Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Convolution Properties for Some Subclasses of Meromorphic Functions of Complex Order Thu, 30 Jul 2015 09:51:30 +0000 http://www.hindawi.com/journals/aaa/2015/973613/ Making use of the operator for functions of the form , which are analytic in the punctured unit disc and , we introduce two subclasses of meromorphic functions and investigate convolution properties, coefficient estimates, and containment properties for these subclasses. M. K. Aouf, A. O. Mostafa, and H. M. Zayed Copyright © 2015 M. K. Aouf et al. All rights reserved. A Fractional-Order Epidemic Model for Bovine Babesiosis Disease and Tick Populations Tue, 28 Jul 2015 10:54:33 +0000 http://www.hindawi.com/journals/aaa/2015/729894/ This paper shows that the epidemic model, previously proposed under ordinary differential equation theory, can be generalized to fractional order on a consistent framework of biological behavior. The domain set for the model in which all variables are restricted is established. Moreover, the existence and stability of equilibrium points are studied. We present the proof that endemic equilibrium point when reproduction number is locally asymptotically stable. This result is achieved using the linearization theorem for fractional differential equations. The global asymptotic stability of disease-free point, when , is also proven by comparison theory for fractional differential equations. The numeric simulations for different scenarios are carried out and data obtained are in good agreement with theoretical results, showing important insight about the use of the fractional coupled differential equations set to model babesiosis disease and tick populations. José Paulo Carvalho dos Santos, Lislaine Cristina Cardoso, Evandro Monteiro, and Nelson H. T. Lemes Copyright © 2015 José Paulo Carvalho dos Santos et al. All rights reserved. Refinements and Generalizations of Functional Dresher’s and Bellman’s Inequalities Tue, 28 Jul 2015 08:33:12 +0000 http://www.hindawi.com/journals/aaa/2015/684763/ We give refinements and generalizations of the Dresher and Bellman inequalities for positive linear functionals. We also give reverse of the new obtained generalized version of these inequalities. Finally, we apply our results on time scales integrals to obtain refinements and generalizations of time scales Dresher’s and Bellman’s inequalities. Rabia Bibi and Muhammad Shahzad Copyright © 2015 Rabia Bibi and Muhammad Shahzad. All rights reserved. The Best Approximation Theorems and Fixed Point Theorems for Discontinuous Increasing Mappings in Banach Spaces Mon, 27 Jul 2015 11:07:07 +0000 http://www.hindawi.com/journals/aaa/2015/165053/ We prove that Fan’s theorem is true for discontinuous increasing mappings in a real partially ordered reflexive, strictly convex, and smooth Banach space . The main tools of analysis are the variational characterizations of the generalized projection operator and order-theoretic fixed point theory. Moreover, we get some properties of the generalized projection operator in Banach spaces. As applications of our best approximation theorems, the fixed point theorems for non-self-maps are established and proved under some conditions. Our results are generalizations and improvements of the recent results obtained by many authors. Dezhou Kong, Lishan Liu, and Yonghong Wu Copyright © 2015 Dezhou Kong et al. All rights reserved. Fixed Points Results for α-Admissible Mapping of Integral Type on Generalized Metric Spaces Mon, 27 Jul 2015 08:30:51 +0000 http://www.hindawi.com/journals/aaa/2015/141409/ We introduce generalized -contractive mappings of integral type in the context of generalized metric spaces. The results of this paper generalize and improve several results on the topic in literature. Erdal Karapınar Copyright © 2015 Erdal Karapınar. All rights reserved. Convergence Theorems of Common Elements for Pseudocontractive Mappings and Monotone Mappings Mon, 27 Jul 2015 07:26:17 +0000 http://www.hindawi.com/journals/aaa/2015/383579/ An algorithm for treating pseudocontractive mappings and monotone mappings is proposed. Convergence analysis of algorithm is investigated in the framework of Hilbert spaces. Jae Ug Jeong Copyright © 2015 Jae Ug Jeong. All rights reserved. Completion of a Dislocated Metric Space Sun, 26 Jul 2015 14:12:19 +0000 http://www.hindawi.com/journals/aaa/2015/460893/ We provide a construction for