Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Nonpoint Symmetry and Reduction of Nonlinear Evolution and Wave Type Equations Wed, 07 Oct 2015 08:59:36 +0000 http://www.hindawi.com/journals/aaa/2015/181275/ We study the symmetry reduction of nonlinear partial differential equations with two independent variables. We propose new ansätze reducing nonlinear evolution equations to system of ordinary differential equations. The ansätze are constructed by using operators of nonpoint classical and conditional symmetry. Then we find solution to nonlinear heat equation which cannot be obtained in the framework of the classical Lie approach. By using operators of Lie-Bäcklund symmetries we construct the solutions of nonlinear hyperbolic equations depending on arbitrary smooth function of one variable too. Ivan Tsyfra and Tomasz Czyżycki Copyright © 2015 Ivan Tsyfra and Tomasz Czyżycki. All rights reserved. Building Infinitely Many Solutions for Some Model of Sublinear Multipoint Boundary Value Problems Thu, 01 Oct 2015 12:18:54 +0000 http://www.hindawi.com/journals/aaa/2015/732761/ We show that the sublinearity hypothesis of some well-known existence results on multipoint Boundary Value Problems (in short BVPs) may allow the existence of infinitely many solutions by using Tietze extension theorem. This is a qualitative result which is of concern in Applied Analysis and can motivate more research on the conditions that ascertain the existence of multiple solutions to sublinear BVPs. The idea of the proof is of independent interest since it shows a constructive way to have ordinary differential equations with multiple solutions. Guy Aymard Degla Copyright © 2015 Guy Aymard Degla. All rights reserved. A Homotopy-Analysis Approach for Nonlinear Wave-Like Equations with Variable Coefficients Thu, 01 Oct 2015 11:23:28 +0000 http://www.hindawi.com/journals/aaa/2015/628310/ We are interested in the approximate analytical solutions of the wave-like nonlinear equations with variable coefficients. We use a wave operator, which provides a convenient way of controlling all initial and boundary conditions. The proposed choice of the auxiliary operator helps to find the approximate series solution without any discretization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. Afgan Aslanov Copyright © 2015 Afgan Aslanov. All rights reserved. Multiple Solutions of Boundary Value Problems for th-Order Singular Nonlinear Integrodifferential Equations in Abstract Spaces Thu, 01 Oct 2015 07:29:47 +0000 http://www.hindawi.com/journals/aaa/2015/736139/ The authors discuss multiple solutions for the nth-order singular boundary value problems of nonlinear integrodifferential equations in Banach spaces by means of the fixed point theorem of cone expansion and compression. An example for infinite system of scalar third-order singular nonlinear integrodifferential equations is offered. Yanlai Chen, Tingqiu Cao, and Baoxia Qin Copyright © 2015 Yanlai Chen et al. All rights reserved. Power Series Solution for Solving Nonlinear Burgers-Type Equations Thu, 01 Oct 2015 06:47:04 +0000 http://www.hindawi.com/journals/aaa/2015/712584/ Power series solution method has been traditionally used to solve ordinary and partial linear differential equations. However, despite their usefulness the application of this method has been limited to this particular kind of equations. In this work we use the method of power series to solve nonlinear partial differential equations. The method is applied to solve three versions of nonlinear time-dependent Burgers-type differential equations in order to demonstrate its scope and applicability. E. López-Sandoval, A. Mello, J. J. Godina-Nava, and A. R. Samana Copyright © 2015 E. López-Sandoval et al. All rights reserved. Numerical Solution of Continuation Problem for 3D Steady-State Diffusion in Cylindrically Layered Medium Thu, 10 Sep 2015 14:15:06 +0000 http://www.hindawi.com/journals/aaa/2015/329052/ This work is based on the application of Fourier and quasi-solution methods for solving the continuation inverse problem for 3D steady-state diffusion model inside a cylindrical layered medium. The diffusion coefficient is supposed to be a piecewise constant function, Cauchy data are given on the outer boundary of the cylinder, and we seek to recover the temperature at the inner boundary of the cylinder. Numerical experiments are investigated and show the capacity of proposed method only for smooth boundary condition. Under