Mathematical Problems in Engineering http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Study and Simulation on Discrete Dynamics of Bertrand Triopoly Team-Game Thu, 26 Mar 2015 13:39:30 +0000 http://www.hindawi.com/journals/mpe/2015/960380/ A Bertrand Triopoly team-game model is considered in which two firms with bounded rational expectations make up a cooperative team and allocate common profits proportionate to their marketing strength. The existence and three-dimensional stable regions of the fixed points are investigated. Complex effects of on bifurcation scenarios and profits are displayed by parameter basin plots and average profits charts. Impact of assigning weight on stable regions, 2D-bifurcation phase portraits, and the average profits is investigated. We find and can cause chaos; chaos resulting from adjustment speed is harmful to all the players as for profits, while chaos resulting from is conducive to firm 3. Basins of attraction are investigated and we find that the attraction domain will become smaller with increase of price modification speed. Lijian Sun and Junhai Ma Copyright © 2015 Lijian Sun and Junhai Ma. All rights reserved. Effective Semisupervised Community Detection Using Negative Information Thu, 26 Mar 2015 13:38:42 +0000 http://www.hindawi.com/journals/mpe/2015/109671/ The semisupervised community detection method, which can utilize prior information to guide the discovery process of community structure, has aroused considerable research interests in the past few years. Most of the former works assume that the exact labels of some nodes are known in advance and presented in the forms of individual labels and pairwise constraints. In this paper, we propose a novel type of prior information called negative information, which indicates whether a node does not belong to a specific community. Then the semisupervised community detection algorithm is presented based on negative information to efficiently make use of this type of information to assist the process of community detection. The proposed algorithm is evaluated on several artificial and real-world networks and shows high effectiveness in recovering communities. Dong Liu, Dequan Duan, Shikai Sui, and Guojie Song Copyright © 2015 Dong Liu et al. All rights reserved. Modeling Heavy Metal Sorption Kinetics Using Fractional Calculus Thu, 26 Mar 2015 12:33:31 +0000 http://www.hindawi.com/journals/mpe/2015/549562/ Heavy metals are commonly regarded as environmentally aggressive and hazardous to human health. Among the different metals, lead plays an important economic role due to its large use in the automotive industry, being an essential component of batteries. Different approaches have been reported in the literature aimed at lead removal, and among them a very successful one considers the use of water hyacinths for sorption-based operation. The modeling of the metal sorption kinetics is a fundamental step towards in-depth studies and proper separation equipment design and optimization. Fractional calculus represents a novel approach and a growing research field for process modeling, which is based on the successful use of derivatives of arbitrary order. This paper reports the modeling of the kinetics of lead sorption by water hyacinths (Eichhornia crassipes) using a fractional calculus. A general procedure on error analysis is also employed to prove the actual fractional nature of the proposed model by the use of parametric variance analysis, which was carried out using two different approaches (with the complete Hessian matrix and with a simplified Hessian matrix). The joint parameter confidence regions were generated, allowing to successfully show the fractional nature of the model and the sorption process. V. C. Friesen, D. P. Leitoles, G. Gonçalves, E. K. Lenzi, and M. K. Lenzi Copyright © 2015 V. C. Friesen et al. All rights reserved. Some Identities Involving Chebyshev Polynomials Thu, 26 Mar 2015 12:22:19 +0000 http://www.hindawi.com/journals/mpe/2015/950695/ The main purpose of this paper is using the combinatorial method and algebraic manipulations to study some sums of powers of Chebyshev polynomials and give several interesting identities. As some applications of these results, we obtained several divisibility properties involving Chebyshev polynomials. Xiaoxue Li Copyright © 2015 Xiaoxue Li. All rights reserved. Numerical Investigations of the Effect of Nonlinear Quadratic Pressure Gradient Term on a Moving Boundary Problem of Radial Flow in Low-Permeable Reservoirs with Threshold Pressure Gradient Thu, 26 Mar 2015 12:19:42 +0000 http://www.hindawi.com/journals/mpe/2015/275057/ The existence of a TPG can generate a relatively high