Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Complex Differences and Difference Equations Mon, 22 Dec 2014 10:28:21 +0000 http://www.hindawi.com/journals/aaa/2014/124843/ Zong-Xuan Chen, Kwang Ho Shon, and Zhi-Bo Huang Copyright © 2014 Zong-Xuan Chen et al. All rights reserved. Analytic and Harmonic Univalent Functions Mon, 22 Dec 2014 09:45:45 +0000 http://www.hindawi.com/journals/aaa/2014/578214/ V. Ravichandran, Om P. Ahuja, and Rosihan M. Ali Copyright © 2014 V. Ravichandran et al. All rights reserved. Composition Operators from Certain -Bloch Spaces to Spaces Mon, 22 Dec 2014 07:12:25 +0000 http://www.hindawi.com/journals/aaa/2014/892146/ Some necessary and sufficient conditions are established for composition operators to be bounded or compact from μ-Bloch type spaces to spaces. Moreover, the boundedness, compactness, and Fredholmness of composition operators on little spaces are also characterized. Chunyu Tan and Maofa Wang Copyright © 2014 Chunyu Tan and Maofa Wang. All rights reserved. On Parametric Gevrey Asymptotics for Some Cauchy Problems in Quasiperiodic Function Spaces Mon, 22 Dec 2014 06:52:39 +0000 http://www.hindawi.com/journals/aaa/2014/153169/ We investigate Gevrey asymptotics for solutions to nonlinear parameter depending Cauchy problems with 2π-periodic coefficients, for initial data living in a space of quasiperiodic functions. By means of the Borel-Laplace summation procedure, we construct sectorial holomorphic solutions which are shown to share the same formal power series as asymptotic expansion in the perturbation parameter. We observe a small divisor phenomenon which emerges from the quasiperiodic nature of the solutions space and which is the origin of the Gevrey type divergence of this formal series. Our result rests on the classical Ramis-Sibuya theorem which asks to prove that the difference of any two neighboring constructed solutions satisfies some exponential decay. This is done by an asymptotic study of a Dirichlet-like series whose exponents are positive real numbers which accumulate to the origin. A. Lastra and S. Malek Copyright © 2014 A. Lastra and S. Malek. All rights reserved. Theory and Algorithms of Variational Inequality and Equilibrium Problems, and Their Applications Mon, 22 Dec 2014 06:42:41 +0000 http://www.hindawi.com/journals/aaa/2014/969303/ Xie-ping Ding, Nan-jing Huang, Fu-quan Xia, Qing-bang Zhang, and Qamrul Hasan Ansari Copyright © 2014 Xie-ping Ding et al. All rights reserved. Nonlinear Analysis: Algorithm, Convergence, and Applications 2014 Mon, 22 Dec 2014 06:24:32 +0000 http://www.hindawi.com/journals/aaa/2014/912910/ Yisheng Song, Rudong Chen, Guoyin Li, Changsen Yang, and Gaohang Yu Copyright © 2014 Yisheng Song et al. All rights reserved. Nonlinear Analysis of Dynamical Complex Networks 2014 Sun, 21 Dec 2014 14:09:00 +0000 http://www.hindawi.com/journals/aaa/2014/976231/ Zidong Wang, Bo Shen, Hongli Dong, Jun Hu, Xiao He, and Derui Ding Copyright © 2014 Zidong Wang et al. All rights reserved. Analytical and Numerical Approaches for Complicated Nonlinear Equations Sun, 21 Dec 2014 07:56:11 +0000 http://www.hindawi.com/journals/aaa/2014/931294/ Hossein Jafari, Abdon Atangana, Adem Kılıçman, and Muhammad Usman Copyright © 2014 Hossein Jafari et al. All rights reserved. Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type Tue, 16 Dec 2014 06:25:32 +0000 http://www.hindawi.com/journals/aaa/2014/265378/ Let be a space of homogeneous type in the sense of Coifman and Weiss, where the quasi-metric d may have no regularity and the measure μ satisfies only the doubling property. Adapting the recently developed randomized dyadic structures of X and applying orthonormal bases of constructed recently by Auscher and Hytönen, we develop the Besov and Triebel-Lizorkin spaces on such a general setting. In this paper, we establish the wavelet characterizations and provide the dualities for these spaces. The results in this paper extend earlier related results with additional assumptions on the quasi-metric d and the measure μ to the full generality of the theory of these function spaces. Chuang Chen, Ji Li, and Fanghui Liao Copyright © 2014 Chuang Chen et al. All rights reserved. Software Component Selection Based on Quality Criteria Using the Analytic Network Process Mon, 15 Dec 2014 00:10:52 +0000 http://www.hindawi.com/journals/aaa/2014/535970/ Component based software development (CBSD) endeavors to deliver cost-effective and quality software systems through the selection and integration of commercially available software components. CBSD emphasizes the design and development of software systems using preexisting components. Software component reusability is an indispensable part of component based software development life cycle (CBSDLC), which consumes a significant amount of organization’s resources, that is, time and effort. It is convenient in component based software system (CBSS) to select the most suitable and appropriate software components that provide all the required functionalities. Selecting the most appropriate