the completion of a dislocated metric space (abbreviated -metric space); we also prove that the completion of the metric associated with a -metric coincides with the metric associated with the completion of the -metric. P. Sumati Kumari, I. Ramabhadra Sarma, J. Madhusudana Rao, and D. Panthi Copyright © 2015 P. Sumati Kumari et al. All rights reserved. Common Fixed Point Theorems for Probabilistic Nearly Densifying Mappings Sun, 26 Jul 2015 11:33:42 +0000 http://www.hindawi.com/journals/aaa/2015/497542/ The aim of this paper is to prove some coincidence and common fixed point theorems for probabilistic nearly densifying mappings in complete Menger spaces. Our results improve the results of Chamola et al. (1991), Dimri and Pant (2002), and Pant et al. (2004) and extend the results of Khan and Liu (1997) in the framework of probabilistic settings. Aeshah Hassan Zakri, Sumitra Dalal, Sunny Chauhan, and Jelena Vujaković Copyright © 2015 Aeshah Hassan Zakri et al. All rights reserved. Second Order Equations in Functional Spaces: Qualitative and Discrete Well-Posedness Sun, 26 Jul 2015 09:57:59 +0000 http://www.hindawi.com/journals/aaa/2015/948321/ The present survey contains the recent results on the local and nonlocal well-posed problems for second order differential and difference equations. Results on the stability of differential problems for second order equations and of difference schemes for approximate solution of the second order problems are presented. A. Ashyralyev, J. Pastor, S. Piskarev, and H. A. Yurtsever Copyright © 2015 A. Ashyralyev et al. All rights reserved. Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces Sun, 26 Jul 2015 08:22:30 +0000 http://www.hindawi.com/journals/aaa/2015/760671/ Let be a smooth Banach space with a norm . Let for any , where stands for the duality pair and is the normalized duality mapping. We define a -strongly nonexpansive mapping by . This nonlinear mapping is nonexpansive in a Hilbert space. However, we show that there exists a -strongly nonexpansive mapping with fixed points which is not nonexpansive in a Banach space. In this paper, we show a weak convergence theorem and strong convergence theorems for fixed points of this elastic nonlinear mapping and give the existence theorem. Hiroko Manaka Copyright © 2015 Hiroko Manaka. All rights reserved. Quasi-Triangular Spaces, Pompeiu-Hausdorff Quasi-Distances, and Periodic and Fixed Point Theorems of Banach and Nadler Types Sun, 26 Jul 2015 07:43:47 +0000 http://www.hindawi.com/journals/aaa/2015/201236/ Let , -index set. A quasi-triangular space is a set with family satisfying . For any , a left (right) family generated by is defined to be , where and furthermore the property    holds whenever two sequences and in satisfy and    and . In , using the left (right) families generated by ( is a special case of ), we construct three types of Pompeiu-Hausdorff left (right) quasi-distances on ; for each type we construct of left (right) set-valued quasi-contraction , and we prove the convergence, existence, and periodic point theorem for such quasi-contractions. We also construct two types of left (right) single-valued quasi-contractions and we prove the convergence, existence, approximation, uniqueness, periodic point, and fixed point theorem for such quasi-contractions. () generalize ultra quasi-triangular and partiall quasi-triangular spaces (in particular, generalize metric, ultra metric, quasi-metric, ultra quasi-metric, -metric, partial metric, partial -metric, pseudometric, quasi-pseudometric, ultra quasi-pseudometric, partial quasi-pseudometric, topological, uniform, quasi-uniform, gauge, ultra gauge, partial gauge, quasi-gauge, ultra quasi-gauge, and partial quasi-gauge spaces). Kazimierz Włodarczyk Copyright © 2015 Kazimierz Włodarczyk. All rights reserved. New Approach to Fractal Approximation of Vector-Functions Sun, 26 Jul 2015 07:31:49 +0000 http://www.hindawi.com/journals/aaa/2015/278313/ This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization of fractal interpolation functions. Best values of fractal interpolation vector-functions parameters are found. We give schemes of approximation of some sets of data and consider examples of approximation of smooth curves with different conditions. Konstantin Igudesman, Marsel Davletbaev, and Gleb Shabernev Copyright © 2015 Konstantin Igudesman et al. All rights reserved. New Interaction Solutions of (3+1)-Dimensional