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  • 1
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    Modified Predictor-Corrector WAF Method for the Shallow Water Equations with Source Terms (2011)
    Hindawi
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    Publication Date: 2011-06-13
    Description: A modified predictor-corrector scheme combining with the depth gradient method (DGM) and the weighted average flux (WAF) method has been presented to solve the one-dimensional shallow water equations with source terms. Approximate solutions in the predictor step are obtained by the DGM with piecewise-linear reconstructions in each cell volume. The source terms can then be calculated directly by these predicted values at the corresponding half-time step. In the corrector step, the TVD version of the WAF method is applied to calculate the numerical fluxes at the same half-time step for each cell face. The accuracy of numerical solutions is shown by applying the method to solve various test cases in both steady and unsteady problems with and without source terms. It shows that the numerical results are in good agreement with the existing analytical solutions as well as experimental data in some test cases.
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  • 2
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    Finite Element Analysis with Iterated Multiscale Analysis for Mechanical Parameters of Composite Materials with Multiscale Random Grains (2011)
    Hindawi
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    Publication Date: 2011-06-15
    Description: Based on the iterated statistically multiscale analysis (SMSA), we present the convergence of the equivalent mechanical parameters (effective moduli), obtain the error result, and prove the symmetric, positive and definite property of the equivalent mechanical parameters tensor computed by the finite element method. The numerical results show the proved results and illustrate that the SMSA-FE algorithm is a rational method for predicting the equivalent mechanical parameters of the composite material with multiscale random grains. In conclusion, we discuss the future work for the inhomogeneous composite material with multiscale random grains.
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  • 3
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    Totally Umbilical Proper Slant and Hemislant Submanifolds of an LP-Cosymplectic Manifold (2011)
    Hindawi
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    Publication Date: 2011-06-15
    Description: In the present note, we study slant and hemislant submanifolds of an LP-cosymplectic manifold which are totally umbilical. We prove that every totally umbilical proper slant submanifold M of an LP-cosymplectic manifold M¯ is either totally geodesic or if M is not totally geodesic in M¯ then we derive a formula for slant angle of M. Also, we obtain the integrability conditions of the distributions of a hemi-slant submanifold, and then we give a result on its classification.
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  • 4
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    Weingarten and Linear Weingarten Type Tubular Surfaces in E3 (2011)
    Hindawi
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    Publication Date: 2011-06-24
    Description: We study tubular surfaces in Euclidean 3-space satisfying some equations in terms of the Gaussian curvature, the mean curvature, the second Gaussian curvature, and the second mean curvature. This paper is a completion of Weingarten and linear Weingarten tubular surfaces in Euclidean 3-space.
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  • 5
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    Analyzing “Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problem” (2011)
    Hindawi
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    Publication Date: 2011-06-17
    Description: We analyze a previous paper by S. T. Mohyud-Din and M. A. Noor (2007) and show the mistakes in it. Then, we demonstrate a more efficient method for solving fourth-order boundary value problems.
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  • 6
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    A Data-Guided Lexisearch Algorithm for the Asymmetric Traveling Salesman Problem (2011)
    Hindawi
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    Publication Date: 2011-06-21
    Description: A simple lexisearch algorithm that uses path representation method for the asymmetric traveling salesman problem (ATSP) is proposed, along with an illustrative example, to obtain exact optimal solution to the problem. Then a data-guided lexisearch algorithm is presented. First, the cost matrix of the problem is transposed depending on the variance of rows and columns, and then the simple lexisearch algorithm is applied. It is shown that this minor preprocessing of the data before the simple lexisearch algorithm is applied improves the computational time substantially. The efficiency of our algorithms to the problem against two existing algorithms has been examined for some TSPLIB and random instances of various sizes. The results show remarkably better performance of our algorithms, especially our data-guided algorithm.
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  • 7
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    An Evolutionary Analytic Method of Multi-DOF Nonlinear Coupling Dynamic Model for Controllable Close-Chain Linkage Mechanism System (2011)
    Hindawi
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    Publication Date: 2011-06-24
    Description: The 2-DOF controllable close-chain linkage mechanism is investigated in this paper. Based on the characteristics of the multi-DOF nonlinear coupling dynamic equation of the system established by the finite element method, an analytic method of multiple-scales Newmark is presented after thinking about the method of perturbation and the method of numerical analysis. Firstly, the first-order approximate solution of the dynamic responses of the system at the time of t is calculated by the multiple scales method. Then, taken the first-order approximate solution as the initialization of the generalized coordinate of the system, the stable dynamic response of the system is obtained by the implicit Newmark method. The simulation and experimental results are given in the end. The studies indicate that the method of multiple-scales Newmark is correct and practicable to study the dynamic characteristics of such kind of multi-DOF nonlinear coupling system.
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    Fractional-Order Control of Pneumatic Position Servosystems (2011)
    Hindawi
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    Publication Date: 2011-06-29
    Description: A fractional-order control strategy for pneumatic position servosystem is presented in this paper. The idea of the fractional calculus application to control theory was introduced in many works, and its advantages were proved. However, the realization of fractional-order controllers for pneumatic position servosystems has not been investigated. Based on the relationship between the pressure in cylinder and the rate of mass flow into the cylinder, the dynamic model of pneumatic position servo system is established. The fractional-order controller for pneumatic position servo and its implementation in industrial computer is designed. The experiments with fractional-order controller are carried out under various conditions, which include sine position signal with different frequency and amplitude, step position signal, and variety inertial load. The results show the effectiveness of the proposed scheme and verify their fine control performance for pneumatic position servo system.
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  • 9
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    Geometry Optimization of Self-Similar Transport Network (2011)
    Hindawi
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    Publication Date: 2011-06-22
    Description: We optimize geometries of various self-similar transport networks using a three-step strategy based on the entransy theory. Using this optimization method, we obtained optimal relationships of geometric parameters of T-shape networks for fluid flow, heat conduction, convective heat transfer, and other transport phenomena. Some optimization results agree well with the existing theories or experimental data. The optimized transport network structure depends strongly on the optimization objective and the constraints, so that both the maximum heat transfer effect and minimum flow resistance cannot be satisfied at the same time.
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    The Simplified Tikhonov Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation (2011)
    Hindawi
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    Publication Date: 2011-06-22
    Description: This paper discusses the problem of determining an unknown source which depends only on one variable for the modified Helmholtz equation. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the simplified Tikhonov regularization method. Convergence estimate is presented between the exact solution and the regularization solution. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.
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  • 11
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    Dynamics of a Stage-Structured Leslie-Gower Predator-Prey Model (2011)
    Hindawi
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    Publication Date: 2011-06-09
    Description: A generalized version of the Leslie-Gower predator-prey model that incorporates the prey population structure is introduced. Our results show that the inclusion of (age) structure in the prey population does not alter the qualitative dynamics of the model; that is, we identify sufficient conditions for the ‘‘trapping’’ of the dynamics in a biological compact set—albeit the analysis is a bit more challenging. The focus is on the study of the boundedness of solutions and identification of sufficient conditions for permanence. Sufficient conditions for the local stability of the nonnegative equilibria of the model are also derived, and sufficient conditions for the global attractivity of positive equilibrium are obtained. Numerical simulations are used to illustrate our results.
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  • 12
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    Rotordynamic Analysis for a Turbo-Machine with Fluid-Solid Interaction and Rotation Effects (2011)
    Hindawi
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    Publication Date: 2011-06-09
    Description: The rotordynamics and fluid dynamics of a turbo-machine considering the effect of fluid-solid interaction (FSI) are numerically investigated using finite element software ADINA. The iterative method is adopted in computation of coupled fields of displacement and fluid. What distinguishes the present study from previous ones is the use of ADINA's rotational meshes and the FSI interface that separates the rotor surface from its surrounding fluid. The rotor's center orbit and frequency response as well as the transient fluid dynamics are obtained with various axial flow speeds. By including real rotating motion of the rotor, this paper presents a better way to solve complicated rotordynamic problems of turbo-machines that are operated in FSI circumstances.
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  • 13
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    Integrating Factors and First Integrals for Liénard Type and Frequency-Damped Oscillators (2011)
    Hindawi
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    Publication Date: 2011-06-14
    Description: We consider Liénard type and frequency-damped oscillator equations. Integrating factors and the associated first integrals are derived from the method to compute λ-symmetries and the associated reduction algorithm. The knowledge of a λ-symmetry of the equation permits the determination of an integrating factor or a first integral by means of coupled first-order linear systems of partial differential equations. We will compare our results with those gained by the other methods.
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  • 14
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    Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System (2011)
    Hindawi
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    Publication Date: 2011-05-11
    Description: Many problems with control theory have led to investigations into switched systems. One of the most urgent problems related to the analysis of the dynamics of switched systems is the stability problem. The stability of a switched system can be ensured by a common Lyapunov function for all switching modes under an arbitrary switching law. Finding a common Lyapunov function is still an interesting and challenging problem. The purpose of the present paper is to prove the stability of equilibrium in a certain class of nonlinear switched systems by introducing a common Lyapunov function; the Lyapunov function is based on generalized Kullback–Leibler divergence or Csiszár's I-divergence between the state and equilibrium. The switched system is useful for finding positive solutions to linear algebraic equations, which minimize the I-divergence measure under arbitrary switching. One application of the stability of a given switched system is in developing a new approach to reconstructing tomographic images, but nonetheless, the presented results can be used in numerous other areas.
