http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Sat, 25 May 2013 15:50:28 +0000 http://www.hindawi.com/journals/aaa/2013/247841/ For a nonlinear generalization of the Camassa-Holm equation, we investigate the dynamic properties of solutions for the equation under the assumption that the initial value lies in the space . A one-sided upper bound estimate on the first-order spatial derivative, bound estimate, and a space-time higher-norm estimate for the solutions are obtained. Zheng Yin Copyright © 2013 Zheng Yin. All rights reserved. Sat, 25 May 2013 15:49:46 +0000 http://www.hindawi.com/journals/aaa/2013/205097/ This paper discusses the fundamentals of negative probabilities and fractional calculus. The historical evolution and the main mathematical concepts are discussed, and several analogies between the two apparently unrelated topics are established. Based on the new conceptual perspective, some experiments are performed shading new light into possible future progress. J. A. Tenreiro Machado Copyright © 2013 J. A. Tenreiro Machado. All rights reserved. Sat, 25 May 2013 15:46:37 +0000 http://www.hindawi.com/journals/aaa/2013/273040/ The classical Valiron-Mohon'ko theorem has many applications in the study of complex equations. In this paper, we investigate rational functions in f(z) and the shifts of f(z). We get some results on their characteristic functions. These results may be viewed as difference analogues of Valiron-Mohon'ko theorem. Ran Ran Zhang and Zhi Bo Huang Copyright © 2013 Ran Ran Zhang and Zhi Bo Huang. All rights reserved. Sat, 25 May 2013 15:45:47 +0000 http://www.hindawi.com/journals/aaa/2013/208964/ Electricity is a special energy which is hard to store, so the electricity demand forecasting remains an important problem. Accurate short-term load forecasting (STLF) plays a vital role in power systems because it is the essential part of power system planning and operation, and it is also fundamental in many applications. Considering that an individual forecasting model usually cannot work very well for STLF, a hybrid model based on the seasonal ARIMA model and BP neural network is presented in this paper to improve the forecasting accuracy. Firstly the seasonal ARIMA model is adopted to forecast the electric load demand day ahead; then, by using the residual load demand series obtained in this forecasting process as the original series, the follow-up residual series is forecasted by BP neural network; finally, by summing up the forecasted residual series and the forecasted load demand series got by seasonal ARIMA model, the final load demand forecasting series is obtained. Case studies show that the new strategy is quite useful to improve the accuracy of STLF. Yi Yang, Jie Wu, Yanhua Chen, and Caihong Li Copyright © 2013 Yi Yang et al. All rights reserved. Fri, 24 May 2013 15:25:34 +0000 http://www.hindawi.com/journals/aaa/2013/854743/ This paper concerns Razumikhin-type theorems on exponential stability of stochastic differential delay equations with Markovian switching, where the modulating Markov chain involves small parameters. The smaller the parameter is, the rapider switching the system will experience. In order to reduce the complexity, we will “replace” the original systems by limit systems with a simple structure. Under Razumikhin-type conditions, we establish theorems that if the limit systems are th-moment exponentially stable; then, the original systems are th-moment exponentially stable in an appropriate sense. Junhao Hu, Xuerong Mao, and Chenggui Yuan Copyright © 2013 Junhao Hu et al. All rights reserved. Thu, 23 May 2013 09:36:20 +0000 http://www.hindawi.com/journals/aaa/2013/160681/ We solve the system of nonlinear fractional Jaulent-Miodek and Whitham-Broer-Kaup equations via the Sumudu transform homotopy method (STHPM). The method is easy to apply, accurate, and reliable. Abdon Atangana and Dumitru Baleanu Copyright © 2013 Abdon Atangana and Dumitru Baleanu. All rights reserved. Wed, 22 May 2013 16:41:01 +0000 http://www.hindawi.com/journals/aaa/2013/704137/ The previously developed new perturbation-iteration algorithm has been applied to differential equation systems for the first time. The iteration algorithm for systems is developed first. The algorithm is tested for a single equation, coupled two equations, and coupled three equations. Solutions are compared with those of variational iteration method and numerical solutions, and a good agreement is found. The method can be applied to differential equation systems with success. Mehmet Şenol, İhsan Timuçin Dolapçı, Yiğit Aksoy, and Mehmet Pakdemirli Copyright © 2013 Mehmet Şenol et al. All rights reserved. Wed, 22 May 2013 15:47:21 +0000 http://www.hindawi.com/journals/aaa/2013/768976/ An explicit multistep mixed finite element method is proposed and