Advances in Mathematical Physics
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The latest articles from Hindawi Publishing Corporation
© 2015 , Hindawi Publishing Corporation . All rights reserved.

Hypersurface Constrained Elasticae in Lorentzian Space Forms
Tue, 24 Nov 2015 13:18:23 +0000
http://www.hindawi.com/journals/amp/2015/458178/
We study geodesics in hypersurfaces of a Lorentzian space form , which are critical curves of the bending energy functional, for variations constrained to lie on the hypersurface. We characterize critical geodesics showing that they live fully immersed in a totally geodesic and that they must be of three different types. Finally, we consider the classification of surfaces in the Minkowski 3space foliated by critical geodesics.
Óscar J. Garay, Álvaro Pámpano, and Changhwa Woo
Copyright © 2015 Óscar J. Garay et al. All rights reserved.

A Regime Switching Model of Schooling Choice as a Job Search Process
Tue, 24 Nov 2015 08:06:29 +0000
http://www.hindawi.com/journals/amp/2015/475279/
We propose a regime switching model of schooling choice as a job search process. We adopt a twostate Markov process and the derived coupled Bellman equations are solved by seeking the root of an auxiliary algebraic equation. Some numerical examples are also considered.
Yong Hyun Shin and HoSeok Lee
Copyright © 2015 Yong Hyun Shin and HoSeok Lee. All rights reserved.

Dynamics of a General Stochastic Nonautonomous LotkaVolterra Model with Delays and Impulsive Perturbations
Sun, 22 Nov 2015 11:20:09 +0000
http://www.hindawi.com/journals/amp/2015/824507/
A stochastic nonautonomous Nspecies LotkaVolterra model with delays and impulsive perturbations is investigated. For this model, sufficient conditions for extinction, nonpersistence in the mean, weak persistence and stochastic permanence are given, respectively. The influences of the stochastic noises, and the impulsive perturbations on the properties of the
stochastic model are also discussed. The critical value between weak persistence and extinction is obtained. Finally, numerical simulations are given to support the theoretical analysis results.
Qing Wang, Yongguang Yu, and Shuo Zhang
Copyright © 2015 Qing Wang et al. All rights reserved.

Construction of Analytic Solution for TimeFractional Boussinesq Equation Using Iterative Method
Sun, 22 Nov 2015 07:25:30 +0000
http://www.hindawi.com/journals/amp/2015/506140/
This paper is aimed at constructing analytical solution for both linear and
nonlinear timefractional Boussinesq equations by an iterative
method. By the iterative process, we can obtain the analytic
solution of the fourthorder timefractional Boussinesq
equation in , , and , the
sixthorder timefractional Boussinesq equation, and the thorder timefractional Boussinesq equation in . Through these examples, it shows that the method is simple and effective.
Fei Xu, Yixian Gao, and Weipeng Zhang
Copyright © 2015 Fei Xu et al. All rights reserved.

On the Nonlinear Fractional Differential Equations with Caputo Sequential Fractional Derivative
Sun, 22 Nov 2015 06:49:22 +0000
http://www.hindawi.com/journals/amp/2015/174156/
The purpose of this paper is to investigate the existence of solutions to the following initial value problem for nonlinear fractional differential equation involving Caputo sequential fractional derivative , , , , where , are Caputo fractional derivatives, , , , and . Local existence of solutions is established by employing Schauder fixed point theorem. Then a growth condition imposed to guarantees not only the global existence of solutions on the interval , but also the fact that the intervals of existence of solutions with any fixed initial value can be extended to . Three illustrative examples are also presented. Existence results for initial value problems of ordinary differential equations with Laplacian on the halfaxis follow as a special case of our results.
Hailong Ye and Rui Huang
Copyright © 2015 Hailong Ye and Rui Huang. All rights reserved.

Thermal Ground State and Nonthermal Probes
Wed, 18 Nov 2015 09:19:04 +0000
http://www.hindawi.com/journals/amp/2015/197197/
The Euclidean formulation of SU(2) YangMills thermodynamics admits periodic, (anti)selfdual solutions to the fundamental, classical equation of motion which possess one unit of topological charge: (anti)calorons. A spatial coarse graining over the central region in a pair of such localised field configurations with trivial holonomy generates an inert adjoint scalar field , effectively describing the pure quantum part of the thermal ground state in the induced quantum field theory. Here we show for the limit of zero holonomy how (anti)calorons associate a temperature independent electric permittivity and magnetic permeability to the thermal ground state of , the YangMills theory conjectured to underlie the fundamental description of thermal photon gases.
Thierry Grandou and Ralf Hofmann
Copyright © 2015 Thierry Grandou and Ralf Hofmann. All rights reserved.

