Advances in Mathematical Physics The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. Remarks on Chern-Simons-Higgs Equations in Thu, 22 Sep 2016 13:46:23 +0000 We prove global existence of solutions to Chern-Simons-Higgs equations under the gauge condition . We also find stationary solutions. Hyungjin Huh and Guanghui Jin Copyright © 2016 Hyungjin Huh and Guanghui Jin. All rights reserved. The Strict AKNS Hierarchy: Its Structure and Solutions Thu, 08 Sep 2016 09:16:48 +0000 We discuss an integrable hierarchy of compatible Lax equations that is obtained by a wider deformation of a commutative algebra in the loop space of than that in the AKNS case and whose Lax equations are based on a different decomposition of this loop space. We show the compatibility of these Lax equations and that they are equivalent to a set of zero curvature relations. We present a linearization of the system and conclude by giving a wide construction of solutions of this hierarchy. G. F. Helminck Copyright © 2016 G. F. Helminck. All rights reserved. Lie Subalgebras of the Matrix Quantum Pseudodifferential Operators Wed, 07 Sep 2016 16:52:29 +0000 We give a complete description of the anti-involutions that preserve the principal gradation of the algebra of matrix quantum pseudodifferential operators and we describe the Lie subalgebras of their minus fixed points. Karina Batistelli and Carina Boyallian Copyright © 2016 Karina Batistelli and Carina Boyallian. All rights reserved. Fractal Dimension versus Process Complexity Wed, 07 Sep 2016 11:33:22 +0000 We look at small Turing machines (TMs) that work with just two colors (alphabet symbols) and either two or three states. For any particular such machine and any particular input , we consider what we call the space-time diagram which is basically the collection of consecutive tape configurations of the computation . In our setting, it makes sense to define a fractal dimension for a Turing machine as the limiting fractal dimension for the corresponding space-time diagrams. It turns out that there is a very strong relation between the fractal dimension of a Turing machine of the above-specified type and its runtime complexity. In particular, a TM with three states and two colors runs in at most linear time, if and only if its dimension is 2, and its dimension is 1, if and only if it runs in superpolynomial time and it uses polynomial space. If a TM runs in time , we have empirically verified that the corresponding dimension is , a result that we can only partially prove. We find the results presented here remarkable because they relate two completely different complexity measures: the geometrical fractal dimension on one side versus the time complexity of a computation on the other side. Joost J. Joosten, Fernando Soler-Toscano, and Hector Zenil Copyright © 2016 Joost J. Joosten et al. All rights reserved. Two Kinds of Darboux-Bäcklund Transformations for the -Deformed KdV Hierarchy with Self-Consistent Sources Wed, 07 Sep 2016 09:28:21 +0000 Two kinds of Darboux-Bäcklund transformations (DBTs) are constructed for the -deformed th KdV hierarchy with self-consistent sources (-NKdVHSCS) by using the -deformed pseudodifferential operators. Note that one of the DBTs provides a nonauto Bäcklund transformation for two -deformed th KdV equations with self-consistent sources (-NKdVESCS) with different degree. In addition, the soliton solution to the first nontrivial equation of -KdVHSCS is also obtained. Hongxia Wu, Liangjuan Gao, Jingxin Liu, and Yunbo Zeng Copyright © 2016 Hongxia Wu et al. All rights reserved. Controlling Neimark-Sacker Bifurcation in Delayed Species Model Using Feedback Controller Sun, 04 Sep 2016 09:40:43 +0000 Based on the stability and orthogonal polynomial approximation theory, the ordinary, dislocated, enhancing, and random feedback control methods are used to suppress the Neimark-Sacker bifurcation to fixed point in this paper. It is shown that the convergence rate of enhancing feedback control and random feedback control can be faster than those of dislocated and ordinary feedback control. The random feedback control method, which does not require any adjustable control parameters of the model, just only slightly changes the random intensity. Finally, numerical simulations are presented to verify the effectiveness of the proposed controllers. Jie Ran, Yanmin Liu, Jun He, and Xiang Li Copyright © 2016 Jie Ran et al. All rights reserved. On the Definition of Energy for a Continuum, Its Conservation Laws, and the Energy-Momentum Tensor Wed, 31 Aug 2016 16:18:18 +0000 We