discussed for regularized long wave (RLW) equation. The spatial direction is approximated by the mixed Galerkin method using mixed linear space finite elements, and the time direction is discretized by the explicit multistep method. The optimal error estimates in and norms for the scalar unknown and its flux based on time explicit multistep method are derived. Some numerical results are given to verify our theoretical analysis and illustrate the efficiency of our method. Yang Liu, Hong Li, Yanwei Du, and Jinfeng Wang Copyright © 2013 Yang Liu et al. All rights reserved. Wed, 22 May 2013 14:49:54 +0000 http://www.hindawi.com/journals/aaa/2013/608943/ An efficient approach based on homotopy perturbation method by using sumudu transform is proposed to solve nonlinear fractional Harry Dym equation. This method is called homotopy perturbation sumudu transform (HPSTM). Furthermore, the same problem is solved by Adomian decomposition method (ADM). The results obtained by the two methods are in agreement, and, hence, this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The numerical solutions obtained by the HPSTM show that the approach is easy to implement and computationally very attractive. Devendra Kumar, Jagdev Singh, and A. Kılıçman Copyright © 2013 Devendra Kumar et al. All rights reserved. Wed, 22 May 2013 09:37:01 +0000 http://www.hindawi.com/journals/aaa/2013/737481/ We make use of the properties of the Sumudu transform to solve nonlinear fractional partial differential equations describing heat-like equation with variable coefficients. The method, namely, homotopy perturbation Sumudu transform method, is the combination of the Sumudu transform and the HPM using He’s polynomials. This method is very powerful, and professional techniques for solving different kinds of linear and nonlinear fractional differential equations arising in different fields of science and engineering. Abdon Atangana and Adem Kılıçman Copyright © 2013 Abdon Atangana and Adem Kılıçman. All rights reserved. Wed, 22 May 2013 09:14:52 +0000 http://www.hindawi.com/journals/aaa/2013/830147/ We studied on the differential geometry of the Hamilton space including trajectories of the motion of particles exposed to gravitational fields and the cotangent bundle. A. Ceylan Coken and Ismet Ayhan Copyright © 2013 A. Ceylan Coken and Ismet Ayhan. All rights reserved. Wed, 22 May 2013 09:09:53 +0000 http://www.hindawi.com/journals/aaa/2013/312527/ This paper focuses on the development of a bilevel optimization model with random coefficients for a production-inventory system. The expected value operator technique is used to deal with the objective function, and rough approximation is applied to convert the stochastic constraint into a crisp constraint. Then an interactive programming method and genetic algorithm are utilized to solve the crisp model. Finally, an application is given to show the efficiency of the proposed model and approaches in solving the problem. Liming Yao and Jiuping Xu Copyright © 2013 Liming Yao and Jiuping Xu. All rights reserved. Wed, 22 May 2013 08:00:02 +0000 http://www.hindawi.com/journals/aaa/2013/496096/ We investigate fixed points of meromorphic solutions for the Pielou logistic equation and obtain some estimates of exponents of convergence of fixed points of and its shifts , differences , and divided differences . Zong-Xuan Chen and Kwang Ho Shon Copyright © 2013 Zong-Xuan Chen and Kwang Ho Shon. All rights reserved. Mon, 20 May 2013 16:15:17 +0000 http://www.hindawi.com/journals/aaa/2013/652083/ With the rapid development of marine economy industry, the activities for exploring and exploiting the marine resources are increasing, and there are more and more marine construction projects, which contribute to the growing trend of eutrophication and frequent occurrence of red tide. Thus, seawater quality has become the topic which the people generally cared about. The seawater quality evaluation could be considered as an analysis process which combined the evaluation indexes with certainty and evaluation factors with uncertainty and its changes. This paper built a model for the assessment of seawater environmental quality based on the multiobjective variable fuzzy set theory (VFEM). The Qingdao marine dumping site in China is taken as an evaluation example. Through the quantitative research of water-quality data from 2004 to 2008, the model is more reliable than other traditional methods, in which uncertainty and ambiguity of the seawater quality evaluation are considered, and trade the stable results as the final results of seawater quality evaluation, which effectively solved the impact of the fuzzy boundary of evaluation standard and monitoring error, is more suitable for evaluation of a multi-index, multilevel, and nonlinear marine environment system and has