http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Thu, 23 May 2013 18:53:36 +0000 http://www.hindawi.com/journals/amp/2013/806984/ This paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus. The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation of Abel’s type. The proof of the existence of the inverse of the fractional Mikusinski operator is presented, providing an alternative method of treating the integral equation of Abel’s type. Ming Li and Wei Zhao Copyright © 2013 Ming Li and Wei Zhao. All rights reserved. Mon, 20 May 2013 11:57:20 +0000 http://www.hindawi.com/journals/amp/2013/890784/ A new method with a different auxiliary equation from the Riccati equation is used for constructing exact travelling wave solutions of nonlinear partial differential equations. The main idea of this method is to take full advantage of a different auxilliary equation from the Riccati equation which has more new solutions. More new solitary solutions are obtained for the RLW Burgers and Hirota Satsuma coupled equations. Bülent Kiliç and Hasan Bulut Copyright © 2013 Bülent Kiliç and Hasan Bulut. All rights reserved. Wed, 15 May 2013 15:35:49 +0000 http://www.hindawi.com/journals/amp/2013/950289/ An approach based on fractal is presented for extracting affine invariant features. Central projection transformation is employed to reduce the dimensionality of the original input pattern, and general contour (GC) of the pattern is derived. Affine invariant features cannot be extracted from GC directly due to shearing. To address this problem, a group of curves (which are called shift curves) are constructed from the obtained GC. Fractal dimensions of these curves can readily be computed and constitute a new feature vector for the original pattern. The derived feature vector is used in question for pattern recognition. Several experiments have been conducted to evaluate the performance of the proposed method. Experimental results show that the proposed method can be used for object classification. Jianwei Yang, Guosheng Cheng, and Ming Li Copyright © 2013 Jianwei Yang et al. All rights reserved. Mon, 13 May 2013 16:45:46 +0000 http://www.hindawi.com/journals/amp/2013/893254/ By using the Hille-Yosida theorem, Phillips theorem, and Fattorini theorem in functional analysis we prove that the /G/1 queueing model with vacation times has a unique nonnegative time-dependent solution. Alim Mijit Copyright © 2013 Alim Mijit. All rights reserved. Sun, 12 May 2013 09:09:04 +0000 http://www.hindawi.com/journals/amp/2013/958120/ This paper is devoted to the study of delta shock waves for a hyperbolic system of conservation laws of Keyfitz-Kranzer type with two linearly degenerate characteristics. The Riemann problem is solved constructively. The Riemann solutions include exactly two kinds. One consists of two (or just one) contact discontinuities, while the other contains a delta shock wave. Under suitable generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta shock solution are established. These analytical results match well the numerical ones. Finally, two kinds of interactions of elementary waves are discussed. Hongjun Cheng Copyright © 2013 Hongjun Cheng. All rights reserved. Sun, 21 Apr 2013 10:39:58 +0000 http://www.hindawi.com/journals/amp/2013/423718/ A conservative three-level linear finite difference scheme for the numerical solution of the initial-boundary value problem of Rosenau-KdV equation is proposed. The difference scheme simulates two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference scheme is of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results. Jinsong Hu, Youcai Xu, and Bing Hu Copyright © 2013 Jinsong Hu et al. All rights reserved. Thu, 18 Apr 2013 16:07:12 +0000 http://www.hindawi.com/journals/amp/2013/787891/ We propose and analyze a new numerical method, called a coupling method based on a new expanded mixed finite element (EMFE) and finite element (FE), for fourth-order partial differential equation of parabolic type. We first reduce the fourth-order parabolic equation to a coupled system of second-order equations and then solve a second-order equation by FE method and approximate the other one by a new EMFE method. We find that the new EMFE method’s gradient belongs to the simple square integrable space, which avoids the use of the classical H(div; Ω) space and reduces the regularity requirement on the gradient solution . For a priori error estimates based on both semidiscrete and fully discrete schemes, we introduce a new expanded mixed projection and some important lemmas. We derive the optimal a priori error estimates in and -norm for both the scalar unknown and the diffusion term γ and a priori error estimates in -norm for its gradient and its flux (the coefficients times the negative gradient). Finally, we provide