http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Fri, 24 May 2013 15:36:47 +0000 http://www.hindawi.com/journals/mpe/2013/906785/ The researchs on the structure and formation mechanism of social networks lead to several models with differences in the attachment patterns of new links (edges). In fact, the driving factor behind the addition of new links is just as important as the attachment patterns, while very little attention has been devoted so far to this exploration. We present an agent-based model which could successfully reproduce large-scale social networks. We find that the structure of social networks is a consequence of continuous individuals’ decision-making processes based on self-evaluations and the turnover of the population. The individuals’ self-evaluation processes are key motivating factors for the addition of new links, while the attachment patterns and the turnover of the population should be responsible for the topology of social networks. The resulting networks of our model display dynamics between order and randomness, which is greatly consistent with current observations and research achievements of social networks. We also find that some plausible properties of empirical data are actually artifacts due to the boundedness of sampling. Our research has revealed the driving factors behind the evolution of social networks as well as the underlying evolving patterns. These findings will lead to a better understanding of social structures. Zhijing Xu, Zhenghu Zu, Tao Zheng, Wendou Zhang, and Qing Xu Copyright © 2013 Zhijing Xu et al. All rights reserved. Fri, 24 May 2013 15:26:05 +0000 http://www.hindawi.com/journals/mpe/2013/950675/ A practical and reliable capability for autonomous navigation needs to reduce operation cost, to improve operational efficiency, and to increase mission safety. Celestial navigation is a very attractive autonomous navigation solution for deep space spacecraft. There are mainly two kinds of celestial navigation methods: the direct calculation method and the filter method. The accuracy of the direct calculation method is low and very sensitive to the measurement noise. The filter method can provide a better navigation performance if a high accuracy dynamical model is available. However, the main practical problem existing in the autonomous celestial navigation of spacecraft on a gravity assist trajectory is that the accuracy of trajectory model is not enough to be used in the real navigation sometimes, which may introduce large estimation error and even cause filter divergence. To solve this problem, a new celestial navigation method is proposed in this paper, which effectively combines the direct calculation method and the filter method using an interacting multiple model unscented Kalman filter (IMMUKF). The ground experimental results demonstrate that this method can provide better navigation performance and higher reliability than the traditional direct calculation method and filter method. Ning Xiaolin, Huang Panpan, and Fang Jiancheng Copyright © 2013 Ning Xiaolin et al. All rights reserved. Fri, 24 May 2013 15:25:05 +0000 http://www.hindawi.com/journals/mpe/2013/835308/ We introduce some important properties of fuzzy soft topological spaces. Furthermore, fuzzy soft continuous mapping, fuzzy soft open and fuzzy soft closed mappings, and fuzzy soft homeomorphism for fuzzy soft topological spaces are given and structural characteristics are discussed and studied. Cigdem Gunduz (Aras) and Sadi Bayramov Copyright © 2013 Cigdem Gunduz (Aras) and Sadi Bayramov. All rights reserved. Fri, 24 May 2013 15:24:24 +0000 http://www.hindawi.com/journals/mpe/2013/783105/ The role of container logistics centre as home bases for merchandise transportation has become increasingly important. The container carriers need to select a suitable centre location of transshipment port to meet the requirements of container shipping logistics. In the light of this, the main purpose of this paper is to develop a fuzzy multi-criteria decision-making (MCDM) model to evaluate the best selection of transshipment ports for container carriers. At first, some concepts and methods used to develop the proposed model are briefly introduced. The performance values of quantitative and qualitative subcriteria are discussed to evaluate the fuzzy ratings. Then, the ideal and anti-ideal concepts and the modified distance measure method are used in the proposed model. Finally, a step-by-step example is illustrated to study the computational process of the quantitative and qualitative fuzzy MCDM model. The proposed approach has successfully accomplished our goal. In addition, the proposed fuzzy MCDM model can be empirically employed to select the best location of transshipment port for container carriers in the future study. Ji-Feng Ding and Chien-Chang Chou Copyright © 2013 Ji-Feng Ding and Chien-Chang Chou. All rights reserved. Thu, 23 May 2013 16:11:34 +0000 http://www.hindawi.com/journals/mpe/2013/401538/ This paper investigates -moment stability of the stochastic differential delay