been proved to be an effective tool for seawater quality evaluation. Lina Ke and Huicheng Zhou Copyright © 2013 Lina Ke and Huicheng Zhou. All rights reserved. Mon, 20 May 2013 15:15:52 +0000 http://www.hindawi.com/journals/aaa/2013/748683/ Fluids subject to thermal gradients produce complex behaviors that arise from the competition with gravitational effects. Although such sort of systems have been widely studied in the literature for simple (Newtonian) fluids, the behavior of viscoelastic fluids has not been explored thus far. We present a theoretical study of the dynamics of a Maxwell viscoelastic fluid in a closed-loop thermosyphon. This sort of fluid presents elastic-like behavior and memory effects. We study the asymptotic properties of the fluid inside the thermosyphon and the exact equations of motion in the inertial manifold that characterizes the asymptotic behavior. We derive, for the first time, the mathematical derivations of the motion of a viscoelastic fluid in the interior of a closed-loop thermosyphon under the effects of natural convection and a given external temperature gradient. Justine Yasappan, Ángela Jiménez-Casas, and Mario Castro Copyright © 2013 Justine Yasappan et al. All rights reserved. Mon, 20 May 2013 14:15:07 +0000 http://www.hindawi.com/journals/aaa/2013/619068/ The existence and uniqueness of local strong solutions for a nonlinear equation are investigated in the Sobolev space provided that the initial value lies in with . Meanwhile, we prove the existence of global weak solutions in for the equation. Meng Wu Copyright © 2013 Meng Wu. All rights reserved. Mon, 20 May 2013 13:14:03 +0000 http://www.hindawi.com/journals/aaa/2013/514174/ In this paper we consider some analogs of the Korovkin approximation theorem via lacunary equistatistical convergence. In particular we study lacunary equi-statistical convergence of approximating operators on spaces, the spaces of all real valued continuous functions de…ned on and satisfying some special conditions. Yusuf Kaya and Nazmiye Gönül Copyright © 2013 Yusuf Kaya and Nazmiye Gönül. All rights reserved. Mon, 20 May 2013 11:55:19 +0000 http://www.hindawi.com/journals/aaa/2013/152518/ The twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems. The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given. The existence or nonexistence of saddle-node bifurcation surfaces is obtained. Finally, the complete bifurcation diagrams and bifurcation curves are also given under different cases. Moreover, the methods adopted in this paper can be extended to a higher dimensional system. Xiaodong Li, Weipeng Zhang, Fengjie Geng, and Jicai Huang Copyright © 2013 Xiaodong Li et al. All rights reserved. Mon, 20 May 2013 11:48:22 +0000 http://www.hindawi.com/journals/aaa/2013/747613/ This paper deals with the extinction and nonextinction properties of the fast diffusion equation of homogeneous Dirichlet boundary condition in a bounded domain of with . For , under appropriate hypotheses, we show that is the critical exponent of extinction for the weak solution. Furthermore, we prove that the solution either extinct or nonextinct in finite time depends strongly on the initial data and the first eigenvalue of with homogeneous Dirichlet boundary. Chunlai Mu, Li Yan, and Yi-bin Xiao Copyright © 2013 Chunlai Mu et al. All rights reserved. Mon, 20 May 2013 11:46:44 +0000 http://www.hindawi.com/journals/aaa/2013/931493/ Nonhomogeneous system of linear differential equations of second order with multiple different delays and pairwise permutable matrices defining the linear parts is considered. Solution of corresponding initial value problem is represented using matrix polynomials. Josef Diblík, Michal Fečkan, and Michal Pospíšil Copyright © 2013 Josef Diblík et al. All rights reserved. Mon, 20 May 2013 10:53:29 +0000 http://www.hindawi.com/journals/aaa/2013/716593/ The aim of this study was to determine spatial distribution and volume of four commercial quartz grades, namely, silicon metal, ferrosilicon, aggregate, and kaolin (depending on content in impurities) in a quartz seam. The chemical and mineralogical composition of the reserves in the seam were determined from samples collected from outcrops, blasting operations, and exploratory drilling, and compositional kriging was used to calculate the volume and distribution of the reserves. A more accurate knowledge of the deposit ensures better mine planning, leading to higher profitability and an improved relationship with the environment. J. Taboada, Á. Saavedra, C. Iglesias, and E. Giráldez Copyright © 2013 J. Taboada et al. All rights reserved. Sun, 19 May 2013 15:38:32 +0000 http://www.hindawi.com/journals/aaa/2013/536910/ The parameter space associated to the parametric family of Chebyshev-Halley on quadratic polynomials shows a dynamical richness