pressure gradient in the process of fluid flow in porous media in low-permeable reservoirs, and neglecting the QPGTs in the governing equations, by assuming a small pressure gradient for such a problem, can cause a significant error in predicting the formation pressure. Based on these concerns, in consideration of the QPGT, a moving boundary model of radial flow in low-permeable reservoirs with the TPG for the case of a constant flow rate at the inner boundary is constructed. Due to strong nonlinearity of the mathematical model, a numerical method is presented: the system of partial differential equations for the moving boundary problem is first transformed equivalently into a closed system of partial differential equations with fixed boundary conditions by a spatial coordinate transformation method; and then a stable, fully implicit finite difference method is used to obtain its numerical solution. Numerical result analysis shows that the mathematical models of radial flow in low-permeable reservoirs with TPG must take the QPGT into account in their governing equations, which is more important than those of Darcy’s flow; the sensitive effects of the QPGT for the radial flow model do not change with an increase of the dimensionless TPG. Wenchao Liu and Jun Yao Copyright © 2015 Wenchao Liu and Jun Yao. All rights reserved. Asymptotic Optimality of Combined Double Sequential Weighted Probability Ratio Test for Three Composite Hypotheses Thu, 26 Mar 2015 11:55:51 +0000 http://www.hindawi.com/journals/mpe/2015/356587/ We propose the weighted expected sample size (WESS) to evaluate the overall performance on the indifference-zones for three composite hypotheses’ testing problem. Based on minimizing the WESS to control the expected sample sizes, a new sequential test is developed by utilizing two double sequential weighted probability ratio tests (2-SWPRTs) simultaneously. It is proven that the proposed test has a finite stopping time and is asymptotically optimal in the sense of asymptotically minimizing not only the expected sample size but also any positive moment of the stopping time on the indifference-zones under some mild conditions. Simulation studies illustrate that the proposed test has the smallest WESS and relative mean index (RMI) compared with Sobel-Wald and Whitehead-Brunier tests. Lei Wang, Xiaolong Pu, and Yan Li Copyright © 2015 Lei Wang et al. All rights reserved. Wiretap Channel with Rate-Limited Channel State Information Thu, 26 Mar 2015 11:39:54 +0000 http://www.hindawi.com/journals/mpe/2015/643265/ We revisit a channel coding problem where the channel state information (CSI) is rate-limited (or coded) and available to the channel encoder. A wiretapper is added into this model, and the confidential message is intended only for the legal receiver and should be kept from being eavesdropped by the wiretapper. Equivocation analysis is provided to evaluate the level of information leakage to the wiretapper. We characterize an achievable rate-equivocation region as well as an outer bound for this security model. To achieve the rate-equivocation triples, we propose an efficient coding scheme, in which the coded CSI serves as the CSI for the channel encoder, based on Gel’fand and Pinsker’s coding and Wyner’s random coding. Furthermore, an example of Gaussian wiretap channel with rate-limited CSI is presented, of which a lower bound on the secrecy capacity is obtained. By simulation, we find there exists an optimal rate of the coded CSI at which the biggest secrecy transmission rate of the Gaussian case is achieved. Xinxing Yin, Liang Pang, and Zhi Xue Copyright © 2015 Xinxing Yin et al. All rights reserved. Stabilisation of Discrete-Time Piecewise Homogeneous Markov Jump Linear System with Imperfect Transition Probabilities Thu, 26 Mar 2015 11:39:19 +0000 http://www.hindawi.com/journals/mpe/2015/720353/ This paper is devoted to investigating the stability and stabilisation problems for discrete-time piecewise homogeneous Markov jump linear system with imperfect transition probabilities. A sufficient condition is derived to ensure the considered system to be stochastically stable. Moreover, the corresponding sufficient condition on the existence of a mode-dependent and variation-dependent state feedback controller is derived to guarantee the stochastic stability of the closed-loop system, and a new method is further proposed to design a static output feedback controller by introducing additional slack matrix variables to eliminate the equation constraint on Lyapunov matrix. