Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Linear Sobolev Type Equations with Relatively -Sectorial Operators in Space of “Noises” Mon, 23 Nov 2015 05:54:09 +0000 http://www.hindawi.com/journals/aaa/2015/697410/ The concept of “white noise,” initially established in finite-dimensional spaces, is transferred to infinite-dimensional case. The goal of this transition is to develop the theory of stochastic Sobolev type equations and to elaborate applications of practical interest. To reach this goal the Nelson-Gliklikh derivative is introduced and the spaces of “noises” are developed. The Sobolev type equations with relatively sectorial operators are considered in the spaces of differentiable “noises.” The existence and uniqueness of classical solutions are proved. The stochastic Dzektser equation in a bounded domain with homogeneous boundary condition and the weakened Showalter-Sidorov initial condition is considered as an application. A. Favini, G. A. Sviridyuk, and N. A. Manakova Copyright © 2015 A. Favini et al. All rights reserved. Corrigendum to “Soft -Open Sets and Soft -Continuous Functions” Wed, 18 Nov 2015 13:25:11 +0000 http://www.hindawi.com/journals/aaa/2015/329509/ Metin Akdag, Alkan Ozkan, A. Ghareeb, and A. K. Mousa Copyright © 2015 Metin Akdag et al. All rights reserved. A Computational Study of HSV-2 with Poor Treatment Adherence Wed, 18 Nov 2015 09:48:37 +0000 http://www.hindawi.com/journals/aaa/2015/850670/ Herpes simplex virus type 2 (HSV-2) is the most prevalent sexually transmitted disease worldwide, despite the availability of highly effective antiviral treatments. In this paper, a basic mathematical model for the spread of HSV-2 incorporating all the relevant biological details and poor treatment adherence is proposed and analysed. Equilibrium states of the model are determined and their stability has been investigated. The basic model is then extended to incorporate a time dependent intervention strategy. The aim of the control is tied to reducing the rate at which HSV-2 patients in treatment quit therapy before completion. Practically, this control can be implemented through monitoring and counselling all HSV-2 patients in treatment. The Pontryagin’s maximum principle is used to characterize the optimal level of the control, and the resulting optimality system is solved numerically. Overall, the study demonstrates that though time dependent control will be effective on controlling new HSV-2 cases it may not be sustainable for certain time intervals. A. Mhlanga, C. P. Bhunu, and S. Mushayabasa Copyright © 2015 A. Mhlanga et al. All rights reserved. Exponential Robust Consensus of Multiagent Systems with Markov Jump Parameters Sun, 15 Nov 2015 06:44:22 +0000 http://www.hindawi.com/journals/aaa/2015/363251/ Exponential robust consensus of stochastic multiagent systems is studied. Coupling structures of multiagent systems are Markov jump switching; that is, multiagent systems contain Markov jump parameters. Sufficient conditions of almost surely exponential robust consensus are derived by utilizing the stochastic method and the approach of the matrix inequality. Finally, two simulations are shown to demonstrate the validity of the achieved theoretical results. He Zhang, Huihui Ji, Zhiyong Ye, and Tan Senping Copyright © 2015 He Zhang et al. All rights reserved. On Tricomi Problem of Chaplygin’s Hodograph Equation Wed, 04 Nov 2015 09:33:03 +0000 http://www.hindawi.com/journals/aaa/2015/754781/ The existence and uniqueness results for the Tricomi problem of Chaplygin’s hodograph equation are shown, in the case that the domain considered is close to the parabolic degenerate line, by adopting the energy integral methods and choosing judiciously suitable multipliers. Meng Xu, Li Liu, and Hairong Yuan Copyright © 2015 Meng Xu et al. All rights reserved. An Efficient Numerical Algorithm for Solving Fractional Higher-Order Nonlinear Integrodifferential Equations Mon, 02 Nov 2015 12:36:45 +0000 http://www.hindawi.com/journals/aaa/2015/616438/ This paper is devoted to both theoretical and numerical study of boundary value problems for higher-order nonlinear fractional integrodifferential equations. Existence and uniqueness results for the considered problem are provided and proved. The numerical method of solution for the problem is based on a conjugate collocation and spline approach combined with shooting method. Some numerical examples are discussed to demonstrate the efficiency and the accuracy of the proposed algorithm. Muhammed I. Syam, Qasem M. Al-Mdallal, and M. Naim Anwar Copyright © 2015 Muhammed I. Syam et al. All rights reserved. Analysis and Models in Interdisciplinary Mathematics 2015 Mon, 02 Nov 2015 08:54:12 +0000 http://www.hindawi.com/journals/aaa/2015/592063/ L. Jódar and E. De la Poza Copyright © 2015 L. Jódar and E. De la Poza. All rights reserved. Effects of Heat Transfer and an Endoscope on Peristaltic Flow of a Fractional Maxwell Fluid in a Vertical Tube Thu, 22 Oct 2015 07:16:14 +0000 http://www.hindawi.com/journals/aaa/2015/360918/ We investigate the unsteady peristaltic transport of a viscoelastic fluid with fractional Maxwell model through two coaxial vertical tubes. This analysis has been carried under low Reynolds number and long wavelength approximations. Analytical solution of the problem is obtained by using a fractional calculus approach. The effects of Grashof number, heat parameter, relaxation time, fractional time derivative parameter, amplitude ratio, and the radius ratio on the pressure gradient, pressure rise, and the friction forces on the inner and outer tubes are graphically presented and discussed. H. Rachid Copyright © 2015 H. Rachid. All rights reserved. Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane Analysis Sun, 18 Oct 2015 13:10:11 +0000 http://www.hindawi.com/journals/aaa/2015/302185/ We consider boundary value problems for scalar differential equation , , , where is a seventh-degree polynomial and is a parameter. We use the phase plane method combined with evaluations of time-map functions and make conclusions on the number of positive solutions. Bifurcation diagrams are constructed and examples are considered illustrating the bifurcation processes. A. Kirichuka and F. Sadyrbaev Copyright © 2015 A. Kirichuka and F. Sadyrbaev. 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.