Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Lattice Boltzmann Simulation of Multiple Bubbles Motion under Gravity Mon, 06 Jul 2015 11:06:33 +0000 http://www.hindawi.com/journals/aaa/2015/706034/ The motion of multiple bubbles under gravity in two dimensions is numerically studied through the lattice Boltzmann method for the Eotvos number ranging from 1 to 12. Two kinds of initial arrangement are taken into account: vertical and horizontal arrangement. In both cases the effects of Eotvos number on the bubble coalescence and rising velocity are investigated. For the vertical arrangement, it has been found that the coalescence pattern is similar. The first coalescence always takes place between the two uppermost bubbles. And the last coalescence always takes place between the coalesced bubble and the bottommost bubble. For four bubbles in a horizontal arrangement, the outermost bubbles travel into the wake of the middle bubbles in all cases, which allows the bubbles to coalesce. The coalescence pattern is more complex for the case of eight bubbles, which strongly depends on the Eotvos number. Deming Nie, Jianzhong Lin, Limin Qiu, and Xiaobin Zhang Copyright © 2015 Deming Nie et al. All rights reserved. Numerical Simulation of Wind-Driven Circulation in a Thermally Stratified Flow Mon, 06 Jul 2015 09:59:31 +0000 http://www.hindawi.com/journals/aaa/2015/727315/ The closed water bodies, such as reservoirs and lakes, can be polluted by an inflow of pollutants in the upstream as well as a stratification caused by seasonal natural phenomena. The vertical circulation particularly plays an important role in reducing environmental pollutants. The factors of the vertical circulation are the temperature, wind, thermal diffusivity, sunlight, and so on. The wind is the most significant factor among all possible factors causing the vertical circulation. Thus, it is necessary to describe the validation and application of a three-dimensional numerical model of wind-driven circulation in a thermally stratified flow. In this study, the numerical model is conducted in three steps to calculate the velocity components from the momentum equations in x- and y-directions, the elevations from the free surface equation, and the temperature from the scalar transport equation. The present model was applied to two tests for verification of the numerical accuracy. Numerical results are compared with analytical solutions of the sloshing free surface movement in a rectangular basin and the model is applied to the circulation for the wind-driven flow in a thermal stratification. Consequently, the developed model is validated by two verifications and phenomena of the internal flow. Jin Woo Lee, He-Rin Cho, and Yong-Sik Cho Copyright © 2015 Jin Woo Lee et al. All rights reserved. Boundary Criteria for the Stability of Delay Differential-Algebraic Equations Wed, 01 Jul 2015 10:24:15 +0000 http://www.hindawi.com/journals/aaa/2015/768345/ This paper is concerned with the asymptotic stability of delay differential-algebraic equations. Two stability criteria described by evaluating a corresponding harmonic analytical function on the boundary of a certain region are presented. Stability regions are also presented so as to show the method geometrically. Our results are not reported. Leping Sun and Yuhao Cong Copyright © 2015 Leping Sun and Yuhao Cong. All rights reserved. Mathematical Model of MDR-TB and XDR-TB with Isolation and Lost to Follow-Up Mon, 29 Jun 2015 06:29:58 +0000 http://www.hindawi.com/journals/aaa/2015/828461/ We present a deterministic model with isolation and lost to follow-up for the transmission dynamics of three strains of Mycobacterium tuberculosis (TB), namely, the drug sensitive, multi-drug-resistant (MDR), and extensively-drug-resistant (XDR) TB strains. The model is analyzed to gain insights into the qualitative features of its associated equilibria. Some of the theoretical and epidemiological findings indicate that the model has locally asymptotically stable (LAS) disease-free equilibrium when the associated reproduction number is less than unity. Furthermore, the model undergoes in the presence of disease reinfection the phenomenon of backward bifurcation, where the stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number is less than unity. Further analysis of the model