Journal of Applied Mathematics Articles (Project Euclid)

An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model

Thu, 05 Aug 2010 15:41 EDT

A. S. Deakin, Matt Davison

Source: J. Appl. Math., Volume 2010, 5 pages.

Abstract:
This paper provides the analytic solution to the partial differential equation for the value of a convertible bond. The equation assumes a Vasicek model for the interest rate and a geometric Brownian motion model for the stock price. The solution is obtained using integral transforms.

Some New Difference Inequalities and an Application to Discrete-Time Control Systems

Wed, 02 Jan 2013 14:07 EST

Hong Zhou, Deqing Huang, Wu-Sheng Wang, Jian-Xin Xu

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
Two new nonlinear difference inequalities are considered, where the inequalities consist of multiple iterated sums, and composite function of nonlinear function and unknown function may be involved in each layer. Under several practical assumptions, the inequalities are solved through rigorous analysis, and explicit bounds for the unknown functions are given clearly. Further, the derived results are applied to the stability problem of a class of linear control systems with nonlinear perturbations.

Some Fixed Point Results in GP -Metric Spaces

Wed, 02 Jan 2013 14:07 EST

Hassen Aydi, Erdal Karapınar, Peyman Salimi

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
Following a recent paper of Zand and Nezhad (2011), we establish some fixed point results in GP -metric spaces. The presented theorems generalize and improve several existing results in the literature. Also, some examples are presented.

Multivariate Extension Principle and Algebraic Operations of Intuitionistic Fuzzy Sets

Wed, 02 Jan 2013 14:07 EST

Yonghong Shen, Wei Chen

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
This paper mainly focuses on multivariate extension of the extension principle of IFSs. Based on the Cartesian product over IFSs, the multivariate extension principle of IFSs is established. Furthermore, three kinds of representation of this principle are provided. Finally, a general framework of the algebraic operation between IFSs is given by using the multivariate extension principle.

A Nonlinear Schrödinger Model for Many-Particle Quantum Systems

Wed, 02 Jan 2013 14:07 EST

Qiang Zhang, Tian Ma

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
Considering both effects of the s-wave scattering and the atom-atom interaction rather than only the effect of the s-wave scattering, we establish a nonlinear Schrödinger model for many-particle quantum systems and we prove the global existence of a solution to the model and obtain the expression of the solution. Furthermore, we show that the Hamilton energy and the total particle number both are conservative quantities.

Iteration Coupling Simulation of Random Waves and Wave-Induced Currents

Wed, 02 Jan 2013 14:07 EST

Jinhai Zheng, Tianwen Wang, Gang Wang, Chenming Zhang, Chi Zhang

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
A two-way coupling algorithm for wave-current interaction is developed and implemented into a nearshore circulation model to investigate the effects of fully wave-current interaction on irregular wave transformation over an elliptic shoal. The wave field is simulated by a spectral wave model WABED, and the wave-induced current is solved by a quasi-three-dimensional model WINCM. The surface roller effects are represented in the formulation of surface stress, and the roller characteristics are solved by a roller evolution model. The proposed two-way coupling algorithm can describe both the generation of wave-induced current and the current-induced wave transformation, which is more physically reasonable than the one-way approaches. The model test with a laboratory experiment shows that wave-induced currents have an important influence on the wave transformation, for example, the wave energy defocusing due to the strong jet-like current along the centerline of the shoal. It is revealed that the accuracy of simulated wave field can be significantly improved by taking into account the two-way wave-current interaction.

A Modified NM-PSO Method for Parameter Estimation Problems of Models

Wed, 02 Jan 2013 14:07 EST

An Liu, Erwie Zahara, Ming-Ta Yang

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
Ordinary differential equations usefully describe the behavior of a wide range of dynamic physical systems. The particle swarm optimization (PSO) method has been considered an effective tool for solving the engineering optimization problems for ordinary differential equations. This paper proposes a modified hybrid Nelder-Mead simplex search and particle swarm optimization (M-NM-PSO) method for solving parameter estimation problems. The M-NM-PSO method improves the efficiency of the PSO method and the conventional NM-PSO method by rapid convergence and better objective function value. Studies are made for three well-known cases, and the solutions of the M-NM-PSO method are compared with those by other methods published in the literature. The results demonstrate that the proposed M-NM-PSO method yields better estimation results than those obtained by the genetic algorithm, the modified genetic algorithm (real-coded GA (RCGA)), the conventional particle swarm optimization (PSO) method, and the conventional NM-PSO method.

A Nonclassical Radau Collocation Method for Nonlinear Initial-Value Problems with Applications to Lane-Emden Type Equations

Wed, 02 Jan 2013 14:07 EST

Mohammad Maleki, M. Tavassoli Kajani, I. Hashim, A. Kilicman, K. A. M. Atan

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
We propose a numerical method for solving nonlinear initial-value problems of Lane-Emden type. The method is based upon nonclassical Gauss-Radau collocation points, and weighted interpolation. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced on arbitrary intervals. Then they are utilized to reduce the computation of nonlinear initial-value problems to a system of nonlinear algebraic equations. We also present the comparison of this work with some well-known results and show that the present solution is very accurate.

A New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for Oscillators

Wed, 02 Jan 2013 14:07 EST

Zhaoxia Chen, Xiong You, Xin Shu, Mei Zhang

Source: J. Appl. Math., Volume 2012, 27 pages.

Abstract:
In order to solve initial value problems of differential equations with oscillatory solutions, this paper improves traditional Runge-Kutta (RK) methods by introducing frequency-depending weights in the update. New practical RK integrators are obtained with the phase-fitting and amplification-fitting conditions and algebraic order conditions. Two of the new methods have updates that are also phase-fitted and amplification-fitted. The linear stability and phase properties of the new methods are examined. The results of numerical experiments on physical and biological problems show the robustness and competence of the new methods compared to some highly efficient integrators in the literature.

Finite Element Method for Linear Multiterm Fractional Differential Equations

Wed, 02 Jan 2013 14:07 EST

Abdallah A. Badr

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
We consider the linear multiterm fractional differential equation (fDE). Existence and uniqueness of the solution of such equation are discussed. We apply the finite element method (FEM) to obtain the numerical solution of this equation using Galerkin approach. A comparison, through examples, between our techniques and other previous numerical methods is established.

A Version of the Euler Equation in Discounted Markov Decision Processes

Wed, 02 Jan 2013 14:07 EST

H. Cruz-Suárez, G. Zacarías-Espinoza, V. Vázquez-Guevara

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
This paper deals with Markov decision processes (MDPs) on Euclidean spaces with an infinite horizon. An approach to study this kind of MDPs is using the dynamic programming technique (DP). Then the optimal value function is characterized through the value iteration functions. The paper provides conditions that guarantee the convergence of maximizers of the value iteration functions to the optimal policy. Then, using the Euler equation and an envelope formula, the optimal solution of the optimal control problem is obtained. Finally, this theory is applied to a linear-quadratic control problem in order to find its optimal policy.

Error Analysis of Galerkin's Method for Semilinear Equations

Wed, 02 Jan 2013 14:07 EST

Tadashi Kawanago

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
We establish a general existence result for Galerkin's approximate solutions of abstract semilinear equations and conduct an error analysis. Our results may be regarded as some extension of a precedent work (Schultz 1969). The derivation of our results is, however, different from the discussion in his paper and is essentially based on the convergence theorem of Newton’s method and some techniques for deriving it. Some of our results may be applicable for investigating the quality of numerical verification methods for solutions of ordinary and partial differential equations.

Pricing and Applications of Digital Installment Options

Wed, 02 Jan 2013 14:07 EST

Pierangelo Ciurlia, Andrea Gheno

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
For its theoretical interest and strong impact on financial markets, option valuation is considered one of the cornerstones of contemporary mathematical finance. This paper specifically studies the valuation of exotic options with digital payoff and flexible payment plan. By means of the Incomplete Fourier Transform, the pricing problem is solved in order to find integral representations of the upfront price for European call and put options. Several applications in the areas of corporate finance, insurance, and real options are discussed. Finally, a new type of digital derivative named supercash option is introduced and some payment schemes are also presented.

Improving Results on Convergence of AOR Method

Wed, 02 Jan 2013 14:07 EST

Guangbin Wang, Ting Wang, Yanli Du

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
We present some sufficient conditions on convergence of AOR method for solving $Ax=b$ with $A$ being a strictly doubly $\alpha $ diagonally dominant matrix. Moreover, we give two numerical examples to show the advantage of the new results.

A Birandom Job Search Problem with Risk Tolerance

Wed, 02 Jan 2013 14:07 EST

Guoli Wang, Wansheng Tang, Ruiqing Zhao

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
This paper considers a novel class of birandom job search problem, in which the job offers are sampled by the job searcher from a finite job set with equivalent probability and their wages are characterized as independent but maybe not identically nonnegative random variables. The job searcher knows the job offer's wage distribution when he samples the job offer. Since the offered wage is a random variable and the reservation wage is a deterministic number, it is meaningless to make comparison directly. In order to rank the random wage and the reservation wage and provide decision support, a risk tolerance criterion is designed, and the job searcher then accepts or rejects the sampled job offer depending on whether the risk tolerance criterion is met or not. Since the offered wages are random variables and the search process is random, it's impossible to obtain the job searcher's real return; in this case, its expected value can be calculated via birandom theory. Simultaneously, some propositions on the expected return as well as the average search times are also studied which may provide some valuable suggestions to the job searcher. Numerical examples are given to illustrate the decision process of the risk tolerance-based birandom job search problem.

Numerical Analysis on the Influence of Thermal Effects on Oil Flow Characteristic in High-Pressure Air Injection (HPAI) Process

Wed, 02 Jan 2013 14:07 EST

Hu Jia, Jin-Zhou Zhao, Wan-Fen Pu

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
In previous laboratory study, we have shown the thermal behavior of Keke Ya light crude oil (Tarim oilfield, branch of CNPC) for high-pressure air injection (HPAI) application potential study. To clarify the influences of thermal effects on oil production, in this paper, we derived a mathematical model for calculating oil flow rate, which is based on the heat conduction property in porous media from the combustion tube experiment. Based on remarkably limited knowledge consisting of very global balance arguments and disregarding all the details of the mechanisms in the reaction zone, the local governing equations are formulated in a dimensionless form. We use finite difference method to solve this model and address the study by way of qualitative analysis. The time-space dimensionless oil flow rate ( qD ) profiles are established for comprehensive studies on the oil flow rate characteristic affected by thermal effects. It also discusses how these findings will impact HPAI project performances, and several guidelines are suggested.

The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations

Wed, 02 Jan 2013 14:07 EST

Yadong Shang, Xiaoxiao Zheng

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type for n and E , the solitary wave solutions of kink-type for E and bell-type for n , the singular traveling wave solutions, periodic wave solutions of triangle functions, Jacobi elliptic function doubly periodic solutions, and Weierstrass elliptic function doubly periodic wave solutions. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.

A Decomposition Algorithm for Learning Bayesian Networks Based on Scoring Function

Wed, 02 Jan 2013 14:07 EST

Mingmin Zhu, Sanyang Liu

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
Learning Bayesian network (BN) structure from data is a typical NP-hard problem. But almost existing algorithms have the very high complexity when the number of variables is large. In order to solve this problem(s), we present an algorithm that integrates with a decomposition-based approach and a scoring-function-based approach for learning BN structures. Firstly, the proposed algorithm decomposes the moral graph of BN into its maximal prime subgraphs. Then it orientates the local edges in each subgraph by the K2-scoring greedy searching. The last step is combining directed subgraphs to obtain final BN structure. The theoretical and experimental results show that our algorithm can efficiently and accurately identify complex network structures from small data set.

Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control

Wed, 02 Jan 2013 14:07 EST

Chunjin Wei, Lansun Chen

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and the method of successor function, we obtain the system with impulsive effects that has an order one periodic solution, and sufficient conditions for existence and stability of order one periodic solution are also obtained. Finally, numerical simulations are performed to illustrate our main results.

Identification of Hysteresis in Human Meridian Systems Based on NARMAX Model

Wed, 02 Jan 2013 14:07 EST

Yonghong Tan, Ruili Dong, Hui Chen, Hong He

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
It has been found that the response of acupuncture point on the human meridian line exhibits nonlinear dynamic behavior when excitation of electroacupuncture is implemented on another meridian point. This nonlinear phenomenon is in fact a hysteretic phenomenon. In order to explore the characteristic of human meridian and finally find a way to improve the treatment of diseases via electro-acupuncture method, it is necessary to identify the model to describe the corresponding dynamic hysteretic phenomenon of human meridian systems stimulated by electric-acupuncture. In this paper, an identification method using nonlinear autoregressive and moving average model with exogenous input (NARMAX) is proposed to model the dynamic hysteresis in human meridian. As the hysteresis is a nonlinear system with multivalued mapping, the traditional NARMAX model is unavailable to it directly. Thus, an expanded input space is constructed to transform the multi-valued mapping of the hysteresis to a one-to-one mapping. Then, the identification method using NARMAX model on the constructed expanded input space is developed. Finally, the proposed method is applied to hysteresis modeling for human meridian systems.

Analysis of a HBV Model with Diffusion and Time Delay

Wed, 02 Jan 2013 14:07 EST

Noé Chan Chí, Eric ÁvilaVales, Gerardo García Almeida

Source: J. Appl. Math., Volume 2012, 25 pages.

Abstract:
This paper discussed a hepatitis B virus infection with delay, spatial diffusion, and standard incidence function. The local stability of equilibrium is obtained via characteristic equations. By using comparison arguments, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. If the basic reproductive number is greater than unity, by means of an iteration technique, sufficiently conditions are obtained for the global asymptotic stability of the infected steady state. Numerical simulations are carried out to illustrate our findings.

An Improved Line Search Filter Method for the System of Nonlinear Equations

Wed, 02 Jan 2013 14:07 EST

Zhong Jin, Yuqing Wang

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
An improved line search filter algorithm for the system of nonlinear equations is presented. We divide the equations into two groups, one contains the equations that are treated as equality constraints and the square of other equations is regarded as objective function. Two groups of equations are updated at every iteration in the works by Nie (2004, 2006, and 2006), by Nie et al. (2008), and by Gu (2011), while we just update them at the iterations when it is needed indeed. As a consequence, the scale of the calculation is decreased in a certain degree. Under some suitable conditions the global convergence can be induced. In the end, numerical experiments show that the method in this paper is effective.

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

Wed, 02 Jan 2013 14:07 EST

Hyontai Sug

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
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.

The Mask of Odd Points $n$ -Ary Interpolating Subdivision Scheme

Wed, 02 Jan 2013 14:07 EST

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

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
We present an explicit formula for the mask of odd points $n$ -ary, for any odd $n⩾3$ , interpolating subdivision schemes. This formula provides the mask of lower and higher arity schemes. The 3-point and 5-point $a$ -ary schemes introduced by Lian, 2008, and ( $2m+1$ )-point $a$ -ary schemes introduced by, Lian, 2009, are special cases of our explicit formula. Moreover, other well-known existing odd point $n$ -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.

Complete Synchronization of Strictly Different Chaotic Systems

Wed, 02 Jan 2013 14:07 EST

Gualberto Solís-Perales

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
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.

An Application of Monte-Carlo-Based Sensitivity Analysis on the Overlap in Discriminant Analysis

Wed, 02 Jan 2013 14:07 EST

S. Razmyan, F. Hosseinzadeh Lotfi

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
Discriminant analysis (DA) is used for the measurement of estimates of a discriminant function by minimizing their group misclassifications to predict group membership of newly sampled data. A major source of misclassification in DA is due to the overlapping of groups. The uncertainty in the input variables and model parameters needs to be properly characterized in decision making. This study combines DEA-DA with a sensitivity analysis approach to an assessment of the influence of banks’ variables on the overall variance in overlap in a DA in order to determine which variables are most significant. A Monte-Carlo-based sensitivity analysis is considered for computing the set of first-order sensitivity indices of the variables to estimate the contribution of each uncertain variable. The results show that the uncertainties in the loans granted and different deposit variables are more significant than uncertainties in other banks’ variables in decision making.

Random $N$ -Policy Geo/G/1 Queue with Startup and Closedown Times

Wed, 02 Jan 2013 14:07 EST

Tsung-Yin Wang

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
This study investigates a random $N$ -policy Geo/G/1 queue with startup and closedown times. $N$ is newly determined every time a new cycle begins. When random $N$ 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.

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

Wed, 02 Jan 2013 14:07 EST

H. Pirali, F. Djavanroodi, M. Haghpanahi

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
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).

Modified Firefly Algorithm

Wed, 02 Jan 2013 14:07 EST

Surafel Luleseged Tilahun, Hong Choon Ong

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
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.

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

Wed, 02 Jan 2013 14:07 EST

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

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
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.

Convergence and Stability in Collocation Methods of Equation ${u}^{\prime }(t)=au(t)+bu([t])$

Wed, 02 Jan 2013 14:07 EST

Han Yan, Shufang Ma, Yanbin Liu, Hongquan Sun

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
This paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for ${u}^{\prime }(t)=au(t)+bu([t])$ . The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained, and some numerical experiments are given.

An Extended Analytic Solution of Combined Refraction andDiffraction of Long Waves Propagating over Circular Island

Wed, 02 Jan 2013 14:07 EST

Yu-Shu Kuo, Tai-Wen Hsu, Chia-Cheng Tsai, Yu-Hsuan Huang

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
An analytic solution of long waves scattering by a cylindrical island mounted on a permeable circular shoal was obtained by solving the linear long wave equation (LWE). The solution is in terms of the Bessel function expressed by complex variables. The present solution is suitable for arbitrary bottom configurations described by a power function with two independent parameters. For the case of the paraboloidal shoal, there exists a singular point ( $\alpha =2$ ) which can be removed using Frobenius series, where α is a real constant. The present solution is reduced to Yu and Zhang’s (2003) solution for impermeable circular shoal. The numerical results show some special features of the combined effect of wave refraction and diffraction caused by a porous circular island. The effect of key parameters of the island dimension, the shoal slope, and permeability on wave scattering was discussed based on the analytic solution.

Optimization on Production-Inventory Problem with Multistage and Varying Demand

Wed, 02 Jan 2013 14:07 EST

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

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
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.

Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs

Wed, 02 Jan 2013 14:07 EST

Cuicui Liao, Xiaohua Ding

Source: J. Appl. Math., Volume 2012, 22 pages.

Abstract:
We use the idea of nonstandard finite difference methods to derive the discrete variational integrators for multisymplectic PDEs. We obtain a nonstandard finite difference variational integrator for linear wave equation with a triangle discretization and two nonstandard finite difference variational integrators for the nonlinear Klein-Gordon equation with a triangle discretization and a square discretization, respectively. These methods are naturally multisymplectic. Their discrete multisymplectic structures are presented by the multisymplectic form formulas. The convergence of the discretization schemes is discussed. The effectiveness and efficiency of the proposed methods are verified by the numerical experiments.

Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact Resistances

Wed, 02 Jan 2013 14:07 EST

Hamid El Qarnia, Fayssal El Adnani, El Khadir Lakhal

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
This work reports an analytical solution for the solidification of a superheating phase change material (PCM) contained in a rectangular enclosure with a finite height. The analytical solution has been obtained by solving nondimensional energy equations by using the perturbation method for a small perturbation parameter: the Stefan number, $\epsilon $ . This analytical solution, which takes into account the effects of the superheating of PCM, finite height of the enclosure, thickness of the wall, and wall-solid shell interfacial thermal resistances, was expressed in terms of nondimensional temperature distributions of the bottom wall of the enclosure and both PCM phases, and the dimensionless solid-liquid interface position and its dimensionless speed. The developed solution was firstly compared with that existing in the literature for the case of nonsuperheating PCM. The predicted results agreed well with those published in the literature. Next, a parametric study was carried out in order to study the impacts of the dimensionless control parameters on the dimensionless temperature distributions of the wall, the solid shell, and liquid phase of the PCM, as well as the solid-liquid interface position and its dimensionless speed.

Computing the Square Roots of a Class of Circulant Matrices

Wed, 02 Jan 2013 14:07 EST

Ying Mei

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
We first investigate the structures of the square roots of a class of circulant matrices and give classifications of the square roots of these circulant matrices. Then, we develop several algorithms for computing their square roots. We show that our algorithms are faster than the standard algorithm which is based on the Schur decomposition.

Parameterized Local Reduction of Decision Systems

Wed, 02 Jan 2013 14:07 EST

Degang Chen, Yanyan Yang, Xiao Zhang

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
One important and valuable topic in rough sets is attribute reduction of a decision system. The existing attribute reductions are designed to just keep confidence of every certain rule as they cannot identify key conditional attributes explicitly for special decision rules. In this paper, we develop the concept of $\theta $ -local reduction in order to offer a minimal description for special $\theta $ -possible decision rules. The approach of discernibility matrix is employed to investigate the structure of a $\theta $ -local reduction and compute all $\theta $ -local reductions. An example of medical diagnosis is employed to illustrate our idea of the $\theta $ -local reduction. Finally, numerical experiments are performed to show that our method proposed in this paper is feasible and valid.

A Coupled Method of Laplace Transform and Legendre Wavelets for Lane-Emden-Type Differential Equations

Wed, 02 Jan 2013 14:07 EST

Fukang Yin, Junqiang Song, Fengshun Lu, Hongze Leng

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
A coupled method of Laplace transform and Legendre wavelets is presented to obtain exact solutions of Lane-Emden-type equations. By employing properties of Laplace transform, a new operator is first introduced and then its Legendre wavelets operational matrix is derived to convert the Lane-Emden equations into a system of algebraic equations. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The results show that the proposed method is very effective and easy to implement.

Abundant Interaction Solutions of Sine-Gordon Equation

Wed, 02 Jan 2013 14:07 EST

DaZhao Lü, YanYing Cui, ChangHe Liu, ShangWen Wu

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
With the help of computer symbolic computation software (e.g., Maple ), abundant interaction solutions of sine-Gordon equation are obtained by means of a constructed Wronskian form expansion method. The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do not satisfy linear partial differential equations. Such interaction solutions are difficultly obtained via other methods. And the method can be automatically carried out in computer.

Positive Data Visualization Using Trigonometric Function

Wed, 02 Jan 2013 14:07 EST

Farheen Ibraheem, Maria Hussain, Malik Zawwar Hussain, Akhlaq Ahmad Bhatti

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
A ${C}^{1}$ piecewise rational trigonometric cubic function with four shape parameters has been constructed to address the problem of visualizing positive data. Simple data-dependent constraints on shape parameters are derived to preserve positivity and assure smoothness. The method is then extended to positive surface data by rational trigonometric bicubic function. The order of approximation of developed interpolant is $O({h}_{i}^{3})$ .

Analysis of an Ecoepidemiological Model with Prey Refuges

Wed, 02 Jan 2013 14:07 EST

Shufan Wang, Zhihui Ma

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
An ecoepidemiological system with prey refuges and disease in prey is proposed. Bilinear incidence and Holling III functional response are used to model the contact process and the predation process, respectively. We will study the stability behavior of the basic system from a local to a global perspective. Permanence of the considered system is also investigated.

Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method

Wed, 02 Jan 2013 14:07 EST

Mojtaba Nazari, Faisal Salah, Zainal Abdul Aziz, Merbakhsh Nilashi

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of the Korteweg-de Vries (KdV) and Burgers equations. The homotopy analysis method (HAM) is an analytic technique which provides us with a new way to obtain series solutions of such nonlinear problems. HAM contains the auxiliary parameter $ħ$ , which provides us with a straightforward way to adjust and control the convergence region of the series solution. The resulted HAM solution at 8th-order and 14th-order approximation is then compared with that of the exact soliton solutions of KdV and Burgers equations, respectively, and shown to be in excellent agreement.

A New Class of Meromorphic Functions Associated with Spirallike Functions

Wed, 02 Jan 2013 14:07 EST

Lei Shi, Zhi-Gang Wang, Jing-Ping Yi

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
We introduce a new class of meromorphic functions associated with spirallike functions. Such results as subordination property, integral representation, convolution property, and coefficient inequalities are proved.

The Expression of the Drazin Inverse with Rank Constraints

Wed, 02 Jan 2013 14:07 EST

Linlin Zhao

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
By using the matrix decomposition and the reverse order law, we provide some new expressions of the Drazin inverse for any $2×2$ block matrix with rank constraints.

Superconvergence Analysis of Finite Element Method for a Second-Type Variational Inequality

Wed, 02 Jan 2013 14:07 EST

Dongyang Shi, Hongbo Guan, Xiaofei Guan

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
This paper studies the finite element (FE) approximation to a second-type variational inequality. The supe rclose and superconvergence results are obtained for conforming bilinear FE and nonconforming ${\text{EQ}}^{\text{rot}}$ FE schemes under a reasonable regularity of the exact solution $u\in {H}^{5/2}(\mathrm{\Omega })$ , which seem to be never discovered in the previous literature. The optimal ${L}^{2}$ -norm error estimate is also derived for ${\text{EQ}}^{\text{rot}}$ FE. At last, some numerical results are provided to verify the theoretical analysis.

Double-Framed Soft Sets with Applications in BCK/BCI-Algebras

Wed, 02 Jan 2013 14:07 EST

Young Bae Jun, Sun Shin Ahn

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
In order to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties, the notion of double-framed soft sets is introduced, and applications in BCK/BCI-algebras are discussed. The notions of double-framed soft algebras in BCK/BCI-algebras are introduced, and related properties are investigated. Characterizations of double-framed soft algebras are considered. Product and int-uni structure of double-framed soft algebras are discussed, and several examples are provided.

Duality of $(h,\phi )$ -Multiobjective Programming Involving Generalized Invex Functions

Wed, 02 Jan 2013 14:07 EST

GuoLin Yu

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
In the setting of Ben-Tal's generalized algebraic operations, this paper deals with Mond-Weir type dual theorems of multiobjective programming problems involving generalized invex functions. Two classes of functions, namely, $(h,\phi )$ -pseudoinvex and $(h,\phi )$ -quasi-invex, are defined for a vector function. By utilizing these two classes of functions, some dual theorems are established for conditionally properefficient solution in $(h,\phi )$ -multiobjective programming problems.

Stable Zero Lagrange Duality for DC Conic Programming

Wed, 02 Jan 2013 14:07 EST

D. H. Fang

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
We consider the problems of minimizing a DC function under a cone-convex constraint and a set constraint. By using the infimal convolution of the conjugate functions, we present a new constraint qualification which completely characterizes the Farkas-type lemma and the stable zero Lagrange duality gap property for DC conical programming problems in locally convex spaces.

Fabric Tensor Characterization of Tensor-Valued Directional Data: Solution, Accuracy, and Symmetrization

Wed, 02 Jan 2013 14:07 EST

Kuang-dai Leng, Qiang Yang

Source: J. Appl. Math., Volume 2012, 22 pages.

Abstract:
Fabric tensor has proved to be an effective tool statistically characterizing directional data in a smooth and frame-indifferent form. Directional data arising from microscopic physics and mechanics can be summed up as tensor-valued orientation distribution functions (ODFs). Two characterizations of the tensor-valued ODFs are proposed, using the asymmetric and symmetric fabric tensors respectively. The later proves to be nonconvergent and less accurate but still an available solution for where fabric tensors are required in full symmetry. Analytic solutions of the two types of fabric tensors characterizing centrosymmetric and anticentrosymmetric tensor-valued ODFs are presented in terms of orthogonal irreducible decompositions in both two- and three-dimensional (2D and 3D) spaces. Accuracy analysis is performed on normally distributed random ODFs to evaluate the approximation quality of the two characterizations, where fabric tensors of higher orders are employed. It is shown that the fitness is dominated by the dispersion degree of the original ODFs rather than the orders of fabric tensors. One application of tensor-valued ODF and fabric tensor in continuum damage mechanics is presented.

Existence of Subharmonic Solutions for a Class of Second-Order $p$ -Laplacian Systems with Impulsive Effects

Fri, 05 Apr 2013 11:07 EDT

Wen-Zhen Gong, Qiongfen Zhang, X. H. Tang

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
By using minimax methods in critical point theory, a new existence theorem of infinitely many periodic solutions is obtained for a class of second-order $p$ -Laplacian systems with impulsive effects. Our result generalizes many known works in the literature.

New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities

Fri, 05 Apr 2013 11:07 EDT

Hua-feng Ge

Source: J. Appl. Math., Volume 2012, 7 pages.

Abstract:
We obtain new sharp bounds for the Bernoulli numbers: $2(2n)!/({\pi }^{2n}({2}^{2n}-1))<|{B}_{2n}|\le (2({2}^{2k}-1)/{2}^{2k})\zeta (2k)(2n)!/({\pi }^{2n}({2}^{2n}-1))$ , $n=k,k+1,\dots , k\in {N}^{+}$ , and establish sharpening of Papenfuss's inequalities, the refinements of Becker-Stark, andSteckin's inequalities. Finally, we show a new simple proof of Ruehr-Shafer inequality.

Analytic Approximation of the Solutions of Stochastic Differential Delay Equations with Poisson Jump and Markovian Switching

Fri, 05 Apr 2013 11:07 EDT

Hua Yang, Feng Jiang

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
We are concerned with the stochastic differential delay equations with Poisson jump and Markovian switching (SDDEsPJMSs). Most SDDEsPJMSs cannot be solved explicitly as stochastic differential equations. Therefore, numerical solutions have become an important issue in the study of SDDEsPJMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEsPJMSs when the drift and diffusion coefficients are Taylor approximations.

Least Squares Problems with Absolute Quadratic Constraints

Fri, 05 Apr 2013 11:07 EDT

R. Schöne, T. Hanning

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.

Bernstein Widths of Some Classes of Functions Defined by a Self-Adjoint Operator

Fri, 05 Apr 2013 11:07 EDT

Guo Feng

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
We consider the classes of periodic functions with formal self-adjoint linear differential operators ${W}_{p}({ℒ}_{r})$ , which include the classical Sobolev class as its special case. Using the iterative method of Buslaev, with the help of the spectrum of linear differential equations, we determine the exact values of Bernstein width of the classes ${W}_{p}({\mathbb{C}}_{r})$ in the space ${L}_{q}$ for $1<p\le q<\infty $ .

Stability of Jensen-Type Functional Equations on Restricted Domains in a Group and Their Asymptotic Behaviors

Fri, 05 Apr 2013 11:07 EDT

Jae-Young Chung, Dohan Kim, John Michael Rassias

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
We consider the Hyers-Ulam stability problems for the Jensen-type functional equations in general restricted domains. The main purpose of this paper is to find the restricted domains for which the functional inequality satisfied in those domains extends to the inequality for whole domain. As consequences of the results we obtain asymptotic behavior of the equations.

Shrinking Projection Method of Fixed Point Problems for Asymptotically Pseudocontractive Mapping in the Intermediate Sense and Mixed Equilibrium Problems in Hilbert Spaces

Fri, 05 Apr 2013 11:07 EDT

Pattanapong Tianchai

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
This paper is concerned with a common element of the set of fixed point for an asymptotically pseudocontractive mapping in the intermediate sense and the set of solutions of the mixed equilibrium problems in Hilbert spaces. The strong convergence theorem for the above two sets is obtained by a general iterative scheme based on the shrinking projection method, which extends and improves that of Qin et al. (2010) and many others.

Robust Stochastic Stability Analysis for Uncertain Neutral-Type Delayed Neural Networks Driven by Wiener Process

Fri, 05 Apr 2013 11:07 EDT

Weiwei Zhang, Linshan Wang

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
The robust stochastic stability for a class of uncertain neutral-type delayed neural networks driven by Wiener process is investigated. By utilizing the Lyapunov-Krasovskii functional and inequality technique, some sufficient criteria are presented in terms of linear matrix inequality (LMI) to ensure the stability of the system. A numerical example is given to illustrate the applicability of the result.

Asymptotic Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying Delays

Fri, 05 Apr 2013 11:07 EDT

Yutian Zhang

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
This work addresses the asymptotic stability for a class of impulsive cellular neural networks with time-varying delays and reaction-diffusion. By using the impulsive integral inequality of Gronwall-Bellman type and Hardy-Sobolev inequality as well as piecewise continuous Lyapunov functions, we summarize some new and concise sufficient conditions ensuring the global exponential asymptotic stability of the equilibrium point. The provided stability criteria are applicable to Dirichlet boundary condition and showed to be dependent on all of the reaction-diffusion coefficients, the dimension of the space, the delay, and the boundary of the spatial variables. Two examples are finally illustrated to demonstrate the effectiveness of our obtained results.

Numerical Solution of Poisson's Equation Using a Combination of Logarithmic and Multiquadric Radial Basis Function Networks

Fri, 05 Apr 2013 11:07 EDT

Mohammad Mehdi Mazarei, Azim Aminataei

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
This paper presents numerical solution of elliptic partial differential equations (Poisson's equation) using a combination of logarithmic and multiquadric radial basis function networks. This method uses a special combination between logarithmic and multiquadric radial basis functions with a parameter $r$ . Further, the condition number which arises in the process is discussed, and a comparison is made between them with our earlier studies and previously known ones. It is shown that the system is stable.

A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators

Fri, 05 Apr 2013 11:07 EDT

Yaqin Wang

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality, the set of solutions of the generalized mixed equilibrium problem, and zeros of maximal monotone operators in a Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. The results obtained in this paper improve and extend the result of Zeng et al. (2010) and many others.

Couple-Stress Fluid Improves Dynamic Response of Gear-Pair System Supported by Journal Bearings

Fri, 05 Apr 2013 11:07 EDT

Cai-Wan Chang-Jian, Shiuh Ming Chang, Hsieh-Chung Hsu

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
A systematic analysis of the dynamic behavior of a gear-bearing system with nonlinear suspension, couple-stress fluid flow effect, nonlinear oil-film force, and nonlinear gear mesh force is performed in the present study. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless rotational speed ratio as a control parameter. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents and fractal dimension of the gear-bearing system. The numerical results reveal that the system exhibits a diverse range of periodic, subharmonic, quasiperiodic, and chaotic behaviors. The couple-stress fluid would be a useful lubricating fluid to suppress nonlinear dynamic responses and improve the steady of the systems. The results presented in this study provide some useful insights into the design and development of a gear-bearing system for rotating machinery that operates in highly rotational speed and highly nonlinear regimes.

Orthogonal Multiwavelet Frames in ${L}^{2}({R}^{d})$

Fri, 05 Apr 2013 11:07 EDT

Liu Zhanwei, Hu Guoen, Wu Guochang

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
We characterize the orthogonal frames and orthogonal multiwavelet frames in ${L}^{2}({R}^{d})$ with matrix dilations of the form $(Df)(x)=\sqrt{|\text{d}\text{e}\text{t}A|}f(Ax)$ , where $A$ is an arbitrary expanding $d×d$ matrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present an algorithm for the construction of arbitrarily many orthogonal multiwavelet tight frames. Finally, we give a general construction algorithm for orthogonal multiwavelet tight frames from a scaling function.