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    Due-Window Assignment and Scheduling with Multiple Rate-Modifying Activities under the Effects of Deterioration and Learning (2011)
    Hindawi
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    Publication Date: 2011-05-11
    Description: This paper discusses due-window assignment and scheduling with multiple rate-modifying activities. Multiple types of rate-modifying activities are allowed to perform on a single machine. The learning effect and job deterioration are also integrated concurrently into the problem which makes the problem more realistic. The objective is to find jointly the optimal location to perform multiple rate-modifying activities, the optimal job sequence, and the optimal location and size of the due window to minimize the total earliness, tardiness, and due-window-related costs. We propose polynomial time algorithms for all the cases of the problem under study.
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  • 16
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    A Multi-Model Stereo Similarity Function Based on Monogenic Signal Analysis in Poisson Scale Space (2011)
    Hindawi
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    Publication Date: 2011-05-17
    Description: A stereo similarity function based on local multi-model monogenic image feature descriptors (LMFD) is proposed to match interest points and estimate disparity map for stereo images. Local multi-model monogenic image features include local orientation and instantaneous phase of the gray monogenic signal, local color phase of the color monogenic signal, and local mean colors in the multiscale color monogenic signal framework. The gray monogenic signal, which is the extension of analytic signal to gray level image using Dirac operator and Laplace equation, consists of local amplitude, local orientation, and instantaneous phase of 2D image signal. The color monogenic signal is the extension of monogenic signal to color image based on Clifford algebras. The local color phase can be estimated by computing geometric product between the color monogenic signal and a unit reference vector in RGB color space. Experiment results on the synthetic and natural stereo images show the performance of the proposed approach.
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    Real-Time Vehicle Routing for Repairing Damaged Infrastructures Due to Natural Disasters (2011)
    Hindawi
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    Publication Date: 2011-05-06
    Description: We address the task of repairing damaged infrastructures as a series of multidepot vehicle-routing problems with time windows in a time-rolling frame. The network size of the tackled problems changes from time to time, as new disaster nodes will be added to and serviced disaster nodes will be deleted from the current network. In addition, an inaccessible disaster node would become accessible when one of its adjacent disaster nodes has been repaired. By the “take-and-conquer” strategy, the repair sequence of the disaster nodes in the affected area can be suitably scheduled. Thirteen instances were tested with our proposed heuristic, that is, Chen et al.'s approach. For comparison, Hsueh et al.'s approach (2008) with necessary modification was also tested. The results show that Chen et al.'s approach performs slightly better for larger size networks in terms of objective value.
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    A Hybrid Approach for the Random Dynamics of Uncertain Systems under Stochastic Loading (2011)
    Hindawi
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    Publication Date: 2011-05-06
    Description: This paper presents a hybrid Galerkin/perturbation approach based on Radial Basis Functions for the dynamic analysis of mechanical systems affected by randomness both in their parameters and loads. In specialized literature various procedures are nowadays available to evaluate the response statistics of such systems, but sometimes a choice has to be made between simpler methods (that could provide unreliable solutions) and more complex methods (where accurate solutions are provided by means of a heavy computational effort). The proposed method combines a Radial Basis Functions (RBF) based Galerkin method with a perturbation approach for the approximation of the system response. In order to keep the number of differential equations to be solved as low as possible, a Karhunen-Loève (KL) expansion for the excitation is used. As case study a non-linear single degree of freedom (SDOF) system with random parameters subjected to a stochastic windtype load is analyzed and discussed in detail; obtained numerical solutions are compared with the results given by Monte Carlo Simulation (MCS) to provide a validation of the proposed approach. The proposed method could be a valid alternative to the classical procedures as it is able to provide satisfactory approximations of the system response.
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    Relationship Matrix Nonnegative Decomposition for Clustering (2011)
    Hindawi
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    Publication Date: 2011-05-06
    Description: Nonnegative matrix factorization (NMF) is a popular tool for analyzing the latent structure of nonnegative data. For a positive pairwise similarity matrix, symmetric NMF (SNMF) and weighted NMF (WNMF) can be used to cluster the data. However, both of them are not very efficient for the ill-structured pairwise similarity matrix. In this paper, a novel model, called relationship matrix nonnegative decomposition (RMND), is proposed to discover the latent clustering structure from the pairwise similarity matrix. The RMND model is derived from the nonlinear NMF algorithm. RMND decomposes a pairwise similarity matrix into a product of three low rank nonnegative matrices. The pairwise similarity matrix is represented as a transformation of a positive semidefinite matrix which pops out the latent clustering structure. We develop a learning procedure based on multiplicative update rules and steepest descent method to calculate the nonnegative solution of RMND. Experimental results in four different databases show that the proposed RMND approach achieves higher clustering accuracy.
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    On the Perturbation of the Three-Dimensional Stokes Flow of Micropolar Fluids by a Constant Uniform Magnetic Field in a Circular Cylinder (2011)
    Hindawi
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    Publication Date: 2011-05-05
    Description: Modern engineering technology involves the micropolar magnetohydrodynamic flow of magnetic fluids. Here, we consider a colloidal suspension of non-conductive ferromagnetic material, which consists of small spherical particles that behave as rigid magnetic dipoles, in a carrier liquid of approximately zero conductivity and low-Reynolds number properties. The interaction of a 3D constant uniform magnetic field with the three-dimensional steady creeping motion (Stokes flow) of a viscous incompressible micropolar fluid in a circular cylinder is investigated, where the magnetization of the ferrofluid has been taken into account and the magnetic Stokes partial differential equations have been presented. Our goal is to apply the proper boundary conditions, so as to obtain the flow fields in a closed analytical form via the potential representation theory, and to study several characteristics of the flow. In view of this aim, we make use of an improved new complete and unique differential representation of magnetic Stokes flow, valid for non-axisymmetric geometries, which provides the velocity and total pressure fields in terms of easy-to-find potentials. We use these results to simulate the creeping flow of a magnetic fluid inside a circular duct and to obtain the flow fields associated with this kind of flow.
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    Hamilton-Poisson Realizations for the Lü System (2011)
    Hindawi
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    Publication Date: 2011-04-01
    Description: The Hamilton-Poisson geometry has proved to be an interesting approach for a lot of dynamics arising from different areas like biology (Gümral and Nutku, 1993), economics (Dănăiasă et al., 2008), or engineering (Ginoux and Rossetto, 2006). The Lü system was first proposed by Lü and Chen (2002) as a model of a nonlinear electrical circuit, and it was studied from various points of view. We intend to study it from mechanical geometry point of view and to point out some of its geometrical and dynamical properties.
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    New Algorithm for the Numerical Solutions of Nonlinear Third-Order Differential Equations Using Jacobi-Gauss Collocation Method (2011)
    Hindawi
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    Publication Date: 2011-03-31
    Description: A new algorithm for solving the general nonlinear third-order differential equation is developed by means of a shifted Jacobi-Gauss collocation spectral method. The shifted Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithm, and some comparisons are made with the existing results. The method is easy to implement and yields very accurate results.
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    Research on the Influence of Switching Frequency on Low-Frequency Oscillation in the Voltage-Controlled Buck-Boost Converter (2011)
    Hindawi
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    Publication Date: 2011-08-03
    Description: The influence of switching frequency on the low-frequency oscillation in the voltage-controlled buck-boost converter is studied in this paper. Firstly, the mathematical model of this system is derived. And then, a glimpse at the influence of switching frequency on the low-frequency oscillation in this system by MATLAB/Simulink is given. The improved averaged model of the system is established, and the corresponding theoretical analysis is presented. It is found that the switching frequency has an important influence on the low-frequency oscillation in the system, that is, the low-frequency oscillation is easy to occur when the switching frequency is low. Finally, the effectiveness of the improved averaged model and the theoretical analysis are confirmed by circuit experiment.
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    Limit Distribution of Inventory Level of Perishable Inventory Model (2011)
    Hindawi
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    Publication Date: 2011-08-08
    Description: This paper studies a perishable inventory model, which assumes that each perishable item has finite lifetime, and only one item is consumed each time. The lifetimes of perishable items are independent random variables with the general distribution and so are the consumption internal. Under this assumption, by using backward equations and limit distribution of Markov skeleton processes, this paper obtains the existence conditions and the explicit expression of the limit distribution of the inventory level of perishable inventory model.
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    An Inverse Eigenvalue Problem for Jacobi Matrices (2011)
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    Publication Date: 2011-05-31
    Description: A kind of inverse eigenvalue problem is proposed which is the reconstruction of a Jacobi matrix by given four or five eigenvalues and corresponding eigenvectors. The solvability of the problem is discussed, and some sufficient conditions for existence of the solution of this problem are proposed. Furthermore, a numerical algorithm and two examples are presented.
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    The Iterative Solution for Electromagnetic Field Coupling to Buried Wires (2011)
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    Publication Date: 2011-05-31
    Description: By integrating the electric field integral equation and the transmission line equation, an iterative solution for the electromagnetic field coupling to buried wires is obtained. At first we establish the integral equation which the difference between solutions of the integral equation and the telegraph equation satisfies. Then the solution of the telegraph equation is used to approximate the solution of this integral equation. Every following step of iteration is an improvement on the transmission line solution, and with several iterations, a well approximation to the solution of electric field integral equation can be obtained.
