Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Solving Nonstiff Higher-Order Ordinary Differential Equations Using 2-Point Block Method Directly Wed, 17 Sep 2014 08:52:12 +0000 http://www.hindawi.com/journals/aaa/2014/867095/ We describe the development of a 2-point block backward difference method (2PBBD) for solving system of nonstiff higher-order ordinary differential equations (ODEs) directly. The method computes the approximate solutions at two points simultaneously within an equidistant block. The integration coefficients that are used in the method are obtained only once at the start of the integration. Numerical results are presented to compare the performances of the method developed with 1-point backward difference method (1PBD) and 2-point block divided difference method (2PBDD). The result indicated that, for finer step sizes, this method performs better than the other two methods, that is, 1PBD and 2PBDD. Hazizah Mohd Ijam, Mohamed Suleiman, Ahmad Fadly Nurullah Rasedee, Norazak Senu, Ali Ahmadian, and Soheil Salahshour Copyright © 2014 Hazizah Mohd Ijam et al. All rights reserved. A New Iterative Method for Finding Approximate Inverses of Complex Matrices Sun, 14 Sep 2014 12:01:56 +0000 http://www.hindawi.com/journals/aaa/2014/563787/ This paper presents a new iterative method for computing the approximate inverse of nonsingular matrices. The analytical discussion of the method is included to demonstrate its convergence behavior. As a matter of fact, it is proven that the suggested scheme possesses tenth order of convergence. Finally, its performance is illustrated by numerical examples on different matrices. M. Kafaei Razavi, A. Kerayechian, M. Gachpazan, and S. Shateyi Copyright © 2014 M. Kafaei Razavi et al. All rights reserved. Function Spaces, Compact Operators, and Their Applications Sun, 14 Sep 2014 11:03:39 +0000 http://www.hindawi.com/journals/aaa/2014/342194/ S. A. Mohiuddine, M. Mursaleen, Adem Kiliçman, and Abdullah Alotaibi Copyright © 2014 S. A. Mohiuddine et al. All rights reserved. A Variance Shift Model for Detection of Outliers in the Linear Measurement Error Model Sun, 14 Sep 2014 07:44:07 +0000 http://www.hindawi.com/journals/aaa/2014/396875/ We present a variance shift model for a linear measurement error model using the corrected likelihood of Nakamura (1990). This model assumes that a single outlier arises from an observation with inflated variance. The corrected likelihood ratio and the score test statistics are proposed to determine whether the th observation has an inflated variance. A parametric bootstrap procedure is used to obtain empirical distributions of the test statistics and a simulation study has been used to show the performance of proposed tests. Finally, a real data example is given for illustration. Babak Babadi, Abdolrahman Rasekh, Ali Akbar Rasekhi, Karim Zare, and Mohammad Reza Zadkarami Copyright © 2014 Babak Babadi et al. All rights reserved. Mathematical Methods and Models in the Natural to the Life Sciences Thu, 11 Sep 2014 09:42:50 +0000 http://www.hindawi.com/journals/aaa/2014/706858/ Rehana Naz, Igor Leite Freire, Imran Naeem, and Mariano Torrisi Copyright © 2014 Rehana Naz et al. All rights reserved. Continuity of the Restriction Maps on Smirnov Classes Thu, 11 Sep 2014 08:28:35 +0000 http://www.hindawi.com/journals/aaa/2014/102169/ We prove the restriction maps define continuous linear operators on the Smirnov classes for some certain domain with analytic boundary. Yüksel Soykan Copyright © 2014 Yüksel Soykan. All rights reserved. A Proof of Łojasiewicz’s Theorem Thu, 11 Sep 2014 07:58:34 +0000 http://www.hindawi.com/journals/aaa/2014/695617/ We give a necessary and sufficient condition for a primitive of a distribution to have the value at a point in the sense of Łojasiewicz. A formula defining the indefinite integral of a distribution with a basepoint is introduced, and further structural results are discussed. Namhoon Kim Copyright © 2014 Namhoon Kim. All rights reserved. A New Difference Sequence Set of Order and Its Geometrical Properties Thu, 11 Sep 2014 06:17:23 +0000 http://www.hindawi.com/journals/aaa/2014/278907/ We introduce a new class of sequences named as and, for this space, we study some inclusion relations, topological properties, and geometrical properties such as order continuous, the Fatou property, and the Banach-Saks property of type . Mikail Et and Vatan Karakaya Copyright © 2014 Mikail Et and Vatan Karakaya. All rights reserved. Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme Thu, 11 Sep 2014 06:02:40 +0000 http://www.hindawi.com/journals/aaa/2014/809431/ We present the Cauchy-Maruyama (CM) approximation scheme and establish the existence theory of stochastic functional differential equations driven by G-Brownian motion (G-SFDEs). Several useful properties of Cauchy-Maruyama (CM) approximate solutions of G-SFDEs are given. We show that the unique solution of G-SFDEs gets convergence from Cauchy-Maruyama (CM) approximate solutions. The existence theorem for G-SFDEs is developed with the above mentioned scheme. Faiz Faizullah Copyright © 2014 Faiz Faizullah. All rights reserved. A Note on the Use of Generalized Sundman Anomalies in the Numerical Integration of the Elliptical Orbital Motion Thu, 11 Sep 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/691926/ The orbital motion around a central body is an interesting problem that involves the theory of artificial satellites and the planetary theories in the solar system. Nevertheless some difficult situations appear while studying this apparently simple problem, depending on each particular case. The real problem consists of searching the perturbed solution from a basic two-body motion problem. In addition, the perturbed problem must be solved using a numerical method and its efficiency depends on the selected coordinate system and the corresponding time. In fact, local and global errors are not necessarily homogeneously distributed over the orbit. In other words, there is a strong relationship between the spatial distribution of the selected points and the temporal independent variable. This is particularly dramatic in specially difficult cases. This issue leads us to consider different anomalies as temporal variables, searching for both precision and efficiency. Therefore, we are interested in the study of techniques to integrate the orbital motion equations using different anomalies as temporal variables which are functions of one or more parameters. The final aim of this paper is the minimization of the integration errors using an appropriate choice of the parameter depending on the eccentricity value in the family of the generalized Sundman anomalies. José Antonio López Ortí, Francisco José Marco Castillo, and María José Martínez Usó Copyright © 2014 José Antonio López Ortí et al. All rights reserved. Perturbation of -Isometries by Nilpotent Operators Tue, 09 Sep 2014 09:00:12 +0000 http://www.hindawi.com/journals/aaa/2014/745479/ We prove that if is an -isometry on a Hilbert space and an -nilpotent operator commuting with , then is a -isometry. Moreover, we show that a similar result for -isometries on Banach spaces is not true. Teresa Bermúdez, Antonio Martinón, Vladimir Müller, and Juan Agustín Noda Copyright © 2014 Teresa Bermúdez et al. All rights reserved. Radius Constants for Functions with the Prescribed Coefficient Bounds Tue, 09 Sep 2014 08:17:12 +0000 http://www.hindawi.com/journals/aaa/2014/454152/ For an analytic univalent function in the unit disk, it is well-known that for . But the inequality does not imply the univalence of . This motivated several authors to determine various radii constants associated with the analytic functions having prescribed coefficient bounds. In this paper, a survey of the related work is presented for analytic and harmonic mappings. In addition, we establish a coefficient inequality for sense-preserving harmonic functions to compute the bounds for the radius of univalence, radius of full starlikeness/convexity of order   () for functions with prescribed coefficient bound on the analytic part. Om P. Ahuja, Sumit Nagpal, and V. Ravichandran Copyright © 2014 Om P. Ahuja et al. All rights reserved. Design and Study of Cognitive Network Physical Layer Simulation Platform Thu, 04 Sep 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/408032/ Cognitive radio technology has received wide attention for its ability to sense and use idle frequency. IEEE 802.22 WRAN, the first to follow the standard in cognitive radio technology, is featured by spectrum sensing and wireless data transmission. As far as wireless transmission is concerned, the availability and implementation of a mature and robust physical layer algorithm are essential to high performance. For the physical layer of WRAN using OFDMA technology, this paper proposes a synchronization algorithm and at the same time provides a public platform for the improvement and verification of that new algorithm. The simulation results show that the performance of the platform is highly close to the theoretical value. Yongli An, Dong Wang, and Yang Xiao Copyright © 2014 Yongli An et al. All rights reserved. Robust Nonfragile Filtering for Uncertain T-S Fuzzy Systems with Interval Delay: A New Delay Partitioning Approach Wed, 03 Sep 2014 13:44:07 +0000 http://www.hindawi.com/journals/aaa/2014/523462/ This paper investigates the problem of robust nonfragile fuzzy filtering for uncertain Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Attention is focused on the design of a filter such that the filtering error system preserves a prescribed performance, where the filter to be designed is assumed to have gain perturbations. By developing a delay decomposition approach, both lower and upper bound information of the delayed plant states can be taken into full consideration; the proposed delay-fractional-dependent stability condition for the filter error systems is obtained based on the direct Lyapunov method allied with an appropriate and variable Lyapunov-Krasovskii functional choice and with tighter upper bound of some integral terms in the derivation process. Then, a new robust nonfragile fuzzy filter scheme is proposed, and a sufficient condition for the existence of such a filter is established in terms of linear matrix inequalities (LMIs). Finally, some numerical examples are utilized to demonstrate the effectiveness and reduced conservatism of the proposed approach. Xianzhong Xia, Renfa Li, and Jiyao An Copyright © 2014 Xianzhong Xia et al. All rights reserved. On the Fekete and Szegö Problem for the Class of Starlike Mappings in Several Complex Variables Wed, 03 Sep 2014 11:17:05 +0000 http://www.hindawi.com/journals/aaa/2014/807026/ Let be the familiar class of normalized univalent functions in the unit disk. Fekete and Szegö proved the well-known result for . We investigate the corresponding problem for the class of starlike mappings defined on the unit ball in a complex Banach space or on the unit polydisk in , which satisfies a certain condition. Qing-Hua Xu and Tai-Shun Liu Copyright © 2014 Qing-Hua Xu and Tai-Shun Liu. All rights reserved. Dynamics of the Oxygen, Carbon Dioxide, and Water Interaction across the Insect Spiracle Wed, 03 Sep 2014 09:33:08 +0000 http://www.hindawi.com/journals/aaa/2014/157573/ This paper explores the dynamics of respiratory gases interactions which are accompanied by the loss of water through an insect’s spiracle. Here we investigate and analyze this interaction by deriving a system of ordinary differential equations for oxygen, carbon dioxide, and water vapor. The analysis is carried out in continuous time. The purpose of the research is to determine bounds for the gas volumes and to discuss the complexity and stability of the equilibria. Numerical simulations also demonstrate the dynamics of our model utilizing the new conditions for stability and instability. S. M. Simelane, S. Abelman, and F. D. Duncan Copyright © 2014 S. M. Simelane et al. All rights reserved. On the Incidence Energy of Some Toroidal Lattices Mon, 01 Sep 2014 09:36:12 +0000 http://www.hindawi.com/journals/aaa/2014/568153/ The incidence energy , defined as the sum of the singular values of the incidence matrix of , is a much studied quantity with well known applications in chemical physics. In this paper, we derived the closed-form formulae expressing the incidence energy of the 3.12.12 lattice, triangular kagomé lattice, and lattice, respectively. Simultaneously, the explicit asymptotic values of the incidence energy in these lattices are obtained by utilizing the applications of analysis method with the help of software calculation. Jia-Bao Liu, Jinde Cao, and Jin Xie Copyright © 2014 Jia-Bao Liu et al. All rights reserved. Notes on Convergence Properties for a Smoothing-Regularization Approach to Mathematical Programs with Vanishing Constraints Mon, 01 Sep 2014 05:44:06 +0000 http://www.hindawi.com/journals/aaa/2014/715015/ We give some improved convergence results about the smoothing-regularization approach to mathematical programs with vanishing constraints (MPVC for short), which is proposed in Achtziger et al. (2013). We show that the Mangasarian-Fromovitz constraints qualification for the smoothing-regularization problem still holds under the VC-MFCQ (see Definition 5) which is weaker than the VC-LICQ (see Definition 7) and the condition of asymptotic nondegeneracy. We also analyze the convergence behavior of the smoothing-regularization method and prove that any accumulation point of a sequence of stationary points for the smoothing-regularization problem is still strongly-stationary under the VC-MFCQ and the condition of asymptotic nondegeneracy. Qingjie Hu, Yu Chen, Zhibin Zhu, and Bishan Zhang Copyright © 2014 Qingjie Hu et al. All rights reserved. Uniform Exponential Stability of Discrete Evolution Families on Space of -Periodic Sequences Sun, 31 Aug 2014 11:55:15 +0000 http://www.hindawi.com/journals/aaa/2014/784289/ We prove that the discrete system is uniformly exponentially stable if and only if the unique solution of the Cauchy problem , , is bounded for any real number and any -periodic sequence with . Here, is a sequence of bounded linear operators on Banach space . Yongfang Wang, Akbar Zada, Nisar Ahmad, Dhaou Lassoued, and Tongxing Li Copyright © 2014 Yongfang Wang et al. All rights reserved. Steepest-Descent Approach to Triple Hierarchical Constrained Optimization Problems Sun, 31 Aug 2014 10:50:52 +0000 http://www.hindawi.com/journals/aaa/2014/264965/ We introduce and analyze a hybrid steepest-descent algorithm by combining Korpelevich’s extragradient method, the steepest-descent method, and the averaged mapping approach to the gradient-projection algorithm. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to the unique solution of a triple hierarchical constrained optimization problem (THCOP) over the common fixed point set of finitely many nonexpansive mappings, with constraints of finitely many generalized mixed equilibrium problems (GMEPs), finitely many variational inclusions, and a convex minimization problem (CMP) in a real Hilbert space. Lu-Chuan Ceng, Cheng-Wen Liao, Chin-Tzong Pang, and Ching-Feng Wen Copyright © 2014 Lu-Chuan Ceng et al. All rights reserved. Robust Control for a Class of Discrete Time-Delay Stochastic Systems with Randomly Occurring Nonlinearities Sun, 31 Aug 2014 07:58:15 +0000 http://www.hindawi.com/journals/aaa/2014/170794/ In this paper, we consider the robust control problem for a class of discrete time-delay stochastic systems with randomly occurring nonlinearities. The parameter uncertainties enter all the system matrices; the stochastic disturbances are both state and control dependent, and the randomly occurring nonlinearities obey the sector boundedness conditions. The purpose of the problem addressed is to design a state feedback controller such that, for all admissible uncertainties, nonlinearities, and time delays, the closed-loop system is robustly asymptotically stable in the mean square, and a prescribed disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and stochastic analysis tools, a linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the existence of the desired controllers, where the conditions are dependent on the lower and upper bounds of the time-varying delays. The explicit parameterization of the desired controller gains is also given. Finally, a numerical example is exploited to show the usefulness of the results obtained. Yamin Wang, Fuad E. Alsaadi, Stanislao Lauria, and Yurong Liu Copyright © 2014 Yamin Wang et al. All rights reserved. Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4+ T-cells Sun, 31 Aug 2014 07:41:40 +0000 http://www.hindawi.com/journals/aaa/2014/838396/ This paper deals with stability and Hopf bifurcation analyses of a mathematical model of HIV infection of T-cells. The model is based on a system of delay differential equations with logistic growth term and antiretroviral treatment with a discrete time delay, which plays a main role in changing the stability of each steady state. By fixing the time delay as a bifurcation parameter, we get a limit cycle bifurcation about the infected steady state. We study the effect of the time delay on the stability of the endemically infected equilibrium. We derive explicit formulae to determine the stability and direction of the limit cycles by using center manifold theory and normal form method. Numerical simulations are presented to illustrate the results. P. Balasubramaniam, M. Prakash, Fathalla A. Rihan, and S. Lakshmanan Copyright © 2014 P. Balasubramaniam et al. All rights reserved. Formal and Executable Specification of Random Waypoint Mobility Model Using Timed Coloured Petri Nets for WMN Sun, 31 Aug 2014 07:05:44 +0000 http://www.hindawi.com/journals/aaa/2014/798927/ The wireless mesh network (WMN) is an emerging and cost-effective alternative paradigm for the next generation wireless networks in many diverse applications. In the performance evaluation of routing protocol for the WMN, it is essential that it should be evaluated under realistic conditions. The usefulness of specific mobility protocol can be determined by selection of mobility model. This paper introduces a coloured Petri nets (CP-nets) based formal model for implementation, simulation, and analysis of most widely used random waypoint (RWP) mobility model for WMNs. The formal semantics of hierarchical timed CP-nets allow us to investigate the terminating behavior of the