indicates that the disease-free equilibrium is globally asymptotically stable (GAS) in the absence of disease reinfection. The result of the global sensitivity analysis indicates that the dominant parameters are the disease progression rate, the recovery rate, the infectivity parameter, the isolation rate, the rate of lost to follow-up, and fraction of fast progression rates. Our results also show that increase in isolation rate leads to a decrease in the total number of individuals who are lost to follow-up. F. B. Agusto, J. Cook, P. D. Shelton, and M. G. Wickers Copyright © 2015 F. B. Agusto et al. All rights reserved. Generalized Solutions for Nonlocal Elliptic Equations and Systems with Nonlinear Singularities Tue, 23 Jun 2015 08:04:44 +0000 http://www.hindawi.com/journals/aaa/2015/823143/ We use the topological degree method to study the existence of solutions for nonlocal elliptic equations (systems) with a strong singular nonlinearity. Youtao Wang and Guangcun Lu Copyright © 2015 Youtao Wang and Guangcun Lu. All rights reserved. Convergence of One-Leg Hybrid Methods for Implicit Mixed Differential Algebraic Systems Thu, 11 Jun 2015 14:01:46 +0000 http://www.hindawi.com/journals/aaa/2015/609015/ This paper focuses on a hybrid multistep and its twin one-leg methods and implementing them on implicit mixed differential algebraic equations. The orders of convergence for the above methods are discussed and numerical tests are solved. Iman H. Ibrahim and Fatma M. Yousry Copyright © 2015 Iman H. Ibrahim and Fatma M. Yousry. All rights reserved. Independent Component Analysis Based on Information Bottleneck Sun, 07 Jun 2015 12:18:18 +0000 http://www.hindawi.com/journals/aaa/2015/386201/ The paper is mainly used to provide the equivalence of two algorithms of independent component analysis (ICA) based on the information bottleneck (IB). In the viewpoint of information theory, we attempt to explain the two classical algorithms of ICA by information bottleneck. Furthermore, via the numerical experiments with the synthetic data, sonic data, and image, ICA is proved to be an edificatory way to solve BSS successfully relying on the information theory. Finally, two realistic numerical experiments are conducted via FastICA in order to illustrate the efficiency and practicality of the algorithm as well as the drawbacks in the process of the recovery images the mixing images. Qiao Ke, Jiangshe Zhang, H. M. Srivastava, Wei Wei, and Guang-Sheng Chen Copyright © 2015 Qiao Ke et al. All rights reserved. On Corrected Quadrature Rules and Optimal Error Bounds Thu, 04 Jun 2015 09:46:49 +0000 http://www.hindawi.com/journals/aaa/2015/461918/ We present an analysis of corrected quadrature rules based on the method of undetermined coefficients and its associated degree of accuracy. The correcting terms use weighted values of the first derivative of the function at the endpoint of the subinterval in such a way that the composite rules contain only two new values. Using Taylor’s expansions and Peano’s kernels we obtain best truncation error bounds which depend on the regularity of the function and the weight parameter. We can minimize the bounds with respect to the parameter, and we can find the best parameter value to increase the order of the error bounds or, equivalently, the degree of accuracy of the rule. François Dubeau Copyright © 2015 François Dubeau. All rights reserved. Enhanced Dynamic Model of Pneumatic Muscle Actuator with Elman Neural Network Tue, 02 Jun 2015 10:59:05 +0000 http://www.hindawi.com/journals/aaa/2015/906126/ To make effective use of model-based control system design techniques, one needs a good model which captures system’s dynamic properties in the range of interest. Here an analytical model of pneumatic muscle actuator with two pneumatic artificial muscles driving a rotational joint is developed. Use of analytical model makes it possible to retain the physical interpretation of the model and the model is validated using open-loop responses. Since it was considered important to design a robust controller based on this model, the effect of changed moment of inertia (as a representation of uncertain parameter) was taken into account and compared with nominal case. To improve the accuracy of the model, these effects are treated as a disturbance modeled using the recurrent (Elman) neural network. Recurrent neural network was preferred over feedforward type due to its better long-term prediction capabilities well suited for simulation use of the model. The results confirm that this method improves the model performance (tested for five of the measured variables: joint angle, muscle pressures, and muscle forces) while retaining its physical interpretation. Alexander Hošovský, Ján Piteľ, and Kamil Židek Copyright © 2015 Alexander Hošovský et al. All rights reserved. Comparative Study of Metaheuristics for the Curve-Fitting Problem: Modeling Neurotransmitter Diffusion and Synaptic Receptor Activation Tue, 02 Jun 2015 06:55:18 +0000 http://www.hindawi.com/journals/aaa/2015/708131/ Synapses are key elements in the information transmission in the nervous system. Among the different approaches to study them, the use of computational simulations is identified as the most promising technique. Simulations, however, do not provide generalized models of the underlying biochemical phenomena, but a set of observations, or time-series curves, displaying the behavior of the synapse in the scenario represented. Finding a general model of these curves, like a set of mathematical equations, could be an achievement in the study of synaptic behavior. In this paper, we propose an exploratory analysis in which selected curve models are proposed, and state-of-the-art metaheuristics are used and compared to fit the free coefficients of these curves to the data obtained from simulations. Experimental results demonstrate that several models can fit these data, though a deeper analysis from a biological perspective reveals that some are better suited for this purpose, as they represent more accurately the biological process. Based on the results of this analysis, we propose a set of mathematical equations and a methodology, adequate for modeling several aspects of biochemical synaptic behavior. Jesús Montes, Antonio LaTorre, Santiago Muelas, Ángel Merchán-Pérez, and José M. Peña Copyright © 2015 Jesús Montes et al. All rights reserved. Integer and Fractional General -System and Its Application to Control Chaos and Synchronization Mon, 01 Jun 2015 11:17:25 +0000 http://www.hindawi.com/journals/aaa/2015/413540/ We propose a three-dimensional autonomous nonlinear system, called the general system, which has potential applications in secure communications and the electronic circuit. For the general system with delayed feedback, regarding the delay as bifurcation parameter, we investigate the effect of the time delay on its dynamics. We determine conditions for the existence of the Hopf bifurcations and analyze their direction and stability. Also, the fractional order general -system is proposed and analyzed. We provide some numerical simulations, where the chaos attractor and the dynamics of the Lyapunov coefficients are taken into consideration. The effectiveness of the chaotic control and synchronization on schemes for the new fractional order chaotic system are verified by numerical simulations. Mihaela Neamţu, Anamaria Liţoiu, and Petru C. Strain Copyright © 2015 Mihaela Neamţu et al. All rights reserved. Bilinear Form and Two Bäcklund Transformations for the (3+1)-Dimensional Jimbo-Miwa Equation Tue, 26 May 2015 11:25:53 +0000 http://www.hindawi.com/journals/aaa/2015/834521/ With Bell polynomials and symbolic computation, this paper investigates the (3+1)-dimensional Jimbo-Miwa equation, which is one of the equations in the Kadomtsev-Petviashvili hierarchy of integrable systems. We derive a bilinear form and construct a bilinear Bäcklund transformation (BT) for the (3+1)-dimensional Jimbo-Miwa equation, by virtue of which the soliton solutions are obtained. Bell-polynomial-typed BT is also constructed and cast into the bilinear BT. He Li and Yi-Tian Gao Copyright © 2015 He Li and Yi-Tian Gao. All rights reserved. Positivity, Betweenness, and Strictness of Operator Means Sun, 24 May 2015 12:14:36 +0000 http://www.hindawi.com/journals/aaa/2015/851568/ An operator mean is a binary operation assigned to each pair of positive operators satisfying monotonicity, continuity from above, the transformer inequality, and the fixed-point property. It is well known that there are one-to-one correspondences between operator means, operator monotone functions, and Borel measures. In this