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    Qualitative Simulation of the Growth of Electrolessly Deposited Cu Thin Films (2011)
    Hindawi
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    Publication Date: 2011-05-31
    Description: Electroless deposition for fabricating copper (Cu) interconnects of integrated circuits has drawn attention due to its low processing temperature, high deposition selectivity, and high coverage. In this paper, three-dimensional computer simulations of the qualitative growth properties of Cu particles and two-dimensional simulations of the trench-filling properties are conducted. The mathematical model employed in the study is a reaction-diffusion equation. An implicit finite difference discretization with a red-black Gauss-Seidel method as a solver is proposed for solving the reaction-diffusion equation. The simulated deposition properties agree with those observed in experimentation. Alternatives to improve the deposition properties are also discussed.
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    State Feedback Guaranteed Cost Repetitive Control for Uncertain Discrete-Time Systems (2011)
    Hindawi
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    Publication Date: 2011-05-31
    Description: This paper considers the problem of guaranteed cost repetitive control for uncertain discrete-time systems. The uncertainty in the system is assumed to be norm-bounded and time-varying. The objective is to develop a novel design method so that the closed-loop repetitive control system is quadratically stable and a certain bound of performance index is guaranteed for all admissible uncertainties. The state feedback control technique is used in the paper. While for the case that the states are not measurable, an observer-based control scheme is adopted. Sufficient conditions for the existence of guaranteed cost control law are derived in terms of linear matrix inequality (LMI). The control and observer gains are characterized by the feasible solutions to these LMIs. The optimal guaranteed cost control law is obtained efficiently by solving an optimization problem with LMI constraints using existing convex optimization algorithms. A simulation example is provided to illustrate the validity of the proposed method.
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    Collective Coordination of High-Order Dynamic Multiagent Systems Guided by Multiple Leaders (2011)
    Hindawi
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    Publication Date: 2011-06-02
    Description: For second-order and high-order dynamic multiagent systems with multiple leaders, the coordination schemes that all the follower agents flock to the polytope region formed by multiple leaders are considered. Necessary and sufficient conditions which the follower agents can enter the polytope region by the leaders are obtained. Finally, numerical examples are given to illustrate our theoretical results.
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    An Efficient Method for Solving System of Third-Order Nonlinear Boundary Value Problems (2011)
    Hindawi
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    Publication Date: 2011-06-03
    Description: we use the modified variation of parameters method for finding the analytical solution of a system of third-order nonlinear boundary value problems associated with obstacle, unilateral, and contact problems. The results are calculated in terms of convergent series with easily computable components. The suggested technique is applied without any discretization, perturbation, transformation, and restrictive assumptions. Moreover, it is free from round off errors. Some examples are given to illustrate the implementation and efficiency of the modified variation of parameters method.
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    Numerical Investigation into CO2 Emission, O2 Depletion, and Thermal Decomposition in a Reacting Slab (2011)
    Hindawi
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    Publication Date: 2011-10-04
    Description: The emission of carbon dioxide (CO2) is closely associated with oxygen (O2) depletion, and thermal decomposition in a reacting stockpile of combustible materials like fossil fuels (e.g., coal, oil, and natural gas). Moreover, it is understood that proper assessment of the emission levels provides a crucial reference point for other assessment tools like climate change indicators and mitigation strategies. In this paper, a nonlinear mathematical model for estimating the CO2 emission, O2 depletion, and thermal stability of a reacting slab is presented and tackled numerically using a semi-implicit finite-difference scheme. It is assumed that the slab surface is subjected to a symmetrical convective heat and mass exchange with the ambient. Both numerical and graphical results are presented and discussed quantitatively with respect to various parameters embedded in the problem.
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    Inverse Problem with Respect to Domain and Artificial Neural Network Algorithm for the Solution (2011)
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    Publication Date: 2011-10-06
    Description: We consider the inverse problem with respect to domain. We suggested a new approach for reducing the inverse problem for a domain to an equivalent problem in a variational setting and gave an effective solution algorithm for solving such problems. In order to solve boundary problem, the artificial neural network is used in each step of the iteration.
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    On the Hermitian Positive Definite Solutions of Nonlinear Matrix Equation Xs+A∗X−t1A+B∗X−t2B=Q (2011)
    Hindawi
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    Publication Date: 2011-10-06
    Description: Nonlinear matrix equation Xs+A∗X−t1A+B∗X−t2B=Q has many applications in engineering; control theory; dynamic programming; ladder networks; stochastic filtering; statistics and so forth. In this paper, the Hermitian positive definite solutions of nonlinear matrix equation Xs+A∗X−t1A+B∗X−t2B=Q are considered, where Q is a Hermitian positive definite matrix, A, B are nonsingular complex matrices, s is a positive number, and 0<ti≤1, i=1,2. Necessary and sufficient conditions for the existence of Hermitian positive definite solutions are derived. A sufficient condition for the existence of a unique Hermitian positive definite solution is given. In addition, some necessary conditions and sufficient conditions for the existence of Hermitian positive definite solutions are presented. Finally, an iterative method is proposed to compute the maximal Hermitian positive definite solution, and numerical example is given to show the efficiency of the proposed iterative method.
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    Analytical Behavior Prediction for Skewed Thick Plates on Elastic Foundation (2011)
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    Publication Date: 2011-10-06
    Description: This paper presents analytical solutions for the problem of skewed thick plates under transverse load on a Winkler foundation, which has not been reported in the literature. The thick plate solution is obtained by using a framework of an oblique coordinate system. First, the governing differential equation in that system is derived, and the solution is obtained using deflection and rotation as derivatives of the potential function developed here. This method is applicable for arbitrary loading conditions, boundary conditions, and materials. The solution technique is applied to two illustrative application examples, and the results are compared with numerical solutions. The two approaches yielded results in good agreement.
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    Dynamic Analysis of Cracked Octagonal Quasicrystals (2011)
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    Publication Date: 2011-10-06
    Description: We focus on the dynamic fracture problem of octagonal quasicrystals by applying a rectangular sample with a Griffith crack which is often used in classical elastic media based on the method of finite difference. This paper mainly is to investigate the variation of phonon, phason fields, and stress singularity around the crack tip including the stress intensity factor. In addition, the moving boundary due to the crack propagation has also been treated by introducing an additional condition for determining solution. The influence of wave propagation and diffusion in the dynamic process is also discussed in detail. Through comparing the results of octagonal quasicrystals with the results of crystal, this paper proclaims the influence of phonon-phason coupling in dynamic fracture problem of octagonal quasicrystals which should not be neglected.
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    Commutativity of Linear Time-Varying Differential Systems with Nonzero Initial Conditions: A Review and Some New Extensions (2011)
    Hindawi
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    Publication Date: 2011-10-11
    Description: Necessary and sufficient conditions for the commutativity of linear time-varying systems are derived in the case of nonzero initial conditions. It is shown that some commutative class of linear time-varying systems may not commute with arbitrary initial conditions. In this respect, commutativity of Euler differential systems is investigated. Explicit commutativity conditions for the fifth-order systems are solved. New results about the effects of commutativity on system sensitivity and disturbance properties are presented, which is very important for network design and industrial applications where many of the systems are composed of subsystems cooperating one after another in a chain. The results are supported by examples treated either analytically or numerically.
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    An Efficient Feature Extraction Method, Global Between Maximum and Local Within Minimum, and Its Applications (2011)
    Hindawi
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    Publication Date: 2011-07-13
    Description: Feature extraction plays an important role in preprocessing procedure in dealing with small sample size problems. Considering the fact that LDA, LPP, and many other existing methods are confined to one case of the data set. To solve this problem, we propose an efficient method in this paper, named global between maximum and local within minimum. It not only considers the global structure of the data set, but also makes the best of the local geometry of the data set through dividing the data set into four domains. This method preserves relations of the nearest neighborhood, as well as demonstrates an excellent performance in classification. Superiority of the proposed method in this paper is manifested in many experiments on data visualization, face representative, and face recognition.
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    Solution of Higher-Order ODEs Using Backward Difference Method (2011)
    Hindawi
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    Publication Date: 2011-07-13
    Description: The current numerical technique for solving a system of higher-order ordinary differential equations (ODEs) is to reduce it to a system of first-order equations then solving it using first-order ODE methods. Here, we propose a method to solve higher-order ODEs directly. The formulae will be derived in terms of backward difference in a constant stepsize formulation. The method developed will be validated by solving some higher-order ODEs directly with constant stepsize. To simplify the evaluations of the integration coefficients, we find the relationship between various orders. The result presented confirmed our hypothesis.
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    Legendre Polynomials Spectral Approximation for the Infinite-Dimensional Hamiltonian Systems (2011)
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    Publication Date: 2011-07-13
    Description: This paper considers a Legendre polynomials spectral approximation for the infinite-dimensional Hamiltonian systems. As a consequence, the Legendre polynomials spectral semidiscrete system is a Hamiltonian system for the Hamiltonian system whose Hamiltonian operator is a constant differential operator.
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    On the Uncontrollability of Nonabelian Group Codes with Uncoded Group ℤp (2011)
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    Publication Date: 2011-12-07
    Description: Error-correcting encoding is a mathematical manipulation of the information against transmission errors over noisy communications channels. One class of error-correcting codes is the so-called group codes. Presently, there are many good binary group codes which are abelian. A group code is a family of bi-infinite sequences produced by a finite state machine (FSM) homomorphic encoder defined on the extension of two finite groups. As a set of sequences, a group code is a dynamical system and it is known that well-behaved dynamical systems must be necessarily controllable. Thus, a good group code must be controllable. In this paper, we work with group codes defined over nonabelian groups. This necessity on the encoder is because it has been shown that the capacity of an additive white Gaussian noise (AWGN) channel using abelian group codes is upper bounded by the capacity of the same channel using phase shift keying (PSK) modulation eventually with different energies per symbol. We will show that when the trellis section group is nonabelian and the input group of the encoder is a cyclic group with, p elements, p prime, then the group code produced by the encoder is noncontrollable.
