Journal of Applied Mathematics The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Computational Science in Smart Grids and Energy Systems Sun, 29 Mar 2015 07:57:43 +0000 Hongjie Jia, Ned Djilali, Xinghuo Yu, H. D. Chiang, and Gongnan Xie Copyright © 2015 Hongjie Jia et al. All rights reserved. Estimating Potential Evapotranspiration by Missing Temperature Data Reconstruction Thu, 26 Mar 2015 12:33:29 +0000 This work studies the statistical characteristics of potential evapotranspiration calculations and their relevance within the water balance used to determine water availability in hydrological basins. The purpose of this study was as follows: first, to apply a missing data reconstruction scheme in weather stations of the Rio Queretaro basin; second, to reduce the generated uncertainty of temperature data: mean, minimum, and maximum values in the evapotranspiration calculation which has a paramount importance in the manner of obtaining the water balance at any hydrological basin. The reconstruction of missing data was carried out in three steps: (1) application of a 4-parameter sinusoidal type regression to temperature data, (2) linear regression to residuals to obtain a regional behavior, and (3) estimation of missing temperature values for a certain year and during a certain season within the basin under study; estimated and observed temperature values were compared. Finally, using the obtained temperature values, the methods of Hamon, Papadakis, Blaney and Criddle, Thornthwaite, and Hargreaves were employed to calculate potential evapotranspiration that was compared to the real observed values in weather stations. With the results obtained from the application of this procedure, the surface water balance was corrected for the case study. Eladio Delgadillo-Ruiz, Eusebio Jr. Ventura-Ramos, Julián González Trinidad, Hugo Enrique Júnez-Ferreira, Carlos Francisco Bautista-Capetillo, and Olivia Delgadillo-Ruiz Copyright © 2015 Eladio Delgadillo-Ruiz et al. All rights reserved. Iterative Methods and Applications 2014 Thu, 26 Mar 2015 07:51:34 +0000 Giuseppe Marino, Filomena Cianciaruso, Claudio H. Morales, Luigi Muglia, and D. R. Sahu Copyright © 2015 Giuseppe Marino et al. All rights reserved. A New Jarratt-Type Fourth-Order Method for Solving System of Nonlinear Equations and Applications Wed, 25 Mar 2015 12:19:58 +0000 Solving systems of nonlinear equations plays a major role in engineering problems. We present a new family of optimal fourth-order Jarratt-type methods for solving nonlinear equations and extend these methods to solve system of nonlinear equations. Convergence analysis is given for both cases to show that the order of the new methods is four. Cost of computations, numerical tests, and basins of attraction are presented which illustrate the new methods as better alternates to previous methods. We also give an application of the proposed methods to well-known Burger's equation. Moin-ud-Din Junjua, Saima Akram, Nusrat Yasmin, and Fiza Zafar Copyright © 2015 Moin-ud-Din Junjua et al. All rights reserved. Lie Group Analysis on Brownian Motion and Thermophoresis Effect on Free Convective Boundary-Layer Flow on a Vertical Cylinder Embedded in a Nanofluid-Saturated Porous Medium Wed, 25 Mar 2015 08:47:45 +0000 Natural convective boundary-layer flow of a nanofluid on a heated vertical cylinder embedded in a nanofluid-saturated porous medium is studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. Lie groups analysis is used to get the similarity transformations, which transform the governing partial differential equations to a system of ordinary differential equations. Two groups of similarity transformations are obtained. Numerical solutions of the resulting ordinary differential systems are obtained and discussed for various values of the governing parameters. Mohammad Ferdows, Mohammed Abdul Ali Hamad, and Mohamed Ali Copyright © 2015 Mohammad Ferdows et al. All rights reserved. Modeling and Control of Complex Dynamic Systems 2014 Wed, 25 Mar 2015 08:42:43 +0000 Zhiwei Gao, De-Xing Kong, and Michael Z. Q. Chen Copyright © 2015 Zhiwei Gao et al. All rights reserved. Advanced Mathematics and Numerical Modeling of IoT Wed, 25 Mar 2015 08:15:04 +0000 Young-Sik Jeong, Mohammad S. Obaidat, Jianhua Ma, and Laurence T. Yang Copyright © 2015 Young-Sik Jeong et al. All rights reserved. Parallel Dynamical Systems over Graphs and Related Topics: A Survey Tue, 24 Mar 2015 13:05:58 +0000 In discrete processes, as computational or genetic ones, there are many entities and each entity has a state at a given time. The update of states of the entities constitutes an evolution in time of the system, that is, a discrete dynamical system. The relations among entities are usually represented by a graph. The update of the