Advances in Mathematical Physics The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Symmetry and Group Theory and Its Application to Few-Body Physics Thu, 18 Dec 2014 11:12:45 +0000 Xiao-Yan Gu, Fabien Gatti, Shi-Hai Dong, and Jian-Qiang Sun Copyright © 2014 Xiao-Yan Gu et al. All rights reserved. Fundamental Solutions for Periodic Media Sun, 14 Dec 2014 06:42:17 +0000 Necessity for the periodic fundamental solutions arises when the periodic boundary value problems should be analyzed. The latter are naturally related to problems of finding the homogenized properties of the dispersed composites, porous media, and media with uniformly distributed microcracks or dislocations. Construction of the periodic fundamental solutions is done in terms of the convergent series in harmonic polynomials. An example of the periodic fundamental solution for the anisotropic porous medium is constructed, along with the simplified lower bound estimate. Sergey V. Kuznetsov Copyright © 2014 Sergey V. Kuznetsov. All rights reserved. Lie Symmetry Reductions and Exact Solutions to the Rosenau Equation Sun, 14 Dec 2014 00:10:45 +0000 The Lie symmetry analysis is performed on the Rosenau equation which arises in modeling many physical phenomena. The similarity reductions and exact solutions are presented. Then the exact analytic solutions are considered by the power series method. Ben Gao and Hongxia Tian Copyright © 2014 Ben Gao and Hongxia Tian. All rights reserved. Investigations on Vehicle Rollover Prevention Using LQG Regulator Tue, 09 Dec 2014 08:40:06 +0000 This paper presents results of an initial investigation into vehicle roll model and control strategies suitable for preventing vehicle untripped rollovers. For vehicles that are deemed to be susceptible to wheel-liftoff, various control strategies are implemented in simulation. In this study, the authors propose a method for rollover prevention that does not require such accurate contact information. The validity of the stability margin is shown, and it is used to realize rollover prevention in the direction of the roll. The primary assumption in their implementation is that the vehicle in question is equipped with a conventional controller system. Binda Mridula Balakrishnan and Marimuthu Rajaram Copyright © 2014 Binda Mridula Balakrishnan and Marimuthu Rajaram. All rights reserved. Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions Wed, 26 Nov 2014 00:10:07 +0000 We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder’s degree theory. Enlightening examples illustrating the obtained results are also presented. Jessada Tariboon, Sotiris K. Ntouyas, and Chatthai Thaiprayoon Copyright © 2014 Jessada Tariboon et al. All rights reserved. Shear Wave Propagation in Multilayered Medium including an Irregular Fluid Saturated Porous Stratum with Rigid Boundary Wed, 12 Nov 2014 06:11:08 +0000 The present investigation is concerned with the study of propagation of shear waves in an anisotropic fluid saturated porous layer over a semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the perturbation technique followed by Fourier transformation. Numerically, the effect of irregularity present is analysed. It is seen that the phase velocity is significantly influenced by the wave number and the depth of the irregularity. The variations of dimensionless phase velocity against dimensionless wave number are shown graphically for the different size of rectangular irregularities with the help of MATLAB. Ravinder Kumar, Dinesh Kumar Madan, and Jitander Singh Sikka Copyright © 2014 Ravinder Kumar et al. All rights reserved. On the Deformation Retract of Kerr Spacetime and Its Folding Mon, 10 Nov 2014 00:00:00 +0000 The deformation retract of the Kerr spacetime is introduced using Lagrangian equations. The equatorial geodesics of the Kerr space have been discussed. The retraction of this space into itself and into geodesics has been presented. The deformation retract of this space into itself and after the isometric folding has been discussed. Theorems concerning these relations have been deduced. H. Rafat Copyright © 2014 H. Rafat. All rights reserved. Solution Theory of Ginzburg-Landau Theory on BCS-BEC Crossover Sun, 02 Nov 2014 11:22:59 +0000 We establish strong solution theory of time-dependent Ginzburg-Landau (TDGL) systems on BCS-BEC crossover. By the properties of Besov, Sobolev spaces, and Fourier functions and the method of bootstrapping argument, we deduce that the global existence of strong solutions to time-dependent Ginzburg-Landau systems on BCS-BEC crossover in various spatial dimensions. Shuhong Chen and Zhong Tan Copyright © 2014 Shuhong Chen and Zhong Tan. All rights reserved. Some Propositions on Generalized Nevanlinna Functions of the Class Thu, 23 Oct 2014 07:15:55 +0000 Some propositions on the generalized Nevanlinna functions are derived. We indicate mainly that (1) the negative inertia index of a Hermitian generalized Loewner matrix generated by a generalized Nevanlinna function in the class does not exceed . This leads to an equivalent definition of a generalized Nevanlinna function; (2) if a generalized Nevanlinna function in the class has a uniform asymptotic expansion at a real point or at infinity, then the negative inertia index of the Hankel matrix constructed with the partial coefficients of that asymptotic expansion does not exceed . Also, an explicit formula for the negative index of a real rational function is given by using relations among Loewner, Bézout, and Hankel matrices. These results will provide first tools for the solution of the indefinite truncated moment problems together with the multiple Nevanlinna-Pick interpolation problems in the class based on the so-called Hankel vector approach. Yan-Ping Song, Hui-Feng Hao, Yong-Jian Hu, and Gong-Ning Chen Copyright © 2014 Yan-Ping Song et al. All rights reserved. Hybrid Dislocated Control and General Hybrid Projective Dislocated Synchronization for Memristor Chaotic Oscillator System