the suitable choice of regularization parameters we recover the distribution of temperature on the inner boundary with satisfactory quality for noisy data. Magira Kulbay, Saule Maussumbekova, and Balgaisha Mukanova Copyright © 2015 Magira Kulbay et al. All rights reserved. Oscillation Criteria for Some Higher Order Integrodynamic Equations on Timescales Sun, 06 Sep 2015 12:19:04 +0000 http://www.hindawi.com/journals/aaa/2015/160240/ We study the oscillation behavior for some higher order integrodynamic equations on timescales. We establish some new sufficient conditions guaranteeing that all solutions of theses equations are oscillatory. Some numerical examples in the continuous case are given to validate the theoretical results. Said R. Grace and Mohamed A. El-Beltagy Copyright © 2015 Said R. Grace and Mohamed A. El-Beltagy. All rights reserved. Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems Sun, 06 Sep 2015 08:44:51 +0000 http://www.hindawi.com/journals/aaa/2015/357934/ Let be a real locally uniformly convex reflexive separable Banach space with locally uniformly convex dual space . Let be maximal monotone and quasibounded generalized pseudomonotone such that there exists a real reflexive separable Banach space , dense and continuously embedded in . Assume, further, that there exists such that d for all and . New surjectivity results are given for noncoercive, not everywhere defined, and possibly unbounded operators of the type . A partial positive answer for Nirenberg's problem on surjectivity of expansive mapping is provided. Leray-Schauder degree is applied employing the method of elliptic superregularization. A new characterization of linear maximal monotone operator is given as a result of surjectivity of , where is of type with respect to . These results improve the corresponding theory for noncoercive and not everywhere defined operators of pseudomonotone type. In the last section, an example is provided addressing existence of weak solution in of a nonlinear parabolic problem of the type ,  ; ,  ; ,  , where , is a nonempty, bounded, and open subset of ,    satisfies certain growth conditions, and , , and is the conjugate exponent of . Teffera M. Asfaw Copyright © 2015 Teffera M. Asfaw. All rights reserved. Perturbation Methods and Formal Modeling for Dynamic Systems Tue, 01 Sep 2015 08:19:52 +0000 http://www.hindawi.com/journals/aaa/2015/384710/ Saeed Islam, Sher Afzal Khan, Gul Zaman, and Il Hyo Jung Copyright © 2015 Saeed Islam et al. All rights reserved. Determination of System Dimensionality from Observing Near-Normal Distributions Mon, 31 Aug 2015 12:48:17 +0000 http://www.hindawi.com/journals/aaa/2015/467195/ This paper identifies a previously undiscovered behavior of uniformly distributed data points or vectors in high dimensional ellipsoidal models. Such models give near normal distributions for each of its dimensions. Converse of this may also be true; that is, for a normal-like distribution of an observed variable, it is possible that the distribution is a result of uniform distribution of data points in a high dimensional ellipsoidal model, to which the observed variable belongs. Given the currently held notion of normal distributions, this new behavior raises many interesting questions. This paper also attempts to answer some of those questions. We cover both volume based (filled) and surface based (shell) ellipsoidal models. The phenomenon is demonstrated using statistical as well as mathematical approaches. We also show that the dimensionality of the latent model, that is, the number of hidden variables in a system, can be calculated from the observed distribution. We call the new distribution “Tanazur” and show through experiments that it is at least observed in one real world scenario, that of the motion of particles in an ideal gas. We show that the Maxwell-Boltzmann distribution of particle speeds can be explained on the basis of Tanazur distributions. Shahid Razzaq and Shehzad Khalid Copyright © 2015 Shahid Razzaq and Shehzad Khalid. All rights reserved. The Multistage Homotopy Perturbation Method for Solving Chaotic and Hyperchaotic Lü System Mon, 31 Aug 2015 11:57:56 +0000 http://www.hindawi.com/journals/aaa/2015/398027/ The multistage homotopy-perturbation method (MHPM) is applied to the nonlinear chaotic and hyperchaotic Lü systems. MHPM is a technique adapted from the standard homotopy-perturbation method (HPM) where the HPM is treated as an algorithm in a sequence of