some numerical results to illustrate the efficiency of our method. Yang Liu, Hong Li, Zhichao Fang, Siriguleng He, and Jinfeng Wang Copyright © 2013 Yang Liu et al. All rights reserved. Wed, 10 Apr 2013 17:10:39 +0000 http://www.hindawi.com/journals/amp/2013/498789/ We study complex processes whose evolution in time rests on the occurrence of a large and random number of events. The mean time interval between two consecutive critical events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that supports the hypothesis that the Mittag-Leffler function is a universal property of nature. The time evolution of these complex systems is properly generated by means of fractional differential equations, thus leading to the interpretation of fractional trajectories as the average over many random trajectories each of which satisfies the stochastic central limit theorem and the condition for the Mittag-Leffler universality. Pensri Pramukkul, Adam Svenkeson, Paolo Grigolini, Mauro Bologna, and Bruce West Copyright © 2013 Pensri Pramukkul et al. All rights reserved. Wed, 10 Apr 2013 14:53:05 +0000 http://www.hindawi.com/journals/amp/2013/186037/ The chaos in a new system with order 3 is studied. We have shown that this chaotic system again will be chaotic when the order of system is less than 3. Generalized Adams-Bashforth algorithm has been used for investigating in stability of fixed points and existence of chaos. Alireza K. Golmankhaneh, Roohiyeh Arefi, and Dumitru Baleanu Copyright © 2013 Alireza K. Golmankhaneh et al. All rights reserved. Thu, 04 Apr 2013 10:39:56 +0000 http://www.hindawi.com/journals/amp/2013/954015/ We present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the Bernstein polynomials (BPs). In the first method, we use the operational matrix of Caputo fractional derivative (OMCFD), and in the second one, we apply the operational matrix of Riemann-Liouville fractional integral (OMRLFI). The obtained results are in good agreement with each other as well as with the analytical solutions. We show that the solutions approach to classical solutions as the order of the fractional derivatives approaches 1. Mohsen Alipour and Dumitru Baleanu Copyright © 2013 Mohsen Alipour and Dumitru Baleanu. All rights reserved. Sun, 31 Mar 2013 15:35:31 +0000 http://www.hindawi.com/journals/amp/2013/630196/ Quark matter is believed to exist in the center of neutron stars. A combined model consisting of quark matter and ordinary matter is used to show that the extreme conditions existing in the center could result in a topology change, that is, in the formation of wormholes. Peter K. F. Kuhfittig Copyright © 2013 Peter K. F. Kuhfittig. All rights reserved. Sun, 31 Mar 2013 11:38:14 +0000 http://www.hindawi.com/journals/amp/2013/871961/ We consider a class of nonlinear two-dimensional dynamic systems of the neutral type We obtain sufficient conditions for all solutions of the system to be oscillatory. Our oscillation results when improve the oscillation results for dynamic systems on time scales that have been established by Fu and Lin (2010), since our results do not restrict to the case where . Also, as a special case when , our results do not require to be a positive real sequence. Some examples are given to illustrate the main results. Xinli Zhang and Shanliang Zhu Copyright © 2013 Xinli Zhang and Shanliang Zhu. All rights reserved. Thu, 28 Mar 2013 11:23:09 +0000 http://www.hindawi.com/journals/amp/2013/823961/ We investigate the existence of solutions for the following multipoint boundary value problem of a fractional order differential inclusion , where is the standard Riemann-Liouville fractional derivative, , satisfies ,  and   is a set-valued map. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or nonconvex values. Nemat Nyamoradi, Dumitru Baleanu, and Ravi P. Agarwal Copyright © 2013 Nemat Nyamoradi et al. All rights reserved. Mon, 25 Mar 2013 16:47:29 +0000 http://www.hindawi.com/journals/amp/2013/469654/ The extended symmetry of the functional of length determined in an affine space of the correlation vectors for homogeneous isotropic turbulence is studied. The two-point velocity-correlation tensor field (parametrized by the time variable ) of the velocity fluctuations is used to equip this space by a family of the pseudo-Riemannian metrics (Grebenev and Oberlack (2011)). First, we observe the results obtained by Grebenev and Oberlack (2011) and Grebenev et al. (2012) about a geometry of the correlation space and expose the Lie algebra associated with the equivalence transformation of the above-mentioned functional for the quadratic form generated by which is similar to the Lie algebra constructed by Grebenev et al. (2012). Then, using the properties of this Lie algebra, we show that there exists a nontrivial central extension wherein the central