Advances in Mathematical Physics The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Antiperiodic Solutions for a Kind of Nonlinear Duffing Equations with a Deviating Argument and Time-Varying Delay Mon, 18 Aug 2014 08:25:50 +0000 This paper deals with a kind of nonlinear Duffing equation with a deviating argument and time-varying delay. By using differential inequality techniques, some very verifiable criteria on the existence and exponential stability of antiperiodic solutions for the equation are obtained. Our results are new and complementary to previously known results. An example is given to illustrate the feasibility and effectiveness of our main results. Changjin Xu and Maoxin Liao Copyright © 2014 Changjin Xu and Maoxin Liao. All rights reserved. On New Conservation Laws of Fin Equation Thu, 14 Aug 2014 11:23:57 +0000 We study the new conservation forms of the nonlinear fin equation in mathematical physics. In this study, first, Lie point symmetries of the fin equation are identified and classified. Then by using the relationship of Lie symmetry and -symmetry, new -functions are investigated. In addition, the Jacobi Last Multiplier method and the approach, which is based on the fact -functions are assumed to be of linear form, are considered as different procedures for lambda symmetry analysis. Finally, the corresponding new conservation laws and invariant solutions of the equation are presented. Gülden Gün Polat, Özlem Orhan, and Teoman Özer Copyright © 2014 Gülden Gün Polat et al. All rights reserved. A Matrix Method Based on the Fibonacci Polynomials to the Generalized Pantograph Equations with Functional Arguments Wed, 13 Aug 2014 13:30:19 +0000 A pseudospectral method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. By using this method, approximate solutions of the problems are easily obtained in form of the truncated Fibonacci series. Some illustrative examples are given to verify the efficiency and effectiveness of the proposed method. Then, the numerical results are compared with other methods. Ayşe Betül Koç, Musa Çakmak, and Aydın Kurnaz Copyright © 2014 Ayşe Betül Koç et al. All rights reserved. Convergence Analysis of Legendre Pseudospectral Scheme for Solving Nonlinear Systems of Volterra Integral Equations Tue, 12 Aug 2014 10:08:22 +0000 We are concerned with the extension of a Legendre spectral method to the numerical solution of nonlinear systems of Volterra integral equations of the second kind. It is proved theoretically that the proposed method converges exponentially provided that the solution is sufficiently smooth. Also, three biological systems which are known as the systems of Lotka-Volterra equations are approximately solved by the presented method. Numerical results confirm the theoretical prediction of the exponential rate of convergence. Emran Tohidi, O. R. Navid Samadi, and S. Shateyi Copyright © 2014 Emran Tohidi et al. All rights reserved. On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard Type Thu, 07 Aug 2014 10:27:25 +0000 In this study we apply partial Noether and -symmetry approaches to a second-order nonlinear autonomous equation of the form , called Liénard equation corresponding to some important problems in classical mechanics field with respect to and functions. As a first approach we utilize partial Lagrangians and partial Noether operators to obtain conserved forms of Liénard equation. Then, as a second approach, based on the -symmetry method, we analyze -symmetries for the case that -function is in the form of . Finally, a classification problem for the conservation forms and invariant solutions are considered. Gülden Gün Polat and Teoman Özer Copyright © 2014 Gülden Gün Polat and Teoman Özer. All rights reserved. Field Equations in the Complex Quaternion Spaces Wed, 06 Aug 2014 08:11:29 +0000 The paper aims to adopt the complex quaternion and octonion to formulate the field equations for electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition to combine some physics contents of two fields, which were considered to be independent of each other in the past. J. C. Maxwell applied simultaneously the vector terminology and the quaternion analysis to depict the electromagnetic theory. This method edified the paper to introduce the quaternion and octonion spaces into the field theory, in order to describe the physical feature of electromagnetic and gravitational fields, while their coordinates are able to be the complex number. The octonion space can be separated into two subspaces, the quaternion space and the -quaternion space. In the quaternion space, it is able to infer the field potential, field strength, field source, field equations, and so forth, in the gravitational field. In the -quaternion space, it