time intervals. To ensure the precision of the technique applied in this work, the results are compared with a fourth-order Runge-Kutta method and the standard HPM. The results show that the MHPM is an efficient and powerful technique in solving both chaotic and hyperchaotic systems. M. S. H. Chowdhury, Nur Isnida Razali, Waqar Asrar, and M. M. Rahman Copyright © 2015 M. S. H. Chowdhury et al. All rights reserved. Exact Solutions of Heat and Mass Transfer with MHD Flow in a Porous Medium under Time Dependent Shear Stress and Temperature Mon, 31 Aug 2015 09:50:40 +0000 http://www.hindawi.com/journals/aaa/2015/975201/ This paper aims to study the influence of thermal radiation on unsteady magnetohyrdodynamic (MHD) natural convection flow of an optically thick fluid over a vertical plate embedded in a porous medium with arbitrary shear stress. Combined phenomenon of heat and mass transfer is considered. Closed-form solutions in general form are obtained by using the Laplace transform technique. They are expressed in terms of exponential and complementary error functions. Velocity is expressed as a sum of thermal and mechanical parts. Corresponding limiting solutions are also reduced from the general solutions. It is found that the obtained solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. Analytical results for the pertinent flow parameters are drawn graphically and discussed in detail. It is found that the velocity profiles of fluid decrease with increasing shear stress. The magnetic parameter develops shear resistance which reduces the fluid motion whereas the inverse permeability parameter increases the fluid flow. Arshad Khan, Ilyas Khan, Farhad Ali, Asma Khalid, and Sharidan Shafie Copyright © 2015 Arshad Khan et al. All rights reserved. Influence of Slip Condition on Unsteady Free Convection Flow of Viscous Fluid with Ramped Wall Temperature Mon, 31 Aug 2015 09:43:13 +0000 http://www.hindawi.com/journals/aaa/2015/327975/ The objective of this study is to explore the influence of wall slip condition on a free convection flow of an incompressible viscous fluid with heat transfer and ramped wall temperature. Exact solution of the problem is obtained by using Laplace transform technique. Graphical results to see the effects of Prandtl number Pr, time , and slip parameter on velocity and skin friction for the case of ramped and constant temperature of the plate are provided and discussed. Sami Ul Haq, Ilyas Khan, Farhad Ali, Arshad Khan, and Tarek Nabil Ahmed Abdelhameed Copyright © 2015 Sami Ul Haq et al. All rights reserved. Recent Results on Fixed Point Approximations and Applications Sun, 30 Aug 2015 08:01:58 +0000 http://www.hindawi.com/journals/aaa/2015/507121/ Jong Kyu Kim, Poom Kumam, Xiaolong Qin, and Kyung Soo Kim Copyright © 2015 Jong Kyu Kim et al. All rights reserved. Approximating Iterations for Nonexpansive and Maximal Monotone Operators Thu, 27 Aug 2015 06:50:04 +0000 http://www.hindawi.com/journals/aaa/2015/451320/ We present two algorithms for finding a zero of the sum of two monotone operators and a fixed point of a nonexpansive operator in Hilbert spaces. We show that these two algorithms converge strongly to the minimum norm common element of the zero of the sum of two monotone operators and the fixed point of a nonexpansive operator. Zhangsong Yao, Sun Young Cho, Shin Min Kang, and Li-Jun Zhu Copyright © 2015 Zhangsong Yao et al. All rights reserved. Recent Developments on Time-Delay Neural Networks Wed, 26 Aug 2015 11:54:54 +0000 http://www.hindawi.com/journals/aaa/2015/865409/ Zheng-Guang Wu, Yun Chen, Xusheng Lei, Kun Liu, and Hui Zhang Copyright © 2015 Zheng-Guang Wu et al. All rights reserved. A New Grünwald-Letnikov Derivative Derived from a Second-Order Scheme Wed, 26 Aug 2015 09:44:31 +0000 http://www.hindawi.com/journals/aaa/2015/952057/ A novel derivation of a second-order accurate Grünwald-Letnikov-type approximation to the fractional derivative of a function is presented. This scheme is shown to be second-order accurate under certain modifications to account for poor accuracy in approximating the asymptotic behavior near the lower limit of differentiation. Some example functions are chosen and numerical results are presented to illustrate the efficacy of this new method over some other popular choices for discretizing fractional derivatives. B. A. Jacobs Copyright © 2015 B. A. Jacobs. All rights reserved. Multimodel Modeling and Predictive Control for Direct-Drive Wind