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods. Ding Zhai, Liwei An, Jinghao Li, and Qingling Zhang Copyright © 2015 Ding Zhai et al. All rights reserved. Semiglobal Stabilization via Output-Feedback for a Class of Nontriangular Nonlinear Systems with an Unknown Coefficient Thu, 26 Mar 2015 09:29:17 +0000 http://www.hindawi.com/journals/mpe/2015/375765/ This paper is devoted to the semiglobal stabilization via output-feedback for a class of uncertain nonlinear systems. Remark that the systems in question contain an unknown control coefficient which inherently depends on the system output and allow larger-than-two order growing unmeasurable states which is the obstruction of global stabilization via output-feedback. By introducing a recursive reduced-order observer and combining with saturated state estimate, a desired output-feedback controller is explicitly constructed for the systems. Under the appropriate choice of design parameters, the controller can make the closed-loop system semiglobally attractive and locally exponentially stable at the origin. A simulation example is provided to illustrate the effectiveness of the proposed approach. Mengliang Liu, Yungang Liu, and Fengzhong Li Copyright © 2015 Mengliang Liu et al. All rights reserved. A New Finite Interval Lifetime Distribution Model for Fitting Bathtub-Shaped Failure Rate Curve Thu, 26 Mar 2015 08:50:32 +0000 http://www.hindawi.com/journals/mpe/2015/954327/ This paper raised a new four-parameter fitting model to describe bathtub curve, which is widely used in research on components’ life analysis, then gave explanation of model parameters, and provided parameter estimation method as well as application examples utilizing some well-known lifetime data. By comparative analysis between the new model and some existing bathtub curve fitting model, we can find that the new fitting model is very convenient and its parameters are clear; moreover, this model is of universal applicability which is not only suitable for bathtub-shaped failure rate curves but also applicable for the constant, increasing, and decreasing failure rate curves. Xiaohong Wang, Chuang Yu, and Yuxiang Li Copyright © 2015 Xiaohong Wang et al. All rights reserved. Research of Chaotic Dynamics of 3D Autonomous Quadratic Systems by Their Reduction to Special 2D Quadratic Systems Thu, 26 Mar 2015 08:30:29 +0000 http://www.hindawi.com/journals/mpe/2015/271637/ New results about the existence of chaotic dynamics in the quadratic 3D systems are derived. These results are based on the method allowing studying dynamics of 3D system of autonomous quadratic differential equations with the help of reduction of this system to the special 2D quadratic system of differential equations. Vasiliy Belozyorov Copyright © 2015 Vasiliy Belozyorov. All rights reserved. A Differential-Algebraic Model for the Once-Through Steam Generator of MHTGR-Based Multimodular Nuclear Plants Thu, 26 Mar 2015 08:03:59 +0000 http://www.hindawi.com/journals/mpe/2015/370101/ Small modular reactors (SMRs) are those fission reactors whose electrical output power is no more than 300 MWe. SMRs usually have the inherent safety feature that can be applicable to power plants of any desired power rating by applying the multimodular operation scheme. Due to its strong inherent safety feature, the modular high temperature gas-cooled reactor (MHTGR), which uses helium as coolant and graphite as moderator and structural material, is a typical SMR for building the next generation of nuclear plants (NGNPs). The once-through steam generator (OTSG) is the basis of realizing the multimodular scheme, and modeling of the OTSG is meaningful to study the dynamic behavior of the multimodular plants and to design the operation and control strategy. In this paper, based upon the conservation laws of mass, energy, and momentum, a new differential-algebraic model for the OTSGs of the MHTGR-based multimodular nuclear plants is given. This newly-built model can describe the dynamic behavior of the OTSG in both the cases of providing superheated steam and generating saturated steam. Numerical simulation results show the feasibility and satisfactory performance of this model. Moreover, this model has been applied to develop the real-time simulation software for the operation and regulation features of the world first underconstructed MHTGR-based commercial nuclear plant—HTR-PM. Zhe Dong Copyright © 2015 Zhe Dong. All rights reserved. Computational Challenge of Fractional Differential Equations and the Potential Solutions: A Survey Thu, 26 Mar 2015 07:23:25 +0000 http://www.hindawi.com/journals/mpe/2015/258265/ We present a survey of fractional differential equations and in particular of the computational cost for their numerical solutions from the view of computer science. The computational complexities of