review the energy concept in the case of a continuum or a system of fields. First, we analyze the emergence of a true local conservation equation for the energy of a continuous medium, taking the example of an isentropic continuum in Newtonian gravity. Next, we consider a continuum or a system of fields in special relativity: we recall that the conservation of the energy-momentum tensor contains two local conservation equations of the same kind as before. We show that both of these equations depend on the reference frame and that, however, they can be given a rigorous meaning. Then, we review the definitions of the canonical and Hilbert energy-momentum tensors from a Lagrangian through the principle of stationary action in general space-time. Using relatively elementary mathematics, we prove precise results regarding the definition of the Hilbert tensor field, its uniqueness, and its tensoriality. We recall the meaning of its covariant conservation equation. We end with a proof of uniqueness of the energy density and flux, when both depend polynomially on the fields. Mayeul Arminjon Copyright © 2016 Mayeul Arminjon. All rights reserved. Classical Logic and Quantum Logic with Multiple and Common Lattice Models Wed, 31 Aug 2016 10:19:25 +0000 We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space. We give an equivalent proof for the classical logic which turns out to have disjoint distributive and nondistributive ortholattices. In particular, we prove that both classical logic and quantum logic are sound and complete with respect to each of these lattices. We also show that there is one common nonorthomodular lattice that is a model of both quantum and classical logic. In technical terms, that enables us to run the same classical logic on both a digital (standard, two-subset, 0-1-bit) computer and a nondigital (say, a six-subset) computer (with appropriate chips and circuits). With quantum logic, the same six-element common lattice can serve us as a benchmark for an efficient evaluation of equations of bigger lattice models or theorems of the logic. Mladen Pavičić Copyright © 2016 Mladen Pavičić. All rights reserved. Characterizations of Fuzzy Ideals in Coresiduated Lattices Tue, 30 Aug 2016 08:24:20 +0000 The notions of fuzzy ideals are introduced in coresiduated lattices. The characterizations of fuzzy ideals, fuzzy prime ideals, and fuzzy strong prime ideals in coresiduated lattices are investigated and the relations between ideals and fuzzy ideals are established. Moreover, the equivalence of fuzzy prime ideals and fuzzy strong prime ideals is proved in prelinear coresiduated lattices. Furthermore, the conditions under which a fuzzy prime ideal is derived from a fuzzy ideal are presented in prelinear coresiduated lattices. Yan Liu and Mucong Zheng Copyright © 2016 Yan Liu and Mucong Zheng. All rights reserved. Curing Black Hole Singularities with Local Scale Invariance Mon, 29 Aug 2016 07:21:03 +0000 We show that Weyl-invariant dilaton gravity provides a description of black holes without classical space-time singularities. Singularities appear due to the ill behaviour of gauge fixing conditions, one example being the gauge in which theory is classically equivalent to standard General Relativity. The main conclusions of our analysis are as follows: (1) singularities signal a phase transition from broken to unbroken phase of Weyl symmetry; (2) instead of a singularity, there is a “baby universe” or a white hole inside a black hole; (3) in the baby universe scenario, there is a critical mass after which reducing mass makes the black hole larger as viewed by outside observers; (4) if a black hole could be connected with white hole through the “singularity,” this would require breakdown of (classical) geometric description; (5) the singularity of Schwarzschild BH solution is nongeneric and so it is dangerous to rely on it in deriving general results. Our results may have important consequences for resolving issues related to information loss puzzle. Though quantum effects are still crucial and may change the proposed classical picture, a position of building quantum theory around essentially regular classical solutions normally provides a much better starting point. Predrag Dominis Prester Copyright © 2016 Predrag Dominis Prester. All rights reserved. The Bi-Integrable Couplings of Two-Component Casimir-Qiao-Liu Type Hierarchy and Their Hamiltonian Structures Sun, 28 Aug 2016 14:19:01 +0000 A new type of two-component Casimir-Qiao-Liu type hierarchy (2-CQLTH) is produced from a new spectral problem and their