ALBERT — All Library Books, journals and Electronic Records Telegrafenberg

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Multipath Adaptive Tabu Search for a Vehicle Control Problem (2012)

Jukkrit Kluabwang, Deacha Puangdownreong, and Sarawut Sujitjorn

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-24

Description: Tabu search has become acceptable worldwide as one of the most efficient intelligent searches applied to various real-world problems. There have been different modifications made to the generic tabu search in recent years to achieve better performances. Among those reviewed in the introduction of this paper, the adaptive tabu search (ATS) has incorporated the backtracking and the adaptive search radius mechanisms that help accelerate the search and release it from a local solution lock. The paper explains an enhancement made to the ATS to accomplish multipath ATS (MATS) algorithms. Performances of the ATS and the MATS are evaluated using surface optimization problems, and results are presented in the paper. Finally, the MATS is applied to solve a real-world vehicle control problem.

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Synchronization of Two Rank-One Chaotic Systems without and with Delay via Linear Delayed Feedback Control (2012)

Hui Fang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-03-16

Description: This paper illustrates the presence of chaos in rank-one chaotic systems with delay via a binary test (called 0-1 test) for chaos. Chaotic synchronization between two rank-one chaotic systems without and with delay is achieved by means of Lyapunov functional and linear delayed feedback control method. Numerical simulations are implemented to verify the effectiveness of the proposed chaos synchronization scheme.

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On a Generalized Hyers-Ulam Stability of Trigonometric Functional Equations (2012)

Jaeyoung Chung and Jeongwook Chang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-03-16

Description: Let G be an Abelian group, let ℂ be the field of complex numbers, and let f,g:G→ℂ. We consider the generalized Hyers-Ulam stability for a class of trigonometric functional inequalities, |f(x-y)-f(x)g(y)+g(x)f(y)|≤ψ(y), |g(x-y)-g(x)g(y)-f(x)f(y)|≤ψ(y), where ψ:G→ℝ is an arbitrary nonnegative function.

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On the Solution of Double-Diffusive Convective Flow due to a Cone by a Linearization Method (2012)

Mahesha Narayana and Precious Sibanda

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-08

Description: The paper details the use of a nonperturbation successive linearization method to solve the coupled nonlinear boundary value problem due to double-diffusive convection from an inverted cone. Diffusion-thermo and thermal-diffusion effects have been taken into account. The governing partial differential equations are transformed into ordinary differential equations using a suitable similarity transformation. The SLM is based on successively linearizing the governing nonlinear boundary layer equations and solving the resulting higher-order deformation equations using spectral methods. The results are compared with the limited cases from previous studies and results obtained using the Matlab inbuilt bvp4c numerical algorithm and a shooting technique that uses Runge-Kutta-Fehlberg (RKF45) and Newton-Raphson schemes. These comparisons reveal the robustness and validate the usage of the linearisation method technique. The results show that the nonperturbation technique in combination with the Chebyshev spectral collocation method is an efficient numerical algorithm with assured convergence that serves as an alternative to numerical methods for solving nonlinear boundary value problems.

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MHD Flow of an Incompressible Viscous Fluid through Convergent or Divergent Channels in Presence of a High Magnetic Field (2012)

Reza Hosseini, Sadegh Poozesh, and Saeed Dinarvand

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-10

Description: The flow of an incompressible electrically conducting viscous fluid in convergent or divergent channels under the influence of an externally applied homogeneous magnetic field is studied both analytically and numerically. Navier-Stokes equations of fluid mechanics and Maxwell’s electromagnetism equations are reduced into highly non-linear ordinary differential equation. The resulting non-linear equation has been solved analytically using a very efficient technique, namely, differential transform method (DTM). The DTM solution is compared with the results obtained by a numerical method (shooting method, coupled with fourth-order Runge-Kutta scheme). The plots have revealed the physical characteristics of flow by changing angles of the channel, Hartmann and Reynolds numbers.

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Hidden and Not So Hidden Symmetries (2012)

P. G. L. Leach, K. S. Govinder, and K. Andriopoulos

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-13

Description: Hidden symmetries entered the literature in the late Eighties when it was observed that there could be gain of Lie point symmetry in the reduction of order of an ordinary differential equation. Subsequently the reverse process was also observed. Such symmetries were termed “hidden”. In each case the source of the “new” symmetry was a contact symmetry or a nonlocal symmetry, that is, a symmetry with one or more of the coefficient functions containing an integral. Recent work by Abraham-Shrauner and Govinder (2006) on the reduction of partial differential equations demonstrates that it is possible for these “hidden” symmetries to have a point origin. In this paper we show that the same phenomenon can be observed in the reduction of ordinary differential equations and in a sense loosen the interpretation of hidden symmetries.

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Analytical and Semi-Analytical Treatment of the Satellite Motion in a Resisting Medium (2012)

S. E. Abd El-Bar and F. A. Abd El-Salam

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-13

Description: The orbital dynamics of an artificial satellite in the Earth's atmosphere is considered. An analytic first-order atmospheric drag theory is developed using Lagrange's planetary equations. The short periodic perturbations due to the geopotential of all orbital elements are evaluated. And to construct a second-order analytical theory, the equations of motion become very complicated to be integrated analytically; thus we are forced to integrate them numerically using the method of Runge-Kutta of fourth order. The validity of the theory is checked on the already decayed Indian satellite ROHINI where its data are available.

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A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method (2012)

Changqing Yang and Jianhua Hou

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-13

Description: A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area of differential equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

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Statistical Behavior of a Financial Model by Lattice Fractal Sierpinski Carpet Percolation (2012)

Xu Wang and Jun Wang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-13

Description: The lattice fractal Sierpinski carpet and the percolation theory are applied to develop a new random stock price for the financial market. Percolation theory is usually used to describe the behavior of connected clusters in a random graph, and Sierpinski carpet is an infinitely ramified fractal. In this paper, we consider percolation on the Sierpinski carpet lattice, and the corresponding financial price model is given and investigated. Then, we analyze the statistical behaviors of the Hong Kong Hang Seng Index and the simulative data derived from the financial model by comparison.

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The Effects of Chemical Reaction, Hall, and Ion-Slip Currents on MHD Micropolar Fluid Flow with Thermal Diffusivity Using a Novel Numerical Technique (2012)

S. S. Motsa and S. Shateyi

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-17

Description: The problem of magnetomicropolar fluid flow, heat, and mass transfer with suction through a porous medium is numerically analyzed. The problem was studied under the effects of chemical reaction, Hall, ion-slip currents, and variable thermal diffusivity. The governing fundamental conservation equations of mass, momentum, angular momentum, energy, and concentration are converted into a system of nonlinear ordinary differential equations by means of similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is the then solved using a fairly new technique known as the successive linearization method together with the Chebyshev collocation method. A parametric study illustrating the influence of the magnetic strength, Hall and ion-slip currents, Eckert number, chemical reaction and permeability on the Nusselt and Sherwood numbers, skin friction coefficients, velocities, temperature, and concentration was carried out.

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Existence of Solutions for the Evolution p(x)-Laplacian Equation Not in Divergence Form (2012)

Changchun Liu, Junchao Gao, and Songzhe Lian

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-17

Description: The existence of weak solutions is studied to the initial Dirichlet problem of the equation ut=udiv(|∇u|p(x)−2∇u), with inf p(x)>2. We adopt the method of parabolic regularization. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions.