states is determined by the relations of the entities and some local functions which together constitute (global) evolution operator of the dynamical system. If the states of the entities are updated in a synchronous manner, the system is called a parallel dynamical system. This paper is devoted to review the main results on the dynamical behavior of parallel dynamical systems over graphs which constitute a generic tool for modeling discrete processes. Juan A. Aledo, Silvia Martinez, and Jose C. Valverde Copyright © 2015 Juan A. Aledo et al. All rights reserved. Numerical Methods of Complex Valued Linear Algebraic System Tue, 24 Mar 2015 09:49:17 +0000 Shi-Liang Wu, Shu-Qian Shen, Masoud Hajarian, Jia Liu, and Lev A. Krukier Copyright © 2015 Shi-Liang Wu et al. All rights reserved. LSMR Iterative Method for General Coupled Matrix Equations Mon, 23 Mar 2015 13:55:49 +0000 By extending the idea of LSMR method, we present an iterative method to solve the general coupled matrix equations , , (including the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases) over some constrained matrix groups , such as symmetric, generalized bisymmetric, and -symmetric matrix groups. By this iterative method, for any initial matrix group , a solution group can be obtained within finite iteration steps in absence of round-off errors, and the minimum Frobenius norm solution or the minimum Frobenius norm least-squares solution group can be derived when an appropriate initial iterative matrix group is chosen. In addition, the optimal approximation solution group to a given matrix group in the Frobenius norm can be obtained by finding the least Frobenius norm solution group of new general coupled matrix equations. Finally, numerical examples are given to illustrate the effectiveness of the presented method. F. Toutounian, D. Khojasteh Salkuyeh, and M. Mojarrab Copyright © 2015 F. Toutounian et al. All rights reserved. The Combined Poisson INMA() Models for Time Series of Counts Mon, 23 Mar 2015 12:21:46 +0000 A new stationary th-order integer-valued moving average process with Poisson innovation is introduced based on decision random vector. Some statistical properties of the process are established. Estimators of the parameters of the process are obtained using the method of moments. Some numerical results of the estimators are presented to assess the performance of moment estimators. Kaizhi Yu and Hong Zou Copyright © 2015 Kaizhi Yu and Hong Zou. All rights reserved. The Polynomial Pivots as Initial Values for a New Root-Finding Iterative Method Mon, 23 Mar 2015 11:28:02 +0000 A new iterative method for polynomial root-finding based on the development of two novel recursive functions is proposed. In addition, the concept of polynomial pivots associated with these functions is introduced. The pivots present the property of lying close to some of the roots under certain conditions; this closeness leads us to propose them as efficient starting points for the proposed iterative sequences. Conditions for local convergence are studied demonstrating that the new recursive sequences converge with linear velocity. Furthermore, an a priori checkable global convergence test inside pivots-centered balls is proposed. In order to accelerate the convergence from linear to quadratic velocity, new recursive functions together with their associated sequences are constructed. Both the recursive functions (linear) and the corrected (quadratic convergence) are validated with two nontrivial numerical examples. In them, the efficiency of the pivots as starting points, the quadratic convergence of the proposed functions, and the validity of the theoretical results are visualized. Mario Lázaro, Pedro Martín, Antonio Agüero, and Ignacio Ferrer Copyright © 2015 Mario Lázaro et al. All rights reserved. Mathematical Modeling and Optimization of Industrial Problems Sun, 22 Mar 2015 12:52:22 +0000 M. Montaz Ali, Aderemi O. Adewumi, Nachamada Blamah, and Olabisi Falowo Copyright © 2015 M. Montaz Ali et al. All rights reserved. Positivity Preserving Interpolation Using Rational Bicubic Spline Sun, 22 Mar 2015 12:23:07 +0000 This paper discusses the positivity preserving interpolation for positive surfaces data by extending the C1 rational cubic spline interpolant of Karim and Kong to the bivariate cases. The partially blended rational bicubic spline has 12 parameters in the descriptions where 8 of them are free parameters. The sufficient conditions for the positivity are derived on every four boundary curves network on the rectangular patch. Numerical comparison with existing schemes also has been done in detail. Based on Root Mean Square Error (RMSE), our partially blended rational bicubic spline is on a par with the established methods. Samsul Ariffin Abdul Karim, Kong Voon