Journal of Applied Mathematics The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. On Fuzzy Solutions for Diffusion Equation Sat, 31 Jan 2015 16:59:00 +0000 Our main goal is to define a fuzzy solution for problems involving diffusion. To this end, the solution of fuzzy diffusion-reaction-advection equation will be defined as Zadeh’s extension of deterministic solution of the associated problem. Important aspects such as unity and stability of these solutions will also be studied. Graphical representations of these solutions will be presented. Jefferson Leite, Moiseis Cecconello, Jackellyne Leite, and R. C. Bassanezi Copyright © 2015 Jefferson Leite et al. All rights reserved. Almost Periodic Time Scales and Almost Periodic Functions on Time Scales Thu, 29 Jan 2015 14:23:47 +0000 We propose some new concepts of almost periodic time scales and almost periodic functions on time scales and give some basic properties of these new types of almost periodic time scales and almost periodic functions on time scales. We also give some comments on a recent paper by Wang and Agarwal (2014) concerning a new almost periodic time scale. Yongkun Li and Bing Li Copyright © 2015 Yongkun Li and Bing Li. All rights reserved. Shear Current Effects on Monochromatic Water Waves Crossing Trenches Thu, 29 Jan 2015 13:32:21 +0000 The reflection coefficients of monochromatic water waves over trenches with shear current are estimated analytically. The diffraction of waves by an abrupt depth change and shear current is formulated by the matched eigenfunction expansion method. The proper number of steps and evanescent modes are proposed by a series of convergence tests. The accuracy of the predicted reflection coefficients is checked by estimating the wave energy. Reflection and transmission characteristics are studied for various shear current conditions. The different combinations of strength, width of shear current, and incident wave angle with constant water depth topography are examined. The optimal figure of the trench with shear current is obtained by estimating the reflection coefficients for various sloped transitions. The resonant reflection of the water waves is found by multiarrayed optimal trenches and the interaction of sinusoidally varying topography with shear current. Jun-Whan Lee, Koo-Yong Park, and Yong-Sik Cho Copyright © 2015 Jun-Whan Lee et al. All rights reserved. A Filled Function Method Dominated by Filter for Nonlinearly Global Optimization Wed, 28 Jan 2015 16:47:11 +0000 This work presents a filled function method based on the filter technique for global optimization. Filled function method is one of the effective methods for nonlinear global optimization, since it can effectively find a better minimizer. Filter technique is applied to local optimization methods for its excellent numerical results. In order to optimize the filled function method, the filter method is employed for global optimizations in this method. A new filled function is proposed first, and then the algorithm and its properties are proved. The numerical results are listed at the end. Wei Wang, Xiaoshan Zhang, and Min Li Copyright © 2015 Wei Wang et al. All rights reserved. An Empirical Study of Hybrid DEA and Grey System Theory on Analyzing Performance: A Case from Indian Mining Industry Tue, 27 Jan 2015 12:36:50 +0000 India, which has long been recognized as a well-endowed nation in natural mineral resources, is a major minerals producer. According to the report of Indian Ministry of Mines 2013, Indian mining and metals sector ranked the fourth among the mineral producer countries, behind China, United States, and Russia and had in fact led the economy into recovery from the global financial crisis. Since this industry has turned into a significant issue, this paper attempts to rank the performance of 23 Indian mining and metal companies and to evaluate and measure the productivity change of these sectors during different time periods (2010–2014). Besides, the authors would like to choose one advanced model of MPI to see the performance of these companies in the past-present period and the 4-year future period (2015–2018) by using forecasting results of Grey system theory. The results revealed that from the past to future period the National Mineral Development Corporation, Hindalco Industries Limited, and Coal India always keep their highest best rankings among 23 DMUs regarding performance scores. This study contributes better insights of Indian mining industry as it is the core of the economy. Lai-Wang Wang, Thanh-Tuyen Tran, and Nhu-Ty Nguyen Copyright © 2015 Lai-Wang Wang et al. All rights reserved. Simulation and Modeling of Flow in a Gas Compressor