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Derivatives of Multivariate Bernstein Operators and Smoothness with Jacobi Weights (2012)

Jianjun Wang, Zuoxiang Peng, Shukai Duan, and Jia Jing

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: Using the modulus of smoothness, directional derivatives of multivariate Bernstein operators with weights are characterized. The obtained results partly generalize the corresponding ones for multivariate Bernstein operators without weights.

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Note on the Choquet Integral as an Interval-Valued Aggregation Operators and Their Applications (2012)

Lee-Chae Jang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: The concept of an interval-valued capacity is motivated by the goal to generalize a capacity, and it can be used for representing an uncertain capacity. In this paper, we define the discrete interval-valued capacities, a measure of the entropy of a discrete interval-valued capacity, and, Choquet integral with respect to a discrete interval-valued capacity. In particular, we discuss the Choquet integral as an interval-valued aggregation operator and discuss an application of them.

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Geodesic Effect Near an Elliptical Orbit (2012)

Alina-Daniela Vîlcu

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: Using a differential geometric treatment, we analytically derived the expression for De Sitter (geodesic) precession in the elliptical motion of the Earth through the gravitational field of the Sun with Schwarzschild's metric. The expression obtained in this paper in a simple way, using a classical approach, agrees with that given in B. M. Barker and R. F. O'Connell (1970, 1975) in a different setting, using the tools of Newtonian mechanics and the Euler-Lagrange equations.

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Three-Step Fixed Point Iteration for Generalized Multivalued Mapping in Banach Spaces (2012)

Zhanfei Zuo

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: The convergence of three-step fixed point iterative processes for generalized multivalued nonexpansive mapping was considered in this paper. Under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the generalized multivalued nonexpansive mapping. Our results extend and improve some recent results.

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(λ,μ)-Fuzzy Version of Ideals, Interior Ideals, Quasi-Ideals, and Bi-Ideals (2012)

Yuming Feng and P. Corsini

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: We introduced (λ,μ)-fuzzy ideals, (λ,μ)-fuzzy interior ideals, (λ,μ)-fuzzy quasi-ideals, and (λ,μ)-fuzzy bi-ideals of an ordered semigroup and studied them. When λ=0 and μ=1, we meet the ordinary fuzzy ones. This paper can be seen as a generalization of Kehayopulu and Tsingelis (2006), Kehayopulu and Tsingelis (2007), and Yao (2009).

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Periodic Points and Fixed Points for the Weaker (ϕ,φ)-Contractive Mappings in Complete Generalized Metric Spaces (2012)

Chi-Ming Chen and W. Y. Sun

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: We introduce the notion of weaker (ϕ,φ)-contractive mapping in complete metric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature.

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An Analytical Approach to the Analysis of Guard-Channel-Based Call Admission Control in Wireless Cellular Networks (2012)

Hyung; Man Kim, Agassi Melikov, Mehriban Fattakhova, and Che; Soong Kim

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: We develop an analytical approach to the performance analysis and optimization of wireless cellular networks for which different types of calls are prioritized based on a channel reservation scheme. We assume that the channel occupancy time differs for new and handover calls. We obtain simple formulas for calculating quality of service (QoS) metrics and solve some problems related to finding the optimal values of guard channels as well as present the results of numerical experiments.

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Filtering-Based Fault Detection for Stochastic Markovian Jump System with Distributed Time-Varying Delays and Mixed Modes (2012)

Yucai Ding, Hong Zhu, Shouming Zhong, Yuping Zhang, and Jianwei Xia

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-26

Description: The problem of fault detection for stochastic Markovian jump system is considered. The system under consideration involves discrete and distributed time-varying delays, Itô-type stochastic disturbance, and different system and delay modes. The aim of this paper is to design a fault detection filter such that the fault detection system is stochastically stable and satisfies a prescribed disturbance attenuation level. By using a novel Lyapunov functional, a mix-mode-dependent sufficient condition is formulated in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed main results.

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Existence and Uniqueness of Homoclinic Solution for a Class of Nonlinear Second-Order Differential Equations (2012)

Lijuan Chen and Shiping Lu

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-26

Description: The authors study the existence and uniqueness of a set with -periodic solutions for a class of second-order differential equations by using Mawhin's continuation theorem and some analysis methods, and then a unique homoclinic orbit is obtained as a limit point of the above set of -periodic solutions.

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Integral Bifurcation Method together with a Translation-Dilation Transformation for Solving an Integrable 2-Component Camassa-Holm Shallow Water System (2012)

Weiguo Rui and Yao Long

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-26

Description: An integrable 2-component Camassa-Holm (2-CH) shallow water system is studied by using integral bifurcation method together with a translation-dilation transformation. Many traveling wave solutions of nonsingular type and singular type, such as solitary wave solutions, kink wave solutions, loop soliton solutions, compacton solutions, smooth periodic wave solutions, periodic kink wave solution, singular wave solution, and singular periodic wave solution are obtained. Further more, their dynamic behaviors are investigated. It is found that the waveforms of some traveling wave solutions vary with the changes of parameter, that is to say, the dynamic behavior of these waves partly depends on the relation of the amplitude of wave and the level of water.

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General Helices of AW(k)-Type in the Lie Group (2012)

Dae Won Yoon

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-26

Description: We study curves of AW(k)-type in the Lie group G with a bi-invariant metric. Also, we characterize general helices in terms of AW(k)-type curve in the Lie group G.

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Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems (2012)

Qi Wang and Jiechang Wen

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-26

Description: This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential -method is applied to and it is shown that the exponential -method has the same order of convergence as that of the classical -method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples.

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Numerical Identification of Multiparameters in the Space Fractional Advection Dispersion Equation by Final Observations (2012)

Dali Zhang, Gongsheng Li, Guangsheng Chi, Xianzheng Jia, and Huiling Li

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-25

Description: This paper deals with an inverse problem for identifying multiparameters in 1D space fractional advection dispersion equation (FADE) on a finite domain with final observations. The parameters to be identified are the fractional order, the diffusion coefficient, and the average velocity in the FADE. The forward problem is solved by a finite difference scheme, and then an optimal perturbation regularization algorithm is introduced to determine the three parameters simultaneously. Numerical inversions are performed both with the accurate data and noisy data, and several factors having influences on realization of the algorithm are discussed. The inversion solutions are in good approximations to the exact solutions demonstrating the efficiency of the proposed algorithm.

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LMI Approach to Stability Analysis of Cohen-Grossberg Neural Networks with -Laplace Diffusion (2012)

Xiongrui Wang, Ruofeng Rao, and Shouming Zhong

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-25

Description: The nonlinear -Laplace diffusion () was considered in the Cohen-Grossberg neural network (CGNN), and a new linear matrix inequalities (LMI) criterion is obtained, which ensures the equilibrium of CGNN is stochastically exponentially stable. Note that, if , -Laplace diffusion is just the conventional Laplace diffusion in many previous literatures. And it is worth mentioning that even if , the new criterion improves some recent ones due to computational efficiency. In addition, the resulting criterion has advantages over some previous ones in that both the impulsive assumption and diffusion simulation are more natural than those of some recent literatures.