systems with impulsive jump and Markovian switching. Some stability criteria are obtained based on Lyapunov functional method and stochastic theory. It is shown that, even if all the subsystems governing the continuous dynamics without impulse are not stable, as impulsive and switching signal satisfies a dwell-time upper bound condition, impulses can stabilize the systems in the -moment stability sense. The opposite situation is also developed for which all the subsystems governing the continuous dynamics are -moment stable. The results can be easily applied to stochastic systems with arbitrarily large delays. The efficiency of the proposed results is illustrated by two numerical examples. Lijun Gao Copyright © 2013 Lijun Gao. All rights reserved. Thu, 23 May 2013 15:11:15 +0000 http://www.hindawi.com/journals/mpe/2013/683137/ This paper is devoted to the stability and convergence analysis of the two-step Runge-Kutta (TSRK) methods with the Lagrange interpolation of the numerical solution for nonlinear neutral delay differential equations. Nonlinear stability and D-convergence are introduced and proved. We discuss the -stability, -stability, and the weak -stability on the basis of -algebraically stable of the TSRK methods; we also discuss the D-convergence properties of TSRK methods with a restricted type of interpolation procedure. Haiyan Yuan, Cheng Song, and Peichen Wang Copyright © 2013 Haiyan Yuan et al. All rights reserved. Thu, 23 May 2013 13:39:04 +0000 http://www.hindawi.com/journals/mpe/2013/738013/ In practical geotechnical engineering, most of rock masses with multiple cracks exist in water environment. Under such circumstance, these adjacent cracks could interact with each other. Moreover, the seepage pressure, produced by the high water pressure, can change cracks’ status and have an impact on the stress state of fragile rocks. According to the theory of fracture mechanics, this paper discusses the law of crack initiation and the evolution law of stress intensity factor at the tip of a wing crack caused by compression-shear stress and seepage pressure. Subsequently, considering the interaction of the wing cracks and the additional stress caused by rock bridge damage, this paper proposes the intensity factor evolution equation under the combined action of compression-shear stress and seepage pressure. In addition, this paper analyzes the propagation of cracks under different seepage pressure which reveals that the existence of seepage pressure facilitates the wing crack’s growth. The result indicates that the high seepage pressure converts wing crack growth from stable form to unstable form. Meanwhile, based on the criterion and mechanism for crack initiation and propagation, this paper puts forward the mechanical model for different fracture transfixion failure modes of the crag bridge under the combined action of seepage pressure and compression-shear stress. At the last part, this paper, through investigating the flexibility tensor of the rock mass’s initial damage and its damage evolution in terms of jointed rock mass's damage mechanics, deduces the damage evolution equation for the rock mass with multiple cracks under the combined action of compression-shear stress and seepage pressure. The achievement of this investigation provides a reliable theoretical principle for quantitative research of the fractured rock mass failure under seepage pressure. Taoying Liu, Ping Cao, and Hang Lin Copyright © 2013 Taoying Liu et al. All rights reserved. Thu, 23 May 2013 13:12:49 +0000 http://www.hindawi.com/journals/mpe/2013/528162/ We develop a path-planning algorithm to guide autonomous amphibious vehicles (AAVs) for flood rescue support missions. Specifically, we develop an algorithm to control multiple AAVs to reach/rescue multiple victims (also called targets) in a flood scenario in 2D, where the flood water flows across the scene and the targets move (drifted by the flood water) along the flood stream. A target is said to be rescued if an AAV lies within a circular region of a certain radius around the target. The goal is to control the AAVs such that each target gets rescued while optimizing a certain performance objective. The algorithm design is based on the theory of partially observable Markov decision process (POMDP). In practice, POMDP problems are hard to solve exactly, so we use an approximation method called nominal belief-state optimization (NBO). We compare the performance of the NBO approach with a greedy approach. Shankarachary Ragi, ChingSeong Tan, and Edwin K. P. Chong Copyright © 2013 Shankarachary Ragi et al. All rights reserved. Thu, 23 May 2013 11:56:47 +0000 http://www.hindawi.com/journals/mpe/2013/452735/ This study reviews the impact of public transit network layout (TNL) on resident mode choice. The review of TNL as a factor uses variables divided into three groups: a variable set without considering the TNL, one considering TNL from the zone level, and one considering TNL from the individual level. Using Baoding’s travel survey data, a Multinomial Logit (MNL) model