components is crucial for the success of the entire system. However, decisions regarding software component reusability are often made in an ad hoc manner, which ultimately results in schedule delay and lowers the entire quality system. In this paper, we have discussed the analytic network process (ANP) method for software component selection. The methodology is explained and assessed using a real life case study. Shah Nazir, Sajid Anwar, Sher Afzal Khan, Sara Shahzad, Muhammad Ali, Rohul Amin, Muhammad Nawaz, Pavlos Lazaridis, and John Cosmas Copyright © 2014 Shah Nazir et al. All rights reserved. On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation Mon, 15 Dec 2014 00:10:49 +0000 http://www.hindawi.com/journals/aaa/2014/763160/ We consider the numerical solutions of a class of nonlinear (nonstandard) Volterra integral equation. We prove the existence and uniqueness of the one point collocation solutions and the solution by the repeated trapezoidal rule for the nonlinear Volterra integral equation. We analyze the convergence of the collocation methods and the repeated trapezoidal rule. Numerical experiments are used to illustrate theoretical results. H. S. Mamba and M. Khumalo Copyright © 2014 H. S. Mamba and M. Khumalo. All rights reserved. Approximate Solutions of Fractional Riccati Equations Using the Adomian Decomposition Method Sun, 14 Dec 2014 00:11:14 +0000 http://www.hindawi.com/journals/aaa/2014/957590/ The fractional derivative equation has extensively appeared in various applied nonlinear problems and methods for finding the model become a popular topic. Very recently, a novel way was proposed by Duan (2010) to calculate the Adomian series which is a crucial step of the Adomian decomposition method. In this paper, it was used to solve some fractional nonlinear differential equations. Fei Wu and Lan-Lan Huang Copyright © 2014 Fei Wu and Lan-Lan Huang. All rights reserved. Epidemic Model of Leptospirosis Containing Fractional Order Thu, 11 Dec 2014 00:10:45 +0000 http://www.hindawi.com/journals/aaa/2014/317201/ We study an epidemic model of leptospirosis in fractional order numerically. The multistep generalized differential transform method is applied to find the accurate approximate solution of the epidemic model of leptospirosis disease in fractional order. A unique positive solution for the epidemic model in fractional order is presented. For the integer case derivative, the approximate solution of MGDTM is compared with the Runge-Kutta order four scheme. The numerical results are presented for the justification purpose. Muhammad Altaf Khan, S. F. Saddiq, Saeed Islam, Ilyas Khan, and Dennis Ling Chuan Ching Copyright © 2014 Muhammad Altaf Khan et al. All rights reserved. On the Sum of Reciprocal Generalized Fibonacci Numbers Wed, 10 Dec 2014 12:15:17 +0000 http://www.hindawi.com/journals/aaa/2014/402540/ We consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibonacci numbers. Pingzhi Yuan, Zilong He, and Junyi Zhou Copyright © 2014 Pingzhi Yuan et al. All rights reserved. Self-Consistent Density Estimation in the Presence of Errors-in-Variables Wed, 10 Dec 2014 09:46:01 +0000 http://www.hindawi.com/journals/aaa/2014/958702/ This paper considers the estimation of the common probability density of independent and identically distributed variables observed with additive measurement errors. The self-consistent estimator of the density function is constructed when the error distribution is known, and a modification of the self-consistent estimation is proposed when the error distribution is unknown. The consistency properties of the proposed estimators and the upper bounds of the mean square error and mean integrated square error are investigated under some suitable conditions. Simulation studies are carried out to assess the performance of our proposed method and compare with the usual deconvolution kernel method. Two real datasets are analyzed for further illustration. Junhua Zhang, Yuping Hu, and Sanying Feng Copyright © 2014 Junhua Zhang et al. All rights reserved. Nontrivial Solutions of a Class of Kirchhoff Type Problems via Local Linking Method Wed, 10 Dec 2014 00:11:12 +0000 http://www.hindawi.com/journals/aaa/2014/573616/ The existence of nontrivial solutions of Kirchhoff type problems is proved by using the local linking method, and the new results do not require classical compactness conditions. Anmin Mao and Lin Zhang Copyright © 2014 Anmin Mao and Lin Zhang. All rights reserved. Global Exponential Stability of Weighted Pseudo-Almost Periodic Solutions of Neutral Type High-Order Hopfield Neural Networks with Distributed Delays Wed, 03 Dec 2014 06:39:01 +0000 http://www.hindawi.com/journals/aaa/2014/506256/ Some sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of weighted pseudo-almost periodic solutions to a class of neutral type high-order Hopfield neural networks with distributed delays by employing fixed point theorem and differential inequality techniques. The results of this paper are new and they complement previously known results. Moreover, an