bi-Hamiltonian structures are constructed. Particularly, a new completely integrable two-component Casimir-Qiao-Liu type equation (2-CQLTE) is presented. Furthermore, based on the semidirect sums of matrix Lie algebras consisting of block matrix Lie algebra, the bi-integrable couplings of the 2-CQLTH are constructed and their bi-Hamiltonian structures are furnished. Juhui Zhang and Yuqin Yao Copyright © 2016 Juhui Zhang and Yuqin Yao. All rights reserved. A Numberable Set of Exact Solutions for the Macroscopic Approach to Extended Thermodynamics of Polyatomic Gases with Many Moments Thu, 25 Aug 2016 12:09:40 +0000 A new model for Polyatomic Gases with an arbitrary but fixed number of moments has been recently proposed and investigated in the framework of Extended Thermodynamics; the arbitrariness of the number of moments is linked to a number and the resulting model is called an -Model. This model has been elaborated in order to take into account the entropy principle, the Galilean relativity principle, and some symmetry conditions. It has been proved that the solution for all these conditions exists, but it has not been written explicitly because hard notation is necessary; it has only been shown how the theory is self-generating in the sense that if we know the closure of the -Model, then we will be able to find that of -Model. Up to now only a single particular solution has been found in this regard. Instead of this, we find here a numberable set of exact solutions which hold for every fixed number . Maria Cristina Carrisi, Rita Enoh Tchame, Marcel Obounou, and Sebastiano Pennisi Copyright © 2016 Maria Cristina Carrisi et al. All rights reserved. From Boole to Leggett-Garg: Epistemology of Bell-Type Inequalities Thu, 25 Aug 2016 11:22:12 +0000 In 1862, George Boole derived an inequality for variables that represents a demarcation line between possible and impossible experience. This inequality forms an important milestone in the epistemology of probability theory and probability measures. In 1985 Leggett and Garg derived a physics related inequality, mathematically identical to Boole’s, that according to them represents a demarcation between macroscopic realism and quantum mechanics. We show that a wide gulf separates the “sense impressions” and corresponding data, as well as the postulates of macroscopic realism, from the mathematical abstractions that are used to derive the inequality of Leggett and Garg. If the gulf can be bridged, one may indeed derive the said inequality, which is then clearly a demarcation between possible and impossible experience: it cannot be violated and is not violated by quantum theory. This implies that the Leggett-Garg inequality does not mean that the SQUID flux is not there when nobody looks, as Leggett and Garg suggest, but instead that the probability measures may not be what Leggett and Garg have assumed them to be, when no data can be secured that directly relate to them. We show that similar considerations apply to other quantum interpretation-puzzles such as two-slit experiments. Karl Hess, Hans De Raedt, and Kristel Michielsen Copyright © 2016 Karl Hess et al. All rights reserved. Two-Dimensional Nonlinear Propagation of Ion Acoustic Waves through KPB and KP Equations in Weakly Relativistic Plasmas Wed, 24 Aug 2016 08:11:15 +0000 Two-dimensional three-component plasma system consisting of nonextensive electrons, positrons, and relativistic thermal ions is considered. The well-known Kadomtsev-Petviashvili-Burgers and Kadomtsev-Petviashvili equations are derived to study the basic characteristics of small but finite amplitude ion acoustic waves of the plasmas by using the reductive perturbation method. The influences of positron concentration, electron-positron and ion-electron temperature ratios, strength of electron and positrons nonextensivity, and relativistic streaming factor on the propagation of ion acoustic waves in the plasmas are investigated. It is revealed that the electrostatic compressive and rarefactive ion acoustic waves are obtained for superthermal electrons and positrons, but only compressive ion acoustic waves are found and the potential profiles become steeper in case of subthermal positrons and electrons. M. G. Hafez, M. R. Talukder, and M. Hossain Ali Copyright © 2016 M. G. Hafez et al. All rights reserved. Higher Spin Symmetries of the Free Schrödinger Equation Sun, 21 Aug 2016 11:18:39 +0000 It is shown that the Schrödinger symmetry algebra of a free particle in spatial dimensions can be embedded into a representation of the higher spin algebra. The