On Exponential Stability Conditions of Descriptor Systems with Time-Varying Delay

Fri, 05 Apr 2013 11:07 EDT

S. Cong, Z.-B. Sheng

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
We are interested in the exponential stability of the descriptor system, which is composed of the slow and fast subsystems with time-varying delay. In computing a kind of Lyapunov functional, we employ a necessary number of slack matrices to render the balance and to yield the convexity condition for reducing the conservatism and dealing with the case of time-varying delay. Therefore, we can get the decay rate of the slow variables. Moreover, we characterize the effect of the fast subsystem on the derived decay rate and then prove the fast variables to decay exponentially through a perturbation approach. Finally, we provide an example to demonstrate the effectiveness of the method.

A Decomposition Algorithm for Convex Nondifferentiable Minimization with Errors

Fri, 05 Apr 2013 11:07 EDT

Yuan Lu, Li-Ping Pang, Jie Shen, Xi-Jun Liang

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
A decomposition algorithm based on proximal bundle-type method with inexact data is presented for minimizing an unconstrained nonsmooth convex function $f$ . At each iteration, only the approximate evaluation of $f$ and its approximate subgradients are required which make the algorithm easier to implement. It is shown that every cluster of the sequence of iterates generated by the proposed algorithm is an exact solution of the unconstrained minimization problem. Numerical tests emphasize the theoretical findings.

An Optimal Iteration Method for Strongly Nonlinear Oscillators

Fri, 05 Apr 2013 11:07 EDT

Vasile Marinca, Nicolae Herişanu

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
We introduce a new method, namely, the Optimal Iteration Perturbation Method (OIPM), to solve nonlinear differential equations of oscillators with cubic and harmonic restoring force. We illustrate that OIPM is very effective and convenient and does not require linearization or small perturbation. Contrary to conventional methods, in OIPM, only one iteration leads to high accuracy of the solutions. The main advantage of this approach consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary. A very good agreement was found between approximate and numerical solutions, which prove that OIPM is very efficient and accurate.

Global Existence of Classical Solutions to a Three-Species Predator-Prey Model with Two Prey-Taxes

Fri, 05 Apr 2013 11:07 EDT

Chenglin Li, Zhangguo Hong

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
We are concerned with three-species predator-prey model including two prey-taxes and Holling type II functional response under no flux boundary condition. By applying the contraction mapping principle, the parabolic Schauder estimates, and parabolic ${L}^{p}$ estimates, we prove that there exists a unique global classical solution of this system.

A Comparison between Fixed-Basis and Variable-Basis Schemes forFunction Approximation and Functional Optimization

Fri, 05 Apr 2013 11:07 EDT

Giorgio Gnecco

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
Fixed-basis and variable-basis approximation schemes are compared for the problems of functionapproximation and functional optimization (also known as infinite programming). Classesof problems are investigated for which variable-basis schemes with sigmoidal computationalunits perform better than fixed-basis ones, in terms of the minimum number of computationalunits needed to achieve a desired error in function approximation or approximate optimization.Previously known bounds on the accuracy are extended, with better rates, to families of $d$ -variable functions whose actual dependence is on a subset of ${d}^{\prime }\ll d$ variables, where the indicesof these ${d}^{\prime }$ variables are not known a priori.

Analysis of the M/M/N/N Queue with Two Types of Arrival Process: Applications to Future Mobile Radio Systems

Fri, 05 Apr 2013 11:07 EDT

Peter J. Smith, Abdulla Firag, Pawel A. Dmochowski, Mansoor Shafi

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
The queueing system considered is essentially a M/M/N/N queue where two types of users compete for the $N$ resources. The users may have different arrival and service rates and are denoted as primary or secondary users. The primary users have priority access to the resources, and three levels of priority are considered: perfect priority, partial priority, and no priority. This system models the recently developed cognitive radio concept, a methodology that has been proposed for future mobile radio systems. In this context, the primary users have certain rights to use the resources, whereas the secondary users must make opportunistic use of the resources without impacting too much on the performance of the primary users. For all priority settings, the mean number of primary and secondary users is derived as are the blocking probabilities for both users. When no priority is given to the primary user, the system collapses to a truncated form of two independent M/M/∞ queues. The product form solution for this special case is known, and, here, these results are given in a novel, compact form. In the case of nonzero priority, the dropping probability for the secondary users is also derived.

An Efficient Collision Detection Method for Computing Discrete Logarithms with Pollard's Rho

Fri, 05 Apr 2013 11:07 EDT

Ping Wang, Fangguo Zhang

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
Pollard's rho method and its parallelized variant are at present known as the best generic algorithms for computing discrete logarithms. However, when we compute discrete logarithms in cyclic groups of large orders using Pollard's rho method, collision detection is always a high time and space consumer. In this paper, we present a new efficient collision detection algorithm for Pollard's rho method. The new algorithm is more efficient than the previousdistinguished point method and can be easily adapted to other applications. However, the new algorithm does not work with the parallelized rho method, but it can be parallelized with Pollard's lambda method. Besides the theoretical analysis, we also compare the performances of the new algorithm with the distinguished point method in experiments with elliptic curve groups. The experiments show that the new algorithm can reduce the expected number of iterations before reaching a match from 1.309 $\sqrt{|G|}$ to 1.295 $\sqrt{|G|}$ under the same space requirements for the single rho method.

Modified and Simplified Sectional Flexibility of a Cracked Beam

Fri, 05 Apr 2013 11:07 EDT

Chih-Shiung Wang, Lin-Tsang Lee

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
This paper presents a new sectional flexibility factor to simulate the reduction of the stiffness of a single-edge open cracked beam. The structural model for crack of the beam is considered as a rotational spring which is related to the ratio of crack depth to the beam height, a/h . The mathematical model of this single-edge open crack beam is considered as an Euler-Bernoulli beam. The modified factor, f(a/h) , derived in this paper is in good agreement with previous researchers' results for crack depth ratio a/h less than 0.5. The natural frequencies and corresponding mode shapes for lateral vibration with different types of single-edge open crack beams can then be evaluated by applying this modified factor f(a/h) . Using the compatibility conditions on the crack and the analytical transfer matrix method, the numerical solutions for natural frequencies of the cracked beam are obtained. The natural frequencies and the mode shapes with crack at different locations are obtained and compared with the latest research literature. The numerical results of the proposed cracked beam model obtained by this method can be extended to construct frequency contour. The natural frequencies measured from field can be used in solving the inverse problem to identify cracks in structures.

Stability of an $n$ -Dimensional Mixed-Type Additive and Quadratic Functional Equation in Random Normed Spaces

Fri, 05 Apr 2013 11:07 EDT

Yang-Hi Lee, Soon-Mo Jung

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
We investigate the stability problems for the $n$ -dimensional mixed-type additive and quadratic functional equation $2f({\sum }_{j=1}^{n}{x}_{j})+{\sum }_{1\le i,j\le n,\mathrm{ }i\ne j}f({x}_{i}-{x}_{j})=(n+1){\sum }_{j=1}^{n}f({x}_{j})+(n-1){\sum }_{j=1}^{n}f(-{x}_{j})$ in random normed spaces by applying the fixed point method.

Well-Posedness for a Class of Strongly Mixed Variational-Hemivariational Inequalities with Perturbations

Fri, 05 Apr 2013 11:07 EDT

Lu-Chuan Ceng, Ngai-Ching Wong, Jen-Chih Yao

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
The concept of well-posedness for a minimization problem is extended to develop the concept of well-posedness for a class of strongly mixed variational-hemivariational inequalities with perturbations which includes as a special case the class of variational-hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed strongly mixed variational-hemivariational inequality and give some conditions under which the strongly mixed variational-hemivariational inequality is strongly well-posed in the generalized sense. On the other hand, it is also proven that under some mild conditions there holds the equivalence between the well posedness for a strongly mixed variational-hemivariational inequality and the well-posedness for the corresponding inclusion problem.

A Basic Inequality for the Tanaka-Webster Connection

Fri, 05 Apr 2013 11:07 EDT

Dae Ho Jin, Jae Won Lee

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
For submanifolds tangent to the structure vector field in Sasakian space forms, we establish a Chen's basic inequality between the main intrinsic invariants of the submanifold (namely, its pseudosectional curvature and pseudosectional curvature on one side) and the main extrinsic invariant (namely, squared pseudomean curvature on the other side) with respect to the Tanaka-Webster connection. Moreover, involving the pseudo-Ricci curvature and the squared pseudo-mean curvature, we obtain a basic inequality for submanifolds of a Sasakian space form tangent to the structure vector field in terms of the Tanaka-Webster connection.

Stabilities of Cubic Mappings in Various Normed Spaces: Direct and Fixed Point Methods

Fri, 05 Apr 2013 11:07 EDT

H. Azadi Kenary, H. Rezaei, S. Talebzadeh, S. Jin Lee

Source: J. Appl. Math., Volume 2012, 28 pages.

Abstract:
In 1940 and 1964, Ulam proposed the general problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?”. In 1941, Hyers solved this stability problem for linear mappings. According to Gruber (1978) this kind of stability problems are of the particular interest in probability theory and in the case of functional equations of different types. In 1981, Skof was the first author to solve the Ulam problem for quadratic mappings. In 1982–2011, J. M. Rassias solved the above Ulam problem for linear and nonlinear mappings and established analogous stability problems even on restricted domains. The purpose of this paper is the generalized Hyers-Ulam stability for the following cubic functional equation: $\mathrm{f}(\mathrm{m}\mathrm{x}+\mathrm{y})+\mathrm{f}(\mathrm{m}\mathrm{x}-\mathrm{y})=\mathrm{m}\mathrm{f}(\mathrm{x}+\mathrm{y})+\mathrm{m}\mathrm{f}(\mathrm{x}-\mathrm{y})+2({\mathrm{m}}^{3}-\mathrm{m})\mathrm{f}(\mathrm{x}),\mathrm{m}\ge 2$ in various normed spaces.

Inverse Source Identification by the Modified Regularization Method on Poisson Equation

Fri, 05 Apr 2013 11:07 EDT

Xiao-Xiao Li, Heng Zhen Guo, Shi Min Wan, Fan Yang

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
This paper deals with an inverse problem for identifying an unknown source which depends only on one variable in two-dimensional Poisson equation, with the aid of an extra measurement at an internal point. Since this problem is illposed, we obtain the regularization solution by the modified regularization method. Furthermore, we obtain the Hölder-type error estimate between the regularization solution and the exact solution. The numerical results show that the proposed method is stable and the unknown source is recovered very well.

Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay

Fri, 05 Apr 2013 11:07 EDT

Yingguo Li

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
We consider the nonlinear dynamical behavior of a three-dimensional recurrent neural network with time delay. By choosing the time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Applying the nor- mal form method and center manifold theory, we obtain some local bifurcation results and derive formulas for determining the bifurcation direction and the stability of the bifurcated periodic solution. Some numerical examples are also presented to verify the theoretical analysis.

Fixed Point Theorems for $\psi $ -Contractive Mappings in Ordered Metric Spaces

Fri, 05 Apr 2013 11:07 EDT

Chi-Ming Chen

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
We obtain some new fixed point theorems for $\psi $ -contractive mappings in ordered metric spaces. Our results generalize or improve many recent fixed point theorems in the literature (e.g., Harjani et al., 2011 and 2010).

A Family of Three-Point Methods of Ostrowski's Type for Solving Nonlinear Equations

Fri, 05 Apr 2013 11:07 EDT

Jovana Džunić, Miodrag S. Petković

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
A class of three-point methods for solving nonlinear equations of eighth order is constructed. These methods are developed by combining two-point Ostrowski's fourth-order methods and a modified Newton's method in the third step, obtained by a suitable approximation of the first derivative using the product of three weight functions. The proposed three-step methods have order eight costing only four function evaluations, which supports the Kung-Traub conjecture on the optimal order of convergence. Two numerical examples for various weight functions are given to demonstrate very fast convergence and high computational efficiency of the proposed multipoint methods.

Analytical Solutions for Corrosion-Induced Cohesive Concrete Cracking

Fri, 05 Apr 2013 11:07 EDT

Hua-Peng Chen, Nan Xiao

Source: J. Appl. Math., Volume 2012, 25 pages.

Abstract:
The paper presents a new analytical model to study the evolution of radial cracking around a corroding steel reinforcement bar embedded in concrete. The concrete cover for the corroding rebar is modelled as a thick-walled cylinder subject to axisymmetrical displacement constraint at the internal boundary generated by expansive corrosion products. A bilinear softening curve reflecting realistic concrete property, together with the crack band theory for concrete fracture, is applied to model the residual tensile stress in the cracked concrete. A governing equation for directly solving the crack width in cover concrete is established for the proposed analytical model. Closed-form solutions for crack width are then obtained at various stages during the evolution of cracking in cover concrete. The propagation of crack front with corrosion progress is studied, and the time to cracking on concrete cover surface is predicted. Mechanical parameters of the model including residual tensile strength, reduced tensile stiffness, and radial pressure at the bond interface are investigated during the evolution of cover concrete cracking. Finally, the analytical predictions are examined by comparing with the published experimental data, and mechanical parameters are analysed with the progress of reinforcement corrosion and through the concrete cover.

Dynamic Properties of a Differential-Algebraic Biological Economic System

Fri, 05 Apr 2013 11:07 EDT

Hongyang Zhang, Chunrui Zhang

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
We analyze a differential-algebraic biological economic system with time delay. The model has two different Holling functional responses. By considering time delay as bifurcation parameter, we find that there exists stability switches when delay varies, and the Hopf bifurcation occurs when delay passes through a sequence of critical values. Furthermore, we also consider the stability and direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, using Matlab software, we do some numerical simulations to illustrate the effectiveness of our results.

Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem

Fri, 05 Apr 2013 11:07 EDT

R. J. Moitsheki, M. D. Mhlongo

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. The effects of thermogeometric fin parameter and the exponent on temperature are studied. Also, the fin efficiency is analyzed.

Efficient Method to Approximately Solve Retrial Systems with Impatience

Fri, 05 Apr 2013 11:07 EDT

Jose Manuel Gimenez-Guzman, M. Jose Domenech-Benlloch, Vicent Pla, Jorge Martinez-Bauset, Vicente Casares-Giner

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
We present a novel technique to solve multiserver retrial systems with impatience. Unfortunately these systems do not present an exact analytic solution, so it is mandatory to resort to approximate techniques. This novel technique does not rely on the numerical solution of the steady-state Kolmogorov equations of the Continuous Time Markov Chain as it is common for this kind of systems but it considers the system in its Markov Decision Process setting. This technique, known as value extrapolation, truncates the infinite state space using a polynomial extrapolation method to approach the states outside the truncated state space. A numerical evaluation is carried out to evaluate this technique and to compare its performance with previous techniques. The obtained results show that value extrapolation greatly outperforms the previous approaches appeared in the literature not only in terms of accuracy but also in terms of computational cost.

Inverse Projective Synchronization between Two Different Hyperchaotic Systems with Fractional Order

Fri, 05 Apr 2013 11:07 EDT

Yi Chai, Liping Chen, Ranchao Wu

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
This paper mainly investigates a novel inverse projective synchronization between two different fractional-order hyperchaotic systems, that is, the fractional-order hyperchaotic Lorenz system and the fractional-order hyperchaotic Chen system. By using the stability theory of fractional-order differential equations and Lyapunov equations for fractional-order systems, two kinds of suitable controllers for achieving inverse projective synchronization are designed, in which the generalized synchronization, antisynchronization, and projective synchronization of fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system are also successfully achieved, respectively. Finally, simulations are presented to demonstrate the validity and feasibility of the proposed method.

New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method

Fri, 05 Apr 2013 11:07 EDT

Hasibun Naher, Farah Aini Abdullah, M. Ali Akbar

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
We construct new analytical solutions of the ( $3+1$ )-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.

Large Eddy Simulation of Turbulent Flow and Heat Transfer in a Ribbed Coolant Passage

Fri, 05 Apr 2013 11:07 EDT

Abhishek G. Ramgadia, Arun K. Saha

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
Numerical simulations of hydrodynamic and thermally fully developed turbulent flow are presented for flow through a stationary duct with periodic array of inline transverse rib turbulators. The rib height to hydraulic diameter ratio $(e/{D}_{h})$ is 0.1 and the rib pitch to rib height ratio $(P/e)$ is 10. The effect of secondary flow due to presence of rib turbulators on heat and mass transfer has been investigated. The present work reviews the use of a large eddy simulation (LES) turbulence model, known as shear-improved Smagorinsky model (SISM), for predicting flow and heat transfer characteristics in the fully developed periodic flow region. The computations are performed for Reynolds number of 2,053 and the working fluid chosen to be air, the Prandtl number of which is 0.7. Instantaneous flow field, time-mean, and turbulent quantities are reported together with heat transfer and a close match with experiments has been observed.

A Dynamic Model for Fishery Resource with Reserve Area and Taxation

Fri, 05 Apr 2013 11:07 EDT

Hai-Feng Huo, Hui-Min Jiang, Xin-You Meng

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
The present paper deals with a dynamic reaction model of a fishery. The dynamics of a fishery resource system in an aquatic environment consists of two zones: a free fishing zone and a reserve zone. To protect fish population from over exploitation, a control instrument tax is imposed. The existence of its steady states and their stability are studied. The optimal harvest policy is discussed next with the help of Pontryagin's maximum principle. Our theoretical results are confirmed by numerical simulation.

The Existence of Solutions for a Fractional 2 $m$ -Point Boundary Value Problems

Fri, 05 Apr 2013 11:07 EDT

Gang Wang, Wenbin Liu, Jinyun Yang, Sinian Zhu, Ting Zheng

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
By using the coincidence degree theory, we consider the following 2 $m$ -point boundary value problem for fractional differential equation ${D}_{0+}^{\alpha }u(t)=f(t,u(t),{D}_{0+}^{\alpha -1}u(t),{D}_{0+}^{\alpha -2}u(t))+e(t)$ , $0<t<1$ , ${{I}_{0+}^{3-\alpha }u(t)|}_{t=0}=0,{D}_{0+}^{\alpha -2}u(1)={\sum }_{i=1}^{m-2}{a}_{i}{D}_{0+}^{\alpha -2}u({\xi }_{i}),u(1)={\sum }_{i=1}^{m-2}{b}_{i}u({\eta }_{i}),$ where $2<\alpha \le 3,$ ${D}_{0+}^{\alpha }$ and ${I}_{0+}^{\alpha }$ are the standard Riemann-Liouville fractional derivative and fractional integral, respectively. A new result on the existence of solutions for above fractional boundary value problem is obtained.

Multiple Positive Solutions of Singular Nonlinear Sturm-Liouville Problems with Carathéodory Perturbed Term

Fri, 05 Apr 2013 11:07 EDT

Yuefeng Han, Xinguang Zhang, Lishan Liu, Yonghong Wu

Source: J. Appl. Math., Volume 2012, 23 pages.

Abstract:
By employing a well-known fixed point theorem, we establish the existence of multiple positive solutions for the following fourth-order singular differential equation $Lu=p(t)f(t,u(t),{u}^{\prime \prime }(t))-g(t,u(t),{u}^{\prime \prime }(t)),0<t<1,{\alpha }_{1}u(0)-{\beta }_{1}u\text{'}(0)=0,{\gamma }_{1}u(1)+{\delta }_{1}u\text{'}(1)=0,{\alpha }_{2}{u}^{\prime \prime }(0)-{\beta }_{2}{u}^{\prime \prime \prime }(0)=0,{\gamma }_{2}{u}^{\prime \prime }(1)+{\delta }_{2}{u}^{\prime \prime \prime }(1)=0$ , with ${\alpha }_{i},{\beta }_{i},{\gamma }_{i},{\delta }_{i}\ge 0$ and ${\beta }_{i}{\gamma }_{i}+{\alpha }_{i}{\gamma }_{i}+{\alpha }_{i}{\delta }_{i}>0,\mathrm{ }\mathrm{ }i=1,2$ , where $L$ denotes the linear operator $Lu:=({ru}^{\prime \prime \prime })\text{'}-q{u}^{\prime \prime },r\in {C}^{1}([0,1],(0,+\infty ))$ , and $q\in C([0,1],[0,+\infty ))$ . This equation is viewed as a perturbation of the fourth-order Sturm-Liouville problem, where the perturbed term $g:(0,1)×[0,+\infty )×(-\infty ,+\infty )\to (-\infty ,+\infty )$ only satisfies the global Carathéodory conditions, which implies that the perturbed effect of $g$ on $f$ is quite large so that the nonlinearity can tend to negative infinity at some singular points.

Generalized Lower and Upper Approximations in Quantales

Fri, 05 Apr 2013 11:07 EDT

Qimei Xiao, Qingguo Li

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
We introduce the concepts of set-valued homomorphism and strong set-valued homomorphism of a quantale which are the extended notions of congruence and complete congruence, respectively. The properties of generalized lower and upper approximations, constructed by a set-valued mapping, are discussed.

On Generalised Interval-Valued Fuzzy Soft Sets

Fri, 05 Apr 2013 11:07 EDT

Xiaoqiang Zhou, Qingguo Li, Lankun Guo

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of generalised interval-valued fuzzy soft set are proposed and their basic properties are studied. The lattice structures of generalised interval-valued fuzzy soft set are also discussed. Furthermore, an application of the new approach in decision making based on generalised interval-valued fuzzy soft set is developed.

About Nodal Systems for Lagrange Interpolation on the Circle

Fri, 05 Apr 2013 11:07 EDT

E. Berriochoa, A. Cachafeiro, J. M. García Amor

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
We study the convergence of the Laurent polynomials of Lagrange interpolation on the unit circle for continuous functions satisfying a condition about their modulus of continuity. The novelty of the result is that now the nodal systems are more general than those constituted by the n roots of complex unimodular numbers and the class of functions is different from the usually studied. Moreover, some consequences for the Lagrange interpolation on $[-1,1]$ and the Lagrange trigonometric interpolation are obtained.

Approximate Implicitization Using Linear Algebra

Fri, 05 Apr 2013 11:07 EDT

Oliver J. D. Barrowclough, Tor Dokken

Source: J. Appl. Math., Volume 2012, 25 pages.

Abstract:
We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD) systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.

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

Fri, 05 Apr 2013 11:07 EDT

Mahesha Narayana, Precious Sibanda

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
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.

Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile Regression

Fri, 05 Apr 2013 11:07 EDT

Dao-Hong Xiang, Ting Hu, Ding-Xuan Zhou

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
We study learning algorithms generated by regularization schemes in reproducingkernel Hilbert spaces associated with an $ϵ$ -insensitive pinball loss. This lossfunction is motivated by the $ϵ$ -insensitive loss for support vector regression and thepinball loss for quantile regression. Approximation analysis is conducted for thesealgorithms by means of a variance-expectation bound when a noise condition issatisfied for the underlying probability measure. The rates are explicitly derivedunder a priori conditions on approximation and capacity of the reproducing kernelHilbert space. As an application, we get approximation orders for the supportvector regression and the quantile regularized regression.

Soret and Dufour Effects on Natural Convection Flow Past a Vertical Surface in a Porous Medium with Variable Viscosity

Fri, 05 Apr 2013 11:07 EDT

M. B. K. Moorthy, K. Senthilvadivu

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
The heat and mass transfer characteristics of natural convection about a vertical surface embedded in a saturated porous medium subject to variable viscosity are numerically analyzed, by taking into account the diffusion-thermo (Dufour) and thermal-diffusion (Soret) effects. The governing equations of continuity, momentum, energy, and concentrations are transformed into nonlinear ordinary differential equations, using similarity transformations, and then solved by using Runge-Kutta-Gill method along with shooting technique. The parameters of the problem are variable viscosity, buoyancy ratio, Lewis number, Prandtl number, Dufour effect, Soret effect, and Schmidt number. The velocity, temperature, and concentration distributions are presented graphically. The Nusselt number and Sherwood number are also derived and discussed numerically.

Wavelet Collocation Method for Solving Multiorder Fractional Differential Equations

Fri, 05 Apr 2013 11:07 EDT

M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, F. Mohammadi

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
The operational matrices of fractional-order integration for the Legendre and Chebyshev wavelets are derived. Block pulse functions and collocation method are employed to derive a general procedure for forming these matrices for both the Legendre and the Chebyshev wavelets. Then numerical methods based on wavelet expansion and these operational matrices are proposed. In this proposed method, by a change of variables, the multiorder fractional differential equations (MOFDEs) with nonhomogeneous initial conditions are transformed to the MOFDEs with homogeneous initial conditions to obtain suitable numerical solution of these problems. Numerical examples are provided to demonstrate the applicability and simplicity of the numerical scheme based on the Legendre and Chebyshev wavelets.

An Energy Conservation Algorithm for Nonlinear Dynamic Equation

Fri, 05 Apr 2013 11:07 EDT

Jian Pang, Yu Du, Ping Hu, Weidong Li, Z. D. Ma

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
An energy conservation algorithm for numerically solving nonlinear multidegree-of-freedom (MDOF) dynamic equations is proposed. Firstly, by Taylor expansion and Duhamel integration, an integral iteration formula for numerically solving the nonlinear problems can be achieved. However, this formula still includes a parameter that is to be determined. Secondly, through some mathematical manipulations, the original dynamical equation can be further converted into an energy conservation equation which can then be used to determine the unknown parameter. Finally, an accurate numerical result for the nonlinear problem is achieved by substituting this parameter into the integral iteration formula. Several examples are used to compare the current method with the well-known Runge-Kutta method. They all show that the energy conservation algorithm introduced in this study can eliminate algorithm damping inherent in the Runge-Kutta algorithm and also has better stability for large integral steps.

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

Fri, 05 Apr 2013 11:07 EDT

Reza Hosseini, Sadegh Poozesh, Saeed Dinarvand

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
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.

Towards a Prototype of a Spherical Tippe Top

Fri, 05 Apr 2013 11:07 EDT

M. C. Ciocci, B. Malengier, B. Langerock, B. Grimonprez

Source: J. Appl. Math., Volume 2012, 34 pages.

Abstract:
Among spinning objects, the tippe top exhibits one of the most bizarre and counterintuitive behaviours. The commercially available tippe tops basically consist of a section of a sphere with a rod. After spinning on its rounded body, the top flips over and continues spinning on the stem. The commonly used simplified mathematical model for the tippe top is a sphere whose mass distribution is axially but not spherically symmetric, spinning on a flat surface subject to a small friction force that is due to sliding. Three main different dynamical behaviours are distinguished: tipping, nontipping, hanging , that is, the top rises but converges to an intermediate state instead of rising all the way to the vertical state. Subclasses according to the stability of relative equilibria can further be distinguished. Our concern is the degree of confidence in the mathematical model predictions, we applied 3D printing and rapid prototyping to manufacture a “3-in-1 toy” that could catch the three main characteristics defining the three main groups in the classification of spherical tippe tops as mentioned above. We propose three designs. This “ toy ” is suitable to validate the mathematical model qualitatively and quantitatively.

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

Fri, 05 Apr 2013 11:07 EDT

Changqing Yang, Jianhua Hou

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
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.

Hidden and Not So Hidden Symmetries

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

Xu Wang, Jun Wang

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
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.

Discrete-Time Indefinite Stochastic LQ Control via SDP and LMI Methods

Fri, 05 Apr 2013 11:07 EDT

Shaowei Zhou, Weihai Zhang

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
This paper studies a discrete-time stochastic LQ problem over an infinite time horizon with state-and control-dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. We mainly use semidefinite programming (SDP) and its duality to treat corresponding problems. Several relations among stability, SDP complementary duality, the existence of the solution to stochastic algebraic Riccati equation (SARE), and the optimality of LQ problem are established. We can test mean square stabilizability and solve SARE via SDP by LMIs method.

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

Fri, 05 Apr 2013 11:07 EDT

S. S. Motsa, S. Shateyi

Source: J. Appl. Math., Volume 2012, 30 pages.

Abstract:
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.

On Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces

Fri, 05 Apr 2013 11:07 EDT

Zhenhua Jiao

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
The author extends two fixed point theorems (due to Gregori, Sapena, and Žikić, resp.) in fuzzy metric spaces to intuitionistic fuzzy metric spaces.

A Class of Semilocal $E$ -Preinvex Functions and Its Applications in Nonlinear Programming

Fri, 05 Apr 2013 11:07 EDT

Hehua Jiao, Sanyang Liu, Xinying Pai

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
A kind of generalized convex set, called as local star-shaped $E$ -invex set with respect to $\mathrm{\eta ,}$ is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal $E$ -preinvex functions, which is a generalization of semi- $E$ -preinvex functions and semilocal $E$ -convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.

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

Fri, 05 Apr 2013 11:07 EDT

Changchun Liu, Junchao Gao, Songzhe Lian

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
The existence of weak solutions is studied to the initial Dirichlet problemof the equation ${u}_{t}=u\text{div}({|\nabla u|}^{p(x)-2}\nabla u)$ , 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.

Forecasting Crude Oil Price and Stock Price by Jump Stochastic Time Effective Neural Network Model

Fri, 05 Apr 2013 11:07 EDT

Jun Wang, Huopo Pan, Fajiang Liu

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
The interacting impact between the crude oil prices and the stock market indices in China is investigated in the present paper, and the corresponding statistical behaviors are also analyzed. The database is based on the crude oil prices of Daqing and Shengli in the 7-year period from January 2003 to December 2009 and also on the indices of SHCI, SZCI, SZPI, and SINOPEC with the same time period. A jump stochastic time effective neural network model is introduced and applied to forecast the fluctuations of the time series for the crude oil prices and the stock indices, and we study the corresponding statistical properties by comparison. The experiment analysis shows that when the price fluctuation is small, the predictive values are close to the actual values, and when the price fluctuation is large, the predictive values deviate from the actual values to some degree. Moreover, the correlation properties are studied by the detrended fluctuation analysis, and the results illustrate that there are positive correlations both in the absolute returns of actual data and predictive data.

Finite-Time ${H}_{\infty }$ Filtering for Singular Stochastic Systems

Fri, 05 Apr 2013 11:07 EDT

Caixia Liu, Yingqi Zhang, Huixia Sun

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
This paper addresses the problem of finite-time ${H}_{\infty }$ filtering for one family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Initially, the definitions of singular stochastic finite-time boundedness and singular stochastic ${H}_{\infty }$ finite-time boundedness are presented. Then, the ${H}_{\infty }$ filtering is designed for the class of singular stochastic systems with or without uncertain parameters to ensure singular stochastic finite-time boundedness of the filtering error system and satisfy a prescribed ${H}_{\infty }$ performance level in some given finite-time interval. Furthermore, sufficient criteria are presented for the solvability of the filtering problems by employing the linear matrix inequality technique. Finally, numerical examples are given to illustrate the validity of the proposed methodology.

Exponential Time Integration and Second-Order Difference Scheme for a Generalized Black-Scholes Equation

Fri, 05 Apr 2013 11:07 EDT

Zhongdi Cen, Anbo Le, Aimin Xu

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
We apply an exponential time integration scheme combined with a central difference scheme on a piecewise uniform mesh with respect to the spatial variable to evaluate a generalized Black-Scholes equation. We show that the scheme is second-order convergent for both time and spatial variables. It is proved that the scheme is unconditionally stable. Numerical results support the theoretical results.

Some Oscillation Results for Linear Hamiltonian Systems

Fri, 05 Apr 2013 11:07 EDT

Nan Wang, Fanwei Meng

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrix Hamiltonian system ${U}^{\prime }=A(t)U+B(t)V$ , ${V}^{\prime }=C(t)U-{A}^{\ast }(t)V$ . By using the standard integral averaging technique and positive functionals, new oscillation and intervaloscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the importance of our results.

An Underactuated Drift-Free Left Invariant Control System on a Specific Lie Group

Fri, 05 Apr 2013 11:07 EDT

Camelia Pop Arieşanu

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
The paper presents a geometrical overview on an optimal control problem on a special Lie group. The Hamilton-Poisson realization of the dynamics offers us the possibility to study the system from mechanical geometry point of view.

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

Fri, 05 Apr 2013 11:07 EDT

HyungMan Kim, Agassi Melikov, Mehriban Fattakhova, CheSoong Kim

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
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.

Geometric Analysis of Reachability and Observability for Impulsive Systems on Complex Field

Fri, 05 Apr 2013 11:07 EDT

Shouwei Zhao, Jitao Sun, Hai Lin

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
Nowadays, quantum systems have become one of the focuses of the ongoing research and they are typical complex systems, whose state variables are defined on the complex field. In this paper, the issue of reachability and observability is addressed for a class of linear impulsive systems on complex field, for simplicity, complex linear impulsive systems. This kind of time-driven impulsive systems allows free impulsive instants, which leads to the limitation of using traditional definitions of reachability and observability directly. New notations about the span reachable set and unobservable set are proposed. Sufficient and necessary conditions for span reachability and observability of such systems are established. Moreover, the explicit characterization of span reachable set and unobservable set is presented by geometric analysis. It is pointed out that the geometric conditions are equivalent to the algebraic ones in known results for special cases. Numerical examples are also presented to show the effectiveness of the proposed methods.

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

Fri, 05 Apr 2013 11:07 EDT

Zhanfei Zuo

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
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.

Radio Frequency Numerical Simulation Techniques Based on Multirate Runge-Kutta Schemes

Fri, 05 Apr 2013 11:07 EDT

Jorge F. Oliveira, José C. Pedro

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
Electronic circuit simulation, especially for radio frequency (RF) and microwave telecommunications, is being challenged by increasingly complex applications presenting signals of very different nature and evolving on widely separated time scales. In this paper, we will briefly review some recently developed ways to address these challenges, by describing some advanced numerical simulation techniques based on multirate Runge-Kutta schemes, which operate in the one-dimensional time and also within multidimensional frameworks.

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

Fri, 05 Apr 2013 11:07 EDT

Lee-Chae Jang

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
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.

Geodesic Effect Near an Elliptical Orbit

Fri, 05 Apr 2013 11:07 EDT

Alina-Daniela Vîlcu

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
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.

Derivatives of Multivariate Bernstein Operators and Smoothness with Jacobi Weights

Fri, 05 Apr 2013 11:07 EDT

Jianjun Wang, Zuoxiang Peng, Shukai Duan, Jia Jing

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
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.