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    Conforming Finite Element Approximations for a Fourth-Order Steklov Eigenvalue Problem (2011)
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    Publication Date: 2011-12-07
    Description: This paper characterizes the spectrum of a fourth-order Steklov eigenvalue problem by using the spectral theory of completely continuous operator. The conforming finite element approximation for this problem is analyzed, and the error estimate is given. Finally, the bounds for Steklov eigenvalues on the square domain are provided by Bogner-Fox-Schmit element and Morley element.
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    A Hybrid Differential Evolution and Tree Search Algorithm for the Job Shop Scheduling Problem (2011)
    Hindawi
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    Publication Date: 2011-11-15
    Description: The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. In terms of the objective function, most existing research has been focused on the makespan criterion. However, in contemporary manufacturing systems, due-date-related performances are more important because they are essential for maintaining a high service reputation. Therefore, in this study we aim at minimizing the total weighted tardiness in JSSP. Considering the high complexity, a hybrid differential evolution (DE) algorithm is proposed for the problem. To enhance the overall search efficiency, a neighborhood property of the problem is discovered, and then a tree search procedure is designed and embedded into the DE framework. According to the extensive computational experiments, the proposed approach is efficient in solving the job shop scheduling problem with total weighted tardiness objective.
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    A New Method for Detecting the Time-Varying Nonlinear Damping in Nonlinear Oscillation Systems: Nonparametric Identification (2011)
    Hindawi
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    Publication Date: 2011-11-17
    Description: This paper presents an original method that can be used for identifying time-varying nonlinear damping characteristics of a nonlinear oscillation system. The method developed involves the nonparametric identification, in which only the system responses, namely, displacement and velocity need to be known for the identification. However, the method is concerned with a Volterra-type integral equation of the first kind, which leads to an instability of numerical solutions. That is, the solutions identified lack stability properties. In order to overcome the difficulty, a stabilization technique is applied to the identification process. A numerical example comprising a highly nonlinear system is examined to demonstrate the workability of the proposed method for the time-varying damping identification.
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    Design of Switching Multiobjective Controller: A New Approach (2011)
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    Publication Date: 2011-11-17
    Description: Design of switching H2/H∞ output-feedback controller for discrete-time LTI systems with state-multiplicative noise is considered. The closed loop system achieves a minimum bound on the stochastic H2 performance level, while satisfying the H∞ performance. The proposed controller is based on a fuzzy supervisor which manages the combination of two separate H2 and H∞ controllers. A convex formulation of the two controllers leads to a structure which benefits from the advantages of both controllers to ensure a good performance in both the transient phase (H2 controller) and the steady phase (H∞ controller). The stability analysis uses the Lyapunov technique, inspired from switching system theory, to prove that the closed loop system with the proposed controller structure remains globally stable despite the configuration changing.
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    Laplace-Type Semi-Invariants for a System of Two Linear Hyperbolic Equations by Complex Methods (2011)
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    Publication Date: 2011-11-22
    Description: In 1773 Laplace obtained two fundamental semi-invariants, called Laplace invariants, for scalar linear hyperbolic partial differential equations (PDEs) in two independent variables. He utilized this in his integration theory for such equations. Recently, Tsaousi and Sophocleous studied semi-invariants for systems of two linear hyperbolic PDEs in two independent variables. Separately, by splitting a complex scalar ordinary differential equation (ODE) into its real and imaginary parts PDEs for two functions of two variables were obtained and their symmetry structure studied. In this work we revisit semi-invariants under equivalence transformations of the dependent variables for systems of two linear hyperbolic PDEs in two independent variables when such systems correspond to scalar complex linear hyperbolic equations in two independent variables, using the above-mentioned splitting procedure. The semi-invariants under linear changes of the dependent variables deduced for this class of hyperbolic linear systems correspond to the complex semi-invariants of the complex scalar linear (1+1) hyperbolic equation. We show that the adjoint factorization corresponds precisely to the complex splitting. We also study the reductions and the inverse problem when such systems of two linear hyperbolic PDEs arise from a linear complex hyperbolic PDE. Examples are given to show the application of this approach.
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    Finite Element Analysis of Dam-Reservoir Interaction Using High-Order Doubly Asymptotic Open Boundary (2011)
    Hindawi
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    Publication Date: 2011-11-25
    Description: The dam-reservoir system is divided into the near field modeled by the finite element method, and the far field modeled by the excellent high-order doubly asymptotic open boundary (DAOB). Direct and partitioned coupled methods are developed for the analysis of dam-reservoir system. In the direct coupled method, a symmetric monolithic governing equation is formulated by incorporating the DAOB with the finite element equation and solved using the standard time-integration methods. In contrast, the near-field finite element equation and the far-field DAOB condition are separately solved in the partitioned coupled methodm, and coupling is achieved by applying the interaction force on the truncated boundary. To improve its numerical stability and accuracy, an iteration strategy is employed to obtain the solution of each step. Both coupled methods are implemented on the open-source finite element code OpenSees. Numerical examples are employed to demonstrate the performance of these two proposed methods.
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    An Auxiliary Function Method for Global Minimization in Integer Programming (2011)
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    Publication Date: 2011-11-25
    Description: An auxiliary function method is proposed for finding the global minimizer of integer programming problem. Firstly, we propose a method to transform the original problem into an integer programming with box constraint, which does not change the properties of the original problem. For the transformed problem, we propose an auxiliary function to escape from the current local minimizer and to get a better one. Then, based on the proposed auxiliary function, a new algorithm to find the global minimizer of integer programming is proposed. At last, numerical results are given to demonstrate the effectiveness and efficiency of the proposed method.
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    How to Generate Chaos from Switching System: A Saddle Focus of Index 1 and Heteroclinic Loop-Based Approach (2011)
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    Publication Date: 2011-11-25
    Description: There exist two different types of equilibrium points in 3-D autonomous systems, named as saddle foci of index 1 and index 2, which are crucial for chaos generation. Although saddle foci of index 2 have been usually applied for creating double-scroll or double-wing chaotic attractors, saddle foci of index 1 are further considered for chaos generation in this paper. A novel approach for constructing chaotic systems is investigated by applying the switching control strategy and yielding a heteroclinic loop which connects two saddle foci of index 1. A basic 3-D linear system with an arbitrary normal direction of the eigenplane, possessing a saddle focus of index 1 whose corresponding eigenvalues satisfy the Shil'nikov inequality, is first introduced. Then a heteroclinic loop connecting two saddle foci of index 1 will be formed by applying the switching control strategy to the basic 3-D linear system. The heteroclinic loop consists of an unstable manifold, a stable manifold, and a heteroclinic point. Under the necessary conditions for forming the heteroclinic loop, the intended two-segmented piecewise linear system which exhibits the chaotic behavior in the sense of the Smale horseshoe can be finally constructed. An illustrative example is given, confirming the effectiveness of the proposed method.
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    A General Three-Step Class of Optimal Iterations for Nonlinear Equations (2011)
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    Publication Date: 2011-11-25
    Description: Many of the engineering problems are reduced to solve a nonlinear equation numerically, and as a result, an especial attention to suggest efficient and accurate root solvers is given in literature. Inspired and motivated by the research going on in this area, this paper establishes an efficient general class of root solvers, where per computing step, three evaluations of the function and one evaluation of the first-order derivative are used to achieve the optimal order of convergence eight. The without-memory methods from the developed class possess the optimal efficiency index 1.682. In order to show the applicability and validity of the class, some numerical examples are discussed.
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    Proportional-Derivative Observer-Based Backstepping Control for an Underwater Manipulator (2011)
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    Publication Date: 2011-11-30
    Description: This paper investigates the performance of a new robust tracking control on the basis of proportional-derivative observer-based backstepping control applied on a three degrees of freedom underwater spatial manipulator. Hydrodynamic forces and moments such as added mass effects, damping effects, and restoring effects can be large and have a significant effect on the dynamic performance of the underwater manipulator. In this paper, a detailed closed-form dynamic model is derived using the recursive Newton-Euler algorithm, which extended to include the most significant hydrodynamic effects. In the dynamic modeling and simulation, the actuator and sensor dynamics of the system are also incorporated. The effectiveness of the proposed control scheme is demonstrated using numerical simulations along with comparative study between conventional proportional-integral-derivative (PID) controls. The results are confirmed that the actual states of joint trajectories of the underwater manipulator asymptotically follow the desired trajectories defined by the reference model even though the system is subjected to external disturbances and parameter uncertainties. Also, stability of the proposed (model reference control) control scheme is analyzed.
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    Fluid-Structure Interaction Analysis on Turbulent Annular Seals of Centrifugal Pumps during Transient Process (2011)
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    Publication Date: 2011-11-21
    Description: The current paper studies the influence of annular seal flow on the transient response of centrifugal pump rotors during the start-up period. A single rotor system and three states of annular seal flow were modeled. These models were solved using numerical integration and finite difference methods. A fluid-structure interaction method was developed. In each time step one of the three annular seal models was chosen to simulate the annular seal flow according to the state of rotor systems. The objective was to obtain a transient response of rotor systems under the influence of fluid-induced forces generated by annular seal flow. This method overcomes some shortcomings of the traditional FSI method by improving the data transfer process between two domains. Calculated results were in good agreement with the experimental results. The annular seal was shown to have a supportive effect on rotor systems. Furthermore, decreasing the seal clearance would enhance this supportive effect. In the transient process, vibration amplitude and critical speed largely changed when the acceleration of the rotor system increased.