is used, and the parameter estimation result shows that TNL has significant effect on resident mode choice. Based on parameter estimation, the factors affecting mode choice are further screened. The screened variable set is regarded as the input data to the BP neural network’s training and forecasting. Both forecasting results indicate that introducing TNL can improve the performance of mode choice forecasting. Jian Gao, Peng Zhao, Chengxiang Zhuge, Hui Zhang, and Edward D. McCormack Copyright © 2013 Jian Gao et al. All rights reserved. Wed, 22 May 2013 16:31:36 +0000 http://www.hindawi.com/journals/mpe/2013/384251/ The coupled nonlinear dynamical equations were developed for a tilted spring packaging system with critical components. The approximate solution and resonance conditions of system were obtained applying a variational iteration method. The resonance conditions, which should be avoided in the packaging design, can be easily obtained by VIM. An-Jun Chen Copyright © 2013 An-Jun Chen. All rights reserved. Wed, 22 May 2013 15:27:26 +0000 http://www.hindawi.com/journals/mpe/2013/635392/ The nonlinear differential equations modeling flow of a reactive third-grade liquid between two parallel isothermal plates is investigated using a novel hybrid of numerical-analytical scheme known as the successive linearization method (SLM). Numerical and graphical results obtained show excellence in agreement with the earlier results reported in the literature. A comparison with numerical results generated using the inbuilt MATLAB boundary value solver bvp4c demonstrates that the new SLM approach is a very efficient technique for tackling highly nonlinear differential equations of the type discussed in this paper. S. S. Motsa, O. D. Makinde, and S. Shateyi Copyright © 2013 S. S. Motsa et al. All rights reserved. Wed, 22 May 2013 15:16:28 +0000 http://www.hindawi.com/journals/mpe/2013/248153/ This paper investigates the antiwindup (AW) control problem for plants with input saturation. The AW compensator is not activated as soon as input saturation occurs as usual. A delayed decoupling structure is first proposed. Then, appropriate linear matrix inequalities (LMIs) are developed to determine a plant-order AW compensator. Effectiveness of the presented AW technique is illustrated by a fighter aircraft model. Huawei Zhu, Guozheng Qin, Yingxin Yan, Zhichao Jiang, and Zhisheng Duan Copyright © 2013 Huawei Zhu et al. All rights reserved. Wed, 22 May 2013 15:03:05 +0000 http://www.hindawi.com/journals/mpe/2013/867079/ This study deals with a mixed static and dynamic optimization of four-parameter functionally graded material (FGM) doubly curved shells and panels. The two constituent functionally graded shell consists of ceramic and metal, and the volume fraction profile of each lamina varies through the thickness of the shell according to a generalized power-law distribution. The Generalized Differential Quadrature (GDQ) method is applied to determine the static and dynamic responses for various FGM shell and panel structures. The mechanical model is based on the so-called First-order Shear Deformation Theory (FSDT). Three different optimization schemes and methodologies are implemented. The Particle Swarm Optimization, Monte Carlo and Genetic Algorithm approaches have been applied to define the optimum volume fraction profile for optimizing the first natural frequency and the maximum static deflection of the considered shell structure. The optimization aim is in fact to reach the frequency and the static deflection targets defined by the designer of the structure: the complete four-dimensional search space is considered for the optimization process. The optimized material profile obtained with the three methodologies is presented as a result of the optimization problem solved for each shell or panel structure. Francesco Tornabene and Alessandro Ceruti Copyright © 2013 Francesco Tornabene and Alessandro Ceruti. All rights reserved. Wed, 22 May 2013 14:54:56 +0000 http://www.hindawi.com/journals/mpe/2013/848120/ Missing-data problems are extremely common in practice. To achieve reliable inferential results, we need to take into account this feature of the data. Suppose that the univariate data set under analysis has missing observations. This paper examines the impact of selecting an auxiliary complete data set—whose underlying stochastic process is to some extent interdependent with the former—to improve the efficiency of the estimators for the relevant parameters of the model. The Vector AutoRegressive (VAR) Model has revealed to be an extremely useful tool in capturing the dynamics of bivariate time series. We propose maximum likelihood estimators for the parameters of the VAR(1) Model based on monotone missing data pattern. Estimators’ precision is also derived. Afterwards, we compare the bivariate modelling scheme with its univariate counterpart. More precisely, the univariate data set with missing observations will be modelled by an AutoRegressive Moving Average (ARMA(2,1)) Model. We will also analyse the behaviour