Hamiltonian Dynamics and Adiabatic Invariants for TimeDependent Superconducting QubitOscillators and Resonators in Quantum Computing Systems
Thu, 12 Nov 2015 06:24:56 +0000
http://www.hindawi.com/journals/amp/2015/120573/
An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for timedependent superconducting qubitoscillator systems and resonators are investigated using the Liouvillevon Neumann equation. At first, we derive an invariant for a simple superconducting qubitoscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a timedependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a timedependent Hamiltonian involving nonlinear terms.
Jeong Ryeol Choi
Copyright © 2015 Jeong Ryeol Choi. All rights reserved.

Stability Criteria for Volterra Integrodynamic System
Wed, 11 Nov 2015 08:29:06 +0000
http://www.hindawi.com/journals/amp/2015/365328/
We study conditions under which the solutions of linear Volterra integrodynamic system of the form are stable on certain time scales. We construct a number of Lyapunov functionals on time scales from which we obtain necessary and sufficient conditions for stability of Volterra integrodynamic system and also we prove several results concerning qualitative behavior of this system.
Nusrat Yasmin, Awais Younus, Usman Ali, and Safia Mirza
Copyright © 2015 Nusrat Yasmin et al. All rights reserved.

Entropic Lower Bound for Distinguishability of Quantum States
Thu, 05 Nov 2015 14:14:40 +0000
http://www.hindawi.com/journals/amp/2015/683658/
For a system randomly prepared in a number of quantum states, we present a lower bound for the distinguishability of the quantum states, that is, the success probability of determining the states in the form of entropy. When the states are all pure, acquiring the entropic lower bound requires only the density operator and the number of the possible states.
This entropic bound shows a relation between the von Neumann entropy and the distinguishability.
Seungho Yang, Jinhyoung Lee, and Hyunseok Jeong
Copyright © 2015 Seungho Yang et al. All rights reserved.

Memory Effects on Nonlinear Temperature and Pressure Wave Propagation in the Boundary between Two FluidSaturated Porous Rocks
Thu, 05 Nov 2015 13:35:46 +0000
http://www.hindawi.com/journals/amp/2015/532150/
The evolution of strong transients of temperature and pressure in two adjacent fluidsaturated porous rocks is described by a Burgers equation in an early model of Natale and Salusti (1996). We here consider the effect of a realistic intermediate region between the two media and infer how transient processes can also happen, such as chemical reactions, diffusion of fine particles, and filter cake formations. This suggests enlarging our analysis and taking into account not only punctual quantities but also “time averaged” quantities. These boundary effects are here analyzed by using a “memory formalism”; that is, we replace the ordinary punctual timederivatives with Caputo fractional timederivatives. We therefore obtain a nonlinear fractional model, whose explicit solution is shown, and finally discuss its geological importance.
R. Garra, E. Salusti, and R. Droghei
Copyright © 2015 R. Garra et al. All rights reserved.

Synthesis of Relativistic Wave Equations: The Noninteracting Case
Thu, 05 Nov 2015 09:15:13 +0000
http://www.hindawi.com/journals/amp/2015/528484/
We study internal structure of the DuffinKemmerPetiau equations for spin 0 and spin 1 mesons. We show that in the noninteracting case full covariant solutions of the and DKP equations are generalized solutions of the Dirac equation.
Andrzej Okniński
Copyright © 2015 Andrzej Okniński. All rights reserved.

The Rabi Oscillation in Subdynamic System for Quantum Computing
Wed, 04 Nov 2015 12:04:31 +0000
http://www.hindawi.com/journals/amp/2015/151690/
A quantum computation for the Rabi oscillation based on quantum dots in the subdynamic system is presented. The working states of the original Rabi oscillation are transformed to the eigenvectors of subdynamic system. Then the dissipation and decoherence of the system are only shown in the change of the eigenvalues as phase errors since the eigenvectors are fixed. This allows both dissipation and decoherence controlling to be easier by only correcting relevant phase errors. This method can be extended to general quantum computation systems.
Bi Qiao and Gu Jiayin
Copyright © 2015 Bi Qiao and Gu Jiayin. All rights reserved.