worthy of study. This analysis has been initiated by the authors in previous works. Every value of the parameter belonging to the same connected component of the parameter space gives rise to similar dynamical behavior. In this paper, we focus on the search of regions in the parameter space that gives rise to the appearance of attractive orbits of period two. Alicia Cordero, Juan R. Torregrosa, and Pura Vindel Copyright © 2013 Alicia Cordero et al. All rights reserved. Sun, 19 May 2013 13:31:48 +0000 http://www.hindawi.com/journals/aaa/2013/528281/ We consider the low-rank approximation problem arising in the generalized Karhunen-Loeve transform. A sufficient condition for the existence of a solution is derived, and the analytical expression of the solution is given. A numerical algorithm is proposed to compute the solution. The new algorithm is illustrated by numerical experiments. Xue-Feng Duan, Qing-Wen Wang, and Jiao-Fen Li Copyright © 2013 Xue-Feng Duan et al. All rights reserved. Sun, 19 May 2013 11:17:38 +0000 http://www.hindawi.com/journals/aaa/2013/635265/ Several new existence theorems on positive, negative, and sign-changing solutions for the following fourth-order beam equation are obtained: ,   ;  , where . In particular, an infinitely many sign changing solution theorem is established. The method of the invariant set of decreasing flow is employed to discuss this problem. Ying Wu and Guodong Han Copyright © 2013 Ying Wu and Guodong Han. All rights reserved. Sun, 19 May 2013 08:54:27 +0000 http://www.hindawi.com/journals/aaa/2013/910624/ A new modified Runge-Kutta-Nyström method of fourth algebraic order is developed. The new modified RKN method is based on the fitting of the coefficients, due to the nullification not only of the phase lag and of the amplification error, but also of their derivatives. Numerical results indicate that the new modified method is much more efficient than other methods derived for solving numerically the Schrödinger equation. D. F. Papadopoulos and T. E. Simos Copyright © 2013 D. F. Papadopoulos and T. E. Simos. All rights reserved. Sun, 19 May 2013 08:20:13 +0000 http://www.hindawi.com/journals/aaa/2013/679075/ This paper introduces the stability and convergence of two-step Runge-Kutta methods with compound quadrature formula for solving nonlinear Volterra delay integro-differential equations. First, the definitions of -algebraically stable and asymptotically stable are introduced; then the asymptotical stability of a -algebraically stable two-step Runge-Kutta method with is proved. For the convergence, the concepts of -convergence, diagonally stable, and generalized stage order are firstly introduced; then it is proved by some theorems that if a two-step Runge-Kutta method is algebraically stable and diagonally stable and its generalized stage order is , then the method with compound quadrature formula is -convergent of order at least , where depends on the compound quadrature formula. Haiyan Yuan and Cheng Song Copyright © 2013 Haiyan Yuan and Cheng Song. All rights reserved. Thu, 16 May 2013 18:17:33 +0000 http://www.hindawi.com/journals/aaa/2013/978738/ Let be a nonempty subset of a Hausdorff topological vector space , and let be a real-valued continuous function on . If for each , there exists such that , then is called -simultaneously proximal and is called -best simultaneous approximation for in . In this paper, we study the problem of -simultaneous approximation for a vector subspace in . Some other results regarding -simultaneous approximation in quotient space are presented. Mahmoud Rawashdeh and Sarah Khalil Copyright © 2013 Mahmoud Rawashdeh and Sarah Khalil. All rights reserved. Thu, 16 May 2013 18:15:57 +0000 http://www.hindawi.com/journals/aaa/2013/187383/ A collocation finite element method for solving fractional diffusion equation for force-free case is considered. In this paper, we develop an approximation method based on collocation finite elements by cubic B-spline functions to solve fractional diffusion equation for force-free case formulated with Riemann-Liouville operator. Some numerical examples of interest are provided to show the accuracy of the method. A comparison between exact analytical solution and a numerical one has been made. O. Tasbozan, A. Esen, N. M. Yagmurlu, and Y. Ucar Copyright © 2013 O. Tasbozan et al. All rights reserved. Thu, 16 May 2013 17:46:24 +0000 http://www.hindawi.com/journals/aaa/2013/941878/ We discuss the construction of solutions to the inverse Cauchy problem by using characteristics. V. G. Danilov Copyright © 2013 V. G. Danilov. All rights reserved. Thu, 16 May 2013 17:29:43 +0000 http://www.hindawi.com/journals/aaa/2013/705482/ Xinguang Zhang, Yong Hong Wu, Dragoş-Pătru Covei, and Xinan Hao Copyright © 2013 Xinguang Zhang et al. All rights reserved.