example is given to show the effectiveness of the proposed method and results. Lili Zhao and Yongkun Li Copyright © 2014 Lili Zhao and Yongkun Li. All rights reserved. Likelihood Inference of Nonlinear Models Based on a Class of Flexible Skewed Distributions Wed, 03 Dec 2014 00:10:24 +0000 http://www.hindawi.com/journals/aaa/2014/542985/ This paper deals with the issue of the likelihood inference for nonlinear models with a flexible skew-t-normal (FSTN) distribution, which is proposed within a general framework of flexible skew-symmetric (FSS) distributions by combining with skew-t-normal (STN) distribution. In comparison with the common skewed distributions such as skew normal (SN), and skew-t (ST) as well as scale mixtures of skew normal (SMSN), the FSTN distribution can accommodate more flexibility and robustness in the presence of skewed, heavy-tailed, especially multimodal outcomes. However, for this distribution, a usual approach of maximum likelihood estimates based on EM algorithm becomes unavailable and an alternative way is to return to the original Newton-Raphson type method. In order to improve the estimation as well as the way for confidence estimation and hypothesis test for the parameters of interest, a modified Newton-Raphson iterative algorithm is presented in this paper, based on profile likelihood for nonlinear regression models with FSTN distribution, and, then, the confidence interval and hypothesis test are also developed. Furthermore, a real example and simulation are conducted to demonstrate the usefulness and the superiority of our approach. Xuedong Chen, Qianying Zeng, and Qiankun Song Copyright © 2014 Xuedong Chen et al. All rights reserved. An Automatic Quadrature Schemes and Error Estimates for Semibounded Weighted Hadamard Type Hypersingular Integrals Mon, 01 Dec 2014 06:47:12 +0000 http://www.hindawi.com/journals/aaa/2014/387246/ The approximate solutions for the semibounded Hadamard type hypersingular integrals (HSIs) for smooth density function are investigated. The automatic quadrature schemes (AQSs) are constructed by approximating the density function using the third and fourth kinds of Chebyshev polynomials. Error estimates for the semibounded solutions are obtained in the class of . Numerical results for the obtained quadrature schemes revealed that the proposed methods are highly accurate when the density function is any polynomial or rational functions. The results are in line with the theoretical findings. Sirajo Lawan Bichi, Z. K. Eshkuvatov, and N. M. A. Nik Long Copyright © 2014 Sirajo Lawan Bichi et al. All rights reserved. A New Method for Solving Supervised Data Classification Problems Thu, 27 Nov 2014 13:14:23 +0000 http://www.hindawi.com/journals/aaa/2014/318478/ Supervised data classification is one of the techniques used to extract nontrivial information from data. Classification is a widely used technique in various fields, including data mining, industry, medicine, science, and law. This paper considers a new algorithm for supervised data classification problems associated with the cluster analysis. The mathematical formulations for this algorithm are based on nonsmooth, nonconvex optimization. A new algorithm for solving this optimization problem is utilized. The new algorithm uses a derivative-free technique, with robustness and efficiency. To improve classification performance and efficiency in generating classification model, a new feature selection algorithm based on techniques of convex programming is suggested. Proposed methods are tested on real-world datasets. Results of numerical experiments have been presented which demonstrate the effectiveness of the proposed algorithms. Parvaneh Shabanzadeh and Rubiyah Yusof Copyright © 2014 Parvaneh Shabanzadeh and Rubiyah Yusof. All rights reserved. Secure OpenID Authentication Model by Using Trusted Computing Thu, 27 Nov 2014 08:33:09 +0000 http://www.hindawi.com/journals/aaa/2014/561487/ The growth of Internet online services has been very quick in recent years. Each online service requires Internet users to create a new account to use the service. The problem can be seen when each user usually needs more than one service and, consequently, has numerous accounts. These numerous accounts have to be managed in a secure and simple way to be protected against identity theft. Single sign-on (SSO) and OpenID have been used to decrease the complexity of managing numerous accounts required in the Internet identity environment. Trusted Platform Module (TPM) and Trust Multitenancy are great trusted computing-based technologies to solve security concerns in the Internet identity environment. Since trust is one of the pillars of security in the cloud, this paper analyzes the existing cloud identity techniques in order to investigate their strengths and weaknesses. This paper proposes a model in which One Time Password (OTP), TPM, and OpenID are used to provide a solution against phishing as a common identity theft in cloud environment. E. Ghazizadeh, Z. S. Shams Dolatabadi, R. Khaleghparast, M. Zamani, A. A. Manaf, and