charge is defined by the same bilinear skew-symmetric form as for the Witt algebra which measures the number of internal degrees of freedom of the system. For the applications in turbulence, as the main result, we establish the asymptotic expansion of the transversal correlation function for large correlation distances in the frame of . V. N. Grebenev, A. N. Grishkov, and M. Oberlack Copyright © 2013 V. N. Grebenev et al. All rights reserved. Mon, 25 Mar 2013 13:26:30 +0000 http://www.hindawi.com/journals/amp/2013/917153/ Proteins are biochemical entities consisting of one or more blocks typically folded in a 3D pattern. Each block (a polypeptide) is a single linear sequence of amino acids that are biochemically bonded together. The amino acid sequence in a protein is defined by the sequence of a gene or several genes encoded in the DNA-based genetic code. This genetic code typically uses twenty amino acids, but in certain organisms the genetic code can also include two other amino acids. After linking the amino acids during protein synthesis, each amino acid becomes a residue in a protein, which is then chemically modified, ultimately changing and defining the protein function. In this study, the authors analyze the amino acid sequence using alignment-free methods, aiming to identify structural patterns in sets of proteins and in the proteome, without any other previous assumptions. The paper starts by analyzing amino acid sequence data by means of histograms using fixed length amino acid words (tuples). After creating the initial relative frequency histograms, they are transformed and processed in order to generate quantitative results for information extraction and graphical visualization. Selected samples from two reference datasets are used, and results reveal that the proposed method is able to generate relevant outputs in accordance with current scientific knowledge in domains like protein sequence/proteome analysis. J. A. Tenreiro Machado, António C. Costa, and Maria Dulce Quelhas Copyright © 2013 J. A. Tenreiro Machado et al. All rights reserved. Tue, 19 Mar 2013 10:44:02 +0000 http://www.hindawi.com/journals/amp/2013/416294/ An anisotropic Bianchi type-III cosmological model is investigated in the presence of a bulk viscous fluid within the framework of Lyra geometry with time-dependent displacement vector. It is shown that the field equations are solvable for any arbitrary function of a scale factor. To get the deterministic model of the universe, we have assumed that (i) a simple power-law form of a scale factor and (ii) the bulk viscosity coefficient are proportional to the energy density of the matter. The exact solutions of the Einstein’s field equations are obtained which represent an expanding, shearing, and decelerating model of the universe. Some physical and kinematical behaviors of the cosmological model are briefly discussed. Priyanka Kumari, M. K. Singh, and Shri Ram Copyright © 2013 Priyanka Kumari et al. All rights reserved. Wed, 27 Feb 2013 12:06:58 +0000 http://www.hindawi.com/journals/amp/2013/934745/ This paper deals with a Neumann boundary value problem for a Keller-Segel model with a cubic source term in a d-dimensional box , which describes the movement of cells in response to the presence of a chemical signal substance. It is proved that, given any general perturbation of magnitude δ, its nonlinear evolution is dominated by the corresponding linear dynamics along a finite number of fixed fastest growing modes, over a time period of the order ln(). Each initial perturbation certainly can behave drastically differently from another, which gives rise to the richness of patterns. Our results provide a mathematical description for early pattern formation in the model. Shengmao Fu and Ji Liu Copyright © 2013 Shengmao Fu and Ji Liu. All rights reserved. Sun, 24 Feb 2013 13:31:53 +0000 http://www.hindawi.com/journals/amp/2013/591852/ Lie symmetry group method is applied to find the Lie point symmetry group of a system of partial differential equations that determines general form of four-dimensional Einstein Walker manifold. Also we will construct the optimal system of one-dimensional Lie subalgebras and investigate some of its group invariant solutions. Mehdi Nadjafikhah and Mehdi Jafari Copyright © 2013 Mehdi Nadjafikhah and Mehdi Jafari. All rights reserved. Wed, 13 Feb 2013 10:13:41 +0000 http://www.hindawi.com/journals/amp/2013/258203/ It is shown that the spanning set for provided by the eigenfunctions of the particle in a box in quantum mechanics provides a very effective variational basis for more general problems. The basis is scaled to , where and are then used as variational parameters. What is perhaps a natural basis for quantum systems confined to a spherical box in turns out to be appropriate also for problems that are