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Empirical Likelihood Estimation for Population Pharmacokinetic Study Based on Generalized Linear Model (2012)

Fang-rong Yan, Jin-guan Lin, Yuan Huang, Jun-lin Liu, and Tao Lu

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-28

Description: To obtain efficient estimation of parameters is a major objective in population pharmacokinetic study. In this paper, we propose an empirical likelihood-based method to analyze the population pharmacokinetic data based on the generalized linear model. A nonparametric version of the Wilk's theorem for the limiting distributions of the empirical likelihood ratio is derived. Simulations are conducted to demonstrate the accuracy and efficiency of empirical likelihood method. An application illustrating our methods and supporting the simulation study results is presented. The results suggest that the proposed method is feasible for population pharmacokinetic data.

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The Effects of Control Domain Position on Optimal Control of Cardiac Arrhythmia (2012)

Kin Wei Ng and Ahmad Rohanin

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-20

Description: We study the effects of control domain position on optimal control problem of cardiac arrhythmia. The well-established mathematical model, namely, the monodomain model, is used to represent the electrical behavior of the cardiac tissue. Two test cases are considered in this paper: the control domain for Test Case 1 is close to the excitation domain, while the control domain for Test Case 2 is a little bit far away from the excitation domain. The modified Dai-Yuan nonlinear conjugate gradient method is employed for computing the optimal applied extracellular current. Our experiment results show that the excitation wavefronts are successfully dampened out for both test cases. Also, experiment results show that the position of the control domain for Test Case 1 is preferable than that of Test Case 2 during the defibrillation process.

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Numerical Solution for Complex Systems of Fractional Order (2012)

Rabha W. Ibrahim

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-21

Description: By using a complex transform, we impose a system of fractional order in the sense of Riemann-Liouville fractional operators. The analytic solution for this system is discussed. Here, we introduce a method of homotopy perturbation to obtain the approximate solutions. Moreover, applications are illustrated.

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The Mask of Odd Points -Ary Interpolating Subdivision Scheme (2012)

Ghulam Mustafa, Jiansong Deng, Pakeeza Ashraf, and Najma Abdul Rehman

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-11-08

Description: We present an explicit formula for the mask of odd points -ary, for any odd , interpolating subdivision schemes. This formula provides the mask of lower and higher arity schemes. The 3-point and 5-point -ary schemes introduced by Lian, 2008, and ()-point -ary schemes introduced by, Lian, 2009, are special cases of our explicit formula. Moreover, other well-known existing odd point -ary schemes including the schemes introduced by Zheng et al., 2009, can easily be generated by our formula. In addition, error bounds between subdivision curves and control polygons of schemes are computed. It has been noticed that error bounds decrease when the complexity of the scheme decreases and vice versa. Also, as we increase arity of the schemes the error bounds decrease. Furthermore, we present brief comparison of total absolute curvature of subdivision schemes having different arity with different complexity. Convexity preservation property of scheme is also presented.

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Applying Randomness Effectively Based on Random Forests for Classification Task of Datasets of Insufficient Information (2012)

Hyontai Sug

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-11-08

Description: Random forests are known to be good for data mining of classification tasks, because random forests are robust for datasets having insufficient information possibly with some errors. But applying random forests blindly may not produce good results, and a dataset in the domain of rotogravure printing is one of such datasets. Hence, in this paper, some best classification accuracy based on clever application of random forests to predict the occurrence of cylinder bands in rotogravure printing is investigated. Since random forests could generate good results with an appropriate combination of parameters like the number of randomly selected attributes for each split and the number of trees in the forests, an effective data mining procedure considering the property of the target dataset by way of trial random forests is investigated. The effectiveness of the suggested procedure is shown by experiments with very good results.

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Complete Synchronization of Strictly Different Chaotic Systems (2012)

Gualberto Solís-Perales

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-11-09

Description: The criteria for complete synchronization of strictly different chaotic systems using feedback control are presented in this paper. Complete synchronization is achieved when all the states in the slave system are synchronous with the corresponding state in the master system. We illustrate that using a single input and single output control scheme, the synchronization of a class of strictly different systems is obtained in partial form. To overcome this problem we show that a multiple input and multiple output control scheme with an equal number of inputs and outputs than the order system is required in order to obtain the complete synchronization. This procedure is used to synchronize the Rössler and the Chen systems as an example. We also demonstrate that if the synchronization scheme considers less inputs and outputs, the partial-state synchronization is obtained.

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Modified Firefly Algorithm (2012)

Surafel Luleseged Tilahun and Hong Choon Ong

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-11-12

Description: Firefly algorithm is one of the new metaheuristic algorithms for optimization problems. The algorithm is inspired by the flashing behavior of fireflies. In the algorithm, randomly generated solutions will be considered as fireflies, and brightness is assigned depending on their performance on the objective function. One of the rules used to construct the algorithm is, a firefly will be attracted to a brighter firefly, and if there is no brighter firefly, it will move randomly. In this paper we modify this random movement of the brighter firefly by generating random directions in order to determine the best direction in which the brightness increases. If such a direction is not generated, it will remain in its current position. Furthermore the assignment of attractiveness is modified in such a way that the effect of the objective function is magnified. From the simulation result it is shown that the modified firefly algorithm performs better than the standard one in finding the best solution with smaller CPU time.

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Numerical Simulation of Solitary Wave Induced Flow Motion around a Permeable Submerged Breakwater (2012)

Jisheng Zhang, Jinhai Zheng, Dong-Sheng Jeng, and Gang Wang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-11-12

Description: This paper presents a numerical model for the simulation of solitary wave transformation around a permeable submerged breakwater. The wave-structure interaction is obtained by solving the Volume-Averaged Reynolds-Averaged Navier-Stokes governing equations (VARANS) and volume of fluid (VOF) theory. This model is applied to understand the effects of porosity, equivalent mean diameter of porous media, structure height, and structure width on the propagation of a solitary wave in the vicinity of a permeable submerged structure. The results show that solitary wave propagation around a permeable breakwater is essentially different from that around impermeable one. It is also found that the structure porosity has more impact than equivalent mean diameter on the wave transformation and flow structure. After interacting with the higher structure, the wave has smaller wave height behind the structure with a lower travelling speed. When the wave propagates over the breakwater with longer width, the wave travelling speed is obviously reduced with more wave energy dissipated inside porous structure.

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Combined Visibility and Surrounding Triangles Method for Simulation of Crack Discontinuities in Meshless Methods (2012)

H. Pirali, F. Djavanroodi, and M. Haghpanahi

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-11-12

Description: In this paper a combined node searching algorithm for simulation of crack discontinuities in meshless methods called combined visibility and surrounding triangles (CVT) is proposed. The element free Galerkin (EFG) method is employed for stress analysis of cracked bodies. The proposed node searching algorithm is based on the combination of surrounding triangles and visibility methods; the surrounding triangles method is used for support domains of nodes and quadrature points generated at the vicinity of crack faces and the visibility method is used for points located on the crack faces. In comparison with the conventional methods, such as the visibility, the transparency, and the diffraction method, this method is simpler with reasonable efficiency. To show the performance of this method, linear elastic fracture mechanics analyses are performed on number of standard test specimens and stress intensity factors are calculated. It is shown that the results are in good agreement with the exact solution and with those generated by the finite element method (FEM).

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Random -Policy Geo/G/1 Queue with Startup and Closedown Times (2012)

Tsung-Yin Wang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-11-12

Description: This study investigates a random -policy Geo/G/1 queue with startup and closedown times. is newly determined every time a new cycle begins. When random customers are accumulated, the server is immediately turned on but is temporarily unavailable to the waiting customers. It needs a startup time before starting providing service. After all customers in the system are served exhaustively, the server is shut down by a closedown time. Using the generating function and supplementary variable technique, analytic solutions of system size, lengths of state periods, and sojourn time are derived.