time fractional, space fractional, and space-time fractional equations are O(N2M), O(NM2), and O(NM(M + N)) compared with O(MN) for the classical partial differential equations with finite difference methods, where M, N are the number of space grid points and time steps. The potential solutions for this challenge include, but are not limited to, parallel computing, memory access optimization (fractional precomputing operator), short memory principle, fast Fourier transform (FFT) based solutions, alternating direction implicit method, multigrid method, and preconditioner technology. The relationships of these solutions for both space fractional derivative and time fractional derivative are discussed. The authors pointed out that the technologies of parallel computing should be regarded as a basic method to overcome this challenge, and some attention should be paid to the fractional killer applications, high performance iteration methods, high order schemes, and Monte Carlo methods. Since the computation of fractional equations with high dimension and variable order is even heavier, the researchers from the area of mathematics and computer science have opportunity to invent cornerstones in the area of fractional calculus. Chunye Gong, Weimin Bao, Guojian Tang, Yuewen Jiang, and Jie Liu Copyright © 2015 Chunye Gong et al. All rights reserved. Approximated Fractional Order Chebyshev Lowpass Filters Thu, 26 Mar 2015 07:16:10 +0000 http://www.hindawi.com/journals/mpe/2015/832468/ We propose the use of nonlinear least squares optimization to approximate the passband ripple characteristics of traditional Chebyshev lowpass filters with fractional order steps in the stopband. MATLAB simulations of , , and order lowpass filters with fractional steps from  = 0.1 to  = 0.9 are given as examples. SPICE simulations of 1.2, 1.5, and 1.8 order lowpass filters using approximated fractional order capacitors in a Tow-Thomas biquad circuit validate the implementation of these filter circuits. Todd Freeborn, Brent Maundy, and Ahmed S. Elwakil Copyright © 2015 Todd Freeborn et al. All rights reserved. Asymptotic Analysis of the Curved-Pipe Flow with a Pressure-Dependent Viscosity Satisfying Barus Law Thu, 26 Mar 2015 07:10:55 +0000 http://www.hindawi.com/journals/mpe/2015/905406/ Curved-pipe flows have been the subject of many theoretical investigations due to their importance in various applications. The goal of this paper is to study the flow of incompressible fluid with a pressure-dependent viscosity through a curved pipe with an arbitrary central curve and constant circular cross section. The viscosity-pressure dependence is described by the well-known Barus law extensively used by the engineers. We introduce the small parameter (representing the ratio of the pipe’s thickness and its length) into the problem and perform asymptotic analysis with respect to . The main idea is to rewrite the governing problem using the appropriate transformation and then to compute the asymptotic solution using curvilinear coordinates and two-scale asymptotic expansion. Applying the inverse transformation, we derive the asymptotic approximation of the flow clearly showing the influence of pipe’s distortion and viscosity-pressure dependence on the effective flow. Igor Pažanin Copyright © 2015 Igor Pažanin. All rights reserved. Reproducing Kernel Particle Method for Radiative Heat Transfer in 1D Participating Media Thu, 26 Mar 2015 07:09:50 +0000 http://www.hindawi.com/journals/mpe/2015/181536/ The reproducing kernel particle method (RKPM), which is a Lagrangian meshless method, is employed for the calculation of radiative heat transfer in participating media. In the present method, for each discrete particle (i.e., spatial node) within a local support domain, the approximate formulas of the radiative intensity and its derivatives are constructed by the reproducing kernel interpolation function, and the residual function is obtained when these parameters are substituted into the radiative transfer equation. Then the least-squares point collocation technique (LSPCT) is introduced by minimizing the summation of residual function. Five test cases are considered and quantified to verify the meshless method, including isotropic scattering medium, first-order forward scattering medium, pure absorbing medium, absorbing scattering medium, and absorbing, scattering emitting medium. The results are in good agreement with the benchmark methods, showing the reproducing kernel particle method is an efficient, accurate, and stable method for the calculation of radiative transfer in participating media. Lei Mu, Zhi-hong He, and Shi-kui Dong Copyright © 2015 Lei Mu et al. All rights