softly confined by U-shaped potentials, including those with strong singularities at . Specific examples are discussed in detail, along with some bound -boson systems. Richard L. Hall and Alexandra Lemus Rodríguez Copyright © 2013 Richard L. Hall and Alexandra Lemus Rodríguez. All rights reserved. Thu, 07 Feb 2013 17:47:06 +0000 http://www.hindawi.com/journals/amp/2013/568632/ The method of approximate transformation groups, which was proposed by Baikov et al. (1988 and 1996), is extended on Hamiltonian and bi-Hamiltonian systems of evolution equations. Indeed, as a main consequence, this extended procedure is applied in order to compute the approximate conservation laws and approximate recursion operators corresponding to these types of equations. In particular, as an application, a comprehensive analysis of the problem of approximate conservation laws and approximate recursion operators associated to the Gardner equation with the small parameters is presented. M. Nadjafikhah and A. Mokhtary Copyright © 2013 M. Nadjafikhah and A. Mokhtary. All rights reserved. Wed, 26 Dec 2012 14:25:42 +0000 http://www.hindawi.com/journals/amp/2012/104856/ The entanglement of states on -independent subalgebras is considered, and equivalent conditions are given for subalgebras to be independent. Shuilin Jin and Li Xu Copyright © 2012 Shuilin Jin and Li Xu. All rights reserved. Tue, 25 Dec 2012 13:49:43 +0000 http://www.hindawi.com/journals/amp/2012/272904/ Based on a well-known Lie algebra, the multicomponent Guo hierarchy with self-consistent sources is proposed. With the help of a set of non-semisimple Lie algebra, the nonlinear bi-integrable couplings of the multicomponent Guo hierarchy with self-consistent sources are obtained. It enriches the content of the integrable couplings of hierarchies with self-consistent sources. Finally, the Hamiltonian structures are worked out by employing the variational identity. Hongwei Yang, Huanhe Dong, Baoshu Yin, and Zhenyu Liu Copyright © 2012 Hongwei Yang et al. All rights reserved. Thu, 20 Dec 2012 18:15:04 +0000 http://www.hindawi.com/journals/amp/2012/197385/ The symmetry algebra of asymptotically flat spacetimes at null infinity in four dimensions in the sense of Newman and Unti is revisited. As in the Bondi-Metzner-Sachs gauge, it is shown to be isomorphic to the direct sum of the abelian algebra of infinitesimal conformal rescalings with . The latter algebra is the semidirect sum of infinitesimal supertranslations with the conformal Killing vectors of the Riemann sphere. Infinitesimal local conformal transformations can then consistently be included. We work out the local conformal properties of the relevant Newman-Penrose coefficients, construct the surface charges, and derive their algebra. Glenn Barnich and Pierre-Henry Lambert Copyright © 2012 Glenn Barnich and Pierre-Henry Lambert. All rights reserved. Wed, 14 Nov 2012 14:03:21 +0000 http://www.hindawi.com/journals/amp/2012/843204/ Teoman Özer, Vladimir B. Taranov, Roman G. Smirnov, Thomas Klemas, Prakash Thamburaja, Sanith Wijesinghe, and Burak Polat Copyright © 2012 Teoman Özer et al. All rights reserved. Sun, 11 Nov 2012 09:20:06 +0000 http://www.hindawi.com/journals/amp/2012/385341/ Ideal occurrence of an event (projector) leads to the known change of a state (density operator) into (the Lüders state). It is shown that two events and give the same Lüders state if and only if the equivalence relation is valid. This relation determines equivalence classes. The set of them and each class, are studied in detail. It is proved that the range projector of the Lüders state can be evaluated as , where denotes the greatest lower bound, and is the null projector of . State-dependent implication extends absolute implication (which, in turn, determines the entire structure of quantum logic). and are investigated in a closely related way to mutual benefit. Inherent in the preorder is the state-dependent equivalence , defining equivalence classes in a given Boolean subalgebra. The quotient set, in which the classes are the elements, has itself a partially ordered structure, and so has each class. In a complete Boolean subalgebra, both structures are complete lattices. Physical meanings are discussed. Fedor Herbut Copyright © 2012 Fedor Herbut. All rights reserved. Wed, 24 Oct 2012 15:24:16 +0000 http://www.hindawi.com/journals/amp/2012/309289/ We consider a class of complex networks with both delayed and nondelayed coupling. In particular, we consider the situation for both time delay-independent and time delay-dependent complex dynamical networks and obtain sufficient conditions for their asymptotic synchronization by using the Lyapunov-Krasovskii stability theorem and the linear matrix inequality (LMI). We also present some simulation results to support the validity of the