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Optimization on Production-Inventory Problem with Multistage and Varying Demand (2012)

Duan Gang, Chen Li, Li Yin-Zhen, Song Jie-Yan, and Akhtar Tanweer

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-11-14

Description: This paper addresses production-inventory problem for the manufacturer by explicitly taking into account multistage and varying demand. A nonlinear hybrid integer constrained optimization is modeled to minimize the total cost including setup cost and holding cost in the planning horizon. A genetic algorithm is developed for the problem. A series of computational experiments with different sizes is used to demonstrate the efficiency and universality of the genetic algorithm in terms of the running time and solution quality. At last the combination of crossover probability and mutation probability is tested for all problems and a law is found for large size.

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Using Wavelets to Understand the Relationship between Mortgages and Gross Domestic Product in Spain (2012)

C. González-Concepción, M. C. Gil-Fariña, and C. Pestano-Gabino

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-09

Description: We use wavelet multiresolution decomposition and cross-wavelet analysis to reveal certain properties in financial data related to mortgages to households and gross domestic product data in Spain. Wavelet techniques possess many desirable properties, some of which are useful as a vehicle for analysing economic and financial data. In our case, wavelets are useful for drawing conclusions both in the time and frequency domains and for obtaining information on the different phases through which the study variables progress.

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Some Aspects of -Units in BCK-Algebras (2012)

Hee Sik Kim, J. Neggers, and Keum Sook So

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-11

Description: We explore properties of the set of d-units of a -algebra. A property of interest in the study of -units in -algebras is the weak associative property. It is noted that many other -algebras, especially -algebras, are in fact weakly associative. The existence of -algebras which are not weakly associative is demonstrated. Moreover, the notions of a -integral domain and a left-injectivity are discussed.

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A Novel Four-Dimensional Energy-Saving and Emission-Reduction System and Its Linear Feedback Control (2012)

Minggang Wang and Hua Xu

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-12

Description: This paper reports a new four-dimensional energy-saving and emission-reduction chaotic system. The system is obtained in accordance with the complicated relationship between energy saving and emission reduction, carbon emission, economic growth, and new energy development. The dynamics behavior of the system will be analyzed by means of Lyapunov exponents and equilibrium points. Linear feedback control methods are used to suppress chaos to unstable equilibrium. Numerical simulations are presented to show these results.

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New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the -Dimensional Evolution Equation (2012)

Hasibun Naher and Farah Aini Abdullah

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-12

Description: The generalized Riccati equation mapping is extended with the basic -expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct twenty-seven traveling wave solutions for the (2+1)-dimensional modified Zakharov-Kuznetsov equation by applying this method. Further, the auxiliary equation is executed with arbitrary constant coefficients and called the generalized Riccati equation. The obtained solutions including solitons and periodic solutions are illustrated through the hyperbolic functions, the trigonometric functions, and the rational functions. In addition, it is worth declaring that one of our solutions is identical for special case with already established result which verifies our other solutions. Moreover, some of obtained solutions are depicted in the figures with the aid of Maple.

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Exponential Admissibility and Control of Switched Singular Time-Delay Systems: An Average Dwell Time Approach (2012)

Jinxing Lin and Zhifeng Gao

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-14

Description: This paper deals with the problems of exponential admissibility and control for a class of continuous-time switched singular systems with time-varying delay. The controllers to be designed include both the state feedback (SF) and the static output feedback (SOF). First, by using the average dwell time scheme, the piecewise Lyapunov function, and the free-weighting matrix technique, an exponential admissibility criterion, which is not only delay-range-dependent but also decay-rate-dependent, is derived in terms of linear matrix inequalities (LMIs). A weighted performance criterion is also provided. Then, based on these, the solvability conditions for the desired SF and SOF controllers are established by employing the LMI technique, respectively. Finally, two numerical examples are given to illustrate the effectiveness of the proposed approach.

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Neurogenetic Algorithm for Solving Combinatorial Engineering Problems (2012)

M. Jalali Varnamkhasti and Nasruddin Hassan

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-09-24

Description: Diversity of the population in a genetic algorithm plays an important role in impeding premature convergence. This paper proposes an adaptive neurofuzzy inference system genetic algorithm based on sexual selection. In this technique, for choosing the female chromosome during sexual selection, a bilinear allocation lifetime approach is used to label the chromosomes based on their fitness value which will then be used to characterize the diversity of the population. The motivation of this algorithm is to maintain the population diversity throughout the search procedure. To promote diversity, the proposed algorithm combines the concept of gender and age of individuals and the fuzzy logic during the selection of parents. In order to appraise the performance of the techniques used in this study, one of the chemistry problems and some nonlinear functions available in literature is used.

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An Inverse Problem for a Class of Linear Stochastic Evolution Equations (2012)

Yuhuan Zhao

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-09-29

Description: An inverse problem for a linear stochastic evolution equation is researched. The stochastic evolution equation contains a parameter with values in a Hilbert space. The solution of the evolution equation depends continuously on the parameter and is Fréchet differentiable with respect to the parameter. An optimization method is provided to estimate the parameter. A sufficient condition to ensure the existence of an optimal parameter is presented, and a necessary condition that the optimal parameter, if it exists, should satisfy is also presented. Finally, two examples are given to show the applications of the above results.

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Theoretical and Empirical Analyses of an Improved Harmony Search Algorithm Based on Differential Mutation Operator (2012)

Longquan Yong, Sanyang Liu, Jianke Zhang, and Quanxi Feng

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-02

Description: Harmony search (HS) method is an emerging metaheuristic optimization algorithm. In this paper, an improved harmony search method based on differential mutation operator (IHSDE) is proposed to deal with the optimization problems. Since the population diversity plays an important role in the behavior of evolution algorithm, the aim of this paper is to calculate the expected population mean and variance of IHSDE from theoretical viewpoint. Numerical results, compared with the HSDE, NGHS, show that the IHSDE method has good convergence property over a test-suite of well-known benchmark functions.

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On the Computation of the Efficient Frontier of the Portfolio Selection Problem (2012)

Clara Calvo, Carlos Ivorra, and Vicente Liern

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-05

Description: An easy-to-use procedure is presented for improving the -constraint method for computing the efficient frontier of the portfolio selection problem endowed with additional cardinality and semicontinuous variable constraints. The proposed method provides not only a numerical plotting of the frontier but also an analytical description of it, including the explicit equations of the arcs of parabola it comprises and the change points between them. This information is useful for performing a sensitivity analysis as well as for providing additional criteria to the investor in order to select an efficient portfolio. Computational results are provided to test the efficiency of the algorithm and to illustrate its applications. The procedure has been implemented in Mathematica.

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Further Results on Derivations of Ranked Bigroupoids (2012)

Young Bae Jun, Hee Sik Kim, and Eun Hwan Roh

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-05

Description: Further properties on -self-(co)derivations of ranked bigroupoids are investigated, and conditions for an -self-(co)derivation to be regular are provided. The notion of ranked -subsystems is introduced, and related properties are investigated.

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Global Stability of a SLIT TB Model with Staged Progression (2012)

Yakui Xue and Xiaohong Wang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-05

Description: Because the latent period and the infectious period of tuberculosis (TB) are very long, it is not reasonable to consider the time as constant. So this paper formulates a mathematical model that divides the latent period and the infectious period into n-stages. For a general n-stage stage progression (SP) model with bilinear incidence, we analyze its dynamic behavior. First, we give the basic reproduction number . Moreover, if , the disease-free equilibrium is globally asymptotically stable and the disease always dies out. If , the unique endemic equilibrium is globally asymptotically stable and the disease persists at the endemic equilibrium.