Turbine with Permanent Magnet Synchronous Generator Tue, 25 Aug 2015 07:45:26 +0000 http://www.hindawi.com/journals/aaa/2015/296436/ The safety and reliability of the wind turbines wholly depend on the completeness and reliability of the control system which is an important problem for the validity of the wind energy conversion systems (WECSs). A method based on multimodel modeling and predictive control is proposed for the optimal operation of direct-drive wind turbine with permanent magnet synchronous generator in this paper. In this strategy, wind turbine with direct-drive permanent magnet synchronous generator is modeled and a backpropagation artificial neural network is designed to estimate the wind speed loaded into the turbine model in real time through the estimated turbine shaft speed and mechanical power. The nonlinear wind turbine system is presented by multiple linear models. The desired trajectory of the nonlinear system is decomposed to be suitable for the reference trajectory of multiple models that are presented by the linear models of the nonlinear system, which simplifies the nonlinear optimization problems and decreases the calculation difficulty. Then a multivariable control strategy based on model predictive control techniques for the control of variable-speed variable-pitch wind turbines is proposed. Finally, simulation results are given to illustrate the effectiveness of the proposed strategy, and the conclusion that multiple model predictive controller (MMPC) has better control performance than the PI control method is obtained. Lei Wang, Tao Shen, and Chen Chen Copyright © 2015 Lei Wang et al. All rights reserved. New Pinning Synchronization of Complex Networks with Time-Varying Coupling Strength and Nondelayed and Delayed Coupling Mon, 24 Aug 2015 11:34:00 +0000 http://www.hindawi.com/journals/aaa/2015/989201/ The pinning synchronization problem for a class of complex networks is studied by a stochastic viewpoint, in which both time-varying coupling strength and nondelayed and delayed coupling are included. Different from the traditionally similar methods, its interval is separated into two subintervals and described by a Bernoulli variable. Both bounds and switching probability of such subintervals are contained. Particularly, the nondelayed and delayed couplings occur alternately in which another independent Bernoulli variable is introduced. Then, a new kind of pinning controller without time-varying coupling strength signal is developed, in which only its bounds and probabilities are contained. When such probabilities are unavailable, two different kinds of adaption laws are established to make the complex network globally synchronous. Finally, the validity of the presented methods is proved through a numerical example. Guoliang Wang, Zhongbao Yue, and Feng Wang Copyright © 2015 Guoliang Wang et al. All rights reserved. Corrigendum to “The Properties of a New Subclass of Harmonic Univalent Mappings” Mon, 24 Aug 2015 11:26:26 +0000 http://www.hindawi.com/journals/aaa/2015/476062/ Zhi-Hong Liu and Ying-Chun Li Copyright © 2015 Zhi-Hong Liu and Ying-Chun Li. All rights reserved. A Novel Model of Conforming Delaunay Triangulation for Sensor Network Configuration Mon, 24 Aug 2015 09:05:40 +0000 http://www.hindawi.com/journals/aaa/2015/720249/ Delaunay refinement is a technique for generating unstructured meshes of triangles for sensor network configuration engineering practice. A new method for solving Delaunay triangulation problem is proposed in this paper, which is called endpoint triangle’s circumcircle model (ETCM). As compared with the original fractional node refinement algorithms, the proposed algorithm can get well refinement stability with least time cost. Simulations are performed under five aspects including refinement stability, the number of additional nodes, time cost, mesh quality after intruding additional nodes, and the aspect ratio improved by single additional node. All experimental results show the advantages of the proposed algorithm as compared with the existing algorithms and confirm the algorithm analysis sufficiently. Yan Ma, Yan-ling Hao, and Feng-min Tian Copyright © 2015 Yan Ma et al. All rights reserved. Quantifying Poincare’s Continuation Method for Nonlinear Oscillators Mon, 17 Aug 2015 12:06:25 +0000 http://www.hindawi.com/journals/aaa/2015/836312/ In the sixties, Loud obtained interesting results of continuation on periodic solutions in driven nonlinear