Mathematical Properties of the Hyperbolicity of Circulant Networks
Mon, 02 Nov 2015 12:09:05 +0000
http://www.hindawi.com/journals/amp/2015/723451/
If is a geodesic metric space and , a geodesic triangle
is the union of the three geodesics , , and in . The space is hyperbolic (in the Gromov sense) if any side of is contained in a neighborhood of the union of the two other sides, for every geodesic triangle in . The study of the hyperbolicity constant in networks is usually a very difficult task; therefore, it is interesting to find bounds for particular classes of graphs. A network is circulant if it has a cyclic group of automorphisms that includes an automorphism taking any vertex to any other vertex. In this paper we obtain several sharp inequalities for the hyperbolicity constant of circulant networks; in some cases we characterize the graphs for which the equality is attained.
Juan C. Hernández, José M. Rodríguez, and José M. Sigarreta
Copyright © 2015 Juan C. Hernández et al. All rights reserved.

Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region
Wed, 28 Oct 2015 08:07:54 +0000
http://www.hindawi.com/journals/amp/2015/147125/
The purpose of this paper is to establish the admitted region for five simultaneous, functionally independent invariants of the strain rate tensor and rotation rate tensor and calculate some simultaneous invariants of these tensors which are encountered in the theory of constitutive relations for turbulent flows. Such a problem, as far as we know, has not yet been considered, though it is obviously an integral part of any problem in which scalar functions of the tensors and are studied. The theory provided inside this paper is the building block for a derivation of new algebraic constitutive relations for threedimensional turbulent flows in the form of expansions of the Reynoldsstress tensor in a tensorial basis formed by the tensors and , in which the scalar coefficients depend on simultaneous invariants of these tensors.
Igor Vigdorovich and Holger Foysi
Copyright © 2015 Igor Vigdorovich and Holger Foysi. All rights reserved.

Constant Mean Curvature Spacelike Surfaces in Lorentzian Warped Products
Thu, 22 Oct 2015 12:11:22 +0000
http://www.hindawi.com/journals/amp/2015/761302/
We characterize the spacelike slices of a Lorentzian warped product as the only constant mean curvature spacelike surfaces under suitable geometrical and physical assumptions. As a consequence of our study, we derive a Bernsteintype result which widely improves and extends the stateoftheart results in this setting.
Juan A. Aledo and Rafael M. Rubio
Copyright © 2015 Juan A. Aledo and Rafael M. Rubio. All rights reserved.

Compound Synchronization of Four Chaotic Complex Systems
Thu, 22 Oct 2015 11:27:55 +0000
http://www.hindawi.com/journals/amp/2015/921515/
The chaotic complex system is designed from the start of the chaotic real system. Dynamical properties of a chaotic complex system in complex space are investigated. In this paper, a compound synchronization scheme is achieved for four chaotic complex systems. According to Lyapunov stability theory and the adaptive control method, four chaotic complex systems are considered and the corresponding controllers are designed to realize the compound synchronization scheme. Four novel design chaotic complex systems are given as an example to verify the validity and feasibility of the proposed control scheme.
Junwei Sun, Yi Shen, and Guangzhao Cui
Copyright © 2015 Junwei Sun et al. All rights reserved.

Explicit Wave Solutions and Qualitative Analysis of the (1 + 2)Dimensional Nonlinear Schrödinger Equation with DualPower Law Nonlinearity
Wed, 21 Oct 2015 09:33:35 +0000
http://www.hindawi.com/journals/amp/2015/408630/
The (1 + 2)dimensional nonlinear Schrödinger equation with dualpower law nonlinearity is studied using the factorization technique, bifurcation theory of dynamical system, and phase portraits analysis. From a dynamic point of view, the existence of smooth solitary wave, and kink and antikink waves is proved and all possible explicit parametric representations of these waves are presented.
Qing Meng, Bin He, and Zhenyang Li
Copyright © 2015 Qing Meng et al. All rights reserved.

Towards Noncommutative Linking Numbers via the SeibergWitten Map
Mon, 19 Oct 2015 06:35:28 +0000
http://www.hindawi.com/journals/amp/2015/845328/
Some geometric and topological implications of noncommutative Wilson loops are explored via the SeibergWitten map. In the abelian ChernSimons theory on a threedimensional manifold, it is shown that the effect of noncommutativity is the appearance of new knots at the th order of the SeibergWitten expansion. These knots are trivial homology cycles which are Poincaré dual to the higherorder SeibergWitten potentials. Moreover the linking number of a standard 1cycle with the Poincaré dual of the gauge field is shown to be written as an expansion of the linking number of this 1cycle with the Poincaré dual of the SeibergWitten gauge fields. In the process we explicitly compute the noncommutative “JonesWitten” invariants up to first order in the noncommutative parameter. Finally in order to exhibit a physical example, we apply these ideas explicitly to the AharonovBohm effect. It is explicitly displayed at first order in the noncommutative parameter; we also show the relation to the noncommutative Landau levels.
H. GarcíaCompeán, O. Obregón, and R. SantosSilva
Copyright © 2015 H. GarcíaCompeán et al. All rights reserved.

