Advances in Mathematical Physics The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. The Intersection Probability of Brownian Motion and SLEκ Wed, 26 Aug 2015 08:53:34 +0000 By using excursion measure Poisson kernel method, we obtain a second-order differential equation of the intersection probability of Brownian motion and . Moreover, we find a transformation such that the second-order differential equation transforms into a hypergeometric differential equation. Then, by solving the hypergeometric differential equation, we obtain the explicit formula of the intersection probability for the trace of the chordal and planar Brownian motion started from distinct points in an upper half-plane . Shizhong Zhou and Shiyi Lan Copyright © 2015 Shizhong Zhou and Shiyi Lan. All rights reserved. Similarity Measures of Sequence of Fuzzy Numbers and Fuzzy Risk Analysis Tue, 25 Aug 2015 08:39:21 +0000 We present the methods to evaluate the similarity measures between sequence of triangular fuzzy numbers for making contributions to fuzzy risk analysis. Firstly, we calculate the COG (center of gravity) points of sequence of triangular fuzzy numbers. After, we present the methods to measure the degree of similarity between sequence of triangular fuzzy numbers. In addition, we give an example to compare the methods mentioned in the text. Furthermore, in this paper, we deal with the type fuzzy number. By defining the algebraic operations on the type fuzzy numbers we can solve the equations in the form , where and are fuzzy number. By this way, we can build an algebraic structure on fuzzy numbers. Additionally, the generalized difference sequence spaces of triangular fuzzy numbers , , and , consisting of all sequences such that is in the spaces , , and , have been constructed, respectively. Furthermore, some classes of matrix transformations from the space and to and are characterized, respectively, where is any sequence space. Zarife Zararsız Copyright © 2015 Zarife Zararsız. All rights reserved. Automorphism Properties and Classification of Adinkras Mon, 24 Aug 2015 07:54:08 +0000 Adinkras are graphical tools for studying off-shell representations of supersymmetry. In this paper we efficiently classify the automorphism groups of Adinkras relative to a set of local parameters. Using this, we classify Adinkras according to their equivalence and isomorphism classes. We extend previous results dealing with characterization of Adinkra degeneracy via matrix products and present algorithms for calculating the automorphism groups of Adinkras and partitioning Adinkras into their isomorphism classes. B. L. Douglas, S. James Gates Jr., B. L. Segler, and J. B. Wang Copyright © 2015 B. L. Douglas et al. All rights reserved. Lie Symmetry Analysis of a First-Order Feedback Model of Option Pricing Sun, 23 Aug 2015 11:39:15 +0000 A first-order feedback model of option pricing consisting of a coupled system of two PDEs, a nonliner generalised Black-Scholes equation and the classical Black-Scholes equation, is studied using Lie symmetry analysis. This model arises as an extension of the classical Black-Scholes model when liquidity is incorporated into the market. We compute the admitted Lie point symmetries of the system and construct an optimal system of the associated one-dimensional subalgebras. We also construct some invariant solutions of the model. Winter Sinkala and Tembinkosi F. Nkalashe Copyright © 2015 Winter Sinkala and Tembinkosi F. Nkalashe. All rights reserved. Infinitely Many Standing Waves for the Nonlinear Chern-Simons-Schrödinger Equations Wed, 19 Aug 2015 12:13:14 +0000 We prove the existence of infinitely many solutions of the nonlinear Chern-Simons-Schrödinger equations under a wide class of nonlinearities. This class includes the standard power-type nonlinearity with exponent . This extends the previous result which covers the exponent . Jinmyoung Seok Copyright © 2015 Jinmyoung Seok. All rights reserved. Hom--Operators and Hom-Yang-Baxter Equations Wed, 12 Aug 2015 08:07:00 +0000 In Hom-Lie set, we introduce the concept of Hom--operators and study its relation with classical Hom-Yang-Baxter equation, as well as left-symmetric Hom-algebras. We construct the corresponding relation between left-symmetric Hom-algebras and Hom-1-cocycles, which are both related to classical Hom-Yang-Baxter equation. Moreover, in Hom-algebra setting, we establish the equivalent relationship between AHYBE (associative Hom-Yang-Baxter