oscillators with small parameter (Loud, 1964). In this paper Loud’s results are extended out for periodically driven Duffing equations with odd symmetry quantifying the continuation parameter for a periodic odd solution which is elliptic and emanates from the equilibrium of the nonperturbed problem. Daniel Núñez and Andrés Rivera Copyright © 2015 Daniel Núñez and Andrés Rivera. All rights reserved. A Second-Order Method for the Numerical Integration of a Size-Structured Cell Population Model Thu, 06 Aug 2015 06:46:18 +0000 http://www.hindawi.com/journals/aaa/2015/549168/ We consider the numerical integration of a size-structured cell population model. We propose a new second-order numerical method to attain its solution. The scheme is analyzed and the optimal rate of convergence is derived. We show experimentally the predicted accuracy of the scheme. O. Angulo, J. C. López-Marcos, and M. A. López-Marcos Copyright © 2015 O. Angulo et al. All rights reserved. Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure Wed, 05 Aug 2015 14:07:46 +0000 http://www.hindawi.com/journals/aaa/2015/289029/ We present two classes of iterative methods whose orders of convergence are four and five, respectively, for solving systems of nonlinear equations, by using the technique of weight functions in each step. Moreover, we show an extension to higher order, adding only one functional evaluation of the vectorial nonlinear function. We perform numerical tests to compare the proposed methods with other schemes in the literature and test their effectiveness on specific nonlinear problems. Moreover, some real basins of attraction are analyzed in order to check the relation between the order of convergence and the set of convergent starting points. Santiago Artidiello, Alicia Cordero, Juan R. Torregrosa, and María P. Vassileva Copyright © 2015 Santiago Artidiello et al. All rights reserved. On Data Space Selection and Data Processing for Parameter Identification in a Reaction-Diffusion Model Based on FRAP Experiments Wed, 05 Aug 2015 12:53:06 +0000 http://www.hindawi.com/journals/aaa/2015/859849/ Fluorescence recovery after photobleaching (FRAP) is a widely used measurement technique to determine the mobility of fluorescent molecules within living cells. While the experimental setup and protocol for FRAP experiments are usually fixed, data (pre)processing represents an important issue. The aim of this paper is twofold. First, we formulate and solve the problem of relevant FRAP data selection. The theoretical findings are illustrated by the comparison of the results of parameter identification when the full data set was used and the case when the irrelevant data set (data with negligible impact on the confidence interval of the estimated parameters) was removed from the data space. Second, we analyze and compare two approaches of FRAP data processing. Our proposition, surprisingly for the FRAP community, claims that the data set represented by the FRAP recovery curves in form of a time series (integrated data approach commonly used by the FRAP community) leads to a larger confidence interval compared to the full (spatiotemporal) data approach. Stefan Kindermann and Štěpán Papáček Copyright © 2015 Stefan Kindermann and Štěpán Papáček. All rights reserved. Birth Rate Effects on an Age-Structured Predator-Prey Model with Cannibalism in the Prey Wed, 05 Aug 2015 11:29:34 +0000 http://www.hindawi.com/journals/aaa/2015/241312/ We develop a family of predator-prey models with age structure and cannibalism in the prey population. It consists of systems of ordinary differential equations, where is a parameter associated with new proposed prey birth rates. We discuss how these new birth rates give the required flexibility to produce differential systems with well-behaved solutions. The main feature required in these models is the coexistence among the involved species, which translates mathematically into stable equilibria and periodic solutions. The search for such characteristics is based on heuristic predation functions that account for cannibalism in the prey. Francisco J. Solis and Roberto A. Ku-Carrillo Copyright © 2015 Francisco J. Solis and Roberto A. Ku-Carrillo. All rights reserved. A Probabilistic Analysis to Quantify the Effect of March 11, 2004, Attacks in Madrid on the March 14 Elections in Spain: A Dynamic Modelling Approach Wed, 05 Aug 2015 11:24:15 +0000 http://www.hindawi.com/journals/aaa/2015/387839/ The bomb attacks in Madrid three