is able to deduce the field potential, field strength, field source, and so forth, in the electromagnetic field. The results reveal that the quaternion space is appropriate to describe the gravitational features; meanwhile, the -quaternion space is proper to depict the electromagnetic features. Zi-Hua Weng Copyright © 2014 Zi-Hua Weng. All rights reserved. Effect of Velocity Slip Boundary Condition on the Flow and Heat Transfer of Cu-Water and TiO2-Water Nanofluids in the Presence of a Magnetic Field Tue, 05 Aug 2014 07:34:09 +0000 In nanofluid mechanics, it has been proven recently that the no slip condition at the boundary is no longer valid which is the reason that we consider the effect of such slip condition on the flow and heat transfer of two types of nanofluids. The present paper considers the effect of the velocity slip condition on the flow and heat transfer of the Cu-water and the TiO2-water nanofluids over stretching/shrinking sheets in the presence of a magnetic field. The exact expression for the fluid velocity is obtained in terms of the exponential function, while an effective analytical procedure is suggested and successfully applied to obtain the exact temperature in terms of the generalized incomplete gamma function. It is found in this paper that the Cu-water nanofluid is slower than the TiO2-water nanofluid for both cases of the stretching/shrinking sheets. However, the temperature of the Cu-water nanofluid is always higher than the temperature of the TiO2-water nanofluid. In the case of shrinking sheet the dual solutions have been obtained at particular values of the physical parameters. In addition, the effect of various physical parameters on such dual solutions is discussed through the graphs. Abdelhalim Ebaid, Fahd Al Mutairi, and S. M. Khaled Copyright © 2014 Abdelhalim Ebaid et al. All rights reserved. New Neumann System Associated with a 3 × 3 Matrix Spectral Problem Thu, 24 Jul 2014 09:34:56 +0000 The nonlinearization approach of Lax pair is applied to the case of the Neumann constraint associated with a 3 × 3 matrix spectral problem, from which a new Neumann system is deduced and proved to be completely integrable in the Liouville sense. As an application, solutions of the first nontrivial equation related to the 3 × 3 matrix spectral problem are decomposed into solving two compatible Hamiltonian systems of ordinary differential equations. Fang Li and Liping Lu Copyright © 2014 Fang Li and Liping Lu. All rights reserved. Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods Tue, 22 Jul 2014 11:02:40 +0000 We apply the functional variable method, exp-function method, and -expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE) in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations. Özkan Güner and Dursun Eser Copyright © 2014 Özkan Güner and Dursun Eser. All rights reserved. Developing a Local Neurofuzzy Model for Short-Term Wind Power Forecasting Wed, 16 Jul 2014 08:56:43 +0000 Large scale integration of wind generation capacity into power systems introduces operational challenges due to wind power uncertainty and variability. Therefore, accurate wind power forecast is important for reliable and economic operation of the power systems. Complexities and nonlinearities exhibited by wind power time series necessitate use of elaborative and sophisticated approaches for wind power forecasting. In this paper, a local neurofuzzy (LNF) approach, trained by the polynomial model tree (POLYMOT) learning algorithm, is proposed for short-term wind power forecasting. The LNF approach is constructed based on the contribution of local polynomial models which can efficiently model wind power generation. Data from Sotavento wind farm in Spain was used to validate the proposed LNF approach. Comparison between performance of the proposed approach and several recently published approaches illustrates capability of the LNF model for accurate wind power forecasting. E. Faghihnia, S. Salahshour, A. Ahmadian, and N. Senu Copyright © 2014 E. Faghihnia et al. All rights reserved. On the Use of Lie Group Homomorphisms for Treating Similarity Transformations in Nonadiabatic Photochemistry Tue, 15 Jul 2014 08:34:52 +0000 A formulation based on Lie group homomorphisms is presented for simplifying the treatment of unitary similarity transformations of Hamiltonian matrices in nonadiabatic photochemistry. A general derivation is provided whereby it is shown that a similarity transformation acting on a traceless, Hermitian matrix through a unitary matrix of is equivalent to the product of a single matrix of by a real vector. We recall how Pauli matrices are the adequate tool when and show how the same is achieved for with Gell-Mann matrices. Benjamin Lasorne Copyright © 2014 Benjamin Lasorne. All rights reserved. A Weak Convergence to Hermite Process by Martingale Differences Mon, 14 Jul 2014 00:00:00 +0000 We consider the weak convergence to general Hermite process of order with index . By applying martingale differences we construct a sequence of multiple Wiener-Itô stochastic integrals such that it converges in distribution to the Hermite process . Xichao Sun and Ronglong Cheng Copyright © 2014 Xichao Sun and Ronglong Cheng. All rights reserved. Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi Equation Wed, 09 Jul 2014 08:52:45 +0000 Using an improved qualitative method which combines characteristics of several methods, we classify all travelling wave solutions of the modified Degasperis-Procesi equation in specified regions of the parametric space. Besides some popular exotic solutions including peaked waves, and looped and cusped waves, this equation also admits some very particular waves, such as fractal-like waves, double stumpons, double kinked waves, and butterfly-like waves. The last three types of solutions have not been reported in the literature. Furthermore, we give the limiting behavior of all periodic solutions as the parameters trend to some special values. Jiuli Yin, Liuwei Zhao, and Shanyu Ding Copyright © 2014 Jiuli Yin et al. All rights reserved. On the Existence of Central Configurations of -Body Problems Wed, 09 Jul 2014 08:04:58 +0000 We prove the existence of central configurations of the -body problems with Newtonian potentials in . In such configuration, masses are symmetrically located on the -axis, masses are symmetrically located on the -axis, and masses are symmetrically located on the -axis, respectively; the masses symmetrically about the origin are equal. Yueyong Jiang and Furong Zhao Copyright © 2014 Yueyong Jiang and Furong Zhao. All rights reserved. Symmetries, Traveling Wave Solutions, and Conservation Laws of a -Dimensional Boussinesq Equation Wed, 02 Jul 2014 00:00:00 +0000 We analyze the -dimensional Boussinesq equation, which has applications in fluid mechanics. We find exact solutions of the -dimensional Boussinesq equation by utilizing the Lie symmetry method along with the simplest equation method. The solutions obtained are traveling wave solutions. Moreover, we construct the conservation laws of the -dimensional Boussinesq equation using the new conservation theorem, which is due to Ibragimov. Letlhogonolo Daddy Moleleki and Chaudry Masood Khalique Copyright © 2014 Letlhogonolo Daddy Moleleki and Chaudry Masood Khalique. All rights reserved. Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators Mon, 30 Jun 2014 12:04:54 +0000 We perform a comparison between the local fractional Adomian decomposition and local fractional function decomposition methods applied to the Laplace equation. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative. Sheng-Ping Yan, Hossein Jafari, and Hassan Kamil Jassim Copyright © 2014 Sheng-Ping Yan et al. All rights reserved. Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow Sun, 29 Jun 2014 00:00:00 +0000 We discuss the line partial differential equations arising in fractal vehicular traffic flow. The nondifferentiable approximate solutions are obtained by using the local fractional Laplace variational iteration method, which is the coupling method of local fractional variational iteration method and Laplace transform. The obtained results show the efficiency and accuracy of implements of the present method. Yang Li, Long-Fei Wang, Sheng-Da Zeng, and Yang Zhao Copyright © 2014 Yang Li et al. All rights reserved. Nonlinear Fluid Flow and Heat Transfer Tue, 24 Jun 2014 06:51:29 +0000 O. D. Makinde, R. J. Moitsheki, R. N. Jana, B. H. Bradshaw-Hajek, and W. A. Khan Copyright © 2014 O. D. Makinde et al. All rights reserved. The Nondifferentiable Solution for Local Fractional Tricomi Equation Arising in Fractal Transonic Flow by Local Fractional Variational Iteration Method Thu, 19 Jun 2014 12:49:50 +0000 We present the nondifferentiable approximate solution for local fractional Tricomi equation arising in fractal transonic flow by local fractional variational iteration method. Some illustrative examples are shown and graphs are also given. Ai-Min Yang, Yu-Zhu Zhang, and Xiao-Long Zhang Copyright © 2014 Ai-Min Yang et al. All rights reserved. Spectral Relaxation Method and Spectral Quasilinearization Method for Solving Unsteady Boundary Layer Flow Problems Wed, 18 Jun 2014 08:54:18 +0000 Nonlinear partial differential equations (PDEs) modelling unsteady boundary-layer flows are solved by the spectral relaxation method (SRM) and the spectral quasilinearization method (SQLM). The SRM and SQLM are Chebyshev pseudospectral based methods that have been successfully used to