Abstract and Applied Analysis
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© 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 fixedpoint property. It is well known that there are onetoone 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 FiniteTime 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 finitetime synchronization problem for a class of complex
dynamical networks by means of periodically intermittent control. Based
on some analysis techniques and finitetime stability theory, some novel and
effective finitetime 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 Rintersection, Runion, Pintersection, and Punion 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 SzàszMirakyan 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 HydrogenNatural Gas Mixture
Wed, 06 May 2015 09:46:30 +0000
http://www.hindawi.com/journals/aaa/2015/510675/
Water hammer on transient flow of hydrogennatural 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 hydrogennatural 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, simpleform 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.
ShihYu Li, ShiAn Chen, ChinTeng Lin, LiWei Ko, ChengHsiung Yang, and HengHui Chen
Copyright © 2015 ShihYu 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 AlOboudi differential operator. Then, we introduce new class of analogue of valently closedtoconvex 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 closetoconvexity, quasiHadamard 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 RuizGalan, 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, XiaoJun 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 BangBang 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 TimeVarying 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 timevarying 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 normbounded, and may vary with time. Then, with the constructed Lyapunov function, a sufficient condition is given to ensure the unforced system is meansquare 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.
YuLin Li, LinSheng Li, ZhiCheng Zhao, and JingGang Zhang
Copyright © 2015 YuLin 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 FourierTransformed 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 Fouriertransformed FokkerPlanckBoltzmann equation with singular Maxwellian kernel,
which may be viewed as a kinetic model for the stochastic timeevolution of characteristic functions governed by Brownian motion and collision dynamics.
YongKum Cho and Eunsil Kim
Copyright © 2015 YongKum 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 DixitStiglitzKrugman Model in an UrbanRural 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 belowaverage real wages. The density of real wages is calculated by solving the nominal wage equation of the continuous DixitStiglitzKrugman model in an urbanrural 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 NewtonKantorovich 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 NewtonKantorovich 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 PhaseType Distributions and Positive Systems
Tue, 14 Apr 2015 11:51:02 +0000
http://www.hindawi.com/journals/aaa/2015/731261/
The relation between phasetype representation and positive system realization in both the discrete and continuous time is discussed. Using the PerronFrobenius theorem of nonnegative matrix theory, a transformation from positive realization to phasetype 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 phasetype representation are discussed. In addition, the connection between the phasetype 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/
BoQing Dong, Caidi Zhao, Xiaohong Qin, Linghai Zhang, and Liangpan Li
Copyright © 2015 BoQing Dong et al. All rights reserved.

On Unique Continuation for NavierStokes 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 NavierStokes equations. We take advantage of rotation transformation of the NavierStokes 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 NavierStokes 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 BDFType 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 RungeKutta 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.