of the AutoRegressive Model of order one, AR(1), due to its practical importance. We focus on the mean value of the main stochastic process. By simulation studies, we conclude that the estimator based on the VAR(1) Model is preferable to those derived from the univariate context. Helena Mouriño and Maria Isabel Barão Copyright © 2013 Helena Mouriño and Maria Isabel Barão. All rights reserved. Wed, 22 May 2013 14:49:09 +0000 http://www.hindawi.com/journals/mpe/2013/605409/ When denoising with the method of Weickert’s anisotropic diffusion equation, the textures and details will be compromised. A fidelity term is added to Weickert’s equation, and the coefficient of fidelity term will vary adaptively with the instant image, which makes the diffusion term and the fidelity term come to a better compromise. Otherwise, when deciding the edge directions, because of the strong smoothness of linear Gaussian function, a few other edge directions hiding in the main direction will be lost. To preserve these detailed edge directions, Gaussian kernel is substituted for nonlinear wavelet threshold. In addition, in order to preserve the textures and details as much as possible, a nonlocal diffusion tensor was introduced, and the two eigenvalues are reset by combining the two methods: edge-enhancing diffusion and coherence-enhancing diffusion. Experiments show that the new model has an obvious effect on preserving textures and details. Xiaoli Sun, Chen Xu, and Min Li Copyright © 2013 Xiaoli Sun et al. All rights reserved. Wed, 22 May 2013 14:17:19 +0000 http://www.hindawi.com/journals/mpe/2013/808565/ An integrated modeling system has been developed for analyzing the impact of climate change on snowmelt runoff in Kaidu Watershed, Northwest China. The system couples Hadley Centre Coupled Model version 3 (HadCM3) outputs with Snowmelt Runoff Model (SRM). The SRM was verified against observed discharge for outlet hydrological station of the watershed during the period from April to September in 2001 and generally performed well for Nash-Sutcliffe coefficient (EF) and water balance coefficient (RE). The EF is approximately over 0.8, and the water balance error is lower than ± 10%, indicating reasonable prediction accuracy. The Statistical Downscaling Model (SDSM) was used to downscale coarse outputs of HadCM3, and then the downscaled future climate data were used as inputs of the SRM. Four scenarios were considered for analyzing the climate change impact on snowmelt flow in the Kaidu Watershed. And the results indicated that watershed hydrology would alter under different climate change scenarios. The stream flow in spring is likely to increase with the increased mean temperature; the discharge and peck flow in summer decrease with the decreased precipitation under Scenarios 1 and 2. Moreover, the consideration of the change in cryosphere area would intensify the variability of stream flow under Scenarios 3 and 4. The modeling results provide useful decision support for water resources management. Yonggang Ma, Yue Huang, Xi Chen, Yongping Li, and Anming Bao Copyright © 2013 Yonggang Ma et al. All rights reserved. Wed, 22 May 2013 14:08:03 +0000 http://www.hindawi.com/journals/mpe/2013/379690/ Assessment of credit risk is of great importance in financial risk management. In this paper, we propose an improved attribute bagging method, weight-selected attribute bagging (WSAB), to evaluate credit risk. Weights of attributes are first computed using attribute evaluation method such as linear support vector machine (LSVM) and principal component analysis (PCA). Subsets of attributes are then constructed according to weights of attributes. For each of attribute subsets, the larger the weights of the attributes the larger the probabilities by which they are selected into the attribute subset. Next, training samples and test samples are projected onto each attribute subset, respectively. A scoring model is then constructed based on each set of newly produced training samples. Finally, all scoring models are used to vote for test instances. An individual model that only uses selected attributes will be more accurate because of elimination of some of redundant and uninformative attributes. Besides, the way of selecting attributes by probability can also guarantee the diversity of scoring models. Experimental results based on two credit benchmark databases show that the proposed method, WSAB, is outstanding in both prediction accuracy and stability, as compared to analogous methods. Jianwu Li, Haizhou Wei, and Wangli Hao Copyright © 2013 Jianwu Li et al. All rights reserved. Wed, 22 May 2013 10:08:09 +0000 http://www.hindawi.com/journals/mpe/2013/613082/ We derive two- and three-dimensional analytical particular solutions of multiquadrics (MQ) associated with the polyharmonic operators, named as the polyharmonic multiquadrics (PMQs). The methods of undetermined coefficients are constructed by observing the first few orders of the PMQs which are obtained by the symbolic software, Mathematica. By expanding the PMQs into the Laurent