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Asymptotic Stability of a Class of Impulsive Delay Differential Equations (2012)

G. L. Zhang, M. H. Song, and M. Z. Liu

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-05

Description: This paper is concerned with a class of linear impulsive delay differential equations. Asymptotic stability of analytic solutions of this kind of equations is studied by the property of delay differential equations without impulsive perturbations. New numerical methods for this kind of equations are constructed. The convergence and asymptotic stability of the methods for this kind of equations are studied.

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Numerical Solution of Weakly Singular Integrodifferential Equations on Closed Smooth Contour in Lebesgue Spaces (2012)

Feras M. Al Faqih

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-05

Description: The present paper deals with the justification of solvability conditions and properties of solutions for weakly singular integro-differential equations by collocation and mechanical quadrature methods. The equations are defined on an arbitrary smooth closed contour of the complex plane. Error estimates and convergence for the investigated methods are established in Lebesgue spaces.

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Simple Motion Evasion Differential Game of Many Pursuers and One Evader with Integral Constraints on Control Functions of Players (2012)

Gafurjan Ibragimov and Yusra Salleh

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-15

Description: We consider an evasion differential game of many pursuers and one evader with integral constraints in the plane. The game is described by simple equations. Each component of the control functions of players is subjected to integral constraint. Evasion is said to be possible if the state of the evader does not coincide with that of any pursuer. Strategy of the evader is constructed based on controls of the pursuers with lag. A sufficient condition of evasion from many pursuers is obtained and an illustrative example is provided.

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Robust Adaptive Generalized Projective Synchronization of Chaotic Systems with Uncertain Disturbances (2012)

Zhen Jia and Guangming Deng

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-15

Description: The generalized projective synchronization (GPS) of chaotic systems with uncertain parameter noise and external disturbance is discussed. Based on the adaptive technique, a response system is constructed, and a novel adaptive controller is designed to guarantee the GPS between the drive-response systems, and to eliminate the effect of external disturbance and parameters noise on GPS. The conclusion is proved theoretically, and corresponding numerical simulations are provided to verify the effectiveness of the proposed method.

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Some Properties of Certain Integral Operators on New Subclasses of Analytic Functions with Complex Order (2012)

Aabed Mohammed and Maslina Darus

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-13

Description: We define new subclasses of -valent meromorphic functions with complex order. We prove some properties for certain integral operators on these subclasses.

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Uniformly Strong Persistence for a Delayed Predator-Prey Model (2012)

Changjin Xu, Yuanfu Shao, and Peiluan Li

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-10

Description: An asymptotically periodic predator-prey model with time delay is investigated. Some sufficient conditions for the uniformly strong persistence of the system are obtained. Our result is an important complementarity to the earlier results.

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An Elite Decision Making Harmony Search Algorithm for Optimization Problem (2012)

Lipu Zhang, Yinghong Xu, and Yousong Liu

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-01

Description: This paper describes a new variant of harmony search algorithm which is inspired by a well-known item “elite decision making.” In the new algorithm, the good information captured in the current global best and the second best solutions can be well utilized to generate new solutions, following some probability rule. The generated new solution vector replaces the worst solution in the solution set, only if its fitness is better than that of the worst solution. The generating and updating steps and repeated until the near-optimal solution vector is obtained. Extensive computational comparisons are carried out by employing various standard benchmark optimization problems, including continuous design variables and integer variables minimization problems from the literature. The computational results show that the proposed new algorithm is competitive in finding solutions with the state-of-the-art harmony search variants.

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Eisenstein Series Identities Involving the Borweins' Cubic Theta Functions (2012)

Ernest X. W. Xia and Olivia X. M. Yao

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-09-26

Description: Based on the theories of Ramanujan's elliptic functions and the (p, k)-parametrization of theta functions due to Alaca et al. (2006, 2007, 2006) we derive certain Eisenstein series identities involving the Borweins' cubic theta functions with the help of the computer. Some of these identities were proved by Liu based on the fundamental theory of elliptic functions and some of them may be new. One side of each identity involves Eisenstein series, the other products of the Borweins' cubic theta functions. As applications, we evaluate some convolution sums. These evaluations are different from the formulas given by Alaca et al.

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Coupled Coincidence Point Results for -Weak Contractions in Partially Ordered Metric Spaces (2012)

A. Razani and V. Parvaneh

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-09-26

Description: In this paper coupled coincidence points of mappings satisfying a nonlinear contractive condition in the framework of partially ordered metric spaces are obtained. Our results extend the results of Harjani et al. (2011). Moreover, an example of the main result is given. Finally, some coupled coincidence point results for mappings satisfying some contraction conditions of integral type in partially ordered complete metric spaces are deduced.

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New Second-Order Finite Difference Scheme for the Problem of Contaminant in Groundwater Flow (2012)

Quanyong Zhu, Quanxiang Wang, Ju Fu, and Zhiyue Zhang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-09-26

Description: We develop a new efficient second-order finite difference scheme for two-dimensional problem of contaminant in groundwater flow. Theoretical analysis shows that the scheme is second-order convergence in the norm and is unconditionally stable. Numerical results demonstrate that the error measures of the second-order scheme are several times smaller than those of the standard implicit finite difference scheme.

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Delayed Stochastic Linear-Quadratic Control Problem and Related Applications (2012)

Li Chen, Zhen Wu, and Zhiyong Yu

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-09-27

Description: We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.

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Comparison Results on Preconditioned GAOR Methods for Weighted Linear Least Squares Problems (2012)

Guangbin Wang, Yanli Du, and Fuping Tan

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-09-27

Description: We present preconditioned generalized accelerated overrelaxation methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GAOR methods converge faster than the GAOR method whenever the GAOR method is convergent. Finally, we give a numerical example to confirm our theoretical results.

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Synchronized Hopf Bifurcation Analysis in a Delay-Coupled Semiconductor Lasers System (2012)

Gang Zhu and Junjie Wei

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-01

Description: The dynamics of a system of two semiconductor lasers, which are delay coupled via a passive relay within the synchronization manifold, are investigated. Depending on the coupling parameters, the system exhibits synchronized Hopf bifurcation and the stability switches as the delay varies. Employing the center manifold theorem and normal form method, an algorithm is derived for determining the Hopf bifurcation properties. Some numerical simulations are carried out to illustrate the analysis results.

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Numerical Recovery of Gas Flows in Pipeline Systems (2012)

Vadim E. Seleznev

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-03

Description: Optimal control, prevention and investigation of accidents, and detection of discrepancies in estimated gas supply and distribution volumes are relevant problems of trunkline operation. Efficient dealing with these production tasks is based on the numerical recovery of spacetime distribution of nonisothermal transient flow parameters of transmitted gas mixtures based on full-scale measurements in a substantially limited number of localities spaced considerable distances apart along the gas pipelines. The paper describes a practical method of such recovery by defining and solving a special identification problem. Simulations of product flow parameters in extended branched pipelines, involving calculations of the target function and constraint function for the identification problem of interest, are done in the 1D statement. In conclusion, results of practical application of the method in the gas industry are briefly discussed.