equations) and -operators on Frobenius monoidal Hom-algebras. Yuanyuan Chen and Liangyun Zhang Copyright © 2015 Yuanyuan Chen and Liangyun Zhang. All rights reserved. Second-Order Integrals for Systems in Involving Spin Thu, 30 Jul 2015 06:09:59 +0000 In two-dimensional Euclidean plane, existence of second-order integrals of motion is investigated for integrable Hamiltonian systems involving spin (e.g., those systems describing interaction between two particles with spin 0 and spin 1/2) and it has been shown that no nontrivial second-order integrals of motion exist for such systems. İsmet Yurduşen Copyright © 2015 İsmet Yurduşen. All rights reserved. Spatial Rotation of the Fractional Derivative in Two-Dimensional Space Mon, 27 Jul 2015 08:32:47 +0000 The transformations of the partial fractional derivatives under spatial rotation in are derived for the Riemann-Liouville and Caputo definitions. These transformation properties link the observation of physical quantities, expressed through fractional derivatives, with respect to different coordinate systems (observers). It is the hope that such understanding could shed light on the physical interpretation of fractional derivatives. Also it is necessary to be able to construct interaction terms that are invariant with respect to equivalent observers. Ehab Malkawi Copyright © 2015 Ehab Malkawi. All rights reserved. Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets Tue, 14 Jul 2015 06:55:49 +0000 A collocation method based on the second kind Chebyshev wavelets is proposed for the numerical solution of eighth-order two-point boundary value problems (BVPs) and initial value problems (IVPs) in ordinary differential equations. The second kind Chebyshev wavelets operational matrix of integration is derived and used to transform the problem to a system of algebraic equations. The uniform convergence analysis and error estimation for the proposed method are given. Accuracy and efficiency of the suggested method are established through comparing with the existing quintic B-spline collocation method, homotopy asymptotic method, and modified decomposition method. Numerical results obtained by the present method are in good agreement with the exact solutions available in the literatures. Xiaoyong Xu and Fengying Zhou Copyright © 2015 Xiaoyong Xu and Fengying Zhou. All rights reserved. Higher-Stage Noether Identities and Second Noether Theorems Mon, 13 Jul 2015 06:20:03 +0000 The direct and inverse second Noether theorems are formulated in a general case of reducible degenerate Grassmann-graded Lagrangian theory of even and odd variables on graded bundles. Such Lagrangian theory is characterized by a hierarchy of nontrivial higher-stage Noether identities which is described in the homology terms. If a certain homology regularity condition holds, one can associate with a reducible degenerate Lagrangian the exact Koszul–Tate chain complex possessing the boundary operator whose nilpotentness is equivalent to all complete nontrivial Noether and higher-stage Noether identities. The second Noether theorems associate with the above-mentioned Koszul–Tate complex a certain cochain sequence whose ascent operator consists of the gauge and higher-order gauge symmetries of a Lagrangian system. If gauge symmetries are algebraically closed, this operator is extended to the nilpotent BRST operator which brings the above-mentioned cochain sequence into the BRST complex and provides a BRST extension of an original Lagrangian. G. Sardanashvily Copyright © 2015 G. Sardanashvily. All rights reserved. Bound-State Solution of s-Wave Klein-Gordon Equation for Woods-Saxon Potential Sun, 12 Jul 2015 06:59:29 +0000 The bound-state solution of s-wave Klein-Gordon equation is calculated for Woods-Saxon potential by using the asymptotic iteration method (AIM). The energy eigenvalues and eigenfunctions are obtained for the required condition of bound-state solutions. Eser Olğar and Haydar Mutaf Copyright © 2015 Eser Olğar and Haydar Mutaf. All rights reserved. Simple Modules for Modular Lie Superalgebras , , and Thu, 09 Jul 2015 14:24:26 +0000 This paper constructs a series of modules from modular Lie superalgebras , , and over a field of prime characteristic . Cartan subalgebras, maximal vectors of these modular Lie superalgebras, can be solved. With certain properties of the positive root vectors, we obtain that the sufficient conditions of these modules are irreducible -modules, where , , and . Zhu Wei, Qingcheng Zhang, Yongzheng Zhang, and Chunyue Wang Copyright © 2015 Zhu Wei et al. All rights reserved. Formal Pseudodifferential Operators in One and Several Variables, Central Extensions, and Integrable Systems Sun, 05 Jul 2015 11:51:02 +0000 We review some aspects of the theory of Lie algebras of (twisted and untwisted) formal pseudodifferential operators in one and several variables in a general algebraic context. We focus mainly on the construction and classification of nontrivial central extensions. As applications, we construct hierarchies of centrally extended Lie algebras of formal differential operators in one and several variables, Manin triples and hierarchies of nonlinear equations in Lax and zero curvature form. Jarnishs Beltran and Enrique G. Reyes Copyright © 2015 Jarnishs Beltran and Enrique G. Reyes. All rights reserved. A Simpler GMRES Method for Oscillatory Integrals with Irregular Oscillations Thu, 02 Jul 2015 11:17:37 +0000 A simpler GMRES method for computing oscillatory integral is presented. Theoretical analysis shows that this method is mathematically equivalent to the GMRES method proposed by Olver (2009). Moreover, the simpler GMRES does not require upper Hessenberg matrix factorization, which leads to much simpler program and requires less work. Numerical experiments are conducted to illustrate the performance of the new method and show that in some cases the simpler GMRES method could achieve higher accuracy than GMRES. Qinghua Wu and Meiying Xiang Copyright © 2015 Qinghua Wu and Meiying Xiang. All rights reserved. Existence of Exponential -Stability Nonconstant Equilibrium of Markovian Jumping Nonlinear Diffusion Equations via Ekeland Variational Principle Thu, 25 Jun 2015 07:09:37 +0000 The authors obtained a delay-dependent exponential -stability criterion for a class of Markovian jumping nonlinear diffusion equations by employing the Lyapunov stability theory and some variational methods. As far as we know, it is the first time to apply Ekeland variational principle to obtain the existence of exponential stability equilibrium of -Laplacian dynamic system so that some methods used in this paper are different from those methods of many previous related literatures. In addition, the obtained existence criterion is only involved in the activation functions so that the criterion is simpler and easier than other existence criteria to be verified in practical application. Moreover, a numerical example shows the effectiveness of the proposed methods owing to the large allowable variation range of time-delay. Ruofeng Rao and Shouming Zhong Copyright © 2015 Ruofeng Rao and Shouming Zhong. All rights reserved. Centroids of Lie Supertriple Systems Thu, 18 Jun 2015 08:40:20 +0000 We derive certain structural results concerning centroids of Lie supertriple systems. Centroids of the tensor product of a Lie supertriple system and a unital commutative associative algebra are studied. Furthermore, the centroid of a tensor product of a simple Lie supertriple system and a polynomial ring is partly determined. Jianrong Peng, Liangyun Chen, and Bing Sun Copyright © 2015 Jianrong Peng et al. All rights reserved. The Breather-Like and Rational Solutions for the Integrable Kadomtsev-Petviashvili-Based System Tue, 16 Jun 2015 07:16:10 +0000 The integrable Kadomtsev-Petviashvili-based system is studied. The breather-like (a pulsating mode) and rational solutions are presented applying Hirota bilinear method and Taylor series. The intricate structures of the rational solitary wave solution are discussed mathematically and graphically. The existence conditions of three different solitary wave solution structure for the short-wave field are given by the theory of extreme value analysis. By controlling the wave number of the background plane wave we may control the the behavior of rational solitary wave. However, the shape of the rational solitary wave solution for the real long-wave field is not affected as the wave number is varied. Chuanjian Wang, Zhengde Dai, and Changfu Liu Copyright © 2015 Chuanjian Wang et al. All rights reserved. Energy Distribution of a Regular Black Hole Solution in Einstein-Nonlinear Electrodynamics Thu, 11 Jun 2015 12:26:00 +0000 A study about the energy momentum of a new four-dimensional spherically symmetric, static and charged, regular black hole solution developed in the context of general relativity coupled to nonlinear electrodynamics is