series, the unknown coefficients of the PMQs can be determined. The homogeneous parts of the PMQs are suitably arranged so that the PMQs are hierarchically unique and infinitely differentiable. Mathematica codes are provided for obtaining the PMQs of arbitrary orders. The derived PMQs are validated by numerical solutions for Poisson’s equation. Numerical results indicate that the solutions obtained by the PMQs are more accurate than those by the MQ. Chia-Cheng Tsai Copyright © 2013 Chia-Cheng Tsai. All rights reserved. Tue, 21 May 2013 13:18:55 +0000 http://www.hindawi.com/journals/mpe/2013/972174/ Recently, a closed-form approximated expression was derived by the same author for the achievable residual intersymbol interference (ISI) case that depends on the step-size parameter, equalizer’s tap length, input signal statistics, signal-to-noise ratio (SNR), and channel power. But this expression was obtained by assuming that the input noise is a white Gaussian process where the Hurst exponent (H) is equal to 0.5. In this paper, we derive a closed-form approximated expression (or an upper limit) for the residual ISI obtained by blind adaptive equalizers valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of . Up to now, the statistical behaviour of the residual ISI was not investigated. Furthermore, the convolutional noise for the latter stages of the deconvolutional process was assumed to be a white Gaussian process (). In this paper, we show that the Hurst exponent of the residual ISI is close to one, almost independent of the SNR or equalizer’s tap length but depends on the step-size parameter. In addition, the convolutional noise obtained in the steady state is a noise process having a Hurst exponent depending on the step-size parameter. Monika Pinchas Copyright © 2013 Monika Pinchas. All rights reserved. Tue, 21 May 2013 11:54:10 +0000 http://www.hindawi.com/journals/mpe/2013/273052/ Explicit analytical expressions for the temperature profile, fin efficiency, and heat flux in a longitudinal fin are derived. Here, thermal conductivity and heat transfer coefficient depend on the temperature. The differential transform method (DTM) is employed to construct the analytical (series) solutions. Thermal conductivity is considered to be given by the power law in one case and by the linear function of temperature in the other, whereas heat transfer coefficient is only given by the power law. The analytical solutions constructed by the DTM agree very well with the exact solutions even when both the thermal conductivity and the heat transfer coefficient are given by the power law. The analytical solutions are obtained for the problems which cannot be solved exactly. The effects of some physical parameters such as the thermogeometric fin parameter and thermal conductivity gradient on temperature distribution are illustrated and explained. Partner L. Ndlovu and Raseelo J. Moitsheki Copyright © 2013 Partner L. Ndlovu and Raseelo J. Moitsheki. All rights reserved. Tue, 21 May 2013 11:50:22 +0000 http://www.hindawi.com/journals/mpe/2013/312585/ Today developed and developing countries have to admit the fact that global warming is affecting the earth, but the fundamental problem of how to divide up necessary greenhouse gas reductions between developed and developing countries remains. In this paper, we propose cooperative and noncooperative stochastic differential game models to describe greenhouse gas emissions decision makings of developed and developing countries, calculate their feedback Nash equilibrium and the Pareto optimal solution, characterize parameter spaces that developed and developing countries can cooperate, design cooperative conditions under which participants buy the cooperative payoff, and distribute the cooperative payoff with Nash bargaining solution. Lastly, numerical simulations are employed to illustrate the above results. Wei Yu and Baogui Xin Copyright © 2013 Wei Yu and Baogui Xin. All rights reserved. Tue, 21 May 2013 11:25:03 +0000 http://www.hindawi.com/journals/mpe/2013/642101/ Heavy metals are widely recognized as being hazardous to human health and environmentally aggressive. The literature reports different approaches for lead removal, for example, water hyacinths. Heavy metal sorption isotherm modeling represents an important tool towards the study of equilibrium conditions. Fractional calculus represents a novel approach and a growing research field for process modeling, based on derivatives of arbitrary order. Recently, a novel isotherm based on fractional calculus was proposed for lead sorption using water hyacinth (Eichhornia crassipes). This paper reports a general procedure on error analysis and its influence on parameter estimation. It was applied to mathematical models based on fractional differential equations, focusing on a heavy metal novel isotherm sorption model. Parameter variance was calculated by using two different approaches (with the complete Hessian matrix and with a simplified Hessian matrix), and joint parameter confidence regions were generated, being