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The Hamiltonian System Method for the Stress Analysis in Axisymmetric Problems of Viscoelastic Solids (2012)

W. X. Zhang, Y. Bai, and F. Yuan

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-03

Description: With the use of the Laplace integral transformation and state space formalism, the classical axial symmetric quasistatic problem of viscoelastic solids is discussed. By employing the method of separation of variables, the governing equations under Hamiltonian system are established, and hence, general solutions including the zero eigensolutions and nonzero eigensolutions are obtained analytically. Due to the completeness property of the general solutions, their linear combinations can describe various boundary conditions. Simply by applying the adjoint relationships of the symplectic orthogonality, the eigensolution expansion method for boundary condition problems is given. In the numerical examples, stress distributions of a circular cylinder under the end and lateral boundary conditions are obtained. The results exhibit that stress concentrations appear due to the displacement constraints, and that the effects are seriously confined near the constraints, decreasing rapidly with the distance from the boundary.

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Method of Infinite System of Equations for Problems in Unbounded Domains (2012)

Dang Quang A and Tran Dinh Hung

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-03

Description: Many problems of mechanics and physics are posed in unbounded (or infinite) domains. For solving these problems one typically limits them to bounded domains and find ways to set appropriate conditions on artificial boundaries or use quasi-uniform grid that maps unbounded domains to bounded ones. Differently from the above methods we approach to problems in unbounded domains by infinite system of equations. In this paper we present starting results in this approach for some one-dimensional problems. The problems are reduced to infinite system of linear equations. A method for obtaining approximate solution with a given accuracy is proposed. Numerical experiments for several examples show the effectiveness of the offered method.

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Global Existence and Boundedness of Solutions to a Second-Order Nonlinear Differential System (2012)

Changjian Wu, Shushuang Hao, and Changwei Xu

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-04

Description: We investigate the global existence and boundedness of solutions to a second-order nonlinear differential system.

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Symmetry Feature and Construction for the 3-Band Tight Framelets with Prescribed Properties (2012)

Jianjun Sun, Bin Huang, Xiaodong Chen, and Lihong Cui

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-04

Description: A construction approach for the 3-band tight wavelet frames by factorization of paraunitary matrix is developed. Several necessary constraints on the filter lengths and symmetric features of wavelet frames are investigated starting at the constructed paraunitary matrix. The matrix is a symmetric extension of the polyphase matrix corresponding to 3-band tight wavelet frames. Further, the parameterizations of 3-band tight wavelet frames with filter lengths are established. Examples of framelets with symmetry/antisymmetry and Sobolev exponent are computed by appropriately choosing the parameters in the scheme.

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Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory (2012)

Jianguo Tang, Kun She, and William Zhu

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-05

Description: Constructing structures with other mathematical theories is an important research field of rough sets. As one mathematical theory on sets, matroids possess a sophisticated structure. This paper builds a bridge between rough sets and matroids and establishes the matroidal structure of rough sets. In order to understand intuitively the relationships between these two theories, we study this problem from the viewpoint of graph theory. Therefore, any partition of the universe can be represented by a family of complete graphs or cycles. Then two different kinds of matroids are constructed and some matroidal characteristics of them are discussed, respectively. The lower and the upper approximations are formulated with these matroidal characteristics. Some new properties, which have not been found in rough sets, are obtained. Furthermore, by defining the concept of lower approximation number, the rank function of some subset of the universe and the approximations of the subset are connected. Finally, the relationships between the two types of matroids are discussed, and the result shows that they are just dual matroids.

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Adaptive Stabilization of the Korteweg-de Vries-Burgers Equation with Unknown Dispersion (2012)

Xiaoyan Deng, Lixin Tian, and Wenxia Chen

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-05

Description: This paper studies the adaptive control problem of the Korteweg-de Vries-Burgers equation. Using the Lyapunov function method, we prove that the closed-loop system including the parameter estimator as a dynamic component is globally stable. Furthermore, we show that the state of the system is regulated to zero by developing an alternative to Barbalat's lemma which cannot be used in the present situation. The closed-loop system is shown to be well posed.

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Hyperspherical Manifold for EEG Signals of Epileptic Seizures (2012)

Tahir Ahmad and Vinod Ramachandran

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-02

Description: The mathematical modelling of EEG signals of epileptic seizures presents a challenge as seizure data is erratic, often with no visible trend. Limitations in existing models indicate a need for a generalized model that can be used to analyze seizures without the need for apriori information, whilst minimizing the loss of signal data due to smoothing. This paper utilizes measure theory to design a discrete probability measure that reformats EEG data without altering its geometric structure. An analysis of EEG data from three patients experiencing epileptic seizures is made using the developed measure, resulting in successful identification of increased potential difference in portions of the brain that correspond to physical symptoms demonstrated by the patients. A mapping then is devised to transport the measure data onto the surface of a high-dimensional manifold, enabling the analysis of seizures using directional statistics and manifold theory. The subset of seizure signals on the manifold is shown to be a topological space, verifying Ahmad's approach to use topological modelling.

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Strong Convergence Theorems for the Split Common Fixed Point Problem for Countable Family of Nonexpansive Operators (2012)

Cuijie Zhang and Songnian He

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-07-03

Description: We introduce a new iterative algorithm for solving the split common fixed point problem for countable family of nonexpansive operators. Under suitable assumptions, we prove that the iterative algorithm strongly converges to a solution of the problem.

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Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms (2012)

Zhigang Pan, Hong Luo, and Tian Ma

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-07-13

Description: We consider the global existence of strong solution u, corresponding to a class of fully nonlinear wave equations with strongly damped terms utt-kΔut=f(x,Δu)+g(x,u,Du,D2u) in a bounded and smooth domain Ω in Rn, where f(x,Δu) is a given monotone in Δu nonlinearity satisfying some dissipativity and growth restrictions and g(x,u,Du,D2u) is in a sense subordinated to f(x,Δu). By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solution u∈Lloc∞((0,∞),W2,p(Ω)∩W01,p(Ω)).

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The Improved ( (2012)

Hasibun Naher and Farah Aini Abdullah

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-17

Description: we apply the improved (

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Asymptotic Behavior for a Nondissipative and Nonlinear System of the Kirchhoff Viscoelastic Type (2012)

Nasser-Eddine Tatar

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-17

Description: A wave equation of the Kirchhoff type with several nonlinearities is stabilized by a viscoelastic damping. We consider the case of nonconstant (and unbounded) coefficients. This is a nondissipative case, and as a consequence the nonlinear terms cannot be estimated in the usual manner by the initial energy. We suggest a way to get around this difficulty. It is proved that if the solution enters a certain region, which we determine, then it will be attracted exponentially by the equilibrium.

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The Hypergroupoid Semigroups as Generalizations of the Groupoid Semigroups (2012)

Jeong Soon Han, Hee Sik Kim, and J. Neggers

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-17

Description: We introduce the notion of hypergroupoids (

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Symbolic Computation and the Extended Hyperbolic Function Method for Constructing Exact Traveling Solutions of Nonlinear PDEs (2012)

Huang Yong, Shang Yadong, and Yuan Wenjun

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-12

Description: On the basis of the computer symbolic system Maple and the extended hyperbolic function method, we develop a more mathematically rigorous and systematic procedure for constructing exact solitary wave solutions and exact periodic traveling wave solutions in triangle form of various nonlinear partial differential equations that are with physical backgrounds. Compared with the existing methods, the proposed method gives new and more general solutions. More importantly, the method provides a straightforward and effective algorithm to obtain abundant explicit and exact particular solutions for large nonlinear mathematical physics equations. We apply the presented method to two variant Boussinesq equations and give a series of exact explicit traveling wave solutions that have some more general forms. So consequently, the efficiency and the generality of the proposed method are demonstrated.