A Newton Interpolation Approach to Generalized Stirling Numbers

Fri, 05 Apr 2013 11:07 EDT

Aimin Xu

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
We employ the generalized factorials to define a Stirling-type pair $\{s(n,k;\mathbf{\alpha },\mathbf{\beta },r),S(n,k;\mathbf{\alpha },\mathbf{\beta },r)\}$ which unifies various Stirling-type numbers investigated by previous authors. We make use of the Newton interpolation and divideddifferences to obtain some basic properties of the generalized Stirling numbers including the recurrence relation, explicit expression, and generating function. The generalizations of the well-known Dobinski's formula are further investigated.

$(\mathbf{\lambda },\mathbf{\mu })$ -Fuzzy Version of Ideals, Interior Ideals, Quasi-Ideals, and Bi-Ideals

Fri, 05 Apr 2013 11:07 EDT

Yuming Feng, P. Corsini

Source: J. Appl. Math., Volume 2012, 7 pages.

Abstract:
We introduced $(\lambda ,\mu )$ -fuzzy ideals, $(\lambda ,\mu )$ -fuzzy interior ideals, $(\lambda ,\mu )$ -fuzzy quasi-ideals, and $(\lambda ,\mu )$ -fuzzy bi-ideals of an ordered semigroup and studied them. When $\lambda =0$ and $\mu =1$ , 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).

Periodic Points and Fixed Points for the Weaker $(\varphi ,\phi )$ -Contractive Mappings in Complete Generalized Metric Spaces

Fri, 05 Apr 2013 11:07 EDT

Chi-Ming Chen, W. Y. Sun

Source: J. Appl. Math., Volume 2012, 7 pages.

Abstract:
We introduce the notion of weaker $(\varphi ,\phi )$ -contractivemapping 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.

Oscillator with a Sum of Noninteger-Order Nonlinearities

Fri, 05 Apr 2013 11:07 EDT

L. Cveticanin, T. Pogány

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
Free and self-excited vibrations of conservative oscillators with polynomial nonlinearity are considered. Mathematical model of the system is a second-order differential equation with a nonlinearity of polynomial type, whose terms are of integer and/or noninteger order. For the case when only one nonlinear term exists, the exact analytical solution of the differential equation is determined as a cosine-Ateb function. Based on this solution, the asymptotic averaging procedure for solving the perturbed strong non-linear differential equation is developed. The method does not require the existence of the small parameter in the system. Special attention is given to the case when the dominant term is a linear one and to the case when it is of any non-linear order. Exact solutions of the averaged differential equations of motion are obtained. The obtained results are compared with “exact” numerical solutions and previously obtained analytical approximate ones. Advantages and disadvantages of the suggested procedure are discussed.

Inequalities between Power Means and Convex Combinations of the Harmonic and Logarithmic Means

Fri, 05 Apr 2013 11:07 EDT

Wei-Mao Qian, Zhong-Hua Shen

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
We prove that $\alpha H(a,b)+(1-\alpha )L(a,b)>{M}_{(1-4\alpha )/3}(a,b)$ for $\alpha \in (0,1)$ and all $a,b>0$ with $a\ne b$ if and only if $\alpha \in [1/4,1)$ and $\alpha H(a,b)+(1-\alpha )L(a,b)<{M}_{(1-4\alpha )/3}(a,b)$ if and only if $\alpha \in (0,3\sqrt{345}/80-11/16)$ , and the parameter $(1-4\alpha )/3$ is the best possible in either case. Here, $H(a,b)=2ab/(a+b)$ , $L(a,b)=(a-b)/(\text{log}\mathrm{ a}-\text{log}\mathrm{ b})$ , and ${M}_{p}(a,b)=(({a}^{p}+{b}^{p})/2{)}^{1/p}(p\ne 0)$ and ${M}_{0}(a,b)=\sqrt{ab}$ are the harmonic, logarithmic, and p th power means of a and b , respectively.

The Generalized Order- $k$ Lucas Sequences in Finite Groups

Fri, 05 Apr 2013 11:07 EDT

Ömür Deveci, Erdal Karaduman

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
We study the generalized order- $k$ Lucas sequences modulo $m$ . Also, we define the $i$ th generalized order- $k$ Lucas orbit ${l}_{A}^{i,\{{\alpha }_{1},{\alpha }_{2},\dots ,{\alpha }_{k-1}\}}$ ( $G$ ) with respect to the generating set $A$ and the constants ${\alpha }_{1},{\alpha }_{2}$ , and ${\alpha }_{k-1}$ for a finite group $G=〈A〉$ . Then, we obtain the lengths of the periods of the $i$ th generalized order- $k$ Lucas orbits of the binary polyhedral groups $〈n,2,2〉,$ $〈2,n,2〉,$ $〈2,2,n〉$ and the polyhedral groups $(n,2,2),(2,n,2),(2,2,n)$ for $1\le i\le k$ .

Studies on the Effects of Interphase Heat Exchange during Thermal Explosion in a Combustible Dusty Gas with General Arrhenius Reaction-Rate Laws

Fri, 05 Apr 2013 11:07 EDT

K. S. Adegbie, F. I. Alao

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
A mathematical model for thermal explosion in a combustible dusty gas containing fuel droplets with general Arrhenius reaction-rate laws, convective and radiative heat losses, and interphase heat exchange between gas and inert solid particles is investigated. The objective of the study is to examine the effects of interphase heat exchange between the gas and solid particles on (i) ignition of reacting gas, (ii) accumulation of heat by the solid particles during combustion process (iii) evaporation of the liquid fuel droplets, and (iv) consumption of reacting gas concentration. The equations governing the physical model with realistic assumptions are stated and nondimensionalised leading to an intractable system of first-order coupled nonlinear differential equations, which is not amenable to exact methods of solution. Therefore, we present numerical solutions as well as different qualitative effects of varying interphase heat exchange parameter. Graphs and Table feature prominently to explain the results obtained.

Multipath Adaptive Tabu Search for a Vehicle Control Problem

Fri, 05 Apr 2013 11:07 EDT

Jukkrit Kluabwang, Deacha Puangdownreong, Sarawut Sujitjorn

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
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.

Zero Triple Product Determined Matrix Algebras

Fri, 05 Apr 2013 11:07 EDT

Hongmei Yao, Baodong Zheng

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
Let $A$ be an algebra over a commutative unital ring $\mathcal{C}$ . We say that $A$ is zero triple product determined if for every $\mathcal{C}$ -module $X$ and every trilinear map $\{\cdot ,\cdot ,\cdot \}$ , the following holds: if $\{x,y,z\}=0$ whenever $xyz=0$ , then there exists a $\mathcal{C}$ -linear operator $T:{A}^{3}⟶X$ such that $\{x,y,z\}=T(xyz)$ for all $x,y,z\in A$ . If the ordinarytriple product in the aforementioned definition is replaced by Jordan triple product, then $A$ is called zero Jordan triple product determined. This paper mainly shows that matrix algebra ${M}_{n}(B)$ , $n\ge 3$ , where B is any commutative unital algebra even different from the above mentioned commutative unital algebra $\mathcal{C}$ , is always zero triple product determined, and ${M}_{n}(F)$ , $n\ge 3$ , where F is any field with ch $F\ne 2$ , is also zero Jordan triple product determined.

Data Reconstruction for a Disturbed Soil-Column Experiment Using an Optimal Perturbation Regularization Algorithm

Fri, 05 Apr 2013 11:07 EDT

Gongsheng Li, De Yao, Yongzai Wang

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
This paper deals with data reconstruction problem for a real disturbed soil-column experiment using an optimal perturbation regularization algorithm. A purpose of doing the experiment is to simulate and study transport behaviors of Ca 2+ , Na + , Mg 2+ , K + , ${\text{SO}}_{\text{4}}^{\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}2-}$ , ${\text{NO}}_{\text{3}}^{\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}-}$ , ${\text{HCO}}_{\text{3}}^{\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}-}$ , and Cl − when they vertically penetrating through sandy soils. By data analysis to breakthrough data of the eight kinds of solute ions, two kinds of models describing their transport behaviors in the column are given. One is the advection-dispersion equation with time-dependent reaction terms suitable for three ions of ${\text{HCO}}_{\text{3}}^{\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}-}$ , ${\text{NO}}_{\text{3}}^{\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}-}$ , and K + , the other is the ordinary advection-dispersion equation suitable for the rest ions. Furthermore, all the unknowns in each model are determined by utilizing the optimal perturbation regularization algorithm, respectively, and then the breakthrough data for each considered ion are reconstructed successfully. The inversion results show that the advection-dispersion model with suitable time-dependent reaction terms can be utilized to describe the experimental process and reconstruct the experimental data.

A Reliable Treatment of Homotopy Perturbation Method for Solving the Nonlinear Klein-Gordon Equation of Arbitrary (Fractional) Orders

Fri, 05 Apr 2013 11:07 EDT

A. M. A. El-Sayed, A. Elsaid, D. Hammad

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
The reliable treatment of homotopy perturbation method (HPM) is applied to solve the Klein-Gordon partial differential equation of arbitrary (fractional) orders. This algorithm overcomes the difficulty that arises in calculating complicated integrals when solving nonlinear equations. Some numerical examples are presented to illustrate the efficiency of this technique.

An Analytical Approximation Method for Strongly Nonlinear Oscillators

Fri, 05 Apr 2013 11:07 EDT

Wang Shimin, Yang Lechang

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of the spring varies with the vibration amplitude for nonstationary oscillations. The varied stiffness is constructed by means of the first and second averaged derivatives of the restoring force with respect to the displacement. Then, this stiffness gives the amplitude frequency and the phase frequency characteristics of the oscillator. Various examples show that this method can be applied extensively to oscillators with nonlinear restoring force, and that the solving process is extremely simple.

Dynamics of Fuzzy BAM Neural Networks with Distributed Delays and Diffusion

Fri, 05 Apr 2013 11:07 EDT

Qianhong Zhang, Lihui Yang, Jingzhong Liu

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
Constructing a new Lyapunov functional and employing inequality technique, the existence, uniqueness, and global exponential stability of the periodic oscillatory solution are investigated for a class of fuzzy bidirectional associative memory (BAM) neural networks with distributed delays and diffusion. We obtained some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic solution. The results remove the usual assumption that the activation functions are differentiable. An example is provided to show the effectiveness of our results.

Application of the Variational Iteration Method to Strongly Nonlinear $q$ -Difference Equations

Fri, 05 Apr 2013 11:07 EDT

Hsuan-Ku Liu

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
The theory of approximate solution lacks development in the area of nonlinear $q$ -difference equations. One of the difficulties in developing a theory of series solutions for the homogeneous equations on time scales is that formulas for multiplication of two $q$ -polynomials are not easily found. In this paper, the formula for the multiplication of two $q$ -polynomials is presented. By applying the obtained results, we extend the use of the variational iteration method to nonlinear $q$ -difference equations. The numerical results reveal that the proposed method is very effective and can be applied to other nonlinear $q$ -difference equations.

Convex Polyhedron Method to Stability of Continuous Systems with Two Additive Time-Varying Delay Components

Fri, 05 Apr 2013 11:07 EDT

Tiejun Li, Junkang Tian

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
This paper is concerned with delay-dependent stability for continuous systems with two additive time-varying delay components. By constructing a new class of Lyapunov functional and using a new convex polyhedron method, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. The obtained stability criterion is less conservative than some existing ones. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Relative and Absolute Perturbation Bounds for Weighted Polar Decomposition

Fri, 05 Apr 2013 11:07 EDT

Pingping Zhang, Hu Yang, Hanyu Li

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
Some new perturbation bounds for both weighted unitary polar factors and generalized nonnegative polar factors of the weighted polar decompositions are presented without the restriction that $A$ and its perturbed matrix $\widetilde{A}$ have the same rank. These bounds improve the corresponding recent results.

Convex Image Segmentation Model Based on Local and Global Intensity Fitting Energy and Split Bregman Method

Fri, 05 Apr 2013 11:07 EDT

Yunyun Yang, Boying Wu

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
We propose a convex image segmentation model in a variational level set formulation. Both the local information and the global information are taken into consideration to get better segmentation results. We first propose a globally convex energy functional to combine the local and global intensity fitting terms. The proposed energy functional is then modified by adding an edge detector to force the active contour to the boundary more easily. We then apply the split Bregman method to minimize the proposed energy functional efficiently. By using a weight function that varies with location of the image, the proposed model can balance the weights between the local and global fitting terms dynamically. We have applied the proposed model to synthetic and real images with desirable results. Comparison with other models also demonstrates the accuracy and superiority of the proposed model.

Rayleigh's, Stoneley's, and Scholte's Interface Waves in Elastic Models Using a Boundary Element Method

Fri, 05 Apr 2013 11:07 EDT

Esteban Flores-Mendez, Manuel Carbajal-Romero, Norberto Flores-Guzmán, Ricardo Sánchez-Martínez, Alejandro Rodríguez-Castellanos

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
This work is focused on studying interface waves for three canonical models, that is, interfaces formed by vacuum-solid, solid-solid, and liquid-solid. These interfaces excited by dynamic loads cause the emergence of Rayleigh's, Stoneley's, and Scholte's waves, respectively. To perform the study, the indirect boundary element method is used, which has proved to be a powerful tool for numerical modeling of problems in elastodynamics. In essence, the method expresses the diffracted wave field of stresses, pressures, and displacements by a boundary integral, also known as single-layer representation, whose shape can be regarded as a Fredholm's integral representation of second kind and zero order. This representation can be considered as an exemplification of Huygens' principle, which is equivalent to Somigliana's representation theorem. Results in frequency domain for the three types of interfaces are presented; then, using the fourier discrete transform, we derive the results in time domain, where the emergence of interface waves is highlighted.

Numerical Analysis of a Linear-Implicit Average Scheme for Generalized Benjamin-Bona-Mahony-Burgers Equation

Fri, 05 Apr 2013 11:07 EDT

Hai-tao Che, Xin-tian Pan, Lu-ming Zhang, Yi-ju Wang

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
A linear-implicit finite difference scheme is given for the initial-boundary problem of GBBM-Burgers equation, which is convergent and unconditionally stable. The unique solvability of numerical solutions is shown. A priori estimate and second-order convergence of the finite difference approximate solution are discussed using energy method. Numerical results demonstrate that the scheme is efficient and accurate.

An Improved AAM Method for Extracting Human Facial Features

Fri, 05 Apr 2013 11:07 EDT

Tao Zhou, Xiao-Jun Wu, Tao Wu, Zhen-Hua Feng

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
Active appearance model is a statistically parametrical model, which is widely used to extract human facial features and recognition. However, intensity values used in original AAM cannot provide enough information for image texture, which will lead to a larger error or a failure fitting of AAM. In order to overcome these defects and improve the fitting performance of AAM model, an improved texture representation is proposed in this paper. Firstly, translation invariant wavelet transform is performed on face images and then image structure is represented using the measure which is obtained by fusing the low-frequency coefficients with edge intensity. Experimental results show that the improved algorithm can increase the accuracy of the AAM fitting and express more information for structures of edge and texture.

Generalized Chessboard Structures Whose Effective Conductivities Are Integer Valued

Fri, 05 Apr 2013 11:07 EDT

Dag Lukkassen, Annette Meidell

Source: J. Appl. Math., Volume 2012, 7 pages.

Abstract:
We consider generalized chessboard structures where the local conductivity takes two values $a$ and $b$ . All integer combinations of $a$ and $b$ which make the components of effective conductivity matrix integer valued are found. Moreover, we discuss the problem of estimating the effective conductivity matrix by using the finite-element method.

Global Stability of Multigroup Dengue Disease Transmission Model

Fri, 05 Apr 2013 11:07 EDT

Deqiong Ding, Xueping Wang, Xiaohua Ding

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
We investigate a class of multigroup dengue epidemicmodel. We show that the global dynamics are determined by the basic reproductivenumber ${R}_{0}$ . We present that when ${R}_{0}\le 1$ , there is a unique disease-freeequilibrium which is globally asymptotically stable; when ${R}_{0}>1$ , there exists aunique endemic equilibrium and it is globally asymptotically stable proved by agraph-theoretic approach to the method of global Lyapunov function.

Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales

Fri, 05 Apr 2013 11:07 EDT

Yongkun Li, Chao Wang

Source: J. Appl. Math., Volume 2012, 28 pages.

Abstract:
Using two successive reductions: B-equivalence of the system on a variable time scale to a system on a time scale and a reduction to an impulsive differential equation and by Leggett-Williams fixed point theorem, we investigate the existence of three positive periodic solutions to the nonlinear neutral functional differential equation on variable time scales with a transition condition between two consecutive parts of the scale $(d/dt)(x(t)+c(t)x(t-\alpha ))=a(t)g(x(t))x(t)-{\sum }_{j=1}^{n}{\lambda }_{j}{f}_{j}(t,x(t-{v}_{j}(t)))$ , $(t,x)\in {\mathbb{T}}_{0}(x)$ , $\Delta t{|}_{(t,x)\in {\mathcal{S}}_{2i}}={\Pi }_{i}^{1}(t,x)-t$ , $\Delta x{|}_{(t,x)\in {\mathcal{S}}_{2i}}={\Pi }_{i}^{2}(t,x)-x$ , where ${\Pi }_{i}^{1}(t,x)={t}_{2i+1}+{\tau }_{2i+1}({\Pi }_{i}^{2}(t,x))$ and ${\Pi }_{i}^{2}(t,x)={B}_{i}x+{J}_{i}(x)+x,\mathrm{ }i=1,2,\dots .\mathrm{ }{\lambda }_{j}\mathrm{ }(j=1,2,\dots ,n)$ are parameters, ${\mathbb{T}}_{0}(x)$ is a variable time scale with $(\omega ,p)$ -property, $c(t),\mathrm{ }a(t)$ , ${v}_{j}(t),$ and ${f}_{j}(t,x)\mathrm{ }(j=1,2,\dots ,n)$ are $\omega $ -periodic functions of $t$ , ${B}_{i+p}={B}_{i},\mathrm{ }{J}_{i+p}(x)={J}_{i}(x)$ uniformly with respect to $i\in \mathbb{Z}$ .

Sufficient Dilated LMI Conditions for ${H}_{\infty }$ Static Output Feedback Robust Stabilization of Linear Continuous-Time Systems

Fri, 05 Apr 2013 11:07 EDT

Kamel Dabboussi, Jalel Zrida

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
New sufficient dilated linear matrix inequality (LMI) conditions for the ${H}_{\infty }$ static output feedback control problem of linear continuous-time systems with no uncertainty are proposed. The used technique easily and successfully extends to systems with polytopic uncertainties, by means of parameter-dependent Lyapunov functions (PDLFs). In order to reduce the conservatism existing in early standard LMI methods, auxiliary slack variables with even more relaxed structure are employed. It is shown that these slack variables provide additional flexibility to the solution. It is also shown, in this paper, that the proposed dilated LMI-based conditions always encompass the standard LMI-based ones. Numerical examples are given to illustrate the merits of the proposed method.

Limiting Behavior of the Maximum of the Partial Sum for Linearly Negative Quadrant Dependent Random Variables under Residual Cesàro Alpha-Integrability Assumption

Fri, 05 Apr 2013 11:07 EDT

Jiangfeng Wang, Qunying Wu

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
Linearly negative quadrant dependence is a special dependence structure. By relating such conditionsto residual Cesàro alpha-integrability assumption, as well as to strongly residual Cesàroalpha-integrability assumption, some ${L}_{p}$ -convergence and complete convergence results of the maximum of the partial sum are derived, respectively.

A PMBGA to Optimize the Selection of Rules for Job Shop Scheduling Based on the Giffler-Thompson Algorithm

Fri, 05 Apr 2013 11:07 EDT

Rui Zhang, Cheng Wu

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
Most existing research on the job shop scheduling problem has been focused on the minimization of makespan (i.e., the completion time of the last job). However, in the fiercely competitive market nowadays, delivery punctuality is more important for maintaining a high service reputation. So in this paper, we aim at solving job shop scheduling problems with the total weighted tardiness objective. Several dispatching rules are adopted in the Giffler-Thompson algorithm for constructing active schedules. It is noticeable that the rule selections for scheduling consecutive operations are not mutually independent but actually interrelated. Under such circumstances, a probabilistic model-building genetic algorithm (PMBGA) is proposed to optimize the sequence of selected rules. First, we use Bayesian networks to model the distribution characteristics of high-quality solutions in the population. Then, the new generation of individuals is produced by sampling the established Bayesian network. Finally, some elitist individuals are further improved by a special local search module based on parameter perturbation. The superiority of the proposed approach is verified by extensive computational experiments and comparisons.

Series Solution for Steady Three-Dimensional Flow due to Spraying on Inclined Spinning Disk by Homotopy Perturbation Method

Fri, 05 Apr 2013 11:07 EDT

Saeed Dinarvand

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
The steady three-dimensional flow of condensation or spraying on inclined spinning disk is studied analytically. The governing nonlinear equations and their associated boundary conditions are transformed into the system of nonlinear ordinary differential equations. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM). The velocity and temperature profiles are shown and the influence of Prandtl number on the heat transfer and Nusselt number is discussed in detail. The validity of our solutions is verified by the numerical results. Unlike free surface flows on an incline, this through flow is highly affected by the spray rate and the rotation of the disk.

Extended Precise Large Deviations of Random Sums in the Presence of END Structure and Consistent Variation

Fri, 05 Apr 2013 11:07 EDT

Shijie Wang, Wensheng Wang

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
The study of precise large deviations of random sums is an important topic in insurance and finance. In this paper, extended precise large deviations of random sums in the presence of END structure and consistent variation are investigated. The obtained results extend those of Chen and Zhang (2007) and Chen et al. (2011). As an application, precise large deviations of the prospective- loss process of a quasirenewal model are considered.

Asymptotic Stability Results for Nonlinear Fractional Difference Equations

Fri, 05 Apr 2013 11:07 EDT

Fulai Chen, Zhigang Liu

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
We present some results for the asymptotic stability of solutions for nonlinear fractional difference equations involvingRiemann-Liouville-likedifference operator. The results are obtained by using Krasnoselskii's fixed point theorem and discrete Arzela-Ascoli's theorem. Three examples are also provided to illustrate our main results.

Optimal Control of a Fed-Batch Fermentation Involving Multiple Feeds

Fri, 05 Apr 2013 11:07 EDT

Chongyang Liu, Zhaohua Gong, Zhaoyi Huo, Bangyu Shen

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
A nonlinear dynamical system, in which the feed rates of glycerol and alkali are taken as the control functions, is first proposed to formulate the fed-batch culture of 1,3-propanediol (1,3-PD) production. To maximize the 1,3-PD concentration at the terminal time, a constrained optimal control model is then presented. A solution approach is developed to seek the optimal feed rates based on control vector parametrization method and improved differential evolution algorithm. The proposed methodology yielded an increase by 32.17% of 1,3-PD concentration at the terminal time.

Optimal Results and Numerical Simulations for Flow Shop Scheduling Problems

Fri, 05 Apr 2013 11:07 EDT

Tao Ren, Yuandong Diao, Xiaochuan Luo

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
This paper considers the m -machine flow shop problem with two objectives: makespan with release dates and total quadratic completion time, respectively. For F $m|{r}_{j}|{\text{C}}_{max}$ , we prove the asymptotic optimality for any dense scheduling when the problem scale is large enough. For F $m{‖\Sigma \text{C}}_{j}^{2}$ , improvement strategy with local search is presented to promote the performance of the classical SPT heuristic. At the end of the paper, simulations show the effectiveness of the improvement strategy.

Cluster Synchronization of Time-Varying Delays Coupled Complex Networks with Nonidentical Dynamical Nodes

Fri, 05 Apr 2013 11:07 EDT

Shuguo Wang, Hongxing Yao, Mingping Sun

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
This paper investigates a new cluster synchronization scheme in the nonlinear coupled complex dynamical networks with nonidentical nodes. The controllers are designed based on the community structure of the networks; some sufficient criteria are derived to ensure cluster synchronization of the network model. Particularly, the weight configuration matrix is not assumed to be symmetric, irreducible. The numerical simulations are performed to verify the effectiveness of the theoretical results.

Exponentiated Gamma Distribution: Different Methods of Estimations

Fri, 05 Apr 2013 11:07 EDT

A. I. Shawky, R. A. Bakoban

Source: J. Appl. Math., Volume 2012, 23 pages.

Abstract:
The exponentiated gamma (EG) distribution and Fisher information matrices for complete, Type I, and Type II censored observations are obtained. Asymptotic variances of the different estimators are derived. Also, we consider different estimators and compare their performance through Monte Carlo simulations.

Exponential Passification of Markovian Jump Nonlinear Systems with Partially Known Transition Rates

Fri, 05 Apr 2013 11:07 EDT

Mengzhuo Luo, Shouming Zhong

Source: J. Appl. Math., Volume 2012, 24 pages.

Abstract:
The problems of delay-dependent exponential passivity analysis and exponential passification of uncertain Markovian jump systems (MJSs) with partially known transition rates are investigated. In the deterministic model, the time-varying delay is in a given range and the uncertainties are assumed to be norm bounded. With constructing appropriate Lyapunov-Krasovskii functional (LKF) combining with Jensen’s inequality and the free-weighting matrix method, delay-dependent exponential passification conditions are obtained in terms of linear matrix inequalities (LMI). Based on the condition, desired state-feedback controllers are designed, which guarantee that the closed-loop MJS is exponentially passive. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

On the Positive Almost Periodic Solutions of a Class of Nonlinear Lotka-Volterra Type System with Feedback Control

Fri, 05 Apr 2013 11:07 EDT

Ni Hua, Tian Li-Xin, Yao Hong-Xing

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
With the help of the variable substitution and applying the fixed point theorem, we derive the sufficient conditions which guarantee the existence of the positive almost periodic solutions for a class of Lotka-Volterra type system. The main results improve and generalize the former corresponding results.

Exponential Stability for a Class of Stochastic Reaction-Diffusion Hopfield Neural Networks with Delays

Fri, 05 Apr 2013 11:07 EDT

Xiao Liang, Linshan Wang

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
This paper studies the asymptotic behavior for a class of delayed reaction-diffusion Hopfield neural networks driven by finite-dimensional Wiener processes. Some new sufficient conditions are established to guarantee the mean square exponential stability of this system by using Poincaré’s inequality and stochastic analysis technique. The proof of the almost surely exponential stability for this system is carried out by using the Burkholder-Davis-Gundy inequality, the Chebyshev inequality and the Borel-Cantelli lemma. Finally, an example is given to illustrate the effectiveness of the proposed approach, and the simulation is also given by using the Matlab.

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

Fri, 05 Apr 2013 11:07 EDT

Hui Fang

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
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.

On a Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

Fri, 05 Apr 2013 11:07 EDT

Jaeyoung Chung, Jeongwook Chang

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
Let $G$ be an Abelian group, let $ℂ$ be the field of complex numbers, and let $f,g:G\to \mathbb{C}$ . We consider the generalized Hyers-Ulam stability for a class of trigonometric functional inequalities, $|f(x-y)-f(x)g(y)+g(x)f(y)|\le \psi (y), |g(x-y)-g(x)g(y)-f(x)f(y)|\le \psi (y)$ , where $\psi :G\to \mathbb{R}$ is an arbitrary nonnegative function.

Approximation by Lupas-Type Operators and Szász-Mirakyan-Type Operators

Fri, 05 Apr 2013 11:07 EDT

Hee Sun Jung, Ryozi Sakai

Source: J. Appl. Math., Volume 2012, 28 pages.

Abstract:
Lupas-type operators and Szász-Mirakyan-type operators are the modifications of Bernstein polynomials to infinite intervals. In this paper, we investigate the convergence of Lupas-type operators and Szász-Mirakyan-type operators on $[0,\infty )$ .

Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Fri, 05 Apr 2013 11:07 EDT

Khaled A. Gepreel, A. R. Shehata

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.

Asymptotic Stability of the Golden-Section Control Law for Multi-Input and Multi-Output Linear Systems

Fri, 05 Apr 2013 11:07 EDT

Duo-Qing Sun, Zhu-Mei Sun

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
This paper is concerned with the problem of the asymptotic stability of the characteristic model-based golden-section control law for multi-input and multi-output linear systems. First, by choosing a set of polynomial matrices of the objective function of the generalized least-square control, we prove that the control law of the generalized least square can become the characteristic model-based golden-section control law. Then, based on both the stability result of the generalized least-square control system and the stability theory of matrix polynomial, the asymptotic stability of the closed loop system for the characteristic model under the control of the golden-section control law is proved for minimum phase system.

Instability Induced by Cross-Diffusion in a Predator-Prey Model with Sex Structure

Fri, 05 Apr 2013 11:07 EDT

Shengmao Fu, Lina Zhang

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
In this paper, we consider a cross-diffusion predator-prey model with sex structure. We prove that cross-diffusion can destabilize a uniform positive equilibrium which is stable for the ODE system and for the weakly coupled reaction-diffusion system. As a result, we find that stationary patterns arise solely from the effect of cross-diffusion.

Fuzzy Case-Based Reasoning in Product Style Acquisition Incorporating Valence-Arousal-Based Emotional Cellular Model

Fri, 05 Apr 2013 11:07 EDT

Fuqian Shi, Jiang Xu, Shouqian Sun

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
Emotional cellular (EC), proposed in our previous works, is a kind of semantic cell that contains kernel and shell and the kernel is formalized by a triple- L = < P , d , $\delta $ >, where P denotes a typical set of positive examples relative to word- L , d is a pseudodistance measure on emotional two-dimensional space: valence-arousal, and $\delta $ is a probability density function on positive real number field. The basic idea of EC model is to assume that the neighborhood radius of each semantic concept is uncertain, and this uncertainty will be measured by one-dimensional density function $\delta $ . In this paper, product form features were evaluated by using ECs and to establish the product style database, fuzzy case based reasoning (FCBR) model under a defined similarity measurement based on fuzzy nearest neighbors (FNN) incorporating EC was applied to extract product styles. A mathematical formalized inference system for product style was also proposed, and it also includes uncertainty measurement tool emotional cellular. A case study of style acquisition of mobile phones illustrated the effectiveness of the proposed methodology.

Global Stability and Hopf Bifurcation for Gause-Type Predator-Prey System

Fri, 05 Apr 2013 11:07 EDT

Shuang Guo, Weihua Jiang

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
A class of three-dimensional Gause-type predator-prey model is considered. Firstly, local stability of equilibrium indicating the extinction of top-predator is obtained. Meanwhile, we construct a Lyapunov function, which is an extension of the Lyapunov functions constructed by Hsu for predator-prey system (2005), to give the global stability of the equilibrium. Secondly, we analyze the stability of coexisting equilibrium of predator-prey system with time delay when the predator catches the prey of pregnancy or with growth time. The delay can lead to periodic solutions, which is consistent with the law of growth for birds and some mammals. Further, an explicit formula is given which determines the stability of the bifurcating periodic solutions theoretically and the existence of periodic solutions is displayed by numerical simulations.

A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations

Fri, 05 Apr 2013 11:07 EDT

M. Y. Waziri, W. J. Leong, M. Mamat

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
We propose an approach to enhance the performance of a diagonal variant of secant method for solving large-scale systems of nonlinear equations. In this approach, we consider diagonal secant method using data from two preceding steps rather than a single step derived using weak secant equation to improve the updated approximate Jacobian in diagonal form. The numerical results verify that the proposed approach is a clear enhancement in numerical performance.

Generalized Hyperbolic Function Solution to a Class of Nonlinear Schrödinger-Type Equations

Fri, 05 Apr 2013 11:07 EDT

Zeid I. A. Al-Muhiameed, Emad A.-B. Abdel-Salam

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Liu equation are investigated and the exact solutions are derived with the aid of the homogenous balance principle and generalized hyperbolic functions. We study the effect of the generalized hyperbolic function parameters p and q in the obtained solutions by using the computer simulation.

Adaptive Backstepping Fuzzy Control Based on Type-2 Fuzzy System

Fri, 05 Apr 2013 11:07 EDT

Ll Yi-Min, Yue Yang, Li Li

Source: J. Appl. Math., Volume 2012, 27 pages.

Abstract:
A novel indirect adaptive backstepping control approach based on type-2 fuzzy system is developed for a class of nonlinear systems. This approach adopts type-2 fuzzy system instead of type-1 fuzzy system to approximate the unknown functions. With type-reduction, the type-2 fuzzy system is replaced by the average of two type-1 fuzzy systems. Ultimately, the adaptive laws, by means of backstepping design technique, will be developed to adjust the parameters to attenuate the approximation error and external disturbance. According to stability theorem, it is proved that the proposed Type-2 Adaptive Backstepping Fuzzy Control (T2ABFC) approach can guarantee global stability of closed-loop system and ensure all the signals bounded. Compared with existing Type-1 Adaptive Backstepping Fuzzy Control (T1ABFC), as the advantages of handling numerical and linguistic uncertainties, T2ABFC has the potential to produce better performances in many respects, such as stability and resistance to disturbances. Finally, a biological simulation example is provided to illustrate the feasibility of control scheme proposed in this paper.

A Mixed Spectral CD-DY Conjugate Gradient Method

Fri, 05 Apr 2013 11:07 EDT

Liu Jinkui, Du Xianglin, Wang Kairong

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
A mixed spectral CD-DY conjugate descent method for solving unconstrained optimization problems is proposed, which combines the advantages of the spectral conjugate gradient method, the CD method, and the DY method. Under the Wolfe line search, the proposed method can generate a descent direction in each iteration, and the global convergence property can be also guaranteed. Numerical results show that the new method is efficient and stationary compared to the CD (Fletcher 1987) method, the DY (Dai and Yuan 1999) method, and the SFR (Du and Chen 2008) method; so it can be widely used in scientific computation.

Decentralized Control of Uncertain Fuzzy Large-Scale System with Time Delay and Optimization

Fri, 05 Apr 2013 11:07 EDT

Hang Zhang, Xia Wang, Yi-Jun Wang, Zhao-Mei Sun

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
This paper studies the decentralized stabilization problem for an uncertain fuzzy large-scale system with time delays. The considered large-scale system is composed of several T-S fuzzy subsystems. The decentralized parallel distributed compensation (PDC) fuzzy control for each subsystem is designed to stabilize the whole system. Based on Lyapunov criterion, some sufficient conditions are proposed. Moreover, the positive definite matrices ${P}_{i}$ and PDC gain ${K}_{ij}$ can be solved by linear matrix inequality (LMI) toolbox of Matlab. Then, the optimization design method for decentralized control is also considered with respect to a quadratic performance index. Finally, numericalexamples are given and compared with those of Zhang et al., 2004 to illustrate the effectiveness and less conservativenessof our method.

Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type for $K(m,n)$ Equation

Fri, 05 Apr 2013 11:07 EDT

Xianbin Wu, Weiguo Rui, Xiaochun Hong

Source: J. Appl. Math., Volume 2012, 23 pages.