solve nonlinear boundary layer flow problems described by systems of ordinary differential equations. In this paper application of these methods is extended, for the first time, to systems of nonlinear PDEs that model unsteady boundary layer flow. The new extension is tested on two problems: boundary layer flow caused by an impulsively stretching plate and a coupled four-equation system that models the problem of unsteady MHD flow and mass transfer in a porous space. Numerous simulation experiments are conducted to determine the accuracy and compare the computational performance of the proposed methods against the popular Keller-box finite difference scheme which is widely accepted as being one of the ideal tools for solving nonlinear PDEs that model boundary layer flow problems. The results indicate that the methods are more efficient in terms of computational accuracy and speed compared with the Keller-box. S. S. Motsa, P. G. Dlamini, and M. Khumalo Copyright © 2014 S. S. Motsa et al. All rights reserved. Delta Shock Wave for the Suliciu Relaxation System Wed, 18 Jun 2014 00:00:00 +0000 We study the one-dimensional Riemann problem for a hyperbolic system of three conservation laws of Temple class. This system is a simplification of a recently proposed system of five conservations laws by Bouchut and Boyaval that model viscoelastic fluids. An important issue is that the considered system is such that every characteristic field is linearly degenerate. We show an explicit solution for the Cauchy problem with initial data in . We also study the Riemann problem for this system. Under suitable generalized Rankine-Hugoniot relation and entropy condition, both existence and uniqueness of particular delta-shock type solutions are established. Richard De la cruz, Juan Galvis, Juan Carlos Juajibioy, and Leonardo Rendón Copyright © 2014 Richard De la cruz et al. All rights reserved. Bifurcation Analysis and Different Kinds of Exact Travelling Wave Solutions of a Generalized Two-Component Hunter-Saxton System Wed, 18 Jun 2014 00:00:00 +0000 This paper focuses on a generalized two-component Hunter-Saxton system. From a dynamic point of view, the existence of different kinds of periodic wave, solitary wave, and blow-up wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given. Also, some exact parametric representations of the travelling waves are presented. Qing Meng and Bin He Copyright © 2014 Qing Meng and Bin He. All rights reserved. Iterative Multistep Reproducing Kernel Hilbert Space Method for Solving Strongly Nonlinear Oscillators Tue, 17 Jun 2014 09:11:01 +0000 A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillator’s models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of convergence for the series solution. The numerical results demonstrate the validity and the applicability of the new technique. A very good agreement was found between the results obtained using the presented algorithm and the Runge-Kutta method, which shows that the multistep reproducing kernel Hilbert space method is very efficient and convenient for solving nonlinear oscillator’s models. Banan Maayah, Samia Bushnaq, Shaher Momani, and Omar Abu Arqub Copyright © 2014 Banan Maayah et al. All rights reserved. Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach Tue, 10 Jun 2014 00:00:00 +0000 From the signal processing point of view, the nondifferentiable data defined on the Cantor sets are investigated in this paper. The local fractional Fourier series is used to process the signals, which are the local fractional continuous functions. Our results can be observed as significant extensions of the previously known results for the Fourier series in the framework of the local fractional calculus. Some examples are given to illustrate the efficiency and implementation of the present method. Zhi-Yong Chen, Carlo Cattani, and Wei-Ping Zhong Copyright © 2014 Zhi-Yong Chen et al. All rights reserved. On the Deformations and Derivations of -Ary Multiplicative Hom-Nambu-Lie Superalgebras Thu, 05 Jun 2014 11:45:46 +0000 We introduce the relevant concepts of -ary multiplicative Hom-Nambu-Lie superalgebras and construct three classes of -ary multiplicative Hom-Nambu-Lie superalgebras. As a generalization of the notion of derivations for -ary multiplicative Hom-Nambu-Lie algebras, we discuss the derivations of -ary multiplicative Hom-Nambu-Lie superalgebras. In addition, the theory of one parameter formal deformation of -ary multiplicative Hom-Nambu-Lie superalgebras is developed by choosing a suitable cohomology. Baoling Guan, Liangyun Chen, and Yao Ma Copyright © 2014 Baoling Guan et al. All rights reserved. A Local Integral Equation Formulation Based on Moving Kriging Interpolation for Solving Coupled Nonlinear