M. S. Abdullah Copyright © 2014 E. Ghazizadeh et al. All rights reserved. Assessment of an Average Controller for a DC/DC Converter via Either a PWM or a Sigma-Delta-Modulator Wed, 26 Nov 2014 08:59:38 +0000 http://www.hindawi.com/journals/aaa/2014/196010/ Sliding mode control is a discontinuous control technique that is, by its nature, appropriate for controlling variable structure systems, such as the switch regulated systems employed in power electronics. However, when designing control laws based on the average models of these systems a modulator is necessary for their experimental implementation. Among the most widely used modulators in power electronics are the pulse width modulation (PWM) and, more recently, the sigma-delta-modulator (-modulator). Based on the importance of achieving an appropriate implementation of average control laws and the relevance of the trajectory tracking task in DC/DC power converters, for the first time, this research presents the assessment of the experimental results obtained when one of these controllers is implemented through either a PWM or a -modulator to perform such a task. A comparative assessment based on the integral square error (ISE) index shows that, at frequencies with similar efficiency, the -modulator provides a better tracking performance for the DC/DC Buck converter. In this paper, an average control based on differential flatness was used to perform the experiments. It is worth mentioning that a different trajectory tracking controller could have been selected for this research. R. Silva-Ortigoza, F. Carrizosa-Corral, J. J. Gálvez-Gamboa, M. Marcelino-Aranda, D. Muñoz-Carrillo, and H. Taud Copyright © 2014 R. Silva-Ortigoza et al. All rights reserved. Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables Tue, 25 Nov 2014 11:14:25 +0000 http://www.hindawi.com/journals/aaa/2014/619035/ Leptospirosis is an infectious disease that damages the liver and kidneys, found mainly in dogs and farm animals and caused by bacteria. In this paper, we present the optimal control problem applied to a dynamical leptospirosis infected vector and human population by using multiple control variables. First, we show the existence of the control problem and then use analytical and numerical techniques to investigate the existence cost effective control efforts for prevention of indirect and direct transmission of this disease. In order to do this, we consider three control functions two for human and one for vector population. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method. Muhammad Altaf Khan, Saeed Islam, Sher Afzal Khan, Ilyas Khan, Sharidan Shafie, and Taza Gul Copyright © 2014 Muhammad Altaf Khan et al. All rights reserved. Combining Interval Branch and Bound and Stochastic Search Mon, 24 Nov 2014 13:46:16 +0000 http://www.hindawi.com/journals/aaa/2014/861765/ This paper presents global optimization algorithms that incorporate the idea of an interval branch and bound and the stochastic search algorithms. Two algorithms for unconstrained problems are proposed, the hybrid interval simulated annealing and the combined interval branch and bound and genetic algorithm. The numerical experiment shows better results compared to Hansen’s algorithm and simulated annealing in terms of the storage, speed, and number of function evaluations. The convergence proof is described. Moreover, the idea of both algorithms suggests a structure for an integrated interval branch and bound and genetic algorithm for constrained problems in which the algorithm is described and tested. The aim is to capture one of the solutions with higher accuracy and lower cost. The results show better quality of the solutions with less number of function evaluations compared with the traditional GA. Dhiranuch Bunnag Copyright © 2014 Dhiranuch Bunnag. All rights reserved. An Analysis of Relationship among Income Inequality, Poverty, and Income Mobility, Based on Distribution Functions Mon, 24 Nov 2014 07:37:28 +0000 http://www.hindawi.com/journals/aaa/2014/186564/ Many studies show that the relationship among income inequality, poverty, and income mobility needs to be further discussed. Meanwhile, some researches on Distribution Function offer new perspective and methods to analyze this issue. First, this paper expresses the relationship among the Gini coefficient, poverty ratio, and income mobility of 5 common Distribution Functions through math deduction; this finding cannot be found in relevant literatures. Furthermore, an empirical research result proves that the income distribution of urban residents in the period from 2005 to 2010 fits Log-Logistic Distribution. On the basis of the above analysis and empirical data, the paper explores the relations of income inequality, poverty, and income mobility of urban residents and draws some useful conclusions. Jiandong Chen, Yaqing Si, Fengying Li, and Aifeng Zhao Copyright © 2014 Jiandong Chen et al. All rights reserved. Blow-Up Solutions and Global Solutions to Discrete -Laplacian Parabolic Equations Mon, 24 