Abstract:
By using the integral bifurcation method, we study the nonlinear $K(m,n)$ equation for all possible values of $m$ and $n$ . Some new exact traveling wave solutions of explicit type, implicit type, and parametric type are obtained. These exact solutions include peculiar compacton solutions, singular periodic wave solutions, compacton-like periodic wave solutions, periodic blowup solutions, smooth soliton solutions, and kink and antikink wave solutions. The great parts of them are different from the results in existing references. In order to show their dynamic profiles intuitively, the solutions of $K(n,n)$ , $K(2n-1,n)$ , $K(3n-2,n)$ , $K(4n-3,n)$ , and $K(m,1)$ equations are chosen to illustrate with the concrete features.

Approximation Algorithm for a System of Pantograph Equations

Fri, 05 Apr 2013 11:07 EDT

Sabir Widatalla, Mohammed Abdulai Koroma

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
We show how to adapt an efficient numerical algorithm to obtain an approximate solution of a system of pantograph equations. This algorithm is based on a combination of Laplace transform and Adomian decomposition method. Numerical examples reveal that the method is quite accurate and efficient, it approximates the solution to a very high degree of accuracy after a few iterates.

Analytic Solution for MHD Falkner-Skan Flow over a Porous Surface

Fri, 05 Apr 2013 11:07 EDT

Fatheah A. Hendi, Majid Hussain

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
This paper discusses the MHD Falkner-Skan flow over a porous surface. The solution to nonlinear problem is first constructed and analyzed for the emerging parameters

An Adaptive Domain Partitioning Technique for Meshfree-Type Methods

Fri, 05 Apr 2013 11:07 EDT

Kamal Shanazari

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
An overlapping domain partitioning based on adapting nodes is presented for the meshless-type methods. The decomposition of the domain is carried out based on the distribution of the nodes produced rather than the geometry of the problem. A set of adaptive nodes is first generated using the dimension reduction and equidistributing along the coordinate directions with respect to arc-length monitor. The domain is then partitioned in such a way that the same number of nodes are allocated to the subdomains. A radial basis function collocation method is applied to each subdomain followed by assembling the global solution from the subproblem's solutions. A generalized thin plate spline with sufficient smoothness is used as a basis function in the collocation method. Some numerical results will be presented to show the performance of the proposed method.

Electromagnetic Low-Frequency Dipolar Excitation of Two Metal Spheres in a Conductive Medium

Fri, 05 Apr 2013 11:07 EDT

Panayiotis Vafeas, Polycarpos K. Papadopoulos, Dominique Lesselier

Source: J. Appl. Math., Volume 2012, 37 pages.

Abstract:
This work concerns the low-frequency interaction of a time-harmonic magnetic dipole, arbitrarily orientated in the three-dimensional space, with two perfectly conducting spheres embedded within a homogeneous conductive medium. In such physical applications, where two bodies are placed near one another, the 3D bispherical geometry fits perfectly. Considering two solid impenetrable (metallic) obstacles, excited by a magnetic dipole, the scattering boundary value problem is attacked via rigorous low-frequency expansions in terms of integral powers ${(ik)}^{n}$ , where $n\ge 0$ , $k$ being the complex wave number of the exterior medium, for the incident, scattered, and total non-axisymmetric electric and magnetic fields. We deal with the static ( $n=0$ ) and the dynamic ( $n=1,2,3$ ) terms of the fields, while for $n\ge 4$ the contribution has minor significance. The calculation of the exact solutions, satisfying Laplace’s and Poisson’s differential equations, leads to infinite linear systems, solved approximately within any order of accuracy through a cut-off procedure and via numerical implementation. Thus, we obtain the electromagnetic fields in an analytically compact fashion as infinite series expansions of bispherical eigenfunctions. A simulation is developed in order to investigate the effect of the radii ratio, the relative position of the spheres, and the position of the dipole on the real and imaginary parts of the calculated scattered magnetic field.

Existence and Duality of Generalized ε-Vector Equilibrium Problems

Fri, 05 Apr 2013 11:07 EDT

Hong-Yong Fu, Bin Dan, Xiang-Yu Liu

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
We consider a generalized ε -vector equilibrium problem which contain vector equilibrium problems and vector variational inequalities as special cases. By using the KKM theorem, we obtain some existence theorems for the generalized ε -vector equilibrium problem. We also investigate the duality of this generalized ε -vector equilibrium problem and discuss the equivalence relation between solutions of primal and dual problems.

Optimizing a Hybrid Two-Step Method for the Numerical Solution of the Schrödinger Equation and Related Problems with Respect to Phase-Lag

Fri, 05 Apr 2013 11:07 EDT

T. E. Simos

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
We use a methodology of optimization of the efficiency of a hybrid two-step method for the numerical solution of the radial Schrödinger equation and related problems with periodic or oscillating solutions. More specifically, we study how the vanishing of the phase-lag and its derivatives optimizes the efficiency of the hybrid two-step method.

Observer-Based Finite-Time ${H}_{\infty }$ Control of Singular Markovian Jump Systems

Fri, 05 Apr 2013 11:07 EDT

Yingqi Zhang, Wei Cheng, Xiaowu Mu, Xiulan Guo

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
This paper addresses the problem of finite-time ${H}_{\infty }$ control via observer-based state feedback for a family ofsingular Markovian jump systems (SMJSs) with time-varying norm-bounded disturbance. Firstly, the concepts ofsingular stochastic finite-time boundedness and singular stochastic finite-time ${H}_{\infty }$ stabilization via observer-basedstate feedback are given. Then an observer-based state feedback controller is designed to ensure singular stochasticfinite-time ${H}_{\infty }$ 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 probleminvolving linear matrix inequalities with a fixed parameter. As an auxiliary result, we also discuss the problemof finite-time stabilization via observer-based state feedback of a class of SMJSs and give sufficient conditions ofsingular stochastic finite-time stabilization via observer-based state feedback for the class of SMJSs. Finally, illustrativeexamples are given to demonstrate the validity of the proposed techniques.

Periodic Solutions of a Cohen-Grossberg-Type BAM Neural Networks with Distributed Delays and Impulses

Fri, 05 Apr 2013 11:07 EDT

Qiming Liu, Rui Xu

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
A class of Cohen-Grossberg-type BAM neural networks with distributed delaysand impulses are investigated in this paper. Sufficient conditions to guarantee the uniquenessand global exponential stability of the periodic solutions of such networks are establishedby using suitable Lyapunov function, the properties of $M$ -matrix, and some suitable mathematical transformation. The results in this paper improve the earlier publications.

A Class of PDEs with Nonlinear Superposition Principles

Fri, 05 Apr 2013 11:07 EDT

Li Peng, Liu Keying, Pan Zuliang, Zhong Weizhou

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
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.

Optimal Inequalities for Power Means

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
We present the best possible power mean bounds for the product ${M}_{p}^{\alpha }(a,b){M}_{-p}^{1-\alpha }(a,b)$ for any $p>0$ , $\alpha \in (0,1)$ , and all $a,b>0$ with $a\ne b$ . Here, ${M}_{p}(a,b)$ is the $p$ th power mean of two positive numbers $a$ and $b$ .

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

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

Gusein Sh. Guseinov

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

Jianhua Hou, Beibo Qin, Changqing Yang

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
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.

Nonnegativity Preserving Interpolation by ${C}^{\text{1}}$ Bivariate Rational Spline Surface

Fri, 05 Apr 2013 11:07 EDT

Xingxuan Peng, Zhihong Li, Qian Sun

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
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 ${C}^{\text{1}}$ 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.

An Improved Particle Swarm Optimization for Solving Bilevel Multiobjective Programming Problem

Fri, 05 Apr 2013 11:07 EDT

Tao Zhang, Tiesong Hu, Yue Zheng, Xuning Guo

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
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.

System Identification Using Multilayer Differential Neural Networks: A New Result

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
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.

Comparison Theorems for the Multidimensional BDSDEs and Applications

Fri, 05 Apr 2013 11:07 EDT

Bo Zhu, Baoyan Han

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
A class of backward doubly stochastic differential equations (BDSDEs) are studied. We obtain a comparison theorem of these multidimensional BDSDEs. As its applications, we derive the existence of solutions for this multidimensional BDSDEs with continuous coefficients. We can also prove that this solution is the minimal solution of the BDSDE.

The Gross-Pitaevskii Model of Spinor BEC

Fri, 05 Apr 2013 11:07 EDT

Dongming Yan, Tian Ma

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
The Gross-Pitaevskii model of spinor Bose-Einstein condensates is studied. Using the abstract results obtained for infinite-dimensional Hamilton system, we establish the mathematical theory for the model of spinor BEC. Furthermore, three conservative quantities of spinor BEC, that is, the energy, total particle number, and magnetization intensity, are also proved.

A Mathematical Model for the Dynamics of a Fish Algae Consumption Model with Impulsive Control Strategy

Fri, 05 Apr 2013 11:07 EDT

Jin Yang, Min Zhao

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
A dynamic mathematical model of fish algae consumption with an impulsive control strategy is proposed and analyzed in detail. It is shown that the system has a globally asymptotically stable algae-eradication periodic solution which can be obtained using the Floquet theory of impulsive differential equations and small-amplitude perturbation techniques. The conditions for the permanence of the system can also be determined. Numerical results for impulsive perturbations show the rich dynamic behavior of the system. All these results may be useful in controlling eutrophication.

Limit Circle/Limit Point Criteria for Second-Order Superlinear Differential Equations with a Damping Term

Fri, 05 Apr 2013 11:07 EDT

Lihong Xing, Wei Song, Zhengqiang Zhang, Qiyi Xu

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
The purpose of the present paper is to establish some new criteria for the classifications of superlinear differential equations as being of the nonlinear limit circle type or of the nonlinear limit point type. The criteria presented here generalize some known results in literature.

Chaos in a Tumor Growth Model with Delayed Responses of the Immune System

Fri, 05 Apr 2013 11:07 EDT

M. Saleem, Tanuja Agrawal

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
A simple prey-predator-type model for the growth of tumor with discrete time delay in the immune system is considered. It is assumed that the resting and hunting cells make the immune system. The present model modifies the model of El-Gohary (2008) in that it allows delay effects in the growth process of the hunting cells. Qualitative and numerical analyses for the stability of equilibriums of the model are presented. Length of the time delay that preserves stability is given. It is found that small delays guarantee stability at the equilibrium level (stable focus) but the delays greater than a critical value may produce periodic solutions through Hopf bifurcation and larger delays may even lead to chaotic attractors. Implications of these results are discussed.

Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays

Fri, 05 Apr 2013 11:07 EDT

Haiyan Yuan, Jingjun Zhao, Yang Xu

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
This paper is devoted to the stability and convergence analysis of the additive Runge-Kutta methods with the Lagrangian interpolation (ARKLMs) for the numerical solution of a delay differential equation with many delays. GDN stability and D-Convergence are introduced and proved. It is shown that strongly algebraically stability gives D-Convergence DA, DAS, and ASI stability give GDN stability. Some examples are given in the end of this paper which confirms our results.

The Extended Hyperbolic Function Method for Generalized Forms of Nonlinear Heat Conduction and Huxley Equations

Fri, 05 Apr 2013 11:07 EDT

Yong Huang, Yadong Shang

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
The extended hyperbolic function method is used to derive abundant exact solutions for generalized forms of nonlinear heat conduction and Huxley equations. The extended hyperbolic function method provides abundant solutions in addition to the existing ones. Some previous results are supplemented and extended greatly.

Bounds for the Kirchhoff Index of Bipartite Graphs

Fri, 05 Apr 2013 11:07 EDT

Yujun Yang

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
A $(m,n)$ -bipartite graph is a bipartite graph such that one bipartition has m vertices and the other bipartition has n vertices. The tree dumbbell $D(n,a,b)$ consists of the path ${P}_{n-a-b}$ together with a independent vertices adjacent to one pendent vertex of ${P}_{n-a-b}$ and b independent vertices adjacent to the other pendent vertex of ${P}_{n-a-b}$ . In this paper, firstly, we show that, among $(m,n)$ -bipartite graphs $(m\le n)$ , the complete bipartite graph ${K}_{m,n}$ has minimal Kirchhoff index and the tree dumbbell $D(m+n,\lfloor n-(m+1)/2\rfloor ,\lceil n-(m+1)/2\rceil )$ has maximal Kirchhoff index. Then, we show that, among all bipartite graphs of order $l$ , the complete bipartite graph ${K}_{\lfloor l/2\rfloor ,l-\lfloor l/2\rfloor }$ has minimal Kirchhoff index and the path ${P}_{l}$ has maximal Kirchhoff index, respectively. Finally, bonds for the Kirchhoff index of $(m,n)$ -bipartite graphs and bipartite graphs of order $l$ are obtained by computing the Kirchhoff index of these extremal graphs.

Almost Sure Central Limit Theory for Self-Normalized Products of Sums of Partial Sums

Fri, 05 Apr 2013 11:07 EDT

Qunying Wu

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
Let $X,{X}_{1},{X}_{2},\dots $ be a sequence of independent and identically distributed random variables in the domain of attraction of a normal law. An almost sure limit theorem for the self-normalized products of sums of partial sums is established.

Higher-Order Dynamic Delay Differential Equations on Time Scales

Fri, 05 Apr 2013 11:07 EDT

Hua Su, Lishan Liu, Xinjun Wang

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
We study the existence of positive solutions for the nonlinear four-point singular boundary value problem with higher-order $p$ -Laplacian dynamic delay differential equations on time scales, subject to some boundary conditions. By using the fixed-point index theory, the existence of positive solution and many positive solutions for nonlinear four-point singular boundary value problem with $p$ -Laplacian operator are obtained.

Hamiltonian Paths in Some Classes of Grid Graphs

Fri, 05 Apr 2013 11:07 EDT

Fatemeh Keshavarz-Kohjerdi, Alireza Bagheri

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
The Hamiltonian path problem for general grid graphs is known to be NP-complete. In this paper, we give necessary and sufficient conditions for the existence of Hamiltonian paths in L -alphabet, C -alphabet, F -alphabet, and E -alphabet grid graphs. We also present linear-time algorithms for finding Hamiltonian paths in these graphs.

Homotopy Interior-Point Method for a General Multiobjective Programming Problem

Fri, 05 Apr 2013 11:07 EDT

X. Zhao, S. G. Zhang, Q. H. Liu

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
We present a combined homotopy interior-point method for a general multiobjective programming problem. For solving the KKT points of the multiobjective programming problem, the homotopy equation is constructed. We prove the existence and convergence of a smooth homotopy path from almost any initial interior point to a solution of the KKT system under some basic assumptions.

Existence of at Least Two Periodic Solutions for a Competition System of Plankton Allelopathy on Time Scales

Fri, 05 Apr 2013 11:07 EDT

Hui Fang

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
We study a competition system of the growth of two species of plankton with competitive and allelopathic effects on each other on time scales. With the help of Mawhin’s continuation theorem of coincidence degree theory, a set of easily verifiable criteria is obtained for the existence of at least two periodic solutions for this model. Some new existence results are obtained. An example and numerical simulation are given to illustrate the validity of our results.

Positive Mild Solutions of Periodic Boundary Value Problems for Fractional Evolution Equations

Fri, 05 Apr 2013 11:07 EDT

Jia Mu, Hongxia Fan

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
The periodic boundary value problem is discussed for a class of fractional evolution equations. The existence and uniqueness results of mild solutions for the associated linear fractional evolution equations are established, and the spectral radius of resolvent operator is accurately estimated. With the aid of the estimation, the existence and uniqueness results of positive mild solutions are obtained by using the monotone iterative technique. As an application that illustrates the abstract results, an example is given.

A Fuzzy Genetic Algorithm Based on Binary Encoding for Solving Multidimensional Knapsack Problems

Fri, 05 Apr 2013 11:07 EDT

M. Jalali Varnamkhasti, L. S. Lee

Source: J. Appl. Math., Volume 2012, 23 pages.

Abstract:
The fundamental problem in genetic algorithms is premature convergence, and it is strongly related to the loss of genetic diversity of the population. This study aims at proposing some techniques to tackle the premature convergence by controlling the population diversity. Firstly, a sexual selection mechanism which utilizes the mate chromosome during selection is used. The second technique focuses on controlling the genetic parameters by applying the fuzzy logic controller. Computational experiments are conducted on the proposed techniques and the results are compared with other genetic operators, heuristics, and local search algorithms commonly used for solving multidimensional 0/1 knapsack problems published in the literature.

General Existence Results for Third-Order Nonconvex State-Dependent Sweeping Process with Unbounded Perturbations

Fri, 05 Apr 2013 11:07 EDT

M. Bounkhel, B. Al-Senan

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
We prove the existence of solutions for third-order nonconvex state-dependent sweeping process with unbounded perturbations of the form: $-A({x}^{(3)}(t))\in N(K(t,\stackrel{\dot{}}{x}(t))$ ; $\mathrm{ }A(\stackrel{̈}{x}(t)))+F(t,x(t),\stackrel{\dot{}}{x}(t),\stackrel{̈}{x}(t))+G(x(t),\stackrel{\dot{}}{x}(t),\stackrel{̈}{x}(t))\mathrm{ }\mathrm{ }\mathrm{ }\text{a}\text{.}\text{e}\text{.}\mathrm{ }[0,T]$ , $A(\stackrel{̈}{x}(t))\in K(t,\stackrel{\dot{}}{x}(t))$ , $\text{a.e.}\mathrm{ }\mathrm{ }t\in [0,T]$ , $x(0)={x}_{0},\stackrel{\dot{}}{x}(0)={u}_{0}$ , $\stackrel{̈}{x}(0)={\upsilon }_{0}$ , where $T>0$ , $K$ is a nonconvex Lipschitz set-valued mapping, $F$ is an unbounded scalarly upper semicontinuous convex set-valued mapping, and $G$ is an unbounded uniformly continuous nonconvex set-valued mapping in a separable Hilbert space $\mathbb{H}$ .

Existence of Periodic Solutions for a Class of Asymptotically $p$ -Linear Discrete Systems Involving $p$ -Laplacian

Fri, 05 Apr 2013 11:07 EDT

Kai Chen, Qiongfen Zhang

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
By applying Mountain Pass Theorem in critical point theory,two existence results are obtained for the following asymptotically $p$ -linear $p$ -Laplacian discrete system $\Delta ({|\Delta u(t-1)|}^{p-2}\Delta u(t-1))+\nabla [-K(t,u(t))+W(t,u(t))]=0$ . The results obtained generalize some known works.

Some Applications of $({C}_{0},1)$ -Semigroups

Fri, 05 Apr 2013 11:07 EDT

Yu-Hsien Chang, Cheng-hong Hong

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
This study is originally motivated by the thermal balance equations for the gas and solidinterphase heat-transfer for the fast-igniting catalytic converter of automobiles. Insteadof solving this problem directly, we proved some results concerning the existence anduniqueness for abstract semilinear initial value problem by means of $({C}_{0},1)$ -semigrouptheories on locally convex topological space. The most enjoyable here is that these results notonly can be applied to solve the interphase heat-transfer for the fast-igniting catalyticconverter of automobile under the situation of preheating at the entry edge of converter,but also can be applied to some other practical problems.

Linearizability Problem of Resonant Degenerate Singular Point for Polynomial Differential Systems

Fri, 05 Apr 2013 11:07 EDT

Yusen Wu, Cui Zhang, Luju Liu

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
The linearizability (or isochronicity) problem is one of the open problems for polynomial differential systems which is far to be solved in general. A progressive way to find necessary conditions for linearizability is to compute period constants. In this paper, we are interested in the linearizability problem of p : − q resonant degenerate singular point for polynomial differential systems. Firstly, we transform degenerate singular point into the origin via a homeomorphism. Moreover, we establish a new recursive algorithm to compute the so-called generalized period constants for the origin of the transformed system. Finally, to illustrate the effectiveness of our algorithm, we discuss the linearizability problems of 1 : −1 resonant degenerate singular point for a septic system. We stress that similar results are hardly seen in published literatures up till now. Our work is completely new and extends existing ones.

On the $q$ -Genocchi Numbers and Polynomials with Weight $\alpha $ and Weak Weight $\beta $

Fri, 05 Apr 2013 11:07 EDT

J. Y. Kang, H. Y. Lee, N. S. Jung

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
We construct a new type of $q$ -Genocchi numbers and polynomials with weight $\alpha $ and weak weight $\beta :{G}_{n,q}^{(\alpha ,\beta )},{G}_{n,q}^{(\alpha ,\beta )}(x)$ , respectively. Some interesting results and relationships are obtained.

Dynamical Behavior of a Stochastic Ratio-Dependent Predator-Prey System

Fri, 05 Apr 2013 11:07 EDT

Zheng Wu, Hao Huang, Lianglong Wang

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
This paper is concerned with a stochastic ratio-dependent predator-prey model with varible coefficients. By the comparison theorem of stochastic equations and the Itô formula, the global existence of a unique positive solution of the ratio-dependent model is obtained. Besides, some results are established such as the stochastically ultimate boundedness and stochastic permanence for this model.

A Simple Circular Cell Method for Multilevel Finite Element Analysis

Fri, 05 Apr 2013 11:07 EDT

Hossein Talebi, Goangseup Zi, Mohammad Silani, Esteban Samaniego, Timon Rabczuk

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed.

Positive Solutions to a Generalized Second-Order Difference Equation with Summation Boundary Value Problem

Fri, 05 Apr 2013 11:07 EDT

Thanin Sitthiwirattham, Jessada Tariboon

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
By using Krasnoselskii's fixed point theorem, we study the existence of positive solutions to the three-point summation boundary value problem ${\Delta }^{2}u(t-1)+a(t)f(u(t))=0$ , $t\in \{1,2,\dots ,T\}$ , $u(0)=\beta {\sum }_{s=1}^{\eta }u(s)$ , $u(T+1)=\alpha {\sum }_{s=1}^{\eta }u(s)$ , where $f$ is continuous, $T\ge 3$ is a fixed positive integer, $\eta \in \{1,2,...,T-1\}$ , $0<\alpha <(2T+2)/\eta (\eta +1)$ , $0<\beta <(2T+2-\alpha \eta (\eta +1))/\eta (2T-\eta +1),$ and $\Delta u(t-1)=u(t)-u(t-1)$ . We show the existence of at least one positive solution if $f$ is either superlinear or sublinear.

Dual Hesitant Fuzzy Sets

Fri, 05 Apr 2013 11:07 EDT

Bin Zhu, Zeshui Xu, Meimei Xia

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type $n$ fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, use a notion of nested interval to reflect their common ground, then propose an extension principle of DHFSs. Additionally, we give an example to illustrate the application of DHFSs in group forecasting.

Some Notes on the Poincaré-Bertrand Formula

Fri, 05 Apr 2013 11:07 EDT

Baruch Schneider

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
The aim of this present paper is to establish the Poincaré-Bertrand formula for the double-layer potential on piecewise Lyapunov curve of integration.

Random Attractors for Stochastic Three-Component Reversible Gray-Scott System with Multiplicative White Noise

Fri, 05 Apr 2013 11:07 EDT

Anhui Gu

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
The paper is devoted to proving the existence of a compact random attractor for the random dynamical system generated by stochastic three-component reversible Gray-Scott system with multiplicative white noise.

Point Pattern Matching Algorithm for Planar Point Sets under Euclidean Transform

Fri, 05 Apr 2013 11:07 EDT

Xiaoyun Wang, Xianquan Zhang

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
Point pattern matching is an important topic of computer vision and pattern recognition. In this paper, we propose a point pattern matching algorithm for two planar point sets under Euclidean transform. We view a point set as a complete graph, establish the relation between the point set and the complete graph, and solve the point pattern matching problem by finding congruent complete graphs. Experiments are conducted to show the effectiveness and robustness of the proposed algorithm.

An Interactive Procedure to Solve Multi-Objective Decision-Making Problem: An Improvment to STEM Method

Fri, 05 Apr 2013 11:07 EDT

R. Roostaee, M. Izadikhah, F. Hosseinzadeh Lotfi

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
Decisions in the real-world contexts are often made in the presence of multiple, conflicting, and incommensurate criteria. Multiobjective programming methods such as multiple objective linear programming (MOLP) are techniques used to solve such multiple-criteria decision-making (MCDM) problems. One of the first interactive procedures to solve MOLP is STEM method. In this paper we try to improve STEM method in a way that we search a point in reduced feasible region whose criterion vector is closest to positive ideal criterion vector and furthest to negative ideal criterion vector. Therefore the presented method tries to increase the rate of satisfactoriness of the obtained solution. Finally, a numerical example for illustration of the new method is given to clarify the main results developed in this paper.

Reduction of Uncertainties for Damage Identification of Bridge Based on Fuzzy Nearness and Modal Data

Fri, 05 Apr 2013 11:07 EDT

Hanbing Liu, Yubo Jiao, Yongchun Cheng, Yafeng Gong

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
To avoid the false results of deterministic identification methods induced by uncertainties, a fuzzy nearness-based method is proposed for the damage identification of bridge. An improved index based on ratios of modal shape components is used as identification measurements. The knowledge base for damage identification is established through corresponding relationship between fuzzified measurements and damage severities. The damage condition of test samples can be assessed based on approaching principle through fuzzy nearness with rules in knowledge base. A numerical analysis on a multigirder bridge considering uncertainty is presented to demonstrate the effectiveness of the proposed method. The results indicate that the fuzzy nearness-based method can achieve an accurate identification with success rate up to 93.75%. Antinoise analysis and the ability for dealing with incomplete information reveal its robustness.

Homomorphisms of Approximation Spaces

Fri, 05 Apr 2013 11:07 EDT

Zhaohao Wang, Lan Shu, Xiuyong Ding

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
The notion of the homomorphism of approximation spaces is introduced. Some properties of homomorphism are investigated, and some characterizations of homomorphism are given. Furthermore, the notion of approximation subspace of approximation spaces is introduced. The relations between approximation subspaces and homomorphisms are studied.

Stability Analysis and Robust ${H}_{\infty }$ Control of Switched Stochastic Systems with Time-Varying Delay

Fri, 05 Apr 2013 11:07 EDT

Zhengrong Xiang, Guoxin Chen

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
The problems of mean-square exponential stability and robust ${H}_{\infty }$ control of switched stochastic systems with time-varying delay are investigated in this paper. Based on the average dwell time method and Gronwall-Bellman inequality, a new mean-square exponential stability criterion of such system is derived in terms of linear matrix inequalities (LMIs). Then, ${H}_{\infty }$ performance is studied and robust ${H}_{\infty }$ controller is designed. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition

Fri, 05 Apr 2013 11:07 EDT

Huimin Yu

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
The asymptotic behavior (as well as the global existence) of classical solutions to the 3D compressible Euler equations are considered. For polytropic perfect gas $(P(\rho )={P}_{0}{\rho }^{\gamma })$ , time asymptotically, it has been proved by Pan and Zhao (2009) that linear damping and slip boundary effect make the density satisfying the porous medium equation and the momentum obeying the classical Darcy's law. In this paper, we use a more general method and extend this result to the 3D compressible Euler equations with nonlinear damping and a more general pressure term. Comparing with linear damping, nonlinear damping can be ignored under small initial data.

Analysis of IVPs and BVPs on Semi-Infinite Domains via Collocation Methods

Fri, 05 Apr 2013 11:07 EDT

Mohammad Maleki, Ishak Hashim, Saeid Abbasbandy

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
We study the numerical solutions to semi-infinite-domain two-point boundary value problems and initial value problems. A smooth, strictly monotonic transformationis used to map the semi-infinite domain $x\in [0,\infty )$ onto a half-open interval $t\in [-1,1)$ . The resulting finite-domain two-point boundary value problem is transcribed to a system of algebraic equations using Chebyshev-Gauss (CG) collocation, while the resulting initialvalue problem over a finite domain is transcribed to a system of algebraic equations using Chebyshev-Gauss-Radau (CGR) collocation. In numerical experiments, the tuning of the map $\varphi :[-1,+1)\to [0,+\infty )$ and its effects on the quality of the discrete approximation are analyzed.

Examining the Chaotic Behavior in Dynamical Systems by Means of the 0-1 Test

Fri, 05 Apr 2013 11:07 EDT

Loukas Zachilas, Iacovos N. Psarianos

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
We perform the stability analysis and we study the chaotic behavior of dynamical systems, which depict the 3-particle Toda lattice truncations through the lens of the 0-1 test, proposed by Gottwald and Melbourne. We prove that the new test applies successfully and with good accuracy in most of the cases we investigated. We perform some comparisons of the well-known maximum Lyapunov characteristic number method with the 0-1 method, and we claim that 0-1 test can be subsidiary to the LCN method. The 0-1 test is a very efficient method for studying highly chaotic Hamiltonian systems of the kind we study in our paper and is particularly useful in characterizing the transition from regularity to chaos.

Existence of Almost-Periodic Solutions for Lotka-Volterra Cooperative Systems with Time Delay

Fri, 05 Apr 2013 11:07 EDT

Kaihong Zhao

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
This paper considers the existence of positive almost-periodic solutions for almost-periodic Lotka-Volterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.

Sharp Bounds by the Generalized Logarithmic Mean for the Geometric Weighted Mean of the Geometric and Harmonic Means

Fri, 05 Apr 2013 11:07 EDT

Wei-Mao Qian, Bo-Yong Long

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
We present sharp upper and lower generalized logarithmic mean bounds for the geometric weighted mean of the geometric and harmonic means.

Generalization of the Analytical Exponential Model for Homogeneous Reactor Kinetics Equations

Fri, 05 Apr 2013 11:07 EDT

Abdallah A. Nahla, Mohammed F. Al-Ghamdi

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
Mathematical form for two energy groups of three-dimensional homogeneous reactor kinetics equations and average one group of the precursor concentration of delayed neutrons is presented. This mathematical form is called “two energy groups of the point kinetics equations.” We rewrite two energy groups of the point kinetics equations in the matrix form. Generalization of the analytical exponential model (GAEM) is developed for solving two energy groups of the point kinetics equations. The GAEM is based on the eigenvalues and the corresponding eigenvectors of the coefficient matrix. The eigenvalues of the coefficient matrix are calculated numerically using visual FORTRAN code, based on Laguerre’s method, to calculate the roots of an algebraic equation with real coefficients. The eigenvectors of the coefficient matrix are calculated analytically. The results of the GAEM are compared with the traditional methods. These comparisons substantiate the accuracy of the results of the GAEM. In addition, the GAEM is faster than the traditional methods.

The Group Involutory Matrix of the Combinations of Two Idempotent Matrices

Fri, 05 Apr 2013 11:07 EDT

Lingling Wu, Xiaoji Liu, Yaoming Yu

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
We discuss the following problem: when $aP+bQ+cPQ+dQP+ePQP+fQPQ+gPQPQ$ of idempotent matrices $P$ and $Q$ , where $a,b,c,d,e,f,g\in \mathbb{C}$ and $a\ne 0,b\ne 0$ , is group involutory.

Eigenvalue Comparisons for Second-Order Linear Equations with Boundary Value Conditions on Time Scales

Fri, 05 Apr 2013 11:07 EDT

Chao Zhang, Shurong Sun

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
This paper studies the eigenvalue comparisons for second-order linear equations with boundary conditions on time scales. Using results from matrix algebras, the existence and comparison results concerning eigenvalues are obtained.

Generalised Interval-Valued Fuzzy Soft Set

Fri, 05 Apr 2013 11:07 EDT

Shawkat Alkhazaleh, Abdul Razak Salleh

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in a medical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised fuzzy soft set; generalised interval-valued fuzzy soft set; interval-valued fuzzy set; interval-valued fuzzy soft set.

Lightlike Submanifolds of a Semi-Riemannian Manifold of Quasi-Constant Curvature

Fri, 05 Apr 2013 11:07 EDT

D. H. Jin, J. W. Lee

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
We study the geometry of lightlike submanifolds $(M,g,S(TM),S(T{M}^{\perp }))$ of a semi-Riemannian manifold $(\widetilde{M},\widetilde{g})$ of quasiconstant curvature subject to the following conditions: (1) the curvature vector field ζ of $\widetilde{M}$ is tangent to $M$ , (2) the screen distribution $S(TM)$ of $M$ is totally geodesic in $M$ , and (3) the coscreen distribution $S(T{M}^{\perp })$ of $M$ is a conformal Killing distribution.

Estimation of Approximating Rate for Neural Network in ${L}_{w}^{p}$ Spaces

Fri, 05 Apr 2013 11:07 EDT

Jian-Jun Wang, Chan-Yun Yang, Jia Jing

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
A class of Soblove type multivariate function is approximated by feedforward network with one hidden layer of sigmoidal units and a linear output. By adopting a set of orthogonal polynomial basis and under certain assumptions for the governing activation functions of the neural network, the upper bound on the degree of approximation can be obtained for the class of Soblove functions. The results obtained are helpful in understanding the approximation capability and topology construction of the sigmoidal neural networks.

Displacement Field Approximations for Force-Based Elements in Large Displacement Analyses

Fri, 05 Apr 2013 11:07 EDT

M. Vahidi, V. Jafari, M. H. Abyaneh, SH. Vahdani

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
This paper investigates different approximation techniques for planar beam column elements in force-based methods. The three fields, introduced in this review, are: curvature-based displacement interpolation (CBDI) used in matrix-based flexibility formulations, linear displacement approximation applied in state space, and higher-order displacement approximation utilized again in state space. Using these three approximation fields, the responses and their accuracies in some systems are compared in examples. Finally, focusing on the accuracy and regarding the performed analyses, it seems that the computational cost is reduced and accuracy of responses is elevated in many engineering problems using the higher-order approximation field in state space.

Ruin Probability in Compound Poisson Process with Investment

Fri, 05 Apr 2013 11:07 EDT

Yong Wu, Xiang Hu

Source: J. Appl. Math., Volume 2012, 7 pages.

Abstract:
We consider that the surplus of an insurer follows compound Poisson process and the insurer would invest its surplus in risky assets, whose prices satisfy the Black-Scholes model. In the risk process, we decompose the ruin probability into the sum of two ruin probabilities which are caused by the claim and the oscillation, respectively. We derive the integro-differential equations for these ruin probabilities these ruin probabilities. When the claim sizes are exponentially distributed, third-order differential equations of the ruin probabilities are derived from the integro-differential equations and a lower bound is obtained.

Two-Dimensional and Axisymmetric Unsteady Flows due to Normally Expanding or Contracting Parallel Plates

Fri, 05 Apr 2013 11:07 EDT

Saeed Dinarvand, Abed Moradi

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates for two cases, the two-dimensional flow case and the axisymmetric flow case, is investigated. The governing nonlinear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM). Graphical results are presented to investigate the influence of the squeeze number on the velocity, skin friction, and pressure gradient. The validity of our solutions is verified by the numerical results obtained by shooting method, coupled with Runge-Kutta scheme.