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    Stochastic Finite-Time Guaranteed Cost Control of Markovian Jumping Singular Systems (2011)
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    Publication Date: 2011-11-23
    Description: The problem of stochastic finite-time guaranteed cost control is investigated for Markovian jumping singular systems with uncertain transition probabilities, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the definitions of stochastic singular finite-time stability, stochastic singular finite-time boundedness, and stochastic singular finite-time guaranteed cost control are presented. Then, sufficient conditions on stochastic singular finite-time guaranteed cost control are obtained for the family of stochastic singular systems. Designed algorithms for the state feedback controller are provided to guarantee that the underlying stochastic singular system is stochastic singular finite-time guaranteed cost control in terms of restricted linear matrix equalities with a fixed parameter. Finally, numerical examples are given to show the validity of the proposed scheme.
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    Constructing Dynamic Multiple-Input Multiple-Output Logic Gates (2011)
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    Publication Date: 2011-10-19
    Description: Investigation of computing devices with dynamic architecture which makes devices have reconfigurable ability is an interesting research direction for designing the next generation of computer chip. In this paper, we present a window threshold method to construct such dynamic logic architecture. Here, dynamic multiple-input multiple-output (MIMO) logic gates are proposed, analyzed, and implemented. By using a curve-intersections-based graphic method, we illustrate the relationships among the threshold, the control parameter, and the functions of logic gates. A noise analysis on all the parameters is also given. The chips based on the proposed schemes can be transformed into different arrangements of logic gates within a single clock cycle. With these schemes in hand, it is conceivable to build more flexible, robust, cost effective, yet general-purpose computing devices.
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    An Optimal Error Estimates of H1-Galerkin Expanded Mixed Finite Element Methods for Nonlinear Viscoelasticity-Type Equation (2011)
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    Publication Date: 2011-10-21
    Description: We investigate a H1-Galerkin mixed finite element method for nonlinear viscoelasticity equations based on H1-Galerkin method and expanded mixed element method. The existence and uniqueness of solutions to the numerical scheme are proved. A priori error estimation is derived for the unknown function, the gradient function, and the flux.
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    Performance Evaluation and Dimensioning of GIX/M/c/N Systems through Kernel Estimation (2011)
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    Publication Date: 2011-10-27
    Description: We extend the analysis of queueing systems for real-life situations, where the arrival pattern of customers is unknown. In real systems, we must understand how the choice of a method of estimation influences the configuration of the system. Using kernel smoothing, we evaluate algorithms to estimate performance measures of a GIX/M/c/N system, including the invariant probability distribution of the number of customers in the system, the blocking probability, the average queue size, and the average client queue time. We successfully apply the method to the arrivals to a call center to plan and improve the performance of these important queueing systems.
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    Financial Applications of Bivariate Markov Processes (2011)
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    Publication Date: 2011-10-30
    Description: This paper describes a methodology to approximate a bivariate Markov process by means of a proper Markov chain and presents possible financial applications in portfolio theory, option pricing and risk management. In particular, we first show how to model the joint distribution between market stochastic bounds and future wealth and propose an application to large-scale portfolio problems. Secondly, we examine an application to VaR estimation. Finally, we propose a methodology to price Asian options using a bivariate Markov process.
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    Spline-Interpolation-Based FFT Approach to Fast Simulation of Multivariate Stochastic Processes (2011)
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    Publication Date: 2011-11-02
    Description: The spline-interpolation-based fast Fourier transform (FFT) algorithm, designated as the SFFT algorithm, is proposed in the present paper to further enhance the computational speed of simulating the multivariate stochastic processes. The proposed SFFT algorithm first introduces the spline interpolation technique to reduce the number of the Cholesky decomposition of a spectral density matrix and subsequently uses the FFT algorithm to further enhance the computational speed. In order to highlight the superiority of the SFFT algorithm, the simulations of the multivariate stationary longitudinal wind velocity fluctuations have been carried out, respectively, with resorting to the SFFT-based and FFT-based spectral representation SR methods, taking into consideration that the elements of cross-power spectral density matrix are the complex values. The numerical simulation results show that though introducing the spline interpolation approximation in decomposing the cross-power spectral density matrix, the SFFT algorithm can achieve the results without a loss of precision with reference to the FFT algorithm. In comparison with the FFT algorithm, the SFFT algorithm provides much higher computational efficiency. Likewise, the superiority of the SFFT algorithm is becoming more remarkable with the dividing number of frequency, the number of samples, and the time length of samples going up.
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    Generic Lightlike Submanifolds of an Indefinite Cosymplectic Manifold (2011)
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    Publication Date: 2011-11-04
    Description: Lightlike geometry has its applications in general relativity, particularly in black hole theory. Indeed, it is known that lightlike hypersurfaces are examples of physical models of Killing horizons in general relativity (Galloway, 2007). In this paper, we introduce the definition of generic lightlike submanifolds of an indefinite cosymplectic manifold. We investigate new results on a class of generic lightlike submanifolds M of an indefinite cosymplectic manifold M¯.
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    A Low Memory Solver for Integral Equations of Chandrasekhar Type in the Radiative Transfer Problems (2011)
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    Publication Date: 2011-11-11
    Description: The problems of radiative transfer give rise to interesting integral equations that must be faced with efficient numerical solver. Very often the integral equations are discretized to large-scale nonlinear equations and solved by Newton's-like methods. Generally, these kind of methods require the computation and storage of the Jacobian matrix or its approximation. In this paper, we present a new approach that was based on approximating the Jacobian inverse into a diagonal matrix by means of variational technique. Numerical results on well-known benchmarks integral equations involved in the radiative transfer authenticate the reliability and efficiency of the approach. The fact that the proposed method can solve the integral equations without function derivative and matrix storage can be considered as a clear advantage over some other variants of Newton's method.
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    The Fractional SIRC Model and Influenza A (2011)
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    Publication Date: 2011-11-16
    Description: This paper deals with the fractional-order SIRC model associated with the evolution of influenza A disease in human population. Qualitative dynamics of the model is determined by the basic reproduction number, R0. We give a detailed analysis for the asymptotic stability of disease-free and positive fixed points. Nonstandard finite difference methods have been used to solve and simulate the system of differential equations.
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    Contractive Mapping in Generalized, Ordered Metric Spaces with Application in Integral Equations (2011)
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    Publication Date: 2011-11-18
    Description: We consider the concept of Ω-distance on a complete, partially ordered G-metric space and prove some fixed point theorems. Then, we present some applications in integral equations of our obtained results.
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    A Lagrange Relaxation Method for Solving Weapon-Target Assignment Problem (2011)
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    Publication Date: 2011-11-25
    Description: We study the weapon-target assignment (WTA) problem which has wide applications in the area of defense-related operations research. This problem calls for finding a proper assignment of weapons to targets such that the total expected damaged value of the targets to be maximized. The WTA problem can be formulated as a nonlinear integer programming problem which is known to be NP-complete. There does not exist any exact method for the WTA problem even small size problems, although several heuristic methods have been proposed. In this paper, Lagrange relaxation method is proposed for the WTA problem. The method is an iterative approach which is to decompose the Lagrange relaxation into two subproblems, and each subproblem can be easy to solve to optimality based on its specific features. Then, we use the optimal solutions of the two subproblems to update Lagrange multipliers and solve the Lagrange relaxation problem iteratively. Our computational efforts signify that the proposed method is very effective and can find high quality solutions for the WTA problem in reasonable amount of time.
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    Characterization of Periodic, Quasiperiodic, and Chaotic States in Nonpremixed Biodiesel/Air Jet Flames (2011)
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    Publication Date: 2011-11-02
    Description: Characterization for nonpremixed biodiesel/air jet flames instability is investigated by the 0-1 test for chaos and recurrence plots. Test conditions involve biodiesel from Jatropha curcas. L-fueled flames have inlet oil pressure of 0.2–0.6 MPa, fuel flow rates (Q1) of 15–30 kg/h, and combustion air flow rate (Q2) of 150–750 m3/h. This method is based on image analysis and nonlinear dynamics. Structures of flame are analyzed using an image analysis technique to extract position series which are representative of the relative change in temperature of combustion chamber. Compared with the method of maximum Lyapunov exponent, the 0-1 test succeeds in detecting the presence of regular and chaotic components in flame position series. Periodic and quasiperiodic characteristics are obtained by the Poincaré sections. A common characteristic of regular nonpremixed flame tip position series is detected by recurrence plots. Experimental results show that these flame oscillations follow a route to chaos via periodic and quasiperiodic states.
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    Optimization of DC-DC Converters via Geometric Programming (2011)
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    Publication Date: 2011-09-16
    Description: The paper presents a new methodology for optimizing the design of DC-DC converters. The magnitudes that we take into account are efficiency, ripples, bandwidth, and RHP zero placement. We apply a geometric programming approach, because the variables are positives and the constraints can be expressed in a posynomial form. This approach has all the advantages of convex optimization. We apply the proposed methodology to a boost converter. The paper also describes the optimum designs of a buck converter and a synchronous buck converter, and the method can be easily extended to other converters. The last example allows us to compare the efficiency and bandwidth between these optimal-designed topologies.