reserved. Face Recognition Using Double Sparse Local Fisher Discriminant Analysis Thu, 26 Mar 2015 06:32:32 +0000 http://www.hindawi.com/journals/mpe/2015/636928/ Local Fisher discriminant analysis (LFDA) was proposed for dealing with the multimodal problem. It not only combines the idea of locality preserving projections (LPP) for preserving the local structure of the high-dimensional data but also combines the idea of Fisher discriminant analysis (FDA) for obtaining the discriminant power. However, LFDA also suffers from the undersampled problem as well as many dimensionality reduction methods. Meanwhile, the projection matrix is not sparse. In this paper, we propose double sparse local Fisher discriminant analysis (DSLFDA) for face recognition. The proposed method firstly constructs a sparse and data-adaptive graph with nonnegative constraint. Then, DSLFDA reformulates the objective function as a regression-type optimization problem. The undersampled problem is avoided naturally and the sparse solution can be obtained by adding the regression-type problem to a penalty. Experiments on Yale, ORL, and CMU PIE face databases are implemented to demonstrate the effectiveness of the proposed method. Zhan Wang, Qiuqi Ruan, and Gaoyun An Copyright © 2015 Zhan Wang et al. All rights reserved. Decoupled Closed-Form Solution for Humanoid Lower Limb Kinematics Thu, 26 Mar 2015 06:28:03 +0000 http://www.hindawi.com/journals/mpe/2015/437979/ This paper presents an explicit, omnidirectional, analytical, and decoupled closed-form solution for the lower limb kinematics of the humanoid robot NAO. The paper starts by decoupling the position and orientation analysis from the overall Denavit-Hartenberg (DH) transformation matrices. Here, the joint activation sequence for the DH matrices is based on the geometry of a triangle. Furthermore, the implementation of a forward and a reversed kinematic analysis for the support and swing phase equations is developed to avoid matrix inversion. The allocation of constant transformations allows the position and orientation end-coordinate systems to be aligned with each other. Also, the redefinition of the DH transformations and the use of constraints allow decoupling the shared DOF between the legs and the torso. Finally, a geometric approach to avoid the singularities during the walking process is indicated. Numerical data is presented along with an experimental implementation to prove the validity of the analytical results. Alejandro Said, Ernesto Rodriguez-Leal, Rogelio Soto, J. L. Gordillo, and Leonardo Garrido Copyright © 2015 Alejandro Said et al. All rights reserved. On a Time-Fractional Integrodifferential Equation via Three-Point Boundary Value Conditions Thu, 26 Mar 2015 06:03:24 +0000 http://www.hindawi.com/journals/mpe/2015/785738/ The existence and the uniqueness theorems play a crucial role prior to finding the numerical solutions of the fractional differential equations describing the models corresponding to the real world applications. In this paper, we study the existence of solutions for a time-fractional integrodifferential equation via three-point boundary value conditions. Dumitru Baleanu, Shahram Rezapour, Sina Etemad, and Ahmed Alsaedi Copyright © 2015 Dumitru Baleanu et al. All rights reserved. Adaptive Sliding Control for a Class of Fractional Commensurate Order Chaotic Systems Thu, 26 Mar 2015 05:47:43 +0000 http://www.hindawi.com/journals/mpe/2015/972914/ This paper proposes adaptive sliding mode control design for a class of fractional commensurate order chaotic systems. We firstly introduce a fractional integral sliding manifold for the nominal systems. Secondly we prove the stability of the corresponding fractional sliding dynamics. Then, by introducing a Lyapunov candidate function and using the Mittag-Leffler stability theory we derive the desired sliding control law. Furthermore, we prove that the proposed sliding manifold is also adapted for the fractional systems in the presence of uncertainties and external disturbances. At last, we design a fractional adaptation law for the perturbed fractional systems. To verify the viability and efficiency of the proposed fractional controllers, numerical simulations of fractional Lorenz’s system and Chen’s system are presented. Jian Yuan, Bao Shi, and Zhentao Yu Copyright © 2015 Jian Yuan et al. All rights reserved. Hybrid Prediction and Fractal Hyperspectral Image Compression Wed, 25 Mar 2015 14:18:28 +0000 http://www.hindawi.com/journals/mpe/2015/950357/ The data size of hyperspectral image is too large for storage and transmission, and it has become a bottleneck restricting its applications. So it is necessary to study a high efficiency