latter spans an infinite dimensional algebra of higher-order symmetry generators of the free Schrödinger equation. An explicit representation of the maximal finite dimensional subalgebra of the higher spin algebra is given in terms of nonrelativistic generators. We show also how to convert Vasiliev’s equations into an explicit nonrelativistic covariant form, such that they might apply to nonrelativistic systems. Our procedure reveals that the space of solutions of the Schrödinger equation can be regarded also as a supersymmetric module. Mauricio Valenzuela Copyright © 2016 Mauricio Valenzuela. All rights reserved. A Mixed Finite Element Formulation for the Conservative Fractional Diffusion Equations Tue, 16 Aug 2016 07:35:49 +0000 We consider a boundary-value problem of one-side conservative elliptic equation involving Riemann-Liouville fractional integral. The appearance of the singular term in the solution leads to lower regularity of the solution of the equation, so to the lower order convergence rate for the numerical solution. In this paper, by the dividing of equation, we drop the lower regularity term in the solution successfully and get a new fractional elliptic equation which has full regularity. We present a theoretical framework of mixed finite element approximation to the new fractional elliptic equation and derive the error estimates for unknown function, its derivative, and fractional-order flux. Some numerical results are illustrated to confirm the optimal error estimates. Suxiang Yang and Huanzhen Chen Copyright © 2016 Suxiang Yang and Huanzhen Chen. All rights reserved. Strong Isomorphism in Eisert-Wilkens-Lewenstein Type Quantum Games Sun, 14 Aug 2016 07:12:15 +0000 The aim of this paper is to bring together the notions of quantum game and game isomorphism. The work is intended as an attempt to introduce a new criterion for quantum game schemes. The generally accepted requirement forces a quantum scheme to generate the classical game in a particular case. Now, given a quantum game scheme and two isomorphic classical games, we additionally require the resulting quantum games to be isomorphic as well. We are concerned with the Eisert-Wilkens-Lewenstein quantum game scheme and the strong isomorphism between games in strategic form. Piotr Frąckiewicz Copyright © 2016 Piotr Frąckiewicz. All rights reserved. Formal First Integrals of General Dynamical Systems Tue, 09 Aug 2016 12:18:33 +0000 The goal of this paper is trying to make a complete study on the integrability for general analytic nonlinear systems by first integrals. We will firstly give an exhaustive discussion on analytic planar systems. Then a class of higher dimensional systems with invariant manifolds will be considered; we will develop several criteria for existence of formal integrals and give some applications to illustrate our results at last. Jia Jiao, Wenlei Li, and Qingjian Zhou Copyright © 2016 Jia Jiao et al. All rights reserved. Theory of Nonlocal Point Transformations in General Relativity Mon, 08 Aug 2016 07:10:28 +0000 A discussion of the functional setting customarily adopted in General Relativity (GR) is proposed. This is based on the introduction of the notion of nonlocal point transformations (NLPTs). While allowing the extension of the traditional concept of GR-reference frame, NLPTs are important because they permit the explicit determination of the map between intrinsically different and generally curved space-times expressed in arbitrary coordinate systems. For this purpose in the paper the mathematical foundations of NLPT-theory are laid down and basic physical implications are considered. In particular, explicit applications of the theory are proposed, which concern a solution to the so-called Einstein teleparallel problem in the framework of NLPT-theory; the determination of the tensor transformation laws holding for the acceleration 4-tensor with respect to the group of NLPTs and the identification of NLPT-acceleration effects, namely, the relationship established via general NLPT between particle 4-acceleration tensors existing in different curved space-times; the construction of the nonlocal transformation law connecting different diagonal metric tensors solution to the Einstein field equations; and the diagonalization of nondiagonal metric tensors. Massimo Tessarotto and Claudio Cremaschini Copyright © 2016 Massimo Tessarotto and Claudio Cremaschini. All rights reserved. Vector Solitons of a Coupled Schrödinger System with Variable Coefficients Thu, 04 Aug 2016 07:59:34 +0000 We show the existence of waveforms