Nov 2014 07:27:14 +0000 http://www.hindawi.com/journals/aaa/2014/351675/ We discuss the conditions under which blow-up occurs for the solutions of discrete -Laplacian parabolic equations on networks with boundary as follows: , ; , ; , where , , , and the initial data is nontrivial on . The main theorem states that the solution to the above equation satisfies the following: (i) if and , then the solution blows up in a finite time, provided , where and ; (ii) if , then the nonnegative solution is global; (iii) if , then the solution is global. In order to prove the main theorem, we first derive the comparison principles for the solution of the equation above, which play an important role throughout this paper. Moreover, when the solution blows up, we give an estimate for the blow-up time and also provide the blow-up rate. Finally, we give some numerical illustrations which exploit the main results. Soon-Yeong Chung and Min-Jun Choi Copyright © 2014 Soon-Yeong Chung and Min-Jun Choi. All rights reserved. Automatic Gauge Control in Rolling Process Based on Multiple Smith Predictor Models Mon, 24 Nov 2014 07:16:30 +0000 http://www.hindawi.com/journals/aaa/2014/872418/ Automatic rolling process is a high-speed system which always requires high-speed control and communication capabilities. Meanwhile, it is also a typical complex electromechanical system; distributed control has become the mainstream of computer control system for rolling mill. Generally, the control system adopts the 2-level control structure—basic automation (Level 1) and process control (Level 2)—to achieve the automatic gauge control. In Level 1, there is always a certain distance between the roll gap of each stand and the thickness testing point, leading to the time delay of gauge control. Smith predictor is a method to cope with time-delay system, but the practical feedback control based on traditional Smith predictor cannot get the ideal control result, because the time delay is hard to be measured precisely and in some situations it may vary in a certain range. In this paper, based on adaptive Smith predictor, we employ multiple models to cover the uncertainties of time delay. The optimal model will be selected by the proposed switch mechanism. Simulations show that the proposed multiple Smith model method exhibits excellent performance in improving the control result even for system with jumping time delay. Jiangyun Li, Kang Wang, and Yang Li Copyright © 2014 Jiangyun Li et al. All rights reserved. Low-Rank Representation-Based Object Tracking Using Multitask Feature Learning with Joint Sparsity Sun, 23 Nov 2014 13:19:02 +0000 http://www.hindawi.com/journals/aaa/2014/147353/ We address object tracking problem as a multitask feature learning process based on low-rank representation of features with joint sparsity. We first select features with low-rank representation within a number of initial frames to obtain subspace basis. Next, the features represented by the low-rank and sparse property are learned using a modified joint sparsity-based multitask feature learning framework. Both the features and sparse errors are then optimally updated using a novel incremental alternating direction method. The low-rank minimization problem for learning multitask features can be achieved by a few sequences of efficient closed form update process. Since the proposed method attempts to perform the feature learning problem in both multitask and low-rank manner, it can not only reduce the dimension but also improve the tracking performance without drift. Experimental results demonstrate that the proposed method outperforms existing state-of-the-art tracking methods for tracking objects in challenging image sequences. Hyuncheol Kim and Joonki Paik Copyright © 2014 Hyuncheol Kim and Joonki Paik. All rights reserved. On One 2-Valued Transformation: Its Invariant Measure and Application to Masked Dynamical Systems Wed, 19 Nov 2014 08:12:55 +0000 http://www.hindawi.com/journals/aaa/2014/513061/ We consider one family of 2-valued transformations on the interval [0, 1] with measure , endowed with a set of weight functions. We construct invariant measure for this multivalued dynamical system with weights and show the interplay between such systems and masked dynamical systems, which leads to image processing. P. I. Troshin Copyright © 2014 P. I. Troshin. All rights reserved. Bifurcation Structure in a Bimodal Piecewise Linear Business Cycle Model Wed, 19 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/401319/ We study the bifurcation structure of the parameter space of a 1D continuous piecewise linear bimodal map which describes dynamics of a business cycle model introduced by Day-Shafer. In particular, we obtain the analytical expression of the boundaries of several periodicity regions associated with attracting cycles of the map (principal cycles and related fin structure). By crossing these boundaries the map displays robust chaos. Viktor Avrutin, Iryna Sushko, and Fabio Tramontana Copyright © 2014 Viktor Avrutin et al. All rights reserved.