compression method for hyperspectral image. Prediction encoding is easy to realize and has been studied widely in the hyperspectral image compression field. Fractal coding has the advantages of high compression ratio, resolution independence, and a fast decoding speed, but its application in the hyperspectral image compression field is not popular. In this paper, we propose a novel algorithm for hyperspectral image compression based on hybrid prediction and fractal. Intraband prediction is implemented to the first band and all the remaining bands are encoded by modified fractal coding algorithm. The proposed algorithm can effectively exploit the spectral correlation in hyperspectral image, since each range block is approximated by the domain block in the adjacent band, which is of the same size as the range block. Experimental results indicate that the proposed algorithm provides very promising performance at low bitrate. Compared to other algorithms, the encoding complexity is lower, the decoding quality has a great enhancement, and the PSNR can be increased by about 5 dB to 10 dB. Shiping Zhu, Dongyu Zhao, and Fengchao Wang Copyright © 2015 Shiping Zhu et al. All rights reserved. Inversion Study of Vertical Eddy Viscosity Coefficient Based on an Internal Tidal Model with the Adjoint Method Wed, 25 Mar 2015 14:10:35 +0000 http://www.hindawi.com/journals/mpe/2015/915793/ Based on an isopycnic-coordinate internal tidal model with the adjoint method, the inversion of spatially varying vertical eddy viscosity coefficient (VEVC) is studied in two groups of numerical experiments. In Group One, the influences of independent point schemes (IPSs) exerting on parameter inversion are discussed. Results demonstrate that the VEVCs can be inverted successfully with IPSs and the model has the best performance with the optimal IPSs. Using the optimal IPSs obtained in Group One, the inversions of VEVCs on two different Gaussian bottom topographies are carried out in Group Two. In addition, performances of two optimization methods of which one is the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method and the other is a simplified gradient descent method (GDM-S) are also investigated. Results of the experiments indicate that this adjoint model is capable to invert the VEVC with spatially distribution, no matter which optimization method is taken. The L-BFGS method has a better performance in terms of the convergence rate and the inversion results. In general, the L-BFGS method is a more effective and efficient optimization method than the GDM-S. Guangzhen Jin, Qiang Liu, and Xianqing Lv Copyright © 2015 Guangzhen Jin et al. All rights reserved. An Enhanced Analytical Target Cascading and Kriging Model Combined Approach for Multidisciplinary Design Optimization Wed, 25 Mar 2015 14:05:36 +0000 http://www.hindawi.com/journals/mpe/2015/685958/ Multidisciplinary design optimization (MDO) has been applied widely in the design of complex engineering systems. To ease MDO problems, analytical target cascading (ATC) organizes MDO process into multilevels according to the components of engineering systems, which provides a promising way to deal with MDO problems. ATC adopts a coordination strategy to coordinate the couplings between two adjacent levels in the design optimization process; however, existing coordination strategies in ATC face the obstacles of complicated coordination process and heavy computation cost. In order to conquer this problem, a quadratic exterior penalty function (QEPF) based ATC (QEPF-ATC) approach is proposed, where QEPF is adopted as the coordination strategy. Moreover, approximate models are adopted widely to replace the expensive simulation models in MDO; a QEPF-ATC and Kriging model combined approach is further proposed to deal with MDO problems, owing to the comprehensive performance, high approximation accuracy, and robustness of Kriging model. Finally, the geometric programming and reducer design cases are given to validate the applicability and efficiency of the proposed approach. Ping Jiang, Jianzhuang Wang, Qi Zhou, and Xiaolin Zhang Copyright © 2015 Ping Jiang et al. All rights reserved. A Numerical Study of Natural Convection Heat Transfer in Fin Ribbed Radiator Wed, 25 Mar 2015 13:34:32 +0000 http://www.hindawi.com/journals/mpe/2015/989260/ This paper numerically investigates the thermal flow and heat transfer by natural convection in a cavity fixed with a fin array. The computational domain consists of both solid (copper) and fluid (air) areas. The finite volume method and the SIMPLE scheme are used to simulate the steady flow in the domain. Based on the numerical results, the energy gradient function