi and Na Zhou. All rights reserved. Nonlinear Partial Differential Equations in Mathematics and Physics Wed, 01 Apr 2015 07:43:47 +0000 http://www.hindawi.com/journals/aaa/2015/593126/ Bo-Qing Dong, Caidi Zhao, Xiaohong Qin, Linghai Zhang, and Liangpan Li Copyright © 2015 Bo-Qing Dong et al. All rights reserved. On Unique Continuation for Navier-Stokes Equations Mon, 30 Mar 2015 11:51:50 +0000 http://www.hindawi.com/journals/aaa/2015/597946/ We study the unique continuation properties of solutions of the Navier-Stokes equations. We take advantage of rotation transformation of the Navier-Stokes equations to prove the “logarithmic convexity” of certain quantities, which measure the suitable Gaussian decay at infinity to obtain the Gaussian decay weighted estimates, as well as Carleman inequality. As a consequence we obtain sufficient conditions on the behavior of the solution at two different times and which guarantee the “global” unique continuation of solutions for the Navier-Stokes equations. Zhiwen Duan, Shuxia Han, and Peipei Sun Copyright © 2015 Zhiwen Duan et al. All rights reserved. Numerical Studies for Fractional Functional Differential Equations with Delay Based on BDF-Type Shifted Chebyshev Approximations Sun, 29 Mar 2015 13:12:26 +0000 http://www.hindawi.com/journals/aaa/2015/510875/ Fractional functional differential equations with delay (FDDEs) have recently played a significant role in modeling of many real areas of sciences such as physics, engineering, biology, medicine, and economics. FDDEs often cannot be solved analytically so the approximate and numerical methods should be adapted to solve these types of equations. In this paper we consider a new method of backward differentiation formula- (BDF-) type for solving FDDEs. This approach is based on the interval approximation of the true solution using the Clenshaw and Curtis formula that is based on the truncated shifted Chebyshev polynomials. It is shown that the new approach can be reformulated in an equivalent way as a Runge-Kutta method and the Butcher tableau of this method is given. Estimation of local and global truncating errors is deduced and this leads to the proof of the convergence for the proposed method. Illustrative examples of FDDEs are included to demonstrate the validity and applicability of the proposed approach. V. G. Pimenov and A. S. Hendy Copyright © 2015 V. G. Pimenov and A. S. Hendy. All rights reserved. Analytical and Numerical Methods for Solving Partial Differential Equations and Integral Equations Arising in Physical Models 2014 Sun, 29 Mar 2015 13:03:29 +0000 http://www.hindawi.com/journals/aaa/2015/193030/ Santanu Saha Ray, Rasajit K. Bera, Adem Kılıçman, Om P. Agrawal, and Yasir Khan Copyright © 2015 Santanu Saha Ray et al. All rights reserved.