transitions using state space analysis techniques. The proposed implementation improves the RWP mobility model by removing the “border effect” and resolves the “speed decay” problem. Naeem Akhtar Khan, Farooq Ahmad, and Sher Afzal Khan Copyright © 2014 Naeem Akhtar Khan et al. All rights reserved. Scaling, Self-Similarity, and Systems of Fractional Order Sun, 31 Aug 2014 07:03:36 +0000 http://www.hindawi.com/journals/aaa/2014/843018/ Carlo Cattani, Martin Ehler, Ming Li, Zhiwu Liao, and Mohammadreza Hooshmandasl Copyright © 2014 Carlo Cattani et al. All rights reserved. Gaussian Fibonacci Circulant Type Matrices Sun, 31 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/592782/ Circulant matrices have become important tools in solving integrable system, Hamiltonian structure, and integral equations. In this paper, we prove that Gaussian Fibonacci circulant type matrices are invertible matrices for and give the explicit determinants and the inverse matrices. Furthermore, the upper bounds for the spread on Gaussian Fibonacci circulant and left circulant matrices are presented, respectively. Zhaolin Jiang, Hongxia Xin, and Fuliang Lu Copyright © 2014 Zhaolin Jiang et al. All rights reserved. Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks Thu, 28 Aug 2014 15:27:17 +0000 http://www.hindawi.com/journals/aaa/2014/419850/ We prove that a homeomorphism is a quasiconformal mapping if and only if is an arcwise connected domain for any arcwise connected domain , and is a quasidisk if and only if both and its exterior are arcwise connected domains. Yu-Ming Chu Copyright © 2014 Yu-Ming Chu. All rights reserved. Improvement of the Asymptotic Properties of Zero Dynamics for Sampled-Data Systems in the Case of a Time Delay Thu, 28 Aug 2014 12:24:11 +0000 http://www.hindawi.com/journals/aaa/2014/817534/ It is well known that the existence of unstable zero dynamics is recognized as a major barrier in many control systems, and deeply limits the achievable control performance. When a continuous-time system with relative degree greater than or equal to three is discretized using a zero-order hold (ZOH), at least one of the zero dynamics of the resulting sampled-data model is obviously unstable for sufficiently small sampling periods, irrespective of whether they involve time delay or not. Thus, attention is here focused on continuous-time systems with time delay and relative degree two. This paper analyzes the asymptotic behavior of zero dynamics for the sampled-data models corresponding to the continuous-time systems mentioned above, and further gives an approximate expression of the zero dynamics in the form of a power series expansion up to the third order term of sampling period. Meanwhile, the stability of the zero dynamics is discussed for sufficiently small sampling periods and a new stability condition is also derived. The ideas presented here generalize well-known results from the delay-free control system to time-delay case. Cheng Zeng, Shan Liang, Jiaqi Zhong, and Yingying Su Copyright © 2014 Cheng Zeng et al. All rights reserved. Finite and Infinite Arithmetic Progressions Related to Beta-Expansion Thu, 28 Aug 2014 11:44:35 +0000 http://www.hindawi.com/journals/aaa/2014/678769/ Let and be the -expansion of . Denote by the set of positions where the digit 1 appears in . We consider the sets of points such that contains arbitrarily long arithmetic progressions and includes infinite arithmetic progressions, respectively. Their sizes are investigated from the topological, metric, and dimensional viewpoints. Bing Li and Chao Ma Copyright © 2014 Bing Li and Chao Ma. All rights reserved. Global Existence of Solution to Initial Boundary Value Problem for Bipolar Navier-Stokes-Poisson System Thu, 28 Aug 2014 11:32:51 +0000 http://www.hindawi.com/journals/aaa/2014/214546/ This paper concerns initial boundary value problem for 3-dimensional compressible bipolar Navier-Stokes-Poisson equations with density-dependent viscosities. When the initial data is large, discontinuous, and spherically symmetric, we prove the global existence of the weak solution. Jian Liu and Haidong Liu Copyright © 2014 Jian Liu and Haidong Liu. All rights reserved. Wave Breaking Phenomenon for DGH Equation with Strong Dissipation Thu, 28 Aug 2014 11:28:10 +0000 http://www.hindawi.com/journals/aaa/2014/169423/ The present work is mainly concerned with the Dullin-Gottwald-Holm (DGH) equation with strong dissipative term. We establish some sufficient conditions to guarantee finite time blow-up of strong solutions. Zhengguang Guo and Min Zhao Copyright © 2014 Zhengguang Guo and Min Zhao. All rights reserved.