of the energy gradient theory is calculated. It is observed from contours of the temperature and energy gradient function that the position where thermal instability takes place correlates well with the region of large values, which demonstrates that the energy gradient method reveals the physical mechanism of the flow instability. Furthermore, the effects of the fin height, the fin number, and the fin shape on the heat transfer rate are also investigated. It is found that the thermal performance of the fin array is determined by the combined effect of the fin space and fin height. It is also observed that the effect of fin shape on heat transfer is insignificant. Hua-Shu Dou, Gang Jiang, and Lite Zhang Copyright © 2015 Hua-Shu Dou et al. All rights reserved. A Directly Numerical Algorithm for a Backward Time-Fractional Diffusion Equation Based on the Finite Element Method Wed, 25 Mar 2015 13:25:10 +0000 http://www.hindawi.com/journals/mpe/2015/414727/ We study a backward problem for a time-fractional diffusion equation, which is formulated into a regularized optimization problem. After solving a sequence of well-posed direct problems by the finite element method, a directly numerical algorithm is proposed for solving the regularized optimization problem. In order to obtain a reasonable regularization solution, we utilize the discrepancy principle with decreasing geometric sequence to choose regularization parameters. One- and two-dimensional examples are given to verify the efficiency and stability of the proposed method. Zhousheng Ruan, Zewen Wang, and Wen Zhang Copyright © 2015 Zhousheng Ruan et al. All rights reserved. Vibration Analysis of Steel-Concrete Composite Box Beams considering Shear Lag and Slip Wed, 25 Mar 2015 13:17:41 +0000 http://www.hindawi.com/journals/mpe/2015/601757/ In order to investigate dynamic characteristics of steel-concrete composite box beams, a longitudinal warping function of beam section considering self-balancing of axial forces is established. On the basis of Hamilton principle, governing differential equations of vibration and displacement boundary conditions are deduced by taking into account coupled influencing of shear lag, interface slip, and shear deformation. The proposed method shows an improvement over previous calculations. The central difference method is applied to solve the differential equations to obtain dynamic responses of composite beams subjected to arbitrarily distributed loads. The results from the proposed method are found to be in good agreement with those from ANSYS through numerical studies. Its validity is thus verified and meaningful conclusions for engineering design can be drawn as follows. There are obvious shear lag effects in the top concrete slab and bottom plate of steel beams under dynamic excitation. This shear lag increases with the increasing degree of shear connections. However, it has little impact on the period and deflection amplitude of vibration of composite box beams. The amplitude of deflection and strains in concrete slab reduce as the degree of shear connections increases. Nevertheless, the influence of shear connections on the period of vibration is not distinct. Zhou Wangbao, Li Shu-jin, Jiang Lizhong, and Qin Shiqiang Copyright © 2015 Zhou Wangbao et al. All rights reserved. Limit Theorems for Local Cumulative Shock Models with Cluster Shock Structure Wed, 25 Mar 2015 12:43:59 +0000 http://www.hindawi.com/journals/mpe/2015/828979/ This paper considers a more general shock model with insurance and financial risk background, in which the system is subject to two types of shocks called primary shocks and secondary shocks. Each primary shock causes a series of secondary shocks according to some cluster pattern. In reliability applications, a primary shock can represent an issue of insurance policies of an insurer company, and the secondary shocks then denote the relevant insurance claims generated by the policy. We focus on the local cumulative shock process where only a certain number of the most recent primary and secondary shocks are accumulated. This process is a very new topic in the available literature which is more flexible and realistic in modeling some more complex reliability situations such as bankrupt behavior of an insurance company. Based on the theory of infinite divisibility and stable distributions, we establish a central limit theorem for the local cumulative shock process and obtain the conditions for the process to converge to an infinitely divisible distribution or to an -stable law. Also, by choosing the proper scale parameters, the process converges to a normal distribution. Jianming Bai, Yun Chen, Chun Yuan, and Xiaoling