A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method

Fri, 05 Apr 2013 11:07 EDT

Qiaojie Li, Zhoushun Zheng, Shuang Wang, Jiankang Liu

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmann method. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have been compared with the exact solutions reported in previous studies. The ${L}_{2}$ , ${L}_{\infty }$ and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.

On the Interval Baker-Thompson Rule

Fri, 05 Apr 2013 11:07 EDT

S. Z. Alparslan Gök

Source: J. Appl. Math., Volume 2012, 5 pages.

Abstract:
The main aim of this paper is to give an axiomatic characterization of the interval Baker-Thompson rule.

Common Fixed-Point Theorems in Complete Generalized Metric Spaces

Fri, 05 Apr 2013 11:07 EDT

Chi-Ming Chen

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
We introduce the notions of the $\mathrm{𝒲}$ function and $\mathrm{𝒮}$ function, and then we prove two common fixed point theorems in complete generalized metric spaces under contractive conditions with these two functions. Our results generalize or improve many recent common fixed point results in the literature.

Higher-Order Weakly Generalized Epiderivatives and Applications to Optimality Conditions

Fri, 05 Apr 2013 11:07 EDT

Qilin Wang, Guolin Yu

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
The notions of higher-order weakly generalized contingent epiderivative and higher-order weakly generalized adjacent epiderivative for set-valued maps are proposed. By virtue of the higher-order weakly generalized contingent (adjacent) epiderivatives, both necessary and sufficient optimality conditions are obtained for Henig efficient solutions to a set-valued optimization problem whose constraint set is determined by a set-valued map. The imposed assumptions are relaxed in comparison with those of recent results in the literature. Examples are provided to show some advantages of our notions and results.

Asymptotic Stability of Differential Equations with Infinite Delay

Fri, 05 Apr 2013 11:07 EDT

D. Piriadarshani, T. Sengadir

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
A theorem on asymptotic stability is obtained for a differential equation with an infinite delay in a function space which is suitable for the numerical computation of the solution to the infinite delay equation.

Best Periodic Proximity Points for Cyclic Weaker Meir-Keeler Contractions

Fri, 05 Apr 2013 11:07 EDT

Chiming Chen, Chingju Lin

Source: J. Appl. Math., Volume 2012, 7 pages.

Abstract:
The purpose of this paper is to present the existence of the best period proximity point for cyclic weaker Meir-Keeler contractions and asymptotic cyclic weaker Meir-Keeler contractions in metric spaces.

Continuity of the Solution Maps for Generalized Parametric Set-Valued Ky Fan Inequality Problems

Fri, 05 Apr 2013 11:07 EDT

Z. Y. Peng, X. B. Li

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
Under new assumptions, we provide suffcient conditions for the (upper and lower) semicontinuity and continuity of the solution mappings to a class of generalized parametric set-valued Ky Fan inequality problems in linear metric space. These results extend and improve some known results in the literature (e.g., Gong, 2008; Gong and Yoa, 2008; Chen and Gong, 2010; Li and Fang, 2010). Some examples are given to illustrate our results.

Generalized Fuzzy Quasi-Ideals of an Intraregular Abel-Grassmann's Groupoid

Fri, 05 Apr 2013 11:07 EDT

Bijan Davvaz, Madad Khan, Saima Anis, Shamsul Haq

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
We have introduced a new nonassociative class of Abel-Grassmann's groupoid, namely, intraregular and characterized it in terms of its $(\in ,\in {\vee }_{q})$ -fuzzy quasi-ideals.

Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term

Fri, 05 Apr 2013 11:07 EDT

Qiong Liu, Dengfeng Lü

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
We study the following fourth-order elliptic equations: ${\Delta }^{2}u+a\Delta u=f(x,u),\mathrm{ }x\in \Omega ,\mathrm{ }u=\Delta u=0, x\in \partial \Omega $ , where $\Omega \subset {\mathbb{R}}^{N}$ is a bounded domain with smooth boundary $\partial \Omega $ and $f(x,u)$ is asymptotically linear with respect to $u$ at infinity. Using an equivalent version of Cerami's condition and the symmetric mountain pass lemma, we obtain the existence of multiple solutions for the equations.

Reliability Analysis of Wireless Sensor Networks Using Markovian Model

Fri, 05 Apr 2013 11:07 EDT

Jin Zhu, Liang Tang, Hongsheng Xi, Zhenghuan Zhang

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
This paper investigates reliability analysis of wireless sensor networks whose topology is switching among possible connections which are governed by a Markovian chain. We give the quantized relations between network topology, data acquisition rate, nodes' calculation ability, and network reliability. By applying Lyapunov method, sufficient conditions of network reliability are proposed for such topology switching networks with constant or varying data acquisition rate. With the conditions satisfied, the quantity of data transported over wireless network node will not exceed node capacity such that reliability is ensured. Our theoretical work helps to provide a deeper understanding of real-world wireless sensor networks, which may find its application in the fields of network design and topology control.

Low-Order Nonconforming Mixed Finite Element Methods for Stationary Incompressible Magnetohydrodynamics Equations

Fri, 05 Apr 2013 11:07 EDT

Dongyang Shi, Zhiyun Yu

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
The nonconforming mixed finite element methods (NMFEMs) are introduced and analyzed for the numerical discretization of a nonlinear, fully coupled stationary incompressible magnetohydrodynamics (MHD) problem in 3D. A family of the low-order elements on tetrahedra or hexahedra are chosen to approximate the pressure, the velocity field, and the magnetic field. The existence and uniqueness of the approximate solutions are shown, and the optimal error estimates for the corresponding unknown variables in ${L}^{2}$ -norm are established, as well as those in a broken ${H}^{1}$ -norm for the velocity and the magnetic fields. Furthermore, a new approach is adopted to prove the discrete Poincaré-Friedrichs inequality, which is easier than that of the previous literature.

Unsteady Stagnation Point Flow and Heat Transfer over a Stretching/Shrinking Sheet with Suction or Injection

Fri, 05 Apr 2013 11:07 EDT

M. Suali, N. M. A. Nik Long, N. M. Ariffin

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
The unsteady stagnation point flow and heat transfer over a stretching/shrinking sheet with suction/injection is studied. The governing partial differential equations are converted into nonlinear ordinary differential equations using a similarity transformation and solved numerically. Both stretching and shrinking cases are considered. Results for the skin friction coefficient, local Nusselt number, velocity, and temperature profiles are presented for different values of the governing parameters. It is found that the dual solutions exist for the shrinking case, whereas the solution is unique for the stretching case. Numerical results show that the range of dual solutions increases with mass suction and decreases with mass injection.

A Note on Inclusion Intervals of Matrix Singular Values

Fri, 05 Apr 2013 11:07 EDT

Shu-Yu Cui, Gui-Xian Tian

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
We establish an inclusion relation between two known inclusion intervals of matrix singular values in some special case. In addition, based on the use of positive scale vectors, a known inclusion interval of matrix singular values is also improved.

LMI-Based Approach for Exponential Robust Stability of High-Order Hopfield Neural Networks with Time-Varying Delays

Fri, 05 Apr 2013 11:07 EDT

Yangfan Wang, Linshan Wang

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
This paper studies the problems of global exponential robust stability of high-order hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high-order neural networks are established, which are easily verifiable and have a wider adaptive.

On a Quasi-Neutral Approximation to the Incompressible Euler Equations

Fri, 05 Apr 2013 11:07 EDT

Jianwei Yang, Zhitao Zhuang

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
We rigorously justify a singular Euler-Poisson approximation of the incompressible Euler equations in the quasi-neutral regime for plasma physics. Using the modulated energy estimates, the rate convergence of Euler-Poisson systems to the incompressible Euler equations is obtained.

Induced Interval-Valued Intuitionistic Fuzzy Hybrid Aggregation Operators with TOPSIS Order-Inducing Variables

Fri, 05 Apr 2013 11:07 EDT

Jun-Ling Zhang, Xiao-Wen Qi

Source: J. Appl. Math., Volume 2012, 24 pages.

Abstract:
Two induced aggregation operators with novelly designed TOPSIS order-inducing variables are proposed: Induced Interval-valued Intuitionistic Fuzzy Hybrid Averaging (I-IIFHA) operator and Induced Interval-valued Intuitionistic Fuzzy Hybrid Geometric (I-IIFHG) operator. The merit of two aggregation operators is that they can consider additional preference information of decision maker’s attitudinal characteristics besides argument-dependent information and argument-independent information. Some desirable properties of I-IIFHA and I-IIFHG are studied and theoretical analysis also shows that they can include a wide range of aggregation operators as special cases. Further, we extend these operators to form a novel group decision-making method for selecting the most desirable alternative in multiple attribute multi-interest group decision-making problems with attribute values and decision maker’s interest values taking the form of interval-valued intuitionistic fuzzy numbers, and application research to real estate purchase selection shows its practicality.

The Asymptotic Expansion Method via Symbolic Computation

Fri, 05 Apr 2013 11:07 EDT

Juan F. Navarro

Source: J. Appl. Math., Volume 2012, 24 pages.

Abstract:
This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.

Logarithmically Improved Blow up Criterion for Smooths Solution to the 3D Micropolar Fluid Equations

Fri, 05 Apr 2013 11:07 EDT

Yin-Xia Wang, Hengjun Zhao

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
Blow-up criteria of smooth solutions for the 3D micropolar fluid equations are investigated. Logarithmically improved blow-up criteria are established in the Morrey-Campanto space.

Strong Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Fixed Point Problems for Total Quasi- $\varphi $ -Asymptotically Nonexpansive Mappings in Banach Spaces

Fri, 05 Apr 2013 11:07 EDT

Zhaoli Ma, Lin Wang, Yunhe Zhao

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
We introduce an iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of fixed points for countable families of total quasi- $\varphi $ -asymptotically nonexpansive mappings in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper improve and extend some recent corresponding results.

Generalized Quadratic Augmented Lagrangian Methods with Nonmonotone Penalty Parameters

Fri, 05 Apr 2013 11:07 EDT

Xunzhi Zhu, Jinchuan Zhou, Lili Pan, Wenling Zhao

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
For nonconvex optimization problem with both equality and inequality constraints, we introduce a new augmented Lagrangian function and propose the corresponding multiplier algorithm. New iterative strategy on penalty parameter is presented. Different global convergence properties are established depending on whether the penalty parameter is bounded. Even if the iterative sequence $\{{x}^{k}\}$ is divergent, we present a necessary and sufficient condition for the convergence of $\{f({x}^{k})\}$ to the optimal value. Finally, preliminary numerical experience is reported.

The Point Zoro Symmetric Single-Step Procedure for Simultaneous Estimation of Polynomial Zeros

Fri, 05 Apr 2013 11:07 EDT

Mansor Monsi, Nasruddin Hassan, Syaida Fadhilah Rusli

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
The point symmetric single step procedure PSS1 has R -order of convergence at least 3. This procedure is modified by adding another single-step, which is the third step in PSS1. This modified procedure is called the point zoro symmetric single-step PZSS1. It is proven that the R -order of convergence of PZSS1 is at least 4 which is higher than the R -order of convergence of PT1, PS1, and PSS1. Hence, computational time is reduced since this procedure is more efficient for bounding simple zeros simultaneously.

Synchronization for a Class of Fractional-Order Hyperchaotic System and Its Application

Fri, 05 Apr 2013 11:07 EDT

Wen Tan, Feng Ling Jiang, Chuang Xia Huang, Lan Zhou

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
A new controller design method is proposed to synchronize the fractional-order hyperchaotic system through the stability theory of fractional calculus; the synchronization between two identical fractional-order Chen hyperchaotic systems is realized by designing only two suitable controllers in the response system. Furthermore, this control scheme can be used in secure communication via the technology of chaotic masking using the complex nonperiodic information as trial message, and the useful information can be recovered at the receiver. Numerical simulations coincide with the theoretical analysis.

Presentation of Malaria Epidemics Using Multiple Optimal Controls

Fri, 05 Apr 2013 11:07 EDT

Abid Ali Lashari, Shaban Aly, Khalid Hattaf, Gul Zaman, Il Hyo Jung, Xue-Zhi Li

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
An existing model is extended to assess the impact of some antimalaria control measures, by re-formulating the model as an optimal control problem. This paper investigates the fundamental role of three type of controls, personal protection, treatment, and mosquito reduction strategies in controlling the malaria. We work in the nonlinear optimal control framework. The existence and the uniqueness results of the solution are discussed. A characterization of the optimal control via adjoint variables is established. The optimality system is solved numerically by a competitive Gauss-Seidel-like implicit difference method. Finally, numerical simulations of the optimal control problem, using a set of reasonable parameter values, are carried out to investigate the effectiveness of the proposed control measures.

Simulating Evacuations with Obstacles Using a Modified Dynamic Cellular Automata Model

Fri, 05 Apr 2013 11:07 EDT

Lim Eng Aik, Tan Wee Choon

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
A modified dynamic cellular automata model is proposed to simulate the evacuation of occupants from a room with obstacles. The model takes into account some factors that play an important role in an evacuation process, such as human emotions and crowd density around the exits. It also incorporates people’s ability to select a less congested exit route, a factor that is rarely investigated. The simulation and experimental results show that modifications to the exits provide reasonable improvement to evacuation time, after taking into account the fact that people will tend to select exit routes based on the distance to the exits and the crowd density around the exits. In addition, the model is applied to simulations of classroom and restaurant evacuation. Results obtained with the proposed model are compared with those of several existing models. The outcome of the comparison demonstrates that it performs better than existing models.

Flow and Heat Transfer of Cu-Water Nanofluid between a Stretching Sheet and a Porous Surface in a Rotating System

Fri, 05 Apr 2013 11:07 EDT

M. Sheikholeslami, H. R. Ashorynejad, G. Domairry, I. Hashim

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
The aim of the present paper is to study the flow of nanofluid and heat transfer characteristics between two horizontal plates in a rotating system. The lower plate is a stretching sheet and the upper one is a solid porous plate. Copper (Cu) as nanoparticle and water as its base fluid have been considered. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved analytically using the homotopy analysis method (HAM). Comparison between HAM and numerical solutions results showed an excellent agreement. The results for the flow and heat transfer characteristics are obtained for various values of the nanoparticle volume fraction, suction/injection parameter, rotation parameter, and Reynolds number. It is shown that the inclusion of a nanoparticle into the base fluid of this problem is capable of causing change in the flow pattern. It is found that for both suction and injection, the heat transfer rate at the surface increases with increasing the nanoparticle volume fraction, Reynolds number, and injection/suction parameter and it decreases with power of rotation parameter.

On a Dual Model with Barrier Strategy

Fri, 05 Apr 2013 11:07 EDT

Yuzhen Wen, Chuancun Yin

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
We consider the dual of the generalized Erlang $(n)$ risk model with a barrier dividend strategy. We derive integro-differential equations with boundary conditions satisfied by the expectation of the sum of discounted dividends until ruin and the moment-generating function of the discounted dividend payments until ruin, respectively. The results are illustrated by several examples.

The Adjacency Matrix of One Type of Directed Graph and the Jacobsthal Numbers and Their Determinantal Representation

Fri, 05 Apr 2013 11:07 EDT

Fatih Yılmaz, Durmuş Bozkurt

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we consider one type of directed graph. Then we obtain a general form of the adjacency matrices of the graph. By using the well-known property which states the $(i,j)$ entry of ${A}^{m}$ ( $A$ is adjacency matrix) is equal to the number of walks of length $m$ from vertex $i$ to vertex $j$ , we show that elements of $m$ th positive integer power of the adjacency matrix correspond to well-known Jacobsthal numbers. As a consequence, we give a Cassini-like formula for Jacobsthal numbers. We also give a matrix whose permanents are Jacobsthal numbers.

Parseval Relationship of Samples in the Fractional Fourier Transform Domain

Fri, 05 Apr 2013 11:07 EDT

Bing-Zhao Li, Tian-Zhou Xu

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
This paper investigates the Parseval relationship of samples associated with the fractional Fourier transform. Firstly, the Parseval relationship for uniform samples of band-limited signal is obtained. Then, the relationship is extended to a general set of nonuniform samples of band-limited signal associated with the fractional Fourier transform. Finally, the two dimensional case is investigated in detail, it is also shown that the derived results can be regarded as the generalization of the classical ones in the Fourier domain to the fractional Fourier transform domain.

A New Positive Definite Expanded Mixed Finite Element Method for Parabolic Integrodifferential Equations

Fri, 05 Apr 2013 11:07 EDT

Yang Liu, Hong Li, Jinfeng Wang, Wei Gao

Source: J. Appl. Math., Volume 2012, 24 pages.

Abstract:
A new positive definite expanded mixed finite element method is proposed for parabolic partial integrodifferential equations. Compared to expanded mixed scheme, the new expanded mixed element system is symmetric positive definite and both the gradient equation and the flux equation are separated from its scalar unknown equation. The existence and uniqueness for semidiscrete scheme are proved and error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are provided to confirm our theoretical analysis.

Numerical Solution of the Inverse Problem of Determining an Unknown Source Term in a Heat Equation

Fri, 05 Apr 2013 11:07 EDT

Xiuming Li, Suping Qian

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions. Firstly, the problem is reduced to an equivalent problem which is easy to handle using variational iteration method. Secondly, variational iteration method is used to solve the reduced problem. Using this method a rapid convergent sequence can be produced which tends to the exact solution of the problem. Furthermore, variational iteration method does not require the discretization of the problem. Two numerical examples are presented to illustrate the strength of the method.

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

Fri, 05 Apr 2013 11:07 EDT

Cuijie Zhang, Songnian He

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
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.

On Decomposable Measures Induced by Metrics

Fri, 05 Apr 2013 11:07 EDT

Dong Qiu, Weiquan Zhang

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
We prove that for a given normalized compact metric space it can induce a $\sigma $ -max-superdecomposable measure, by constructing a Hausdorff pseudometric on its power set. We also prove that the restriction of this set function to the algebra of all measurable sets is a $\sigma $ -max-decomposable measure. Finally we conclude this paper with two open problems.

Boundary Layer Flow and Heat Transfer with Variable Fluid Properties on a Moving Flat Plate in a Parallel Free Stream

Fri, 05 Apr 2013 11:07 EDT

Norfifah Bachok, Anuar Ishak, Ioan Pop

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
The steady boundary layer flow and heat transfer of a viscous fluid on a moving flat plate in a parallel free stream with variable fluid properties are studied. Two special cases, namely, constant fluid properties and variable fluid viscosity, are considered. The transformed boundary layer equations are solved numerically by a finite-difference scheme known as Keller-box method. Numerical results for the flow and the thermal fields for both cases are obtained for various values of the free stream parameter and the Prandtl number. It is found that dual solutions exist for both cases when the fluid and the plate move in the opposite directions. Moreover, fluid with constant properties shows drag reduction characteristics compared to fluid with variable viscosity.

Unsteady Unidirectional MHD Flow of Voigt Fluids Moving between Two Parallel Surfaces for Variable Volume Flow Rates

Fri, 05 Apr 2013 11:07 EDT

Wei-Fan Chen, Hsin-Yi Lai, Cha'o-Kuang Chen

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
The velocity profile and pressure gradient of an unsteady state unidirectional MHD flow of Voigt fluids moving between two parallel surfaces under magnetic field effects are solved by the Laplace transform method. The flow motion between parallel surfaces is induced by a prescribed inlet volume flow rate that varies with time. Four cases of different inlet volume flow rates are considered in this study including (1) constant acceleration piston motion, (2) suddenly started flow, (3) linear acceleration piston motion, and (4) oscillatory piston motion. The solution for each case is elaborately derived, and the results of associated velocity profile and pressure gradients are presented in analytical forms.

Model Reference Control for an Economic Growth Cycle Model

Fri, 05 Apr 2013 11:07 EDT

Pengfei Zhao, Cai Liu, Xuan Feng

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
A useful method in intelligent engineering, called model reference control (MRC), is applied in an economic control problem. The authors review the main framework of MRC and Goodwin growth cycle (GGC) model between two countries and drive the employment rate to be approximate stable in a high level by controlling the workers' share in the national income automatically. It is very helpful to constitute economic policies for a country or an economic union.

On Fuzzy Corsini's Hyperoperations

Fri, 05 Apr 2013 11:07 EDT

Yuming Feng, P. Corsini

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
We generalize the concept of C-hyperoperation and introduce the concept of F-C-hyperoperation. We list some basic properties of F-C-hyperoperation and the relationship between the concept of C-hyperoperation and the concept of F-C-hyperoperation. We also research F-C-hyperoperations associated with special fuzzy relations.

Evaluating Projects Based on Intuitionistic Fuzzy Group Decision Making

Fri, 05 Apr 2013 11:07 EDT

Babak Daneshvar Rouyendegh

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
There are various methods regarding project selection in different fields. This paper deals with an actual application of construction project selection, using two aggregation operators. First, the opinion of experts is used in a model of group decision making called intuitionistic fuzzy TOPSIS (IFT). Secondly, project evaluation is formulated by dynamic intuitionistic fuzzy weighted averaging (DIFWA). Intuitionistic fuzzy weighted averaging (IFWA) operator is utilized to aggregate individual opinions of decision makers (DMs) for rating the importance of criteria and alternatives. A numerical example for project selection is given to clarify the main developed result in this paper.

Modeling the Dynamics of an Epidemic under Vaccination in Two Interacting Populations

Fri, 05 Apr 2013 11:07 EDT

Ibrahim H. I. Ahmed, Peter J. Witbooi, Kailash Patidar

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
We present a model for an SIR epidemic in a population consisting of two components—locals and migrants. We identify three equilibrium points and we analyse the stability of the disease free equilibrium. Then we apply optimal control theory to find an optimal vaccination strategy for this 2-group population in a very simple form. Finally we support our analysis by numerical simulation using the fourth order Runge-Kutta method.

Refinements of Hermite-Hadamard Inequalities for Functions When a Power of the Absolute Value of the Second Derivative Is P -Convex

Fri, 05 Apr 2013 11:07 EDT

A. Barani, S. Barani, S. S. Dragomir

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
We extend some estimates of the right-hand side of Hermite-Hadamard-type inequalities for functions whose second derivatives absolute values are $P$ -convex. Applications to some special means are considered.

Numerical Solutions of Stochastic Differential Equations with Piecewise Continuous Arguments under Khasminskii-Type Conditions

Fri, 05 Apr 2013 11:07 EDT

Minghui Song, Ling Zhang

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
The main purpose of this paper is to investigate the convergence of the Euler method to stochastic differential equations with piecewise continuous arguments (SEPCAs). The classical Khasminskii-type theorem gives a powerful tool to examine the global existence of solutions for stochastic differential equations (SDEs) without the linear growth condition by the use of the Lyapunov functions. However, there is no such result for SEPCAs. Firstly, this paper shows SEPCAs which have nonexplosion global solutions under local Lipschitz condition without the linear growth condition. Then the convergence in probability of numerical solutions to SEPCAs under the same conditions is established. Finally, an example is provided to illustrate our theory.

Attacks on One Designated Verifier Proxy Signature Scheme

Fri, 05 Apr 2013 11:07 EDT

Baoyuan Kang

Source: J. Appl. Math., Volume 2012, 6 pages.

Abstract:
In a designated verifier proxy signature scheme, there are three participants, namely, the original signer, the proxy signer, and the designated verifier. The original signer delegates his or her signing right to the proxy signer, then the proxy signer can generate valid signature on behalf of the original signer. But only the designated verifier can verify the proxy signature. Several designated verifier proxy signature schemes have been proposed. However, most of them were proven secure in the random oracle model, which has received a lot of criticism since the security proofs in the random oracle model are not sound with respect to the standard model. Recently, by employing Water's hashing technique, Yu et al. proposed a new construction of designated verifier proxy signature. They claimed that the new construction is the first designated verifier proxy signature, whose security does not rely on the random oracles. But, in this paper, we will show some attacks on Yu et al.'s scheme. So, their scheme is not secure.

Wigner-Ville Distribution Associated with the Linear Canonical Transform

Fri, 05 Apr 2013 11:07 EDT

Rui-Feng Bai, Bing-Zhao Li, Qi-Yuan Cheng

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
The linear canonical transform is shown to be one of the most powerful tools for nonstationary signal processing. Based on the properties of the linear canonical transform and the classical Wigner-Ville transform, this paper investigates the Wigner-Ville distribution in the linear canonical transform domain. Firstly, unlike the classical Wigner-Ville transform, a new definition of Wigner-Ville distribution associated with the linear canonical transform is given. Then, the main properties of the newly defined Wigner-Ville transform are investigated in detail. Finally, the applications of the newly defined Wigner-Ville transform in the linear-frequency-modulated signal detection are proposed, and the simulation results are also given to verify the derived theory.

Exact Matrix Representation of the Transverse Magnetic Multiple Scattering of Obliquely Incident Plane Waves by the Diffraction Grating of Penetrable Cylinders

Fri, 05 Apr 2013 11:07 EDT

Ömer Kavaklıoğlu, Roger Henry Lang

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
“ An exact matrix conformation model ” associated with the equations describing the exact behavior of the Fourier-Bessel multiple scattering coefficients of the diffraction grating consisting of an infinite number of infinitely long parallel penetrable circular cylinders, corresponding to the obliquely incident transverse-magnetic plane waves in “ Twersky-Wait-Kavaklıoğlu representation ,” originally excogitated in (Kavaklıoğlu, 2000), is acquired, and the exact solution for “ the Fourier-Bessel multiple scattering coefficients of the diffraction grating at oblique incidence ” is obtained by a matrix inversion procedure.

Global Solutions to the Spherically Symmetric Compressible Navier-Stokes Equations with Density-Dependent Viscosity

Fri, 05 Apr 2013 11:07 EDT

Ruxu Lian, Lan Huang, Jian Liu

Source: J. Appl. Math., Volume 2012, 22 pages.

Abstract:
We consider the exterior problem and the initial boundary value problem for the spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient in this paper. For regular initial density, we show that there exists a unique global strong solution to the exterior problem or the initial boundary value problem, respectively. In particular, the strong solution tends to the equilibrium state as $t\to +\infty $ .

Survival Analysis of a Nonautonomous Logistic Model with Stochastic Perturbation

Fri, 05 Apr 2013 11:07 EDT

Chun Lu, Xiaohua Ding

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
Taking white noise into account, a stochastic nonautonomous logistic model is proposed and investigated. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, stochastic permanence, and global asymptotic stability are established. Moreover, the threshold between weak persistence and extinction is obtained. Finally, we introduce some numerical simulink graphics to illustrate our main results.

On Some Pursuit and Evasion Differential Game Problems for an Infinite Number of First-Order Differential Equations

Fri, 05 Apr 2013 11:07 EDT

Abbas Badakaya Ja'afaru, Gafurjan Ibragimov

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
We study pursuit and evasion differential game problems described by infinite number of first-order differential equations with function coefficients in Hilbert space l 2 . Problems involving integral, geometric, and mix constraints to the control functions of the players are considered. In each case, we give sufficient conditions for completion of pursuit and for which evasion is possible. Consequently, strategy of the pursuer and control function of the evader are constructed in an explicit form for every problem considered.

Quadruple Fixed Point Theorems under Nonlinear Contractive Conditions in Partially Ordered Metric Spaces

Fri, 05 Apr 2013 11:07 EDT

Erdal Karapınar, Wasfi Shatanawi, Zead Mustafa

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
We prove a number of quadruple fixed point theorems under $\varphi $ -contractive conditions for a mapping $F:{X}^{4}\to X$ in ordered metric spaces. Also, we introduce an example to illustrate the effectiveness of our results.

Computational Procedure of Performance Assessment of Lifetime Index of Products for the Weibull Distribution with the Progressive First-Failure-Censored Sampling Plan

Fri, 05 Apr 2013 11:07 EDT

Ching-Wen Hong, Wen-Chuan Lee, Jong-Wuu Wu

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
Process capability analysis has been widely applied in the field of quality control to monitor the performance of industrial processes. In practice, lifetime performance index ${C}_{L}$ is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. This study will apply the large-sample theory to construct a maximum likelihood estimator (MLE) of ${C}_{L}$ with the progressive first-failure-censored sampling plan under the Weibull distribution. The MLE of ${C}_{L}$ is then utilized to develop a new hypothesis testing procedure in the condition of known L .

Constructions of Vector-Valued Filters and Vector-Valued Wavelets

Fri, 05 Apr 2013 11:07 EDT

Jianxun He, Shouyou Huang

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
Let a $=({a}_{1},{a}_{2},\dots ,{a}_{m})$ $\in {ℂ}^{m}$ be an m -dimensional vector. Then, it can be identified with an $m×m$ circulant matrix. By using the theory of matrix-valued wavelet analysis (Walden and Serroukh, 2002), we discuss the vector-valued multiresolution analysis. Also, we derive several different designs of finite length of vector-valued filters. The corresponding scaling functions and wavelet functions are given. Specially, we deal with the construction of filters on symmetric matrix-valued functions space.

Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption

Fri, 05 Apr 2013 11:07 EDT

Yulan Wang, Zhaoyin Xiang, Jinsong Hu

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
We investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of solutions blowing up in finite time, or for the global existence and boundedness of all solutions. For the blowup solutions, we also study the blowup rate estimates and the localization of blowup set. Moreover, we show some numerical experiments which illustrate our results.

A New Efficient Method for Nonlinear Fisher-Type Equations

Fri, 05 Apr 2013 11:07 EDT

Hossein Aminikhah, Farshid Mehrdoust, Ali Jamalian

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
Laplace transform and new homotopy perturbation methods are adopted to study Fisher-type equations analytically. The solutions introduced in this study can be used to obtain the closed form of the solutions if they are required. The combined method needs less work in comparison with the other homotopy perturbation methods and decreases volume of calculations considerably. The method is tested on various examples, and results show that new method is more effective and convenient to use, and high accuracy of it is evident.

New Approximate Analytical Solutions of the Falkner-Skan Equation

Fri, 05 Apr 2013 11:07 EDT

Beong In Yun

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
We propose an iterative method for solving the Falkner-Skan equation. The method provides approximate analytical solutions which consist of coefficients of the previous iterate solution. By some examples, we show that the presented method with a small number of iterations is competitive with the existing method such as Adomian decomposition method. Furthermore, to improve the accuracy of the proposed method, we suggest an efficient correction method. In practice, for some examples one can observe that the correction method results in highly improved approximate solutions.

Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained Optimization

Fri, 05 Apr 2013 11:07 EDT

Mahboubeh Farid, Wah June Leong, Lihong Zheng

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
This paper focuses on developing diagonal gradient-type methods that employ accumulative approach in multistep diagonal updating to determine a better Hessian approximation in each step. The interpolating curve is used to derive a generalization of the weak secant equation, which will carry the information of the local Hessian. The new parameterization of the interpolating curve in variable space is obtained by utilizing accumulative approach via a norm weighting defined by two positive definite weighting matrices. We also note that the storage needed for all computation of the proposed method is just $O(n)$ . Numerical results show that the proposed algorithm is efficient and superior by comparison with some other gradient-type methods.

Variational Iteration Method for q -Difference Equations of Second Order

Fri, 05 Apr 2013 11:07 EDT

Guo-Cheng Wu

Source: J. Appl. Math., Volume 2012, 5 pages.

Abstract:
Recently, Liu extended He's variational iteration method to strongly nonlinear q -difference equations. In this study, the iteration formula and the Lagrange multiplier are given in a more accurate way. The q -oscillation equation of second order is approximately solved to show the new Lagrange multiplier's validness.

Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables

Fri, 05 Apr 2013 11:07 EDT

Qunying Wu

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
The complete convergence for pairwise negative quadrant dependent (PNQD) random variables is studied. So far there has not been the general moment inequality for PNQD sequence, and therefore the study of the limit theory for PNQD sequence is very difficult and challenging. We establish a collection that contains relationship to overcome the difficulties that there is no general moment inequality. Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables are obtained. Our results generalize and improve those on complete convergence theorems previously obtained by Baum and Katz (1965) and Wu (2002).

Best Proximity Point Theorems for Some New Cyclic Mappings

Fri, 05 Apr 2013 11:07 EDT

Chi-Ming Chen, Chao-Hung Chen

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
By using the stronger Meir-Keeler mapping, we introduce the concepts of the sMK- G -cyclic mappings, sMK- K -cyclic mappings, and sMK- C -cyclic mappings, and then we prove some best proximity point theorems for these various types of contractions. Our results generalize or improve many recent best proximity point theorems in the literature (e.g., Elderd and Veeramani, 2006; Sadiq Basha et al., 2011).

Chover-Type Laws of the Iterated Logarithm for Continuous Time Random Walks

Fri, 05 Apr 2013 11:07 EDT

Kyo-Shin Hwang, Wensheng Wang

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
A continuous time random walk is a random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper, we establish Chover-type laws of the iterated logarithm for continuous time random walks with jumps and waiting times in the domains of attraction of stable laws.

Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients

Fri, 05 Apr 2013 11:07 EDT

Hui Yu, Minghui Song

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
The numerical methods in the current known literature require the stochastic differential equations (SDEs) driven by Poisson random measure satisfying the global Lipschitz condition and the linear growth condition. In this paper, Euler's method is introduced for SDEs driven by Poisson random measure with non-Lipschitz coefficients which cover more classes of such equations than before. The main aim is to investigate the convergence of the Euler method in probability to such equations with non-Lipschitz coefficients. Numerical example is given to demonstrate our results.

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

Fri, 05 Apr 2013 11:07 EDT

Zhigang Pan, Hong Luo, Tian Ma

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
We consider the global existence of strong solution $u$ , corresponding to a class of fully nonlinear wave equations with strongly damped terms ${u}_{tt}-k\mathrm{\Delta }{u}_{t}=f(x,\mathrm{\Delta }u)+g(x,u,Du,{D}^{2}u)$ in a bounded and smooth domain $\mathrm{\Omega }$ in ${R}^{n}$ , where $f(x,\mathrm{\Delta }u)$ is a given monotone in $\mathrm{\Delta }u$ nonlinearity satisfying some dissipativity and growth restrictions and $g(x,u,Du,{D}^{2}u)$ is in a sense subordinated to $f(x,\mathrm{\Delta }u)$ . By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solution $u\in {L}_{\text{l}\text{o}\text{c}}^{\infty }((0,\infty ),{W}^{2,p}(\mathrm{\Omega })\cap {W}_{0}^{1,p}(\mathrm{\Omega }))$ .

Approximation Analysis of Gradient Descent Algorithm for Bipartite Ranking

Fri, 05 Apr 2013 11:07 EDT

Hong Chen, Fangchao He, Zhibin Pan

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
We introduce a gradient descent algorithm for bipartite ranking with general convex losses. The implementation of this algorithm is simple, and its generalization performance is investigated. Explicit learning rates are presented in terms of the suitable choices of the regularization parameter and the step size. The result fills the theoretical gap in learning rates for ranking problem with general convex losses.