presented. Asymptotically, this new black hole solution behaves as the Reissner-Nordström solution only for the particular value , where is a positive integer parameter appearing in the mass function of the solution. The calculations are performed by use of the Einstein, Landau-Lifshitz, Weinberg, and Møller energy momentum complexes. In all the aforementioned prescriptions, the expressions for the energy of the gravitating system considered depend on the mass of the black hole, its charge , a positive integer α, and the radial coordinate r. In all these pseudotensorial prescriptions, the momenta are found to vanish, while the Landau-Lifshitz and Weinberg prescriptions give the same result for the energy distribution. In addition, the limiting behavior of the energy for the cases , , and is studied. The special case and is also examined. We conclude that the Einstein and Møller energy momentum complexes can be considered as the most reliable tools for the study of the energy momentum localization of a gravitating system. I. Radinschi, F. Rahaman, Th. Grammenos, A. Spanou, and Sayeedul Islam Copyright © 2015 I. Radinschi et al. All rights reserved. Comparative Solution of Nonlinear Quintic Cubic Oscillator Using Modified Homotopy Perturbation Method Wed, 03 Jun 2015 14:00:12 +0000 We use modified homotopy perturbation method to find out the solution of nonlinear cubic quintic equation. Besides this method solution of the problem with the following methods is discussed, Energy Balance Method and He’s Frequency Formulation method and then compare the results with each other and Global Error Method. The results show that these three methods are effective as global error method for nonlinear cubic quintic oscillator equation with multiple nonlinear terms and have different effects on the solution. In particular, the homotopy perturbation solution is quite surprising. A cubic quintic nonlinear oscillator is used as an example to compare the results. Muhammad Suleman and Qingbiao Wu Copyright © 2015 Muhammad Suleman and Qingbiao Wu. All rights reserved. Geometry of the Solutions of Localized Induction Equation in the Pseudo-Galilean Space Sun, 31 May 2015 16:45:26 +0000 We study the surfaces corresponding to solutions of the localized induction equation in the pseudo-Galilean space . We classify such surfaces with null curvature and characterize some special curves on these surfaces in . Muhittin Evren Aydin, Adela Mihai, Alper Osman Ogrenmis, and Mahmut Ergut Copyright © 2015 Muhittin Evren Aydin et al. All rights reserved. Adaptive Synchronization of Chaotic Systems considering Performance Parameters of Operational Amplifiers Sun, 31 May 2015 06:26:42 +0000 This paper addresses an adaptive control approach for synchronizing two chaotic oscillators with saturated nonlinear function series as nonlinear functions. Mathematical models to characterize the behavior of the transmitter and receiver circuit were derived, including in the latter the adaptive control and taking into account, for both chaotic oscillators, the most influential performance parameters associated with operational amplifiers. Asymptotic stability of the full synchronization system is studied by using Lyapunov direct method. Theoretical derivations and related results are experimentally validated through implementations from commercially available devices. Finally, the full synchronization system can easily be reproducible at a low cost. Sergio Ruíz-Hernández, Eduardo Ortega-Torres, Carlos Sánchez-López, Miguel Angel Carrasco-Aguilar, Rocio Ochoa-Montiel, Rocio Ilhuicatzi-Roldán, and Marco Antonio Taneco-Hernández Copyright © 2015 Sergio Ruíz-Hernández et al. All rights reserved. Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States Wed, 27 May 2015 09:59:44 +0000 Previously, a formula, incorporating a hypergeometric function, for the Hilbert-Schmidt-averaged determinantal moments of density-matrices () and their partial transposes (), was applied with to the generalized two-qubit separability probability question. The formula can, furthermore, be viewed, as we note here, as an averaging over “induced measures in the space of mixed quantum states.” The associated induced-measure separability probabilities () are found—via a high-precision density approximation procedure—to assume interesting, relatively simple rational values in the two-re[al]bit (), (standard) two-qubit (), and two-quater[nionic]bit () cases. We deduce rather simple