paper, we provide various characterizations for the concepts of positivity, betweenness, and strictness of operator means in terms of operator inequalities, operator monotone functions, Borel measures, and certain operator equations. Pattrawut Chansangiam Copyright © 2015 Pattrawut Chansangiam. All rights reserved. Semiglobal Finite-Time Synchronization of Complex Dynamical Networks via Periodically Intermittent Control Wed, 20 May 2015 07:31:46 +0000 http://www.hindawi.com/journals/aaa/2015/381078/ This paper studies the finite-time synchronization problem for a class of complex dynamical networks by means of periodically intermittent control. Based on some analysis techniques and finite-time stability theory, some novel and effective finite-time synchronization criteria are given in terms of a set of linear matrix inequalities. Particularly, the previous synchronization problem by using periodically intermittent control has been extended in this paper. Finally, numerical simulations are presented to verify the theoretical results. Yihan Fan, Hongmei Liu, and Jun Mei Copyright © 2015 Yihan Fan et al. All rights reserved. A Cubic Set Theoretical Approach to Linear Space Wed, 13 May 2015 11:46:53 +0000 http://www.hindawi.com/journals/aaa/2015/523129/ The main motivation of this paper is to introduce the notion of cubic linear space. This inspiration is received from the structure of cubic sets. The notions of R-intersection, R-union, P-intersection, and P-union of cubic linear spaces are defined and we provide some results on these. We further introduce the notion of internal cubic linear space and external cubic linear space and establish some results on them. S. Vijayabalaji and S. Sivaramakrishnan Copyright © 2015 S. Vijayabalaji and S. Sivaramakrishnan. All rights reserved. Quantitative Estimates for Positive Linear Operators in terms of the Usual Second Modulus Mon, 11 May 2015 12:02:23 +0000 http://www.hindawi.com/journals/aaa/2015/915358/ We give accurate estimates of the constants appearing in direct inequalities of the form   , , ,  and   where is a positive linear operator reproducing linear functions and acting on real functions defined on the interval , is a certain subset of such functions, is the usual second modulus of , and is an appropriate weight function. We show that the size of the constants mainly depends on the degree of smoothness of the functions in the set and on the distance from the point to the boundary of . We give a closed form expression for the best constant when is a certain set of continuous piecewise linear functions. As illustrative examples, the Szàsz-Mirakyan operators and the Bernstein polynomials are discussed. José A. Adell and A. Lekuona Copyright © 2015 José A. Adell and A. Lekuona. All rights reserved. Analysis of Water Hammer with Different Closing Valve Laws on Transient Flow of Hydrogen-Natural Gas Mixture Wed, 06 May 2015 09:46:30 +0000 http://www.hindawi.com/journals/aaa/2015/510675/ Water hammer on transient flow of hydrogen-natural gas mixture in a horizontal pipeline is analysed to determine the relationship between pressure waves and different modes of closing and opening of valves. Four types of laws applicable to closing valve, namely, instantaneous, linear, concave, and convex laws, are considered. These closure laws describe the speed variation of the hydrogen-natural gas mixture as the valve is closing. The numerical solution is obtained using the reduced order modelling technique. The results show that changes in the pressure wave profile and amplitude depend on the type of closing laws, valve closure times, and the number of polygonal segments in the closing function. The pressure wave profile varies from square to triangular and trapezoidal shape depending on the type of closing laws, while the amplitude of pressure waves reduces as the closing time is reduced and the numbers of polygonal segments are increased. The instantaneous and convex closing laws give rise to minimum and maximum pressure, respectively. Norazlina Subani and Norsarahaida Amin Copyright © 2015 Norazlina Subani and Norsarahaida Amin. All rights reserved. Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy Thu, 30 Apr 2015 13:21:46 +0000 http://www.hindawi.com/journals/aaa/2015/725674/ A novel bioinspired control strategy design is proposed for generalized synchronization of nonlinear chaotic systems, combining the bioinspired stability theory, fuzzy modeling, and a novel, simple-form Lyapunov control function design of derived high efficient, heuristic and bioinspired controllers. Three main contributions are concluded: (1) apply the bioinspired stability theory to further analyze the stability of fuzzy error systems; the high performance of controllers has been shown in previous study by Li and Ge 2009, (2) a new Lyapunov control function based on bioinspired stability theory is designed to achieve synchronization without using traditional LMI method, which is a simple linear homogeneous function of states and the process of designing controller to synchronize two fuzzy chaotic systems becomes much simpler, and (3) three different situations of synchronization are proposed; classical master and slave Lorenz systems, slave Chen’s system, and Rossler’s system as functional system are illustrated to further show the effectiveness and feasibility of our novel strategy. The simulation results show that our novel control strategy can be applied to different and complicated control situations with high effectiveness. Shih-Yu Li, Shi-An Chen, Chin-Teng Lin, Li-Wei Ko, Cheng-Hsiung Yang, and Heng-Hui Chen Copyright © 2015 Shih-Yu Li et al. All rights reserved. A New Method for Proving Existence Theorems for Abstract Hammerstein Equations Thu, 30 Apr 2015 11:12:22 +0000 http://www.hindawi.com/journals/aaa/2015/627260/ An abstract Hammerstein equation is an equation of the form . A new method is introduced to prove the existence of a solution of this equation where and are nonlinear accretive (monotone) operators. The method does not involve the complicated technique of factorizing a linear map via a Hilbert space and does not involve the use of deep variational techniques. C. E. Chidume, C. O. Chidume, and Ma’aruf Shehu Minjibir Copyright © 2015 C. E. Chidume et al. All rights reserved. On the Equivalence of Differential Equations in the Sense of Coincidence Reflecting Functions Tue, 28 Apr 2015 06:32:30 +0000 http://www.hindawi.com/journals/aaa/2015/456364/ We use a new method for constructing some differential equations which are equivalent to a given equation in the sense of having the same reflecting function. We completely solve the problem: when is a polynomial differential equation equivalent to a given polynomial differential equation? Many sufficient conditions have been established for one differential equation to be equivalent to a given differential equation. We apply the obtained results to study the boundary value problem of two equivalent differential equations. Zhengxin Zhou Copyright © 2015 Zhengxin Zhou. All rights reserved. Applications of Fractional -Calculus to Certain Subclass of Analytic -Valent Functions with Negative Coefficients Wed, 22 Apr 2015 13:37:30 +0000 http://www.hindawi.com/journals/aaa/2015/273236/ By making use of the concept of fractional -calculus, we firstly define -extension of the generalization of the generalized Al-Oboudi differential operator. Then, we introduce new class of -analogue of -valently closed-to-convex function, and, consequently, new class by means of this new general differential operator. Our main purpose is to determine the general properties on such class and geometric properties for functions belonging to this class with negative coefficient. Further, the -extension of interesting properties, such as distortion inequalities, inclusion relations, extreme points, radii of generalized starlikeness, convexity and close-to-convexity, quasi-Hadamard properties, and invariant properties, is obtained. Finally, we briefly indicate the relevant connections of our presented results to the former results. Ben Wongsaijai and Nattakorn Sukantamala Copyright © 2015 Ben Wongsaijai and Nattakorn Sukantamala. All rights reserved. New Trends in Nonlinear Control Systems and Applications Tue, 21 Apr 2015 07:04:24 +0000 http://www.hindawi.com/journals/aaa/2015/637632/ Zhitao Liu, Deqing Huang, Yifan Xing, Chuanke Zhang, Zhengguang Wu, and Xiaofu Ji Copyright © 2015 Zhitao Liu et al. All rights reserved. Optimal Control: Theory and Application to Science, Engineering, and Social Sciences Mon, 20 Apr 2015 13:37:59 +0000 http://www.hindawi.com/journals/aaa/2015/890527/ Davide La Torre, Herb