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    Lie Symmetry Analysis of Kudryashov-Sinelshchikov Equation (2011)
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    Publication Date: 2011-09-19
    Description: The Lie symmetry method is performed for the fifth-order nonlinear evolution Kudryashov-Sinelshchikov equation. We will find ones and two-dimensional optimal systems of Lie subalgebras. Furthermore, preliminary classification of its group-invariant solutions is investigated.
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    Mathematical Extrapolating of Highly Efficient Fin Systems (2011)
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    Publication Date: 2011-09-26
    Description: Different high-performance fins are mathematically analyzed in this work. Initially, three types are considered: (i) exponential, (ii) parabolic, and (iii) triangular fins. Analytical solutions are obtained. Accordingly, the effective thermal efficiency and the effective volumetric heat dissipation rate are calculated. The analytical results were validated against numerical solutions. It is found that the triangular fin has the maximum effective thermal length. In addition, the exponential pin fin is found to have the largest effective thermal efficiency. However, the effective efficiency for the straight one is the maximum when its effective thermal length based on profile area is greater than 1.4. Furthermore, the exponential straight fin is found to have effective volumetric heat dissipation that can be 440% and 580% above the parabolic and triangular straight fins, respectively. In contrast, the exponential pin fin is found to possess effective volumetric heat dissipation that can be 120% and 132% above the parabolic and triangular pin fins, respectively. Finally, new high performance fins are mathematically generated that can have effective volumetric heat dissipation of 24% and 12% above those of exponential pin and straight fins, respectively.
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    Neural Network Approach for Analyzing Seismic Data to Identify Potentially Hazardous Bridges (2011)
    Hindawi
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    Publication Date: 2011-06-05
    Description: Examining the effect of strong ground motions on civil engineering structures is important as it concerns public safety. The present study initially selects twenty-one bridges with lengths over 500 m in the Formosa freeway of Taiwan and collects a series of recorded seismic data from checking stations near these bridges. Then, three seismic parameters including focal depth, epicenter distance, and local magnitude are used as the input data sets, and a model for estimating the key seismic parameter—peak ground acceleration—for each of bridge site is developed by using the neural network approach. This model is finally combined with a simple distribution method and a new weight-based method to estimate peak ground acceleration at each of the bridges along the freeway. Based on the seismic design value in the current building code as the evaluation criteria, the model identifies five bridges, out of all the bridges investigated, as having the potential to be subjected to significantly higher horizontal peak ground accelerations than that recommended for design in the building code. The method presented in this study hence provides a valuable reference for dealing with nonlinear seismic data by developing neural network model, and the approach presented is also applicable to other areas of interest around the world.
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    Stochastic Fractional Programming Approach to a Mean and Variance Model of a Transportation Problem (2011)
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    Publication Date: 2011-06-07
    Description: In this paper, we propose a stochastic programming model, which considers a ratio of two nonlinear functions and probabilistic constraints. In the former, only expected model has been proposed without caring variability in the model. On the other hand, in the variance model, the variability played a vital role without concerning its counterpart, namely, the expected model. Further, the expected model optimizes the ratio of two linear cost functions where as variance model optimize the ratio of two non-linear functions, that is, the stochastic nature in the denominator and numerator and considering expectation and variability as well leads to a non-linear fractional program. In this paper, a transportation model with stochastic fractional programming (SFP) problem approach is proposed, which strikes the balance between previous models available in the literature.
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    Integrating Independent Component Analysis and Principal Component Analysis with Neural Network to Predict Chinese Stock Market (2011)
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    Publication Date: 2011-07-10
    Description: We investigate the statistical behaviors of Chinese stock market fluctuations by independent component analysis. The independent component analysis (ICA) method is integrated into the neural network model. The proposed approach uses ICA method to analyze the input data of neural network and can obtain the latent independent components (ICs). After analyzing and removing the IC that represents noise, the rest of ICs are used as the input of neural network. In order to forect the fluctuations of Chinese stock market, the data of Shanghai Composite Index is selected and analyzed, and we compare the forecasting performance of the proposed model with those of common BP model integrating principal component analysis (PCA) and single BP model. Experimental results show that the proposed model outperforms the other two models no matter in relatively small or relatively large sample, and the performance of BP model integrating PCA is closer to that of the proposed model in relatively large sample. Further, the prediction results on the points where the prices fluctuate violently by the above three models relatively deviate from the corresponding real market data.
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    On the Stabilization of the Inverted-Cart Pendulum Using the Saturation Function Approach (2011)
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    Publication Date: 2011-10-18
    Description: A simple stabilizing controller for the cart-pendulum system is designed in this paper. Our control strategy describes the underactuated system as a chain of integrators with a high-order smooth nonlinear perturbation and assumes initialization of the system in the upper half plane. The design procedure involves two sequentially associated control actions: one linear and one bounded quasilinear. The first control action brings the nonactuated coordinate near to the upright position and keeps it inside of a well-characterized small vicinity, whereas the second control action asymptotically brings the whole state of the system to the origin. The corresponding closed-loop stability analysis uses standard linear stability arguments as well as the traditional Lyapunov method and the LaSalle's theorem. Our proposed control law ensures global stability of the system in the upper half plane. We illustrate the effectiveness of the proposed control strategy via numerical simulations.
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    Strategic and Tactical Design of Competing Decentralized Supply Chain Networks with Risk-Averse Participants for Markets with Uncertain Demand (2011)
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    Publication Date: 2011-10-19
    Description: An integrated equilibrium model for tactical decisions in network design is developed. We consider a decentralized supply chain network operating in markets under uncertain demands when there is a rival decentralized chain. The primary assumption is that two chains provide partial substitutable products to the markets, and markets' demands are affected by tactical decisions such as price, service level, and advertising expenditure. Each chain consists of one risk-averse manufacturer and a set of risk-averse retailers. The strategic decisions are frequently taking precedence over tactical ones. Therefore, we first find equilibrium of tactical decisions for each possible scenario of supply chain network. Afterwards, we find optimal distribution network of the new supply chain by the scenario evaluation method. Numerical example, including sensitivity analysis will illustrate how the conservative behaviors of chains' members affect expected demand, profit, and utility of each distribution scenario.
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    Linearizability of Systems of Ordinary Differential Equations Obtained by Complex Symmetry Analysis (2011)
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    Publication Date: 2011-10-21
    Description: Five equivalence classes had been found for systems of two second-order ordinary differential equations, transformable to linear equations (linearizable systems) by a change of variables. An “optimal (or simplest) canonical form” of linear systems had been established to obtain the symmetry structure, namely, with 5-, 6-, 7-, 8-, and 15-dimensional Lie algebras. For those systems that arise from a scalar complex second-order ordinary differential equation, treated as a pair of real ordinary differential equations, we provide a “reduced optimal canonical form.” This form yields three of the five equivalence classes of linearizable systems of two dimensions. We show that there exist 6-, 7-, and 15-dimensional algebras for these systems and illustrate our results with examples.
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    Multiple Fractional Dual Solutions in PEMC Backed Chiral Nihility Slab (2011)
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    Publication Date: 2011-10-21
    Description: Inside a chiral nihility slab which is backed by perfect electromagnetic conductor, all valid fractional dual solutions are determined using the fractional curl operator. Fractional dual solutions may be regarded as intermediate step between the original and dual to the original solution. Corresponding fields outside the nihility slab for each case are also determined and analyzed. It is noted that only for one out of three cases the corresponding field outside chiral nihility slab is also fractional dual, while for other two cases, corresponding fields are not fractional dual. It is noted that time average power density vanishes inside the PEC-backed chiral nihility slab, while it exists outside the nihility slab.
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    Effect of Rotation and Magnetic Field through Porous Medium on Peristaltic Transport of a Jeffrey Fluid in Tube (2011)
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    Publication Date: 2011-10-20
    Description: This paper is concerned with the analysis of peristaltic motion of a Jeffrey fluid in a tube with sinusoidal wave travelling down its wall. The effect of rotation, porous medium, and magnetic field on peristaltic transport of a Jeffrey fluid in tube is studied. The fluid is electrically conducting in the presence of rotation and a uniform magnetic field. An analytic solution is carried out for long wavelength, axial pressure gradient, and low Reynolds number considerations. The results for pressure rise and frictional force per wavelength were obtained, evaluated numerically, and discussed briefly.
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    Moving Heat Source Reconstruction from Cauchy Boundary Data: The Cartesian Coordinates Case (2011)
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    Publication Date: 2011-10-25
    Description: We consider the problem of reconstruction of an unknown characteristic interval and block transient thermal source inside a domain. By exploring the definition of an Extended Dirichlet to Neumann map in the time space cylinder that has been introduced in Roberty and Rainha (2010a), we can treat the problem with methods similar to that used in the analysis of the stationary source reconstruction problem. Further, the finite difference θ-scheme applied to the transient heat conduction equation leads to a model based on a sequence of modified Helmholtz equation solutions. For each modified Helmholtz equation the characteristic interval and parallelepiped source function may be reconstructed uniquely from the Cauchy boundary data. Using representation formula we establish reciprocity functional mapping functions that are solutions of the modified Helmholtz equation to their integral in the unknown characteristic support. Numerical experiment for capture of an interval and an rectangular parallelepiped characteristic source inside a cubic box domain from boundary data are presented in threedimensional and one-dimensional implementations. The problem of centroid determination is addressed and questions are discussed from an computational points of view.