An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations $\mathrm{AXB}=E$ , $\mathrm{CXD}=F$

Fri, 05 Apr 2013 11:07 EDT

Deqin Chen, Feng Yin, Guang-Xin Huang

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
An iterative algorithm is constructed to solve the linear matrix equation pair $AXB=E, CXD=F$ over generalized reflexive matrix $X$ . When the matrix equation pair $AXB=E, CXD=F$ is consistent over generalized reflexive matrix $X$ , for any generalized reflexive initial iterative matrix ${X}_{1}$ , the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors. The unique least-norm generalized reflexive iterative solution of the matrix equation pair can be derived when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate solution of $AXB=E, CXD=F$ for a given generalized reflexive matrix ${X}_{0}$ can be derived by finding the least-norm generalized reflexive solution of a new corresponding matrix equation pair $A\stackrel{̃}{X}B=\stackrel{̃}{E}, C\stackrel{̃}{X}D=\stackrel{̃}{F}$ with $\stackrel{̃}{E}=E-A{X}_{0}B, \stackrel{̃}{F}=F-C{X}_{0}D$ . Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.

Blow-Up Time for Nonlinear Heat Equations with Transcendental Nonlinearity

Fri, 05 Apr 2013 11:07 EDT

Hee Chul Pak

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
A blow-up time for nonlinear heat equations with transcendental nonlinearity is investigated. An upper bound of the first blow-up time is presented. It is pointed out that the upper bound of the first blow-up time depends on the support of the initial datum.

Application of Piecewise Successive Linearization Method for the Solutions of the Chen Chaotic System

Fri, 05 Apr 2013 11:07 EDT

S. S. Motsa, Y. Khan, S. Shateyi

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
This paper centres on the application of the new piecewise successive linearization method (PSLM) in solving the chaotic and nonchaotic Chen system. Numerical simulations are presented graphically and comparison is made between the PSLM and Runge-Kutta-based methods. The work shows that the proposed method provides good accuracy and can be easily extended to other dynamical systems including those that are chaotic in nature.

A Preconditioned Iteration Method for Solving Sylvester Equations

Fri, 05 Apr 2013 11:07 EDT

Jituan Zhou, Ruirui Wang, Qiang Niu

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
A preconditioned gradient-based iterative method is derived by judicious selection of two auxil- iary matrices. The strategy is based on the Newton’s iteration method and can be regarded as a generalization of the splitting iterative method for system of linear equations. We analyze the convergence of the method and illustrate that the approach is able to considerably accelerate the convergence of the gradient-based iterative method.

A New Approach for Analyzing the Reliability of the Repair Facility in a Series System with Vacations

Fri, 05 Apr 2013 11:07 EDT

Renbin Liu, Yong Wu

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
Based on the renewal process theory we develop a decomposition method to analyze the reliability of the repair facility in an n -unit series system with vacations. Using this approach, we study the unavailability and the mean replacement number during $(0,t]$ of the repair facility. The method proposed in this work is novel and concise, which can make us see clearly the structures of the facility indices of a series system with an unreliable repair facility, two convolution relations. Special cases and numerical examples are given to show the validity of our method.

Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions

Fri, 05 Apr 2013 11:07 EDT

Lianwen Wang, Rhonda McKee

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
The continuability, boundedness, monotonicity, and asymptotic properties of nonoscillatory solutions for a class of second-order nonlinear differential equations ${[p(t)h(x(t))f({x}^{\prime }(t))]}^{\prime }=q(t)g(x(t))$ are discussed without monotonicity assumption for function g . It is proved that all solutions can be extended to infinity, are eventually monotonic, and can be classified into disjoint classes that are fully characterized in terms of several integral conditions. Moreover, necessary and sufficient conditions for the existence of solutions in each class and for the boundedness of all solutions are established.

Periodic Wave Solutions and Their Limits for the Generalized KP-BBM Equation

Fri, 05 Apr 2013 11:07 EDT

Ming Song, Zhengrong Liu

Source: J. Appl. Math., Volume 2012, 25 pages.

Abstract:
We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain periodic wave solutions, kink wave solutions, unbounded wave solutions, blow-up wave solutions, and solitary wave solutions.

Approximate Solutions for Nonlinear Initial Value Problems Using the Modified Variational Iteration Method

Fri, 05 Apr 2013 11:07 EDT

Taher A. Nofal

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
We have used the modified variational iteration method (MVIM) to find the approximate solutions for some nonlinear initial value problems in the mathematical physics, via the Burgers-Fisher equation, the Kuramoto-Sivashinsky equation, the coupled Schrodinger-KdV equations, and the long-short wave resonance equations together with initial conditions. The results of these problems reveal that the modified variational iteration method is very powerful, effective, convenient, and quite accurate to systems of nonlinear equations. It is predicted that this method can be found widely applicable in engineering and physics.

A Hamilton-Poisson Model of the Chen-Lee System

Fri, 05 Apr 2013 11:07 EDT

Camelia Pop Arieşanu

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
We will present some dynamical and geometrical properties of Chen-Lee system from the Poisson geometry point of view.

Stability and Probability 1 Convergence for Queueing Networks via Lyapunov Optimization

Fri, 05 Apr 2013 11:07 EDT

Michael J. Neely

Source: J. Appl. Math., Volume 2012, 35 pages.

Abstract:
Lyapunov drift is a powerful tool for optimizing stochastic queueing networks subject to stability. However, the most convenient drift conditions often provide results in terms of a time average expectation, rather than a pure time average. This paper provides an extended drift-plus-penalty result that ensures stability with desired time averages with probability 1. The analysis uses the law of large numbers for martingale differences. This is applied to quadratic and subquadratic Lyapunov methods for minimizing the time average of a network penalty function subject to stability and to additional time average constraints. Similar to known results for time average expectations, this paper shows that pure time average penalties can be pushed arbitrarily close to optimality, with a corresponding tradeoff in average queue size. Further, in the special case of quadratic Lyapunov functions, the basic drift condition is shown to imply all major forms of queue stability.

He-Laplace Method for Linear and Nonlinear Partial Differential Equations

Fri, 05 Apr 2013 11:07 EDT

Hradyesh Kumar Mishra, Atulya K. Nagar

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
A new treatment for homotopy perturbation method is introduced. The new treatment is called He-Laplace method which is the coupling of the Laplace transform and the homotopy perturbation method using He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The method is implemented on linear and nonlinear partial differential equations. It is found that the proposed scheme provides the solution without any discretization or restrictive assumptions and avoids the round-off errors.

Coupled Fixed Point Theorems of Single-Valued Mapping for c -Distance in Cone Metric Spaces

Fri, 05 Apr 2013 11:07 EDT

Zaid Mohammed Fadail, Abd Ghafur Bin Ahmad

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
A new concept of the c -distance in cone metric space has been introduced recently in 2011. The aim of this paper is to extend and generalize some coupled fixed-point theorems on c -distance in cone metric space. Some examples are given.

The Merrifield-Simmons Index and Hosoya Index of $C(n,k,\lambda )$ Graphs

Fri, 05 Apr 2013 11:07 EDT

Shaojun Dai, Ruihai Zhang

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
The Merrifield-Simmons index $\mathrm{i(G)}$ of a graph $G$ is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, that is, the number of independent vertex sets of $G$ The Hosoya index $\mathrm{z(G)}$ of a graph $G$ is defined as the total number of independent edge subsets, that is, the total number of its matchings. By $C(n,k,\lambda )$ we denote the set of graphs with $n$ vertices, $k$ cycles, the length of every cycle is $\lambda $ , and all the edges not on the cycles are pendant edges which are attached to the same vertex. In this paper, we investigate the Merrifield-Simmons index $\mathrm{i(G)}$ and the Hosoya index $\mathrm{z(G)}$ for a graph $G$ in $C(n,k,\lambda )$ .

Lie Group Analysis of Natural Convective Flow from a Convectively Heated Upward Facing Radiating Permeable Horizontal Plate in Porous Media Filled with Nanofluid

Fri, 05 Apr 2013 11:07 EDT

Md. Jashim Uddin, W. A. Khan, A. I. Md. Ismail

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
Two-dimensional, steady, laminar and incompressible natural convective flow of a nanofluid over a connectively heated permeable upward facing radiating horizontal plate in porous medium is studied numerically. The present model incorporates Brownian motion and thermophoresis effects. The similarity transformations for the governing equations are developed by Lie group analysis. The transformed equations are solved numerically by Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. Effects of the governing parameters on the dimensionless velocity, temperature and nanoparticle volume fraction as well as on the dimensionless rate of heat and mass transfer are presented graphically and the results are compared with the published data for special cases. Good agreement is found between numerical results of the present paper and published results. It is found that Lewis number, Brownian motion and convective heat transfer parameters increase the heat and mass transfer rates whilst thermophoresis decreases both heat and mass transfer rates.

Peculiarities of Bounds on States through the Concept of Linear Superposition

Fri, 05 Apr 2013 11:07 EDT

Amit Bhar

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
We investigate the effect of superposition of states on local conversion of pure bipartite states under deterministic LOCC. We also investigate the entanglement behaviour of such classes of states, specifically their monotone nature. Finally we are able to construct some counterintuitive situations, on the bounds of different measures of entanglement, emphasis on the idea of comparability and incomparability under deterministic LOCC.

Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators

Fri, 05 Apr 2013 11:07 EDT

Zhen Jia, Guangming Deng

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
We propose a mathematical model of a complex dynamical network consisting of two types of chaotic oscillators and investigate the schemes and corresponding criteria for cluster synchronization. The global asymptotically stable criteria for the linearly or adaptively coupled network are derived to ensure that each group of oscillators is synchronized to the same behavior. The cluster synchronization can be guaranteed by increasing the inner coupling strength in each cluster or enhancing the external excitation. Theoretical analysis and numerical simulation results show that the external excitation is more conducive to the cluster synchronization. All of the results are proved rigorously. Finally, a network with a scale-free subnetwork and a small-world subnetwork is illustrated, and the corresponding numerical simulations verify the theoretical analysis.

Multiple Positive Solutions for Singular Semipositone Periodic Boundary Value Problems with Derivative Dependence

Fri, 05 Apr 2013 11:07 EDT

Huiqin Lu

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
By constructing a special cone in ${C}^{1}[0,2\pi ]$ and the fixed point theorem, this paper investigates second-order singular semipositone periodic boundary value problems with dependence on the first-order derivative and obtains the existence of multiple positive solutions. Further, an example is given to demonstrate the applications of our main results.

On Arc Connectivity of Direct-Product Digraphs

Fri, 05 Apr 2013 11:07 EDT

Tiedan Zhu, Jianping Ou

Source: J. Appl. Math., Volume 2012, 6 pages.

Abstract:
Four natural orientations of the direct product of two digraphs are introduced in this paper. Sufficient and necessary conditions for these orientations to be strongly connected are presented, as well as an explicit expression of the arc connectivity of a class of direct-product digraphs.

On the Rate of Convergence of Kirk-Type Iterative Schemes

Fri, 05 Apr 2013 11:07 EDT

Nawab Hussain, Renu Chugh, Vivek Kumar, Arif Rafiq

Source: J. Appl. Math., Volume 2012, 22 pages.

Abstract:
The purpose of this paper is to introduce Kirk-type new iterative schemes called Kirk-SP and Kirk-CR schemes and to study the convergence of these iterative schemes by employing certain quasi-contractive operators. By taking an example, we will compare Kirk-SP, Kirk-CR, Kirk-Mann, Kirk-Ishikawa, and Kirk-Noor iterative schemes for aforementioned class of operators. Also, using computer programs in C++, we compare the above-mentioned iterative schemes through examples of increasing, decreasing, sublinear, superlinear, and oscillatory functions.

An Elite Decision Making Harmony Search Algorithm for Optimization Problem

Fri, 05 Apr 2013 11:07 EDT

Lipu Zhang, Yinghong Xu, Yousong Liu

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
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.

Convergence Theorems for Equilibrium Problems and Fixed-Point Problems of an Infinite Family of ${k}_{i}$ -Strictly Pseudocontractive Mapping in Hilbert Spaces

Fri, 05 Apr 2013 11:07 EDT

Haitao Che, Meixia Li, Xintian Pan

Source: J. Appl. Math., Volume 2012, 23 pages.

Abstract:
We first extend the definition of W n from an infinite family of nonexpansive mappings to an infinite family of strictly pseudocontractive mappings, and then propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an infinite family of ${k}_{i}$ -strictly pseudocontractive mappings in Hilbert spaces. The results obtained in this paper extend and improve the recent ones announced by many others. Furthermore, a numerical example is presented to illustrate the effectiveness of the proposed scheme.

Generalized Fuzzy Soft Expert Set

Fri, 05 Apr 2013 11:07 EDT

Ayman A. Hazaymeh, Ismail B. Abdullah, Zaid T. Balkhi, Rose I. Ibrahim

Source: J. Appl. Math., Volume 2012, 22 pages.

Abstract:
In 2011 Alkhazaleh and Salleh defined the concept of soft expert sets where the user can know the opinion of all the experts in one model and give an application of this concept in decision-making problems. Also, they introduced the concept of the fuzzy soft expert set as a combination between the soft expert set and the fuzzy set. In 2010 Majumdar and Samanta presented the concept of a generalized fuzzy soft sets. The purpose of this paper is to combine the work of Alkhazaleh and Salleh (2011) and Majumdar and Samanta (2010), from which we can obtain a new concept: generalized fuzzy soft expert sets (GFSESs). We also introduce its operations, namely, complement, union intersection, “AND” and “OR”, and study their properties. The generalized fuzzy soft expert sets are used to analyze a decision-making problem. Also in our model the user can know the opinion of all experts in one model. In this work we also introduce the concept of a generalized fuzzy soft expert sets with multiopinions (four opinions), which will be more effective and useful. Finally, we give an application of this concept in decision-making problem.

Differential Quadrature Solution of Hyperbolic Telegraph Equation

Fri, 05 Apr 2013 11:07 EDT

B. Pekmen, M. Tezer-Sezgin

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
Differential quadrature method (DQM) is proposed for the numerical solution of one- and two-space dimensional hyperbolic telegraph equation subject to appropriate initial and boundary conditions. Both polynomial-based differential quadrature (PDQ) and Fourier-based differential quadrature (FDQ) are used in space directions while PDQ is made use of in time direction. Numerical solution is obtained by using Gauss-Chebyshev-Lobatto grid points in space intervals and equally spaced and/or GCL grid points for the time interval. DQM in time direction gives the solution directly at a required time level or steady state without the need of iteration. DQM also has the advantage of giving quite good accuracy with considerably small number of discretization points both in space and time direction.

A Numerical Scheme to Solve Fuzzy Linear Volterra Integral Equations System

Fri, 05 Apr 2013 11:07 EDT

A. Jafarian, S. Measoomy Nia, S. Tavan

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
The current research attempts to offer a new method for solving fuzzy linear Volterra integral equations system. This method converts the given fuzzy system into a linear system in crisp case by using the Taylor expansion method. Now the solution of this system yields the unknown Taylor coefficients of the solution functions. The proposed method is illustrated by an example and also results are compared with the exact solution by using computer simulations.

Hyperspherical Manifold for EEG Signals of Epileptic Seizures

Fri, 05 Apr 2013 11:07 EDT

Tahir Ahmad, Vinod Ramachandran

Source: J. Appl. Math., Volume 2012, 22 pages.

Abstract:
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.

A Note on tvs-G -Cone Metric Fixed Point Theory

Fri, 05 Apr 2013 11:07 EDT

Ing-Jer Lin, Chi-Ming Chen, Chao-Hung Chen, Tien-Ying Cheng

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
For a tvs-G -cone metric space $(X,G)$ and for the family $\mathrm{𝒜}$ of subsets of X , we introduce a new notion of the tvs-ℋ -cone metric ℋ with respect to G , and we get a fixed result for the $\mathrm{𝒞}ℬ\mathrm{𝒲}$ -tvs-G -cone-type function in a complete tvs-G -cone metric space $(\mathrm{𝒜},ℋ)$ . Our resultsgeneralize some recent results in the literature.

Existence of Solutions of Nonlinear Mixed Two-Point Boundary Value Problems for Third-Order Nonlinear Differential Equation

Fri, 05 Apr 2013 11:07 EDT

Yongxin Gao, Fengqin Wang

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
The authors use the upper and lower solution method to study the existence of solutions of nonlinear mixed two-point boundary value problems for third-order nonlinear differential equation $\mathrm{ }y\mathrm{\prime \prime \prime }=f(x,y,y\prime ,y\mathrm{\prime \prime }),\mathrm{ }y\prime (b)=h(y\prime (a)),\mathrm{ }p(y(a),y(b),y\prime (a),y\prime (b))=0,\mathrm{ }g(y(a),y(b),y\prime (a),y\prime (b),y\mathrm{\prime \prime }(a),y\mathrm{\prime \prime }(b))=0$ . Some new existence results are obtained by developing the upper and lower solution method. Some applications are also presented.

Collocation for High-Order Differential Equations with Lidstone Boundary Conditions

Fri, 05 Apr 2013 11:07 EDT

Francesco Costabile, Anna Napoli

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
A class of methods for the numerical solution of high-order differential equations with Lidstone and complementary Lidstone boundary conditions are presented. It is a collocation method which provides globally continuous differentiable solutions. Computation of the integrals which appear in the coefficients is generated by a recurrence formula. Numerical experiments support theoretical results.

Spectral Ratios for Crack Detection Using P and Rayleigh Waves

Fri, 05 Apr 2013 11:07 EDT

Enrique Olivera-Villaseñor, Norberto Flores-Guzmán, Ernesto Pineda-León, Jaime Núñez-Farfán, Manuel Carbajal-Romero, Alejandro Rodríguez-Castellanos

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
We obtain numerical results to help the detection and characterization of subsurface cracks in solids by the application of P and Rayleigh elastic waves. The response is obtained from boundary integral equations, which belongs to the field of elastodynamics. Once the implementation of the boundary conditions has been done, a system of Fredholm integral equations of the second kind and order zero is found. This system is solved using the method of Gaussian elimination. Resonance peaks in the frequency domain allow us to infer the presence of cracks using spectral ratios. Several models of cracked media were analyzed, where effects due to different crack orientations and locations were observed. The results obtained are in good agreement with those published in the references.

Removal of Noise Oscillation Term Appearing in the Nonlinear Equation Solution

Fri, 05 Apr 2013 11:07 EDT

Yasir Khan, Hector Vázquez-Leal, Luis Hernandez-Martínez

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
This paper suggests a novel modified Laplace method for removal of noise oscillation term appearing in the nonlinear equation solutions. The modified method overcomes the noise oscillation during the iteration procedure by suitable choice of an initial solution. Several examples are tested, and the obtained results suggest that this newly developed technique could lead to a promising tool and powerful improvement for many applications in differential and integral equations.

Coupled Coincidence Points in Partially Ordered Cone Metric Spaces with a c -Distance

Fri, 05 Apr 2013 11:07 EDT

Wasfi Shatanawi, Erdal Karapınar, Hassen Aydi

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
Cho et al. (2012) proved some coupled fixed point theorems in partially ordered cone metric spaces by using the concept of a c -distance in cone metric spaces. In this paper, we prove some coincidence point theorems in partially ordered cone metric spaces by using the notion of a c -distance. Our results generalize several well-known comparable results in the literature. Also, we introduce an example to support the usability of our results.

Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model

Fri, 05 Apr 2013 11:07 EDT

Viviane Klein, Malgorzata Peszynska

Source: J. Appl. Math., Volume 2012, 26 pages.

Abstract:
Double-diffusion model is used to simulate slightly compressible fluid flow in periodic porous media as a macro-model in place of the original highly heterogeneous micro-model. In this paper, we formulate an adaptive two-grid numerical finite element discretization of the double-diffusion system and perform a comparison between the micro- and macro-model. Our numerical results show that the micro-model solutions appear to converge to the macro-model linearly with the parameter ε of periodic geometry. For the two-grid discretization, the a priori and a posteriori error estimates are proved, and we show how to adapt the grid for each component independently.

Dynamic Complexity of an Ivlev-Type Prey-Predator System with Impulsive State Feedback Control

Fri, 05 Apr 2013 11:07 EDT

Chuanjun Dai, Min Zhao, Lansun Chen

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
The dynamic complexities of an Ivlev-type prey-predator system with impulsive state feedback control are studied analytically and numerically. Using the analogue of the Poincaré criterion, sufficient conditions for the existence and the stability of semitrivial periodic solutions can be obtained. Furthermore, the bifurcation diagrams and phase diagrams are investigated by means of numerical simulations, which illustrate the feasibility of the main results presented here.

On the Convergence of Continuous-Time Waveform Relaxation Methods for Singular Perturbation Initial Value Problems

Fri, 05 Apr 2013 11:07 EDT

Yongxiang Zhao, Li Li

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
This paper extends the continuous-time waveform relaxation method to singular perturbation initial value problems. The sufficient conditions for convergence of continuous-time waveform relaxation methods for singular perturbation initial value problems are given.

Asymptotic Properties of Derivatives of the Stieltjes Polynomials

Fri, 05 Apr 2013 11:07 EDT

Hee Sun Jung, Ryozi Sakai

Source: J. Appl. Math., Volume 2012, 25 pages.

Abstract:
Let ${w}_{\lambda }(x):={(1-{x}^{2})}^{\lambda -1/2}$ and ${P}_{\lambda ,n}(x)$ be the ultraspherical polynomials with respect to ${w}_{\lambda }(x)$ . Then, we denote the Stieltjes polynomials with respect to ${w}_{\lambda }(x)$ by ${E}_{\lambda ,n+1}(x)$ satisfying ${\int }_{-1}^{1}{w}_{\lambda }(x){P}_{\lambda ,n}(x){E}_{\lambda ,n+1}(x){x}^{m}dx=0$ , $0\le m<n+1$ , ${\int }_{-1}^{1}{w}_{\lambda }(x){P}_{\lambda ,n}(x){E}_{\lambda ,n+1}(x){x}^{m}dx\ne 0$ , $m=n+1$ . In this paper, we investigate asymptotic properties of derivatives of the Stieltjes polynomials ${E}_{\lambda ,n+1}(x)$ and the product ${E}_{\lambda ,n+1}(x){P}_{\lambda ,n}(x)$ . Especially, we estimate the even-order derivative values of ${E}_{\lambda ,n+1}(x)$ and ${E}_{\lambda ,n+1}(x){P}_{\lambda ,n}(x)$ at the zeros of ${E}_{\lambda ,n+1}(x)$ and the product ${E}_{\lambda ,n+1}(x){P}_{\lambda ,n}(x)$ , respectively. Moreover, we estimate asymptotic representations for the odd derivatives values of ${E}_{\lambda ,n+1}(x)$ and ${E}_{\lambda ,n+1}(x){P}_{\lambda ,n}(x)$ at the zeros of ${E}_{\lambda ,n+1}(x)$ and ${E}_{\lambda ,n+1}(x){P}_{\lambda ,n}(x)$ on a closed subset of $(-1,1)$ , respectively. These estimates will play important roles in investigating convergence and divergence of the higher-order Hermite-Fejér interpolation polynomials.

Coupled Fixed Point Theorems for a Pair of Weakly Compatible Maps along with CLRg Property in Fuzzy Metric Spaces

Fri, 05 Apr 2013 11:07 EDT

Manish Jain, Kenan Tas, Sanjay Kumar, Neetu Gupta

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
The aim of this paper is to extend the notions of E.A. property and CLRg property for coupled mappings and use these notions to generalize the recent results of Xin-Qi Hu (2011). The main result is supported by a suitable example.

A Note on Some Generalized Closed Sets in Bitopological Spaces Associated to Digraphs

Fri, 05 Apr 2013 11:07 EDT

K. Kannan

Source: J. Appl. Math., Volume 2012, 5 pages.

Abstract:
Many investigations are undergoing of the relationship between topological spaces and graph theory. The aim of this short communication is to study the nature and properties of some generalized closed sets in the bitopological spaces associated to the digraph. In particular, some relations between generalized closed sets in the bitopological spaces associated to the digraph are characterized.

Least-Squares Parameter Estimation Algorithm for a Class of Input Nonlinear Systems

Fri, 05 Apr 2013 11:07 EDT

Weili Xiong, Wei Fan, Rui Ding

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
This paper studies least-squares parameter estimation algorithms for input nonlinear systems, including the input nonlinear controlled autoregressive (IN-CAR) model and the input nonlinear controlled autoregressive autoregressive moving average (IN-CARARMA) model. The basic idea is to obtain linear-in-parameters models by overparameterizing such nonlinear systems and to use the least-squares algorithm to estimate the unknown parameter vectors. It is proved that the parameter estimates consistently converge to their true values under the persistent excitation condition. A simulation example is provided.

Bacterial Foraging-Tabu Search Metaheuristics for Identification of Nonlinear Friction Model

Fri, 05 Apr 2013 11:07 EDT

Nuapett Sarasiri, Kittiwong Suthamno, Sarawut Sujitjorn

Source: J. Appl. Math., Volume 2012, 23 pages.

Abstract:
This paper proposes new metaheuristic algorithms for an identification problem of nonlinear friction model. The proposed cooperative algorithms are formed from the bacterial foraging optimization (BFO) algorithm and the tabu search (TS). The paper reports the search comparison studies of the BFO, the TS, the genetic algorithm (GA), and the proposed metaheuristics. Search performances are assessed by using surface optimization problems. The proposed algorithms show superiority among them. A real-world identification problem of the Stribeck friction model parameters is presented. Experimental setup and results are elaborated.

Interval Oscillation Criteria for Super-Half-Linear Impulsive Differential Equations with Delay

Fri, 05 Apr 2013 11:07 EDT

Zhonghai Guo, Xiaoliang Zhou, Wu-Sheng Wang

Source: J. Appl. Math., Volume 2012, 22 pages.

Abstract:
We study the following second-order super-half-linear impulsive differential equations with delay $[r(t){\phi }_{\gamma }(x\prime (t))]\prime +p(t){\phi }_{\gamma }(x(t-\sigma ))+q(t)f(x(t-\sigma ))=e(t)$ , $t\ne {\tau }_{k}$ , $x({t}^{+})={a}_{k}x(t),x\prime ({t}^{+})={b}_{k}x\prime (t)$ , $t={\tau }_{k}$ , where $t\ge {t}_{0}\in \mathbb{R}$ , ${\phi }_{*}(u)=|u{|}^{*-1}u$ , $\sigma $ is a nonnegative constant, $\{{\tau }_{k}\}$ denotes the impulsive moments sequence with ${\tau }_{1}<{\tau }_{2}<\cdots <{\tau }_{k}<\cdots $ , ${\mathrm{lim} }_{k\to \infty }{\tau }_{k}=\infty $ , and ${\tau }_{k+1}-{\tau }_{k}>\sigma $ . By some classical inequalities, Riccati transformation, and two classes of functions, we give several interval oscillation criteria which generalize and improve some known results. Moreover, we also give two examples to illustrate the effectiveness and nonemptiness of our results.

A Generalization of Itô's Formula and the Stability of Stochastic Volterra Integral Equations

Fri, 05 Apr 2013 11:07 EDT

Wenxue Li, Meng Liu, Ke Wang

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
It is well known that Itô’s formula is an essential tool in stochastic analysis. But it cannot be used for general stochastic Volterra integral equations (SVIEs). In this paper, we first introduce the concept of quasi-Itô process which is a generalization of well-known Itô process. And then we extend Itô’s formula to a more general form applicable to some kinds of SVIEs. Furthermore, the stability in probability for some SVIEs is analyzed by the generalized Itô’s formula. Our work shows that the generalized Itô’s formula is powerful and flexible to use in many relevant fields.

The Dual of Generalized Fuzzy Subspaces

Fri, 05 Apr 2013 11:07 EDT

Wenjuan Chen, Yanyong Guan

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
We define the dual of generalized fuzzy subspaces first. These concepts generalize the dual of fuzzy subspaces. And then we investigate the double dual of generalized fuzzy subspaces.

Extinction and Permanence of a General Predator-Prey System with Impulsive Perturbations

Fri, 05 Apr 2013 11:07 EDT

Xianning Liu, Lansun Chen

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
A general predator-prey system is studied in a scheme where there is periodic impulsive perturbations. This scheme has the potential to protect the predator from extinction but under some conditions may also serve to lead to extinction of the prey. Conditions for extinction and permanence are obtained via the comparison methods involving monotone theory of impulsive systems and multiple Liapunov functions, which establish explicit bounds on solutions. The existence of a positive periodic solution is also studied by the bifurcation theory. Application is given to a Lotka-Volterra predator-prey system with periodic impulsive immigration of the predator. It is shown that the results are quite different from the corresponding system without impulsive immigration, where extinction of the prey can never be achieved. The prey will be extinct or permanent independent of whether the system without impulsive effect immigration is permanent or not. The model and its results suggest an approach of pest control which proves more effective than the classical one.

Lattices Generated by Orbits of Subspaces under Finite Singular Orthogonal Groups II

Fri, 05 Apr 2013 11:07 EDT

You Gao, XinZhi Fu

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
Let ${\mathrm{𝔽}}_{q}^{(2\nu +\delta +l)}$ be a $(2\nu +\delta +l)$ -dimensional vector space over the finite field ${\mathrm{𝔽}}_{q}$ . In this paper we assume that ${\mathrm{𝔽}}_{q}$ is a finite field of odd characteristic, and ${O}_{2\nu +\delta +l,\mathrm{ }\mathrm{\Delta }}({\mathrm{𝔽}}_{q})$ the singular orthogonal groups of degree $2\nu +\delta +l$ over ${\mathrm{𝔽}}_{q}$ . Let $\mathcal{M}$ be any orbit of subspaces under ${O}_{2\nu +\delta +l,\mathrm{ }\mathrm{\Delta }}({\mathrm{𝔽}}_{q})$ . Denote by $\mathcal{L}$ the set of subspaces which are intersections of subspaces in $\mathcal{M}$ , where we make the convention that the intersection of an empty set of subspaces of ${\mathrm{𝔽}}_{q}^{(2\nu +\delta +l)}$ is assumed to be ${\mathrm{𝔽}}_{q}^{(2\nu +\delta +l)}$ . By ordering $\mathcal{L}$ by ordinary or reverse inclusion, two lattices are obtained. This paper studies the questions when these lattices $ℒ$ are geometric lattices.

Robust Control for Uncertain Switched Systems with Interval Nondifferentiable Time-Varying Delays

Fri, 05 Apr 2013 11:07 EDT

T. La-inchua, P. Niamsup

Source: J. Appl. Math., Volume 2012, 24 pages.

Abstract:
This paper addresses the conditions for robust stabilization of a class of uncertain switched systems with delay. The system to be considered is autonomous and the state delay is time-varying. Using Lyapunov functional approach, restriction on the derivative of time-delay function is not required to design switching rule for the robust stabilization of switched systems with time-varying delays. The delay-dependent stability conditions are presented in terms of the solution of LMIs which can be solved by various available algorithms. A numerical example is given to illustrate the effectiveness of theoretical results.

A Note on Practical Stability of Nonlinear Vibration Systems with Impulsive Effects

Fri, 05 Apr 2013 11:07 EDT

Qishui Zhong, Hongcai Li, Hui Liu, Juebang Yu

Source: J. Appl. Math., Volume 2012, 7 pages.

Abstract:
This paper addresses the issue of vibration characteristics of nonlinear systems with impulsive effects. By utilizing a T-S fuzzy model to represent a nonlinear system, a general strict practical stability criterion is derived for nonlinear impulsive systems.

On the Bankruptcy Situations and the Alexia Value

Fri, 05 Apr 2013 11:07 EDT

S. Z. Alparslan Gök, A. Sarıarslan

Source: J. Appl. Math., Volume 2012, 7 pages.

Abstract:
The main result of this paper is to show that the three ancient bankruptcy situations from the 2000-year-old Babylonian Talmud can be solved by using the average lexicographic value (Alexia) from cooperative game theory.

New Nonlinear Conditions and Inequalities for the Existence of Coincidence Points and Fixed Points

Fri, 05 Apr 2013 11:07 EDT

Wei-Shih Du, Shao-Xuan Zheng

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
Some new fixed point theorems for nonlinear maps are established. By using these results, we can obtain some new coincidence point theorems. Our results are quite different in the literature and references therein.

The Improved $(G’/G)$ -Expansion Method for the (2+1)-Dimensional Modified Zakharov-Kuznetsov Equation

Fri, 05 Apr 2013 11:07 EDT

Hasibun Naher, Farah Aini Abdullah

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
we apply the improved $({G}^{\prime }/G)$ -expansion method for constructing abundant new exact traveling wave solutions of the (2+1)-dimensional Modified Zakharov-Kuznetsov equation. In addition, ${G}^{″}+\lambda {G}^{\prime }+\mu G=0$ together with $b(\alpha )={\sum }_{q=-w}^{w}{p}_{q}{({G}^{\prime }/G)}^{q}$ is employed in this method, where ${p}_{q}(q=0,±1,±2,\dots ,±$ $w)$ , $\lambda $ and $\mu $ are constants. Moreover, the obtained solutions including solitons and periodic solutions are described by three different families. Also, it is noteworthy to mention out that, some of our solutions are coincided with already published results, if parameters taken particular values. Furthermore, the graphical presentations are demonstrated for some of newly obtained solutions.

The Hypergroupoid Semigroups as Generalizations of the Groupoid Semigroups

Fri, 05 Apr 2013 11:07 EDT

Jeong Soon Han, Hee Sik Kim, J. Neggers

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
We introduce the notion of hypergroupoids $(H\text{Bin}(X),\square )$ , and show that $(H\text{Bin}(X),\square )$ is a super-semigroup of the semigroup $(\text{Bin}(X),\square )$ via the identification $x↔\{x\}$ . We prove that $(H\text{Bi}{\text{n}}^{*}(X),\ominus ,[\varnothing ])$ is a $BCK$ -algebra, and obtain several properties of $(H\text{Bi}{\text{n}}^{*}(X),\square )$ .

A Finite Element Study of Double Diffusive Mixed Convection in a Concentration Stratified Darcian Fluid Saturated Porous Enclosure under Injection/Suction Effect

Fri, 05 Apr 2013 11:07 EDT

B. V. Rathish Kumar, S. V. S. S. N. V. G. Krishna Murthy

Source: J. Appl. Math., Volume 2012, 29 pages.