of finite-energy (vector solitons) for a coupled nonlinear Schrödinger system with inhomogeneous coefficients. Furthermore, some of these solutions are approximated using a Newton-type iteration, combined with a collocation-spectral strategy to discretize the corresponding soliton equations. Some numerical simulations concerned with analysis of a collision of two oncoming vector solitons of the system are also performed. Juan Carlos Muñoz Grajales Copyright © 2016 Juan Carlos Muñoz Grajales. All rights reserved. Explicit Solutions of the Boundary Value Problems for an Ellipse with Double Porosity Sun, 31 Jul 2016 12:53:50 +0000 The basic two-dimensional boundary value problems of the fully coupled linear equilibrium theory of elasticity for solids with double porosity structure are reduced to the solvability of two types of a problem. The first one is the BVPs for the equations of classical elasticity of isotropic bodies, and the other is the BVPs for the equations of pore and fissure fluid pressures. The solutions of these equations are presented by means of elementary (harmonic, metaharmonic, and biharmonic) functions. On the basis of the gained results, we constructed an explicit solution of some basic BVPs for an ellipse in the form of absolutely uniformly convergent series. Lamara Bitsadze and Natela Zirakashvili Copyright © 2016 Lamara Bitsadze and Natela Zirakashvili. All rights reserved. Electromagnetic Scattering at the Waveguide Step between Equilateral Triangular Waveguides Sun, 31 Jul 2016 11:47:18 +0000 The analysis of the electromagnetic scattering at discontinuities between equilateral triangular waveguides is studied. The complete electromagnetic solution is derived using analytical closed form expressions for the mode spectrum of the equilateral waveguide. The mathematical formulation of the electromagnetic scattering problem is based on the quasi-analytical Mode-Matching method. This method benefits from the electromagnetic field division into symmetries as well as from the plane wave formulation presented for the expressions involved. The unification of the surface integrals used in the method thanks to the plane wave formulation is revealed, leading to expressions that are very well suited for its implementation in an electromagnetic analysis and design code. The obtained results for some cases of interest (building blocks for microwave components for communication systems) are verified using other numerical methods included in a commercial software package, showing the potential of the presented approach based on quasi-analytic expressions. Ana Morán-López, Juan Córcoles, Jorge A. Ruiz-Cruz, José R. Montejo-Garai, and Jesús M. Rebollar Copyright © 2016 Ana Morán-López et al. All rights reserved. Elastic Equilibrium of Porous Cosserat Media with Double Porosity Sun, 31 Jul 2016 10:06:36 +0000 The static equilibrium of porous elastic materials with double porosity is considered in the case of an elastic Cosserat medium. The corresponding three-dimensional system of differential equations is derived. Detailed consideration is given to the case of plane deformation. A two-dimensional system of equations of plane deformation is written in the complex form and its general solution is represented by means of three analytic functions of a complex variable and two solutions of Helmholtz equations. The constructed general solution enables one to solve analytically a sufficiently wide class of plane boundary value problems of the elastic equilibrium of porous Cosserat media with double porosity. A concrete boundary value problem for a concentric ring is solved. Roman Janjgava Copyright © 2016 Roman Janjgava. All rights reserved. Thermal Stability Investigation in a Reactive Sphere of Combustible Material Sun, 31 Jul 2016 08:30:21 +0000 An investigation of thermal stability in a stockpile of combustible material is considered. The combustible material is any carbon containing material that can react with oxygen trapped in a stockpile due to exothermic chemical reaction. The complicated process is modelled in a sphere and one-dimensional energy equation is used to solve the problem. The semi-implicit finite difference method (FDM) is applied to tackle the nonlinear differential equation governing the problem. Graphical solutions are displayed to describe effects of embedded kinetic parameters on the temperature of the system. R. S. Lebelo Copyright © 2016 R. S. Lebelo. All rights reserved. Lax Triples for Integrable Surfaces in Three-Dimensional Space Thu, 28 Jul 2016 09:55:15 +0000 We study Lax triples (i.e., Lax representations consisting of three linear equations) associated with families of surfaces immersed in three-dimensional Euclidean space . We begin with a natural integrable deformation of the principal chiral model. Then, we show that all deformations linear in the spectral parameter are trivial unless we admit Lax representations in a larger space. We present an explicit example of triply orthogonal systems with Lax representation in the group . Finally, the obtained results are interpreted in the context of the soliton surfaces approach. Jan L. Cieśliński and Artur Kobus Copyright © 2016 Jan L. Cieśliński and Artur Kobus. All rights reserved. Drinfeld Realization of Quantum Twisted Affine Algebras via Braid Group Wed, 27 Jul 2016 10:54:42 +0000 The Drinfeld realization of quantum affine algebras has been tremendously useful since its discovery. Combining techniques of Beck and Nakajima with our previous approach, we give a complete and conceptual proof of the Drinfeld realization for the twisted quantum affine algebras using Lusztig’s braid group action. Naihuan Jing and Honglian Zhang Copyright © 2016 Naihuan Jing and Honglian Zhang. All rights reserved. New Applications of a Kind of Infinitesimal-Operator Lie Algebra Mon, 25 Jul 2016 11:30:43 +0000 Applying some reduced Lie algebras of Lie symmetry operators of a Lie transformation group, we obtain an invariant of a second-order differential equation which can be generated by a Euler-Lagrange formulism. A corresponding discrete equation approximating it is given as well. Finally, we make use of the Lie algebras to generate some new integrable systems including () and () dimensions. Honwah Tam, Yufeng Zhang, and Xiangzhi Zhang Copyright © 2016 Honwah Tam et al. All rights reserved. A Lipschitz Stability Estimate for the Inverse Source Problem and the Numerical Scheme Wed, 20 Jul 2016 07:12:40 +0000 We consider the inverse source problem for heat equation, where the source term has the form . We give a numerical algorithm to compute unknown source term . Also, we give a stability estimate in the case that is a piecewise constant function. Xianzheng Jia Copyright © 2016 Xianzheng Jia. All rights reserved. A General Scheme for Information Interception in the Ping-Pong Protocol Sun, 17 Jul 2016 13:24:51 +0000 The existence of undetectable eavesdropping of dense coded information has been already demonstrated by Pavičić for the quantum direct communication based on the ping-pong paradigm. However, (a) the explicit scheme of the circuit is only given and no design rules are provided; (b) the existence of losses is implicitly assumed; (c) the attack has been formulated against qubit based protocol only and it is not clear whether it can be adapted to higher dimensional systems. These deficiencies are removed in the presented contribution. A new generic eavesdropping scheme built on a firm theoretical background is proposed. In contrast to the previous approach, it does not refer to the properties of the vacuum state, so it is fully consistent with the absence of losses assumption. Moreover, the scheme applies to the communication paradigm based on signal particles of any dimensionality. It is also shown that some well known attacks are special cases of the proposed scheme. Piotr Zawadzki and Jarosław Adam Miszczak Copyright © 2016 Piotr Zawadzki and Jarosław Adam Miszczak. All rights reserved. Multidimensional Analysis of Plates with Irregularities Using Higher-Order Finite Elements Based on Lobatto Shape Functions Wed, 13 Jul 2016 06:49:50 +0000 Direct modeling and simulation of engineering problems with various irregularities are computationally very inefficient and in some cases impossible, even in these days of massively parallel computational systems. As a result, in recent times, a number of schemes have been put forward to tract such problems in a computationally efficient manner. Needless to say, such schemes are still going through evolutionary stages. This paper addresses direct solution based on the selective use of different dimensional models at different regions of the problem domain. For the multidimensional approach, a higher-order transition element is developed to connect the different element types where two- and three-dimensional laminated elements based on higher-order subparametric concept are considered. Modeling simplicity and calculation efficiency of the multidimensional approach are shown for the analysis of cantilever plates with stepped section and patch-repaired plates. Jae S. Ahn Copyright © 2016 Jae S. Ahn. All rights reserved.