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    Structure Identification-Based Clustering According to Density Consistency (2011)
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    Publication Date: 2011-10-25
    Description: Structure of data set is of critical importance in identifying clusters, especially the density difference feature. In this paper, we present a clustering algorithm based on density consistency, which is a filtering process to identify same structure feature and classify them into same cluster. This method is not restricted by the shapes and high dimension data set, and meanwhile it is robust to noises and outliers. Extensive experiments on synthetic and real world data sets validate the proposed the new clustering algorithm.
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    Numerical Solution of Nonlinear Fredholm Integrodifferential Equations of Fractional Order by Using Hybrid of Block-Pulse Functions and Chebyshev Polynomials (2011)
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    Publication Date: 2011-11-01
    Description: A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm-type equations, which have many applications in mathematical physics, are then considered. The method is based upon hybrid function approximate. The properties of hybrid of block-pulse functions and Chebyshev series are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.
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    Rough Set Approach to Approximation Reduction in Ordered Decision Table with Fuzzy Decision (2011)
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    Publication Date: 2011-10-26
    Description: In practice, some of information systems are based on dominance relations, and values of decision attribute are fuzzy. So, it is meaningful to study attribute reductions in ordered decision tables with fuzzy decision. In this paper, upper and lower approximation reductions are proposed in this kind of complicated decision table, respectively. Some important properties are discussed. The judgement theorems and discernibility matrices associated with two reductions are obtained from which the theory of attribute reductions is provided in ordered decision tables with fuzzy decision. Moreover, rough set approach to upper and lower approximation reductions is presented in ordered decision tables with fuzzy decision as well. An example illustrates the validity of the approach, and results show that it is an efficient tool for knowledge discovery in ordered decision tables with fuzzy decision.
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    A Compensatory Approach to Multiobjective Linear Transportation Problem with Fuzzy Cost Coefficients (2011)
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    Publication Date: 2011-11-01
    Description: This paper deals with the Multiobjective Linear Transportation Problem that has fuzzy cost coefficients. In the solution procedure, many objectives may conflict with each other; therefore decision-making process becomes complicated. And also due to the fuzziness in the costs, this problem has a nonlinear structure. In this paper, fuzziness in the objective functions is handled with a fuzzy programming technique in the sense of multiobjective approach. And then we present a compensatory approach to solve Multiobjective Linear Transportation Problem with fuzzy cost coefficients by using Werner's μand operator. Our approach generates compromise solutions which are both compensatory and Pareto optimal. A numerical example has been provided to illustrate the problem.
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    On New Numerical Techniques for the MHD Flow Past a Shrinking Sheet with Heat and Mass Transfer in the Presence of a Chemical Reaction (2011)
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    Publication Date: 2011-11-02
    Description: We use recent innovative solution techniques to investigate the problem of MHD viscous flow due to a shrinking sheet with a chemical reaction. A comparison is made of the convergence rates, ease of use, and expensiveness (the number of iterations required to give convergent results) of three seminumerical techniques in solving systems of nonlinear boundary value problems. The results were validated using a multistep, multimethod approach comprising the use of the shooting method, the Matlab bvp4c numerical routine, and with results in the literature.
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    Simulation and Statistical Analysis of Market Return Fluctuation by Zipf Method (2011)
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    Publication Date: 2011-03-26
    Description: We investigate the fluctuation behaviors of financial stock markets by Zipf analysis. In the present paper, the empirical research is made to describe ensembles and specifics of stock price returns for global stock indices, and the corresponding Zipf distributions are given. First we study the fluctuation behavior of global stock markets by (m,k)-Zipf method. Then we consider a dynamic stock price model, and we analyze the absolute frequencies and the relative frequencies for this financial model. Further, the Zipf distributions of returns for SSE Composite Index are studied for different time scales.
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    On Output Feedback Multiobjective Control for Singularly Perturbed Systems (2011)
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    Publication Date: 2011-03-29
    Description: A new design procedure for a robust H2 and H∞ control of continuous-time singularly perturbed systems via dynamic output feedback is presented. By formulating all objectives in terms of a common Lyapunov function, the controller will be designed through solving a set of inequalities. Therefore, a dynamic output feedback controller is developed such that H∞ and H2 performance of the resulting closed-loop system is less than or equal to some prescribed value. Also, H∞ and H2 performance for a given upperbound of singular perturbation parameter ε∈(0,ε∗] are guaranteed. It is shown that the ε-dependent controller is well defined for any ε∈(0,ε∗] and can be reduced to an ε-independent one so long as ε is sufficiently small. Finally, numerical simulations are provided to validate the proposed controller. Numerical simulations coincide with the theoretical analysis.
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    Existence and Iteration of Monotone Positive Solution of BVP for an Elastic Beam Equation (2011)
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    Publication Date: 2011-03-30
    Description: This paper is concerned with the existence of monotone positive solution of boundary value problem for an elastic beam equation. By applying iterative techniques, we not only obtain the existence of monotone positive solution but also establish iterative scheme for approximating the solution. It is worth mentioning that the iterative scheme starts off with zero function, which is very useful and feasible for computational purpose. An example is also included to illustrate the main results.
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    Efficient and Effective Total Variation Image Super-Resolution: A Preconditioned Operator Splitting Approach (2011)
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    Publication Date: 2011-02-22
    Description: Super-resolution is a fusion process for reconstructing a high-resolution image from a set of low-resolution images. This paper proposes a novel approach to image super-resolution based on total variation (TV) regularization. We applied the Douglas-Rachford splitting technique to the constrained TV-based variational SR model which is separated into three subproblems that are easy to solve. Then, we derive an efficient and effective iterative scheme, which includes a fast iterative shrinkage/thresholding algorithm for denoising problem, a very simple noniterative algorithm for fusion part, and linear equation systems for deblurring process. Moreover, to speed up convergence, we provide an accelerated scheme based on precondition design of initial guess and forward-backward splitting technique which yields linear systems of equations with a nice structure. The proposed algorithm shares a remarkable simplicity together with a proven global rate of convergence which is significantly better than currently known lagged diffusivity fixed point iteration algorithm and fast decoupling algorithm by exploiting the alternating minimizing approach. Experimental results are presented to illustrate the effectiveness of the proposed algorithm.
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    Fatigue Reliability Sensitivity Analysis of Complex Mechanical Components under Random Excitation (2011)
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    Publication Date: 2011-02-23
    Description: Fatigue failure is the typical failure mode of mechanical components subjected to random load-time history. It is important to ensure that the mechanical components have an expected life with a high reliability. However, it is difficult to reduce the influence of factors that affect the fatigue reliability and thus a reliability sensitivity analysis is necessary. An approach of fatigue reliability sensitivity analysis of complex mechanical components under random excitation is presented. Firstly, load spectra are derived using a theoretical method. A design of experiment (DOE) is performed to study the stresses of dangerous points according to the change of design parameters of the mechanical component. By utilizing a Back-Propagation (BP) algorithm, the explicit function relation between stresses and design parameters is formulated and thus solves the problem of implicit limit state function. Based on the damage accumulation (DA) approach, the probability perturbation method, the fourth-moment method, the Edgeworth expansion is adopted to calculate the fatigue reliability and reliability-based sensitivity. The fatigue reliability sensitivity analysis of a train wheel is performed as an example. The results of reliability are compared with that obtained using Monte Carlo simulation. The reliability sensitivity of design parameters in the train wheel is analyzed.
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    Positive Solution for the Elliptic Problems with Sublinear and Superlinear Nonlinearities (2011)
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    Publication Date: 2011-01-25
    Description: This paper deals with the existence of positive solutions for the elliptic problems with sublinear and superlinear nonlinearities -Δu=λa(x)up+b(x)uq in Ω, u>0 in Ω, u=0 on ∂Ω, where λ>0 is a real parameter, 0<p<1<q. Ω is a bounded domain in RN   (N≥ 3), and a(x) and b(x) are some given functions. By means of variational method and super-subsolution method, we obtain some results about existence of positive solutions.
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    Multiobjective Optimal Control of HIV Dynamics (2011)
    Hindawi
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    Publication Date: 2011-01-25
    Description: Various aspects of the interaction of HIV with the human immune system can be modeled by a system of ordinary differential equations. This model is utilized, and a multiobjective optimal control problem (MOOCP) is proposed to maximize the CD4+ T cells population and minimize both the viral load and drug costs. The weighted sum method is used, and continuous Pareto optimal solutions are derived by solving the corresponding optimality system. Moreover, a model predictive control (MPC) strategy is applied, with the final goal of implementing Pareto optimal structured treatment interruptions (STI) protocol. In particular, by using a fuzzy approach, the MOOCP is converted to a single-objective optimization problem to derive a Pareto optimal solution which among other Pareto optimal solutions has the best satisfaction performance. Then, by using an embedding method, the problem is transferred into a modified problem in an appropriate space in which the existence of solution is guaranteed by compactness of the space. The metamorphosed problem is approximated by a linear programming (LP) model, and a piecewise constant solution which shows the desired combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficacies is achieved.
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    On a Variational Approach to Optimization of Hybrid Mechanical Systems (2011)
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    Publication Date: 2011-03-04
    Description: This paper deals with multiobjective optimization techniques for a class of hybrid optimal control problems in mechanical systems. We deal with general nonlinear hybrid control systems described by boundary-value problems associated with hybrid-type Euler-Lagrange or Hamilton equations. The variational structure of the corresponding solutions makes it possible to reduce the original “mechanical” problem to an auxiliary multiobjective programming reformulation. This approach motivates possible applications of theoretical and computational results from multiobjective optimization related to the original dynamical optimization problem. We consider first order optimality conditions for optimal control problems governed by hybrid mechanical systems and also discuss some conceptual algorithms.