successfully able to show that the fractional nature of the model is statistically valid. Enrico M. Gomes, Rosana R. L. Araújo, Marcelo K. Lenzi, Fernanda R. G. B. Silva, and Ervin K. Lenzi Copyright © 2013 Enrico M. Gomes et al. All rights reserved. Mon, 20 May 2013 18:48:42 +0000 http://www.hindawi.com/journals/mpe/2013/367105/ We propose a scene classification method for speeding up the multisensor remote sensing image fusion by using the singular value decomposition of quaternion matrix and the kernel principal component analysis (KPCA) to extract features. At first, images are segmented to patches by a regular grid, and for each patch, we extract color features by using quaternion singular value decomposition (QSVD) method, and the grey features are extracted by Gabor filter and then by using orientation histogram to describe the grey information. After that, we combine the color features and the orientation histogram together with the same weight to obtain the descriptor for each patch. All the patch descriptors are clustered to get visual words for each category. Then we apply KPCA to the visual words to get the subspaces of the category. The descriptors of a test image then are projected to the subspaces of all categories to get the projection length to all categories for the test image. Finally, support vector machine (SVM) with linear kernel function is used to get the scene classification performance. We experiment with three classification situations on OT8 dataset and compare our method with the typical scene classification method, probabilistic latent semantic analysis (pLSA), and the results confirm the feasibility of our method. Ji Li and Zhen Liu Copyright © 2013 Ji Li and Zhen Liu. All rights reserved. Mon, 20 May 2013 18:39:30 +0000 http://www.hindawi.com/journals/mpe/2013/713560/ A fault detection approach based on nonlinear robust observer is designed for the networked suspension control system of Maglev train with random induced time delay. First, considering random bounded time-delay and external disturbance, the nonlinear model of the networked suspension control system is established. Then, a nonlinear robust observer is designed using the input of the suspension gap. And the estimate error is proved to be bounded with arbitrary precision by adopting an appropriate parameter. When sensor faults happen, the residual between the real states and the observer outputs indicates which kind of sensor failures occurs. Finally, simulation results using the actual parameters of CMS-04 maglev train indicate that the proposed method is effective for maglev train. Yun Li, Guang He, and Jie Li Copyright © 2013 Yun Li et al. All rights reserved. Mon, 20 May 2013 18:38:31 +0000 http://www.hindawi.com/journals/mpe/2013/424108/ One of the known methods for solving the problems with exponential time complexity such as NP-complete problems is using the brute force algorithms. Recently, a new parallel computational framework called Membrane Computing is introduced which can be applied in brute force algorithms. The usual way to find a solution for the problems with exponential time complexity with Membrane Computing techniques is by P System with active membrane using division rule. It makes an exponential workspace and solves the problems with exponential complexity in a polynomial (even linear) time. On the other hand, searching is currently one of the most used methods for finding solution for problems in real life, that the blind search algorithms are accurate, but their time complexity is exponential such as breadth-first search (BFS) algorithm. In this paper, we proposed a new approach for implementation of BFS by using P system with division rule technique for first time. The theorem shows time complexity of BSF in this framework on randomly binary trees reduced from to . Einallah Salehi, Siti Mariyam Shamsuddin, and Kourosh Nemati Copyright © 2013 Einallah Salehi et al. All rights reserved. Mon, 20 May 2013 17:01:37 +0000 http://www.hindawi.com/journals/mpe/2013/836058/ Magnetically suspended flywheel (MSFW) with gimballing capability fulfills requirements of precision and maneuvers for space applications. A novel reluctance force-type hybrid magnetic bearing (RFHMB) is presented based on analysis of demerits of Lorentz force-type magnetic bearing and common RFHMB. It features that radial and axial magnetic bearing units are integrated into a compact assembly with four separate biased permanent magnets and two conical stators; four radial poles with shoes and rotor made of iron-based amorphousness can reduce eddy loss. Equivalent magnetic circuits of permanent magnets and their control currents are presented. Simulation results indicate flux density fluctuates from 0.272 T to 0.41 T; rotor tilting does not affect the suspension force when rotor only tilts around -axis or -axis. When rotor drifts in , , or direction and tilts around -axis or -axis simultaneously, force in corresponding directions slightly increases with tilting angle’s enlargement, but the maximum change does not exceed 