Kunze, Manuel Ruiz-Galan, Tufail Malik, and Simone Marsiglio Copyright © 2015 Davide La Torre et al. All rights reserved. Dynamical Aspects of Initial/Boundary Value Problems for Ordinary Differential Equations 2014 Sun, 19 Apr 2015 12:07:01 +0000 http://www.hindawi.com/journals/aaa/2015/287490/ Jifeng Chu, Yongli Song, Juntao Sun, Patricia J. Y. Wong, and Yonghui Xia Copyright © 2015 Jifeng Chu et al. All rights reserved. Advances on Integrodifferential Equations and Transforms Sun, 19 Apr 2015 09:03:25 +0000 http://www.hindawi.com/journals/aaa/2015/462905/ H. M. Srivastava, Xiao-Jun Yang, Dumitru Baleanu, Juan J. Nieto, and Jordan Hristov Copyright © 2015 H. M. Srivastava et al. All rights reserved. Optimal Control of Renewable Resources Based on the Effective Utilization Rate Thu, 16 Apr 2015 14:15:30 +0000 http://www.hindawi.com/journals/aaa/2015/369493/ The effective utilization rate of exploited renewable resources affects the final total revenue and the further exploitation of renewable resources. Considering the effective utilization rate, we propose an optimal control model for the exploitation of the renewable resources in this study. Firstly, we can prove that the novel model is nonsingular compared with the singular basic model. Secondly, we solve the novel model and obtain the optimal solution by Bang-Bang theory. Furthermore, we can determine the optimal total resources and the maximal total revenue. Finally, a numerical example is provided to verify the obtained theoretical results. Rui Wu, Zhengwei Shen, and Fucheng Liao Copyright © 2015 Rui Wu et al. All rights reserved. Corrigendum to “Krasnosel’skii Type Hybrid Fixed Point Theorems and Their Applications to Fractional Integral Equations” Thu, 16 Apr 2015 13:03:00 +0000 http://www.hindawi.com/journals/aaa/2015/467569/ H. M. Srivastava, Sachin V. Bedre, S. M. Khairnar, and B. S. Desale Copyright © 2015 H. M. Srivastava et al. All rights reserved. Reliable Control for Uncertain Singular Systems with Randomly Occurring Time-Varying Delay and Actuator Faults Thu, 16 Apr 2015 11:49:59 +0000 http://www.hindawi.com/journals/aaa/2015/238692/ The problem of reliable control is investigated for uncertain continuous singular systems with randomly occurring time-varying delay and actuator faults in this work. The delay occurs in a random way, and such randomly occurring delay obeys certain mutually uncorrelated Bernoulli distributed white noise sequences. The uncertainties under consideration are norm-bounded, and may vary with time. Then, with the constructed Lyapunov function, a sufficient condition is given to ensure the unforced system is mean-square exponentially stable and the corresponding controller can be derived from such condition, and the actuator faults problem is guaranteed. A numerical example is provided to show the effectiveness of the methods. Yu-Lin Li, Lin-Sheng Li, Zhi-Cheng Zhao, and Jing-Gang Zhang Copyright © 2015 Yu-Lin Li et al. All rights reserved. Approximate Controllability of Semilinear Impulsive Evolution Equations Thu, 16 Apr 2015 11:24:47 +0000 http://www.hindawi.com/journals/aaa/2015/797439/ We prove the approximate controllability of the following semilinear impulsive evolution equation: where , and are Hilbert spaces, , is a bounded linear operator, are smooth functions, and is an unbounded linear operator in which generates a strongly continuous semigroup . We suppose that is bounded and the linear system is approximately controllable on for all . Under these conditions, we prove the following statement: the semilinear impulsive evolution equation is approximately controllable on . Hugo Leiva Copyright © 2015 Hugo Leiva. All rights reserved. Fractional Cauchy Problem with Caputo Nabla Derivative on Time Scales Thu, 16 Apr 2015 08:22:52 +0000 http://www.hindawi.com/journals/aaa/2015/486054/ The definition of Caputo fractional derivative is given and some of its properties are discussed in detail. After then, the existence of the solution and the dependency of the solution upon the initial value for Cauchy type problem with fractional Caputo nabla derivative are studied. Also the explicit solutions to homogeneous equations and nonhomogeneous equations are derived by using Laplace transform method. Jiang Zhu and Ling Wu Copyright © 2015 Jiang Zhu and Ling Wu. All rights reserved.