companion (rebit, qubit, quaterbit, …) formulas that successfully reproduce the rational values assumed for general  . These formulas are observed to share certain features, possibly allowing them to be incorporated into a single master formula. Paul B. Slater and Charles F. Dunkl Copyright © 2015 Paul B. Slater and Charles F. Dunkl. All rights reserved. Coupling Influence on Signal Readout of a Dual-Parameter LC Resonant System Mon, 25 May 2015 11:59:08 +0000 Dual-parameter inductive-capacitive (LC) resonant sensor is gradually becoming the measurement trend in complex harsh environments; however, the coupling between inductors greatly affects the readout signal, which becomes very difficult to resolve by means of simple mathematical tools. By changing the values of specific variables in a MATLAB code, the influence of coupling between coils on the readout signal is analyzed. Our preliminary conclusions underline that changing the coupling to antenna greatly affects the readout signal, but it simultaneously influences the other signal. When , it is better to broaden the difference between the two coupling coefficients and . On the other side, when is smaller than , it is better to decrease the coupling between sensor inductors , in order to obtain two readout signals averaged in strength. Finally, a test system including a discrete capacitor soldered to a printed circuit board (PCB) based planar spiral coil is built, and the readout signals under different relative inductors positions are analyzed. All experimental results are in good agreement with the results of the MATLAB simulation. Jijun Xiong, Tanyong Wei, Tao Luo, Qiulin Tan, Chenyang Xue, Jun Liu, and Wendong Zhang Copyright © 2015 Jijun Xiong et al. All rights reserved. Comparison of 3D Adaptive Remeshing Strategies for Finite Element Simulations of Electromagnetic Heating of Gold Nanoparticles Sun, 24 May 2015 11:54:32 +0000 The optical properties of metallic nanoparticles are well known, but the study of their thermal behavior is in its infancy. However the local heating of surrounding medium, induced by illuminated nanostructures, opens the way to new sensors and devices. Consequently the accurate calculation of the electromagnetically induced heating of nanostructures is of interest. The proposed multiphysics problem cannot be directly solved with the classical refinement method of Comsol Multiphysics and a 3D adaptive remeshing process based on an a posteriori error estimator is used. In this paper the efficiency of three remeshing strategies for solving the multiphysics problem is compared. The first strategy uses independent remeshing for each physical quantity to reach a given accuracy. The second strategy only controls the accuracy on temperature. The third strategy uses a linear combination of the two normalized targets (the electric field intensity and the temperature). The analysis of the performance of each strategy is based on the convergence of the remeshing process in terms of number of elements. The efficiency of each strategy is also characterized by the number of computation iterations, the number of elements, the CPU time, and the RAM required to achieve a given target accuracy. Fadhil Mezghani, Dominique Barchiesi, Abel Cherouat, Thomas Grosges, and Houman Borouchaki Copyright © 2015 Fadhil Mezghani et al. All rights reserved. Exact Solutions for Some Fractional Differential Equations Wed, 20 May 2015 11:31:02 +0000 The extended Jacobi elliptic function expansion method is used for solving fractional differential equations in the sense of Jumarie’s modified Riemann-Liouville derivative. By means of this approach, a few fractional differential equations are successfully solved. As a result, some new Jacobi elliptic function solutions including solitary wave solutions and trigonometric function solutions are established. The proposed method can also be applied to other fractional differential equations. Abdullah Sonmezoglu Copyright © 2015 Abdullah Sonmezoglu. All rights reserved. Analytical Models for Gravitating Radiating Systems Mon, 11 May 2015 12:39:46 +0000 We analyse the gravitational behaviour of a relativistic heat conducting fluid in a shear-free spherically symmetric spacetime. We show that the isotropy of pressure is a consistency condition which realises a second order nonlinear ordinary differential equation with variable coefficients in the gravitational potentials. Several new classes of solutions are found to