14%. Additional tilting torque mainly determined by uniformity of flux density in conical air gaps is 0.05 Nm which is far smaller than 11 Nm in common RFHMB; magnetic suspension force is effectively decoupled among , , and directions; results prove that MSFW with gimballing capability theoretically meets maneuvering requirement of spacecraft. Chun'e Wang and Jiqiang Tang Copyright © 2013 Chun'e Wang and Jiqiang Tang. All rights reserved. Mon, 20 May 2013 14:44:41 +0000 http://www.hindawi.com/journals/mpe/2013/530932/ Numerical solutions of the linear differential boundary issues are obtained by using a local polynomial estimator method with kernel smoothing. To achieve this, a combination of a local polynomial-based method and its differential form has been used. The computed results with the use of this technique have been compared with the exact solution and other existing methods to show the required accuracy of it. The effectiveness of this method is verified by three illustrative examples. The presented method is seen to be a very reliable alternative method to some existing techniques for such realistic problems. Numerical results show that the solution of this method is more accurate than that of other methods. Liyun Su, Tianshun Yan, Yanyong Zhao, and Fenglan Li Copyright © 2013 Liyun Su et al. All rights reserved. Mon, 20 May 2013 14:43:38 +0000 http://www.hindawi.com/journals/mpe/2013/745637/ The Multiple Encounters Problem is described in the literature as the problem of finding trajectories for a spacecraft that leaves from a mother planet, describes a trajectory in the interplanetary space, and then goes back to the mother planet. The present paper extends the literature and the departure and arrival angles of the spacecraft are generalized to be nonsymmetrical. The solutions are shown in terms of the true () and eccentric anomaly (). The velocity variation () required for the transfer is also shown. Then, this study is generalized to consider the possibility that the spacecraft makes a close approach with the mother planet to change its energy in the return trip. The velocity () and energy variation () due to this passage are obtained. The topics studied here can be applied in missions that leave and come back to the Earth, with the goal of studying the interplanetary space, as well as for missions whose objective is to make an alteration in the energy of the space vehicle through a swing-by with the mother body. Denilson Paulo Souza dos Santos, Antônio Fernando Bertachini de Almeida Prado, and Evandro Marconi Rocco Copyright © 2013 Denilson Paulo Souza dos Santos et al. All rights reserved. Mon, 20 May 2013 14:12:57 +0000 http://www.hindawi.com/journals/mpe/2013/498385/ This paper presents an approach to bearing fault diagnosis based on the Teager energy operator (TEO) and Elman neural network. The TEO can estimate the total mechanical energy required to generate signals, thereby resulting in good time resolution and self-adaptability to transient signals. These attributes reflect the advantage of detecting signal impact characteristics. To detect the impact characteristics of the vibration signals of bearing faults, we used the TEO to extract the cyclical impact caused by bearing failure and applied the wavelet packet to reduce the noise of the Teager energy signal. This approach also enabled the extraction of bearing fault feature frequencies, which were identified using the fast Fourier transform of Teager energy. The feature frequencies of the inner and outer faults, as well as the ratio of resonance frequency band energy to total energy in the Teager spectrum, were extracted as feature vectors. In order to avoid a frequency leak error, the weighted Teager spectrum around the fault frequency was extracted as feature vector. These vectors were then used to train the Elman neural network and improve the robustness of the diagnostic algorithm. Experimental results indicate that the proposed approach effectively detects bearing faults under variable conditions. Hongmei Liu, Jing Wang, and Chen Lu Copyright © 2013 Hongmei Liu et al. All rights reserved. Mon, 20 May 2013 13:28:22 +0000 http://www.hindawi.com/journals/mpe/2013/803462/ We develop the Fuzzy Improved Runge-Kutta Nystrom (FIRKN) method for solving second-order fuzzy differential equations (FDEs) based on the generalized concept of higher-order fuzzy differentiability. The scheme is two-step in nature and requires less number of stages which leads to less number of function evaluations in comparison with the existing Fuzzy Runge-Kutta Nystrom method. Therefore, the new method has a lower computational cost which effects the time consumption. We assume that the fuzzy function and its derivative are Hukuhara differentiable. FIRKN methods of orders three, four, and five are derived with two, three, and four stages, respectively. The numerical examples are given to illustrate the efficiency of the methods. Faranak Rabiei, Fudziah Ismail, Ali Ahmadian, and Soheil Salahshour Copyright © 2013 Faranak Rabiei et al. All rights reserved.