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

The Relationship between Focal Surfaces and Surfaces at a Constant Distance from the Edge of Regression on a Surface
Tue, 01 Sep 2015 13:17:34 +0000
http://www.hindawi.com/journals/amp/2015/397126/
We investigate the relationship between focal surfaces and surfaces at a constant distance from the edge of regression on a surface. We show that focal surfaces F1 and F2 of the surface M can be obtained by means of some special surfaces at a constant distance from the edge of regression on the surface M.
Semra Yurttancikmaz and Omer Tarakci
Copyright © 2015 Semra Yurttancikmaz and Omer Tarakci. All rights reserved.

The Steiner Formula and the Polar Moment of Inertia for the Closed Planar Homothetic Motions in Complex Plane
Tue, 01 Sep 2015 07:33:45 +0000
http://www.hindawi.com/journals/amp/2015/978294/
The Steiner area formula and the polar moment of inertia were expressed during oneparameter closed planar homothetic motions in complex plane. The Steiner point or Steiner normal concepts were described according to whether rotation number was different from zero or equal to zero, respectively. The moving pole point was given with its components and its relation between Steiner point or Steiner normal was specified. The sagittal motion of a winch was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of winch and the moving arm of winch. The results obtained in the second section of this study were applied for this motion.
Ayhan Tutar and Onder Sener
Copyright © 2015 Ayhan Tutar and Onder Sener. All rights reserved.

Optimal Homotopy Asymptotic Solution for Exothermic Reactions Model with Constant Heat Source in a Porous Medium
Tue, 01 Sep 2015 06:19:46 +0000
http://www.hindawi.com/journals/amp/2015/825683/
The heat flow patterns profiles are required for heat transfer simulation in each type of the thermal insulation. The exothermic reaction models in porous medium can prescribe the problems in the form of nonlinear ordinary differential equations. In this research, the driving force model due to the temperature gradients is considered. A governing equation of the model is restricted into an energy balance equation that provides the temperature profile in conduction state with constant heat source on the steady state. The proposed optimal homotopy asymptotic method (OHAM) is used to compute the solutions of the exothermic reactions equation.
Fazle Mabood and Nopparat Pochai
Copyright © 2015 Fazle Mabood and Nopparat Pochai. All rights reserved.

WeylEulerLagrange Equations of Motion on Flat Manifold
Tue, 01 Sep 2015 06:12:03 +0000
http://www.hindawi.com/journals/amp/2015/808016/
This paper deals with WeylEulerLagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the EulerLagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.
Zeki Kasap
Copyright © 2015 Zeki Kasap. All rights reserved.

On Finsler Geometry and Applications in Mechanics: Review and New Perspectives
Mon, 31 Aug 2015 14:15:02 +0000
http://www.hindawi.com/journals/amp/2015/828475/
In Finsler geometry, each point of a base manifold can be endowed with coordinates describing its position as well as a set of one or more vectors describing directions, for example. The associated metric tensor may generally depend on
direction as well as position, and a number of connections emerge associated with various covariant derivatives involving affine and nonlinear coefficients. Finsler geometry encompasses Riemannian, Euclidean, and Minkowskian geometries as special cases, and thus it affords great generality for describing a number of phenomena in physics. Here, descriptions of finite deformation of continuous media are of primary focus. After a review of necessary mathematical definitions and derivations, prior work involving application of Finsler geometry in continuum mechanics of solids is reviewed. A new theoretical description of continua with microstructure is then outlined, merging concepts from Finsler geometry and phase field theories of materials science.
J. D. Clayton
Copyright © 2015 J. D. Clayton. All rights reserved.

A Variational Approach to Electrostatics of Polarizable Heterogeneous Substances
Mon, 31 Aug 2015 14:06:18 +0000
http://www.hindawi.com/journals/amp/2015/659127/
We discuss equilibrium conditions for heterogeneous substances subject
to electrostatic or magnetostatic effects. We demonstrate that the
forcelike aleph tensor and the energylike beth tensor for polarizable
deformable substances are divergencefree: and .
We introduce two additional tensors: the divergencefree energylike gimel
tensor for rigid dielectrics and the general electrostatic gamma tensor which is not divergencefree.
Our approach is based on a logically consistent extension of the Gibbs
energy principle that takes into account polarization effects. While the
model is mathematically rigorous, we caution against the assumption that
it can reliably predict physical phenomena. On the contrary, clear models
often lead to conclusions that are at odds with experiment and therefore
should be treated as physical paradoxes that deserve the attention of the
scientific community.
Michael Grinfeld and Pavel Grinfeld
Copyright © 2015 Michael Grinfeld and Pavel Grinfeld. All rights reserved.

Comparison of Optimal Homotopy Asymptotic and Adomian Decomposition Methods for a Thin Film Flow of a Third Grade Fluid on a Moving Belt
Mon, 31 Aug 2015 14:02:05 +0000
http://www.hindawi.com/journals/amp/2015/642835/
We have investigated a thin film flow of a third grade fluid on a moving belt using a powerful and relatively new approximate analytical technique known as optimal homotopy asymptotic method (OHAM). The variation of velocity profile for different parameters is compared with the numerical values obtained by RungeKutta Fehlberg fourthfifth order method and with Adomian Decomposition Method (ADM). An interesting result of the analysis is that the three terms OHAM solution is more accurate than five terms of the ADM solution and this thus confirms the feasibility of the proposed method.
Fazle Mabood and Nopparat Pochai
Copyright © 2015 Fazle Mabood and Nopparat Pochai. All rights reserved.