Geometrical Applications of Split Octonions
Sun, 18 Oct 2015 13:07:54 +0000
http://www.hindawi.com/journals/amp/2015/196708/
It is shown that physical signals and spacetime intervals modeled on splitoctonion geometry naturally exhibit properties from conventional (3 + 1)theory (e.g., number of dimensions, existence of maximal velocities, Heisenberg uncertainty, and particle generations). This paper demonstrates these properties using an explicit representation of the automorphisms on splitoctonions, the noncompact form of the exceptional Lie group . This group generates specific rotations of (3 + 4)vector parts of split octonions with three extra timelike coordinates and in infinitesimal limit imitates standard Poincare transformations. In this picture translations are represented by noncompact Lorentztype rotations towards the extra timelike coordinates. It is shown how the algebra’s chirality yields an intrinsic leftright asymmetry of a certain 3vector (spin), as well as a parity violating effect on light emitted by a moving quantum system. Elementary particles are connected with the special elements of the algebra which nullify octonionic intervals. Then the zeronorm conditions lead to free particle Lagrangians, which allow virtual trajectories also and exhibit the appearance of spatial horizons governing by mass parameters.
Merab Gogberashvili and Otari Sakhelashvili
Copyright © 2015 Merab Gogberashvili and Otari Sakhelashvili. All rights reserved.

Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective
Sun, 18 Oct 2015 07:02:11 +0000
http://www.hindawi.com/journals/amp/2015/608940/
This review is devoted to measure theoretical methods in the canonical quantization of scalar field theories. We present in some detail the canonical quantization of the free scalar field. We study the measures associated with the free fields and present two characterizations of the support of these measures. The first characterization concerns local properties of the quantum fields, whereas for the second one we introduce a sequence of variables that test the field behaviour at large distances, thus allowing distinguishing between the typical quantum fields associated with different values of the mass.
José Velhinho
Copyright © 2015 José Velhinho. All rights reserved.

OneDimensional Coulomb Multiparticle Systems
Tue, 13 Oct 2015 07:41:44 +0000
http://www.hindawi.com/journals/amp/2015/857846/
We consider the system of particles with equal charges and nearest neighbour Coulomb interaction on the interval. We study local properties of this system, in particular the distribution of distances between neighbouring charges. For zero temperature case there is sufficiently complete picture and we give a short review. For Gibbs distribution the situation is more difficult and we present two related results.
V. A. Malyshev and A. A. Zamyatin
Copyright © 2015 V. A. Malyshev and A. A. Zamyatin. All rights reserved.

LongTime Behavior of Solution for a Reactor Model
Sun, 11 Oct 2015 12:28:28 +0000
http://www.hindawi.com/journals/amp/2015/547363/
In this paper, we would consider the dynamical behaviors of the chemical model represented by Satnoianu et al. (2001). Using the Kuratowski measure of noncompactness method, we prove the existence of global attractor
for the weak solution semiflow of system. Finally, several numerical experiments confirm the theoretical results.
Yantao Guo, Jianwei Shen, and Qianqian Zheng
Copyright © 2015 Yantao Guo et al. All rights reserved.

Reconstruction of the Magnetic Particle Imaging System Matrix Using Symmetries and Compressed Sensing
Thu, 08 Oct 2015 14:01:49 +0000
http://www.hindawi.com/journals/amp/2015/460496/
Magnetic particle imaging (MPI) is a tomographic imaging technique that allows the determination of the 3D spatial distribution of superparamagnetic iron oxide nanoparticles. Due to the complex dynamic nature of these nanoparticles, a timeconsuming calibration measurement has to be performed prior to image reconstruction. During the calibration a small delta sample filled with the particle suspension is measured at all positions in the field of view where the particle distribution will be reconstructed. Recently, it has been shown that the calibration procedure can be significantly shortened by sampling the field of view only at few randomly chosen positions and applying compressed sensing to reconstruct the full MPI system matrix. The purpose of this work is to reduce the number of necessary calibration scans even further. To this end, we take into account symmetries of the MPI system matrix and combine this knowledge with the compressed sensing method. Experiments on 2D MPI data show that the combination of symmetry and compressed sensing allows reducing the number of calibration scans compared to the pure compressed sensing approach by a factor of about three.
A. Weber and T. Knopp
Copyright © 2015 A. Weber and T. Knopp. All rights reserved.