Wed, 21 Jan 2015 06:32:50 +0000 The presented research demonstrates the results of a series of numerical simulations of gas flow through a single-stage centrifugal compressor with a vaneless diffuser. Numerical results were validated with experiments consisting of eight regimes with different mass flow rates. The steady-state and unsteady simulations were done in ANSYS FLUENT 13.0 and NUMECA FINE/TURBO 8.9.1 for one-period geometry due to periodicity of the problem. First-order discretization is insufficient due to strong dissipation effects. Results obtained with second-order discretization agree with the experiments for the steady-state case in the region of high mass flow rates. In the area of low mass flow rates, nonstationary effects significantly influence the flow leading stationary model to poor prediction. Therefore, the unsteady simulations were performed in the region of low mass flow rates. Results of calculation were compared with experimental data. The numerical simulation method in this paper can be used to predict compressor performance. Anna Avramenko, Alexey Frolov, and Jari Hämäläinen Copyright © 2015 Anna Avramenko et al. All rights reserved. Nonlinearities Distribution Homotopy Perturbation Method Applied to Solve Nonlinear Problems: Thomas-Fermi Equation as a Case Study Tue, 20 Jan 2015 14:26:16 +0000 We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM). Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results. U. Filobello-Nino, H. Vazquez-Leal, K. Boubaker, A. Sarmiento-Reyes, A. Perez-Sesma, A. Diaz-Sanchez, V. M. Jimenez-Fernandez, J. Cervantes-Perez, J. Sanchez-Orea, J. Huerta-Chua, L. J. Morales-Mendoza, M. Gonzalez-Lee, C. Hernandez-Mejia, and F. J. Gonzalez-Martinez Copyright © 2015 U. Filobello-Nino et al. All rights reserved. Data Transformation Technique to Improve the Outlier Detection Power of Grubbs’ Test for Data Expected to Follow Linear Relation Wed, 14 Jan 2015 11:17:44 +0000 Grubbs test (extreme studentized deviate test, maximum normed residual test) is used in various fields to identify outliers in a data set, which are ranked in the order of . However, ranking of data eliminates the actual sequence of a data series, which is an important factor for determining outliers in some cases (e.g., time series). Thus in such a data set, Grubbs test will not identify outliers correctly. This paper introduces a technique for transforming data from sequence bound linear form to sequence unbound form . Applying Grubbs test to the new transformed data set detects outliers more accurately. In addition, the new technique improves the outlier detection capability of Grubbs test. Results show that, Grubbs test was capable of identifing outliers at significance level 0.01 after transformation, while it was unable to identify those prior to transforming at significance level 0.05. K. K. L. B. Adikaram, M. A. Hussein, M. Effenberger, and T. Becker Copyright © 2015 K. K. L. B. Adikaram et al. All rights reserved. Palmprint Authentication System Based on Local and Global Feature Fusion Using DOST Wed, 31 Dec 2014 14:17:43 +0000 Palmprint is the region between wrist and fingers. In this paper, a palmprint personal identification system is proposed based on the local and global information fusion. The local and global information is critical for the image observation based on the results of the relationship between physical stimuli and perceptions. The local features of the enhanced palmprint are extracted using discrete orthonormal Stockwell transform. The global feature is obtained by reducing the scale of discrete orthonormal Stockwell transform to infinity. The local and global matching distances of the two palmprint images are fused to get the final matching distance of the proposed scheme. The results show that the fusion of local and global features outperforms the existing works on the available three datasets. N. B. Mahesh Kumar and K. Premalatha Copyright © 2014 N. B. Mahesh Kumar and K. Premalatha. All rights reserved. Completely Monotonic and Related Functions: Their Applications Wed, 31 Dec 2014 12:51:56 +0000 Senlin Guo, Andrea Laforgia, Necdet Batir, and Qiu-Ming Luo Copyright © 2014 Senlin Guo et al. All rights reserved. A Comparison of Evolutionary Computation Techniques for IIR Model Identification Thu, 25 Dec 2014 06:49:51 +0000 System identification is a complex optimization problem which has recently attracted the attention in the field of science and engineering. In particular, the use of infinite impulse response (IIR) models for identification is preferred over their equivalent FIR (finite impulse response) models since the former yield more accurate models of physical plants for