Abstract:
Numerical investigation of mixed convection flow in a concentration-stratified fluid-saturated vertical square porous enclosure is investigated by Galerkin finiteelement method. The forced flow conditions are imposed by providing an inlet at the bottom wall and an outlet with a suction on the top wall. The free convection is induced byintroducing a hot but isothermal temperature on the left vertical wall together with Boussinesq approximation on density. Numerical results are presented by tracing the cumulativeheat and mass fluxes, streamline and isotherms of the fluid for a wide range of governing parameters such as suction/injection velocity “ $a$ ”, suction/injection width ( $D/H$ ), massstratification parameters ( ${S}_{C}$ ), Rayleigh number “Ra”, buoyancy ratio “ $B$ ”, and Lewis number “Le”.

Surface and Internal Waves due to a Moving Load on a Very Large Floating Structure

Fri, 05 Apr 2013 11:07 EDT

Taro Kakinuma, Kei Yamashita, Keisuke Nakayama

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
Interaction of surface/internal water waves with a floating platform is discussed with nonlinearity of fluid motion and flexibility of oscillating structure. The set of governing equations based on a variational principle is applied to a one- or two-layer fluid interacting with a horizontally very large and elastic thin plate floating on the water surface. Calculation results of surface displacements are compared with the existing experimental data, where a tsunami, in terms of a solitary wave, propagates across one-layer water with a floating thin plate. We also simulate surface and internal waves due to a point load, such as an airplane, moving on a very large floating structure in shallow water. The wave height of the surface or internal mode is amplified when the velocity of moving point load is equal to the surface- or internal-mode celerity, respectively.

Solving Flexible Job-Shop Scheduling Problem Using Gravitational Search Algorithm and Colored Petri Net

Fri, 05 Apr 2013 11:07 EDT

Behnam Barzegar, Homayun Motameni, Hossein Bozorgi

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
Scheduled production system leads to avoiding stock accumulations, losses reduction, decreasing or even eliminating idol machines, and effort to better benefitting from machines for on time responding customer orders and supplying requested materials in suitable time. In flexible job-shop scheduling production systems, we could reduce time and costs by transferring and delivering operations on existing machines, that is, among NP-hard problems. The scheduling objective minimizes the maximal completion time of all the operations, which is denoted by Makespan. Different methods and algorithms have been presented for solving this problem. Having a reasonable scheduled production system has significant influence on improving effectiveness and attaining to organization goals. In this paper, new algorithm were proposed for flexible job-shop scheduling problem systems (FJSSP-GSPN) that is based on gravitational search algorithm (GSA). In the proposed method, the flexible job-shop scheduling problem systems was modeled by color Petri net and CPN tool and then a scheduled job was programmed by GSA algorithm. The experimental results showed that the proposed method has reasonable performance in comparison with other algorithms.

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

Fri, 05 Apr 2013 11:07 EDT

Nasser-Eddine Tatar

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
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.

Further Research on the M/G/1 Retrial Queueing Model with Server Breakdowns

Fri, 05 Apr 2013 11:07 EDT

Ehmet Kasim, Geni Gupur

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
We study spectral properties of the operator which corresponds to the M/G/1 retrial queueing model with server breakdowns and obtain that all points on the imaginary axis except zero belong to the resolvent set of the operator and 0 is not an eigenvalue of the operator. Our results show that the time-dependent solution of the model is probably strongly asymptotically stable.

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

Fri, 05 Apr 2013 11:07 EDT

Pin-Lin Liu

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
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.

Fixed Point Theorem for Cyclic Chatterjea Type Contractions

Fri, 05 Apr 2013 11:07 EDT

Erdal Karapınar, Hemant Kumar Nashine

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

Feng Yin, Guang-Xin Huang

Source: J. Appl. Math., Volume 2012, 28 pages.

Abstract:
An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations $(AXB-CYD,EXF-GYH)=(M,N)$ , which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matrices $X$ and $Y$ . When the matrix equations are consistent, for any initial generalized reflexive matrix pair $[{X}_{1},{Y}_{1}]$ , the generalized reflexive solutions can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors, and the least Frobenius norm generalized reflexive solutions can be obtained by choosing a special kind of initial matrix pair. The unique optimal approximation generalized reflexive solution pair $[\stackrel{̂}{X},\stackrel{̂}{Y}]$ to a given matrix pair $[{X}_{0},{Y}_{0}]$ in Frobenius norm can be derived by finding the least-norm generalized reflexive solution pair $[{\stackrel{̃}{X}}^{*},{\stackrel{̃}{Y}}^{*}]$ of a new corresponding generalized coupled Sylvester matrix equation pair $(A\stackrel{̃}{X}B-C\stackrel{̃}{Y}D,E\stackrel{̃}{X}F-G\stackrel{̃}{Y}H)=(\stackrel{̃}{M},\stackrel{̃}{N})$ , where $\stackrel{̃}{M}=M-A{X}_{0}B+C{Y}_{0}D,\stackrel{̃}{N}=N-E{X}_{0}F+G{Y}_{0}H$ . Several numerical examples are given to show the effectiveness of the presented iterative algorithm.

Cluster Anti-Synchronization of Complex Networks with Nonidentical Dynamical Nodes

Fri, 05 Apr 2013 11:07 EDT

Shuguo Wang, Chunyuan He, Hongxing Yao

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

Kanit Mukdasai

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
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.

Fixed Point and Asymptotic Analysis of Cellular Neural Networks

Fri, 05 Apr 2013 11:07 EDT

Xianghong Lai, Yutian Zhang

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
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.

Strong Convergence Theorems for a Countable Family of Total Quasi- $\mathbf{\varphi }$ -Asymptotically Nonexpansive Nonself Mappings

Fri, 05 Apr 2013 11:07 EDT

Liang-cai Zhao, Shih-sen Chang

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

M. Zarebnia, M. Birjandi

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
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.

Calculation of the Reproducing Kernel on the Reproducing Kernel Space with Weighted Integral

Fri, 05 Apr 2013 11:07 EDT

Er Gao, Songhe Song, Xinjian Zhang

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

I-Chung Liu, Ahmed M. Megahed

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
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.

A Granular Reduction Algorithm Based on Covering Rough Sets

Fri, 05 Apr 2013 11:07 EDT

Tian Yang, Zhaowen Li, Xiaoqing Yang

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
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.

A Family of Iterative Methods with Accelerated Eighth-Order Convergence

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 24 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

Amar Debbouche, Dumitru Baleanu

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
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.

A Remark on Myhill-Nerode Theorem for Fuzzy Languages

Fri, 05 Apr 2013 11:07 EDT

Shou-feng Wang

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
Regular fuzzy languages are characterized by some algebraic approaches. In particular, an extended version of Myhill-Nerode theorem for fuzzy languages is obtained.

Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems

Fri, 05 Apr 2013 11:07 EDT

Hong Shi, Guangming Xie

Source: J. Appl. Math., Volume 2012, 24 pages.

Abstract:
Impulsive differential systems are an important class of mathematical models for many practical systems in physics, chemistry, biology, engineering, and information science that exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. This paper studies the controllability and observability of linear piecewise constant impulsive systems. Necessary and sufficient criteria for reachability and controllability are established, respectively. It is proved that the reachability is equivalent to the controllability under some mild conditions. Then, necessary and sufficient criteria for observability and determinability of such systems are established, respectively. It is also proved that the observability is equivalent to the determinability under some mild conditions. Our criteria are of the geometric type, and they can be transformed into algebraic type conveniently. Finally, a numerical example is given to illustrate the utility of our criteria.

Traveling Wave Solutions of the Nonlinear $(3+1)$ -Dimensional Kadomtsev-Petviashvili Equation Using the Two Variables $({G}^{\prime }/G,1/G)$ -Expansion Method

Fri, 05 Apr 2013 11:07 EDT

E. M. E. Zayed, S. A. Hoda Ibrahim, M. A. M. Abdelaziz

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
The two variables $({G}^{\prime }/G,1/G)$ -expansion method is proposed in this paper to construct new exact traveling wave solutions with parameters of the nonlinear $(3+1)$ -dimensional Kadomtsev-Petviashvili equation. This method can be considered as an extension of the basic $({G}^{\prime }/G)$ -expansion method obtained recently by Wang et al. When the parameters are replaced by special values, the well-known solitary wave solutions and the trigonometric periodic solutions of this equation were rediscovered from the traveling waves.

Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation

Fri, 05 Apr 2013 11:07 EDT

Dang Quang A., Nguyen Van Thien

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
Solving boundary value problems (BVPs) for the fourth-order differential equations by the reduction of them to BVPs for the second-order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by ourselves in recent works, we construct iterative method for the second BVP for biharmonic-type equation, which describes the deflection of a plate resting on a biparametric elastic foundation. The convergence rate of the method is established. The optimal value of the iterative parameter is found. Several numerical examples confirm the efficiency of the proposed method.

Quasilinearization of the Initial Value Problem for Difference Equations with “Maxima”

Fri, 05 Apr 2013 11:07 EDT

S. Hristova, A. Golev, K. Stefanova

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
The object of investigation of the paper is a special type of difference equations containing the maximum value of the unknown function over a past time interval. These equations are adequate models of real processes which present state depends significantly on their maximal value over a past time interval. An algorithm based on the quasilinearization method is suggested to solve approximately the initial value problem for the given difference equation. Every successive approximation of the unknown solution is the unique solution of an appropriately constructed initial value problem for a linear difference equation with “maxima,” and a formula for its explicit form is given. Also, each approximation is a lower/upper solution of the given mixed problem. It is proved the quadratic convergence of the successive approximations. The suggested algorithm is realized as a computer program, and it is applied to an example, illustrating the advantages of the suggested scheme.

Intuitionistic Fuzzy Normalized Weighted Bonferroni Mean and Its Application in Multicriteria Decision Making

Fri, 05 Apr 2013 11:07 EDT

Wei Zhou, Jian-min He

Source: J. Appl. Math., Volume 2012, 22 pages.

Abstract:
The Bonferroni mean (BM) was introduced by Bonferroni six decades ago but has been a hot research topic recently since its usefulness of the aggregation techniques. The desirable characteristic of the BM is its capability to capture the interrelationship between input arguments. However, the classical BM and GBM ignore the weight vector of aggregated arguments, the general weighted BM (WBM) has not the reducibility, and the revised generalized weighted BM (GWBM) cannot reflect the interrelationship between the individual criterion and other criteria. To deal with these issues, in this paper, we propose the normalized weighted Bonferroni mean (NWBM) and the generalized normalized weighted Bonferroni mean (GNWBM) and study their desirable properties, such as reducibility, idempotency, monotonicity, and boundedness. Furthermore, we investigate the NWBM and GNWBM operators under the intuitionistic fuzzy environment which is more common phenomenon in modern life and develop two new intuitionistic fuzzy aggregation operators based on the NWBM and GNWBM, that is, the intuitionistic fuzzy normalized weighted Bonferroni mean (IFNWBM) and the generalized intuitionistic fuzzy normalized weighted Bonferroni mean (GIFNWBM). Finally, based on the GIFNWBM, we propose an approach to multicriteria decision making under the intuitionistic fuzzy environment, and a practical example is provided to illustrate our results.

Simulation of Magnetorheological Fluids Based on Lattice Boltzmann Method with Double Meshes

Fri, 05 Apr 2013 11:07 EDT

Xinhua Liu, Hao Liu, Yongzhi Liu

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
In order to study the rheological characteristics of magnetorheological fluids, a novel approach based on the two-component Lattice Boltzmann method with double meshes was proposed, and the micro-scale structures of magnetorheological fluids in different strength magnetic fields were simulated. The framework composed of three steps for the simulation of magnetorheological fluids was addressed, and the double meshes method was elaborated. Moreover, the various internal and external forces acting on the magnetic particles were analyzed and calculated. The two-component Lattice Boltzmann model was set up, and the flowchart for the simulation of magnetorheological fluids based on the two-component Lattice Boltzmann method with double meshes was designed. Finally, a physics experiment was carried out, and the simulation examples were provided. The comparison results indicated that the proposed approach was feasible, efficient, and outperforming others.

Extended Mapping Method and Its Applications to Nonlinear Evolution Equations

Fri, 05 Apr 2013 11:07 EDT

J. F. Alzaidy

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
We use extended mapping method and auxiliary equation method for finding new periodic wave solutions of nonlinear evolution equations in mathematical physics, and we obtain some new periodic wave solution for the Boussinesq system and the coupled KdV equations. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.

Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization Problem

Fri, 05 Apr 2013 11:07 EDT

Zhe Chen

Source: J. Appl. Math., Volume 2012, 7 pages.

Abstract:
We characterize the asymptotic cone of the solution set of a convex composite optimization problem. We then apply the obtained results to study the necessary and sufficient conditions for the nonemptiness and compactness of the solution set of the problem. Our results generalize and improve some known results in literature.

An Interior Point Method for Solving Semidefinite Programs Using Cutting Planes and Weighted Analytic Centers

Fri, 05 Apr 2013 11:07 EDT

John Machacek, Shafiu Jibrin

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton’s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed.

Some Properties of the $(p,q)$ -Fibonacci and $(p,q)$ -Lucas Polynomials

Fri, 05 Apr 2013 11:07 EDT

GwangYeon Lee, Mustafa Asci

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
Riordan arrays are useful for solving the combinatorial sums by the help of generating functions. Many theorems can be easily proved by Riordan arrays. In this paper we consider the Pascal matrix and define a new generalization of Fibonacci polynomials called $(p,q)$ -Fibonacci polynomials. We obtain combinatorial identities and by using Riordan method we get factorizations of Pascal matrix involving $(p,q)$ -Fibonacci polynomials.

Refractured Well Selection for Multicriteria Group Decision Making by Integrating Fuzzy AHP with Fuzzy TOPSIS Based on Interval-Typed Fuzzy Numbers

Fri, 05 Apr 2013 11:07 EDT

Tiejun Li, Jianhua Jin, Chunquan Li

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
Multicriteria group decision making (MCGDM) research has rapidly been developed and become a hot topic for solving complex decision problems. Because of incomplete or non-obtainable information, the refractured well-selection problem often exists in complex and vague conditions that the relative importance of the criteria and the impacts of the alternatives on these criteria are difficult to determine precisely. This paper presents a new model for MCGDM by integrating fuzzy analytic hierarchy process (AHP) with fuzzy TOPSIS based on interval-typed fuzzy numbers, to help group decision makers for well-selection during refracturing treatment. The fuzzy AHP is used to analyze the structure of the selection problem and to determine weights of the criteria with triangular fuzzy numbers, and fuzzy TOPSIS with interval-typed triangular fuzzy numbers is proposed to determine final ranking for all the alternatives. Furthermore, the algorithm allows finding the best alternatives. The feasibility of the proposed methodology is also demonstrated by the application of refractured well-selection problem and the method will provide a more effective decision-making tool for MCGDM problems.

Normal Criterion Concerning Shared Values

Fri, 05 Apr 2013 11:07 EDT

Wei Chen, Yingying Zhang, Jiwen Zeng, Honggen Tian

Source: J. Appl. Math., Volume 2012, 7 pages.

Abstract:
We study normal criterion of meromorphic functions shared values, we obtain the following. Let $F$ be a family of meromorphic functions in a domain $D$ , such that function $f\in F$ has zeros of multiplicity at least 2, there exists nonzero complex numbers ${b}_{f},{c}_{f}$ depending on $f$ satisfying $(\text{i}) {b}_{f}/{c}_{f}$ is a constant; $(\text{i}\text{i})\mathrm{min} \{\sigma (0,{b}_{f}),\sigma (0,{c}_{f}),\sigma ({b}_{f},{c}_{f})\ge m\}$ for some $m>0$ ; $(\text{i}\text{i}\text{i}) (1/{c}_{f}^{k-1})({f}^{\prime }{)}^{k}(z)+f(z)\ne {b}_{f}^{k}/{c}_{f}^{k-1}$ or $(1/{c}_{f}^{k-1})({f}^{\prime }{)}^{k}(z)+f(z)={b}_{f}^{k}/{c}_{f}^{k-1}⇒f(z)={b}_{f}$ , then $F$ is normal. These results improve some earlier previous results.

Bernstein-Polynomials-Based Highly Accurate Methods for One-Dimensional Interface Problems

Fri, 05 Apr 2013 11:07 EDT

Jiankang Liu, Zhoushun Zheng, Qinwu Xu

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
A new numerical method based on Bernstein polynomials expansion is proposed for solving one-dimensional elliptic interface problems. Both Galerkin formulation and collocation formulation are constructed to determine the expansion coefficients. In Galerkin formulation, the flux jump condition can be imposed by the weak formulation naturally. In collocation formulation, the results obtained by B-polynomials expansion are compared with that obtained by Lagrange basis expansion. Numerical experiments show that B-polynomials expansion is superior to Lagrange expansion in both condition number and accuracy. Both methods can yield high accuracy even with small value of N .

Coderivations of Ranked Bigroupoids

Fri, 05 Apr 2013 11:07 EDT

Young Bae Jun, Kyoung Ja Lee, Chul Hwan Park

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
The notion of (co)derivations of ranked bigroupoids is discussed by Alshehri et al. (in press), and their generalized version is studied by Jun et al. (under review press). In particular, Jun et al. (under review press) studied coderivations of ranked bigroupoids. In this paper, the generalization of coderivations of ranked bigroupoids is discussed. The notion of generalized coderivations in ranked bigroupoids is introduced, and new generalized coderivations of ranked bigroupoids are obtained by combining a generalized self-coderivation with a rankomorphism. From the notion of ( $X,\ast ,&$ )-derivation, the existence of a rankomorphism of ranked bigroupoids is established.

Analysis of a System for Linear Fractional Differential Equations

Fri, 05 Apr 2013 11:07 EDT

Fang Wang, Zhen-hai Liu, Ping Wang

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
The main purpose of this paper is to obtain the unique solution of the constant coefficient homogeneous linear fractional differential equations ${D}_{{t}_{0}}^{q}X(t)=PX(t),X(a)=B$ and the constant coefficient nonhomogeneous linear fractional differential equations ${D}_{{t}_{0}}^{q}X(t)=PX(t)+D,X(a)=B$ if $P$ is a diagonal matrix and $X(t)\in {C}_{1-q}[{t}_{0},T]×{C}_{1-q}[{t}_{0},T]×\cdots ×{C}_{1-q}[{t}_{0},T]$ and prove the existence and uniqueness of these two kinds of equations for any $P\in L({R}^{m})$ and $X(t)\in {C}_{1-q}[{t}_{0},T]×{C}_{1-q}[{t}_{0},T]×\cdots ×{C}_{1-q}[{t}_{0},T]$ . Then we give two examples to demonstrate the main results.

The Sum and Difference of Two Lognormal Random Variables

Fri, 05 Apr 2013 11:07 EDT

C. F. Lo

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
We have presented a new unified approach to model the dynamics of both the sum and difference of two correlated lognormal stochastic variables. By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. In terms of the approximate probability distributions, we have also obtained an analytical series expansion of the exact solutions, which can allow us to improve the approximation in a systematic manner. Moreover, we believe that this new approach can be extended to study both (1) the algebraic sum of N lognormals, and (2) the sum and difference of other correlated stochastic processes, for example, two correlated CEV processes, two correlated CIR processes, and two correlated lognormal processes with mean-reversion.

Robust Adaptive Finite-Time Synchronization of Two Different Chaotic Systems with Parameter Uncertainties

Fri, 05 Apr 2013 11:07 EDT

Yun-An Hu, Hai-Yan Li, Chun-Ping Zhang, Liang Liu

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
This paper is concerned with the finite-time synchronization problem for two different chaotic systems with parameter uncertainties. Using finite-time control approach and robust control method, an adaptive synchronization scheme is proposed to make the synchronization errors of the systems with parameter uncertainties zero in a finite time. On the basis of Lyapunov stability theory, appropriate adaptive laws are derived to deal with the unknown parameters of the systems. And the convergence of the parameter errors is guaranteed in a finite time. The proposed method can be applied to a variety of chaos systems. Numerical simulations are given to demonstrate the efficiency of the proposed control scheme.

Two Weighted Fuzzy Goal Programming Methods to Solve Multiobjective Goal Programming Problem

Fri, 05 Apr 2013 11:07 EDT

Mousumi Gupta, Debasish Bhattacharjee

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
We propose two new methods to find the solution of fuzzy goal programming (FGP) problem by weighting method. Here, the relative weights represent the relative importance of the objective functions. The proposed methods involve one additional goal constraint by introducing only underdeviation variables to the fuzzy operator λ (resp., 1- λ ), which is more efficient than some well-known existing methods such as those proposed by Zimmermann, Hannan, Tiwari, and Mohamed. Mohamed proposed that every fuzzy linear program has an equivalent weighted linear goal program where the weights are restricted as the reciprocals of the admissible violation constants. But the above proposition of Mohamed is not always true. Furthermore, the proposed methods are easy to apply in real-life situations which give better solution in the sense that the objective values are sufficiently closer to their aspiration levels. Finally, for illustration, two real examples are used to demonstrate the correctness and usefulness of the proposed methods.

Homotopy Analysis Method for the Rayleigh Equation Governing the Radial Dynamics of a Multielectron Bubble

Fri, 05 Apr 2013 11:07 EDT

F. A. Godínez, M. A. Escobedo, M. Navarrete

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
The homotopy analysis method is used to obtain analytical solutions of the Rayleigh equation for the radial oscillations of a multielectron bubble in liquid helium. The small order approximations for amplitude and frequency fit well with those computed numerically. The results confirm that the homotopy analysis method is a powerful and manageable tool for finding analytical solutions of strongly nonlinear dynamical systems.

Some New Common Fixed Point Theorems under Strict Contractive Conditions in G -Metric Spaces

Fri, 05 Apr 2013 11:07 EDT

Zead Mustafa

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
We introduce some new types of pairs of mappings $(f,g)$ on G -metric space called G -weakly commuting of type ( ${A}_{f}$ ) and G - R -weakly commuting of type ( ${A}_{f}$ ). We obtain also several common fixed point results for these mappings under certain contractive condition in G -metric space. Also some examples illustrated to support our results, and comparison between different types of pairs of mappings are studied.

On the One-Leg Methods for Solving Nonlinear Neutral Differential Equations with Variable Delay

Fri, 05 Apr 2013 11:07 EDT

Wansheng Wang, Shoufu Li

Source: J. Appl. Math., Volume 2012, 27 pages.

Abstract:
Based on A -stable one-leg methods and linear interpolations, we introduce four algorithms for solving neutral differential equations with variable delay. A natural question is which algorithm is better. To answer this question, we analyse the error behavior of the four algorithms and obtain their error bounds under a one-sided Lipschitz condition and some classical Lipschitz conditions. After extensively numerically experimenting, we give a positive conclusion.

Analysis of Edge Detection in Bar Code Symbols: An Overview and Open Problems

Fri, 05 Apr 2013 11:07 EDT

Saša Krešić-Jurić

Source: J. Appl. Math., Volume 2012, 31 pages.

Abstract:
Accurate edge localization is essential in bar code decoding. Since speckle noise is the most dominant form of noise in laser bar code scanners, it is important to fully understand its effects on edge detection. Starting with the basic statistical properties of speckle patterns, we present stochastic analysis of speckle noise. We derive the autocorrelation function and power spectral density (PSD) of the noise in terms of intensity distribution of the scanning beam. We then study the signal-to-noise ratio for signals that result from scanning different configurations of edges. Next, we consider statistical properties of edge localization error caused by speckle noise. We show that the standard deviation of the error is determined by the PSD of the noise and relative positions of edges in a bar code symbol. Based on the analysis presented here, we propose new criteria for system design.

Numerical Studies for Fractional-Order Logistic Differential Equation with Two Different Delays

Fri, 05 Apr 2013 11:07 EDT

N. H. Sweilam, M. M. Khader, A. M. S. Mahdy

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
A numerical method for solving the fractional-order logistic differential equation with two different delays (FOLE) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based upon Chebyshev approximations. The properties of Chebyshev polynomials are utilized to reduce FOLE to a system of algebraic equations. Special attention is given to study the convergence and the error estimate of the presented method. Numerical illustrations are presented to demonstrate utility of the proposed method. Chaotic behavior is observed and the smallest fractional order for the chaotic behavior is obtained. Also, FOLE is studied using variational iteration method (VIM) and the fractional complex transform is introduced to convert fractional Logistic equation to its differential partner, so that its variational iteration algorithm can be simply constructed. Numerical experiment is presented to illustrate the validity and the great potential of both proposed techniques.

Rational Homotopy Perturbation Method

Fri, 05 Apr 2013 11:07 EDT

Héctor Vázquez-Leal

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
The solution methods of nonlinear differential equations are very important because most of the physical phenomena are modelled by using such kind of equations. Therefore, this work presents a rational version of homotopy perturbation method (RHPM) as a novel tool with high potential to find approximate solutions for nonlinear differential equations. We present two case studies; for the first example, a comparison between the proposed method and the HPM method is presented; it will show how the RHPM generates highly accurate approximate solutions requiring less iteration, in comparison to results obtained by the HPM method. For the second example, which is a Van der Pol oscillator problem, we compare RHPM, HPM, and VIM, finding out that RHPM method generates the most accurate approximated solution.

Neurogenetic Algorithm for Solving Combinatorial Engineering Problems

Fri, 05 Apr 2013 11:07 EDT

M. Jalali Varnamkhasti, Nasruddin Hassan

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
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.

Eisenstein Series Identities Involving the Borweins' Cubic Theta Functions

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
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.

Coupled Coincidence Point Results for $(\psi ,\alpha ,\beta )$ -Weak Contractions in Partially Ordered Metric Spaces

Fri, 05 Apr 2013 11:07 EDT

A. Razani, V. Parvaneh

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

Quanyong Zhu, Quanxiang Wang, Ju Fu, Zhiyue Zhang

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
We develop a new efficient second-order finite difference scheme fortwo-dimensional problem of contaminant in groundwater flow. Theoretical analysis shows thatthe scheme is second-order convergence in the ${L}^{2}$ norm and is unconditionally stable. Numericalresults demonstrate that the error measures of the second-order scheme are several times smallerthan those of the standard implicit finite difference scheme.

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

Fri, 05 Apr 2013 11:07 EDT

Guangbin Wang, Yanli Du, Fuping Tan

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
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.

Delayed Stochastic Linear-Quadratic Control Problem and Related Applications

Fri, 05 Apr 2013 11:07 EDT

Li Chen, Zhen Wu, Zhiyong Yu

Source: J. Appl. Math., Volume 2012, 22 pages.

Abstract:
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.

An Inverse Problem for a Class of Linear Stochastic Evolution Equations

Fri, 05 Apr 2013 11:07 EDT

Yuhuan Zhao

Source: J. Appl. Math., Volume 2012, 25 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

Gang Zhu, Junjie Wei

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

Longquan Yong, Sanyang Liu, Jianke Zhang, Quanxi Feng

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
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.

Numerical Recovery of Gas Flows in Pipeline Systems

Fri, 05 Apr 2013 11:07 EDT

Vadim E. Seleznev

Source: J. Appl. Math., Volume 2012, 25 pages.

Abstract:
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.

Delay-Dependent Robust Exponential Stability for Uncertain Neutral Stochastic Systems with Interval Time-Varying Delay

Fri, 05 Apr 2013 11:07 EDT

Weihua Mao, Feiqi Deng, Anhua Wan

Source: J. Appl. Math., Volume 2012, 22 pages.

Abstract:
This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities (LMIs). By free-weight matrices method, the usual restriction that the stability conditions only bear slow-varying derivative of the delay is removed. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

Almost Periodic Solutions to Dynamic Equations on Time Scales and Applications

Fri, 05 Apr 2013 11:07 EDT

Yongkun Li, Chao Wang

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
We first introduce the concept of admitting an exponential dichotomy to a class of linear dynamic equations on time scales and study the existence and uniqueness of almost periodic solution and its expression form to this class of linear dynamic equations on time scales. Then, as an application, using these concepts and results, we establish sufficient conditions for the existence and exponential stability of almost periodic solution to a class of Hopfield neural networks with delays. Finally, two examples and numerical simulations given to illustrate our results are plausible and meaningful.

The Core and Nucleolus in a Model of Information Transferal

Fri, 05 Apr 2013 11:07 EDT

Dongshuang Hou, Theo Driessen

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
Galdeano et al. introduced the so-called information market game involving n identical firms acquiring a new technology owned by an innovator. For this specific cooperative game, the nucleolus is determined through a characterization of the symmetrical part of the core. The nonemptiness of the (symmetrical) core is shown to be equivalent to one of each, super additivity, zero-monotonicity, or monotonicity.

Method of Infinite System of Equations for Problems in Unbounded Domains

Fri, 05 Apr 2013 11:07 EDT

Dang Quang A, Tran Dinh Hung

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
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.

On the Blow-Up of Solutions of a Weakly Dissipative Modified Two-Component Periodic Camassa-Holm System

Fri, 05 Apr 2013 11:07 EDT

Yongsheng Mi, Chunlai Mu, Weian Tao

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
We study the Cauchy problem of a weakly dissipative modified two-component periodic Camassa-Holm equation. We first establish the local well-posedness result. Then we derive the precise blow-up scenario and the blow-up rate for strong solutions to the system. Finally, we present two blow-up results for strong solutions to the system.

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

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
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.

Approximation Theorems for Generalized Complex Kantorovich-Type Operators

Fri, 05 Apr 2013 11:07 EDT

N. I. Mahmudov, M. Kara

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
The order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex q -Kantorovich polynomials ( $q>0$ ) attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in $\{z\in ℂ:|z|<R\}$ , $R>q$ , the rate of approximation by the q -Kantorovich operators ( $q>1$ ) is of order ${q}^{-n}$ versus $1/n$ for the classical Kantorovich operators.

Fixed Point Theorems for Various Classes of Cyclic Mappings

Fri, 05 Apr 2013 11:07 EDT

Hassen Aydi, Erdal Karapınar, Bessem Samet

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
We introduce new classes of cyclic mappings and we study the existence and uniqueness of fixed points for such mappings. The presented theorems generalize and improve several existing results in the literature.

On Simple Graphs Arising from Exponential Congruences

Fri, 05 Apr 2013 11:07 EDT

M. Aslam Malik, M. Khalid Mahmood

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
We introduce and investigate a new class of graphs arrived from exponential congruences. For each pair of positive integers $a$ and $b$ , let $G(n)$ denote the graph for which $V=\{0,1,\dots ,n-1\}$ is the set of vertices and there is an edge between $a$ and $b$ if the congruence ${a}^{x}\equiv b (\text{mod\hspace\{0.17em\}}n)$ is solvable. Let $n={p}_{1}^{{k}_{1}}{p}_{2}^{{k}_{2}}\cdots {p}_{r}^{{k}_{r}}$ be the prime power factorization of an integer $n$ , where ${p}_{1}<{p}_{2}<\cdots <{p}_{r}$ are distinct primes. The number of nontrivial self-loops of the graph $G(n)$ has been determined and shown to be equal to ${\prod }_{i=1}^{r}(\varphi ({p}_{i}^{{k}_{i}})+1)$ . It is shown that the graph $G(n)$ has ${2}^{r}$ components. Further, it is proved that the component ${\mathrm{\Gamma }}_{p}$ of the simple graph $G({p}^{2})$ is a tree with root at zero, and if $n$ is a Fermat's prime, then the component ${\mathrm{\Gamma }}_{\varphi (n)}$ of the simple graph $G(n)$ is complete.

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

Fri, 05 Apr 2013 11:07 EDT

Jianjun Sun, Bin Huang, Xiaodong Chen, Lihong Cui

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
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 $3N+1$ filter lengths are established. Examples of framelets with symmetry/antisymmetry and Sobolev exponent are computed by appropriately choosing the parameters in the scheme.

Homoclinic Orbits for a Class of Noncoercive Discrete Hamiltonian Systems

Fri, 05 Apr 2013 11:07 EDT

Long Yuhua

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
A class of first-order noncoercive discrete Hamiltonian systems are considered. Based on a generalized mountain pass theorem, some existence results of homoclinic orbits are obtained when the discrete Hamiltonian system is not periodical and need not satisfy the global Ambrosetti-Rabinowitz condition.

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

Fri, 05 Apr 2013 11:07 EDT

Changjian Wu, Shushuang Hao, Changwei Xu

Source: J. Appl. Math., Volume 2012, 12 pages.

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

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

Fri, 05 Apr 2013 11:07 EDT

Feras M. Al Faqih

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
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.

Generalizations of $\mathrm{𝒩}$ -Subalgebras in BCK/BCI-Algebras Based on Point $\mathrm{𝒩}$ -Structures

Fri, 05 Apr 2013 11:07 EDT

Young Bae Jun, Kyoung Ja Lee, Min Su Kang

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
The aim of this article is to obtain more general forms than the papers of (Jun et al. (2010); Jun et al. (in press)). The notions of $\mathrm{𝒩}$ -subalgebras of types $(\in ,{q}_{k}),(\in ,\in \vee {q}_{k})$ , and $(q,\in \vee {q}_{k})$ are introduced, and the concepts of $\mathrm{ }{q}_{k}$ -support and $\in \vee {q}_{k}$ -support are also introduced. Several related properties are investigated. Characterizations of $\mathrm{𝒩}$ -subalgebra of type $(\in ,\in \vee {q}_{k})$ are discussed, and conditions for an $\mathrm{𝒩}$ -subalgebra of type $(\in ,\in \vee {q}_{k})$ to be an $\mathrm{𝒩}$ -subalgebra of type $(\in ,\in )$ are considered.

Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory

Fri, 05 Apr 2013 11:07 EDT

Jianguo Tang, Kun She, William Zhu

Source: J. Appl. Math., Volume 2012, 27 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

Xiaoyan Deng, Lixin Tian, Wenxia Chen

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
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 ${L}^{2}$ 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.

Asymptotic Stability of a Class of Impulsive Delay Differential Equations

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
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.

Solitonic Solutions for Homogeneous KdV Systems by Homotopy Analysis Method

Fri, 05 Apr 2013 11:07 EDT

Mohammed Ali, Marwan Alquran, Mahmoud Mohammad

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
We study two-component evolutionary systems of a homogeneous KdV equations of second and third order. The homotopy analysis method (HAM) is used for analytical treatment of these systems. The auxiliary parameter h of HAM is freely chosen from the stability region of the h -curve obtained for each proposed system.

Global Stability of a SLIT TB Model with Staged Progression

Fri, 05 Apr 2013 11:07 EDT

Yakui Xue, Xiaohong Wang

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
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 ${R}_{0}$ . Moreover, if ${R}_{0}\le 1$ , the disease-free equilibrium ${P}_{0}$ is globally asymptotically stable and the disease always dies out. If ${R}_{0}>1$ , the unique endemic equilibrium ${P}^{\ast }$ is globally asymptotically stable and the disease persists at the endemic equilibrium.

Further Results on Derivations of Ranked Bigroupoids

Fri, 05 Apr 2013 11:07 EDT

Young Bae Jun, Hee Sik Kim, Eun Hwan Roh

Source: J. Appl. Math., Volume 2012, 9 pages.