The Periodic Boundary Value Problem for the Weakly Dissipative HunterSaxton Equation
Mon, 05 Oct 2015 08:44:47 +0000
http://www.hindawi.com/journals/amp/2015/743432/
We study the periodic boundary value problem for the weakly dissipative HunterSaxton equation. We establish the local wellposedness in Besov space , which extends the previous regularity range to the critical case.
Zhengyong Ouyang, Xiangdong Wang, and Haiwu Rong
Copyright © 2015 Zhengyong Ouyang et al. All rights reserved.

A Numerical Method for Solving Fractional Differential Equations by Using Neural Network
Sun, 04 Oct 2015 07:06:37 +0000
http://www.hindawi.com/journals/amp/2015/439526/
We present a new method for solving the fractional differential equations
of initial value problems by using neural networks which are constructed from
cosine basis functions with adjustable parameters. By training the neural networks
repeatedly the numerical solutions for the fractional differential equations were
obtained. Moreover, the technique is still applicable for the coupled differential equations
of fractional order. The computer graphics and numerical solutions show
that the proposed method is very effective.
Haidong Qu and Xuan Liu
Copyright © 2015 Haidong Qu and Xuan Liu. All rights reserved.

Existence of Multiple Positive Solutions for Choquard Equation with Perturbation
Wed, 30 Sep 2015 13:58:25 +0000
http://www.hindawi.com/journals/amp/2015/760157/
This paper is concerned with the following Choquard equation with perturbation: , , where , , and . This kind of equations is well known as the Choquard or nonlinear SchrödingerNewton equation. Under some assumptions for the functions , we prove the existence of multiple positive solutions of the equation. Moreover, we also show that these results still hold for more generalized Choquard equation with perturbation.
Tao Xie, Lu Xiao, and Jun Wang
Copyright © 2015 Tao Xie et al. All rights reserved.

Generalized Bilinear Differential Operators Application in a (3+1)Dimensional Generalized Shallow Water Equation
Thu, 10 Sep 2015 11:16:13 +0000
http://www.hindawi.com/journals/amp/2015/291804/
The relations between operators and
multidimensional binary Bell polynomials are explored and applied
to construct the bilinear forms with operators of nonlinear equations
directly and quickly. Exact periodic wave solution of a
(3+1)dimensional generalized shallow water equation is obtained
with the help of the operators and a general Riemann theta
function in terms of the Hirota method, which illustrate that bilinear
operators can provide a method for seeking exact periodic solutions
of nonlinear integrable equations. Furthermore, the asymptotic
properties of the periodic wave solutions indicate that the soliton
solutions can be derived from the periodic wave solutions.
Jingzhu Wu, Xiuzhi Xing, and Xianguo Geng
Copyright © 2015 Jingzhu Wu et al. All rights reserved.

The Thermal Statistics of QuasiProbabilities’ Analogs in Phase Space
Tue, 08 Sep 2015 16:38:55 +0000
http://www.hindawi.com/journals/amp/2015/145684/
We focus attention upon the thermal statistics of the classical analogs of quasiprobabilities (QP) in phase space for the important case of quadratic Hamiltonians. We consider the three more important OPs: Wigner’s, , and Husimi’s. We show that, for all of them, the ensuing semiclassical entropy is a function only of the fluctuation product . We ascertain that the semiclassical analog of distribution seems to become unphysical at very low temperatures. The behavior of several other information quantifiers reconfirms such an assertion in manifold ways. We also examine the behavior of the statistical complexity and of thermal quantities like the specific heat.
F. Pennini, A. Plastino, and M. C. Rocca
Copyright © 2015 F. Pennini et al. All rights reserved.

Mechanics and Geometry of Solids and Surfaces
Thu, 03 Sep 2015 08:43:27 +0000
http://www.hindawi.com/journals/amp/2015/382083/
J. D. Clayton, M. A. Grinfeld, T. Hasebe, and J. R. Mayeur
Copyright © 2015 J. D. Clayton et al. All rights reserved.

Structures and Low Dimensional Classifications of HomPoisson Superalgebras
Wed, 02 Sep 2015 06:16:27 +0000
http://www.hindawi.com/journals/amp/2015/354341/
HomPoisson superalgebras can be considered as a deformation of
Poisson superalgebras. We prove that HomPoisson superalgebras are
closed under tensor products. Moreover, we show that HomPoisson
superalgebras can be described using only the twisting map and one
binary operation. Finally, all algebra endomorphisms on 2dimensional
complex Poisson superalgebras are computed, and their associated
HomPoisson superalgebras are described explicitly.
Qingcheng Zhang, Chunyue Wang, and Zhu Wei
Copyright © 2015 Qingcheng Zhang et al. All rights reserved.