real world applications. However, IIR structures tend to produce multimodal error surfaces whose cost functions are significantly difficult to minimize. Evolutionary computation techniques (ECT) are used to estimate the solution to complex optimization problems. They are often designed to meet the requirements of particular problems because no single optimization algorithm can solve all problems competitively. Therefore, when new algorithms are proposed, their relative efficacies must be appropriately evaluated. Several comparisons among ECT have been reported in the literature. Nevertheless, they suffer from one limitation: their conclusions are based on the performance of popular evolutionary approaches over a set of synthetic functions with exact solutions and well-known behaviors, without considering the application context or including recent developments. This study presents the comparison of various evolutionary computation optimization techniques applied to IIR model identification. Results over several models are presented and statistically validated. Erik Cuevas, Jorge Gálvez, Salvador Hinojosa, Omar Avalos, Daniel Zaldívar, and Marco Pérez-Cisneros Copyright © 2014 Erik Cuevas et al. All rights reserved. Analysis of Repairable Geo/G/1 Queues with Negative Customers Wed, 24 Dec 2014 13:32:15 +0000 We consider discrete-time Geo/G/1 queues with negative customers and a repairable server. The server is subject to failure due to a negative customer arrival. As soon as a negative customer arrives at a system, the server fails and one positive (ordinary) customer is forced to leave. At a failure instant, the server is turned off and the repair process immediately begins. We construct the mathematical model and present the probability generating functions of the system size distribution and the FCFS sojourn time distribution. Finally, some numerical examples are given to show the influence of negative customer arrival on the performance measures of the system. Doo Ho Lee and Kilhwan Kim Copyright © 2014 Doo Ho Lee and Kilhwan Kim. All rights reserved. Applied Mathematics in Biomedical Sciences and Engineering 2014 Wed, 24 Dec 2014 08:44:25 +0000 Chang-Hwan Im, Kiwoon Kwon, Hang Joon Jo, and Pedro Serranho Copyright © 2014 Chang-Hwan Im et al. All rights reserved. Radial Basis Point Interpolation Method with Reordering Gauss Domains for 2D Plane Problems Tue, 23 Dec 2014 06:27:10 +0000 We present novel Gauss integration schemes with radial basis point interpolation method (RPIM). These techniques define new Gauss integration scheme, researching Gauss points (RGD), and reconstructing Gauss domain (RGD), respectively. The developments lead to a curtailment of the elapsed CPU time without loss of the accuracy. Numerical results show that the schemes reduce the computational time to 25% or less in general. Shi-Chao Yi, Fu-jun Chen, and Lin-Quan Yao Copyright © 2014 Shi-Chao Yi et al. All rights reserved. Intelligent Modeling and Verification 2014 Mon, 22 Dec 2014 09:38:10 +0000 Guiming Luo, Xiaoyu Song, Xiaojing Yang, and Krishnaiyan Thulasiraman Copyright © 2014 Guiming Luo et al. All rights reserved. Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals Mon, 22 Dec 2014 00:10:31 +0000 We investigate the qualitative behavior of a perturbed causal differential equation that differs in initial position and initial time with respect to the unperturbed causal differential equations. We compare the classical notion of stability of the causal differential systems to the notion of initial time difference stability of causal differential systems and present a comparison result in terms of Lyapunov functions. We have utilized Lyapunov functions and Lyapunov functional in the study of stability theory of causal differential systems when establishing initial time difference stability of the perturbed causal differential system with respect to the unperturbed causal differential system. Coşkun Yakar and Mustafa Bayram Gücen Copyright © 2014 Coşkun Yakar and Mustafa Bayram Gücen. All rights reserved. Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations Sun, 21 Dec 2014 11:27:24 +0000 The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily. Rong Haiwu, Wang Xiangdong, Luo Qizhi, Xu Wei, and Fang Tong Copyright © 2014 Rong Haiwu et al. All rights reserved. A General Setting and Solution of Bellman Equation in Monetary Theory Sun, 21 Dec 2014 10:08:45 +0000 As an important tool in theoretical economics, Bellman equation is very powerful in solving optimization problems of discrete time and is frequently used in monetary theory. Because there is not a general method to solve this problem in monetary theory, it is hard to grasp the setting and solution of Bellman equation and easy to reach wrong conclusions. In this paper, we discuss the rules and problems that should be paid attention to when incorporating money into general equilibrium models. A general setting and solution of Bellman equation in monetary theory are provided. The proposed method is clear, is easy to grasp, is generalized, and always leads to the correct results. Xiaoli Gan and Wanbo Lu Copyright © 2014 Xiaoli Gan and Wanbo Lu. All rights reserved. Variational Inequalities and Vector Optimization 2014 Sun, 21 Dec 2014 08:59:23 +0000 Xian-Jun Long, Jian-Wen Peng, Nan-Jing Huang, and Jen-Chih Yao Copyright © 2014 Xian-Jun Long et al. All rights reserved. 1 : 3 Resonance and Chaos in a Discrete Hindmarsh-Rose Model Wed, 17 Dec 2014 09:01:08 +0000 1 : 3 resonance of a two-dimensional discrete Hindmarsh-Rose model is discussed by normal form method and bifurcation theory. Numerical simulations are presented to illustrate the theoretical analysis, which predict the occurrence of a closed invariant circle, period-three saddle cycle, and homoclinic structure. Furthermore, it also displays the complex dynamical behaviors, especially the transitions between three main dynamical behaviors, namely, quiescence, spiking, and bursting. Bo Li and Zhimin He Copyright © 2014 Bo Li and Zhimin He. All rights reserved. Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions Wed, 10 Dec 2014 00:11:09 +0000 We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations. Zakieh Avazzadeh, Mohammad Heydari, Wen Chen, and G. B. Loghmani Copyright © 2014 Zakieh Avazzadeh et al. All rights reserved. Working with Missing Data: Imputation of Nonresponse Items in Categorical Survey Data with a Non-Monotone Missing Pattern Sun, 07 Dec 2014 10:23:31 +0000 The imputation of missing data is often a crucial step in the analysis of survey data. This study reviews typical problems with missing data and discusses a method for the imputation of missing survey data with a large number of categorical variables which do not have a monotone missing pattern. We develop a method for constructing a monotone missing pattern that allows for imputation of categorical data in data sets with a large number of variables using a model-based MCMC approach. We report the results of imputing the missing data from a case study, using educational, sociopsychological, and socioeconomic data from the National Latino and Asian American Study (NLAAS). We report the results of multiply imputed data on a substantive logistic regression analysis predicting socioeconomic success from several educational, sociopsychological, and familial variables. We compare the results of conducting inference using a single imputed data set to those using a combined test over several imputations. Findings indicate that, for all variables in the model, all of the single tests were consistent with the combined test. Machelle D. Wilson and Kerstin Lueck Copyright © 2014 Machelle D. Wilson and Kerstin Lueck. All rights reserved. An Improved Central Force Optimization Algorithm for Multimodal Optimization Sun, 07 Dec 2014 08:00:51 +0000 This paper proposes the hybrid CSM-CFO algorithm based on the simplex method (SM), clustering technique, and central force optimization (CFO) for unconstrained optimization. CSM-CFO is still a deterministic swarm intelligent algorithm, such that the complex statistical analysis of the numerical results can be omitted, and the convergence intends to produce faster and more accurate by clustering technique and good points set. When tested against benchmark functions, in low and high dimensions, the CSM-CFO algorithm has competitive performance in terms of accuracy and convergence speed compared to other evolutionary algorithms: particle swarm optimization, evolutionary program, and simulated annealing. The comparison results demonstrate that the proposed algorithm is effective and efficient. Jie Liu and Yu-ping Wang Copyright © 2014 Jie Liu and Yu-ping Wang. All rights reserved. A QFD-Based Mathematical Model for New Product Development Considering the Target Market Segment Mon, 01 Dec 2014 06:58:43 +0000 Responding to customer needs is important for business success. Quality function deployment provides systematic procedures for converting customer needs into technical requirements to ensure maximum customer satisfaction. The existing literature mainly focuses on the achievement of maximum customer satisfaction under a budgetary limit via mathematical models. The market goal of the new product for the target market segment is usually ignored. In this study, the proposed approach thus considers the target customer satisfaction degree for the