KP and (2+1)-Dimensional Boussinesq Equations Thu, 16 Jul 2015 11:54:16 +0000 http://www.hindawi.com/journals/aaa/2015/213847/ The consistent tanh expansion (CTE) method has been succeeded to apply to the nonintegrable (3+1)-dimensional Kadomtsev-Petviashvili (KP) and (2+1)-dimensional Boussinesq equations. The interaction solution between one soliton and one resonant soliton solution for the (3+1)-dimensional KP equation is obtained with CTE method. The interaction solutions among one soliton and cnoidal waves for these two equations are also explicitly given. These interaction solutions are investigated in both analytical and graphical ways. It demonstrates that the interactions between one soliton and cnoidal waves are elastic with phase shifts. Bo Ren, Jun Yu, and Xi-Zhong Liu Copyright © 2015 Bo Ren et al. All rights reserved. Estimation of Hazard Rate and Mean Residual Life Ordering for Fuzzy Random Variable Tue, 14 Jul 2015 10:52:39 +0000 http://www.hindawi.com/journals/aaa/2015/164795/ -metric is used to find the distance between triangular fuzzy numbers. The mean and variance of a fuzzy random variable are also determined by this concept. The hazard rate is estimated and its relationship with mean residual life ordering of fuzzy random variable is investigated. Additionally, we have focused on deriving bivariate characterization of hazard rate ordering which explicitly involves pairwise interchange of two fuzzy random variables and . S. Ramasubramanian and P. Mahendran Copyright © 2015 S. Ramasubramanian and P. Mahendran. All rights reserved. Some Inequalities for the Omori-Yau Maximum Principle Mon, 13 Jul 2015 11:34:32 +0000 http://www.hindawi.com/journals/aaa/2015/410896/ We generalize A. Borbély’s condition for the conclusion of the Omori-Yau maximum principle for the Laplace operator on a complete Riemannian manifold to a second-order linear semielliptic operator with bounded coefficients and no zeroth order term. Also, we consider a new sufficient condition for the existence of a tamed exhaustion function. From these results, we may remark that the existence of a tamed exhaustion function is more general than the hypotheses in the version of the Omori-Yau maximum principle that was given by A. Ratto, M. Rigoli, and A. G. Setti. Kyusik Hong Copyright © 2015 Kyusik Hong. All rights reserved. Positive Definite Solutions of the Matrix Equation Sun, 12 Jul 2015 12:30:03 +0000 http://www.hindawi.com/journals/aaa/2015/473965/ We investigate the nonlinear matrix equation , where is a positive integer and . We establish necessary and sufficient conditions for the existence of positive definite solutions of this equation. A sufficient condition for the equation to have a unique positive definite solution is established. An iterative algorithm is provided to compute the positive definite solutions for the equation and error estimate. Finally, some numerical examples are given to show the effectiveness and convergence of this algorithm. Asmaa M. Al-Dubiban Copyright © 2015 Asmaa M. Al-Dubiban. All rights reserved. Some Inequalities of Simpson Type for -Convex Functions via Fractional Integrals Sun, 12 Jul 2015 11:42:16 +0000 http://www.hindawi.com/journals/aaa/2015/956850/ We establish some inequalities of Simpson type involving Riemann-Liouville fractional integrals for mappings whose first derivatives are h-convex. Marian Matłoka Copyright © 2015 Marian Matłoka. All rights reserved. Geometric Properties of a New Integral Operator Thu, 09 Jul 2015 07:18:08 +0000 http://www.hindawi.com/journals/aaa/2015/430197/ We obtain sufficient conditions for the univalence, starlikeness, and convexity of a new integral operator defined on the space of normalized analytic functions in the open unit disk. Some subordination results for the new integral operator are also given. Several corollaries follow as special cases. Roberta Bucur, Loriana Andrei, and Daniel Breaz Copyright © 2015 Roberta Bucur et al. All rights reserved. Comment on “Existence Theorem for Integral and Functional Integral Equations with Discontinuous Kernels” Wed, 08 Jul 2015 06:09:13 +0000 http://www.hindawi.com/journals/aaa/2015/698121/ We present a counterexample to the main result of the abovementioned paper showing that this result is false and cannot be improved in a simple way. Krzysztof A. Topolski Copyright © 2015 Krzysztof A. Topolski. 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.