Pang, and Azizan Saaban Copyright © 2015 Samsul Ariffin Abdul Karim et al. All rights reserved. Investigation Methodology of a Virtual Desktop Infrastructure for IoT Sun, 22 Mar 2015 10:07:09 +0000 Cloud computing for IoT (Internet of Things) has exhibited the greatest growth in the IT market in the recent past and this trend is expected to continue. Many companies are adopting a virtual desktop infrastructure (VDI) for private cloud computing to reduce costs and enhance the efficiency of their servers. As a VDI is widely used, threats of cyber terror and invasion are also increasing. To minimize the damage, response procedure for cyber intrusion on a VDI should be systematized. Therefore, we propose an investigation methodology for VDI solutions in this paper. Here we focus on a virtual desktop infrastructure and introduce various desktop virtualization solutions that are widely used, such as VMware, Citrix, and Microsoft. In addition, we verify the integrity of the data acquired in order that the result of our proposed methodology is acceptable as evidence in a court of law. During the experiment, we observed an error: one of the commonly used digital forensic tools failed to mount a dynamically allocated virtual disk properly. Doowon Jeong, Jungheum Park, Sangjin Lee, and Chulhoon Kang Copyright © 2015 Doowon Jeong et al. All rights reserved. Evolution of Black-Box Models Based on Volterra Series Thu, 19 Mar 2015 13:51:17 +0000 This paper presents a historical review of the many behavioral models actually used to model radio frequency power amplifiers and a new classification of these behavioral models. It also discusses the evolution of these models, from a single polynomial to multirate Volterra models, presenting equations and estimation methods. New trends in RF power amplifier behavioral modeling are suggested. Daniel D. Silveira, Thiago V. N. Coelho, and Alexandre Bessa dos Santos Copyright © 2015 Daniel D. Silveira et al. All rights reserved. A Class of Weighted Low Rank Approximation of the Positive Semidefinite Hankel Matrix Thu, 19 Mar 2015 08:43:28 +0000 We consider the weighted low rank approximation of the positive semidefinite Hankel matrix problem arising in signal processing. By using the Vandermonde representation, we firstly transform the problem into an unconstrained optimization problem and then use the nonlinear conjugate gradient algorithm with the Armijo line search to solve the equivalent unconstrained optimization problem. Numerical examples illustrate that the new method is feasible and effective. Jianchao Bai, Xuefeng Duan, Kexin Cheng, and Xuewei Zhang Copyright © 2015 Jianchao Bai et al. All rights reserved. New Contribution to the Advancement of Fixed Point Theory, Equilibrium Problems, and Optimization Problems 2014 Mon, 09 Mar 2015 14:08:52 +0000 Wei-Shih Du, Erdal Karapinar, Lai-Jiu Lin, and Gue Myung Lee Copyright © 2015 Wei-Shih Du et al. All rights reserved. Fault Modeling and Testing for Analog Circuits in Complex Space Based on Supply Current and Output Voltage Mon, 09 Mar 2015 07:05:46 +0000 This paper deals with the modeling of fault for analog circuits. A two-dimensional (2D) fault model is first proposed based on collaborative analysis of supply current and output voltage. This model is a family of circle loci on the complex plane, and it simplifies greatly the algorithms for test point selection and potential fault simulations, which are primary difficulties in fault diagnosis of analog circuits. Furthermore, in order to reduce the difficulty of fault location, an improved fault model in three-dimensional (3D) complex space is proposed, which achieves a far better fault detection ratio (FDR) against measurement error and parametric tolerance. To address the problem of fault masking in both 2D and 3D fault models, this paper proposes an effective design for testability (DFT) method. By adding redundant bypassing-components in the circuit under test (CUT), this method achieves excellent fault isolation ratio (FIR) in ambiguity group isolation. The efficacy of the proposed model and testing method is validated through experimental results provided in this paper. Hongzhi Hu, Shulin Tian, and Qing Guo Copyright © 2015 Hongzhi Hu et al. All rights reserved. Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method Wed, 04 Mar 2015 09:34:27 +0000 User friendly algorithm based on the optimal homotopy analysis transform method (OHATM) is proposed to find the approximate solutions to generalized Abel’s integral equations. The classical theory of elasticity of material is modeled by the system of Abel integral equations. It is observed that the approximate solutions converge rapidly to the exact solutions. Illustrative numerical examples are given to demonstrate the efficiency and simplicity of the proposed method. Finally, several numerical examples are given to illustrate the accuracy and stability of this method. Comparison of the approximate solution with the exact solutions shows that the proposed method is very efficient and computationally attractive. We can use this method for solving more complicated integral equations in mathematical physical. Mohamed S. Mohamed, Khaled A. Gepreel, Faisal A. Al-Malki, and Maha Al-Humyani Copyright © 2015 Mohamed S. Mohamed et al. All rights reserved. Hyperelliptic Curves for the Vector Decomposition Problem over Fields of Even Characteristic Wed, 04 Mar 2015 08:37:44 +0000 We present an infinite family of hyperelliptic curves of genus two over a finite field of even characteristic which are suitable for the vector decomposition problem. Seungkook Park Copyright © 2015 Seungkook Park. All rights reserved. Dynamic Output Feedback Robust Model Predictive Control via Zonotopic Set-Membership Estimation for Constrained Quasi-LPV Systems Tue, 03 Mar 2015 13:51:14 +0000 For the quasi-linear parameter varying (quasi-LPV) system with bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC) is investigated. The estimation error set is represented by a zonotope and refreshed by the zonotopic set-membership estimation method. By properly refreshing the estimation error set online, the bounds of true state at the next sampling time can be obtained. Furthermore, the feasibility of the main optimization problem at the next sampling time can be determined at the current time. A numerical example is given to illustrate the effectiveness of the approach. Xubin Ping and Ning Sun Copyright © 2015 Xubin Ping and Ning Sun. All rights reserved. On a Nonlinear Degenerate Evolution Equation with Nonlinear Boundary Damping Tue, 03 Mar 2015 10:01:09 +0000 This paper deals essentially with a nonlinear degenerate evolution equation of the form supplemented with nonlinear boundary conditions of Neumann type given by . Under suitable conditions the existence and uniqueness of solutions are shown and that the boundary damping produces a uniform global stability of the corresponding solutions. A. T. Lourêdo, G. Siracusa, and C. A. Silva Filho Copyright © 2015 A. T. Lourêdo et al. All rights reserved. Reliability Analysis in Presence of Random Variables and Fuzzy Variables Mon, 02 Mar 2015 09:33:46 +0000 For mixed uncertainties of random variables and fuzzy variables in engineering, three indices, that is, interval reliability index, mean reliability index, and numerical reliability index, are proposed to measure safety of structure. Comparing to the reliability membership function for measuring the safety in case of mixed uncertainties, the proposed indices are more intuitive and easier to represent the safety degree of the engineering structure, and they are more suitable for the reliability design in the case of the mixed uncertainties. The differences and relations among three proposed indices are investigated, and their applicability is compared. Furthermore, a technique based on the probability density function evolution method is employed to improve the computational efficiency of the proposed indices. At last, a numerical example and two engineering examples are illustrated to demonstrate the feasibility, reasonability, and efficiency of the computational technique of the proposed indices. Cui Lijie, Lü Zhenzhou, and Li Guijie Copyright © 2015 Cui Lijie et al. All rights reserved. Chinese Gini Coefficient from 2005 to 2012, Based on 20 Grouped Income Data Sets of Urban and Rural Residents Mon, 02 Mar 2015 09:03:02 +0000 Data insufficiency has become the primary factor affecting research on income disparity in China. To resolve this issue, this paper explores Chinese income distribution and income inequality using distribution functions. First, it examines 20 sets of grouped data on family income between 2005 and 2012 by the China Yearbook of Household Surveys, 2013, and compares the fitting effects of eight distribution functions. The results show that the generalized beta distribution of the second kind has a high fitting to the income distribution of urban and rural residents in China. Next, these results are used to calculate the Chinese Gini ratio, which is then compared with the findings of relevant studies. Finally, this paper discusses the influence of urbanization on income inequality in China and suggests that accelerating urbanization can play an important role in narrowing the income gap of Chinese residents. Jiandong Chen, Fuqian Fang, Wenxuan Hou, Fengying Li, Ming Pu, and Malin Song Copyright © 2015 Jiandong Chen et al. All rights reserved. Feng’s First Integral Method Applied to the ZKBBM and the Generalized Fisher Space-Time Fractional Equations Mon, 02 Mar 2015 