target market segment in the model by formulating the overall customer satisfaction as a function of the quality level. In addition, the proposed approach emphasizes the cost-effectiveness concept in the design stage via the achievement of the target customer satisfaction degree using the minimal total cost. A numerical example is used to demonstrate the applicability of the proposed approach and its characteristics are discussed. Liang-Hsuan Chen and Cheng-Nien Chen Copyright © 2014 Liang-Hsuan Chen and Cheng-Nien Chen. All rights reserved. Refinements of Generalized Hölder’s Inequalities Thu, 27 Nov 2014 13:13:51 +0000 We present some new versions of generalized Hölder’s inequalities. The results are used to improve Minkowski’s inequality and a Beckenbach-type inequality. Jingfeng Tian, Wen-Li Wang, and Donal O’Regan Copyright © 2014 Jingfeng Tian et al. All rights reserved. New Results on Robust Model Predictive Control for Time-Delay Systems with Input Constraints Thu, 27 Nov 2014 09:50:08 +0000 This paper investigates the problem of model predictive control for a class of nonlinear systems subject to state delays and input constraints. The time-varying delay is considered with both upper and lower bounds. A new model is proposed to approximate the delay. And the uncertainty is polytopic type. For the state-feedback MPC design objective, we formulate an optimization problem. Under model transformation, a new model predictive controller is designed such that the robust asymptotical stability of the closed-loop system can be guaranteed. Finally, the applicability of the presented results are demonstrated by a practical example. Qing Lu, Yiyong Sun, Qi Zhou, and Zhiguang Feng Copyright © 2014 Qing Lu et al. All rights reserved. Recent Advances on Mathematical Modeling and Control Methods for Complex Vehicle Systems Thu, 27 Nov 2014 09:47:52 +0000 Hamid Reza Karimi, Zheping Yan, Yuxin Zhao, Weichao Sun, and Mohammed Chadli Copyright © 2014 Hamid Reza Karimi et al. All rights reserved. Modified Homotopy Perturbation Method for Solving Fractional Differential Equations Wed, 26 Nov 2014 11:24:03 +0000 The modified homotopy perturbation method is extended to derive the exact solutions for linear (nonlinear) ordinary (partial) differential equations of fractional order in fluid mechanics. The fractional derivatives are taken in the Caputo sense. This work will present a numerical comparison between the considered method and some other methods through solving various fractional differential equations in applied fields. The obtained results reveal that this method is very effective and simple, accelerates the rapid convergence of the series solution, and reduces the size of work to only one iteration. A. A. Hemeda Copyright © 2014 A. A. Hemeda. All rights reserved. The Nonpermutation Flowshop Scheduling Problem: Adjustment and Bounding Procedures Wed, 26 Nov 2014 07:17:11 +0000 We consider the makespan minimization in a flowshop environment where the job sequence does not have to be the same for all the machines. Contrarily to the classical permutation flowshop scheduling problem, this strongly NP-hard problem received very scant attention in the literature. In this paper, some improved single-machine-based adjustment procedures are proposed, and a new two-machine-based one is introduced. Based on these adjustments, new lower and upper bounding schemes are derived. Our experimental analysis shows that the proposed procedures provide promising results. Anis Gharbi, Mohamed Labidi, and Mohamed Aly Louly Copyright © 2014 Anis Gharbi et al. All rights reserved. Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems Tue, 25 Nov 2014 00:00:00 +0000 One of the most important optimality conditions to aid in solving a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptions on the objective functions and on the constraint set. The present work is concerned with the constrained vector quadratic fractional optimization problem. It shows that sufficient Pareto optimality conditions and the main duality theorems can be established without the assumption of generalized convexity in the objective functions, by considering some assumptions on a linear combination of Hessian matrices instead. The main aspect of this contribution is the development of Pareto optimality conditions based on a similar second-order sufficient condition for problems with convex constraints, without convexity assumptions on the objective functions. These conditions might be useful to determine termination criteria in the development of algorithms. W. A. Oliveira, A. Beato-Moreno, A. C. Moretti, and L. L. Salles Neto Copyright © 2014 W. A. Oliveira et al. All rights reserved.