days before the general elections of March 14, 2004, and their possible influence on the victory of PSOE (Spanish Workers Socialist Party), defeating PP (Popular Party), have been a matter of study from several points of view (i.e., sociological, political, or statistical). In this paper, we present a dynamic model based on a system of differential equations such that it, using data from Spanish CIS (National Center of Sociological Research), describes the evolution of voting intention of the Spanish people over time. Using this model, we conclude that the probability is very low that the PSOE would have won had the attack not happened. Moreover, after the attack, the PSOE increased an average of 5.6% in voting on March 14 and an average of 11.2% of the Spanish people changed their vote between March 11 and March 14. These figures are in accordance with other studies. Juan-Carlos Cortés, Francisco Sánchez, Francisco-José Santonja, and Rafael-Jacinto Villanueva Copyright © 2015 Juan-Carlos Cortés et al. All rights reserved. A Data Mining Approach for Visual and Analytical Identification of Neurorehabilitation Ranges in Traumatic Brain Injury Cognitive Rehabilitation Wed, 05 Aug 2015 11:11:28 +0000 http://www.hindawi.com/journals/aaa/2015/823562/ Traumatic brain injury (TBI) is a critical public health and socioeconomic problem throughout the world. Cognitive rehabilitation (CR) has become the treatment of choice for cognitive impairments after TBI. It consists of hierarchically organized tasks that require repetitive use of impaired cognitive functions. One important focus for CR professionals is the number of repetitions and the type of task performed throughout treatment leading to functional recovery. However, very little research is available that quantifies the amount and type of practice. The Neurorehabilitation Range (NRR) and the Sectorized and Annotated Plane (SAP) have been introduced as a means of identifying formal operational models in order to provide therapists with decision support information for assigning the most appropriate CR plan. In this paper we present a novel methodology based on combining SAP and NRR to solve what we call the Neurorehabilitation Range Maximal Regions (NRRMR) problem and to generate analytical and visual tools enabling the automatic identification of NRR. A new SAP representation is introduced and applied to overcome the drawbacks identified with existing methods. The results obtained show patterns of response to treatment that might lead to reconsideration of some of the current clinical hypotheses. Alejandro García-Rudolph and Karina Gibert Copyright © 2015 Alejandro García-Rudolph and Karina Gibert. All rights reserved. The Role of the Risk-Neutral Jump Size Distribution in Single-Factor Interest Rate Models Wed, 05 Aug 2015 09:27:06 +0000 http://www.hindawi.com/journals/aaa/2015/805695/ We obtain a result that relates the risk-neutral jump size of interest rates with yield curve data. This function is unobservable; therefore, this result opens a way to estimate the jump size directly from data in the markets together with the risk-neutral drift and jump intensity estimations. Then, we investigate the finite sample performance of this approach with a test problem. Moreover, we analyze the effect of estimating the risk-neutral jump size instead of assuming that it is artificially absorbed by the jump intensity, as usual in the interest rate literature. Finally, an application to US Treasury Bill data is also illustrated. L. Gómez-Valle and J. Martínez-Rodríguez Copyright © 2015 L. Gómez-Valle and J. Martínez-Rodríguez. All rights reserved. Fault Detection for Discrete-Time Nonlinear Impulsive Switched Systems Sun, 02 Aug 2015 08:22:49 +0000 http://www.hindawi.com/journals/aaa/2015/694319/ This paper investigates the fault detection problem for discrete-time nonlinear impulsive switched systems. Attention is focused on designing the fault detection filters to guarantee the robust performance and the detection performance. Based on these performances, sufficient conditions for the existence of filters are given in the framework of linear matrix inequality; furthermore, the filter gains are characterized by a convex optimization problem. The presented technique is validated by an example. Simulation results indicate that the proposed method can effectively detect the faults. Qingyu Su, Xiaolong Jia, and Zhengfan Song Copyright © 2015 Qingyu Su et al. All rights reserved.