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The Dynamics of an Eco-Epidemiological Model with Nonlinear Incidence Rate (2012)

Raid Kamel Naji and Arkan N. Mustafa

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-12

Description: This paper treats the dynamical behavior of eco-epidemiological model with nonlinear incidence rate. A Holling type II prey-predator model with SI-type of disease in prey has been proposed and analyzed. The existence, uniqueness, and boundedness of the solution of the system are studied. The local and global dynamical behaviors are investigated. The conditions, which guarantee the occurring of Hopf bifurcation of the system, are established. Finally, further investigations for the global dynamics of the proposed system are carried out with the help of numerical simulations.

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The Global Convergence of a New Mixed Conjugate Gradient Method for Unconstrained Optimization (2012)

Yang Yueting and Cao Mingyuan

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-18

Description: We propose and generalize a new nonlinear conjugate gradient method for unconstrained optimization. The global convergence is proved with the Wolfe line search. Numerical experiments are reported which support the theoretical analyses and show the presented methods outperforming CGDESCENT method.

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Fuzzy Linguistic Induced Ordered Weighted Averaging Operator and Its Application (2012)

Sidong Xian

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-10-18

Description: With respect to multiple attribute group decision making (MAGDM) problems, in which the attribute weights take the form of real numbers, and the attribute values take the form of fuzzy linguistic scale variables, a decision analysis approach is proposed. In this paper, we develop a new fuzzy linguistic induce OWA (FLIOWA) operator and analyze the properties of it by utilizing some operational laws of fuzzy linguistic scale variables. A method based on the FLIOWA operators for multiple attribute group decision making is presented. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.

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Observer-Based Finite-Time H∞ Control of Singular Markovian Jump Systems (2012)

Yingqi Zhang, Wei Cheng, Xiaowu Mu, and Xiulan Guo

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-04-05

Description: This paper addresses the problem of finite-time H∞ control via observer-based state feedback for a family of singular Markovian jump systems (SMJSs) with time-varying norm-bounded disturbance. Firstly, the concepts of singular stochastic finite-time boundedness and singular stochastic finite-time H∞ stabilization via observer-based state feedback are given. Then an observer-based state feedback controller is designed to ensure singular stochastic finite-time H∞ stabilization via observer-based state feedback of the resulting closed-loop error dynamic SMJS. Sufficient criteria are presented for the solvability of the problem, which can be reduced to a feasibility problem involving linear matrix inequalities with a fixed parameter. As an auxiliary result, we also discuss the problem of finite-time stabilization via observer-based state feedback of a class of SMJSs and give sufficient conditions of singular stochastic finite-time stabilization via observer-based state feedback for the class of SMJSs. Finally, illustrative examples are given to demonstrate the validity of the proposed techniques.

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A Class of PDEs with Nonlinear Superposition Principles (2012)

Li Peng, Liu Keying, Pan Zuliang, and Zhong Weizhou

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-04-06

Description: Through assuming that nonlinear superposition principles (NLSPs) are embedded in a Lie group, a class of 3rd-order PDEs is derived from a general determining equation that determine the invariant group. The corresponding NLSPs and transformation to linearize the nonlinear PDE are found, hence the governing PDE is proved C-integrable. In the end, some applications of the PDEs are explained, which shows that the result has very subtle relations with linearization of partial differential equation.

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Active Sliding Mode Control Antisynchronization of Chaotic Systems with Uncertainties and External Disturbances (2012)

Wafaa Jawaada, M. S. M. Noorani, and M. Mossa Al-sawalha

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-04-09

Description: The antisynchronization behavior of chaotic systems with parametric uncertainties and external disturbances is explored by using robust active sliding mode control method. The sufficient conditions for achieving robust antisynchronization of two identical chaotic systems with different initial conditions and two different chaotic systems with terms of uncertainties and external disturbances are derived based on the Lyapunov stability theory. Analysis and numerical simulations are shown for validation purposes.

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Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation (2012)

Gusein Sh. Guseinov

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-04-10

Description: Using spectral properties of the Laplace operator and some structural formula for rapidly decreasing functions of the Laplace operator, we offer a novel method to derive explicit formulae for solutions to the Cauchy problem for classical wave equation in arbitrary dimensions. Among them are the well-known d'Alembert, Poisson, and Kirchhoff representation formulae in low space dimensions.

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Numerical Solution of Nonlinear Fredholm Integrodifferential Equations of Fractional Order by Using Hybrid Functions and the Collocation Method (2012)

Jianhua Hou, Beibo Qin, and Changqing Yang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-04-10

Description: A numerical method to solve nonlinear Fredholm integral equations of second kind is presented in this work. The method is based upon hybrid function approximate. The properties of hybrid of block-pulse functions and Taylor series are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of algebraic equations. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

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Optimal Inequalities for Power Means (2012)

Yong-Min Li, Bo-Yong Long, Yu-Ming Chu, and Wei-Ming Gong

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-04-09

Description: We present the best possible power mean bounds for the product Mpα(a,b)M-p1-α(a,b) for any p>0, α∈(0,1), and all a,b>0 with a≠b. Here, Mp(a,b) is the pth power mean of two positive numbers a and b.

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Nonnegativity Preserving Interpolation by C1 Bivariate Rational Spline Surface (2012)

Xingxuan Peng, Zhihong Li, and Qian Sun

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-04-11

Description: This paper is concerned with the nonnegativity preserving interpolation of data on rectangular grids. The function is a kind of bivariate rational interpolation spline with parameters, which is C1 in the whole interpolation region. Sufficient conditions are derived on coefficients in the rational spline to ensure that the surfaces are always nonnegative if the original data are nonnegative. The gradients at the data sites are modified if necessary to ensure that the nonnegativity conditions are fulfilled. Some numerical examples are illustrated in the end of this paper.

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An Improved Particle Swarm Optimization for Solving Bilevel Multiobjective Programming Problem (2012)

Tao Zhang, Tiesong Hu, Yue Zheng, and Xuning Guo

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-04-11

Description: An improved particle swarm optimization (PSO) algorithm is proposed for solving bilevel multiobjective programming problem (BLMPP). For such problems, the proposed algorithm directly simulates the decision process of bilevel programming, which is different from most traditional algorithms designed for specific versions or based on specific assumptions. The BLMPP is transformed to solve multiobjective optimization problems in the upper level and the lower level interactively by an improved PSO. And a set of approximate Pareto optimal solutions for BLMPP is obtained using the elite strategy. This interactive procedure is repeated until the accurate Pareto optimal solutions of the original problem are found. Finally, some numerical examples are given to illustrate the feasibility of the proposed algorithm.

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System Identification Using Multilayer Differential Neural Networks: A New Result (2012)

J. Humberto Pérez-Cruz, A. Y. Alanis, José de Jesús Rubio, and Jaime Pacheco

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-04-13

Description: In previous works, a learning law with a dead zone function was developed for multilayer differential neural networks. This scheme requires strictly a priori knowledge of an upper bound for the unmodeled dynamics. In this paper, the learning law is modified in such a way that this condition is relaxed. By this modification, the tuning process is simpler and the dead-zone function is not required anymore. On the basis of this modification and by using a Lyapunov-like analysis, a stronger result is here demonstrated: the exponential convergence of the identification error to a bounded zone. Besides, a value for upper bound of such zone is provided. The workability of this approach is tested by a simulation example.