theories. Ze Tang and Jianwen Feng Copyright © 2012 Ze Tang and Jianwen Feng. All rights reserved. Thu, 13 Sep 2012 10:35:20 +0000 http://www.hindawi.com/journals/amp/2012/156573/ Most quantum logics do not allow for a reasonable calculus of conditional probability. However, those ones which do so provide a very general and rich mathematical structure, including classical probabilities, quantum mechanics, and Jordan algebras. This structure exhibits some similarities with Alfsen and Shultz's noncommutative spectral theory, but these two mathematical approaches are not identical. Barnum, Emerson, and Ududec adapted the concept of higher-order interference, introduced by Sorkin in 1994, into a general probabilistic framework. Their adaption is used here to reveal a close link between the existence of the Jordan product and the nonexistence of interference of third or higher order in those quantum logics which entail a reasonable calculus of conditional probability. The complete characterization of the Jordan algebraic structure requires the following three further postulates: a Hahn-Jordan decomposition property for the states, a polynomial functional calculus for the observables, and the positivity of the square of an observable. While classical probabilities are characterized by the absence of any kind of interference, the absence of interference of third (and higher) order thus characterizes a probability calculus which comes close to quantum mechanics but still includes the exceptional Jordan algebras. Gerd Niestegge Copyright © 2012 Gerd Niestegge. All rights reserved. Mon, 10 Sep 2012 15:24:44 +0000 http://www.hindawi.com/journals/amp/2012/702681/ An analysis is performed to investigate the effect of MHD and thermal radiation on the two-dimensional steady flow of an incompressible, upper-convected Maxwells (UCM) fluid in presence of external magnetic field. The governing system of partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and is solved numerically by efficient shooting technique. Velocity and temperature fields have been computed and shown graphically for various values of physical parameters. For a Maxwell fluid, a thinning of the boundary layer and a drop in wall skin friction coefficient is predicted to occur for the higher elastic number which agrees with the results of Hayat et al. 2007 and Sadeghy et al. 2006. The objective of the present work is to investigate the effect of elastic parameter β, magnetic parameter Mn, Eckert number Ec, Radiation parameter N, and Prandtl number Pr on flow and heat transfer charecteristics. M. Subhas Abel, Jagadish V. Tawade, and Jyoti N. Shinde Copyright © 2012 M. Subhas Abel et al. All rights reserved. Wed, 29 Aug 2012 15:08:52 +0000 http://www.hindawi.com/journals/amp/2012/193190/ For a class of multiparameter statistical models based on 𝑁2×𝑁2 braid matrices, the eigenvalues of the transfer matrix 𝐓(𝑟) are obtained explicitly for all (𝑟,𝑁). Our formalism yields them as solutions of sets of linear equations with simple constant coefficients. The role of zero-sum multiplets constituted in terms of roots of unity is pointed out, and their origin is traced to circular permutations of the indices in the tensor products of basis states induced by our class of 𝐓(𝑟) matrices. The role of free parameters, increasing as 𝑁2 with N, is emphasized throughout. Spin chain Hamiltonians are constructed and studied for all N. Inverse Cayley transforms of the Yang-Baxter matrices corresponding to our braid matrices are obtained for all N. They provide potentials for factorizable S-matrices. Main results are summarized, and perspectives are indicated in the concluding remarks. B. Abdesselam and A. Chakrabarti Copyright © 2012 B. Abdesselam and A. Chakrabarti. All rights reserved. Thu, 16 Aug 2012 08:21:52 +0000 http://www.hindawi.com/journals/amp/2012/679063/ This paper investigates the positions and linear stability of an infinitesimal body around the equilibrium points in the framework of the Robe’s circular restricted three-body problem, with assumptions that the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second primary is an oblate body as well. It is found that equilibrium point exists near the centre of the first primary. Further, there can be one more equilibrium point on the line joining the centers of both primaries. Points on the circle within the first primary are also equilibrium points under certain conditions and the existence of two out-of-plane points is also observed. The linear stability of this configuration is examined and it is found that points near the center of the first primary are conditionally stable, while the circular and out of plane equilibrium points are unstable. Jagadish Singh and Abubakar Umar Sandah Copyright © 2012 Jagadish Singh and Abubakar Umar Sandah. All rights reserved.