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

On the Computation of the Efficient Frontier of the Portfolio Selection Problem

Fri, 05 Apr 2013 11:07 EDT

Clara Calvo, Carlos Ivorra, Vicente Liern

Source: J. Appl. Math., Volume 2012, 25 pages.

Abstract:
An easy-to-use procedure is presented for improving the $\epsilon $ -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.

Positive Solution for a Class of Boundary Value Problems with Finite Delay

Fri, 05 Apr 2013 11:07 EDT

Hongzhou Wang

Source: J. Appl. Math., Volume 2012, 7 pages.

Abstract:
We study a class of boundary value problems with equation of the form ${x}^{″}(t)+f(t,x(t),{x}^{\prime }(t-\tau ))=0$ . Some sufficient conditions for existence of positive solution are obtained by using the Krasnoselskii fixed point theorem in cones.

The Location-Scale Mixture Exponential Power Distribution: A Bayesian and Maximum Likelihood Approach

Fri, 05 Apr 2013 11:07 EDT

Z. Rahnamaei, N. Nematollahi, R. Farnoosh

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
We introduce an alternative skew-slash distribution by using the scale mixture of the exponential power distribution. We derive the properties of this distribution and estimate its parameter by Maximum Likelihood and Bayesian methods. By a simulation study we compute the mentioned estimators and their mean square errors, and we provide an example on real data to demonstrate the modeling strength of the new distribution.

Uniformly Strong Persistence for a Delayed Predator-Prey Model

Fri, 05 Apr 2013 11:07 EDT

Changjin Xu, Yuanfu Shao, Peiluan Li

Source: J. Appl. Math., Volume 2012, 7 pages.

Abstract:
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.

On the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with $n$ Vertices and $m$ Pendent Vertices

Fri, 05 Apr 2013 11:07 EDT

Xinying Pai, Sanyang Liu

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
Let $\mathrm{\Phi }(G,\lambda )=\text{d}\text{e}\text{t}(\lambda {I}_{n}-L(G))={\sum }_{k=0}^{n}(-1{)}^{k}{c}_{k}(G){\lambda }^{n-k}$ be the characteristic polynomial of the Laplacian matrix of a graph $G$ of order $n$ . In this paper, we give four transforms on graphs that decrease all Laplacian coefficients ${c}_{k}(G)$ and investigate a conjecture A. Ilić and M. Ilić (2009) about the Laplacian coefficients of unicyclic graphs with $n$ vertices and $m$ pendent vertices. Finally, we determine the graph with the smallest Laplacian-like energy among all the unicyclic graphs with $n$ vertices and $m$ pendent vertices.

Steady State Solution to Atmospheric Circulation Equations with Humidity Effect

Fri, 05 Apr 2013 11:07 EDT

Hong Luo

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
The steady state solution to atmospheric circulation equations with humidity effect is studied. A sufficient condition of existence of steady state solution to atmospheric circulation equations is obtained, and regularity of steady state solution is verified.

A Best Possible Double Inequality for Power Mean

Fri, 05 Apr 2013 11:07 EDT

Yong-Min Li, Bo-Yong Long, Yu-Ming Chu

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
We answer the question: for any $p,q\in \mathbb{R}$ with $p\ne q$ and $p\ne -q$ , what are the greatest value $\lambda =\lambda (p,q)$ and the least value $\mu =\mu (p,q)$ , such that the double inequality ${M}_{\lambda }(a,b)<\sqrt{{M}_{p}(a,b){M}_{q}(a,b)}<{M}_{\mu }(a,b)$ holds for all $a,b>0$ with $a\ne b$ ? Where ${M}_{p}(a,b)$ is the $p$ th power mean of two positive numbers $a$ and $b$ .

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

Fri, 05 Apr 2013 11:07 EDT

Huang Yong, Shang Yadong, Yuan Wenjun

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

Raid Kamel Naji, Arkan N. Mustafa

Source: J. Appl. Math., Volume 2012, 24 pages.

Abstract:
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.

Robust Stability of Switched Delay Systems with Average Dwell Time under Asynchronous Switching

Fri, 05 Apr 2013 11:07 EDT

Jun Cheng, Hong Zhu, Shouming Zhong, Yuping Zhang

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
The problem of robust stability of switched delay systems with average dwell time under asynchronous switching is investigated. By taking advantage of the average dwell-time method and an integral inequality, two sufficient conditions are developed to guarantee the global exponential stability of the considered switched system. Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed techniques.

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

Fri, 05 Apr 2013 11:07 EDT

Aabed Mohammed, Maslina Darus

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
We define new subclasses of $p$ -valent meromorphic functions with complex order. We prove some properties for certain integral operators onthese subclasses.

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

Fri, 05 Apr 2013 11:07 EDT

Gafurjan Ibragimov, Yusra Salleh

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
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.

Robust Adaptive Generalized Projective Synchronization of Chaotic Systems with Uncertain Disturbances

Fri, 05 Apr 2013 11:07 EDT

Zhen Jia, Guangming Deng

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
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.

Forced ILW-Burgers Equation as a Model for Rossby Solitary Waves Generated by Topography in Finite Depth Fluids

Fri, 05 Apr 2013 11:07 EDT

Hongwei Yang, Baoshu Yin, Yunlong Shi, Qingbiao Wang

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
The paper presents an investigation of the generation, evolution of Rossby solitary waves generated by topography in finite depth fluids. The forced ILW- (Intermediate Long Waves-) Burgers equation as a model governing the amplitude of solitary waves is first derived and shown to reduce to the KdV- (Korteweg-de Vries-) Burgers equation in shallow fluids and BO- (Benjamin-Ono-) Burgers equation in deep fluids. By analysis and calculation, the perturbation solution and some conservation relations of the ILW-Burgers equation are obtained. Finally, with the help of pseudospectral method, the numerical solutions of the forced ILW-Burgers equation are given. The results demonstrate that the detuning parameter $\alpha $ holds important implications for the generation of the solitary waves. By comparing with the solitary waves governed by ILW-Burgers equation and BO-Burgers equation, we can conclude that the solitary waves generated by topography in finite depth fluids are different from that in deep fluids.

Optimal Bounds for Seiffert Mean in terms of One-Parameter Means

Fri, 05 Apr 2013 11:07 EDT

Hua-Nan Hu, Guo-Yan Tu, Yu-Ming Chu

Source: J. Appl. Math., Volume 2012, 7 pages.

Abstract:
The authors present the greatest value ${r}_{1}$ and the least value ${r}_{2}$ such that the double inequality ${J}_{r1}(a\text{,\hspace\{0.17em\}}b)<T(a\text{,\hspace\{0.17em\}}b)<{J}_{r2}(a\text{,\hspace\{0.17em\}}b)$ holds for all $a\text{,\hspace\{0.17em\}}b>0$ with $a\ne b$ , where $T(a\text{,\hspace\{0.17em\}}b)$ and ${J}_{p}(a\text{,\hspace\{0.17em\}}b)$ denote the Seiffert and p th one-parameter means of two positive numbers a and b , respectively.

Fixed Point Theorems via Auxiliary Functions

Fri, 05 Apr 2013 11:07 EDT

Erdal Karapınar, Peyman Salimi

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
We prove new fixed point theorems in the framework of partially ordered metric spaces. The main result is an extension and a generalization of many existing results in the literature. An example is also considered to illustrate the main result.

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

Fri, 05 Apr 2013 11:07 EDT

Yang Yueting, Cao Mingyuan

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
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.

Fuzzy Linguistic Induced Ordered Weighted Averaging Operator and Its Application

Fri, 05 Apr 2013 11:07 EDT

Sidong Xian

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
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.

A Boundary Integral Equation with the Generalized Neumann Kernel for a Certain Class of Mixed Boundary Value Problem

Fri, 05 Apr 2013 11:07 EDT

Mohamed M. S. Nasser, Ali H. M. Murid, Samer A. A. Al-Hatemi

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
We present a uniquely solvable boundary integral equation with the generalized Neumann kernel for solving two-dimensional Laplace’s equation on multiply connected regions with mixed boundary condition. Two numerical examples are presented to verify the accuracy of the proposed method.

A New Calculation for Boolean Derivative Using Cheng Product

Fri, 05 Apr 2013 11:07 EDT

Hao Chen, Jitao Sun

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
The matrix expression and relationships among several definitions of Boolean derivatives are given by using the Cheng product. We introduce several definitions of Boolean derivatives. By using the Cheng product, the matrix expressions of Boolean derivative are given, respectively. Furthermore, the relationships among different definitions are presented. The logical calculation is converted into matrix product. This helps to extend the application of Boolean derivative. At last, an example is given to illustrate the main results.

The Modified Rational Jacobi Elliptic Functions Method for Nonlinear Differential Difference Equations

Fri, 05 Apr 2013 11:07 EDT

Khaled A. Gepreel, Taher A. Nofal, Ali A. Al-Thobaiti

Source: J. Appl. Math., Volume 2012, 30 pages.

Abstract:
We modified the rational Jacobi elliptic functions method to construct some new exact solutions for nonlinear differential difference equations in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, the discrete nonlinear Klein-Gordon equation, and the quintic discrete nonlinear Schrodinger equation. Some new types of the Jacobi elliptic solutions are obtained for some nonlinear differential difference equations in mathematical physics. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.

Rational Biparameter Homotopy Perturbation Method and Laplace-Padé Coupled Version

Fri, 05 Apr 2013 11:07 EDT

Hector Vazquez-Leal, Arturo Sarmiento-Reyes, Yasir Khan, Uriel Filobello-Nino, Alejandro Diaz-Sanchez

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
The fact that most of the physical phenomena are modelled by nonlinear differential equations underlines the importance of having reliable methods for solving them. This work presents the rational biparameter homotopy perturbation method (RBHPM) as a novel tool with the potential to find approximate solutions for nonlinear differential equations. The method generates the solutions in the form of a quotient of two power series of different homotopy parameters. Besides, in order to improve accuracy, we propose the Laplace-Padé rational biparameter homotopy perturbation method (LPRBHPM), when the solution is expressed as the quotient of two truncated power series. The usage of the method is illustrated with two case studies. On one side, a Ricatti nonlinear differential equation is solved and a comparison with the homotopy perturbation method (HPM) is presented. On the other side, a nonforced Van der Pol Oscillator is analysed and we compare results obtained with RBHPM, LPRBHPM, and HPM in order to conclude that the LPRBHPM and RBHPM methods generate the most accurate approximated solutions.

Adaptive Fuzzy Control with Supervisory Compensator for Three-Phase Active Power Filter

Fri, 05 Apr 2013 11:07 EDT

Juntao Fei, Shixi Hou

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
An adaptive fuzzy control system with supervisory controller is proposed to improve dynamic performance of three-phase active power filter (APF). The proposed adaptive fuzzy controller for APF does not build an accurate mathematical model but approximates the nonlinear characteristics of APF using fuzzy approximation. The adaptive law based on the Lyapunov analysis can adaptively adjust the fuzzy rules; therefore the asymptotical stability of the adaptive fuzzy control system can be guaranteed. Simulation results demonstrate that the APF control system has excellent dynamic performance such as small current tracking error, reduced total harmonic distortion (THD) index, strong robustness in the presence of parameters variation, and nonlinear load.

Stability of the Stochastic Reaction-Diffusion Neural Network with Time-Varying Delays and p -Laplacian

Fri, 05 Apr 2013 11:07 EDT

Pan Qingfei, Zhang Zifang, Huang Jingchang

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
The main aim of this paper is to discuss moment exponential stability for a stochastic reaction-diffusion neural network with time-varying delays and p -Laplacian. Using the Itô formula, a delay differential inequality and the characteristics of the neural network, the algebraic conditions for the moment exponential stability of the nonconstant equilibrium solution are derived. An example is also given for illustration.

Iterative Algorithm for Solving a System of Nonlinear Matrix Equations

Fri, 05 Apr 2013 11:07 EDT

Asmaa M. Al-Dubiban

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
We discuss the positive definite solutions for the system of nonlinear matrix equations $X-{A}^{\ast }{Y}^{-n}A=I$ and $Y-{B}^{\ast }{X}^{-m}B=I$ , where $n$ , $m$ are two positive integers. Some properties of solutions are studied, and the necessary and sufficient conditions for the existence of positive definite solutions are given. An iterative algorithm for obtaining positive definite solutions of the system is proposed. Moreover, the error estimations are found. Finally, some numerical examples are given to show the efficiency of the proposed iterative algorithm.

Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay

Fri, 05 Apr 2013 11:07 EDT

Xiaojian Zhou, Xin Chen, Yongzhong Song

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
We investigate the dynamics of a differential-algebraic bioeconomic model with two time delays. Regarding time delay as a bifurcation parameter, we show that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Using the theories of normal form and center manifold, we also give the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical tests are provided to verify our theoretical analysis.

Matroidal Structure of Rough Sets Based on Serial and Transitive Relations

Fri, 05 Apr 2013 11:07 EDT

Yanfang Liu, William Zhu

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
The theory of rough sets is concerned with the lower and upper approximations of objects through a binary relation on a universe. It has been applied to machine learning, knowledge discovery, and data mining. The theory of matroids is a generalization of linear independence in vector spaces. It has been used in combinatorial optimization and algorithm design. In order to take advantages of both rough sets and matroids, in this paper we propose a matroidal structure of rough sets based on a serial and transitive relation on a universe. We define the family of all minimal neighborhoods of a relation on a universe and prove it satisfies the circuit axioms of matroids when the relation is serial and transitive. In order to further study this matroidal structure, we investigate the inverse of this construction: inducing a relation by a matroid. The relationships between the upper approximation operators of rough sets based on relations and the closure operators of matroids in the above two constructions are studied. Moreover, we investigate the connections between the above two constructions.

Numerical Study of Hall Thruster Plume and Sputtering Erosion

Fri, 05 Apr 2013 11:07 EDT

Li Yan, Ping-Yang Wang, Yang-Hua Ou, Xiao-Lu Kang

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
Potential sputtering erosion caused by the interactions between spacecraft and plasma plume of Hall thrusters is a concern for electric propulsion. In this study, calculation model of Hall thruster’s plume and sputtering erosion is presented. The model is based on three dimensional hybrid particle-in-cell and direct simulation Monte Carlo method (PIC/DSMC method) which is integrated with plume-wall sputtering yield model. For low-energy heavy-ion sputtering in Hall thruster plume, the Matsunami formula for the normal incidence sputtering yield and the Yamamura angular dependence of sputtering yield are used. The validation of the simulation model is realized through comparing plume results with the measured data. Then, SPT-70’s sputtering erosion on satellite surfaces is assessed and effect of mass flow rate on sputtering erosion is analyzed.

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

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
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.

Some Aspects of $d$ -Units in $d/$ BCK-Algebras

Fri, 05 Apr 2013 11:07 EDT

Hee Sik Kim, J. Neggers, Keum Sook So

Source: J. Appl. Math., Volume 2012, 10 pages.

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

New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the $(2+1)$ -Dimensional Evolution Equation

Fri, 05 Apr 2013 11:07 EDT

Hasibun Naher, Farah Aini Abdullah

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
The generalized Riccati equation mapping is extended with the basic $({G}^{\prime }/G)$ -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 ${G}^{\prime }(\eta )=w+uG(\eta )+v{G}^{2}(\eta )$ 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.

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

Fri, 05 Apr 2013 11:07 EDT

Minggang Wang, Hua Xu

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
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.

Exponential Admissibility and ${H}_{\infty }$ Control of Switched Singular Time-Delay Systems: An Average Dwell Time Approach

Fri, 05 Apr 2013 11:07 EDT

Jinxing Lin, Zhifeng Gao

Source: J. Appl. Math., Volume 2012, 28 pages.

Abstract:
This paper deals with the problems of exponential admissibility and ${H}_{\infty }$ control for a class of continuous-time switched singular systems with time-varying delay. The ${H}_{\infty }$ 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 ${H}_{\infty }$ 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 aregiven to illustrate the effectiveness of the proposed approach.

Matched Asymptotic Expansions to the Circular Sitnikov Problem with Long Period

Fri, 05 Apr 2013 11:07 EDT

Marco Rosales-Vera

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
The circular Sitnikov problem is revisited, using matched asymptotic expansions. In the case of large oscillation periods, approximate analytical expressions for the period and the orbit of the third body are found. The results are compared with those described in the literature and show that the movement of the third body can be well described by two analytical solutions, the inner and outer solutions.

A Novel Mesh Quality Improvement Method for Boundary Elements

Fri, 05 Apr 2013 11:07 EDT

Hou-lin Liu, Cui Dai, Liang Dong, Ming-gao Tan

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
In order to improve the boundary mesh quality while maintaining the essential characteristics of discrete surfaces, a new approach combining optimization-based smoothing and topology optimization is developed. The smoothing objective function is modified, in which two functions denoting boundary and interior quality, respectively, and a weight coefficient controlling boundary quality are taken into account. In addition, the existing smoothing algorithm can improve the mesh quality only by repositioning vertices of the interior mesh. Without destroying boundary conformity, bad elements with all their vertices on the boundary cannot be eliminated. Then, topology optimization is employed, and those elements are converted into other types of elements whose quality can be improved by smoothing. The practical application shows that the worst elements can be eliminated and, with the increase of weight coefficient, the average quality of boundary mesh can also be improved. Results obtained with the combined approach are compared with some common approach. It is clearly shown that it performs better than the existing approach.

Modeling Electromechanical Overcurrent Relays Using Singular Value Decomposition

Fri, 05 Apr 2013 11:07 EDT

Feng-Jih Wu, Chih-Ju Chou, Ying Lu, Jarm-Long Chung

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
This paper presents a practical and effective novel approach to curve fit electromechanical (EM) overcurrent (OC) relay characteristics. Based on singular value decomposition (SVD), the curves are fitted with equation in state space under modal coordinates. The relationships between transfer function and Markov parameters are adopted in this research to represent the characteristic curves of EM OC relays. This study applies the proposed method to two EM OC relays: the GE IAC51 relay with moderately inverse-time characteristic and the ABB CO-8 relay with inverse-time characteristic. The maximum absolute values of errors of hundreds of sample points taken from four time dial settings (TDS) for each relay between the actual characteristic curves and the corresponding values from the curve-fitting equations are within the range of 10 milliseconds. Finally, this study compares the SVD with the adaptive network and fuzzy inference system (ANFIS) to demonstrate its accuracy and identification robustness.

A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models

Fri, 05 Apr 2013 11:07 EDT

Shengwu Zhou, Wei Li, Yu Wei, Cui Wen

Source: J. Appl. Math., Volume 2012, 20 pages.

Abstract:
A positivity-preserving numerical method for nonlinear Black-Scholes models is developed in this paper. The numerical method is based on a nonstandard approximation of the second partial derivative. The scheme is not only unconditionally stable and positive, but also allows us to solve the discrete equation explicitly. Monotone properties are studied in order to avoid unwanted oscillations of the numerical solution. The numerical results for European put option and European butterfly spread are compared to the standard finite difference scheme. It turns out that the proposed scheme is efficient and reliable.

The Effect of Time Delay on Dynamical Behavior in an Ecoepidemiological Model

Fri, 05 Apr 2013 11:07 EDT

Changjin Xu, Yusen Wu

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
A delayed predator-prey model with disease in the prey is investigated. The conditions for the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are derived. The effect of the two different time delays on the dynamical behavior has been given. Numerical simulations are performed to illustrate the theoretical analysis. Finally, the main conclusions are drawn.

A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods

Fri, 05 Apr 2013 11:07 EDT

Hakima Benlarbi, Ahmed-Salah Chibi

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
A posteriori error estimates for the generalized overlapping domain decomposition method (GODDM) (i.e., with Robin boundary conditions on the interfaces), for second order boundary value problems, are derived. We show that the error estimate in the continuous case depends on the differences of the traces of the subdomain solutions on the interfaces. After discretization of the domain by finite elements we use the techniques of the residual a posteriori error analysis to get an a posteriori error estimate for the discrete solutions on subdomains. The results of some numerical experiments are presented to support the theory.

Password Authentication Based on Fractal Coding Scheme

Fri, 05 Apr 2013 11:07 EDT

Nadia M. G. Al-Saidi, Mohamad Rushdan Md. Said, Wan Ainun M. Othman

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
Password authentication is a mechanism used to authenticate user identity over insecure communication channel. In this paper, a new method to improve the security of password authentication is proposed. It is based on the compression capability of the fractal image coding to provide an authorized user a secure access to registration and login process. In the proposed scheme, a hashed password string is generated and encrypted to be captured together with the user identity using text to image mechanisms. The advantage of fractal image coding is to be used to securely send the compressed image data through a nonsecured communication channel to the server. The verification of client information with the database system is achieved in the server to authenticate the legal user. The encrypted hashed password in the decoded fractal image is recognized using optical character recognition. The authentication process is performed after a successful verification of the client identity by comparing the decrypted hashed password with those which was stored in the database system. The system is analyzed and discussed from the attacker’s viewpoint. A security comparison is performed to show that the proposed scheme provides an essential security requirement, while their efficiency makes it easier to be applied alone or in hybrid with other security methods. Computer simulation and statistical analysis are presented.

Stochastic PDEs and Infinite Horizon Backward Doubly Stochastic Differential Equations

Fri, 05 Apr 2013 11:07 EDT

Bo Zhu, Baoyan Han

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
We give a sufficient condition on the coefficients of a class of infinite horizon BDSDEs, under which the infinite horizon BDSDEs have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations. A probabilistic interpretation for solutions to a class of stochastic partial differential equations is given.

Stability and Bifurcation in a Delayed Holling-Tanner Predator-Prey System with Ratio-Dependent Functional Response

Fri, 05 Apr 2013 11:07 EDT

Juan Liu, Zizhen Zhang, Ming Fu

Source: J. Appl. Math., Volume 2012, 19 pages.

Abstract:
We analyze a delayed Holling-Tanner predator-prey system with ratio-dependent functional response. The local asymptotic stability and the existence of the Hopf bifurcation are investigated. Direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are studied by deriving the equation describing the flow on the center manifold. Finally, numerical simulations are presented for the support of our analytical findings.

Geometric Lattice Structure of Covering-Based Rough Sets through Matroids

Fri, 05 Apr 2013 11:07 EDT

Aiping Huang, William Zhu

Source: J. Appl. Math., Volume 2012, 25 pages.

Abstract:
Covering-based rough set theory is a useful tool to deal with inexact, uncertain, or vague knowledge in information systems. Geometric lattice has been widely used in diverse fields, especially search algorithm design, which plays an important role in covering reductions. In this paper, we construct three geometric lattice structures of covering-based rough sets through matroids and study the relationship among them. First, a geometric lattice structure of covering-based rough sets is established through the transversal matroid induced by a covering. Then its characteristics, such as atoms, modular elements, and modular pairs, are studied. We also construct a one-to-one correspondence between this type of geometric lattices and transversal matroids in the context of covering-based rough sets. Second, we present three sufficient and necessary conditions for two types of covering upper approximation operators to be closure operators of matroids. We also represent two types of matroids through closure axioms and then obtain two geometric lattice structures of covering-based rough sets. Third, we study the relationship among these three geometric lattice structures. Some core concepts such as reducible elements in covering-based rough sets are investigated with geometric lattices. In a word, this work points out an interesting view, namely, geometric lattice, to study covering-based rough sets.

Mixed Convection Flow along a Stretching Cylinder in a Thermally Stratified Medium

Fri, 05 Apr 2013 11:07 EDT

Swati Mukhopadhyay, Anuar Ishak

Source: J. Appl. Math., Volume 2012, 8 pages.

Abstract:
An analysis for the axisymmetric laminar boundary layer mixed convection flow of a viscous and incompressible fluid towards a stretching cylinder immersed in a thermally stratified medium is presented in this paper. Similarity transformation is employed to convert the governing partial differential equations into highly nonlinear ordinary differential equations. Numerical solutions of these equations are obtained by a shooting method. It is found that the heat transfer rate at the surface is lower for flow in a thermally stratified medium compared to that of an unstratified medium. Moreover, both the skin friction coefficient and the heat transfer rate at the surface are larger for a cylinder compared to that for a flat plate.

Type-2 Fuzzy Soft Sets and Their Applications in Decision Making

Fri, 05 Apr 2013 11:07 EDT

Zhiming Zhang, Shouhua Zhang

Source: J. Appl. Math., Volume 2012, 35 pages.

Abstract:
Molodtsov introduced the theory of soft sets, which can be used as a general mathematical tool for dealing with uncertainty. This paper aims to introduce the concept of the type-2 fuzzy soft set by integrating the type-2 fuzzy set theory and the soft set theory. Some operations on the type-2 fuzzy soft sets are given. Furthermore, we investigate the decision making based on type-2 fuzzy soft sets. By means of level soft sets, we propose an adjustable approach to type-2 fuzzy-soft-set based decision making and give some illustrative examples. Moreover, we also introduce the weighted type-2 fuzzy soft set and examine its application to decision making.

The Effects of Control Domain Position on Optimal Control of Cardiac Arrhythmia

Fri, 05 Apr 2013 11:07 EDT

Kin Wei Ng, Ahmad Rohanin

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
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.

Electromagnetic Gyroscopic Motion

Fri, 05 Apr 2013 11:07 EDT

A. I. Ismail, T. S. Amer, S. A. El Banna, M. A. El-Ameen

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
A problem of the gyroscopic motions around a fixed point, under the action of a gyrostatic moment vector, in presence of electromagnetic field and Newtonian one, is considered. The small parameter technique is used to investigate the periodic solutions for the derived equations of such motion problem. A geometric interpretation of motion will be given in terms of Euler’s angles ( $\theta ,\psi ,\varphi $ ). Computer programs are carried out to integrate the attained quasilinear autonomous system using a fourth-order Runge-Kutta method. A comparison between the obtained analytical solutions and the numerical ones is investigated to calculate the errors between them.

Existence of Traveling Fronts in a Food-Limited Population Model with Spatiotemporal Delay

Fri, 05 Apr 2013 11:07 EDT

Hai-Qin Zhao, San-Yang Liu

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
This paper is concerned with the traveling fronts of a diffusive food-limited population model with spatiotemporal delay. Sufficient conditions are established for the existence of traveling wave fronts by choosing different kinds of delay kernels. The approach used here is the upper-lower solution method and monotone iteration technique. Our work extends and/or covers some previous results.

Numerical Solution for Complex Systems of Fractional Order

Fri, 05 Apr 2013 11:07 EDT

Rabha W. Ibrahim

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
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.

Prevention of Influenza Pandemic by Multiple Control Strategies

Fri, 05 Apr 2013 11:07 EDT

Roman Ullah, Gul Zaman, Saeed Islam

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
We present the prevention of influenza pandemic by using multiple control functions. First, we adjust the control functions in the pandemic model, then we show the existence of the optimal control problem, and, by using both analytical and numerical techniques, we investigate cost-effective control effects for the prevention of transmission of disease. To do this, we use four control functions, the first one for increasing the effect of vaccination, the second one for the strategies to isolate infected individuals, and the last two for the antiviral treatment to control clinically infectious and hospitalization cases, respectively. We completely characterized the optimal control and compute the numerical solution of the optimality system by using an iterative method.

The Generalization of the Poisson Sum Formula Associated with the Linear Canonical Transform

Fri, 05 Apr 2013 11:07 EDT

Jun-Fang Zhang, Shou-Ping Hou

Source: J. Appl. Math., Volume 2012, 9 pages.

Abstract:
The generalization of the classical Poisson sum formula, by replacing the ordinary Fourier transform by the canonical transformation, has been derived in the linear canonical transform sense. Firstly, a new sum formula of Chirp-periodic property has been introduced, and then the relationship between this new sum and the original signal is derived. Secondly, the generalization of the classical Poisson sum formula to the linear canonical transform sense has been obtained.

LMI Approach to Stability Analysis of Cohen-Grossberg Neural Networks with $p$ -Laplace Diffusion

Fri, 05 Apr 2013 11:07 EDT

Xiongrui Wang, Ruofeng Rao, Shouming Zhong

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
The nonlinear $p$ -Laplace diffusion ( $p>1$ ) 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 $p=2$ , $p$ -Laplace diffusion is just the conventional Laplace diffusion in many previous literatures. And it is worth mentioning that even if $p=2$ , 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.

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

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 14 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

Qi Wang, Jiechang Wen

Source: J. Appl. Math., Volume 2012, 17 pages.

Abstract:
This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential $\theta $ -method is applied to ${p}^{\prime }(t)={\beta }_{0}{\omega }^{\mu }p(t-\tau )/{\mathrm{(\omega }}^{\mu }+{p}^{\mu }(t-\tau ))-\gamma p(t)$ and it is shown that the exponential $\theta $ -method has the same order of convergence as that of the classical $\theta $ -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.

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

Fri, 05 Apr 2013 11:07 EDT

Dae Won Yoon

Source: J. Appl. Math., Volume 2012, 10 pages.

Abstract:
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 .

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

Fri, 05 Apr 2013 11:07 EDT

Weiguo Rui, Yao Long

Source: J. Appl. Math., Volume 2012, 21 pages.

Abstract:
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.

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

Fri, 05 Apr 2013 11:07 EDT

Lijuan Chen, Shiping Lu

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
The authors study the existence and uniqueness of a set with $\mathrm{2}kT$ -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 $\mathrm{2}kT$ -periodic solutions.

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

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 22 pages.

Abstract:
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 ${H}_{\infty }$ 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.

On the Security of Some Aggregate Signature Schemes

Fri, 05 Apr 2013 11:07 EDT

Baoyuan Kang

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
Aggregate signature scheme proposed by Boneh, Gentry, Lynn, and Shacham allows n signatures on n distinct messages from n distinct users to aggregate a single signature that convince any verifier that n users did indeed sign the n messages, respectively. The main benefit of such schemes is that they allow bandwidth and computational savings. In this paper, we question about whether the existing aggregate signature schemes satisfy the basic property that they can convince any verifier that every user indeed signed the message which should be signed by him. We show that Rückert et al.’s scheme, and Shim’s scheme do not satisfy the property. As a comparison, we investigate Boneh et al.’s scheme and show that under the assumption that each signer correctly signs one message, Boneh et al.’s scheme satisfies this property under two users' setting. Furthermore, we propose the concept of inside attack on aggregate signatures and give an improved aggregate signature scheme based on Shim’s scheme. We also prove that the improved scheme is secure against inside attack.

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

Fri, 05 Apr 2013 11:07 EDT

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

Source: J. Appl. Math., Volume 2012, 13 pages.

Abstract:
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.

Successive Matrix Squaring Algorithm for Computing the Generalized Inverse ${A}_{T,S}^{(2)}$

Fri, 05 Apr 2013 11:07 EDT

Xiaoji Liu, Yonghui Qin

Source: J. Appl. Math., Volume 2012, 12 pages.

Abstract:
We investigate successive matrix squaring (SMS) algorithms forcomputing the generalized inverse ${A}_{T,S}^{(2)}$ of a given matrix $A\in {C}^{m×n}$ .

A Discontinuous Finite Volume Method for the Darcy-Stokes Equations

Fri, 05 Apr 2013 11:07 EDT

Zhe Yin, Ziwen Jiang, Qiang Xu

Source: J. Appl. Math., Volume 2012, 16 pages.

Abstract:
This paper proposes a discontinuous finite volume method for the Darcy-Stokes equations. An optimal error estimate for the approximation of velocity is obtained in a mesh-dependent norm. First-order ${L}^{2}$ -error estimates are derived for the approximations of both velocity and pressure. Some numerical examples verifying the theoretical predictions are presented.

Robust ${H}_{\infty }$ Filtering for Uncertain Discrete-Time Fuzzy Stochastic Systems with Sensor Nonlinearities and Time-Varying Delay

Fri, 05 Apr 2013 11:07 EDT

Mingang Hua, Pei Cheng, Juntao Fei, Jianyong Zhang, Junfeng Chen

Source: J. Appl. Math., Volume 2012, 25 pages.

Abstract:
The robust filtering problem for a class of uncertain discrete-time fuzzy stochastic systems with sensor nonlinearities and time-varying delay is investigated. The parameter uncertainties are assumed to be time varying norm bounded in both the state and measurement equations. By using the Lyapunov stability theory and some new relaxed techniques, sufficient conditions are proposed to guarantee the robustly stochastic stability with a prescribed ${H}_{\infty }$ performance level of the filtering error system for all admissible uncertainties, sensor nonlinearities, and time-varying delays. These conditions are dependent on the lower and upper bounds of the time-varying delays and are obtained in terms of a linear matrix inequality (LMI). Finally, two simulation examples are provided to illustrate the effectiveness of the proposed methods.

Application of Rational Second Kind Chebyshev Functions for System of Integrodifferential Equations on Semi-Infinite Intervals

Fri, 05 Apr 2013 11:07 EDT

M. Tavassoli Kajani, S. Vahdati, Zulkifly Abbas, Mohammad Maleki

Source: J. Appl. Math., Volume 2012, 11 pages.

Abstract:
Rational Chebyshev bases and Galerkin method are used to obtain the approximate solution of a system of high-order integro-differential equations on the interval [0,∞). This method is based on replacement of the unknown functions by their truncated series of rational Chebyshev expansion. Test examples are considered to show the high accuracy, simplicity, and efficiency of this method.

Oscillation Criteria of Certain Third-Order Differential Equation with Piecewise Constant Argument

Fri, 05 Apr 2013 11:07 EDT

Haihua Liang, Gen-qiang Wang

Source: J. Appl. Math., Volume 2012, 18 pages.

Abstract:
We study the oscillation and asymptotic behavior of third-order nonlinear delay differential equation with piecewise constant argument of the form $({r}_{2}(t)({r}_{1}(t)x\text{'}(t))\text{'})\text{'}+p(t)x\text{'}(t)+f(t,x([t]))=0$ . We establish several sufficient conditions which insure that any solution of this equation oscillates or converges to zero. Some examples are given to illustrate the importance of our results.

Closed Int Soft $\mathrm{BCI}$ -Ideals and Int Soft c- $\mathrm{BCI}$ -Ideals

Fri, 05 Apr 2013 11:07 EDT

Young Bae Jun, Kyoung Ja Lee, Eun Hwan Roh

Source: J. Appl. Math., Volume 2012, 15 pages.

Abstract:
The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notions of closed intersectional soft $\mathrm{BCI}$ -ideals and intersectional soft commutative $\mathrm{BCI}$ -ideals are introduced, and related properties are investigated. Conditions for an intersectional soft $\mathrm{BCI}$ -ideal to be closed are provided. Characterizations of an intersectional soft commutative $\mathrm{BCI}$ -ideal are established, and a new intersectional soft c- $\mathrm{BCI}$ -ideal from an old one is constructed.