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Robust Exponential Stability for LPD Discrete-Time System with Interval Time-Varying Delay (2012)

Kanit Mukdasai

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-29

Description: This paper investigates the problem of robust exponential stability for uncertain linear-parameter dependent (LPD) discrete-time system with delay. The delay is of an interval type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on combination of the linear matrix inequality (LMI) technique and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust exponential stability are obtained in terms of LMI. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

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Homotopy Perturbation Method for Thin Film Flow and Heat Transfer over an Unsteady Stretching Sheet with Internal Heating and Variable Heat Flux (2012)

I-Chung Liu and Ahmed M. Megahed

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-31

Description: We have analyzed the effects of variable heat flux and internal heat generation on the flow and heat transfer in a thin film on a horizontal sheet in the presence of thermal radiation. Similarity transformations are used to transform the governing equations to a set of coupled nonlinear ordinary differential equations. The obtained differential equations are solved approximately by the homotopy perturbation method (HPM). The effects of various parameters governing the flow and heat transfer in this study are discussed and presented graphically. Comparison of numerical results is made with the earlier published results under limiting cases.

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Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations via Implicit Evolution System (2012)

Amar Debbouche and Dumitru Baleanu

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-09-03

Description: We introduce a new concept called implicit evolution system to establish the existence results of mild and strong solutions of a class of fractional nonlocal nonlinear integrodifferential system, then we prove the exact null controllability result of a class of fractional evolution nonlocal integrodifferential control system in Banach space. As an application that illustrates the abstract results, two examples are provided.

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Fixed Point Theorem for Cyclic Chatterjea Type Contractions (2012)

Erdal Karapınar and Hemant Kumar Nashine

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-24

Description: We introduce the notion of cyclic weakly Chatterjea type contraction and generalized cyclic weakly Chatterjea type contraction in metric spaces. We discussed the existence of fixed point theorems of (generalized) cyclic weakly Chatterjea type contraction mappings in the context of complete metric spaces. Our main theorems extend and improve some fixed point theorems in the literature.

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Topics: Mathematics

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Delay-Range-Dependent Stability Criteria for Takagi-Sugeno Fuzzy Systems with Fast Time-Varying Delays (2012)

Pin-Lin Liu

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-23

Description: The problem of delay-range-dependent stability for T-S fuzzy system with interval time-varying delay is investigated. The constraint on the derivative of the time-varying delay is not required, which allows the time delay to be a fast time-varying function. By developing delay decomposition approach, integral inequalities approach (IIA), and Leibniz-Newton formula, the information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Simulation examples show resulting criteria outperform all existing ones in the literature. It is worth pointing out that our criteria are carried out more efficiently for computation and less conservatism of the proposed criteria.

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Strong Convergence Theorems for a Countable Family of Total Quasi- (2012)

Liang-cai Zhao and Shih-sen Chang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-29

Description: The purpose of this paper is to introduce a class of total quasi-ϕ-asymptotically nonexpansive-nonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the corresponding results announced by some authors recently.

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Cluster Anti-Synchronization of Complex Networks with Nonidentical Dynamical Nodes (2012)

Shuguo Wang, Chunyuan He, and Hongxing Yao

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-29

Description: This paper investigates a new cluster antisynchronization scheme in the time-varying delays coupled complex dynamical networks with nonidentical nodes. Based on the community structure of the networks, the controllers are designed differently between the nodes in one community that have direct connections to the nodes in other communities and the nodes without direct connections with the nodes in other communities strategy; some sufficient criteria are derived to ensure cluster anti-synchronization of the network model. Particularly, the weight configuration matrix is not assumed to be irreducible. The numerical simulations are performed to verify the effectiveness of the theoretical results.

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Fixed Point and Asymptotic Analysis of Cellular Neural Networks (2012)

Xianghong Lai and Yutian Zhang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-29

Description: We firstly employ the fixed point theory to study the stability of cellular neural networks without delays and with time-varying delays. Some novel and concise sufficient conditions are given to ensure the existence and uniqueness of solution and the asymptotic stability of trivial equilibrium at the same time. Moreover, these conditions are easily checked and do not require the differentiability of delays.

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The Numerical Solution of Problems in Calculus of Variation Using B-Spline Collocation Method (2012)

M. Zarebnia and M. Birjandi

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-30

Description: A B-spline collocation method is developed for solving boundary value problems which arise from the problems of calculus of variations. Some properties of the B-spline procedure required for subsequent development are given, and they are utilized to reduce the solution computation of boundary value problems to some algebraic equations. The method is applied to a few test examples to illustrate the accuracy and the implementation of the method.

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A Granular Reduction Algorithm Based on Covering Rough Sets (2012)

Tian Yang, Zhaowen Li, and Xiaoqing Yang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-31

Description: The granular reduction is to delete dispensable elements from a covering. It is an efficient method to reduce granular structures and get rid of the redundant information from information systems. In this paper, we develop an algorithm based on discernability matrixes to compute all the granular reducts of covering rough sets. Moreover, a discernibility matrix is simplified to the minimal format. In addition, a heuristic algorithm is proposed as well such that a granular reduct is generated rapidly.

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A Family of Iterative Methods with Accelerated Eighth-Order Convergence (2012)

Alicia Cordero, Mojtaba Fardi, Mehdi Ghasemi, and Juan R. Torregrosa

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-31

Description: We propose a family of eighth-order iterative methods without memory for solving nonlinear equations. The new iterative methods are developed by using weight function method and using an approximation for the last derivative, which reduces the required number of functional evaluations per step. Their efficiency indices are all found to be 1.682. Several examples allow us to compare our algorithms with known ones and confirm the theoretical results.

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An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations (2012)

Feng Yin and Guang-Xin Huang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-27

Description: An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations (

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Calculation of the Reproducing Kernel on the Reproducing Kernel Space with Weighted Integral (2012)

Er Gao, Songhe Song, and Xinjian Zhang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-30

Description: We provide a new definition for reproducing kernel space with weighted integral and present a method to construct and calculate the reproducing kernel for the space. The new reproducing kernel space is an enlarged reproducing kernel space, which contains the traditional reproducing kernel space. The proposed method of this paper is a universal method and is suitable for the case of that the weight is variable. Obviously, this new method will generalize a number of applications of reproducing kernel theory to many areas.

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Nonlinear Analysis for Shear Augmented Dispersion of Solutes in Blood Flow through Narrow Arteries (2012)

D. S. Sankar, Nurul Aini Binti Jaafar, and Yazariah Yatim

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-08-31

Description: The shear augmented dispersion of solutes in blood flow (i) through circular tube and (ii) between parallel flat plates is analyzed mathematically, treating blood as Herschel-Bulkley fluid model. The resulting system of nonlinear differential equations are solved with the appropriate boundary conditions, and the expressions for normalized velocity, concentration of the fluid in the core region and outer region, flow rate, and effective axial diffusivity are obtained. It is found that the normalized velocity of blood, relative diffusivity, and axial diffusivity of solutes are higher when blood is modeled by Herschel-Bulkley fluid rather than by Casson fluid model. It is also noted that the normalized velocity, relative diffusivity, and axial diffusivity of solutes are higher when blood flows through circular tube than when it flows between parallel flat plates.

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