Thu, 16 Oct 2014 06:13:07 +0000 Some important dynamical properties of the memristor chaotic oscillator system have been studied in the paper. A novel hybrid dislocated control method and a general hybrid projective dislocated synchronization scheme have been realized for memristor chaotic oscillator system. The paper firstly presents hybrid dislocated control method for stabilizing chaos to the unstable equilibrium point. Based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization has been studied for the drive memristor chaotic oscillator system and the same response memristor chaotic oscillator system. For the different dimensions, the memristor chaotic oscillator system and the other chaotic system have realized general hybrid projective dislocated synchronization. Numerical simulations are given to show the effectiveness of these methods. Junwei Sun, Chun Huang, and Guangzhao Cui Copyright © 2014 Junwei Sun et al. All rights reserved. Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity Mon, 15 Sep 2014 09:33:33 +0000 We derive the solitonic solution of the nonlinear Schrödinger equation with cubic nonlinearity, complex potentials, and time-dependent coefficients using the Darboux transformation. We establish the integrability condition for the most general nonlinear Schrödinger equation with cubic nonlinearity and discuss the effect of the coefficients of the higher-order terms in the solitonic solution. We find that the third-order dispersion term can be used to control the soliton motion without the need for an external potential. We discuss the integrability conditions and find the solitonic solution of some of the well-known nonlinear Schrödinger equations with cubic nonlinearity and time-dependent coefficients. We also investigate the higher-order nonlinear Schrödinger equation with cubic and quintic nonlinearities. H. Chachou Samet, M. Benarous, M. Asad-uz-zaman, and U. Al Khawaja Copyright © 2014 H. Chachou Samet et al. All rights reserved. Exact Solutions of the Time Fractional BBM-Burger Equation by Novel -Expansion Method Thu, 11 Sep 2014 10:23:57 +0000 The fractional derivatives are used in the sense modified Riemann-Liouville to obtain exact solutions for BBM-Burger equation of fractional order. This equation can be converted into an ordinary differential equation by using a persistent fractional complex transform and, as a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions are attained. The performance of the method is reliable, useful, and gives newer general exact solutions with more free parameters than the existing methods. Numerical results coupled with the graphical representation completely reveal the trustworthiness of the method. Muhammad Shakeel, Qazi Mahmood Ul-Hassan, Jamshad Ahmad, and Tauseef Naqvi Copyright © 2014 Muhammad Shakeel et al. All rights reserved. Low Temperature Expansion in the Lifshitz Formula Tue, 09 Sep 2014 00:00:00 +0000 The low temperature expansion of the free energy in a Casimir effect setup is considered in detail. The starting point is the Lifshitz formula in Matsubara representation and the basic method is its reformulation using the Abel-Plana formula making full use of the analytic properties. This provides a unified description of specific models. We rederive the known results and, in a number of cases, we are able to go beyond. We also discuss the cases with dissipation. It is an aim of the paper to give a coherent exposition of the asymptotic expansions for . The paper includes the derivations and should provide a self-contained representation. M. Bordag Copyright © 2014 M. Bordag. All rights reserved. On Generalized Jordan Prederivations and Generalized Prederivations of Lie Superalgebras Tue, 02 Sep 2014 13:05:24 +0000 The concepts of (generalized) -prederivations and (generalized) Jordan -prederivations on a Lie superalgebra are introduced. It is proved that Jordan -prederivations (resp., generalized Jordan -prederivations) are -prederivations (resp., generalized -prederivations) on a Lie superalgebra under some conditions. In particular, Jordan -prederivations are -prederivations on a Lie superalgebra. Yao Ma and Liangyun Chen Copyright © 2014 Yao Ma and Liangyun Chen. All rights reserved. -Soliton Solutions of the Nonisospectral Generalized Sawada-Kotera Equation Mon, 01 Sep 2014 06:09:27 +0000 The soliton interaction is investigated based on solving the nonisospectral generalized Sawada-Kotera (GSK) equation. By using Hirota method, the analytic one-, two-, three-, and -soliton solutions of this model are obtained. According to those solutions, the relevant properties and features of line-soliton and bright-soliton are illustrated. The results of this paper will be useful to the study of soliton resonance in the inhomogeneous media. Jian Zhou, Xiang-Gui Li, and Deng-Shan Wang Copyright © 2014 Jian Zhou et al. All rights reserved. An Alternative Approach to Energy Eigenvalue Problems of Anharmonic Potentials Wed, 27 Aug 2014 08:24:33 +0000 Energy eigenvalues of quartic and sextic type anharmonic potentials are obtained by using an alternative method called asymptotic Taylor expansion method (ATEM) which is an approximate approach based on the asymptotic Taylor series expansion of a function. It is shown that the energy eigenvalues found by ATEM are in excellent agreement with the existing results. Okan Ozer and Halide Koklu Copyright © 2014 Okan Ozer and Halide Koklu. All rights reserved. Fujita Exponent for a Nonlinear Degenerate Parabolic Equation with Localized Source Sun, 24 Aug 2014 12:37:37 +0000 This paper is devoted to understand the blow-up properties of reaction-diffusion equations which combine a localized reaction term with nonlinear diffusion. In particular, we study the critical exponent of a -Laplacian equation with a localized reaction. We obtain the Fujita exponent of the equation. Yulan Wang, Xiaojun Song, and Chao Ye Copyright © 2014 Yulan Wang et al. 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.