Reaction-Diffusion Equations Wed, 04 Jun 2014 12:50:05 +0000 The meshless local Pretrov-Galerkin method (MLPG) with the test function in view of the Heaviside step function is introduced to solve the system of coupled nonlinear reaction-diffusion equations in two-dimensional spaces subjected to Dirichlet and Neumann boundary conditions on a square domain. Two-field velocities are approximated by moving Kriging (MK) interpolation method for constructing nodal shape function which holds the Kronecker delta property, thereby enhancing the arrangement nodal shape construction accuracy, while the Crank-Nicolson method is chosen for temporal discretization. The nonlinear terms are treated iteratively within each time step. The developed formulation is verified in two numerical examples with investigating the convergence and the accuracy of numerical results. The numerical experiments revealing the solutions by the developed formulation are stable and more precise. Kanittha Yimnak and Anirut Luadsong Copyright © 2014 Kanittha Yimnak and Anirut Luadsong. All rights reserved. Effects of a Fluctuating Carrying Capacity on the Generalized Malthus-Verhulst Model Wed, 04 Jun 2014 00:00:00 +0000 We consider a generalized Malthus-Verhulst model with a fluctuating carrying capacity and we study its effects on population growth. The carrying capacity fluctuations are described by a Poissonian process with an exponential correlation function. We will find an analytical expression for the average of a number of individuals and show that even in presence of a fluctuating carrying capacity the average tends asymptotically to a constant quantity. Héctor Calisto, Kristopher J. Chandía, and Mauro Bologna Copyright © 2014 Héctor Calisto et al. All rights reserved. The Faddeev Equation and the Essential Spectrum of a Model Operator Associated with the Hamiltonian of a Nonconserved Number of Particles Mon, 02 Jun 2014 07:31:36 +0000 A model describing a truncated operator H (truncated with respect to the number of particles) and acting in the direct sum of zero-, one-, and two-particle subspaces of fermionic Fock space over is investigated. The location of the essential spectrum of the model operator H is described by means of the spectrum of the Friedreich model . Moreover, for the resolvent of H, the Faddeev type system of integral equations is obtained. Zahriddin Muminov, Fudziah Ismail, and Jamshid Rasulov Copyright © 2014 Zahriddin Muminov et al. All rights reserved. Effects of Behavioral Tactics of Predators on Dynamics of a Predator-Prey System Mon, 26 May 2014 11:19:37 +0000 A predator-prey model incorporating individual behavior is presented, where the predator-prey interaction is described by a classical Lotka-Volterra model with self-limiting prey; predators can use the behavioral tactics of rock-paper-scissors to dispute a prey when they meet. The predator behavioral change is described by replicator equations, a game dynamic model at the fast time scale, whereas predator-prey interactions are assumed acting at a relatively slow time scale. Aggregation approach is applied to combine the two time scales into a single one. The analytical results show that predators have an equal probability to adopt three strategies at the stable state of the predator-prey interaction system. The diversification tactics taking by predator population benefits the survival of the predator population itself, more importantly, it also maintains the stability of the predator-prey system. Explicitly, immediate contest behavior of predators can promote density of the predator population and keep the preys at a lower density. However, a large cost of fighting will cause not only the density of predators to be lower but also preys to be higher, which may even lead to extinction of the predator populations. Hui Zhang, Zhihui Ma, Gongnan Xie, and Lukun Jia Copyright © 2014 Hui Zhang et al. All rights reserved. A New Kind of Shift Operators for Infinite Circular and Spherical Wells Thu, 22 May 2014 08:09:25 +0000 A new kind of shift operators for infinite circular and spherical wells is identified. These shift operators depend on all spatial variables of quantum systems and connect some eigenstates of confined systems of different radii sharing energy levels with a common eigenvalue. In circular well, the momentum operators play the role of shift operators. The and operators, the third projection of the orbital angular momentum operator , and the Hamiltonian form a complete set of commuting operators with the SO(2) symmetry. In spherical well, the shift operators establish a novel relation between and . Guo-Hua Sun, K. D. Launey, T. Dytrych, Shi-Hai Dong, and J. P. Draayer Copyright © 2014 Guo-Hua Sun et al. All rights reserved.