Yin Copyright © 2015 Jianming Bai et al. All rights reserved. Compressed Sensing MRI Reconstruction from Highly Undersampled -Space Data Using Nonsubsampled Shearlet Transform Sparsity Prior Wed, 25 Mar 2015 12:41:21 +0000 http://www.hindawi.com/journals/mpe/2015/615439/ Compressed sensing has shown great potential in speeding up MR imaging by undersampling -space data. Generally sparsity is used as a priori knowledge to improve the quality of reconstructed image. Compressed sensing MR image (CS-MRI) reconstruction methods have employed widely used sparsifying transforms such as wavelet or total variation, which are not preeminent in dealing with MR images containing distributed discontinuities and cannot provide a sufficient sparse representation and the decomposition at any direction. In this paper, we propose a novel CS-MRI reconstruction method from highly undersampled -space data using nonsubsampled shearlet transform (NSST) sparsity prior. In particular, we have implemented a flexible decomposition with an arbitrary even number of directional subbands at each level using NSST for MR images. The highly directional sensitivity of NSST and its optimal approximation properties lead to improvement in CS-MRI reconstruction applications. The experimental results demonstrate that the proposed method results in the high quality reconstruction, which is highly effective at preserving the intrinsic anisotropic features of MRI meanwhile suppressing the artifacts and added noise. The objective evaluation indices outperform all compared CS-MRI methods. In summary, NSST with even number directional decomposition is very competitive in CS-MRI applications as sparsity prior in terms of performance and computational efficiency. Min Yuan, Bingxin Yang, Yide Ma, Jiuwen Zhang, Runpu Zhang, and Caiyuan Zhang Copyright © 2015 Min Yuan et al. All rights reserved. A Novel High Efficiency Fractal Multiview Video Codec Wed, 25 Mar 2015 12:28:33 +0000 http://www.hindawi.com/journals/mpe/2015/613714/ Multiview video which is one of the main types of three-dimensional (3D) video signals, captured by a set of video cameras from various viewpoints, has attracted much interest recently. Data compression for multiview video has become a major issue. In this paper, a novel high efficiency fractal multiview video codec is proposed. Firstly, intraframe algorithm based on the H.264/AVC intraprediction modes and combining fractal and motion compensation (CFMC) algorithm in which range blocks are predicted by domain blocks in the previously decoded frame using translational motion with gray value transformation is proposed for compressing the anchor viewpoint video. Then temporal-spatial prediction structure and fast disparity estimation algorithm exploiting parallax distribution constraints are designed to compress the multiview video data. The proposed fractal multiview video codec can exploit temporal and spatial correlations adequately. Experimental results show that it can obtain about 0.36 dB increase in the decoding quality and 36.21% decrease in encoding bitrate compared with JMVC8.5, and the encoding time is saved by 95.71%. The rate-distortion comparisons with other multiview video coding methods also demonstrate the superiority of the proposed scheme. Shiping Zhu, Dongyu Zhao, and Ling Zhang Copyright © 2015 Shiping Zhu et al. All rights reserved. Optimal Day-Time Charging Strategies for Electric Vehicles considering Photovoltaic Power System and Distribution Grid Constraints Wed, 25 Mar 2015 12:19:58 +0000 http://www.hindawi.com/journals/mpe/2015/765362/ Electric vehicles (EVs) charging stations with a photovoltaic (PV) system for day-time charging have been studied. This paper investigates the issues such as how to coordinate the EVs customers for coordinated charging, maximize photovoltaic utilization, and reduce customers cost of EVs charging and operator electricity. Firstly, an ideal charging load curve was built through using the linear programming algorithm. This optimal curve, which realized maximum photovoltaic power and minimum electricity cost, was used as the objective curve. Secondly, a customer response model was utilized, to propose an optimization method and strategy for charging service tariffs. Particle swarm optimization algorithm was used for time-of-use tariffs and peak-flat-valley time division so that the charging load after price regulation was adjusted to best fit the objective curve, and both the EVs customers and the operator benefit from this. Finally, the proposed model and method have been verified by two cases. Weige Zhang, Wenjie Ge, Mei Huang, and Jiuchun Jiang Copyright © 2015 Weige Zhang et al. All rights reserved.