Leaky Modes of Waveguides as a Classical Optics Analogy of Quantum Resonances
Sun, 30 Aug 2015 12:18:03 +0000
http://www.hindawi.com/journals/amp/2015/281472/
A classical optics waveguide structure is proposed to simulate resonances of short range onedimensional potentials in quantum mechanics. The analogy is based on the wellknown resemblance between the guided and radiation modes of a waveguide with the bound and scattering states of a quantum well. As resonances are scattering states that spend some time in the zone of influence of the scatterer, we associate them with the leaky modes of a waveguide, the latter characterized by suffering attenuation in the direction of propagation but increasing exponentially in the transverse directions. The resemblance is complete because resonances (leaky modes) can be interpreted as bound states (guided modes) with definite lifetime (longitudinal shift). As an immediate application we calculate the leaky modes (resonances) associated with a dielectric homogeneous slab (square well potential) and show that these modes are attenuated as they propagate.
Sara Cruz y Cruz and Oscar RosasOrtiz
Copyright © 2015 Sara Cruz y Cruz and Oscar RosasOrtiz. All rights reserved.

The Intersection Probability of Brownian Motion and SLEκ
Wed, 26 Aug 2015 08:53:34 +0000
http://www.hindawi.com/journals/amp/2015/627423/
By using excursion measure Poisson kernel method, we obtain a secondorder differential equation of the intersection probability of Brownian motion and . Moreover, we find a transformation such that the secondorder 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 halfplane .
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
http://www.hindawi.com/journals/amp/2015/724647/
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
http://www.hindawi.com/journals/amp/2015/584542/
Adinkras are graphical tools for studying offshell 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 FirstOrder Feedback Model of Option Pricing
Sun, 23 Aug 2015 11:39:15 +0000
http://www.hindawi.com/journals/amp/2015/361785/
A firstorder feedback model of option pricing consisting of a coupled system of two PDEs, a nonliner generalised BlackScholes equation and the classical BlackScholes equation, is studied using Lie symmetry analysis. This model arises as an extension of the classical BlackScholes 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 onedimensional 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 ChernSimonsSchrödinger Equations
Wed, 19 Aug 2015 12:13:14 +0000
http://www.hindawi.com/journals/amp/2015/519374/
We prove the existence of infinitely many solutions of the nonlinear ChernSimonsSchrödinger
equations under a wide class of nonlinearities. This class includes the standard powertype nonlinearity with exponent . This extends the previous result which covers the exponent .
Jinmyoung Seok
Copyright © 2015 Jinmyoung Seok. All rights reserved.

HomOperators and HomYangBaxter Equations
Wed, 12 Aug 2015 08:07:00 +0000
http://www.hindawi.com/journals/amp/2015/823756/
In HomLie set, we introduce the concept of Homoperators and study its relation with classical HomYangBaxter equation, as well as leftsymmetric Homalgebras. We construct the corresponding relation between leftsymmetric Homalgebras and Hom1cocycles, which are both related to classical HomYangBaxter equation. Moreover, in Homalgebra setting, we establish the equivalent relationship between AHYBE (associative HomYangBaxter equations) and operators on Frobenius monoidal Homalgebras.
Yuanyuan Chen and Liangyun Zhang
Copyright © 2015 Yuanyuan Chen and Liangyun Zhang. All rights reserved.

SecondOrder Integrals for Systems in Involving Spin
Thu, 30 Jul 2015 06:09:59 +0000
http://www.hindawi.com/journals/amp/2015/952646/
In twodimensional Euclidean plane, existence of secondorder 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 secondorder integrals of motion exist for such systems.
İsmet Yurduşen
Copyright © 2015 İsmet Yurduşen. All rights reserved.

Spatial Rotation of the Fractional Derivative in TwoDimensional Space
Mon, 27 Jul 2015 08:32:47 +0000
http://www.hindawi.com/journals/amp/2015/719173/
The transformations of the partial fractional derivatives under spatial rotation in are derived for the RiemannLiouville 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 EighthOrder Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets
Tue, 14 Jul 2015 06:55:49 +0000
http://www.hindawi.com/journals/amp/2015/964623/
A collocation method based on the second kind Chebyshev wavelets is proposed for the numerical solution of eighthorder twopoint 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 Bspline 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.

HigherStage Noether Identities and Second Noether Theorems
Mon, 13 Jul 2015 06:20:03 +0000
http://www.hindawi.com/journals/amp/2015/127481/
The direct and inverse second Noether theorems are formulated in a general case of reducible degenerate Grassmanngraded Lagrangian theory of even and odd variables on graded bundles. Such Lagrangian theory is characterized by a hierarchy of nontrivial higherstage 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 higherstage Noether identities. The second
Noether theorems associate with the abovementioned Koszul–Tate complex a certain cochain sequence whose ascent operator consists of the gauge and higherorder gauge symmetries of a Lagrangian system. If gauge symmetries are algebraically closed, this operator is extended to the nilpotent BRST operator which brings the abovementioned cochain sequence into the BRST complex and provides a BRST extension of an original Lagrangian.
G. Sardanashvily
Copyright © 2015 G. Sardanashvily. All rights reserved.

BoundState Solution of sWave KleinGordon Equation for WoodsSaxon Potential
Sun, 12 Jul 2015 06:59:29 +0000
http://www.hindawi.com/journals/amp/2015/923076/
The boundstate solution of swave KleinGordon equation is calculated for WoodsSaxon potential by using the asymptotic iteration method (AIM). The energy eigenvalues and eigenfunctions are obtained for the required condition of boundstate 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
http://www.hindawi.com/journals/amp/2015/250570/
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
http://www.hindawi.com/journals/amp/2015/210346/
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
http://www.hindawi.com/journals/amp/2015/103074/
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.