07:38:30 +0000 The fractional derivatives in the sense of the modified Riemann-Liouville derivative and Feng’s first integral method are employed to obtain the exact solutions of the nonlinear space-time fractional ZKBBM equation and the nonlinear space-time fractional generalized Fisher equation. The power of this manageable method is presented by applying it to the above equations. Our approach provides first integrals in polynomial form with high accuracy. Exact analytical solutions are obtained through establishing first integrals. The present method is efficient and reliable, and it can be used as an alternative to establish new solutions of different types of fractional differential equations applied in mathematical physics. Huitzilin Yépez-Martínez, Ivan O. Sosa, and Juan M. Reyes Copyright © 2015 Huitzilin Yépez-Martínez et al. All rights reserved. Iterative Algorithms for Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators Sun, 01 Mar 2015 08:27:54 +0000 Consider the variational inequality of finding a point satisfying the property for all , where is a level set of a convex function defined on a real Hilbert space and is a boundedly Lipschitzian (i.e., Lipschitzian on bounded subsets of ) and strongly monotone operator. He and Xu proved that this variational inequality has a unique solution and devised iterative algorithms to approximate this solution (see He and Xu, 2009). In this paper, relaxed and self-adaptive iterative algorithms are proposed for computing this unique solution. Since our algorithms avoid calculating the projection (calculating by computing a sequence of projections onto half-spaces containing the original domain ) directly and select the stepsizes through a self-adaptive way (having no need to know any information of bounded Lipschitz constants of (i.e., Lipschitz constants on some bounded subsets of )), the implementations of our algorithms are very easy. The algorithms in this paper improve and extend the corresponding results of He and Xu. Caiping Yang and Songnian He Copyright © 2015 Caiping Yang and Songnian He. All rights reserved. A Float-Path Theory and Its Application to the Time-Cost Tradeoff Problem Thu, 26 Feb 2015 08:41:19 +0000 Activity floats are vital for project scheduling, such as total floats which determine the maximum permissible delays of activities. Moreover, activity paths in activity networks present essences of many project scheduling problems; for example, the time-cost tradeoff is to shorten long paths at lower costs. We discovered relationships between activity floats and paths and established a float-path theory. The theory helps to compute path lengths using activity floats and analyze activity floats using paths, which helps to transmute a problem into the other simpler one. We discussed applications of the float-path theory and applied it to solve the time-cost tradeoff problem (TCTP), especially the nonlinear and discrete versions. We proposed a simplification from an angle of path as a preprocessing technique for the TCTP. The simplification is a difficult path problem, but we transformed it into a simple float problem using the float-path theory. We designed a polynomial algorithm for the simplification, and then the TCTP may be solved more efficiently. Zhi-xiong Su, Jian-xun Qi, and Han-ying Wei Copyright © 2015 Zhi-xiong Su et al. All rights reserved. Stability Results for an Age-Structured SIS Epidemic Model with Vector Population Tue, 24 Feb 2015 14:52:29 +0000 We formulate an age-structured SIS epidemic model with periodic parameters, which includes host population and vector population. The host population is described by two partial differential equations, and the vector population is described by a single ordinary differential equation. The existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on locally integrable periodic functions. We obtain that if the spectral radius of the Fréchet derivative of the fixed point operator at zero is greater than one, there exists a unique endemic periodic solution, and we investigate the global attractiveness of disease-free steady state of the normalized system. He-Long Liu, Jing-Yuan Yu, and Guang-Tian Zhu Copyright © 2015 He-Long Liu et al. All rights reserved. Generalized Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems Tue, 24 Feb 2015 09:08:34 +0000 We introduce and study well-posedness in connection with the symmetric vector quasi-equilibrium problem, which unifies its Hadamard and Levitin-Polyak well-posedness. Using the nonlinear scalarization function, we give some sufficient conditions to guarantee the existence of well-posedness for the symmetric vector quasi-equilibrium problem. Wei-bing Zhang, Nan-jing Huang, and Donal O’Regan Copyright © 2015 Wei-bing Zhang et al. All rights reserved.