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    The Application of Memetic Algorithms for Forearm Crutch Design: A Case Study (2011)
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    Publication Date: 2011-03-04
    Description: Product design has normally been performed by teams, each with expertise in a specific discipline such as material, structural, and electrical systems. Traditionally, each team would use its member's experience and knowledge to develop the design sequentially. Collaborative design decisions explore the use of optimization methods to solve the design problem incorporating a number of disciplines simultaneously. It is known that such optimized product design is superior to the design found by optimizing each discipline sequentially due to the fact that it enables the exploitation of the interactions between the disciplines. In this paper, a bi-level decentralized framework based on Memetic Algorithm (MA) is proposed for collaborative design decision making using forearm crutch as the case. Two major decisions are considered: the weight and the strength. We introduce two design agents for each of the decisions. At the system level, one additional agent termed facilitator agent is created. Its main function is to locate the optimal solution for the system objective function which is derived from the Pareto concept. Thus to Pareto optimum for both weight and strength is obtained. It is demonstrated that the proposed model can converge to Pareto solutions.
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    Temporary Workforce Planning with Firm Contracts: A Model and a Simulated Annealing Heuristic (2011)
    Hindawi
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    Publication Date: 2011-03-03
    Description: The aim of this paper is to introduce a model for temporary staffing when temporary employment is managed by firm contracts and to propose a simulated annealing-based method to solve the model. Temporary employment is a policy frequently used to adjust the working hour capacity to fluctuating demand. Temporary workforce planning models have been unnecessarily simplified to account for only periodic hiring and laying off; a company can review its workforce requirement every period and make hire-fire decisions accordingly, usually with a layoff cost. We present a more realistic temporary workforce planning model that assumes a firm contract between the worker and the company, which can extend to several periods. The model assumes the traditional constraints, such as inventory balance constraints, worker availability, and labor hour mix. The costs are the inventory holding cost, training cost of the temporary workers, and the backorder cost. The mixed integer model developed for this case has been found to be difficult to solve even for small problem sizes; therefore, a simulated annealing algorithm is proposed to solve the mixed integer model. The performance of the SA algorithm is compared with the CPLEX solution.
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    A Polynomial Preconditioner for the CMRH Algorithm (2011)
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    Publication Date: 2011-03-23
    Description: Many large and sparse linear systems can be solved efficiently by restarted GMRES and CMRH methods Sadok 1999. The CMRH(m) method is less expensive and requires slightly less storage than GMRES(m). But like GMRES, the restarted CMRH method may not converge. In order to remedy this defect, this paper presents a polynomial preconditioner for CMRH-based algorithm. Numerical experiments are given to show that the polynomial preconditioner is quite simple and easily constructed and the preconditioned CMRH(m) with the polynomial preconditioner has better performance than CMRH(m).
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    Solution of Fractional Order System of Bagley-Torvik Equation Using Evolutionary Computational Intelligence (2011)
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    Publication Date: 2011-03-23
    Description: A stochastic technique has been developed for the solution of fractional order system represented by Bagley-Torvik equation. The mathematical model of the equation was developed with the help of feed-forward artificial neural networks. The training of the networks was made with evolutionary computational intelligence based on genetic algorithm hybrid with pattern search technique. Designed scheme was successfully applied to different forms of the equation. Results are compared with standard approximate analytic, stochastic numerical solvers and exact solutions.
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    Computation of Energy Release Rates for a Nearly Circular Crack (2011)
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    Publication Date: 2011-03-09
    Description: This paper deals with a nearly circular crack, Ω in the plane elasticity. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over a considered domain, Ω and it is then transformed into a similar equation over a circular region, D, using conformal mapping. Appropriate collocation points are chosen on the region D to reduce the hypersingular integral equation into a system of linear equations with (2N+1)(N+1) unknown coefficients, which will later be used in the determination of energy release rate. Numerical results for energy release rate are compared with the existing asymptotic solution and are displayed graphically.
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    Dual Solutions on Thermosolutal Marangoni Forced Convection Boundary Layer with Suction and Injection (2011)
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    Publication Date: 2011-03-10
    Description: This paper considers the extended problem of the thermosolutal Marangoni forced convection boundary layer by Pop et al. (2001) when the wall is permeable, namely, there is a suction or injection effect. The governing system of partial differential equations is transformed into a system of ordinary differential equations, and the transformed equations are solved numerically using the shooting method. The effects of suction or injection parameter f0 on the velocity, temperature, and concentration profiles are illustrated and presented in tables and figures. It is shown that dual solutions exist for the similarity parameter β less than 0.5.
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    Change Point Detection with Robust Control Chart (2011)
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    Publication Date: 2011-03-23
    Description: Monitoring a process over time using a control chart allows quick detection of unusual states. In phase I, some historical process data, assumed to come from an in-control process, are used to construct the control limits. In Phase II, the process is monitored for an ongoing basis using control limits from Phase I. In Phase II, observations falling outside the control limits or unusual patterns of observations signal that the process has shifted from in-control process settings. Such signals trigger a search for assignable cause and, if the cause is found, corrective action will be implemented to prevent its recurrence. The purpose of this paper is to introduce a new methodology appropriate for constructing a robust control chart when a nonnormal or a contaminated data that may arise in phase I state. Through extensive Monte Carlo simulations, we examine the behaviors and performances of the proposed MM robust control chart when there is a process shift in mean.
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    Robust Optimization-Based Generation Self-Scheduling under Uncertain Price (2011)
    Hindawi
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    Publication Date: 2011-03-24
    Description: This paper considers generation self-scheduling in electricity markets under uncertain price. Based on the robust optimization (denoted as RO) methodology, a new self-scheduling model, which has a complicated max-min optimization structure, is set up. By using optimal dual theory, the proposed model is reformulated to an ordinary quadratic and quadratic cone programming problems in the cases of box and ellipsoidal uncertainty, respectively. IEEE 30-bus system is used to test the new model. Some comparisons with other methods are done, and the sensitivity with respect to the uncertain set is analyzed. Comparing with the existed uncertain self-scheduling approaches, the new method has twofold characteristics. First, it does not need a prediction of distribution of random variables and just requires an estimated value and the uncertain set of power price. Second, the counterpart of RO corresponding to the self-scheduling is a simple quadratic or quadratic cone programming. This indicates that the reformulated problem can be solved by many ordinary optimization algorithms.
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    Frequency Monitoring and Control during Power System Restoration Based on Wide Area Measurement System (2011)
    Hindawi
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    Publication Date: 2011-03-01
    Description: Frequency control during power system restoration has not been strongly addressed. Operators are often concerned with the offline sizing of load and generation steps, but, nowadays, the introduction of Wide Area Measurement System (WAMS) makes it possible to monitor the stability of power system online. The constraints of WAMS operation result in some changes in power system frequency control. This paper proposes a novel methodology for frequency control and monitoring during the early steps of power system restoration based on WAMS. Detailed load modeling is achieved based on the static load modeling approach. Power generators' modeling is also accomplished utilizing the single machine equivalent of the power system based on PMU measurements. Simulation results of the presented methodology on the 39 bus New England power system clearly show the effectiveness and applicability of the proposed method. The simulation results show that the presented approach has a completely acceptable precision and an outstanding speed with less than 0.05% error. The outstanding speed of the presented approach along with the result precision will result in a great promotion in power system restoration methodologies.
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    First Integrals for Two Linearly Coupled Nonlinear Duffing Oscillators (2011)
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    Publication Date: 2011-03-01
    Description: We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Moreover, if the partial Euler-Lagrange equations are independent of derivatives, then the partial Noether operators become Noether point symmetry generators for such equations. The difference arises in the gauge terms due to Lagrangians being different for respective approaches. This study points to new ways of constructing first integrals for nonlinear equations without regard to a Lagrangian. We have illustrated it here for nonlinear Duffing oscillators.
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    Voltage Stability Control of Electrical Network Using Intelligent Load Shedding Strategy Based on Fuzzy Logic (2011)
    Hindawi
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    Publication Date: 2011-03-01
    Description: As a perspective to ensure the power system stability and to avoid the vulnerability leading to the blackouts, several preventive and curative means are adopted. In order to avoid the voltage collapse, load shedding schemes represent a suitable action to maintain the power system service quality and to control its vulnerability. In this paper, we try to propose an intelligent load shedding strategy as a new approach based on fuzzy controllers. This strategy was founded on the calculation of generated power sensitivity degree related to those injected at different network buses. During the fault phase, fuzzy controller algorithms generate monitor vectors ensuring a precalculated load shedding ratio in the purpose to reestablish the power balance and conduct the network to a new steady state.
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    A New Global Optimization Algorithm for Solving Generalized Geometric Programming (2011)
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    Publication Date: 2011-03-01
    Description: A global optimization algorithm for solving generalized geometric programming (GGP) problem is developed based on a new linearization technique. Furthermore, in order to improve the convergence speed of this algorithm, a new pruning technique is proposed, which can be used to cut away a large part of the current investigated region in which the global optimal solution does not exist. Convergence of this algorithm is proved, and some experiments are reported to show the feasibility of the proposed algorithm.
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