the governing equation by imposing various forms on one of the potentials. Interestingly, a complex transformation leads to an exact solution with only real metric functions. All solutions are written in terms of elementary functions. We demonstrate graphically that the fluid pressure, energy density, and heat flux are well behaved for the model, and the model is consistent with a core-envelope framework. B. P. Brassel, S. D. Maharaj, and G. Govender Copyright © 2015 B. P. Brassel et al. All rights reserved. Integrodifferential Equations of the Vector Problem of Electromagnetic Wave Diffraction by a System of Nonintersecting Screens and Inhomogeneous Bodies Wed, 06 May 2015 07:11:42 +0000 The vector problem of electromagnetic wave diffraction by a system of bodies and infinitely thin screens is considered in a quasi-classical formulation. The solution is sought in the classical sense but is defined not in the entire space but rather everywhere except for the screen edges. The original boundary value problem for Maxwell’s equations system is reduced to a system of integrodifferential equations in the regions occupied by the bodies and on the screen surfaces. The integrodifferential operator is treated as a pseudodifferential operator in Sobolev spaces and is shown to be zero-index Fredholm operator. Y. G. Smirnov and A. A. Tsupak Copyright © 2015 Y. G. Smirnov and A. A. Tsupak. All rights reserved. Study on Impeller Fracture Model Based on Vibration Characteristics and Fractal Theory Tue, 05 May 2015 12:27:44 +0000 During the operation of centrifugal compressor, failure easily occurs in the presence of complicated external forces. The failure process characterizes with strong nonlinearity, and hence it is difficult to be described by conventional methods. In this paper, firstly, the cracks in different positions are described using crack fractal theory. The basic failure modes of the impeller are summarized. Secondly, a three-dimensional finite element model of the impeller is constructed. Then the von Mises stress under the centrifugal force is calculated, and the corresponding impeller failure process is simulated by “element life and death technology” in ANSYS. Finally, the impeller failure mechanism is analyzed. It can be found that the static stress is not the main cause of the impeller failure, and the dynamic characteristics of the impeller are not perfect because of the pitch vibration modes which appeared in the investigated frequency range. Meanwhile, the natural frequency of the impeller also cannot avoid the frequency of the excitation force. Xiaolong Zhang, Ruishan Yuan, and Yonghui Xie Copyright © 2015 Xiaolong Zhang et al. All rights reserved. Existence of Center for Planar Differential Systems with Impulsive Perturbations Tue, 05 May 2015 07:35:26 +0000 We present a method that uses successor functions in ordinary differential systems to address the “center-focus” problem of a class of planar systems that have an impulsive perturbation. By deriving solution formulae for impulsive systems, several interesting criteria for distinguishing between the center and the focus of linear and nonlinear planar systems with state-dependent impulsions are established. The conditions describing the stability of the focus of the considered models are also given. The computing methods presented here are more convenient for determining the center of impulsive systems than those in the literature. Numerical examples are given to show the effectiveness of the theoretical results. Dengguo Xu Copyright © 2015 Dengguo Xu. All rights reserved. ()-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves Tue, 28 Apr 2015 07:36:32 +0000 By constructing a kind of generalized Lie algebra, based on generalized Tu scheme, a new ()-dimensional mKdV hierarchy is derived which popularizes the results of ()-dimensional integrable system. Furthermore, the ()-dimensional mKdV equation can be applied to describe the propagation of the Rossby solitary waves in the plane of ocean and atmosphere, which is different from the ()-dimensional mKdV equation. By virtue of Riccati equation, some solutions of ()-dimensional mKdV equation are obtained. With the help of solitary wave solutions, similar to the fiber soliton communication, the chirp effect of Rossby solitary waves is discussed and some conclusions are given. Chunlei Wang, Yong Zhang, Baoshu Yin, and Xiaoen Zhang Copyright © 2015 Chunlei Wang et al. All rights reserved.